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Evokation
  
 
Index
  

 

 

 

NUCLEAR FAMILY 19769

 

 

 

 

 

 

 

 

THE

MAGICALALPHABET

 

..................

 

 

-
-
-
-
-
THE RAINBOW LIGHT
-
-
-
T
=
2
-
3
THE
33
15
6
R
=
9
-
7
RAINBOW
82
37
1
L
=
3
-
5
LIGHT
56
29
2
-
-
14
-
15
THE RAINBOW LIGHT
171
81
9
-
-
1+4
-
1+5
-
1+7+1
8+1
-
Q
-
5
-
6
THE RAINBOW LIGHT
9
9
9

 

 

 

 

 

 

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
First Total
189
90
18
1+8
Add to Reduce
1+8+9
9+0
1+8
9
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
9
Essence of Number
9
9
9

 

 

THE DIVINE COMEDY

OF

DANTE ALIGHIERI (1265-1321)

THE FLORENTINE

CANTICA I

HELL

(L'INFERNO)

INTRODUCTION

Page 9

"Midway this way of life we're bound upon

I woke to find myself in a dark wood,

Where the right road was wholly lost and gone."

 

 

M
=
4
-
6
MIDWAY
75
30
3
T
=
2
-
4
THIS
56
20
2
W
=
5
-
3
WAY
49
13
4
O
=
6
-
2
OF
21
12
3
L
=
3
-
4
LIFE
32
23
5
W
=
5
-
4
WE'RE
51
24
6
B
=
2
-
5
BOUND
56
20
2
U
=
3
-
4
UPON
66
21
3
-
-
30
-
32
-
406
163
28
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
W
=
5
-
4
WOKE
54
18
9
T
=
2
-
2
TO
35
8
8
F
=
6
-
4
FIND
33
24
6
M
=
4
-
6
MYSELF
80
26
8
I
=
9
-
2
IN
23
14
5
A
=
1
-
1
A
1
1
1
D
=
4
-
4
DARK
34
16
7
W
=
5
-
4
WOOD
57
21
3
-
-
45
-
28
-
326
137
56
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WHERE
59
32
5
T
=
2
-
3
THE
33
15
6
R
=
9
-
5
RIGHT
62
35
8
R
=
9
-
4
ROAD
38
20
2
W
=
5
-
3
WAS
43
7
7
W
=
5
-
6
WHOLLY
95
32
5
L
=
3
-
4
LOST
66
12
3
A
=
1
-
3
AND
19
10
1
G
=
7
-
4
GONE
41
23
5
-
-
46
-
37
-
456
186
42
-
-
-
-
-
-
-
-
-
-
-
121
-
97
First Total
1188
486
126
-
-
1+2+1
-
9+7
Add to Reduce
1+1+8+8
4+8+6
1+2+6
Q
-
4
-
16
Second Total
18
18
9
-
-
-
-
1+6
Reduce to Deduce
1+8
1+8
-
-
-
4
-
7
Essence of Number
9
9
9

 

 

THE DIVINE COMEDY

OF

DANTE ALIGHIERI (1265-1321)

THE FLORENTINE

CANTICA I

HELL

(L'INFERNO)

INTRODUCTION

Page 9

"Power failed high fantasy here; yet, swift to move

Even as a wheel moves equal, free from jars,

Already my heart and will were wheeled by love,

The Love that moves the sun and other stars."

 

P
=
7
-
5
POWER
77
32
5
F
=
6
-
6
FAILED
37
28
1
H
=
8
-
4
HIGH
32
32
5
F
=
6
-
7
FANTASY
86
23
5
H
=
8
-
4
HERE
36
27
9
Y
=
7
-
3
YET
50
14
5
S
=
1
-
5
SWIFT
77
23
5
T
=
2
-
2
TO
35
8
8
M
=
4
-
4
MOVE
55
19
1
-
-
49
-
40
First Total
485
206
44
-
-
4+9
-
4+0
Add to Reduce
4+8+5
2+0+6
4+4
Q
-
13
-
4
Second Total
17
8
8
-
-
1+3
-
-
Reduce to Deduce
1+7
-
-
-
-
4
-
4
Essence of Number
8
8
8

 

 

E
=
5
-
4
EVEN
46
19
1
A
=
1
-
2
AS
20
2
2
A
=
1
-
1
A
1
1
1
W
=
5
-
5
WHEEL
53
26
8
M
=
4
-
5
MOVES
74
20
2
E
=
5
-
5
EQUAL
56
20
2
F
=
6
-
4
FREE
34
25
7
F
=
6
-
4
FROM
52
25
7
J
=
1
-
4
JARS
48
12
3
-
-
34
-
34
First Total
384
150
33
-
-
3+4
-
3+4
Add to Reduce
3+8+4
1+5+0
3+3
Q
-
7
-
7
Second Total
15
6
6
-
-
-
-
-
Reduce to Deduce
1+5
-
-
-
-
7
-
7
Essence of Number
6
6
6

 

 

A
=
1
-
7
ALREADY
66
30
3
M
=
4
-
2
MY
38
11
2
H
=
8
-
5
HEART
52
25
7
A
=
1
-
3
AND
19
10
1
W
=
5
-
4
WILL
56
20
2
W
=
5
-
4
WERE
51
24
7
W
=
5
-
7
WHEELED
62
35
8
B
=
2
-
2
BY
27
9
9
L
=
3
-
4
LOVE
54
18
9
-
-
34
-
38
First Total
425
182
47
-
-
3+4
-
3+8
Add to Reduce
4+2+5
1+8+2
4+7
Q
-
7
-
11
Second Total
11
11
11
-
-
-
-
1+1
Reduce to Deduce
1+1
1+1
1+1
-
-
7
-
2
Essence of Number
2
2
2

 

 

T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LOVE
54
18
9
T
=
2
-
4
THAT
49
13
4
M
=
4
-
5
MOVES
74
20
2
T
=
2
-
3
THE
33
15
6
S
=
1
-
3
SUN
54
9
9
A
=
1
-
3
AND
19
10
1
O
=
6
-
5
OTHER
66
30
3
S
=
1
-
5
STARS
77
14
5
-
-
22
-
35
First Total
459
144
45
-
-
2+2
-
3+5
Add to Reduce
4+5+9
1+4+4
4+5
Q
-
4
-
8
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
4
-
8
Essence of Number
9
9
9

 

 

3
THE
33
15
6
4
HOLY
60
24
6
7
MESSAGE
-
-
-
2
M+E
18
9
9
1
S
19
10
1
3
S+A+G
27
18
9
1
E
5
5
5
7
MESSAGE
69
42
24
14
Add
162
81
36
1+4
Reduce
1+6+2
8+1
3+6
5
Deduce
9
9
9

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN SWIFT REPEAT SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

AT THE THROW OF THE NINTH NUMBER WHEN IN CONJUNCTION SET

THE

FAR YONDER SCRIBE

MADE RECORD OF THEIR FALL

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
5
ADDED
18
18
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
2
TO
35
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
3
ALL
25
7
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
5
MINUS
76
22
4
-
-
-
-
4
-
-
-
-
-
N
=
5
-
4
NONE
48
21
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
6
SHARED
55
28
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
10
EVERYTHING
133
61
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
10
MULTIPLED
121
49
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
A
=
1
-
9
ABUNDANCE
65
29
2
-
-
2
-
-
-
-
-
-
-
-
-
35
-
58
First Total
626
266
59
-
1
2
3
8
5
6
14
8
18
-
-
3+5
-
5+8
Add to Reduce
6+2+6
2+6+6
5+9
-
-
-
-
-
-
-
1+4
-
1+8
-
-
8
-
13
Second Total
14
14
10
-
1
2
3
8
5
6
5
8
9
-
-
-
-
1+3
Reduce to Deduce
1+4
1+4
1+0
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Essence of Number
5
5
5
-
1
2
3
8
5
6
5
8
9

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
=
7
=
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
=
7
=
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
=
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
=
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
=
9
=
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
=
9
=
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
=
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
=
7
=
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
=
7
=
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
=
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
=
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
=
9
=
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
=
9
=
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
=
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
34
-
36
Add
458
197
44
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
9
-
-
-
7
4
9
Deduce
17
17
8
-
-
-
-
-
-
-
Produce
1+7
1+7
-
9
-
-
-
7
-
9
Essence
8
8
8

 

 

0
-
Z
=
8
-
4
ZERO
64
28
1
1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
42
-
40
Add
522
225
45
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
9
-
-
-
6
-
4
Deduce
9
9
9

 

 

ADVENT 999 ADVENT

 

 

...

 

 

 

A

MAZE

IN

ZAZAZA ENTER AZAZAZ

AZAZAZAZAZAZAZZAZAZAZAZAZAZA

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGICALALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZZYXWVUTSRQPONMLKJIHGFEDCBA

 12345678910111213141516171819202122232425262625242322212019181716151413121110987654321

 

 

WORK DAYS OF GOD

Herbert W Morris D.D.circa 1883

Page 22

"As all the words in the English language are composed out of the twenty-six letters of the alphabet,.."

 

 

LIGHT AND LIFE

Lars Olof Bjorn 1976

Page 197

"By writing the 26 letters of the alphabet in a certain order one may put down almost any message (this book 'is written with the same letters' as the Encyclopaedia Britannica and Winnie the Pooh, only the order of the letters differs). In the same way Nature is able to convey with her language how a cell and a whole organism is to be constructed and how it is to function. Nature has succeeded better than we humans; for the genetic code there is only one universal language which is the same in a man, a bean plant and a bacterium."

"BY WRITING THE 26 LETTERS OF THE ALPHABET IN A CERTAIN ORDER

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

A
B
C
D
E
F
G
H
I
1
2
3
4
5
6
7
8
9
 =
 =
 =
 =
 =
 =
 =
 =
=
 =
 =
 =
 =
 =
 =
 =
 =
=
J
K
L
M
N
O
P
Q
R
10
11
12
13
14
15
16
17
18
1+0
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1
2
3
4
5
6
7
8
9
 =
 =
 =
 =
 =
 =
 =
 =
=
 =
 =
 =
 =
 =
 =
 =
 =
=
S
T
U
V
W
X
Y
Z
I
19
20
21
22
23
24
25
26
9
1+9
2+0
2+1
2+2
2+3
2+4
2+5
2+6
ME
1
2
3
4
5
6
7
8
9
 =
 =
 =
 =
 =
 =
 =
 =
=
 =
 =
 =
 =
 =
 =
 =
 =
=
I
ME
I
ME
I
ME
I
ME
I
9
18
9
18
9
18
9
18
9
=
1+8
=
1+8
=
1+8
=
1+8
=
=
9
=
9
=
9
=
9
=
I
ME
I
ME
I
ME
I
ME
1
9
9
9
9
9
9
9
9
9
I
ME
I
ME
I
ME
I
ME
1

 

 

"BY WRITING THE 26 LETTERS OF THE ALPHABET IN A CERTAIN ORDER

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
-
-
-
-
-
-
-
-
-
1+0
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+0
2+1
2+2
2+3
2+4
2+5
2+6
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
 -
-
-
-
-
-
-
-
-
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z

 

 

A

HISTORY OF GOD

Karen Armstrong 1993

The God of the Mystics

Page 250

"Perhaps the most famous of the early Jewish mystical texts is the fifth century Sefer Yezirah (The Book of Creation). There is no attempt to describe the creative process realistically; the account is unashamedly symbolic and shows God creating the world by means of language as though he were writing a book. But language has been entirely transformed and the message of creation is no longer clear. Each letter of the Hebrew alphabet is given a numerical value; by combining the letters with the sacred numbers, rearranging them in endless configurations, the mystic weaned his mind away from the normal connotations of words."

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
First Total
189
90
18
1+8
Add to Reduce
1+8+9
9+0
1+8
9
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
9
Essence of Number
9
9
9

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN

SWIFT REPEAT SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

Our minds seem to be organised to search for relationships and sequences. We look for hidden orders.

These intuitions seem to be more important than the facts themselves, for there is always the thrill at finding something, a pattern, it is a discovery - what was unknown is now revealed. Imagine looking up at the stars and finding the zodiac!

Searching out patterns is a pure delight.

Suddenly the counters fall into place and a connection is found, not necessarily a geometric one, but a relationship between numbers, pictures of the mind, that were not obvious before. There is that excitement of finding order in something that was otherwise hidden.

And there is the knowledge that a huge unseen world lurks behind the facades we see of the numbers themselves."

 

 

FINGERPRINTS OF THE GODS

A QUEST FOR THE BEGINNING AND THE END

Graham Hancock 1995

Chapter 32

Speaking to the Unborn

Page 285

"It is understandable that a huge range of myths from all over the ancient world should describe geological catastrophes in graphic detail. Mankind survived the horror of the last Ice Age, and the most plausible source for our enduring traditions of flooding and freezing, massive volcanism and devastating earthquakes is in the tumultuous upheavals unleashed during the great meltdown of 15,000 to 8000 BC. The final retreat of the ice sheets, and the consequent 300-400 foot rise in global sea levels, took place only a few thousand years before the beginning of the historical period. It is therefore not surprising that all our early civilizations should have retained vivid memories of the vast cataclysms that had terrified their forefathers.
Much harder to explain is the peculiar but distinctive way the myths of cataclysm seem to bear the intelligent imprint of a guiding hand.l Indeed the degree of convergence between such ancient stories is frequently remarkable enough to raise the suspicion that they must all have been 'written' by the same 'author'.
Could that author have had anything to do with the wondrous deity, or superhuman, spoken of in so many of the myths we have reviewed, who appears immediately after the world has been shattered by a horrifying geological catastrophe and brings comfort and the gifts of civilization to the shocked and demoralized survivors?
White and bearded, Osiris is the Egyptian manifestation of this / Page 286 / universal figure, and it may not be an accident that one of the first acts he is remembered for in myth is the abolition of cannibalism among the primitive inhabitants of the Nile Valley.2 Viracocha, in South America, was said to have begun his civilizing mission immediately after a great flood; Quetzalcoatl, the discoverer of maize, brought the benefits of crops, mathematics, astronomy and a refined culture to Mexico after the Fourth Sun had been overwhelmed by a destroying deluge.
Could these strange myths contain a record of encounters between scattered palaeolithic tribes which survived the last Ice Age and an as yet unidentified high civilization which passed through the same epoch?
And could the myths be attempts to communicate?

A message in the bottle of time"

'Of all the other stupendous inventions,' Galileo once remarked,

what sublimity of mind must have been his who conceived how to communicate his most secret thoughts to any other person, though very distant either in time or place, speaking with those who are in the Indies, speaking to those who are not yet born, nor shall be this thousand or ten thousand years? And with no greater difficulty than the various arrangements of two dozen little signs on paper? Let this be the seal of all the admirable inventions of men.3

If the 'precessional message' identified by scholars like Santillana, von Dechend and Jane Sellers is indeed a deliberate attempt at communication by some lost civilization of antiquity, how come it wasn't just written down and left for us to find? Wouldn't that have been easier than encoding it in myths? Perhaps.
Nevertheless, suppose that whatever the message was written on got destroyed or worn away after many thousands of years? Or suppose that the language in which it was inscribed was later forgotten utterly (like the enigmatic Indus Valley script, which has been studied closely for more than half a century but has so far resisted all attempts at decoding)? It must be obvious that in such circumstances a written / Page 287 / legacy to the future would be of no value at all, because nobody would be able to make sense of it.
What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them - and the city of Teotihuacan may be the calling-card of a lost civilization written in the eternal language of mathematics.
Geodetic data, related to the exact positioning of fixed geographical points and to the shape and size of the earth, would also remain valid and recognizable for tens of thousands of years, and might be most conveniently expressed by means of cartography (or in the construction of giant geodetic monuments like the Great Pyramid of Egypt, as we shall see).
Another 'constant' in our solar system is the language of time: the great but regular intervals of time calibrated by the inch-worm creep of precessional motion. Now, or ten thousand years in the future, a message that prints out numbers like 72 or 2160 or 4320 or 25,920 should be instantly intelligible to any civilization that has evolved a modest talent for mathematics and the ability to detect and measure the almost imperceptible reverse wobble that the sun appears to make along the ecliptic against the background of the fixed stars..."

"What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them"

"WRITTEN IN THE ETERNAL LANGUAGE OF MATHEMATICS"

 

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

 

15
THE RAINBOW LIGHT
-
-
-
-
THE
33
15
6
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
-
L
12
3
3
-
I
9
9
9
-
G+H+T
35
17
8
15
THE RAINBOW LIGHT
171
81
54
1+5
-
1+7+1
8+1
5+4
6
THE RAINBOW LIGHT
9
9
9

 

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
-
7
-
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
-
7
-
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
-
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
-
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
-
9
-
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
-
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
-
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
-
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

 

 

 

 

THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY

THE ACCOUNT IS SYMBOLIC AND SHOWS GOD CREATING THE WORLD BY MEANS OF LANGUAGE

AS THOUGH WRITING A BOOK BUT LANGUAGE ENTIRELY TRANSFORMED

THE MESSAGE OF CREATION IS CLEAR EACH LETTER OF

THE

ALPHABET

IS

GIVEN

A

NUMERICAL

VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS

REARRANGING THEM IN ENDLESS CONFIGURATIONS

THE MYSTIC WEANED THE MIND AWAY FROM THE NORMAL CONNOTATIONS OF WORDS

 

 

THE DEATH OF GODS IN ANCIENT EGYPT

Jane B. Sellars 1992

Page 204

"The overwhelming awe that accompanies the realization, of the measurable orderliness of the universe strikes modern man as well. Admiral Weiland E. Byrd, alone In the Antarctic for five months of polar darkness, wrote these phrases of intense feeling:

Here were the imponderable processes and forces of the cosmos, harmonious and soundless. Harmony, that was it! I could feel no doubt of oneness with the universe. The conviction came that the rhythm was too orderly. too harmonious, too perfect to be a product of blind chance - that, therefore there must be purpose in the whole and that man was part of that whole and not an accidental offshoot. It was a feeling that transcended reason; that went to the heart of man's despair and found it groundless. The universe was a cosmos, not a chaos; man was as rightfully a part of that cosmos as were the day and night.10

Returning to the account of the story of Osiris, son of Cronos god of' Measurable Time, Plutarch takes, pains to remind the reader of the original Egyptian year consisting of 360 days.

Phrases are used that prompt simple mental. calculations and an attention to numbers, for example, the 360-day year is described as being '12 months of 30 days each'. Then we are told that, Osiris leaves on a long journey, during which Seth, his evil brother, plots with 72 companions to slay Osiris: He also secretly obtained the measure of Osiris and made ready a chest in which to entrap him.

The, interesting thing about this part of the-account is that nowhere in the original texts of the Egyptians are we told that Seth, has 72 companions. We have already been encouraged to equate Osiris with the concept of measured time; his father being Cronos. It is also an observable fact that Cronos-Saturn has the longest sidereal period of the known planets at that time, an orbit. of 30 years. Saturn is absent from a specific constellation for that length of time.

A simple mathematical fact has been revealed to any that are even remotely sensitive to numbers: if you multiply 72 by 30, the years of Saturn's absence (and the mention of Osiris's absence prompts one to recall this other), the resulting product is 2,160: the number of years required, for one 30° shift, or a shift: through one complete sign of the zodiac. This number multplied by the /Page205 / 12 signs also gives 25,920. (And Plutarch has reminded us of 12)

If you multiply the unusual number 72 by 360, a number that Plutarch mentions several times, the product will be 25,920, again the number of years symbolizing the ultimate rebirth.

This 'Eternal Return' is the return of, say, Taurus to the position of marking the vernal equinox by 'riding in the solar bark with. Re' after having relinquished this honoured position to Aries, and subsequently to the to other zodiacal constellations.

Such a return after 25,920 years is indeed a revisit to a Golden Age, golden not only because of a remarkable symmetry In the heavens, but golden because it existed before the Egyptians experienced heaven's changeability.

But now to inform the reader of a fact he or she may already know. Hipparaus did: not really have the exact figures: he was a trifle off in his observations and calculations. In his published work, On the Displacement of the Solstitial and Equinoctial Signs, he gave figures of 45" to 46" a year, while the truer precessional lag along the ecliptic is about 50 seconds. The exact measurement for the lag, based on the correct annual lag of 50'274" is 1° in 71.6 years, or 360° in 25,776 years, only 144 years less than the figure of 25,920.

With Hipparchus's incorrect figures a 'Great Year' takes from 28,173.9 to 28,800 years, Incorrect by a difference of from 2,397.9 years to 3,024.

Since Nicholas Copernicus (AD 1473-1543) has always been credited with giving the correct numbers (although Arabic astronomer Nasir al-Din Tusi,11 born AD 1201, is known to have fixed the Precession at 50°), we may correctly ask, and with justifiable astonishment 'Just whose information was Plutarch transmitting'

AN IMPORTANT POSTSCRIPT

Of course, using our own notational system, all the important numbers have digits that reduce to that amazing number 9 a number that has always delighted budding mathematician.

Page 206

Somewhere along the way, according to Robert Graves, 9 became the number of lunar wisdom.12

This number is found often in the mythologies of the world. the Viking god Odin hung for nine days and nights on the World Tree in order to acquire the secret of the runes, those magic symbols out of which writing and numbers grew. Only a terrible sacrifice would give away this secret, which conveyed upon its owner power and dominion over all, so Odin hung from his neck those long 9 days and nights over the 'bottomless abyss'. In the tree were 9 worlds, and another god was said to have been born of 9 mothers.

Robert Graves, in his White Goddess, Is intrigued by the seemingly recurring quality of the number 72 in early myth and ritual. Graves tells his reader that 72 is always connected with the number 5, which reflects, among other things, the five Celtic dialects that he was investigating. Of course, 5 x 72= 360, 360 x 72= 25,920. Five is also the number of the planets known to the ancient world, that is, Saturn, Jupiter, Mars, Venus Mercury.

Graves suggests a religious mystery bound up with two ancient Celtic 'Tree Alphabets' or cipher alphabets, which as genuine articles of Druidism were orally preserved and transmitted for centuries. He argues convincingly that the ancient poetry of Europe was ultimately based on what its composers believed to be magical principles, the rudiments of which formed a close religious secret for centuries. In time these were-garbled, discredited and forgotten.

Among the many signs of the transmission of special numbers he points out that the aggregate number of letter strokes for the complete 22-letter Ogham alphabet that he is studying is 72 and that this number is the multiple of 9, 'the number of lunar wisdom'. . . . he then mentions something about 'the seventy day season during which Venus moves successively from. maximum eastern elongation 'to inferior conjunction and maximum western elongation'.13

Page 207

"...Feniusa Farsa, Graves equates this hero with Dionysus Farsa has 72 assistants who helped him master the 72 languages created at the confusion of Babel, the tower of which is said to be built of 9 different materials

We are also reminded of the miraculous translation into Greek of the Five Books of Moses that was done by 72 scholars working for 72 days, Although the symbol for the Septuagint is LXX, legend, according to the fictional letter of Aristeas, records 72. The translation was done for Ptolemy Philadelphus (c.250 BC), by Hellenistic Jews, possibly from Alexandra.14

Graves did not know why this number was necessary, but he points out that he understands Frazer's Golden Bough to be a a book hinting that 'the secret involves the truth that the Christian dogma, and rituals, are the refinement of a great body of primitive beliefs, and that the only original element in Christianity- is the personality of Christ.15

Frances A. Yates, historian of Renaissance hermetisma tells, us the cabala had 72 angels through which the sephiroth (the powers of God) are believed to be approached, and further, she supplies the information that although the Cabala supplied a set of 48 conclusions purporting to confirm the Christian religion from the foundation of ancient wisdom, Pico Della Mirandola, a Renaissance magus, introduced instead 72, which were his 'own opinion' of the correct number. Yates writes, 'It is no accident there are seventy-two of Pico's Cabalist conclusions, for the conclusion shows that he knew something of the mystery of the Name of God with seventy-two letters.'16

In Hamlet's Mill de Santillarta adds the facts that 432,000 is the number of syllables in the Rig-Veda, which when multiplied by the soss (60) gives 25,920" (The reader is forgiven for a bit of laughter at this point)

Thee Bible has not escaped his pursuit. A prominent Assyriologist of the last century insisted that the total of the years recounted
mounted in Genesis for the lifetimes of patriarchs from the Flood also contained the needed secret numbers. (He showed that in the 1,656.years recounted in the Bible there are 86,400 7 day weeks, and dividing this number yields / Page 208 / 43,200.) In Indian yogic schools it is held that all living beings exhale and inhale 21,600 times a day, .multiply this by 2 and again we have.the necessary 432 digits.

Joseph Campbell discerns the secret in the date set for the coming of Patrick to Ireland. Myth-gives this date-as.- the interest-
ing number of AD.432.18

Whatever one may think-of some of these number coincidences, it becomes. difficult to escape the suspicion that many signs (number and otherwise) -indicate that early man observed the results.. of the movement of Precession . and that the-.transmission of this information was .considered of prime importance.

'With the awareness of the phenomenon, observers would certainly have tried for its measure, and such an endeavour would
have constituted the construction-of a 'Unified Field Theory' for nothing .less than Creation itself. Once determined, it would have been information worthy of secrecy and worthy of the passing on to future adepts.

But one last word about mankind's romance with number coincidences.The antagonist in John Updike's novel, Roger's Version, is a computer hacker, who, convinced.,that scientific evidence of God's existence is accumulating, endeavours to prove it by feeding -all the available scientific information. into a comuter. In his search for God 'breaking, through', he has become fascinated by certain numbers that have continually been cropping up. He explains them excitedly as 'the terms of Creation':

"...after a while I noticed that all over the sheet there seemed to hit these twenty-fours Jumping out at me. Two four; two,four.Planck time, for instance, divided by the radiation constant yields a figure near eight times ten again to the negative twenty-fourth, and the permittivity of free space, or electric constant, into the Bohr radiusekla almost exactly six times ten to the negative twenty-fourth. On positive side, the electromagnetic line-structure constant times Hubble radius - that is, the size of the universe as we now perceive it gives us something quite close to ten to the twenty-fourth, and the strong-force constant times the charge on the proton produces two point four times ten to the negative eighteenth, for another I began to circle twenty-four wherever it appeared on the Printout here' - he held it up. his piece of striped and striped wallpaper, decorated / Page 209 / with a number of scarlet circles - 'you can see it's more than random.'19
This inhabitant of the twentieth century is convinced that the striking occurrences of 2 and 4 reveal the sacred numbers by which God is speaking to us.

So much for any scorn directed to ancient man's fascination with number coincidences. That fascination is alive and well, Just a bit more incomprehensible"

 

 

3
THE
33
15
6
4
NINE
42
24
6
7
BILLION
73
37
1
5
NAMES
52
16
7
2
OF
21
12
3
3
GOD
26
17
8
24
-
247
121
31
2+4
-
2+4+7
1+2+1
3+1
6
-
13
4
4
-
-
1+3
-
-
6
-
4
4
4

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

FOREWORD

"'Into the Comet' and 'The Nine Billion Names of God' both involve computers and the troubles they may cause us. While writing this preface, I had occasion to call upon my own HP 9100A computer, Hal Junior, to answer an interesting question. Looking at my records, I find that I have now written just about one hundred short stories. This volume contains eighteen of them: therefore, how many possible 18-story collections will I be able to put together? The answer ­as I am sure will be instantly obvious to you - is 100 x 99. . . x 84 x 83 divided by 18 x 17 x 16 ... x .2 x 1. This is an impressive number - Hal Junior tells me that it is approximately 20,772,733,124,605,000,000.

Page 15

The Nine Billion Names of God


'This is a slightly unusual request,' said Dr Wagner, with what he hoped was commendable restraint. 'As far as I know, it's the first time anyone's been asked to supply a Tibetan monastery with an Automatic Sequence Computer. I don't wish to be inquisitive, but I should hardly have thought that your - ah - establishment had much use for such a machine. Could you explain just what you intend to do with it?'
'Gladly,' replied the lama, readjusting his silk robes and carefully putting away the slide rule he had been using far currency conversions. 'Your Mark V Computer can carry out any routine mathematical operation involving up to ten digits. However, for our work we are interested in letters, not numbers. As we wish you to modify the output circuits, the machine will be printing words, not columns of figures.'
'I don't quite understand. . .'
'This is a project on which we have been working for the last three centuries - since the lamasery was founded, in fact. It is somewhat alien to your way of thought, so I hope you will listen with an open mind while I explain it.'
'Naturally.'
'It is really quite simple. We have been compiling a list which shall contain all the possible names of God.'
'I beg your pardon?'

Page16

'We have reason to believe,' continued the lama imperturbably, 'that all such names can be written with not more than nine letters in an alphabet we have devised.'
'And you have been doing this for three centuries?'
'Yes: we expected it would take us about fifteen thousand years to complete the task.'
'Oh,' Dr Wagner looked a little dazed. 'Now I see why you wanted to hire one of our machines. But what exactly is the purpose of this project?'
The lama hesitated for a fraction of a second, and Wagner wondered if he had offended him. If so, there was no trace of annoyance in the reply.
'Call it ritual, if you like, but it's a fundamental part of our belief. All the many names of the Supreme Being - God Jehova, Allah, and so on - they are only man-made labels. There is a philosophical problem of some difficulty here, which I do not propose to discuss, but somewhere among all the possible combinations of letters that can occur are what one may call the real names of God. By systematic permutation of letters, we have been trying to list them all.'
'I see. You've been starting at AAAAAAA . . . and working up to ZZZZZZZZ . . .'
'Exactly - though we use a special alphabet of our own. Modifying the electromatic typewriters to deal with this is, of course, trivial. A rather more interesting problem is that of devising suitable circuits to eliminate ridiculous combinations. For example, no letter must occur more than three times in succession.'
,'Three? Surely you mean two.'
'Three is correct: I am afraid it would take too long to explain why, even if you understood our language.' "

Page 68

Into the Comet


"Pickett's fingers danced over the beads, sliding them up and down the wires with lightning speed. There were twelve wires in all, so that the abacus could handle numbers up to 999,999,999,999 - or could be divided into separate sections where several independent calculations could be carried out simultaneously.
'374072,' said Pickett, after an incredibly brief interval of time. 'Now see how long you take to do it, with pencil and paper.'
There was a much longer delay before Martens, who like most mathematicians was poor at arithmetic, called out '375072'. A hasty check soon confirmed that Martens had taken at least three times as long as Pickett to arrive at the wrong answer.
The atronomer's face was a study in mingled chagrin, astonishment, and curiosity.
'Where did you learn that trick?' he asked. 'I thought those things could only add and subtract.'
'Well - multiplication's only repeated addition, isn't it? All I did was to add 856 seven times in the unit column, three times in the tens column, and four times in the hundreds column. You do the same thing when you use pencil and paper. Of course, there are some short cuts, but if you think I'm fast, you should have seen my granduncle. He used to work in a Yokohama bank, and you couldn't see his fingers / Page 69 / when he was going at speed"

 

 

I

SAY

THREAD THAT THREAD

THREAD READ DEATH DEATH READ THREAD

THREAD R DEATH DEATH R THREAD

THREAD READ DEAR DAERHT

 

 

THE NEW ELIZABETHAN

REFERENCE DICTIONARY

An up-to-date vocabulary of the living English language

Circa 1900

FOURTH EDITION

Page 1472

thread (thred) [A.-S. thraed, from thrawan, to THROW (cp. Dut. draad, G. draht, Icel. thrathr)], n. A slender cord consisting of two or more yarns doubled or twisted ; a single filament of cotton, silk, wool, etc., esp. Lisle thread ; anything resembling this ; a fine line of colour etc. ; a thin seam or vein ; the spiral on a screw ; (fig.) a continuous course (of life etc.). v.t. To pass a thread through the eye or aperture of ; to string (beads etc.) on a thread ; (fig.) to pick (one's way) or to go through an intricate or crowded place, etc. ; to streak (the hair) with grey etc. ; to cut a thread on (a screw). thread and thrum : Good and bad together, all alike. threadbare, a. Worn so that the thread is visible, having the nap worn off ; (fig.) worn, trite, hackneyed. threadbareness, n. thread-mark, n. A mark produced by coloured silk fibres in banknotes to prevent counterfeiting. thread-paper, n. Soft paper for wrapping up thread, thread-worm, n. A thread-like nematode worm, esp. one infesting the rectum of children. threader, n. threadlike, a. and adv. thready, a. threadiness, n.

 

 

THE NEW ELIZABETHAN

REFERENCE DICTIONARY

An up-to-date vocabulary of the living English language

FOURTH EDITION

Circa 1900

Page 1472

thread (thred) [A.-S. thraed, from thrawan, to THROW (cp. Dut. draad, G. draht, Icel. thrathr)], n. A slender cord consisting of two or more yarns doubled or twisted ; a single filament of cotton, silk, wool, etc., esp. Lisle thread ; anything resembling this ; a fine line of colour etc. ; a thin seam or vein ; the spiral on a screw ; (fig.) a continuous course (of life etc.). v.t. To pass a thread through the eye or aperture of ; to string (beads etc.) on a thread ; (fig.) to pick (one's way) or to go through an intricate or crowded place, etc. ; to streak (the hair) with grey etc. ; to cut a thread on (a screw). thread and thrum : Good and bad together, all alike. threadbare, a. Worn so that the thread is visible, having the nap worn off ; (fig.) worn, trite, hackneyed. threadbareness, n. thread-mark, n. A mark produced by coloured silk fibres in banknotes to prevent counterfeiting. thread-paper, n. Soft paper for wrapping up thread, thread-worm, n. A thread-like nematode worm, esp. one infesting the rectum of children. threader, n. threadlike, a. and adv. thready, a. threadiness, n.

 

 

lisle thread: lisle thread

A strong tightly twisted cotton thread (usually made of long-staple cotton) - lisle. Derived forms: lisle threads. Type of: cotton. Nearest ... www.wordwebonline.com/en/LISLETHREAD

 

 

Definition - of Lisle from Dictionary.net

Lisle thread, a hard twisted cotton thread, originally produced at Lisle. Source:

Webster's Revised Unabridged Dictionary (1913) ... www.dictionary.net/lisle - 9k

 

 

CASSELL'S ENGLISH DICTIONARY

1974

Lisle thread (lil thred) [ town in France, now Lille], n, A fine, hard thread orig. made at Lille.

 

 

HOLY BIBLE

C

9 V 9

Page 575

JOB

Which maketh Arcturus, Orion, and Pleiades, and the chambers of the south.

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

Our minds seem to be organised to search for relationships and sequences. We look for hidden orders.

These intuitions seem to be more important than the facts themselves, for there is always the thrill at finding something, a pattern, it is a discovery - what was unknown is now revealed. Imagine looking up at the stars and finding the zodiac!

Searching out patterns is a pure delight.

Suddenly the counters fall into place and a connection is found, not necessarily a geometric one, but a relationship between numbers, pictures of the mind, that were not obvious before. There is that excitement of finding order in something that was otherwise hidden.

And there is the knowledge that a huge unseen world lurks behind the facades we see of the numbers themselves."

 

 

 

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
-
189
90
18
1+8
-
1+8+9
9+0
1+8
9
-
18
9
9
-
-
1+8
-
-
9
-
9
9
9

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

Our minds seem to be organised to search for relationships and sequences. We look for hidden orders.

These intuitions seem to be more important than the facts themselves, for there is always the thrill at finding something, a pattern, it is a discovery - what was unknown is now revealed. Imagine looking up at the stars and finding the zodiac!

Searching out patterns is a pure delight.

Suddenly the counters fall into place and a connection is found, not necessarily a geometric one, but a relationship between numbers, pictures of the mind, that were not obvious before. There is that excitement of finding order in something that was otherwise hidden.

And there is the knowledge that a huge unseen world lurks behind the facades we see of the numbers themselves."

 

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

Shakespeare Quotes - Such Stuff as Dreams Are Made on.
www.enotes.com/shakespeare-quotes/we-such-stuff-dreams-made

The Tempest Act 4, scene 1, William Shakespeare

Prospero:
Our revels now are ended. These our actors,
As I foretold you, were all spirits, and
Are melted into air, into thin air:
And like the baseless fabric of this vision,
The cloud-capp'd tow'rs, the gorgeous palaces,
The solemn temples, the great globe itself,
Yea, all which it inherit, shall dissolve,
And, like this insubstantial pageant faded,
Leave not a rack behind. We are such stuff
As dreams are made on; and our little life
Is rounded with a sleep.

 

 

2
WE
28
10
1
3
ARE
24
15
6
4
SUCH
51
15
6
5
STUFF
72
18
9
2
AS
20
2
2
6
DREAMS
60
24
6
3
ARE
24
15
6
4
MADE
23
14
5
2
ON
29
11
2
3
AND
19
10
1
3
OUR
54
18
9
4
LITTLE
78
24
6
4
LIFE
32
23
5
2
IS
28
10
1
7
ROUNDED
81
36
9
4
WITH
60
24
6
1
A
1
1
1
5
SLEEP
57
21
3
66
First Total
741
291
84
6+6
Add to Reduce
7+4+1
2+9+1
8+4
12
Second Total
12
12
12
1+2
Reduce to Deduce
1+2
1+2
1+2
3
Essence of Number
3
3
3

 

 

F
=
6
3
FOR
56
29
2
E
=
5
5
EVERY
28
19
1
A
=
1
6
ACTION
29
11
2
T
=
2
5
THERE
26
17
8
I
=
9
2
IS
43
7
7
A
=
1
2
AN
26
17
8
E
=
5
5
EQUAL
56
29
2
A
=
1
3
AND
28
19
1
O
=
6
8
OPPOSITE
29
11
2
R
=
9
8
REACTION
26
17
8
-
-
45
47
First Total
550
235
37
-
-
4+5
4+7
Add to Reduce
5+5+0
2+3+5
3+7
Q
-
5
11
Second Total
10
1
10
-
-
-
1+1
Reduce to Deduce
1+0
-
 1+0
-
-
5
2
Essence of Number
1
1
1

 

 

-
-
-
-
PHYSICS
-
-
-
P
=
7
1
P
16
7
7
H
=
8
1
H
8
8
8
Y
=
7
1
Y
25
7
7
S
=
1
1
S
19
10
1
I
=
9
1
I
9
9
9
C
=
3
1
C
3
3
3
S
=
1
1
S
19
10
1
-
-
-
-
PHYSICS
-
-
-
-
-
36
7
Add to Reduce
99
54
36
-
-
3+6
-
First Total
9+9
8+1
3+6
-
-
9
7
Reduce to Deduce
18
9
9
-
-
-
-
Second Total
1+8
-
-
-
-
9
7
Essence of Number
9
9
9

 

 

-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
9
-
1
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
8
-
19
9
-
19
+
=
55
5+5
=
10
1+0
1
=
1
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
7
-
7
-
-
3
-
+
=
17
1+7
=
8
=
8
=
8
-
-
16
-
25
-
-
3
-
+
=
44
4+4
=
8
=
8
=
8
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
16
8
25
19
9
3
19
+
=
99
9+9
=
18
1+8
9
=
9
-
-
7
8
7
1
9
3
1
+
=
36
3+6
=
9
=
9
=
9
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
7
-
7
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-``
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
17
7
P
H
Y
S
I
C
S
-
-
28
-
-
7
-
36
-
27
1+7
-
-
-
-
-
9
-
-
-
-
2+8
-
-
-
-
3+6
-
2+7
8
7
P
H
Y
S
I
C
S
-
-
10
-
-
7
-
9
-
9
-
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
8
7
P
H
Y
S
I
C
S
-
-
1
-
-
7
-
9
-
9

 

 

7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
9
-
1
+
=
19
1+9
=
10
1+0
1
=
1
-
-
8
-
19
9
-
19
+
=
55
5+5
=
10
1+0
1
=
1
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
7
-
7
-
-
3
-
+
=
17
1+7
=
8
=
8
=
8
-
16
-
25
-
-
3
-
+
=
44
4+4
=
8
=
8
=
8
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
16
8
25
19
9
3
19
+
=
99
9+9
=
18
1+8
9
=
9
-
7
8
7
1
9
3
1
+
=
36
3+6
=
9
=
9
=
9
7
P
H
Y
S
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
7
-
7
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
7
P
H
Y
S
I
C
S
-
-
28
-
-
7
-
36
-
27
-
-
-
-
-
9
-
-
-
-
2+8
-
-
-
-
3+6
-
2+7
7
P
H
Y
S
I
C
S
-
-
10
-
-
7
-
9
-
9
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
7
P
H
Y
S
I
C
S
-
-
1
-
-
7
-
9
-
9

 

 

-
-
-
-
PHYSICS
-
-
-
P
=
7
1
P
16
7
7
H
=
8
1
H
8
8
8
Y
=
7
1
Y
25
7
7
S
=
1
1
S
19
10
1
I
=
9
1
I
9
9
9
C
=
3
1
C
3
3
3
S
=
1
1
S
19
10
1
-
-
-
-
PHYSICS
-
-
-
-
-
36
7
Add to Reduce
99
54
36
-
-
3+6
-
First Total
9+9
8+1
3+6
-
-
9
7
Reduce to Deduce
18
9
9
-
-
-
-
Second Total
1+8
-
-
-
-
9
7
Essence of Number
9
9
9

 

 

 

.....

 

 

23
THE ELECTRO MAGNETIC FIELD
219
111
3
10
DARK MATTER
111
39
3
9
LIGHT MIND
96
51
6

 

 

6
MATTER
77
23
5
4
MIND
40
22
4

 

 

4
DARK
34
16
7
5
LIGHT
56
29
2
9
Add to Reduce
90
45
9
-
Reduce to Deduce
9+0
4+5
-
9
Essence of Number
9
9
9

 

 

GRAVITY GODS RA VITALITY

 

 

T
=
2
-
3
THE
33
15
6
G
=
7
-
13
GRAVITATIONAL
149
59
5
F
=
6
-
5
FIELD
36
27
9
-
-
15
-
21
First Total
218
101
20
-
-
1+5
-
2+1
Add to Reduce
2+1+8
1+0+1
2+0
-
-
6
-
3
Second Total
11
2
2
-
-
-
-
-
Reduce to Deduce
1+1
-
-
-
-
6
-
3
Essence of Number
2
2
2

 

 

T
=
2
-
3
THE
33
15
6
F
=
6
-
5
FORCE
47
29
2
O
=
6
-
2
OF
21
12
3
G
=
7
-
7
GRAVITY
102
39
3
-
-
21
-
17
First Total
203
95
14
-
-
2+1
-
1+7
Add to Reduce
2+0+3
9+5
1+4
-
-
3
-
8
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
-
-
-
3
-
8
Essence of Number
5
5
5

 

 

-
7
G
R
A
V
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
9
-
-
+
=
9
-
=
9
=
9
=
9
-
7
G
R
A
V
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
7
9
1
4
-
2
7
+
=
30
3+0
=
3
=
3
=
3
-
-
7
18
1
22
-
20
25
+
=
93
9+3
=
12
1+2
3
=
3
-
7
G
R
A
V
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
7
18
1
22
9
20
25
+
=
102
1+0+2
=
3
=
3
=
3
-
-
7
9
1
4
9
2
7
+
=
39
3+9
=
12
1+2
3
=
3
-
7
G
R
A
V
I
T
Y
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
--
-
-`-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-`-
7
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
8
-`-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
22
7
G
R
A
V
I
T
Y
-
-
23
-
1
7
-
39
-
21
2+2
-
-
9
-
-
9
-
-
-
-
2+3
-
-
-
-
3+9
-
2+1
4
7
G
R
A
V
I
T
Y
-
-
5
-
1
7
-
12
-
3
-
-
7
9
1
4
9
2
7
-
-
-
-
-
-
-
1+2
-
-
4
7
G
R
A
V
I
T
Y
-
-
5
-
1
7
-
3
-
3

 

 

7
G
R
A
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
`-
-
-
-
-
9
-
-
+
=
9
-
=
9
=
9
=
9
`-
-
-
-
-
9
-
-
+
=
9
-
=
9
=
9
=
9
7
G
R
A
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
7
9
1
4
-
2
7
+
=
30
3+0
=
3
=
3
=
3
`-
7
18
1
22
-
20
25
+
=
93
9+3
=
12
1+2
3
=
3
7
G
R
A
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
`-
7
18
1
22
9
20
25
+
=
102
1+0+2
=
3
=
3
=
3
-
7
9
1
4
9
2
7
+
=
39
3+9
=
12
1+2
3
=
3
7
G
R
A
V
I
T
Y
-T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
=
2
-`-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-`-
7
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
7
G
R
A
V
I
T
Y
-
-
23
-
1
7
-
39
-
21
-
-
9
-
-
9
-
-
-
-
2+3
-
-
-
-
3+9
-
2+1
7
G
R
A
V
I
T
Y
-
-
5
-
1
7
-
12
-
3
-
7
9
1
4
9
2
7
-
-
-
-
-
-
-
1+2
-
-
7
G
R
A
V
I
T
Y
-
-
5
-
1
7
-
3
-
3

 

 

GODS RA VITALITY GRAVITY VITALITY RA GODS

 

G
=
7
-
7
GRAVITY
102
39
3
G
=
7
-
4
GODS
45
18
9
R
=
9
-
2
RA
19
10
1
V
=
4
-
8
VITALITY
118
37
1
-
-
27
-
21
First Total
284
104
14
-
-
2+7
-
2+1
Add to Reduce
2+8+4
9+5
1+4
-
-
9
-
3
Second Total
14
14
5
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
9
-
3
Essence of Number
5
5
5

 

 

9
LIGHT MIND
96
51
6
10
DARK MATTER
111
39
3
19
First Total
207
90
9
1+9
Add to Reduce
2+0+7
9+0
-
10
Second Total
9
9
9
1+0
Reduce to Deduce
-
-
-
1
Essence of Number
9
9
9

 

 

20
ELECTRO MAGNETIC FIELD
186
96
6

 

 

4
DARK
34
16
7
6
ENERGY
74
38
2
10
Add to Reduce
108
54
9
1+0
Reduce to Deduce
1+0+8
5+4
-
1
Essence of Number
9
9
9

 

 

7
GRAVITY
102
39
3
5
LIGHT
56
29
2
7
ELECTRO
78
33
6
8
MAGNETIC
72
36
9
5
FIELD
36
27
9

 

 

7
ELEKTRA
72
27
9

 

 

7
SCIENCE
-
-
-
1
S+C+I+E
36
18
9
7
N+C+E
22
13
4
7
SCIENCE
58
31
4
-
5+8
3+1
-
7
SCIENCE
13
4
4
-
1+3
-
-
7
SCIENCE
4
4
4

 

 

M
=
4
4
MIND
40
22
4
I
=
9
15
INTERPENETRATES
189
72
9
M
=
4
6
MATTER
77
23
5
-
-
17
25
Add to Reduce
306
117
18
-
-
1+7
2+5
Reduce to Deduce
3+0+6
1+1+7
1+8
-
-
8
7
Essence of Number
9
9
9

 

 

-
25
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
-
-
9
5
-
-
-
-
-
5
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
34
3+4
=
7
-
7
-
7
-
-
-
9
14
-
-
9
14
-
-
-
-
-
14
-
-
-
-
-
-
19
-
-
-
-
-
-
-
+
=
79
7+9
=
16
1+6
7
-
7
-
25
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
-
-
-
2
5
9
7
5
-
5
2
9
1
2
5
-
-
4
1
2
2
5
9
+
=
83
8+3
=
11
1+1
2
-
2
-
-
13
-
-
4
-
-
-
20
5
18
16
5
-
5
20
18
1
20
5
-
-
13
1
20
20
5
18
+
=
227
2+2+7
=
11
1+1
2
-
2
-
25
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
13
9
14
4
-
9
14
20
5
18
16
5
14
5
20
18
1
20
5
19
-
13
1
20
20
5
18
+
=
306
3+0+6
=
9
-
9
-
9
-
-
4
9
5
4
-
9
5
2
5
9
7
5
5
5
2
9
1
2
5
1
-
4
1
2
2
5
9
+
=
117
1+1+7
=
9
=
9
-
9
-
25
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
-
3
-
``-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
2
2
-
-
-
-
2
occurs
x
5
=
10
1+0
1
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
4
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
5
-
-
-
5
-
5
-
-
5
5
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
8
=
40
4+0
4
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
5
=
45
4+5
9
17
25
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
28
-
-
25
-
117
-
27
1+7
2+5
-
9
-
-
-
9
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
2+8
-
-
2+5
-
1+1+7
-
2+7
8
7
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
10
-
-
7
-
9
-
9
-
-
4
9
5
4
-
9
5
2
5
9
7
5
5
5
2
9
1
2
5
1
-
4
1
2
2
5
9
-
-
1+0
1
-
-
-
-
-
-
8
7
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
1
-
-
7
-
9
-
9

 

 

25
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
9
5
-
-
9
5
-
-
-
-
-
5
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
34
3+4
=
7
-
7
-
7
-
-
9
14
-
-
9
14
-
-
-
-
-
14
-
-
-
-
-
-
19
-
-
-
-
-
-
-
+
=
79
7+9
=
16
1+6
7
-
7
25
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
-
-
-
2
5
9
7
5
-
5
2
9
1
2
5
-
-
4
1
2
2
5
9
+
=
83
8+3
=
11
1+1
2
-
2
-
13
-
-
4
-
-
-
20
5
18
16
5
-
5
20
18
1
20
5
-
-
13
1
20
20
5
18
+
=
227
2+2+7
=
11
1+1
2
-
2
25
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
13
9
14
4
-
9
14
20
5
18
16
5
14
5
20
18
1
20
5
19
-
13
1
20
20
5
18
+
=
306
3+0+6
=
9
-
9
-
9
-
4
9
5
4
-
9
5
2
5
9
7
5
5
5
2
9
1
2
5
1
-
4
1
2
2
5
9
+
=
117
1+1+7
=
9
=
9
-
9
25
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
-
3
``-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
2
2
-
-
-
-
2
occurs
x
5
=
10
1+0
1
-
4
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
5
-
-
-
5
-
5
-
-
5
5
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
8
=
40
4+0
4
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
9
-
-
-
9
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
5
=
45
4+5
9
25
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
28
-
-
25
-
117
-
27
2+5
-
9
-
-
-
9
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
-
-
2+8
-
-
2+5
-
1+1+7
-
2+7
7
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
10
-
-
7
-
9
-
9
-
4
9
5
4
-
9
5
2
5
9
7
5
5
5
2
9
1
2
5
1
-
4
1
2
2
5
9
-
-
1+0
1
-
-
-
-
-
-
7
M
I
N
D
-
I
N
T
E
R
P
E
N
E
T
R
A
T
E
S
-
M
A
T
T
E
R
-
-
1
-
-
7
-
9
-
9

 

 

-
-
-
-
ISAAC NEWTON
-
-
-
I
=
9
5
ISAAC
33
15
6
N
=
5
6
NEWTON
91
28
1
-
-
14
11
ISAAC NEWTON
124
43
7
-
4+5
 1+1  
1+2+4
4+3
-
Q
-
5
2
ISAAC NEWTON
7
7
7

 

 

-
PSYCHICS
-
-
-
4
C
3
3
3
7
PHYSICS
99
36
9
16
PSYCHICS-
102
39
12
1+8
-
1+0+2
3+9
1+2
9
-
3
12
3
-
-
-
 1+2
-
9
-
3
3
3

 

 

-
ELECTRICITY
-
-
-
5
ELECT
45
18
9
1
R
18
9
9
1
I
9
9
9
1
C
3
3
3
1
I
9
9
9
2
T+Y
45
9
9
11
ELECTRICITY
129
57
48
1+1
-
1+2+9
5+7
4+8
2
ELECTRICITY
12
12
12
-
-
1+2
1+2
1+2
2
ELECTRICITY
3
3
3

 

 

-
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
+
=
18
1+8
=
9
=
9
=
9
-
-
-
-
-
-
-
-
9
-
9
-
-
+
=
18
1+8
=
9
=
9
=
9
-
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
3
-
2
7
+
=
39
3+9
=
12
1+2
3
=
3
-
-
5
12
5
3
20
18
-
3
-
20
25
+
=
111
1+1+1
=
3
=
3
=
3
-
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
5
12
5
3
20
18
9
3
9
20
25
+
=
129
1+2+9
=
12
1+2
3
=
3
-
-
5
3
5
3
2
9
9
3
9
2
7
+
=
57
5+7
=
12
1+2
3
=
3
-
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
3
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
19
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
26
-
-
11
-
57
-
30
1+9
1+1
-
-
-
-
-
9
9
-
9
-
-
-
-
2+6
-
-
1+1
-
5+7
-
3+0
10
2
E
L
E
C
T
R
I
C
I
T
Y
-
-
8
-
-
2
-
12
-
3
1+0
-
5
3
5
3
2
9
9
3
9
2
7
-
-
-
-
-
-
-
1+2
-
-
1
2
E
L
E
C
T
R
I
C
I
T
Y
-
-
8
-
-
2
-
3
-
3

 

 

11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
+
=
18
1+8
=
9
=
9
=
9
-
-
-
-
-
-
-
9
-
9
-
-
+
=
18
1+8
=
9
=
9
=
9
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
3
-
2
7
+
=
39
3+9
=
12
1+2
3
=
3
-
5
12
5
3
20
18
-
3
-
20
25
+
=
111
1+1+1
=
3
=
3
=
3
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
5
12
5
3
20
18
9
3
9
20
25
+
=
129
1+2+9
=
12
1+2
3
=
3
-
5
3
5
3
2
9
9
3
9
2
7
+
=
57
5+7
=
12
1+2
3
=
3
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
5
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
9
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
26
-
-
11
-
57
-
30
1+1
-
-
-
-
-
9
9
-
9
-
-
-
-
2+6
-
-
1+1
-
5+7
-
3+0
2
E
L
E
C
T
R
I
C
I
T
Y
-
-
8
-
-
2
-
12
-
3
-
5
3
5
3
2
9
9
3
9
2
7
-
-
-
-
-
-
-
1+2
-
-
2
E
L
E
C
T
R
I
C
I
T
Y
-
-
8
-
-
2
-
3
-
3

 

 

-
ELECTRIC
-
-
-
5
ELECT
75
18
9
1
R
18
9
9
1
I
9
9
9
1
C
3
3
3
8
ELECTRIC
75
39
30
-
-
7+5
3+9
3+0
8
ELECTRIC
12
12
3
-
-
1+2
1+2
-
8
ELECTRIC
3
3
3

 

ELECTRIC ET CIRCLE ET ELECTRIC

 

 

ELECTRIC = ET CIRCLE = ELECTRIC

 

-
-
-
-
-
ELECTRIC
-
-
-
E
-
5
-
1
E
5
5
5
T
-
2
-
1
T
20
2
2
C
-
3
-
1
C
3
3
3
I
-
9
-
1
I
9
9
9
R
-
9
-
1
R
18
9
9
C
=
3
-
1
C
3
3
3
L
=
3
-
1
L
12
3
3
E
=
5
-
1
E
5
5
5
-
-
39
-
8
ELECTRIC
75
39
39
-
-
3+9
-
-
-
7+5
3+9
3+9
-
-
12
-
8
ELECTRIC
12
12
12
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
3
-
8
ELECTRIC
3
3
3

 

ELECTRIC = ET CIRCLE = ELECTRIC

 

-
-
-
-
-
ELECTRIC
-
-
-
E
-
5
-
2
E+T
25
7
7
C
-
3
-
1
C
3
3
3
I
-
9
-
1
I
9
9
9
R
-
9
-
1
R
18
9
9
C
=
3
-
1
C
3
3
3
L
=
3
-
1
L
12
3
3
E
=
5
-
1
E
5
5
5
-
-
39
3
8
ELECTRIC
75
39
39
-
-
3+9
-
-
-
7+5
3+9
3+9
-
-
12
3
8
ELECTRIC
12
12
12
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
3
3
8
ELECTRIC
3
3
3

 

 

-
ELECTRIC
-
-
-
5
E
5
5
5
1
L
12
3
3
5
E
5
5
5
5
C
3
3
3
5
T
20
2
2
1
R
18
9
9
1
I
9
9
9
1
C
3
3
3
8
ELECTRIC
75
39
30
-
-
7+5
3+9
3+0
8
ELECTRIC
12
12
3
-
-
1+2
1+2
-
8
ELECTRIC
3
3
3

 

 

-
8
E
L
E
C
T
R
I
C
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
=
9
=
9
-
8
E
L
E
C
T
R
I
C
-
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
3
+
=
30
3+9
=
12
1+2
3
=
3
-
-
5
12
5
3
20
18
-
3
+
=
66
1+1+1
=
3
=
3
=
3
-
8
E
L
E
C
T
R
I
C
-
-
-
-
-
-
-
-
-
-
-
-
5
12
5
3
20
18
9
3
+
=
75
7+5
=
12
1+2
3
=
3
-
-
5
3
5
3
2
9
9
3
+
=
39
3+9
=
12
1+2
3
=
3
-
8
E
L
E
C
T
R
I
C
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
3
-
3
-
-
-
3
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
9
occurs
x
2
=
18
1+8
9
26
8
E
L
E
C
T
R
I
C
-
-
19
-
-
8
-
39
-
21
2+6
-
-
-
-
-
-
9
9
-
-
-
1+9
-
-
-
-
3+9
-
2+1
8
8
E
L
E
C
T
R
I
C
-
-
10
-
-
8
-
12
-
3
-
-
5
3
5
3
2
9
9
3
-
-
1+0
-
-
-
-
-
-
-
8
8
E
L
E
C
T
R
I
C
-
-
1
-
-
8
-
3
-
3

 

 

-
CIRCUITRY
--
-
-
1
C
3
3
3
1
I
9
9
9
1
R
18
9
9
1
C
3
3
3
1
U
21
3
3
1
I
9
9
9
3
T+R+Y
63
18
9
9
CIRCUITRY
126
54
45
-
-
1+2+6
5+4
4+5
9
CIRCUITRY
9
9
9

 

 

-
9
C
I
R
C
U
I
T
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
+
=
18
1+8
9
-
=
9
=
9
-
-
-
9
-
-
-
9
-
-
-
+
=
18
1+8
9
-
=
9
=
9
-
9
C
I
R
C
U
I
T
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
-
2
9
7
+
=
36
3+6
9
-
=
9
=
9
-
-
3
-
18
3
21
-
20
18
25
+
=
108
1+0+8
9
-
=
9
=
9
-
9
C
I
R
C
U
I
T
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
9
20
18
25
+
=
126
1+2+6
9
-
=
9
=
9
-
-
3
9
9
3
3
9
2
9
7
+
=
54
5+4
9
-
=
9
=
9
-
9
C
I
R
C
U
I
T
R
Y
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
3
3
-
-
-
-
-
-
3
occurs
x
3
=
0
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
9
-
9
-
-
-
9
occurs
x
4
=
36
3+6
9
24
9
C
I
R
C
U
I
T
R
Y
-
-
21
-
-
9
-
54
-
27
2+4
-
-
9
9
-
-
9
-
9
-
-
-
2+1
-
-
-
-
5+4
-
2+7
6
9
C
I
R
C
U
I
T
R
Y
-
-
3
-
-
9
-
9
-
9
-
-
3
9
9
3
3
9
2
9
7
-
-
-
-
-
-
  
-
-
-
6
9
C
I
R
C
U
I
T
R
Y
-
-
3
-
-
9
-
9
-
9

 

 

9
C
I
R
C
U
I
T
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
+
=
18
1+8
9
-
=
9
=
9
-
-
9
-
-
-
9
-
-
-
+
=
18
1+8
9
-
=
9
=
9
9
C
I
R
C
U
I
T
R
Y
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
-
2
9
7
+
=
36
3+6
9
-
=
9
=
9
-
3
-
18
3
21
-
20
18
25
+
=
108
1+0+8
9
-
=
9
=
9
9
C
I
R
C
U
I
T
R
Y
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
9
20
18
25
+
=
126
1+2+6
9
-
=
9
=
9
-
3
9
9
3
3
9
2
9
7
+
=
54
5+4
9
-
=
9
=
9
9
C
I
R
C
U
I
T
R
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
3
3
-
-
-
-
-
-
3
occurs
x
3
=
0
=
9
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
-
9
9
-
-
9
-
9
-
-
-
9
occurs
x
4
=
36
3+6
9
9
C
I
R
C
U
I
T
R
Y
-
-
21
-
-
9
-
54
-
27
-
-
9
9
-
-
9
-
9
-
-
-
2+1
-
-
-
-
5+4
-
2+7
9
C
I
R
C
U
I
T
R
Y
-
-
3
-
-
9
-
9
-
9
-
3
9
9
3
3
9
2
9
7
-
-
-
-
-
-
  
-
-
-
9
C
I
R
C
U
I
T
R
Y
-
-
3
-
-
9
-
9
-
9

 

 

-
CIRCUITS
--
-
-
1
C
3
3
3
1
I
9
9
9
1
R
18
9
9
1
C
3
3
3
1
U
21
3
3
1
I
9
9
9
2
T+S
39
12
3
8
CIRCUITS
102
48
39
-
-
1+0+2
4+8
3+9
8
CIRCUITS
3
12
12
-
-
-
1+2
1+2
8
CIRCUITS
3
3
3

 

 

8
ELECTRIC
75
39
3
8
CIRCUITS
102
48
3

 

 

10
ELECTRICAL
88
43
7
8
CIRCUITS
102
48
3
18
First Total
190
91
10
2+6
Add to Reduce
1+9+0
9+1
1+0
8
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
8
Essence of Number
1
1
1

 

 

-
ELECTRICAL
-
-
-
-
-
-
1
E
5
5
5
-
-
-
1
L
12
3
3
-
3
-
1
E
5
5
5
-
-
-
1
C
3
3
3
-
3
-
1
T
20
2
2
-
-
-
1
R
18
9
9
-
-
9
1
I
9
9
9
-
-
9
1
C
3
3
3
-
3
-
1
A
1
1
1
-
-
-
1
L
12
3
3
-
3
-
10
ELECTRICAL
88
43
43
-
-
-
-
CIRCUITS
--
-
-
-
-
-
1
C
3
3
3
-
3
-
1
I
9
9
9
-
-
9
1
R
18
9
9
-
-
9
1
C
3
3
3
-
3
-
1
U
21
3
3
-
3
-
1
I
9
9
9
-
-
9
1
T+S
39
12
3
-
3
-
8
CIRCUITS
102
48
39
-
-
-
-
-
--
-
-
-
-
-
18
First Total
190
91
82
-
-
-
2+6
Add to Reduce
1+9+0
9+1
8+2
-
-
-
8
Second Total
10
10
10
-
-
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
-
8
Essence of Number
1
1
1
-
-
-

 

 

-
18
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
1
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
19
+
=
46
4+6
=
10
1+0
1
=
1
-
18
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
3
1
3
-
3
-
9
3
3
-
2
-
+
=
54
5+4
=
9
=
9
=
9
-
-
5
12
5
3
20
18
-
3
1
12
-
3
-
18
3
21
-
20
-
+
=
144
1+4+4
=
3
=
9
=
9
-
18
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
-
5
12
5
3
20
18
9
3
1
12
-
3
9
18
3
21
9
20
19
+
=
190
1+9+0
=
10
1+0
1
=
1
-
-
5
3
5
3
2
9
9
3
1
3
-
3
9
9
3
3
9
2
1
+
=
82
8+2
=
10
1+0
1
=
1
-
18
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
3
-
3
-
-
-
3
-
3
-
3
-
-
3
3
-
-
-
-
-
3
occurs
x
7
=
21
2+1
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
9
-
-
9
-
-
-
-
9
occurs
x
5
=
45
4+5
9
25
18
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
20
-
-
18
-
82
-
19
2+5
1+8
-
-
-
-
-
9
9
-
-
-
-
-
9
9
-
-
9
-
-
-
-
2+0
-
-
1+8
-
8+2
-
1+9
7
9
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
2
-
-
9
-
10
-
10
-
-
5
3
5
3
2
9
9
3
1
3
-
3
9
9
3
3
9
2
1
-
-
-
-
-
-
-
1+0
-
1+0
7
9
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
1
-
-
9
-
1
-
1

 

 

18
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
1
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
9
-
19
+
=
46
4+6
=
10
1+0
1
=
1
18
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
3
1
3
-
3
-
9
3
3
-
2
-
+
=
54
5+4
=
9
=
9
=
9
-
5
12
5
3
20
18
-
3
1
12
-
3
-
18
3
21
-
20
-
+
=
144
1+4+4
=
3
=
9
=
9
18
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
5
12
5
3
20
18
9
3
1
12
-
3
9
18
3
21
9
20
19
+
=
190
1+9+0
=
10
1+0
1
=
1
-
5
3
5
3
2
9
9
3
1
3
-
3
9
9
3
3
9
2
1
+
=
82
8+2
=
10
1+0
1
=
1
18
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
3
-
-
-
3
-
3
-
3
-
-
3
3
-
-
-
-
-
3
occurs
x
7
=
21
2+1
3
-
5
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
9
9
-
-
-
-
-
9
9
-
-
9
-
-
-
-
9
occurs
x
5
=
45
4+5
9
18
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
20
-
-
18
-
82
-
19
1+8
-
-
-
-
-
9
9
-
-
-
-
-
9
9
-
-
9
-
-
-
-
2+0
-
-
1+8
-
8+2
-
1+9
9
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
2
-
-
9
-
10
-
10
-
5
3
5
3
2
9
9
3
1
3
-
3
9
9
3
3
9
2
1
-
-
-
-
-
-
-
1+0
-
1+0
9
E
L
E
C
T
R
I
C
A
L
-
C
I
R
C
U
I
T
S
-
-
1
-
-
9
-
1
-
1

 

 

18
E
L
E
C
T
R
I
C
A
L
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
9
-
1
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
9
-
19
+
=
46
4+6
=
10
1+0
1
=
1
18
E
L
E
C
T
R
I
C
A
L
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
3
1
3
3
-
9
3
3
-
2
-
+
=
54
5+4
=
9
=
9
=
9
-
5
12
5
3
20
18
-
3
1
12
3
-
18
3
21
-
20
-
+
=
144
1+4+4
=
3
=
9
=
9
18
E
L
E
C
T
R
I
C
A
L
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
5
12
5
3
20
18
9
3
1
12
3
9
18
3
21
9
20
19
+
=
190
1+9+0
=
10
1+0
1
=
1
-
5
3
5
3
2
9
9
3
1
3
3
9
9
3
3
9
2
1
+
=
82
8+2
=
10
1+0
1
=
1
18
E
L
E
C
T
R
I
C
A
L
C
I
R
C
U
I
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
3
-
-
-
3
-
3
3
-
-
3
3
-
-
-
-
-
3
occurs
x
7
=
21
2+1
3
-
5
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
9
9
-
-
-
-
9
9
-
-
9
-
-
-
-
9
occurs
x
5
=
45
4+5
9
18
E
L
E
C
T
R
I
C
A
L
C
I
R
C
U
I
T
S
-
-
20
-
-
18
-
82
-
19
1+8
-
-
-
-
-
9
9
-
-
-
-
9
9
-
-
9
-
-
-
-
2+0
-
-
1+8
-
8+2
-
1+9
9
E
L
E
C
T
R
I
C
A
L
C
I
R
C
U
I
T
S
-
-
2
-
-
9
-
10
-
10
-
5
3
5
3
2
9
9
3
1
3
3
9
9
3
3
9
2
1
-
-
-
-
-
-
-
1+0
-
1+0
9
E
L
E
C
T
R
I
C
A
L
C
I
R
C
U
I
T
S
-
-
1
-
-
9
-
1
-
1

 

 

3
VAN
37
10
1
2
DE
9
9
9
6
GRAAFF
39
30
3
10
GENERATORS
122
50
5
21
First Total
207
99
18
2+1
Add to Reduce
2+0+7
9+9
1+8
3
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
3
Essence of Number
9
9
9

 

 

6
DYNAMO
72
27
9

 

 

THE PERIODIC KINGDOM

A JOURNEY INTO THE LAND OF THE CHEMICAL ELEMENTS

Peter Atkins 1995

Page 17

"...carbon has established itself as king of the periodic kingdom. Carbon, of course, is the element of organic compounds: the extraordinary and complex property we term "life" stems almost in its entirety from this black northern region of the kingdom.

"Carbon's principal products, living organisms, have struggled over a few billion years to establish mechanisms for the accumulation and dispersal of information (an austere distillation and definition of what we mean by "life"), and silicon has lain in wait, The recent alliance of the two regions, in which carbon-based organisms have developed the use of silicon based artifacts for information technology, has resulted in the enslavement of silicon. However such is the precosity of carbon's organisms that they are steadily developing silicons latent powers, and one day silicon may well overturn the suzerainty of its northern neighbor and assume the dominant role. It certainly has long-term potential, for its metabolism and replication need not be as messy as carbon's. Here we may see one of the most subtle interplays of alliances anywhere in the kingdom, for silicon will not realize its full potential without the burden of development being carried out by carbon."

 

7
CARBONS
72
27
9
6
CARBON
53
26
8
7
SILICON
81
36
9
8
SILICONS
100
37
1
6
OXYGEN
90
36
9

 

 

-
7
C
A
R
B
O
N
S
-
-
-
-
-
--
-
-
-
`-
-
-
-
-
15
14
19
+
=
48
4+8
=
12
1+2
3
-
-
-
-
-
-
6
5
1
+
=
12
1+2
=
3
-
3
-
7
C
A
R
B
O
N
S
-
-
-
-
-
--
-
-
-
`-
3
1
18
2
-
-
-
+
=
24
2+4
=
6
-
6
-
-
3
1
9
2
-
-
-
+
=
15
1+5
=
6
-
6
-
7
C
A
R
B
O
N
S
-
-
-
-
-
--
-
-
-
`-
3
1
18
2
15
14
19
+
=
72
7+2
=
9
-
9
-
-
3
1
9
2
6
5
1
+
=
27
2+7
=
9
-
9
-
7
C
A
R
B
O
N
S
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
1
-
-
1
occurs
x
2
=
2
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
-
3
-
4
-
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
5
occurs
x
1
=
5
-
-
-
-
4
-
6
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
4
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
4
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
19
7
C
A
R
B
O
N
S
-
-
26
-
-
7
-
27
1+9
-
-
-
9
-
-
-
-
-
-
2+6
-
-
-
-
2+7
10
7
C
A
R
B
O
N
S
-
-
8
-
-
7
-
9
1+0
-
3
1
9
2
6
5
1
-
-
-
-
-
-
-
-
1
7
C
A
R
B
O
N
S
-
-
8
-
-
7
-
9

 

 

7
C
A
R
B
O
N
S
-
-
-
-
-
--
-
-
`-
-
-
-
-
15
14
19
+
=
48
4+8
=
12
1+2
3
-
-
-
-
-
6
5
1
+
=
12
1+2
=
3
-
3
7
C
A
R
B
O
N
S
-
-
-
-
-
--
-
-
`-
3
1
18
2
-
-
-
+
=
24
2+4
=
6
-
6
-
3
1
9
2
-
-
-
+
=
15
1+5
=
6
-
6
7
C
A
R
B
O
N
S
-
-
-
-
-
--
-
-
`-
3
1
18
2
15
14
19
+
=
72
7+2
=
9
-
9
-
3
1
9
2
6
5
1
+
=
27
2+7
=
9
-
9
7
C
A
R
B
O
N
S
-
-
-
-
-
-
-
-
-
-
1
1
-
-
1
1
-
-
1
occurs
x
2
=
2
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
3
-
4
-
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
5
-
5
-
-
-
5
occurs
x
1
=
5
-
-
-
4
-
6
-
-
-
-
6
occurs
x
1
=
6
9
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
7
C
A
R
B
O
N
S
-
-
26
-
-
7
-
27
-
-
-
9
-
-
-
-
-
-
2+6
-
-
-
-
2+7
7
C
A
R
B
O
N
S
-
-
8
-
-
7
-
9
-
3
1
9
2
6
5
1
-
-
-
-
-
-
-
-
7
C
A
R
B
O
N
S
-
-
8
-
-
7
-
9

 

 

-
4
Z
E
R
O
-
-
-
-
-
--
-
-
-
-
8
-
-
6
+
=
14
1+4
=
5
=
5
-
-
26
-
-
15
+
=
41
4+1
=
5
=
5
-
4
Z
E
R
O
-
-
-
-
-
--
-
-
-
-
-
5
9
-
+
=
14
1+4
=
5
=
5
-
-
-
5
18
-
+
=
23
2+3
=
5
=
5
-
4
Z
E
R
O
-
-
-
-
-
--
-
-
-
-
26
5
18
15
+
=
64
6+4
=
10
1+0
1
-
-
8
5
9
6
+
=
28
2+8
=
10
1+0
1
-
4
Z
E
R
O
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
17
4
Z
E
R
O
-
-
28
-
-
4
-
28
1+7
-
-
-
9
-
-
-
2+8
-
-
-
-
2+8
8
4
Z
E
R
O
-
-
10
-
-
4
-
10
-
-
-
-
-
 -
-
-
1+0
-
-
-
-
1+0
8
4
Z
E
R
O
-
-
1
-
-
4
-
1

 

 

4
Z
E
R
O
-
-
-
-
-
--
-
-
-
8
-
-
6
+
=
14
1+4
=
5
=
5
-
26
-
-
15
+
=
41
4+1
=
5
=
5
4
Z
E
R
O
-
-
-
-
-
--
-
-
-
-
5
9
-
+
=
14
1+4
=
5
=
5
-
-
5
18
-
+
=
23
2+3
=
5
=
5
4
Z
E
R
O
-
-
-
-
-
--
-
-
-
26
5
18
15
+
=
64
6+4
=
10
1+0
1
-
8
5
9
6
+
=
28
2+8
=
10
1+0
1
4
Z
E
R
O
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
8
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
9
-
-
-
9
occurs
x
1
=
9
4
Z
E
R
O
-
-
28
-
-
4
-
28
-
-
-
9
-
-
-
2+8
-
-
-
-
2+8
4
Z
E
R
O
-
-
10
-
-
4
-
10
-
-
-
-
-
-
-
1+0
-
-
-
-
1+0
4
Z
E
R
O
-
-
1
-
-
4
-
1

 

 

- GEOPHYSICS

-

-

 -
3 GEO

27

18

 9
7 PHYSICS

99

36

 9
10 GEOPHYSICS

126

54

 18
1+0
 - 1+2+6 5+4 1+8
1 GEOPHYSICS

9

9

 9

 

 

-
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
8
-
1
9
-
1
+
=
25
2+5
=
7
=
7
=
7
-
-
-
-
15
-
-
8
-
19
9
-
19
+
=
70
7+0
=
7
=
7
=
7
-
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
-
7
-
7
-
-
3
-
+
=
29
2+9
=
11
1+1
2
=
2
-
-
7
5
-
-
16
-
25
-
-
3
-
+
=
56
5+6
=
11
1+1
2
=
2
-
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
-
16
8
25
19
9
3
19
+
=
126
1+2+6
=
9
=
9
=
9
-
-
7
5
6
-
7
8
7
1
9
3
1
+
=
54
5+4
=
9
=
9
=
9
-
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
--
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
7
-
7
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
6
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
37
-
-
10
-
54
-
36
-
1+0
-
-
-
-
-
-
-
-
9
-
-
-
-
3+7
-
-
1+0
-
5+4
-
3+6
6
1
G
E
O
-
P
H
Y
S
I
C
S
-
-
10
-
-
1
-
9
-
9
-
-
7
5
6
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
6
1
G
E
O
-
P
H
Y
S
I
C
S
-
-
1
-
-
1
-
9
-
9

 

 

10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
8
-
1
9
-
1
+
=
25
2+5
=
7
=
7
=
7
-
-
-
15
-
-
8
-
19
9
-
19
+
=
70
7+0
=
7
=
7
=
7
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
7
5
-
-
7
-
7
-
-
3
-
+
=
29
2+9
=
11
1+1
2
=
2
-
7
5
-
-
16
-
25
-
-
3
-
+
=
56
5+6
=
11
1+1
2
=
2
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
7
5
15
-
16
8
25
19
9
3
19
+
=
126
1+2+6
=
9
=
9
=
9
-
7
5
6
-
7
8
7
1
9
3
1
+
=
54
5+4
=
9
=
9
=
9
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
7
-
-
-
7
-
7
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
37
-
-
10
-
54
-
36
1+0
-
-
-
-
-
-
-
-
9
-
-
-
-
3+7
-
-
1+0
-
5+4
-
3+6
1
G
E
O
-
P
H
Y
S
I
C
S
-
-
10
-
-
1
-
9
-
9
-
7
5
6
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
1
G
E
O
-
P
H
Y
S
I
C
S
-
-
1
-
-
1
-
9
-
9

 

 

GOD'S SECRET FORMULA

Peter Plichta 1995

Deciphering The Riddle Of The Universe And The Prime Number Code

Page 33

"Table 1. The 81 stable chemical elements

Atomic Name number

Hafnium 72

 

7
HAFNIUM
72
36
9

 

--
7
H
A
F
N
I
U
M
-
-
-
-
-
--
-
-
-
-
8
-
-
5
9
-
-
+
=
22
2+2
=
4
=
4
-
-
8
-
-
14
9
-
-
+
=
31
3+1
=
4
=
4
--
7
H
A
F
N
I
U
M
-
-
-
-
-
--
-
-
-
-
-
1
6
-
-
3
4
+
=
14
1+4
=
5
=
5
-
-
-
1
6
-
-
21
13
+
=
41
4+1
=
5
=
5
--
7
H
A
F
N
I
U
M
-
-
-
-
-
--
-
-
-
-
8
1
6
14
9
21
13
+
=
72
7+2
=
9
=
9
-
-
8
1
6
5
9
3
4
+
=
36
3+6
=
9
=
9
-
7
H
A
F
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
9
7
H
A
F
N
I
U
M
-
-
36
-
-
7
-
36
-
-
-
-
-
-
9
-
-
-
-
3+6
-
-
-
-
3+6
9
7
H
A
F
N
I
U
M
-
-
9
-
-
7
-
9

 

 

-
7
U
R
A
N
I
U
M
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
9
-
-
+
=
14
1+4
=
5
=
5
-
5
-
`-
-
-
-
14
9
-
-
+
=
23
2+3
=
5
=
5
-
5
-
7
U
R
A
N
I
U
M
-
-
-
-
-
--
-
-
-
-
-
-
3
9
1
-
-
3
4
+
=
20
2+0
=
2
=
2
-
2
-
-
21
18
1
-
-
21
13
+
=
74
7+4
=
11
1+1
2
-
2
-
7
U
R
A
N
I
U
M
-
-
-
-
-
--
-
-
-
-
-
`-
21
18
1
14
9
21
13
+
=
97
9+7
=
16
1+6
7
-
7
-
-
3
9
1
5
9
3
4
+
=
34
3+4
=
7
=
7
-
7
-
7
U
R
A
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
1
1
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
4
-
-
4
-
-
-
-
2
-
-
-
-
-
-
-
-
-
3
4
-
-
4
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
1
=
5
=
5
6
-
-
4
-
-
4
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
4
-
-
4
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
4
-
-
4
-
-
-
-
8
-
-
-
-
-
-
-
-
-
9
9
-
-
9
9
9
-
-
9
occurs
x
2
=
18
1+8
9
23
7
U
R
A
N
I
U
M
-
-
22
-
-
7
-
33
-
24
2+3
-
9
9
9
9
9
9
-
-
-
2+2
-
-
-
-
3+3
-
2+4
5
7
U
R
A
N
I
U
M
-
-
4
-
-
7
-
6
-
6

 

 
U
R
A
N
I
U
M
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
9
-
-
+
=
14
1+4
=
5
=
5
-
5
`-
-
-
-
14
9
-
-
+
=
23
2+3
=
5
=
5
-
5
7
U
R
A
N
I
U
M
-
-
-
-
-
--
-
-
-
-
-
3
9
1
-
-
3
4
+
=
20
2+0
=
2
=
2
-
2
-
21
18
1
-
-
21
13
+
=
74
7+4
=
11
1+1
2
-
2
7
U
R
A
N
I
U
M
-
-
-
-
-
--
-
-
-
-
`-
21
18
1
14
9
21
13
+
=
97
9+7
=
16
1+6
7
-
7
-
3
9
1
5
9
3
4
+
=
34
3+4
=
7
=
7
-
7
7
U
R
A
N
I
U
M
-
-
-
-
-
-
-
-
-
-
-
-
1
1
1
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
3
4
-
-
4
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
9
9
-
-
9
9
9
-
-
9
occurs
x
2
=
18
1+8
9
7
U
R
A
N
I
U
M
-
-
22
-
-
7
-
33
-
24
-
9
9
-
9
9
-
-
-
2+2
-
-
-
-
3+3
-
2+4
7
U
R
A
N
I
U
M
-
-
4
-
-
7
-
6
-
6

 

 

-
6
O
X
Y
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
6
6
-
-
-
5
+
=
17
1+7
=
8
=
8
=
8
-
-
15
24
-
-
-
14
+
=
53
5+3
=
8
=
8
=
8
-
6
O
X
Y
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
7
7
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
-
25
7
5
-
+
=
37
3+7
=
10
1+0
1
=
1
-
6
O
X
Y
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
15
24
25
7
5
14
+
=
90
9+0
=
9
=
9
=
9
-
-
6
6
7
7
5
5
+
=
36
3+6
=
9
=
9
=
9
-
6
O
X
Y
G
E
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
6
6
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
7
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
27
6
O
X
Y
G
E
N
-
-
18
-
-
6
-
36
-
9
2+7
-
-``
-
-
-
-
-
-
-
1+8
-
-
-
-
3+6
-
-
9
6
O
X
Y
G
E
N
-
-
9
-
-
6
-
9
-
9

 

 

6
O
X
Y
G
E
N
-
-
-
-
-
--
-
-
-
-
-
6
6
-
-
-
5
+
=
17
1+7
=
8
=
8
=
8
-
15
24
-
-
-
14
+
=
53
5+3
=
8
=
8
=
8
6
O
X
Y
G
E
N
-
-
-
-
-
--
-
-
-
-
-
-
-
7
7
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
25
7
5
-
+
=
37
3+7
=
10
1+0
1
=
1
6
O
X
Y
G
E
N
-
-
-
-
-
--
-
-
-
-
-
15
24
25
7
5
14
+
=
90
9+0
=
9
=
9
=
9
-
6
6
7
7
5
5
+
=
36
3+6
=
9
=
9
=
9
6
O
X
Y
G
E
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
6
6
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
7
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
6
O
X
Y
G
E
N
-
-
18
-
-
6
-
36
-
9
-
-``
-
-
-
-
-
-
-
1+8
-
-
-
-
3+6
-
-
6
O
X
Y
G
E
N
-
-
9
-
-
6
-
9
-
9

 

 

-
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
9
5
-
9
5
9
-
-
+
=
37
3+7
=
10
1+0
1
=
1
-
-
9
14
-
9
14
9
-
-
+
=
55
5+5
=
10
1+0
1
=
1
-
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
-
2
7
+
=
15
-
=
6
=
6
=
6
-
-
-
-
6
-
-
-
20
25
+
=
51
-
=
6
=
6
=
6
-
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
9
14
6
9
14
9
20
25
+
=
106
1+0+6
=
7
=
7
=
7
-
-
9
5
6
9
5
9
2
7
+
=
52
5+2
=
7
=
7
=
7
-
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
-
-
5
-`
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
9
-
-
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
16
8
I
N
F
I
N
I
T
Y
-
-
29
-
-
8
-
52
-
25
1+6
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
-
-
5+2
-
2+5
7
8
I
N
F
I
N
I
T
Y
-
-
11
-
-
8
-
7
-
7
-
-
9
5
6
9
5
9
2
7
-
-
-
-
-
-
-
-
-
-
7
8
I
N
F
I
N
I
T
Y
-
-
2
-
-
8
-
7
-
7

 

 

8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
9
5
-
9
5
9
-
-
+
=
37
3+7
=
10
1+0
1
=
1
-
9
14
-
9
14
9
-
-
+
=
55
5+5
=
10
1+0
1
=
1
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
2
7
+
=
15
-
=
6
=
6
=
6
-
-
-
6
-
-
-
20
25
+
=
51
-
=
6
=
6
=
6
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
9
14
6
9
14
9
20
25
+
=
106
1+0+6
=
7
=
7
=
7
-
9
5
6
9
5
9
2
7
+
=
52
5+2
=
7
=
7
=
7
8
I
N
F
I
N
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
=
2
-
-
5
-
-
5
-`
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
9
-
-
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
8
I
N
F
I
N
I
T
Y
-
-
29
-
-
8
-
52
-
25
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
-
-
5+2
-
2+5
8
I
N
F
I
N
I
T
Y
-
-
11
-
-
8
-
7
-
7
-
9
5
6
9
5
9
2
7
-
-
 1+1
-
-
-
-
-
-
-
8
I
N
F
I
N
I
T
Y
-
-
2
-
-
8
-
7
-
7

 

 

S
=
1
-
12
SCHRODINGERS
139
67
4
C
=
3
-
3
CAT
24
6
6
D
=
4
-
3
DID
17
17
8
C
=
3
-
10
CURIOUSITY
160
52
7
K
=
2
-
4
KILL
44
17
6
T
=
2
-
3
THE
33
15
6
C
=
3
-
3
CAT
24
6
6
-
-
18
4
38
First Total
441
180
19
-
-
1+8
-
3+8
Add to Reduce
4+4+1
1+8+0
6+2
-
-
9
-
11
Second Total
9
10
10
4
4
-
4
1+1
Reduce to Deduce
-
1+0
1+0
Q
-
9
5
2
Essence of Number
9
7
7

 

 

-
COSMOLOGICAL CONSTANT
-
-
-
8
C+O+S+M+O+L+O+G
99
36
9
1
I
9
9
9
3
C+A+L
16
7
7
2
C+O
18
9
9
4
N+S+T+A
54
9
9
2
N+T
34
7
7
20
COSMOLOGICAL CONSTANT
230
77
50
2+0
-
2+3+0
7+7
5+0
2
COSMOLOGICAL CONSTANT
5
14
5
-
-
-
1+4
-
2
COSMOLOGICAL CONSTANT
5
5
5

 

 

-
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
-
-
-
-
-
-
-
-
-
-
-
6
1
-
6
-
6
-
9
-
-
-
-
-
6
5
1
-
-
5
-
+
=
45
4+5
=
9
-
9
-
9
-
--
-
15
19
-
15
-
15
-
9
-
-
-
-
-
15
14
19
-
-
14
-
+
=
135
1+3+5
=
9
-
9
-
9
-
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
-
3
-
7
-
3
1
3
-
3
-
-
-
2
1
-
2
+
=
32
3+2
=
5
-
5
-
5
-
-
3
-
-
13
-
12
-
7
-
3
1
12
-
3
-
-
-
20
1
-
20
+
=
95
9+5
=
14
1+4
5
-
5
-
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
--
-
-
-
-
-
-
-
-
-
-
-
3
15
19
13
15
12
15
7
9
3
1
12
-
3
15
14
19
20
1
14
20
+
=
230
2+3+0
=
5
-
5
-
5
-
-
3
6
1
4
6
3
6
7
9
3
1
3
-
3
6
5
1
2
1
5
2
+
=
77
7+7
=
14
1+4
5
-
5
-
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
--
-
-
-
-
-
-
-
-
-
-
-
-
1
1
1
-
-
-
-
-
-
1
-
-
-
-
-
1
-
1
-
-
-
-
1
occurs
x
4
=
4
-
4
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
-
-
2
occurs
x
2
=
4
-
4
-
-
3
-
-
-
-
3
-
-
-
3
-
3
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
5
=
15
1+5
6
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
6
-
6
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
8
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
37
-
-
20
-
77
-
41
-
-
3
-
-
-
-
3
-
-
-
3
-
3
-
3
-
-
-
-
-
-
-
-
-
3+7
-
-
2+0
-
7+7
-
4+1
8
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
10
-
-
2
-
14
-
5
-
-
3
6
1
4
6
3
6
7
9
3
1
3
-
3
6
5
1
2
1
5
2
-
-
 1+0
-
-
-
-
1+4
-
-
8
20
C
O
S
M
O
L
O
G
I
C
A
L
-
C
O
N
S
T
A
N
T
-
-
1
-
-
2
-
5
-
5

 

 

24
SUPERNATURAL SUPERSTITION
351
126
9
25
GENERAL THEORY OF RELATIVITY
315
135
9
26
ABCDEFGHIJKLMNOPQRSTUVWXYZ
351
135
9

 

 

Q
=
8
7
QUANTUM
107
26
8
M
=
4
9
MECHANICS
75
39
3
-
-
12
16
First Total
182
65
11
-
-
1+2
1+6
Add to Reduce
1+8+2
6+5
1+1
-
-
3
7
Second Total
11
11
2
-
-
-
-
Reduce to Deduce
1+1
1+1
-
-
-
3
7
Essence of Number
2
2
2

 

 

-
16
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
8
-
5
9
-
1
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
-
14
-
-
-
-
-
-
-
8
-
14
9
-
19
+
=
64
6+4
=
10
1+0
1
=
1
-
16
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
8
3
1
-
2
3
4
-
4
5
3
-
1
-
-
3
-
+
=
37
3+7
=
10
1+0
1
=
1
-
-
17
21
1
-
20
21
13
-
13
5
3
-
1
-
-
3
-
+
=
118
1+1+8
=
10
1+0
1
=
1
-
16
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
17
21
1
14
20
21
13
-
13
5
3
8
1
14
9
3
19
+
=
182
1+8+2
=
11
1+1
2
=
2
-
-
8
3
1
5
2
3
4
-
4
5
3
8
1
5
9
3
1
+
=
65
6+5
=
11
1+1
2
=
2
-
16
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
-
``-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
``-
-
3
-
-
-
3
-
-
-
-
3
-
-
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
13
16
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
32
-
-
16
-
65
-
38
1+3
1+6
-
3
-
-
-
3
-
-
-
-
3
-
-
-
-
3
-
-
-
3+2
-
-
1+6
-
6+5
-
3+8
4
7
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
5
-
-
7
-
11
-
11
-
-
8
3
1
5
2
3
4
-
4
5
3
8
1
5
9
3
1
-
-
-
-
-
-
-
1+1
-
1+1
4
7
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
5
-
-
7
-
2
-
2

 

 

16
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
8
-
5
9
-
1
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
14
-
-
-
-
-
-
-
8
-
14
9
-
19
+
=
64
6+4
=
10
1+0
1
=
1
16
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
-
-
-
--
-
-
-
-
-
8
3
1
-
2
3
4
-
4
5
3
-
1
-
-
3
-
+
=
37
3+7
=
10
1+0
1
=
1
-
17
21
1
-
20
21
13
-
13
5
3
-
1
-
-
3
-
+
=
118
1+1+8
=
10
1+0
1
=
1
16
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
-
-
-
--
-
-
-
-
-
17
21
1
14
20
21
13
-
13
5
3
8
1
14
9
3
19
+
=
182
1+8+2
=
11
1+1
2
=
2
-
8
3
1
5
2
3
4
-
4
5
3
8
1
5
9
3
1
+
=
65
6+5
=
11
1+1
2
=
2
16
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
3
-
-
-
-
3
-
-
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
16
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
32
-
-
16
-
65
-
38
1+6
-
3
-
-
-
3
-
-
-
-
3
-
-
-
-
3
-
-
-
3+2
-
-
1+6
-
6+5
-
3+8
7
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
5
-
-
7
-
11
-
11
-
8
3
1
5
2
3
4
-
4
5
3
8
1
5
9
3
1
-
-
-
-
-
-
-
1+1
-
1+1
7
Q
U
A
N
T
U
M
-
M
E
C
H
A
N
I
C
S
-
-
5
-
-
7
-
2
-
2

 

 

Q
=
8
7
QUANTUM
107
26
8
E
=
5
6
ENERGY
74
38
2
-
-
13
13
First Total
181
64
10
-
-
1+3
1+3
Add to Reduce
1+8+1
6+4
1+0
-
-
4
4
Second Total
10
10
1
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
4
4
Essence of Number
1
1
1

 

 

Q
=
8
7
QUANTUM
107
26
8
E
=
5
8
ENERGIES
82
46
1
-
-
13
15
First Total
189
72
9
-
-
1+3
1+5
Add to Reduce
1+8+9
7+2
-
-
-
4
6
Second Total
18
9
9
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
4
6
Essence of Number
9
9
9

 

 

-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
5
-
-
-
9
-
1
+
=
20
2+0
=
2
-
2
-
2
-
-
-
-
-
14
-
-
-
-
-
14
-
-
-
9
-
19
+
=
56
5+6
=
11
1+1
2
-
2
-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
8
3
1
-
2
3
4
-
5
-
5
9
7
-
5
-
+
=
52
5+2
=
7
-
7
=
7
-
-
17
21
1
-
20
21
13
-
5
-
5
18
7
-
5
-
+
=
133
1+3+3
=
7
-
7
-
7
-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
17
21
1
14
20
21
13
-
5
14
5
18
7
9
5
19
+
=
189
1+8+9
=
18
1+8
9
-
9
-
-
8
3
1
5
2
3
4
-
5
5
5
9
7
9
5
1
+
=
72
7+2
=
9
-
9
=
9
-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
2
-
``-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
``-
-
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
2
=
6
-
6
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
-
5
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
``-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
6
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
39
-
-
15
-
72
-
45
=
1+5
-
-
-
-
-
-
-``
-
-
-
-
9
-
9
-
-
-
-
3+9
-
-
1+5
-
7+2
-
4+5
6
6
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
12
-
-
6
-
9
-
9
-
-
8
3
1
5
2
3
4
-
5
5
5
9
7
9
5
1
-
-
1+2
-
-
-
-
-
-
-
6
6
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
3
-
-
6
-
9
-
9

 

 

-
-
-
-
-
RANDOM
-
-
-
-
-
-
-
1
R
18
9
9
-
-
-
-
3
A+N+D
19
10
1
-
-
-
-
2
O+M
28
10
1
R
=
9
Q
8
RANDOM
65
29
11
-
-
-
-
-
-
-
-
-
Q
=
8
Q
7
QUANTUM
107
26
8
-
-
-
-
-
-
-
-
-
F
=
6
Q
12
FLUCTUATIONS
161
44
8
-
-
-
-
-
-
-
-
-
-
-
23
-
27
First Total
333
99
27
-
-
2+3
-
2+7
Add to Reduce
3+3+3
9+9
2+7
-
-
5
-
9
Second Total
9
18
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
5
Q
9
Essence of Number
9
9
9

 

 

3
THE
33
15
6
7
KINETIC
71
35
8
6
NATURE
79
25
7
2
OF
21
12
3
6
THINGS
77
32
5

 

 

-
KINETICS
--
-
-
-
-
--
-
-
-
-
-
-
-
KINETICS
--
-
-
-
-
1
K
11
2
2
-
2
1
I
9
9
9
9
-
3
N+E+T
39
12
3
-
3
1
I
9
9
9
9
-
2
C+S
22
4
4
-
4
8
KINETICS
-
-
-
-
-

 

 

K
=
2
-
-
KINETICS
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
-
-
-
-
1
S
19
10
1
K
=
2
Q
8
KINETICS
90
45
36
-
-
-
-
-
-
9+0
4+5
3+6
K
=
2
Q
8
KINETICS
9
9
9

 

 

-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
1
+
=
24
2+4
=
6
=
6
=
6
-
-
-
9
14
-
-
9
-
19
+
=
51
5+1
=
6
=
6
=
6
-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
+
=
12
1+2
=
3
=
3
=
3
-
-
11
-
-
5
20
-
3
-
+
=
39
3+9
=
12
1+2
3
=
3
-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
19
+
=
90
9+0
=
9
=
9
=
9
-
-
2
9
5
5
2
9
3
1
+
=
36
3+6
=
9
=
9
=
9
-
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
--
--
-
--
--
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
--
-
5
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
8
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
--
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
25
8
K
I
N
E
T
I
C
S
-
-
20
-
-
8
-
36
-
18
2+5
-
-
9
-
-
-
9
-
-
-
-
2+0
-
-
-
-
3+6
-
1+8
7
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9
-
-
2
9
5
5
2
9
3
1
-
-
-
-
-
-
-
-
-
-
7
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9

 

 

8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
1
+
=
24
2+4
=
6
=
6
=
6
-
-
9
14
-
-
9
-
19
+
=
51
5+1
=
6
=
6
=
6
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
+
=
12
1+2
=
3
=
3
=
3
-
11
-
-
5
20
-
3
-
+
=
39
3+9
=
12
1+2
3
=
3
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
19
+
=
90
9+0
=
9
=
9
=
9
-
2
9
5
5
2
9
3
1
+
=
36
3+6
=
9
=
9
=
9
8
K
I
N
E
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
--
-
--
--
3
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
5
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
9
-
-
--
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
K
I
N
E
T
I
C
S
-
-
20
-
-
8
-
36
-
18
-
-
9
-
-
-
9
-
-
-
-
2+0
-
-
-
-
3+6
-
1+8
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9
-
2
9
5
5
2
9
3
1
-
-
-
-
-
-
-
-
-
-
8
K
I
N
E
T
I
C
S
-
-
2
-
-
8
-
9
-
9

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8

 

 

E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
8+2
5+5
4+6
E
=
5
Q
8
ENERGIES
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
E
=
5
Q
8
ENERGIES
1
1
1

 

 

-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
9
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
-
14
-
-
-
9
-
19
+
=
42
4+2
=
6
=
6
=
6
-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
9
7
-
5
-
+
=
31
3+1
=
4
=
4
=
4
-
-
5
-
5
18
7
-
5
-
+
=
40
4+0
=
4
=
4
=
4
-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
14
5
18
7
9
5
19
+
=
82
8+2
=
10
1+0
1
=
1
-
-
5
5
5
9
7
9
5
1
+
=
46
4+6
=
10
1+0
1
=
1
-
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
23
8
E
N
E
R
G
I
E
S
-
-
22
-
-
8
-
46
-
19
2+3
-
5
5
5
-
-
-
5
-
-
-
2+2
-
-
-
-
4+6
-
1+9
5
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
10
-
10
-
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
1+0
-
1+0
5
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
1
-
1

 

 

8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
9
-
1
+
=
15
1+5
=
6
=
6
=
6
-
-
14
-
-
-
9
-
19
+
=
42
4+2
=
6
=
6
=
6
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
5
-
5
9
7
-
5
-
+
=
31
3+1
=
4
=
4
=
4
-
5
-
5
18
7
-
5
-
+
=
40
4+0
=
4
=
4
=
4
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
5
14
5
18
7
9
5
19
+
=
82
8+2
=
10
1+0
1
=
1
-
5
5
5
9
7
9
5
1
+
=
46
4+6
=
10
1+0
1
=
1
8
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
E
N
E
R
G
I
E
S
-
-
22
-
-
8
-
46
-
19
-
5
5
5
-
-
-
5
-
-
-
2+2
-
-
-
-
4+6
-
1+9
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
10
-
10
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
1+0
-
1+0
8
E
N
E
R
G
I
E
S
-
-
4
-
-
8
-
1
-
1

 

 

E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
8+2
5+5
4+6
E
=
5
Q
8
ENERGIES
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
E
=
5
Q
8
ENERGIES
1
1
1

 

 

K
=
2
Q
7
KINETIC
71
35
8
E
=
5
Q
8
ENERGIES
82
55
1
Q
Q
7
Q
15
Add to Reduce
153
90
9
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
-
Q
Q
7
Q
6
Essence of Number
9
9
9

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
-
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
-
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
Q
7
KINETIC
71
35
35
E
=
5
Q
8
ENERGIES
82
55
46
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
Q
Q
7
Q
6
Essence of Number
9
9
9

 

 

K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
8+2
5+5
4+6
E
=
5
Q
8
ENERGIES
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
E
=
5
Q
8
ENERGIES
1
1
1

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
-
-
-
-
-
  
-
-
-
-
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
K
=
2
-
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
-
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
1
4
3
4
30
6
7
8
36
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
-
-
-
-
-
3+0
-
-
-
8+1
Q
Q
7
Q
6
Essence of Number
9
9
9
-
1
4
3
4
3
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
K
-
2
1
1
K
11
2
2
-
-
2
-
4
-
6
-
8
-
I
-
9
2
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
N
-
5
3
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
E
-
5
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
T
-
2
5
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
I
-
9
6
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
C
-
3
7
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
-
-
46
-
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ENERGIES
-
-
-
-
-
-
-
-
-
-
-
-
-
E
-
5
8
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
N
-
5
9
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
E
-
5
10
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
R
-
9
11
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
G
-
7
12
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
I
-
9
13
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
E
-
5
14
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
S
-
1
15
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
-
-
46
-
8
ENERGIES
82
55
46
-
1
4
3
4
30
6
7
8
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+0
-
-
-
8+1
K
=
2
Q
7
KINETIC
71
35
35
-
1
4
3
4
3
6
7
8
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
1
4
3
4
3
6
7
8
9
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
6
Essence of Number
9
9
9
-
1
4
3
4
3
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
K
-
2
1
1
K
11
2
2
-
-
2
-
4
-
6
-
8
-
I
-
9
2
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
N
-
5
3
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
E
-
5
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
T
-
2
5
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
I
-
9
6
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
C
-
3
7
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
E
-
5
8
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
N
-
5
9
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
E
-
5
10
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
R
-
9
11
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
G
-
7
12
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
I
-
9
13
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
E
-
5
14
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
S
-
1
15
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
-
-
-
-
-
ENERGIES
-
-
-
-
1
4
3
4
30
6
7
8
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+0
-
-
-
8+1
K
=
2
Q
7
KINETIC
71
35
35
-
1
4
3
4
3
6
7
8
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
1
4
3
4
3
6
7
8
9
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
6
Essence of Number
9
9
9
-
1
4
3
4
3
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
-
-
-
-
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
-
1
15
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
K
-
2
1
1
K
11
2
2
-
-
2
-
4
-
6
-
8
-
T
-
2
5
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
C
-
3
7
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
N
-
5
3
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
E
-
5
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
E
-
5
8
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
N
-
5
9
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
E
-
5
10
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
E
-
5
14
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
G
-
7
12
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
I
-
9
6
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
I
-
9
13
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
R
-
9
11
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
I
-
9
2
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
-
-
-
ENERGIES
-
-
-
-
1
4
3
4
30
6
7
8
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3+0
-
-
-
8+1
K
=
2
Q
7
KINETIC
71
35
35
-
1
4
3
4
3
6
7
8
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
1
4
3
4
3
6
7
8
9
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
-
-
-
-
-
-
-
-
-
-
Q
Q
7
Q
6
Essence of Number
9
9
9
-
1
4
3
4
3
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
5
7
9
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
-
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
5
7
9
S
-
1
15
1
S
19
10
1
-
1
-
-
-
-
-
K
-
2
1
1
K
11
2
2
-
-
2
-
-
-
-
T
-
2
5
1
T
20
2
2
-
-
2
-
-
-
-
C
-
3
7
1
C
3
3
3
-
-
-
3
-
-
-
N
-
5
3
1
N
14
5
5
-
-
-
-
5
-
-
E
-
5
4
1
E
5
5
5
-
-
-
-
5
-
-
E
-
5
8
1
E
5
5
5
-
-
-
-
5
-
-
N
-
5
9
1
N
14
5
5
-
-
-
-
5
-
-
E
-
5
10
1
E
5
5
5
-
-
-
-
5
-
-
E
-
5
14
1
E
5
5
5
-
-
-
-
5
-
-
G
-
7
12
1
G
7
7
7
-
-
-
-
-
7
-
I
-
9
6
1
I
9
9
9
-
-
-
-
-
-
9
I
-
9
13
1
I
9
9
9
-
-
-
-
-
-
9
R
-
9
11
1
R
18
9
9
-
-
-
-
-
-
9
I
-
9
2
1
I
9
9
9
-
-
-
-
-
-
9
-
-
-
-
-
ENERGIES
-
-
-
-
1
4
3
30
7
36
-
-
-
-
-
-
-
-
-
-
-
-
-
3+0
-
8+1
K
=
2
Q
7
KINETIC
71
35
35
-
1
4
3
3
7
9
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
-
Q
Q
7
Q
15
Add to Reduce
153
90
81
-
1
4
3
3
7
9
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
8+1
-
-
-
-
-
-
-
Q
Q
7
Q
6
Essence of Number
9
9
9
-
1
4
3
3
7
9

 

 

K
=
2
Q
7
KINETIC
71
35
8
E
=
5
Q
8
ENERGIES
82
55
1
Q
Q
7
Q
15
Add to Reduce
153
90
9
-
-
-
-
1+5
Reduce to Deduce
1+5+3
9+0
-
Q
Q
7
Q
6
Essence of Number
9
9
9

 

 

-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
-
-
5
-
-
-
9
-
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
-
9
14
-
-
9
-
-
-
14
-
-
-
9
-
19
+
=
74
7+4
=
11
1+1
2
=
2
-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
5
-
5
9
7
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
-
11
-
-
5
20
-
3
-
5
-
5
18
7
-
5
-
+
=
79
7+9
=
16
1+6
7
=
7
-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
-
5
14
5
18
7
9
5
19
+
=
153
1+5+3
=
9
=
9
=
9
-
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
+
=
81
8+1
=
9
=
9
=
9
-
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
--
--
-
--
--
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
--
-
5
5
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
--
9
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
18
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
27
-
-
15
-
81
-
27
1+8
1+5
-
9
-
-
-
9
-
-
5
5
5
-
-
-
5
-
-
-
2+7
-
-
1+5
-
8+1
-
2+7
9
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9
-
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
-
-
-
9
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9

 

 

15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
-
-
5
-
-
-
9
-
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
9
14
-
-
9
-
-
-
14
-
-
-
9
-
19
+
=
74
7+4
=
11
1+1
2
=
2
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
-
5
-
5
9
7
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
11
-
-
5
20
-
3
-
5
-
5
18
7
-
5
-
+
=
79
7+9
=
16
1+6
7
=
7
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
-
5
14
5
18
7
9
5
19
+
=
153
1+5+3
=
9
=
9
=
9
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
+
=
81
8+1
=
9
=
9
=
9
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
--
-
--
--
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
5
5
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
-
--
9
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
15
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
27
-
-
15
-
81
-
27
1+5
-
9
-
-
-
9
-
-
5
5
5
-
-
-
5
-
-
-
2+7
-
-
1+5
-
8+1
-
2+7
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9
-
2
9
5
5
2
9
3
-
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
-
-
-
6
K
I
N
E
T
I
C
-
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9

 

 

15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
5
--
-
9
-
-
5
-
-
-
9
-
1
+
=
38
3+8
=
11
1+1
2
=
2
-
-
9
14
-
-
9
-
-
14
-
-
-
9
-
19
+
=
74
7+4
=
11
1+1
2
=
2
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
2
-
-
5
2
-
3
5
-
5
9
7
-
5
-
+
=
43
4+3
=
7
=
7
=
7
-
11
-
-
5
20
-
3
5
-
5
18
7
-
5
-
+
=
79
7+9
=
16
1+6
7
=
7
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
11
9
14
5
20
9
3
5
14
5
18
7
9
5
19
+
=
153
1+5+3
=
9
=
9
=
9
-
2
9
5
5
2
9
3
5
5
5
9
7
9
5
1
+
=
81
8+1
=
9
=
9
=
9
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
--
--
-
--
--
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
5
5
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
-
--
9
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
15
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
27
-
-
15
-
81
-
27
1+5
-
9
-
-
-
9
-
5
5
5
-
-
-
5
-
-
-
2+7
-
-
1+5
-
8+1
-
2+7
6
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9
-
2
9
5
5
2
9
3
5
5
5
9
7
9
5
1
-
-
-
-
-
-
-
-
-
-
6
K
I
N
E
T
I
C
E
N
E
R
G
I
E
S
-
-
9
-
-
6
-
9
-
9

 

 

-
-
-
-
-
-
-
-
-
K
=
2
-
-
KINETIC
-
-
-
-
-
-
-
1
K
11
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
T
20
2
2
-
-
-
-
1
I
9
9
9
-
-
-
-
1
C
3
3
3
K
=
2
Q
7
KINETIC
71
35
35
-
-
-
-
-
-
7+1
3+5
3+5
K
=
2
Q
7
KINETIC
8
8
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
-
ENERGIES
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
1
G
7
7
7
-
-
-
-
1
I
9
9
9
-
-
-
-
1
E
5
5
5
-
-
-
-
1
S
19
10
1
E
=
5
Q
8
ENERGIES
82
55
46
-
-
-
-
-
-
8+2
5+5
4+6
E
=
5
Q
8
ENERGIES
10
10
10
-
-
-
-
-
-
1+0
1+0
1+0
E
=
5
Q
8
ENERGIES
1
1
1

 

 

5
MESON
-
-
-
-
M+E
18
9
9
-
S+O+N
48
12
3
5
MESON
66
21
12
-
-
6+6
2+1
1+2
5
MESON
12
3
3
-
-
1+2
-
-
5
MESON
3
3
3

 

 

6
MESONS
-
-
-
-
M+E
18
9
9
-
S+O+N+S
67
13
4
6
MESONS
85
22
13
-
-
8+5
2+2
1+3
6
MESONS
13
4
4
8
THIRTEEN
99
45
9

 

 

11
SCHRODINGERS
139
67
4
3
CAT
24
6
6
14
First Total
163
73
10
1+4
Add to Reduce
1+6+3
7+3
1+0
5
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
5
Essence of Number
1
1
1

 

 

W
=
5
4
WAVE
51
15
6
P
=
7
8
PARTICLE
84
39
3
-
-
12
12
Add to Reduce
135
54
9
-
-
 1+2
1+2
Reduce to Deduce
1+3+5
5+4
-
-
-
3
3
Essence of Number
9
9
9

 

 

5
WAVES
70
16
7
9
PARTICLES
103
40
4

 

 

4
WAVE
51
15
6
9
PARTICLES
103
40
4
13
First Total
154
55
10
1+3
Add to Reduce
1+5+4
5+5
1+0
4
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
4
Essence of Number
1
1
1

 

 

-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
-
9
-
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
5
1
4
5
-
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
-
9
-
9
-
-
23
1
22
5
-
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
-
9
-
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
23
1
22
5
-
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
-
9
=
9
-
-
5
1
4
5
-
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
-
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
-
6
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
14
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+4
1+2
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
5
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
-
5
1
4
5
-
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
5
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
-
9
-
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
5
1
4
5
-
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
-
9
-
9
-
23
1
22
5
-
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
-
9
-
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
23
1
22
5
-
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
-
9
=
9
-
5
1
4
5
-
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
-
9
=
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
-
6
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
5
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+2
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
5
1
4
5
-
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

6
ENERGY
74
38
2
8
ENERGIES
82
46
1

 

 

5
FORCE
47
29
2
6
FORCES
66
30
3

 

 

-
15
F
O
R
C
E
S
-
O
F
-
G
R
A
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
1
-
6
-
-
-
-
-
-
9
-
-
+
=
22
2+2
=
4
=
4
=
4
-
-
-
15
-
-
-
19
-
15
-
-
-
-
-
-
9
-
-
+
=
58
5+8
=
13
1+3
4
=
4
-
15
F
O
R
C
E
S
-
O
F
-
G
R
A
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
6
-
9
3
5
-
-
-
6
-
7
9
1
4
-
2
7
+
=
59
5+9
=
14
1+4
5
=
5
-
-
6
-
18
3
5
-
-
-
6
-
7
18
1
22
-
20
25
+
=
131
1+3+1
=
5
=
5
=
5
-
15
F
O
R
C
E
S
-
O
F
-
G
R
A
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
6
15
18
3
5
19
-
15
6
-
7
18
1
22
9
20
25
+
=
189
1+8+9
=
18
1+8
9
=
9
-
-
6
6
9
3
5
1
-
6
6
-
7
9
1
4
9
2
7
+
=
81
8+1
=
9
=
9
=
9
-
15
F
O
R
C
E
S
-
O
F
-
G
R
A
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-``
-
6
6
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
8
15
F
O
R
C
E
S
-
O
F
-
G
R
A
V
I
T
Y
-
-
37
-
-
15
-
81
-
36
-
1+5
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
3+7
-
-
1+5
-
8+1
-
3+6
8
6
F
O
R
C
E
S
-
O
F
-
G
R
A
V
I
T
Y
-
-
10
-
-
6
-
9
-
9
-
-
6
6
9
3
5
1
-
6
6
-
7
9
1
4
9
2
7
-
-
1+0
-
-
-
-
-
-
-
8
6
F
O
R
C
E
S
-
O
F
-
G
R
A
V
I
T
Y
-
-
1
-
-
6
-
9
-
9

 

 

4
HEAT
34
16
7
5
LIGHT
56
29
2
9
Add to Reduce
90
45
9
-
Reduce to Deduce
9+0
4+5
-
9
Essence of Number
9
9
9

 

 

4
MIND
40
22
4
6
MATTER
77
23
5
10
Add to Reduce
117
45
9
1+0
Reduce to Deduce
1+1+7
4+5
-
1
Essence of Number
9
9
9

 

 

-
SPECTRUM
-
-
-
5
SPECT
63
18
9
1
R
18
9
9
2
UM
34
7
7
8
SPECTRUM
115
34
25
-
-
1+1+5
3+4
2+5
8
SPECTRUM
7
7
7

 

 

--
12
S
P
E
C
T
R
O
S
C
O
P
E
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
-
-
-
6
1
-
6
-
-
+
=
14
1+4
=
5
-
5
=
5
-
-
19
-
-
-
-
-
15
19
-
15
-
-
+
=
68
6+8
=
14
1+4
5
=
5
--
12
S
P
E
C
T
R
O
S
C
O
P
E
-
-
-
-
-
--
-
-
-
-
-
-
-
7
5
3
2
9
-
-
3
-
7
5
+
=
41
4+1
=
5
-
5
=
5
-
-
-
16
5
3
20
18
-
-
3
-
16
5
+
=
86
8+6
=
14
1+4
5
=
5
--
12
S
P
E
C
T
R
O
S
C
O
P
E
-
-
-
-
-
--
-
-
-
-
-
-
19
16
5
3
20
18
15
19
3
15
16
5
+
+
154
1+5+4
=
10
1+0
1
=
1
-
-
1
7
5
3
2
9
6
1
3
6
7
5
+
+
55
5+5
=
10
1+0
1
=
1
-
12
S
P
E
C
T
R
O
S
C
O
P
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
--
1
-
--
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
6
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
4
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
12
S
P
E
C
T
R
O
S
C
O
P
E
-
-
33
-
-
12
-
55
-
28
1+2
1+2
-
-
-
-
-
9
-
-
-
-
-
-
-
-
3+3
-
-
1+2
-
5+5
-
2+8
3
3
S
P
E
C
T
R
O
S
C
O
P
E
-
-
6
-
-
3
-
10
-
10
-
-
1
7
5
3
2
9
6
1
3
6
7
5
-
-
-
-
-
-
-
1+0
-
1+0
3
3
S
P
E
C
T
R
O
S
C
O
P
E
-
-
6
-
-
3
-
1
-
1

 

 

12
S
P
E
C
T
R
O
S
C
O
P
E
-
-
-
-
-
--
-
-
-
-
-
1
-
-
-
-
-
6
1
-
6
-
-
+
=
14
1+4
=
5
-
5
=
5
-
19
-
-
-
-
-
15
19
-
15
-
-
+
=
68
6+8
=
14
1+4
5
=
5
12
S
P
E
C
T
R
O
S
C
O
P
E
-
-
-
-
-
--
-
-
-
-
-
-
7
5
3
2
9
-
-
3
-
7
5
+
=
41
4+1
=
5
-
5
=
5
-
-
16
5
3
20
18
-
-
3
-
16
5
+
=
86
8+6
=
14
1+4
5
=
5
12
S
P
E
C
T
R
O
S
C
O
P
E
-
-
-
-
-
--
-
-
-
-
-
19
16
5
3
20
18
15
19
3
15
16
5
+
+
154
1+5+4
=
10
1+0
1
=
1
-
1
7
5
3
2
9
6
1
3
6
7
5
+
+
55
5+5
=
10
1+0
1
=
1
12
S
P
E
C
T
R
O
S
C
O
P
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
--
1
-
--
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
6
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
S
P
E
C
T
R
O
S
C
O
P
E
-
-
33
-
-
12
-
55
-
28
1+2
-
-
-
-
-
9
-
-
-
-
-
-
-
-
3+3
-
-
1+2
-
5+5
-
2+8
3
S
P
E
C
T
R
O
S
C
O
P
E
-
-
6
-
-
3
-
10
-
10
-
1
7
5
3
2
9
6
1
3
6
7
5
-
-
-
-
-
-
-
1+0
-
1+0
3
S
P
E
C
T
R
O
S
C
O
P
E
-
-
6
-
-
3
-
1
-
1

 

 

-
SPECTRUM
-
-
-
5
SPECT
63
18
9
1
R
18
9
9
2
UM
34
7
7
8
SPECTRUM
115
34
25
-
-
1+1+5
3+4
2+5
8
SPECTRUM
7
7
7

 

 

-
8
S
P
E
C
T
R
U
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
-
=
1
=
1
-
-
19
-
-
-
-
-
-
-
+
=
19
1+9
=
10
1+0
1
--
8
S
P
E
C
T
R
U
M
-
-
-
-
-
-
-
-
-
-
-
7
5
3
2
9
3
4
+
=
33
3+3
=
6
=
6
-
-
-
16
5
3
20
18
21
13
+
=
96
96
=
15
1+5
6
--
8
S
P
E
C
T
R
U
M
-
-
-
-
-
-
-
-
-
-
19
16
5
3
20
18
21
13
+
+
115
1+1+5
=
7
=
7
-
-
1
7
5
3
2
9
3
4
+
+
34
3+4
=
7
=
7
-
8
S
P
E
C
T
R
U
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
-
3
-
-
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
14
8
S
P
E
C
T
R
U
M
-
-
33
-
-
8
-
34
1+4
-
-
-
-
-
-
9
-
-
-
-
3+3
-
-
-
-
3+4
5
8
S
P
E
C
T
R
U
M
-
-
6
-
-
8
-
7
-
-
1
7
5
3
2
9
3
4
-
-
-
-
-
-
-
-
5
8
S
P
E
C
T
R
U
M
-
-
6
-
-
8
-
7

 

 

8
S
P
E
C
T
R
U
M
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
-
=
1
=
1
-
19
-
-
-
-
-
-
-
+
=
19
1+9
=
10
1+0
1
8
S
P
E
C
T
R
U
M
-
-
-
-
-
-
-
-
-
-
7
5
3
2
9
3
4
+
=
33
3+3
=
6
=
6
-
-
16
5
3
20
18
21
13
+
=
96
96
=
15
1+5
6
8
S
P
E
C
T
R
U
M
-
-
-
-
-
-
-
-
-
19
16
5
3
20
18
21
13
+
+
115
1+1+5
=
7
=
7
-
1
7
5
3
2
9
3
4
+
+
34
3+4
=
7
=
7
8
S
P
E
C
T
R
U
M
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
3
-
-
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
8
S
P
E
C
T
R
U
M
-
-
33
-
-
8
-
34
-
-
-
-
-
-
9
-
-
-
-
3+3
-
-
-
-
3+4
8
S
P
E
C
T
R
U
M
-
-
6
-
-
3
-
7
-
1
7
5
3
2
9
3
4
-
-
-
-
-
-
-
-
8
S
P
E
C
T
R
U
M
-
-
6
-
-
3
-
7

 

 

7
RAINBOW
82
37
1
6
COLOUR
84
30
3

 

 

7
RAINBOW
82
37
1
7
COLOURS
103
31
4

 

 

8
SPECTRUM
115
34
7
2
OF
21
12
3
3
THE
33
15
6
7
RAINBOW
82
37
1

 

 

3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2

 

 

-
RAINBOW
-
-
-
1
BRAIN
44
26
8
4
OW
54
18
9
7
RAINBOW
82
37
28
-
-
8+2
3+7
3+7
7
RAINBOW
10
10
10
-
-
1+0
1+0
1+0
7
RAINBOW
1
1
1

 

 

15
THE RAINBOW LIGHT
-
-
-
-
THE
33
15
6
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
-
L
12
3
3
-
I
9
9
9
-
G+H+T
35
17
8
15
THE RAINBOW LIGHT
171
81
54
1+5
-
1+7+1
8+1
5+4
6
THE RAINBOW LIGHT
9
9
9

 

 

-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
9
5
-
6
-
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
-
8
-
-
-
-
9
14
-
15
-
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
9
1
-
-
2
-
5
-
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
-
20
-
5
-
18
1
-
-
2
-
23
-
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
18
1
9
14
2
15
23
-
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
4
FOUR
4
-
-
-
-
-
--
--
--
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
4
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
-
1+5
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
4
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
4
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
9
5
-
6
-
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
8
-
-
-
-
9
14
-
15
-
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
9
1
-
-
2
-
5
-
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
20
-
5
-
18
1
-
-
2
-
23
-
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
18
1
9
14
2
15
23
-
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
--
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
1+5
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
9
5
-
6
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
8
-
-
-
9
14
-
15
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
2
-
5
9
1
-
-
2
-
5
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
20
-
5
18
1
-
-
2
-
23
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
18
1
9
14
2
15
23
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
2
8
5
9
1
9
5
2
6
5
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
--
-
5
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
9
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
1+5
-
-
-
9
-
9
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
6
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
2
8
5
9
1
9
5
2
6
5
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
6
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
-
-
-
9
-
8
-
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
-
-
8
-
-
14
-
-
-
9
-
8
-
+
=
39
3+9
=
12
1+2
3
=
3
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
2
9
3
2
-
-
1
-
4
-
3
-
7
-
2
+
=
33
3+3
=
6
-
6
=
6
-
-
20
18
21
20
-
-
1
-
4
-
12
-
7
-
20
+
=
123
1+2+3
=
6
-
6
=
6
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
20
18
21
20
8
-
1
14
4
-
12
9
7
8
20
+
=
162
1+6+2
=
9
-
9
=
9
-T
-
2
9
3
2
8
-T
1
5
4
-T
3
9
7
8
2
+
=
63
6+3
=
9
-
9
=
9
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
18
1+8
9
6
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
39
-
1
12
-
54
-
45
-
1+2
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+2
-
5+4
-
4+5
6
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
12
-
1
3
-
9
-
9
-
-
2
9
3
2
8
-
1
5
4
-
3
9
7
8
2
-
-
1+2
-
-
-
-
-
-
-
6
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
3
-
-
3
-
9
-
9

 

 

12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
-
-
-
9
-
8
-
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
-
8
-
-
14
-
-
-
9
-
8
-
+
=
39
3+9
=
12
1+2
3
=
3
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
9
3
2
-
-
1
-
4
-
3
-
7
-
2
+
=
33
3+3
=
6
-
6
=
6
-
20
18
21
20
-
-
1
-
4
-
12
-
7
-
20
+
=
123
1+2+3
=
6
-
6
=
6
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
20
18
21
20
8
-
1
14
4
-
12
9
7
8
20
+
=
162
1+6+2
=
9
-
9
=
9
-
2
9
3
2
8
-T
1
5
4
-T
3
9
7
8
2
+
=
63
6+3
=
9
-
9
=
9
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
--
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
18
1+8
9
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
39
-
1
12
-
54
-
45
1+2
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+2
-
5+4
-
4+5
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
12
-
1
3
-
9
-
9
-
2
9
3
2
8
-
1
5
4
-
3
9
7
8
2
-
-
1+2
-
-
-
-
-
-
-
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
3
-
-
3
-
9
-
9

 

 

12
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
-
-
9
-
8
-
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
-
8
-
14
-
-
9
-
8
-
+
=
39
3+9
=
12
1+2
3
=
3
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
9
3
2
-
1
-
4
3
-
7
-
2
+
=
33
3+3
=
6
-
6
=
6
-
20
18
21
20
-
1
-
4
12
-
7
-
20
+
=
123
1+2+3
=
6
-
6
=
6
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
20
18
21
20
8
1
14
4
12
9
7
8
20
+
=
162
1+6+2
=
9
-
9
=
9
-
2
9
3
2
8
1
5
4
3
9
7
8
2
+
=
63
6+3
=
9
-
9
=
9
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
2
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
--
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
18
1+8
9
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
39
-
1
12
-
54
-
45
1+2
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+2
-
5+4
-
4+5
3
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
12
-
1
3
-
9
-
9
-
2
9
3
2
8
1
5
4
3
9
7
8
2
-
-
1+2
-
-
-
-
-
-
-
3
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
3
-
-
3
-
9
-
9

 

 

-
-
-
-
-
LIGHT
-
-
-
-
-
-
-
4
LIGH
36
27
9
-
-
-
-
1
T
20
2
2
L
=
3
-
5
LIGHT
56
29
11
-
-
1+0
-
-
-
5+6
2+9
1+1
-
-
1
-
9
LIGHT
11
11
7
-
-
1+0
-
-
-
1+1
1+1
-
-
-
1
-
9
LIGHT
2
2
2

 

 

-
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
-
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
-
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
+
=
12
1+2
=
3
=
3
-
3
-
-
12
-
7
-
20
+
=
39
3+9
=
12
1+2
3
-
3
-
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
12
9
7
8
20
+
=
56
5+6
=
11
1+1
2
-
2
-
-
3
9
7
8
2
+
=
29
2+9
=
11
1+1
2
-
2
-
5
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
--
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
16
5
L
I
G
H
T
-
-
29
-
1
5
-
29
-
29
1+6
-
-
9
-
-
-
-
-
2+9
-
-
-
-
2+9
-
2+9
7
5
L
I
G
H
T
-
-
11
-
1
5
-
11
-
11
-
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
7
5
L
I
G
H
T
-
-
2
-
-
5
-
2
-
2

 

 

5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
+
=
12
1+2
=
3
=
3
-
3
-
12
-
7
-
20
+
=
39
3+9
=
12
1+2
3
-
3
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
12
9
7
8
20
+
=
56
5+6
=
11
1+1
2
-
2
-
3
9
7
8
2
+
=
29
2+9
=
11
1+1
2
-
2
5
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
5
L
I
G
H
T
-
-
29
-
1
5
-
29
-
29
-
-
9
-
-
-
-
-
2+9
-
-
-
-
2+9
-
2+9
5
L
I
G
H
T
-
-
11
-
1
5
-
11
-
11
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
5
L
I
G
H
T
-
-
2
-
-
5
-
2
-
2

 

 

L
=
3
-
6
LIVING
73
37
1
H
=
8
-
4
HEAT
34
16
7
L
=
3
-
5
LIGHT
56
29
2
-
-
14
-
15
-
163
82
10
-
-
1+4
-
1+5
-
1+6+3
8+2
1+0
-
-
5
-
6
-
10
10
1
-
-
-
-
-
-
1+0
1+0
-
-
-
5
-
6
-
1
1
9

 

 

L
=
3
-
6
LOVING
79
34
7
H
=
8
-
4
HEAT
34
16
7
L
=
3
-
5
LIGHT
56
29
2
-
-
14
-
15
-
169
79
16
-
-
1+4
-
1+5
-
1+6+9
7+9
1+6
-
-
5
-
6
-
16
10
7
-
-
-
-
-
-
1+6
1+0
-
-
-
5
-
6
-
7
7
7

 

 

P
=
7
-
4
PARTICLES
103
40
4
O
=
6
-
1
OF
21
12
3
L
=
3
-
5
LIGHT
56
29
2
-
-
16
-
10
-
180
81
9
-
-
1+6
-
1+0
-
1+8+0
8+1
-
-
-
7
-
1
-
9
9
9

 

 

9
PARTICLES
103
40
4
2
OF
21
12
3
5
LIGHT
56
29
2
16
Add to Reduce
180
81
9
1+6
Reduce to Deduce
1+8+0
8+1
-
7
Essence of Number
9
9
9

 

 

-T
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-T
`-
-
-
-
-
9
-
-
-
1
-
6
-
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
-
`-
-
-
-
-
9
-
-
-
19
-
15
-
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
-
-
6
-
3
-
7
-
2
+
=
48
4+8
=
12
1+2
3
=
3
-
`-
16
1
18
20
-
3
12
5
-
-
-
6
-
12
-
7
-
20
+
=
120
1+2+0
=
3
=
3
=
3
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
`-
16
1
18
20
9
3
12
5
19
-
15
6
-
12
9
7
8
20
+
=
180
1+8+0
=
9
=
9
=
9
-
-
7
1
9
2
9
3
3
5
1
-T
6
6
-T
3
9
7
8
2
+
=
81
8+1
=
9
=
9
=
9
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
3
3
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
--
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
41
-
1
16
-
81
-
45
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+6
-
8+1
-
4+5
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
1
7
-
9
-
9
-
-
7
1
9
2
9
3
-
5
1
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
-
7
-
9
-
9

 

 

16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
-
9
-
-
-
1
-
6
-
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
-
9
-
-
-
19
-
15
-
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
-
-
6
-
3
-
7
-
2
+
=
48
4+8
=
12
1+2
3
=
3
`-
16
1
18
20
-
3
12
5
-
-
-
6
-
12
-
7
-
20
+
=
120
1+2+0
=
3
=
3
=
3
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
16
1
18
20
9
3
12
5
19
-
15
6
-
12
9
7
8
20
+
=
180
1+8+0
=
9
=
9
=
9
-
7
1
9
2
9
3
3
5
1
-T
6
6
-T
3
9
7
8
2
+
=
81
8+1
=
9
=
9
=
9
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
3
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
--
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
41
-
1
16
-
81
-
45
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+6
-
8+1
-
4+5
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
1
7
-
9
-
9
-
7
1
9
2
9
3
-
5
1
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
-
7
-
9
-
9

 

 

16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
-
9
-
-
-
1
6
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
-
9
-
-
-
19
15
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
-
6
3
-
7
-
2
+
=
48
4+8
=
12
1+2
3
=
3
`-
16
1
18
20
-
3
12
5
-
-
6
12
-
7
-
20
+
=
120
1+2+0
=
3
=
3
=
3
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
16
1
18
20
9
3
12
5
19
15
6
12
9
7
8
20
+
=
180
1+8+0
=
9
=
9
=
9
-
7
1
9
2
9
3
3
5
1
6
6
3
9
7
8
2
+
=
81
8+1
=
9
=
9
=
9
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
3
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
--
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
41
-
1
16
-
81
-
45
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+6
-
8+1
-
4+5
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
5
-
1
7
-
9
-
9
-
7
1
9
2
9
3
-
5
1
6
6
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
5
-
-
7
-
9
-
9

 

 

-
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
-
1
+
=
18
1+8
=
9
=
9
=
9
-
`-
-
9
-
8
-
-
-
-
-
-
19
+
=
36
3+6
=
9
=
9
=
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
-
5
1
4
5
-
+
=
27
2+7
=
9
=
9
=
9
-
`-
12
-
7
-
20
-
23
1
22
5
-
+
=
90
7+5
=
9
=
9
=
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
`-
12
9
7
8
20
-
23
1
22
5
19
+
=
126
1+2+6
=
9
=
9
=
9
-
-
3
9
7
8
2
-T
5
1
4
5
1
+
=
45
4+5
=
9
=
9
=
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
6
10
L
I
G
H
T
-
W
A
V
E
S
-
-
39
-
1
12
-
45
-
36
-
1+0
-
9
-
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+2
-
4+5
-
3+6
6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
12
-
1
3
-
9
-
9
-
-
3
9
7
8
2
-
5
1
4
5
1
-
-
1+2
-
-
-
-
-
-
-
6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
3
-
-
3
-
9
-
9

 

 

10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
-
1
+
=
18
1+8
=
9
=
9
=
9
`-
-
9
-
8
-
-
-
-
-
-
19
+
=
36
3+6
=
9
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
-
5
1
4
5
-
+
=
27
2+7
=
9
=
9
=
9
`-
12
-
7
-
20
-
23
1
22
5
-
+
=
90
7+5
=
9
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
`-
12
9
7
8
20
-
23
1
22
5
19
+
=
126
1+2+6
=
9
=
9
=
9
-
3
9
7
8
2
-T
5
1
4
5
1
+
=
45
4+5
=
9
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-
-
39
-
1
12
-
45
-
36
1+0
-
9
-
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+2
-
4+5
-
3+6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
12
-
1
3
-
9
-
9
-
3
9
7
8
2
-
5
1
4
5
1
-
-
1+2
-
-
-
-
-
-
-
1
L
I
G
H
T
-
W
A
V
E
S
-
-
3
-
-
3
-
9
-
9

 

 

10
L
I
G
H
T
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
1
+
=
18
-
=
9
=
9
=
9
`-
-
9
-
8
-
-
-
-
-
19
+
=
38
-
=
9
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
5
1
4
5
-
+
=
27
2+7
=
9
=
9
=
9
`-
12
-
7
-
20
23
1
22
5
-
+
=
90
7+5
=
9
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
`-
12
9
7
8
20
23
1
22
5
19
+
=
126
1+2+6
=
9
=
9
=
9
-
3
9
7
8
2
5
1
4
5
1
+
=
45
4+5
=
9
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-
-
39
-
1
12
-
45
-
36
1+0
-
9
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+2
-
4+5
-
3+6
1
L
I
G
H
T
W
A
V
E
S
-
-
12
-
1
3
-
9
-
9
-
3
9
7
8
2
5
1
4
5
1
-
-
1+2
-
-
-
-
-
-
-
1
L
I
G
H
T
W
A
V
E
S
-
-
3
-
-
3
-
9
-
9

 

 

5
WAVES
70
16
7
9
PARTICLES
103
40
4

 

 

4
WAVE
51
15
6
9
PARTICLES
103
40
4
13
First Total
154
55
10
1+3
Add to Reduce
1+5+4
5+5
1+0
4
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
4
Essence of Number
1
1
1

 

 

W
=
5
4
WAVE
51
15
6
P
=
7
8
PARTICLE
84
39
3
-
-
12
12
Add to Reduce
135
54
9
-
-
1+2
1+2
Reduce to Deduce
1+3+5
5+4
-
-
-
3
3
Essence of Number
9
9
9

 

 

-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
5
1
4
5
-
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
=
9
=
9
-
-
23
1
22
5
-
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
=
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
23
1
22
5
-
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
=
9
=
9
-
-
5
1
4
5
-
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
=
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
14
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+4
1+2
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
5
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
-
5
1
4
5
-
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
5
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
5
1
4
5
-
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
=
9
=
9
-
23
1
22
5
-
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
=
9
=
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
23
1
22
5
-
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
=
9
=
9
-
5
1
4
5
-
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
=
9
=
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+2
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
5
1
4
5
-
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
5
1
4
5
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
=
9
=
9
-
23
1
22
5
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
=
9
=
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
23
1
22
5
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
=
9
=
9
-
5
1
4
5
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
=
9
=
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+2
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
3
W
A
V
E
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
5
1
4
5
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
3
W
A
V
E
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

S
=
1
-
5
SPEED
49
22
4
O
=
6
-
2
OF
21
12
3
L
=
3
-
5
LIGHT
56
29
2
-
-
10
-
12
-
126
63
9
-
-
1+0
-
1+2
-
1+2+6
6+3
-
-
-
1
-
3
-
9
9
9

 

 

-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
6
-
-
-
9
-
8
-
+
=
24
2+4
=
6
=
6
=
6
-
-
19
-
-
-
-
-
15
-
-
-
9
-
8
-
+
=
51
5+1
=
6
=
6
=
6
-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
7
5
5
4
-
-
6
-
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
-
-
-
16
5
5
4
-
-
6
-
12
-
7
-
20
+
=
75
7+5
=
12
1+2
3
=
3
-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
19
16
5
5
4
-
15
6
-
12
9
7
8
20
+
=
126
1+2+6
=
9
=
9
=
9
--
-
1
7
5
5
4
-T
6
6
-T
3
9
7
8
2
+
=
63
6+3
=
9
=
9
=
9
-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
--
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
27
=
9
45
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
45
-
1
12
-
81
-
36
4+5
1+2
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+2
-
8+1
-
3+4
9
3
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
9
-
1
3
-
9
-
9
-
-
1
7
5
5
4
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
3
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
9
-
-
3
-
9
-
9

 

 

-
12
S
P
E
E
D
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
6
-
-
9
-
8
-
+
=
24
2+4
=
6
=
6
=
6
-
-
19
-
-
-
-
15
-
-
9
-
8
-
+
=
51
5+1
=
6
=
6
=
6
-
12
S
P
E
E
D
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
7
5
5
4
-
6
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
-
-
-
16
5
5
4
-
6
12
-
7
-
20
+
=
75
7+5
=
12
1+2
3
=
3
-
12
S
P
E
E
D
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
19
16
5
5
4
15
6
12
9
7
8
20
+
=
126
1+2+6
=
9
=
9
=
9
--
-
1
7
5
5
4
6
6
3
9
7
8
2
+
=
63
6+3
=
9
=
9
=
9
-
12
S
P
E
E
D
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
--
-
7
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
27
=
9
45
12
S
P
E
E
D
O
F
L
I
G
H
T
-
-
45
-
1
12
-
81
-
36
4+5
1+2
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+2
-
8+1
-
3+4
9
3
S
P
E
E
D
O
F
L
I
G
H
T
-
-
9
-
1
3
-
9
-
9
-
-
1
7
5
5
4
6
6
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
3
S
P
E
E
D
O
F
L
I
G
H
T
-
-
9
-
-
3
-
9
-
9

 

 

16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
1
-
9
-
-
-
-
6
-
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
19
-
9
-
-
-
-
15
-
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
2
-
4
1
3
-
-
6
-
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
`-
-
6
5
-
20
-
22
1
12
-
-
6
-
12
-
7
-
20
+
=
111
1+1+1
=
3
=
3
=
3
16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
6
5
19
20
9
22
1
12
-
15
6
-
12
9
7
8
20
+
=
171
1+7+1
=
9
=
9
=
9
-
-
6
5
1
2
9
4
1
3
-T
6
6
-T
3
9
7
8
2
+
=
72
7+2
=
9
=
9
=
9
16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
6
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
45
-
1
15
-
72
-
54
4+5
1+5
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+5
-
7+2
-
5+4
9
6
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
9
-
1
6
-
9
-
9
-
-
6
5
1
2
9
4
1
3
-T
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
6
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
9
-
-
6
-
9
-
9

 

 

16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
1
-
9
-
-
-
6
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
19
-
9
-
-
-
15
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
2
-
4
1
3
-
6
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
`-
-
6
5
-
20
-
22
1
12
-
6
12
-
7
-
20
+
=
111
1+1+1
=
3
=
3
=
3
16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
6
5
19
20
9
22
1
12
15
6
12
9
7
8
20
+
=
171
1+7+1
=
9
=
9
=
9
-
-
6
5
1
2
9
4
1
3
6
6
3
9
7
8
2
+
=
72
7+2
=
9
=
9
=
9
16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
3
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
6
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
--
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
45
-
1
15
-
72
-
54
4+5
1+5
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+5
-
7+2
-
5+4
9
6
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
9
-
1
6
-
9
-
9
-
-
6
5
1
2
9
4
1
3
6
6
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
6
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
9
-
-
6
-
9
-
9

 

 

3
THE
33
15
6
7
RAINBOW
82
37
1
8
SPECTRUM
115
34
7
2
OF
21
12
3
6
COLOUR
84
30
3

 

 

8
COLOURED
-
-
-
-
C+O
18
9
9
9
L+O
27
9
9
9
U
21
3
3
-
R
18
9
9
9
E+D
9
9
9
8
COLOURED
-
-
-

 

 

6
COLOUR
84
30
3
3
RED
27
18
9

 

 

-
QUANTUM
8
-
-
1
Q
17
8
8
3
UAN
35
9
9
3
TUM
54
9
9
7
QUANTUM
107
26
26
-
-
1+0+7
2+6
2+6
7
QUANTUM
8
8
8

 

 

-
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
-
-
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
-
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
8
3
1
-
2
3
4
+
=
21
2+1
=
3
=
3
-
-
17
21
1
-
20
21
13
+
=
93
9+3
=
12
 1+2
3
-
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
17
21
1
14
20
21
13
+
=
107
1+0+7
=
8
=
8
-
-
8
3
1
5
2
3
4
+
=
26
2+6
=
8
=
8
-
7
Q
U
A
N
T
U
M
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
-
``-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
``-
-
3
-
-
-
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
-
6
SIX
-
-
-
-
7
``-
-
-
-
-
-
-
-
-
-
7
SEVEN
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
-
9
NINE
-
-
-
-
22
7
Q
U
A
N
T
U
M
-
-
23
-
-
7
-
26
2+2
-
-
-
-
-
-
-
-``
-
-
2+3
-
-
-
-
2+6
4
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8
-
-
8
3
1
5
2
3
4
-
-
-
-
-
-
-
-
4
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8

 

 

7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
-
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
8
3
1
-
2
3
4
+
=
21
2+1
=
3
=
3
-
17
21
1
-
20
21
13
+
=
93
9+3
=
12
 1+2
3
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
17
21
1
14
20
21
13
+
=
107
1+0+7
=
8
=
8
-
8
3
1
5
2
3
4
+
=
26
2+6
=
8
=
8
7
Q
U
A
N
T
U
M
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
``-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
``-
-
3
-
-
-
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
-
-
-
5
occurs
x
1
=
5
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
7
Q
U
A
N
T
U
M
-
-
23
-
-
7
-
26
-
-
-
-
-
-
-
-``
-
-
2+3
-
-
-
-
2+6
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8
-
8
3
1
5
2
3
4
-
-
-
-
-
-
-
-
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8

 

 

7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
-
-
-
5
-
-
-
+
=
5
-
=
5
=
5
-
-
-
-
14
-
-
-
+
=
14
1+4
=
5
=
5
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
8
3
1
-
2
3
4
+
=
21
2+1
=
3
=
3
-
17
21
1
-
20
21
13
+
=
93
9+3
=
12
 1+2
3
7
Q
U
A
N
T
U
M
-
-
-
-
-
--
-
-
-
17
21
1
14
20
21
13
+
=
107
1+0+7
=
8
=
8
-
8
3
1
5
2
3
4
+
=
26
2+6
=
8
=
8
7
Q
U
A
N
T
U
M
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
``-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
``-
-
3
-
-
-
3
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
-
-
-
5
occurs
x
1
=
5
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
7
Q
U
A
N
T
U
M
-
-
23
-
-
7
-
26
-
-
-
1
-
2
3
4
-
-
2+3
-
-
-
-
2+6
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8
-
8
3
1
5
2
3
4
-
-
-
-
-
-
-
-
7
Q
U
A
N
T
U
M
-
-
5
-
-
7
-
8

 

RA ATUM ATUM RA

 

Q
=
8
-
7
QUANTUM
107
26
8
E
=
5
-
8
ENERGIES
82
46
1
-
-
13
-
27
First Total
189
72
9
-
-
1+3
-
2+7
Add to Reduce
1+8+9
7+2
-
Q
-
4
-
9
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
4
5
9
Essence of Number
9
9
9

 

 

-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
5
-
-
-
9
-
1
+
=
20
2+0
=
2
-
2
=
2
-
-
-
-
-
14
-
-
-
-
-
14
-
-
-
9
-
19
+
=
56
5+6
=
11
1+1
2
=
2
-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
8
3
1
-
2
3
4
-
5
-
5
9
7
-
5
-
+
=
52
5+2
=
7
-
7
=
7
-
-
17
21
1
-
20
21
13
-
5
-
5
18
7
-
5
-
+
=
133
1+3+3
=
7
-
7
=
7
-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
--
-
-
-
-
-
-
17
21
1
14
20
21
13
-
5
14
5
18
7
9
5
19
+
=
189
1+8+9
=
18
1+8
9
=
9
-
-
8
3
1
5
2
3
4
-
5
5
5
9
7
9
5
1
+
=
72
7+2
=
9
-
9
=
9
-
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
``-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
``-
-
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
-
-
5
5
5
-
-
-
5
-
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
-
-
-
-
-
-
-
``-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
6
15
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
39
-
-
15
-
72
-
45
=
1+5
-
-
-
-
-
-
-``
-
-
-
-
9
-
9
-
-
-
-
3+9
-
-
1+5
-
7+2
-
4+5
6
6
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
12
-
-
6
-
9
-
9
-
-
8
3
1
5
2
3
4
-
5
5
5
9
7
9
5
1
-
-
1+2
-
-
-
-
-
-
-
6
6
Q
U
A
N
T
U
M
-
E
N
E
R
G
I
E
S
-
-
3
-
-
6
-
9
-
9

 

QUANTUM THOUGHTS THOUGHTS QUANTUM

 

A
=
1
-
3
AND
19
10
1
Q
=
8
-
7
QUANTUM
107
26
8
I
=
9
-
2
IS
28
10
1
A
=
1
-
2
AS
20
2
2
Q
=
8
-
7
QUANTUM
107
26
8
D
=
4
-
4
DOES
43
16
7
-
-
31
-
25
First Total
324
90
27
-
-
3+1
-
2+5
Add to Reduce
3+2+4
9+0
2+7
Q
-
4
-
7
Second Total
9
9
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
4
5
7
Essence of Number
9
9
9

 

 

Q
=
8
7
QUANTUM
107
26
8
T
=
2
6
THEORY
91
37
1
-
-
10
13
First Total
198
63
9
-
-
1+0
1+3
Add to Reduce
1+9+8
6+3
-
-
-
1
4
Second Total
18
9
9
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
1
4
Essence of Number
9
9
9

 

 

-
13
Q
U
A
N
T
U
M
-
T
H
E
O
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
8
-
6
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
-
-
14
-
-
-
-
-
8
-
15
-
-
+
=
37
3+7
=
10
1+0
1
=
1
-
13
Q
U
A
N
T
U
M
-
T
H
E
O
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
8
3
1
-
2
3
4
-
2
-
5
-
9
7
+
=
44
4+4
=
8
-
8
=
8
-
-
17
21
1
-
20
21
13
-
20
-
5
-
18
25
+
=
161
1+6+1
=
8
-
8
=
8
-
13
Q
U
A
N
T
U
M
-
T
H
E
O
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
17
21
1
14
20
21
13
-
20
8
5
15
18
25
+
+
198
1+9+8
=
18
1+8
9
=
9
-
-
8
3
1
5
2
3
4
-
2
8
5
6
9
7
+
+
63
6+3
=
9
-
9
=
9
-
13
Q
U
A
N
T
U
M
-
T
H
E
O
R
Y
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
``-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
3
``-
-
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
2
=
6
-
6
4
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
45
13
Q
U
A
N
T
U
M
-
T
H
E
O
R
Y
-
-
45
-
-
13
-
63
-
45
4+5
1+3
-
-
-
-
-
-
-``
-
-
-
-
-
9
-
-
-
4+5
-
-
1+3
-
6+3
-
4+5
9
4
Q
U
A
N
T
U
M
-
T
H
E
O
R
Y
-
-
9
-
-
4
-
9
-
9
-
-
8
3
1
5
2
3
4
-
2
8
5
6
9
7
-
-
-
-
-
-
-
-
-
-
9
4
Q
U
A
N
T
U
M
-
T
H
E
O
R
Y
-
-
9
-
-
4
-
9
-
9

 

 

IN SEARCH OF SCHRODINGER'S CAT

John Gribbin 1984

QUANTUM PHYSICS AND REALITY

 

-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
Q
=
2
-
7
QUANTUM
107
26
8
P
=
7
-
7
PHYSICS
99
54
9
A
=
2
-
3
AND
19
10
1
R
=
6
-
7
REALITY
90
36
9
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
-
2+2
-
2+4
-`
3+1+5
1+2+6
2+7
-
-
4
-
6
QUANTUM PHYSICS AND REALITY
9
9
9

 

 

-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
1
2
3
4
5
6
7
8
9
Q
=
2
-
7
QUANTUM
107
26
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
-
-
-
-
-
-
-
A
=
2
-
3
AND
19
10
1
-
-
-
-
-
-
-
-
-
-
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
QUANTUM
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
=
8
1
1
Q
17
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
3
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
6
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
-
-
26
-
7
QUANTUM
107
26
26
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
PHYSICS
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
Y
=
7
10
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
14
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
36
-
7
PHYSICS
99
54
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
AND
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
15
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
17
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
10
-
3
AND
19
10
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
REALITY
-
-
-
-
-
-
-
-
-
-
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
19
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
20
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
21
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
22
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
Y
=
7
24
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
36
-
7
REALITY
90
36
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
=
2
-
7
QUANTUM
107
26
8
-
5
4
12
8
15
6
21
16
27
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
1+2
-
1+5
-
2+1
1+6
2+7
A
=
2
-
3
AND
19
10
1
-
5
4
3
8
6
6
3
7
9
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
5
4
3
8
6
6
3
7
9
-
-
2+2
-
2+4
-`
3+1+5
1+2+6
2+7
-
-
-
-
-
-
-
-
-
-
-
-
4
-
6
QUANTUM PHYSICS AND REALITY
9
9
9
-
5
4
3
8
6
6
3
7
9

 

 

-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
1
2
3
4
5
6
7
8
9
Q
=
2
-
7
QUANTUM
107
26
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
-
-
-
-
-
-
-
A
=
2
-
3
AND
19
10
1
-
-
-
-
-
-
-
-
-
-
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
Q
=
8
1
1
Q
17
8
8
-
-
-
-
-
-
6
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
6
-
-
-
A
=
1
3
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
U
=
3
6
1
U
21
3
3
-
-
-
3
-
-
6
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
6
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
6
7
-
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
6
-
8
-
Y
=
7
10
1
Y
25
7
7
-
-
-
-
-
-
6
7
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
6
-
-
-
S
=
1
14
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
A
=
1
15
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
D
=
4
17
1
D
4
4
4
-
-
-
-
4
-
6
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
6
-
-
9
E
=
5
19
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
A
=
1
20
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
L
=
3
21
1
L
12
3
3
-
-
-
3
-
-
6
-
-
-
I
=
9
22
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
Y
=
7
24
1
Y
25
7
7
-
-
-
-
-
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
=
2
-
7
QUANTUM
107
26
8
-
5
4
12
8
15
6
21
16
27
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
1+2
-
1+5
-
2+1
1+6
2+7
A
=
2
-
3
AND
19
10
1
-
5
4
3
8
6
6
3
7
9
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
5
4
3
8
6
6
3
7
9
-
-
2+2
-
2+4
-`
3+1+5
1+2+6
2+7
-
-
-
-
-
-
-
-
-
-
-
-
4
-
6
QUANTUM PHYSICS AND REALITY
9
9
9
-
5
4
3
8
6
6
3
7
9

 

 

-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
1
2
3
4
5
6
7
8
9
Q
=
2
-
7
QUANTUM
107
26
8
-
-
-
-
-
-
-
-
-
-
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
-
-
-
-
-
-
-
A
=
2
-
3
AND
19
10
1
-
-
-
-
-
-
-
-
-
-
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
3
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
S
=
1
14
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
A
=
1
15
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
A
=
1
20
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
T
=
2
23
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
6
-
-
-
U
=
3
6
1
U
21
3
3
-
-
-
3
-
-
6
-
-
-
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
6
-
-
-
L
=
3
21
1
L
12
3
3
-
-
-
3
-
-
6
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
6
-
-
-
D
=
4
17
1
D
4
4
4
-
-
-
-
4
-
6
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
N
=
5
16
1
N
14
5
5
-
-
-
-
-
5
6
-
-
-
E
=
5
19
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
6
7
-
-
Y
=
7
10
1
Y
25
7
7
-
-
-
-
-
-
6
7
-
-
Y
=
7
24
1
Y
25
7
7
-
-
-
-
-
-
6
7
-
-
Q
=
8
1
1
Q
17
8
8
-
-
-
-
-
-
6
-
8
-
H
=
8
9
1
H
8
8
8
-
-
-
-
-
-
6
-
8
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
6
-
-
9
I
=
9
22
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
QUANTUM PHYSICS AND REALITY
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
=
2
-
7
QUANTUM
107
26
8
-
5
4
12
8
15
6
21
16
27
P
=
7
-
7
PHYSICS
99
54
9
-
-
-
1+2
-
1+5
-
2+1
1+6
2+7
A
=
2
-
3
AND
19
10
1
-
5
4
3
8
6
6
3
7
9
R
=
6
-
7
REALITY
90
36
9
-
-
-
-
-
-
-
-
-
-
-
-
22
-
24
QUANTUM PHYSICS AND REALITY
315
126
27
-
5
4
3
8
6
6
3
7
9
-
-
2+2
-
2+4
-`
3+1+5
1+2+6
2+7
-
-
-
-
-
-
-
-
-
-
-
-
4
-
6
QUANTUM PHYSICS AND REALITY
9
9
9
-
5
4
3
8
6
6
3
7
9

 

LETTERS TRANSPOSED INTO NUMBER RE-ARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
QUANTUM
-
-
-
-
-
-
-
-
-
-
-
-
-
Q
=
8
1
1
Q
17
8
8
-
-
-
-
-
-
-
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
3
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
6
1
U
12
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
-
-
26
-
7
QUANTUM
107
26
26
-
2
2
6
4
5
6
7
8
6
-
-
2+6
-
-
-
1+0+7
2+6
2+6
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
QUANTUM
8
8
8
-
2
2
6
4
5
6
7
8
9

 

 

3
THE
33
15
6
7
QUANTUM
107
26
8
4
MIND
40
22
4
14
Add to Reduce
180
63
18
1+4
Reduce to Deduce
1+8+0
6+3
1+8
5
Essence of Number
9
9
9

 

 

A
=
1
-
3
AND
19
10
1
Q
=
8
-
7
QUANTUM
107
26
8
I
=
9
-
2
IS
28
10
1
A
=
1
-
2
AS
20
2
2
Q
=
8
-
7
QUANTUM
107
26
8
D
=
4
-
4
DOES
43
16
7
-
-
31
-
25
First Total
324
90
27
-
-
3+1
-
2+5
Add to Reduce
3+2+4
9+0
2+7
Q
-
4
-
7
Second Total
9
9
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
4
5
7
Essence of Number
9
9
9

 

 

-
-
-
-
-
PHYSICS
-
-
-
P
=
7
-
1
P
16
7
7
H
=
8
-
1
H
8
8
8
Y
=
7
-
1
Y
25
7
7
S
=
1
-
1
S
19
10
1
I
=
9
-
1
I
9
9
9
C
=
3
-
1
C
3
3
3
S
=
1
-
1
S
19
10
1
-
-
36
-
7
PHYSICS
99
54
36
-
-
3+6
-
-
-
9+9
8+1
3+6
-
-
9
-
7
PHYSICS
18
9
9
-
-
-
-
-
-
1+8
-
-
-
-
9
-
7
PHYSICS
9
9
9

 

 

IN SEARCH OF SCHRODINGER'S CAT

John Gribbin 1984

QUANTUM PHYSICS AND REALITY

NOTHING IS REAL

"The cat of our title is a mythical beast, but Schrodinger was a real person. Erwin Schrodinger was an Austrian scientist instrumental in the development, in the mid-1920s, of the equations of a branch of science now known as quantum mechanics. Branch of science is hardly the correct expres-sion, however, because quantum mechanics provides the fundamental underpinning of all of modem science. The equations describe the behavior of very small objects-gen-erally speaking, the size of atoms or smaller-and they provide the only understanding of the world of the very small. Without these equations, physicists would be unable to design working nuclear power stations (or bombs), build lasers, or explain how the sun stays hot. Without quantum mechanics, chemistry would still be in the Dark Ages, and there would be no science of molecular biology-no under-standing of DNA, no genetic engineering-at all "

QUANTUM THEORY

107 + 91 = 198 1 + 9 + 8 = 18 1 + 8 = 9

1 x 9 x 8 = 72

" Quantum theory represents the greatest achievement of science, far more significant and of far more direct, prac-tical use than relativity theory. And yet, it makes some very strange predictions. The world of quantum mechanics is so strange, indeed, that even Albert Einstein found it in-comprehensible, and refused to accept all of the implica-tions of the theory developed by Schrodinger and his colleagues. Einstein, and many other scientists, found it more comfortable to believe that the equations of quantum mechanics simply represent some sort of mathematical trick, which just happens to giye a reasonable working guide to the behavior of atomic and subatomic particles but that conceals some deeper truth that corresponds more closely to our everyday sense of reality. For what quantum mechanics says is that nothing is real and that we cannot say anything about what things are doing when we are not looking at them. Schrodinger's mythical cat was invoked to make the differences between the quantum world and the everyday world clear.

In the world of quantum mechanics, the laws of phys-ics that are familiar from the everyday world no longer work. Instead, events are governed by probabilities. A radio-active atom, for example, might decay, emitting an electron, say; or it might not. It is possible to set up an experiment in such a way that there is a precise fifty-fifty chance that one of the atoms in a lump of radioactive material will decay in a certain time and that a detector will register the decay if it does happen. Schrodinger, as upset as Einstein about the implications of quantum theory, tried to show the absurdity of those implications by imagining such an experiment set up in a closed room, or box, which also contains a live cat and a phial of poison, so arranged that if the radioactive decay does occur then the poison container is broken and the cat dies. In the everyday world, there is a fifty-fifty chance that the cat will be killed, and without looking in-side the box we can say, quite happily, that the cat inside is either dead or alive. But now we encounter the strangeness of the quantum world. According to the theory, neither of the two possibilities open to the radioactive material, and therefore to the cat, has any reality unless it is observed. The atomic decay has neither happened nor not happened, the cat has neither been killed nor not killed, / Page 3 / until we look inside the box to see what has happened. Theorists who accept the pure version of quantum mechanics say that the cat exists in some indeterminate state, neither dead nor alive, until an observer looks into the box to see how things are getting on. Nothing is real unless it is observed.

The idea was anathema to Einstein, among others. "God does not play dice," he said, referring to the theory that the world is governed by the accumulation of outcomes of essentially random "choices" of possibilities at the quan-tum level. As for the unreality of the state of Schrodinger's cat, he dismissed it, assuming that there must be some un-derlying "clockwork" that makes for a genuine fundamen-tal reality of things. He spent many years attempting to devise tests that might reveal this underlying reality at work but died before it became possible actually to carry out such a test. Perhaps it is as well that he did not live to see the outcome of one line of reasoning that he initiated.

In the summer of 1982, at the University of Paris-South, in France, a team headed by Alain Aspect completed a series of experiments designed to detect the underlying reality below the unreal world of the quantum. The under-lying reality-the fundamental clockwork-had been given the name " hidden variables," and the experiment con-cerned the behavior of two photons or particles of light fly-ing off in opposite directions from a source. It is described fully in Chapter Ten, but in essence it can be thought of as a test of reality. The two photons from the same source can be observed by two detectors, which measure a property called polarization. According to quantum theory, this prop-erty does not exist until it is measured. According to the hidden-variable idea, each photon has a "real" polarization from the moment it is created. Because the two photons are emitted together, their polarizations are correlated with one another. But the nature of the correlation that is actually measured is different according to the two views of reality.

The results of this crucial experiment are unam-biguous. The kind of correlation predicted by hidden- variable theory is not found; the kind of correlation pre- dicted by quantum mechanics is found, and what is more, again as predicted by quantum theory, the measurement / Page 4 / that is made on one photon has an instantaneous effect on the nature of the other photon. Some interaction links the two inextricably, even though they are flying apart at the speed of light, and relativity theory tells us that no signal can travel faster than light. The experiments prove that there is no underlying reality to the world. "Reality," in the everyday sense, is not a good way to think about the be-havior of the fundamental particles that make up the uni-verse; yet at the same time those particles seem to be inseparably connected into some indivisible whole, each aware of what happens to the other

The search for Schrodinger's cat was the search for quantum reality.. From this brief outline, it may seem that the search has proved fruitless, since there is no reality in the everyday sense of the word. But this is not quite the end of the story, and the search for Schrodinger's cat may lead us to a new understanding of reality that transcends, and yet includes, the conventional interpretation of quantum mechanics. The trail is a long one, however, and it begins with a scientist who would probably have been even more horrified than Einstein if he could have seen the answers we now have to the questions he puzzled over. Isaac New-ton, studying the nature of light three centuries ago, could have had no conception that he was already on the trail leading to Schrodinger's cat."

 

 

THE EMPERORS'S NEW MIND

CONCERNING COMPUTERS, MINDS, AND THE LAWS OF PHYSICS

Roger Penrose 1989

QUANTUM MAGIC AND QUANTUM MYSTERY

 

EXPERIMENTS WITH PHOTONS: A PROBLEM FOR RELATIVITY?

Page 369

"We must ask whether actual experiments have borne out these astonishing quantum expectations. The precise experiment just described is a hypothetical one which has not actually been performed, but similar experiments have been performed using the polarizations of pairs of photons, rather than the spin of spin-one-half massive particles. Apart from this distinction, these experiments are, in their essentials, the same as the one described above - except that the angles concerned (since photons have spin one rather than one-half) would be just one-half of those for spin-one-half particles. The polarizations of the pairs of photons have been measured in various different combinations of directions, and the results are fully in agreement with the predictions of quantum theory, and inconsistent with any local realistic model!
The most accurate and convincing of the experimental results which have been obtained to date are those of Alain Aspect (1986) and his colleagues in Paris.15 Aspect's experiments had another interesting feature. The 'decisions' as to which way to measure the polarizations of the photons, were made only after the photons were in full flight. Thus, if we think of some non-local 'influence' travelling from one photon detector to the photon at the opposite side, signalling the direction in which it intends to measure the polarization direction of the approaching photon, then we see that this 'influence' must travel faster than light! Any kind of realistic description of the quantum world which is consistent with the facts must apparently be non-causal, in the sense that effects must be able to travel faster than light!

Page 370

" But we saw in the last chapter that, so long as relativity holds true, the sending of signals faster than light leads to absurdities (and conflict with our feelings of 'free will', etc., cf. p. 273). This is certainly true, but the non-local 'influences' that arise in EPR-type experiments are not such that they can be used to send messages ­as one can see, for the very reason that they would lead to such absurdities, if so. (A detailed demonstration that such 'influences' cannot be used to signal messages has been carried out by Ghirardi, Rimini, and Weber 1980.) It is of no use to be told that a photon is polarized 'either vertically or horizontally', (as opposed, say, to 'either at 60° or 150°') until one is informed which of the two alternatives it actually is. It is the first piece of 'information' (i.e. the directions of alternative polarization) which arrives faster than light ('instantaneously'), while the knowledge as to which of these two directions it must actually be polarized in arrives more slowly, via an ordinary signal communicating the result of the first polarization measurement.
Although EPR-type experiments do not, in the ordinary sense of sending messages, conflict with the causality of relativity, there is a definite conflict with the spirit of relativity in our picture of 'physical reality'. Let us see how the realistic view of the state­vector applies to the above EPR-type experiment (involving photons). As the two photons move outwards, the state-vector describes the situation as a photon pair, acting as a single unit. Neither photon individually has an objective state: the quantum state applies only to the two together. Neither photon individually has a direction of polarization: the polarization is a combined quality of the two photons together. When the polarization of one of these photons is measured, the state-vector jumps so that the unmeasured photon now does have a definite polarization. When that photon's polarization is subsequently measured, the probability values are correctly obtained by applying the usual quantum rules to its polarization state. This way of looking at the situation provides the correct answers; it is, indeed, the way that we ordinarily apply quantum mechanics. But it is an essentially non-relativistic view. For the two measurements of polarization are what are called space like-separated, which means that each lies outside the other's light cone, like the points R and Q in Fig. / Page 371 / 5.21. The question of which of these measurements actually occurred first is not really physically meaningful, but depends on the 'observer's' state of motion (see Fig. 6.32). If the 'observer' moves rapidly enough to the right, then he considers the right­hand measurement to have occurred first; and if to the left, then it is the left-hand measurement! But if we regard the right-hand photon as having been measured first we get a completely different picture of physical reality from that obtained if we regard the left-hand photon as having been measured first! (It is a different measurement that causes the non-local 'jump'.) There is an essential conflict between our space-time picture of physical reality - even the correctly non-local quantum-mechanical one ­and special relativity! This is a severe puzzle, which 'quantum realists' have not been able adequately to resolve (cf. Aharonov and Albert 1981). I shall need to return to the matter later.

Fig. 6.32. (omitted) Two different observers form mutually inconsistent pictures of 'reality' in an EPR experiment in which two photons are emitted in opposite directions from a spin-O state. The observer moving to the right judges that the left-hand part of the state jumps before it is measured, the jump being caused by the measurement on the right. The observer moving to the left has the opposite opinion!"

 

 

http://home.btconnect.com/scimah/Quantumphenomena.htm

Spooky action at a distance - EPR

"One of the most vivid illustrations of the interactions of the mind of the observer with a quantum system is given by EPR - the 'Einstein Podolsky Rosen Paradox', or 'Spooky action at a distance' as it is sometimes known. The experimental evidence seems to show that the observer's mind goes to its object unobstructedly and instantaneously, for example through ten kilometres of intervening Geneva city-scape (walls, buildings, railway stations, the lot!) at speeds exceeding that of light.

Nor does the effect diminish with distance. According to the Copenhagen interpretation of quantum theory, the 'spooky action' can affect a particle instantaneously whether it is a metre away from the observer or halfway across the universe.

The observation of 'spooky action' relies on the concept of entanglement. It is possible to obtain pairs of fundamental particles where it is known that their properties will always cancel one another out, even when those properties have not been defined. These pairs are said to be 'entangled' . However the entanglement is conceptual rather than physical and the particles are free to move far apart.

Consider an experiment where we create an entangled pair of magnetic particles. Their polar alignments will always be opposite. We allow them to move far apart. We then place a Stern-Gerlach magnet in the path of one of the particles and observe what happens when it passes through. If it is defected upwards then, according to the 'spooky action' hypothesis, its distant partner would be deflected downwards by a similar magnet. By making the nearby observation we have instantaneously defined the properties of the distant particle.

Note that this is not the same thing as saying 'The near particle was always up but we didn't know until we decided to observe it. So the distant particle must always have been down even though we didn't know at the the time.'

The reason the statement above is incompatible with quantum theory is that we could have equally well decided to align the Stern-Gerlach magnet on a left/right axis instead of up/down. In which case we would have fixed the near particle as, say, left-deflected and the distant particle would instantaneously be known to be right-deflected.

For many years both theoretical and technical difficulties stood in the way of determining whether 'spooky action' does indeed take place. However as a result of the theoretical work of John Bell and the ingenious experimental designs of Alain Aspect strong evidence was obtained that the effect occurred over distances of a few metres. The act of making a decision of what attributes of one member of an entangled pair were to be observed immediately determined what could be observed of the other member.

Since then 'spooky action' has been demonstrated over increasing distances. The current record is 10 km obtained by Nicolas Gisin and his team at the University of Geneva [BUCHANAN 1997]. Starting from near Geneva railway station they sent entangled photons along optical fibres through the city to destinations separated by 10km. They showed that observing the state of one member of the pair instantaneously determined the state of the other."

 

 

MUSIC OF THE MIND

Darryl Reanney 1994

An Adventure Into Consciousness

Page 77

REALITIES WE DO NOT SEE

"This is the strange reality-all thoughts, whatever 'waveband' they occupy, exist in the disembodied reality of the quantum dream. The essence of a quantum ripple is that it exists in an indeterminate, non-localised state, in that uninhabited quantum 'space' where there is neither yesterday nor tomorrow, neither here nor there. Moreover, a thought, once created, no longer needs the physical structure of the brain that made it to sustain it further-it is thereafter just as 'real' as an electron or a stone.
Common sense tends to rebel at this. We have such an ingrained tendency to explain aspects of experience in terms of everyday models that our minds stumble when confronted with a phenomenon for which there is no model. But the quantum state poses the ultimate paradox: it seems so alien because it is so familiar. Our thoughts are, in essence, quantum waves so when we see this inner aspect of ourselves in outward projection we think we are seeing the face of a stranger. The nub of the difficulty is the disembodied aspect of the quantum ripple. Because the world we inhabit is limited by the dimensional context of space and time, it is difficult for our minds to grasp the dimensionless reality of the thoughts that enter them.
The best way to resolve one paradox is to invoke another so let me sketch out a further anti-intuitive aspect of quantum mechanics. Consider two subatomic particles, A and B, that are created from the same micro-event in such a way that A has a different 'spin' to B. Suppose further that these two particles now proceed to opposite 'ends' of the universe. They are so far apart that a signal travelling at the speed of light could not bridge the gap between them. The mind-bending scientific truth is that if one changes the spin on A, the spin / Page 78 / on B changes simultaneously. Since no signal can travel faster than light we are obviously dealing with a coupled system that cannot obey the spacetime logic we recognise. This paradoxical non-locality of quantum interactions means that even though human observers measure the space (or time) between the particles in terms of the millions of kilometres (or years) that (seem to) separate them, at a deeper level of reality they are still-somehow-together. So any point we call 'here' can simultaneously access all of space in exactly the same sense that, as the mystics assure us, any moment we call 'now' can simultaneously access all of time.
Mathematical theorist Rudy Rucker believes that mathematical truths occupy a 'mental space' which he dubs the Mindscape. 'A person who does mathematical research,' he opines, 'is an explorer of the Mindscape in much the same way that Armstrong, Livingstone or Cousteau are explorers of the physical features of our universe. '70 Other scientists seem to agree. Roger Penrose states:
When mathematicians communicate, this is made possible by each one having a direct route to truth [author emphasis], the consciousness of each being in a position to perceive mathematical truths directly, through this process of 'seeing'. 71"

 

I

ME

ENTANGLEMENTS

 

Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other ...en.wikipedia.org/wiki/Quantum_entanglement

Quantum entanglement

Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated. This leads to correlations between observable physical properties of the systems. For example, it is possible to prepare two particles in a single quantum state such that when one is observed to be spin-up, the other one will always be observed to be spin-down and vice versa, this despite the fact that it is impossible to predict, according to quantum mechanics, which set of measurements will be observed. As a result, measurements performed on one system seem to be instantaneously influencing other systems entangled with it. But quantum entanglement does not enable the transmission of classical information faster than the speed of light (see discussion in next section below).

Quantum entanglement applications in the emerging technologies of quantum computing and quantum cryptography, and has been used to realize quantum teleportation experimentally. At the same time, it prompts some of the more philosophically oriented discussions concerning quantum theory. The correlations predicted by quantum mechanics, and observed in experiment, reject the principle of local realism , which is that information about the state of a system should only be mediated by interactions in its immediate surroundings. Different views of what is actually occurring in the process of quantum entanglement can be related to different interpretations of quantum mechanics.

 

 

Quantum entanglement just got a whole lot weirder, says Michael Brooks ... The team believe that quantum entanglement between the atoms is the only ..www.biophysica.com/quantum

Entanglement:  The weirdest link

New Scientist vol 181 issue 2440 - 27 March 2004, page 32

That spooky connection between tiny particles is appearing everywhere, and its consequences are even affecting the world that we experience. It seems to unravel the past, and may be what keeps us alive. Quantum entanglement just got a whole lot weirder, says Michael Brooks

ENTANGLEMENT. Erwin Schrödinger called this phenomenon the defining trait of quantum theory. Einstein famously dubbed it spukhafte Fernwirkungen: "spooky action at a distance". It is not hard to understand why. Set things up correctly, and you can instantaneously affect the physical properties of a particle on the other side of the universe simply by prodding its entangled twin.

This is no longer just a curiosity of the quantum world, visible only in excruciatingly delicate experiments. Physicists now believe that entanglement between particles exists everywhere, all the time, and have recently found shocking evidence that it affects the wider, "macroscopic" world that we inhabit.

It is a discovery that might have far-reaching consequences. Not only will it give us a better grip on technological applications, such as quantum computing and cryptography, and the teleportation of quantum states, it could also open up a whole new realm of reality, enabling us to retain and control quantum weirdness in our everyday world. And it's not just a strange kind of "remote control" over matter that is at stake. Entanglement could even be the key to understanding what gives rise to the phenomenon of life. It's enough to set Einstein spinning in his grave.

Entanglement has been an affront to our sensibilities for several decades now. Schrödinger discovered it through his newly formed quantum theory, when he examined the mathematical descriptions of two quantum particles that bump into one other. After the interaction, it is impossible to tease apart the two particles' characteristics. Once they are entangled, it makes no sense to talk about the properties of just one of them. All the information about the particles, such as their momentum and spin, lies only in their joint properties. So if something affects the quantum state of one particle, it will inevitably affect the quantum state of the other, no matter how far apart they are. It is this that gives entanglement the "spooky" character that Einstein found so distasteful.

Although it seems like something from the realm of fantasy, many physicists now use entanglement as a kind of resource for experiments and applications. Entangled pairs of quantum particles such as photons are routinely created and sent down microscopes or fired across vast distances. Their spooky properties are used to perform such feats as high-resolution imaging, quantum teleportation or quantum cryptography.

But, despite the growing use of entanglement as a technological tool, physicists are beginning to realise we have only just scratched the surface of its potential. "Are there some other forms of entanglement that we haven't yet discovered?" asks Benni Reznik, a theoretical physicist at Tel Aviv University in Israel. "I think there are."

Just how little we know about entanglement was made crystal clear last year by a collaboration led by Sayantani Ghosh at the University of Chicago (Nature, vol 425, p 48). The team analysed experiments done more than a decade ago with a sample of a magnetic salt containing holmium atoms, and compared them with theoretical predictions. What they found is extraordinary.

The holmium atoms within the salt behave like tiny magnets and respond to each others' magnetic fields by adjusting their relative orientation, just as a compass needle orients itself to align with the Earth's magnetic field. But the atoms change this settled orientation if they are placed in an external magnetic field. The degree to which they align with the field is known as the salt's "magnetic susceptibility".

Ghosh and his colleagues examined how the susceptibility of the salt varied with temperature. They expected it would decrease as the temperature rose, because the extra energy at higher temperatures disrupts the atoms' ability to maintain the optimum alignment. And it did. But at very low temperatures, the atoms were aligned to a greater degree than would be expected if they had normal quantum energy levels (Graphic omitted). The team believe that quantum entanglement between the atoms is the only explanation for this phenomenon.

It's a big shock: it shows that the quantum phenomenon of entanglement, whose power was thought to be confined to the infinitesimal world of subatomic particles, can produce effects that remain measurable on macroscopic scales.

Ghosh and his colleagues also showed that entanglement affects the salt's heat capacity, defined as the amount of heat needed to change the temperature of a kilogram of substance by 1 kelvin. Throw in some heat, and you can only determine exactly how far the salt's temperature will rise if you take entanglement between atoms into account.

According to Vlatko Vedral, a theoretical physicist at Imperial College in London, these discoveries are highly important. Vedral was one of the team that first predicted the effect, three years ago (Physical Review Letters, vol 87, p 017901). The fact that the prediction has been borne out by experiment catapults the mystery of entanglement into the list of big unanswered questions that scientists need to address, he says.

That's partly because physicists can no longer content themselves with using the quantum and classical energy level descriptions of a material if they want to determine and understand its properties. The effects of entanglement now have to be included as an integral part of any accurate calculation.

But the results also suggest that, if we knew where to look, we might find entanglement causing significant effects in other materials. "It's not just magnetic salts - this should be a more universal thing," Vedral says.

The best place to look first, he believes, might be the enigmatic phenomenon of high-temperature superconductivity. Vedral points out that superconductors contain pairs of electrons whose quantum descriptions, or wave functions, appear to be entangled. "The wave function describing the pair is not equal to the product of two wave functions," he says. "Mathematically, I can see there is entanglement."

So should entanglement be considered as a possible cause of high-temperature superconductivity? Might it show us how to make materials that are superconducting at room temperature? At this stage, it is too early to say: the effects of entanglement on Ghosh's magnetic salt only become noticeable below 1 kelvin. "That is almost absolute zero," Vedral admits. "What would be really interesting would be to find a material that exhibits the effects of entanglement at higher temperatures." Eventually, he thinks, we might well find such a material at room temperature. "I don't think it's going to be a very easy search, but I can't think of anything that would rule this out on the basis of fundamental theory. It doesn't look impossible to me."

While this might seem hopelessly optimistic at first glance, other recent discoveries about entanglement are suggesting otherwise. Entanglements at room temperature appear to be an everyday part of the universe. Reznik, for instance, has shown that all of empty space - what physicists refer to as the vacuum - is filled with pairs of particles that are entangled. "It's an unusual idea," says Reznik. "It was quite hard to get our first paper on this accepted." His paper was finally published last year in Foundations of Physics (vol 33, p 167).

Thomas Durt of Vrije University in Brussels also believes entanglement is everywhere. He has recently shown, from the basic equations that Schrödinger considered, that almost all quantum interactions produce entanglement, whatever the conditions. "When you see light coming from a faraway star, the photon is almost certainly entangled with the atoms of the star and the atoms encountered along the way," he says. And the constant interactions between electrons in the atoms that make up your body are no exception. According to Durt, we are a mass of entanglements.

Curiouser and curiouser

Of course, that is no guarantee we can use them. Reznik says he doesn't think you can take his vacuum entanglement and use it to perform feats such as teleportation. Indeed, he is not even sure how to demonstrate that this entanglement exists. Though the equations of quantum field theory show that it is present, he is still working out how to perform an experiment that makes vacuum entanglement more than a theoretical result.

These are all tantalising revelations, because they suggest that something priceless is within our grasp. But how do we reach it?

We certainly need to find a better handle on practical entanglement: at the moment, the only forms of it we have learned to use are somewhat constraining. The entangled photons used for cryptography and teleportation are produced by firing a photon into a "non-linear" crystal, such as beta barium borate. The optical properties of a non-linear crystal depend on its orientation, and a photon fired in at the correct angle will split into two entangled photons. But the entanglement between the photon pair is an artefact of the internal properties of the original photon - its path and polarisation (Link New Scientist, 30 October 1999, p 32. omitted). So entangled photons from a non-linear crystal effectively remain just one quantum system, rather than being the result of two distinct particles meeting and interacting. "It's a kind of entanglement, but not quite the same as between different quantum systems," Vedral says.

What physicists would dearly like, the resource that would open the way for the best experiments, is an unlimited source of pure two-particle entanglements. Despite the recent progress, this rich source of quantum magic has eluded them so far. So how do we take things forward? Schrödinger first discovered entanglement through analysing the mathematical descriptions of quantum theory, so perhaps mathematicians should be the pioneers. The trouble with this is that entanglement gives mathematicians a severe headache - especially when the entanglement is between anything more than two particles.

In theory, just bouncing particles off an entangled pair will establish another entanglement link that can then be put to work, but it's much easier said than done. Experimental physicists John Rarity and Paul Tapster were the first to entangle three photons, in their laboratory at the UK Defence Evaluation and Research Agency in Malvern, Worcestershire, five years ago. But no one has ever managed to work out how to describe the properties of such a system. For the most part, theorists can't even look at a given quantum state and tell if it is entangled - it is only possible in a few special cases. "Although I can define what it means to be entangled, that is, I can write down a state that's entangled and a state that's not, if you give me a state and ask whether it's entangled, then I have no efficient way of telling you that," says Vedral. In other words, he knows how to formulate the calculation, but it is so difficult that no computer can actually perform it.

But these problems may be nothing compared to the bombshell that Caslav Brukner of the University of Vienna has just dropped. As if our current understanding of entanglement between widely separated particles were not sketchy enough, Brukner, working with Vedral and two other Imperial College researchers, has uncovered a radical twist. They have shown that moments of time can become entangled too (link omitted).

They achieved this through a thought experiment that examines how quantum theory links successive measurements of a single quantum system. Measure a photon's polarisation, for example, and you will get a particular result. Do it again some time later, and you will get a second result. What Brukner and Vedral have found is a strange connection between the past and the future: the very act of measuring the photon polarisation a second time can affect how it was polarised earlier on. "It's really surprising," says Vedral.

This entanglement between moments in time is so bizarre that it could expose a hole in the very fabric of quantum theory, the researchers believe. The formulation does not allow messages to be sent back in time, but it still means that quantum mechanics seems to be bending the laws of cause and effect. On top of that, entanglement in time puts space and time on an equal footing in quantum theory, and that goes sharply against the grain.

Space and time have always been very different in quantum theory. A location in space is an "observable" - like momentum or spin, spatial coordinates are just another property any quantum particle can have. The passing of time, on the other hand, has always been part of the backdrop. An electron can have a particular value of spin, or momentum or location, but it cannot have a particular time.

But if time can become entangled, it should be considered as an observable, and there is no way to write that into quantum theory. "People have tried, but something in quantum mechanics always has to be violated if you want a proper time-observable," Vedral says. "So it could be that something in quantum mechanics has to be reformulated."

In other words, Brukner's result suggests that we might be missing something important in our understanding of how the world works. Maybe that shouldn't surprise us. After all, entanglement between two spatially separated objects already tells us that space doesn't really have the form that classical physics says it does: instantaneous cause and effect across cosmological distances is not something that any theory of the universe can cope with. And now Brukner's result seems to extend this "impossibility" to events separated in time as well.

It's not cause for despair, though. We know that relativity and quantum theory have to be meshed together if we are to create a "final" theory of how the universe works. It is too early to read much into Brukner's result, but maybe it is a clue about how to produce such a theory.

In the meantime, Vedral thinks he's identified an equally significant project to pursue. If, as Ghosh's result suggests, entanglement can produce macroscopic effects, is it such a stretch to reason that quantum entanglement might be the key to understanding life?

We know that quantum mechanics describes how atoms combine into molecules, and so underpins chemistry. And chemical processes underpin all biological processes, including the metabolic cycle and replication. So could entanglement support the emergent, macroscopic characteristic of chemistry that we call life? Reznik and Durt's revelations - that entanglements exist around us and inside us all the time - can only add to the intrigue. "I think it's a speculation worth making," Vedral says. "There may be some experiments in biology or biochemistry where we can see more of these effects, interpret some of the results in a different light. It would be a very exciting find."

Couple that with the ability to create materials that exploit our unfolding understanding of entanglement, and we might one day even gain the ability to use entanglement to create new forms of life. Now that is a spooky thought.

Michael Brooks

 

7
QUANTUM
107
26
8
12
ENTANGLEMENT
130
49
4

 

 

3
THE
33
15
6
6
SPOOKY
101
29
2
6
EFFECT
45
27
9

 

 

6
ELECTRO
78
33
6
8
MAGNETIC
72
36
9
12
ENTANGLEMENT
130
49
4
26
First Total
280
118
19
2+6
Add to Reduce
2+8+0
1+1+8
1+9
8
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
8
Essence of Number
1
1
1

 

 

-
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
5
-
+
=
15
1+5
=
6
-
6
-
6
-
-
-
14
-
-
14
-
-
-
-
-
14
-
+
=
42
4+2
=
6
-
6
-
6
-
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
5
-
2
1
-
7
3
5
4
5
-
2
+
=
34
3+4
=
7
-
7
-
7
-
-
5
-
20
1
-
7
12
5
13
5
-
20
+
=
88
8+8
=
16
1+6
7
-
7
-
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
5
14
20
1
14
7
12
5
13
5
14
20
+
=
130
1+3+0
=
4
-
4
-
4
-
-
5
5
2
1
5
7
3
5
4
5
5
2
+
=
49
4+9
=
13
1+3
4
-
4
-
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
5
5
-
-
5
-
-
5
-
5
5
-
=
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
23
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
22
-
-
12
-
49
-
22
2+3
1+2
5
5
-
-
5
-
-
5
-
5
5
-
-
-
2+2
-
-
1+2
-
4+9
-
2+2
5
3
E
N
T
A
N
G
L
E
M
E
N
T
-
-
4
-
-
3
-
13
-
4
-
-
5
5
2
1
5
7
3
5
4
5
5
2
-
-
-
-
-
-
-
1+3
-
-
5
3
E
N
T
A
N
G
L
E
M
E
N
T
-
-
4
-
-
3
-
4
-
4

 

 

12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
5
-
+
=
15
1+5
=
6
-
6
-
6
-
-
14
-
-
14
-
-
-
-
-
14
-
+
=
42
4+2
=
6
-
6
-
6
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
5
-
2
1
-
7
3
5
4
5
-
2
+
=
34
3+4
=
7
-
7
-
7
-
5
-
20
1
-
7
12
5
13
5
-
20
+
=
88
8+8
=
16
1+6
7
-
7
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
--
-
-
-
-
-
5
14
20
1
14
7
12
5
13
5
14
20
+
=
130
1+3+0
=
4
-
4
-
4
-
5
5
2
1
5
7
3
5
4
5
5
2
+
=
49
4+9
=
13
1+3
4
-
4
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
4
=
5
5
-
-
5
-
-
5
-
5
5
-
=
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
12
E
N
T
A
N
G
L
E
M
E
N
T
-
-
22
-
-
12
-
49
-
22
1+2
5
5
2
1
5
7
3
5
4
5
5
2
-
-
2+2
-
-
1+2
-
4+9
-
2+2
3
E
N
T
A
N
G
L
E
M
E
N
T
-
-
4
-
-
3
-
13
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+3
-
-
3
E
N
T
A
N
G
L
E
M
E
N
T
-
-
4
-
-
3
-
4
-
4

 

 

-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
5
-
1
+
=
16
1+6
=
7
-
7
-
7
-
-
-
14
-
-
14
-
-
-
-
-
14
-
19
+
=
61
6+1
=
7
-
7
-
7
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
5
-
2
1
-
7
3
5
4
5
-
2
-
+
=
34
3+4
=
7
-
7
-
7
-
-
5
-
20
1
-
7
12
5
13
5
-
20
-
+
=
88
8+8
=
16
1+6
7
-
7
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
5
14
20
1
14
7
12
5
13
5
14
20
19
+
=
149
1+4+9
=
14
1+4
5
-
5
-
-
5
5
2
1
5
7
3
5
4
5
5
2
1
+
=
50
5+0
=
5
-
5
-
5
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
5
5
-
-
5
-
-
5
-
5
5
-
-
=
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
23
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
22
-
-
13
-
50
-
23
2+3
1+3
5
5
-
-
5
-
-
5
-
5
5
-
-
-
-
2+2
-
-
1+3
-
5+0
-
2+3
5
4
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
4
-
-
4
-
5
-
5
-
-
5
5
2
1
5
7
3
5
4
5
5
2
1
-
-
-
-
-
-
-
-
-
-
5
4
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
4
-
-
4
-
5
-
5

 

 

-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
-
5
-
-
-
-
-
5
-
1
+
=
16
1+6
=
7
-
7
-
7
-
-
-
14
-
-
14
-
-
-
-
-
14
-
19
+
=
61
6+1
=
7
-
7
-
7
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
5
-
2
1
-
7
3
5
4
5
-
2
-
+
=
34
3+4
=
7
-
7
-
7
-
-
5
-
20
1
-
7
12
5
13
5
-
20
-
+
=
88
8+8
=
16
1+6
7
-
7
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
--
-
-
-
-
-
-
5
14
20
1
14
7
12
5
13
5
14
20
19
+
=
149
1+4+9
=
14
1+4
5
-
5
-
-
5
5
2
1
5
7
3
5
4
5
5
2
1
+
=
50
5+0
=
5
-
5
-
5
-
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
-
4
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
5
5
-
-
5
-
-
5
-
5
5
-
-
=
-
5
occurs
x
6
=
30
3+0
3
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
23
13
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
22
-
-
13
-
50
-
23
2+3
1+3
5
5
-
-
5
-
-
5
-
5
5
-
-
-
-
2+2
-
-
1+3
-
5+0
-
2+3
5
4
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
4
-
-
4
-
5
-
5
-
-
5
5
2
1
5
7
3
5
4
5
5
2
1
-
-
-
-
-
-
-
-
-
-
5
4
E
N
T
A
N
G
L
E
M
E
N
T
S
-
-
4
-
-
4
-
5
-
5

 

 

I

ME

YOU

ENTANGLEMENTS

MENTAL ANGLE ANGEL ANGLE MENTAL

ENTANGLE MENTALLY MENTALLY ENTANGLE

KARMAS THOUGHT ENTANGLEMENT THOUGHT KARMAS

0123456789 REAL REALITY REVEALED REALITY REAL 9876543210

0987654321 GODS REAL REALITY REAL GODS 1234567890

ONE GOD ONE I ONE ME ONE YOU ONE EVERYTHING GODS

INTO THE WITHIN OF THE WITHOUT THAT IS UNIVERSAL MIND OF DIVINE THOUGHT

ABCDEFGHIJKLMNOPQRSTUVWXYZ WELCOME HERO WELCOME ABCDEFGHIJKLMNOPQRSTUVWXYZ

 

 

THE CLOCKS ALL SAY THE HOURS OF HORUS HAVE ARRIVED UPON US

AND THE DICE ALL READ FIVE

LIVING FORM FROM OUT THE IN OF GODS LIVING FORM

 

 

-
20
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
9
5
-
-
-
-
-
9
5
-
9
-
-
-
+
=
42
4+2
=
6
=
6
-
6
-
-
-
14
-
-
-
-
-
9
14
-
-
-
-
-
9
14
-
9
-
-
-
+
=
69
6+9
=
15
1+5
6
-
6
-
20
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
3
5
9
2
1
-
-
2
7
-
7
9
-
-
3
-
7
3
5
+
=
66
6+6
=
12
1+2
3
-
3
-
-
21
-
3
5
18
20
1
-
-
20
25
-
16
18
-
-
3
-
16
12
5
+
=
183
1+8+3
=
12
1+2
3
-
3
-
20
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
-
-
-
-
-
-
-
-
-
-
21
14
3
5
18
20
1
9
14
20
25
-
16
18
9
14
3
9
16
12
5
+
=
252
2+5+2
=
9
-
9
-
9
-
-
3
5
3
5
9
2
1
9
5
2
7
-
7
9
9
5
3
9
7
3
5
+
=
108
1+0+8
=
9
-
9
-
9
-
20
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
occurs
x
2
=
4
-
4
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
-
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
7
-
-
-
-
-
7
-
-
-
-
7
occurs
x
3
=
21
2+1
3
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
-
9
9
-
-
9
-
-
-
-
-
9
occurs
x
5
=
45
4+5
9
18
20
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
27
-
-
20
-
108
-
27
1+8
2+0
-
-
-
-
9
-
-
9
-
-
-
-
-
9
9
-
-
9
-
-
-
-
-
2+7
-
-
2+0
-
1+0+8
-
2+7
9
2
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
9
-
-
2
-
9
-
9
-
-
3
5
3
5
9
2
1
9
5
2
7
-
7
9
9
5
3
9
7
3
5
-
-
-
-
-
-
-
-
-
-
9
2
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
9
-
-
2
-
9
-
9

 

 

20
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
9
5
-
-
-
-
-
9
5
-
9
-
-
-
+
=
42
4+2
=
6
=
6
-
6
-
-
14
-
-
-
-
-
9
14
-
-
-
-
-
9
14
-
9
-
-
-
+
=
69
6+9
=
15
1+5
6
-
6
20
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
-
-
-
-
-
-
-
-
-
3
-
3
5
9
2
1
-
-
2
7
-
7
9
-
-
3
-
7
3
5
+
=
66
6+6
=
12
1+2
3
-
3
-
21
-
3
5
18
20
1
-
-
20
25
-
16
18
-
-
3
-
16
12
5
+
=
183
1+8+3
=
12
1+2
3
-
3
20
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
-
-
-
-
-
-
-
-
-
21
14
3
5
18
20
1
9
14
20
25
-
16
18
9
14
3
9
16
12
5
+
=
252
2+5+2
=
9
-
9
-
9
-
3
5
3
5
9
2
1
9
5
2
7
-
7
9
9
5
3
9
7
3
5
+
=
108
1+0+8
=
9
-
9
-
9
20
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
occurs
x
2
=
4
-
4
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
5
-
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
-
-
-
-
-
-
-
-
7
-
7
-
-
-
-
-
7
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
9
-
-
9
-
-
-
-
-
9
9
-
-
9
-
-
-
-
-
9
occurs
x
5
=
45
4+5
9
20
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
27
-
-
20
-
108
-
27
2+0
-
-
-
-
9
-
-
9
-
-
-
-
-
9
9
-
-
9
-
-
-
-
-
2+7
-
-
2+0
-
1+0+8
-
2+7
2
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
9
-
-
2
-
9
-
9
-
3
5
3
5
9
2
1
9
5
2
7
-
7
9
9
5
3
9
7
3
5
-
-
-
-
-
-
-
-
-
-
2
U
N
C
E
R
T
A
I
N
T
Y
-
P
R
I
N
C
I
P
L
E
-
-
9
-
-
2
-
9
-
9

 

 

5
SPACE
44
17
8
3
AND
19
10
1
4
TIME
47
20
2

 

 

-
9
S
P
A
C
E
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
-
-
-
-
9
-
-
+
=
10
1+0
=
1
=
1
=
1
-
-
19
-
-
-
-
-
-
9
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
9
S
P
A
C
E
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
-
7
1
3
5
-
2
-
4
5
+
=
27
2+7
=
9
=
9
=
9
-
-
-
16
1
3
5
-
20
-
13
5
+
=
63
6+3
=
9
=
9
=
9
-
9
S
P
A
C
E
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
19
16
1
3
5
-
20
9
13
5
+
=
91
9+1
=
10
1+0
1
=
1
-
-
1
7
1
3
5
-
2
9
4
5
+
=
37
3+7
=
10
1+0
1
=
1
-
9
S
P
A
C
E
-
T
I
M
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
14
9
S
P
A
C
E
-
T
I
M
E
-
-
31
-
-
9
-
37
-
28
1+4
-
-
-
-
-
-
-
-
9
-
-
-
-
3+1
-
-
-
-
3+7
-
2+8
5
9
S
P
A
C
E
-
T
I
M
E
-
-
4
-
-
9
-
10
-
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
1+0
5
9
S
P
A
C
E
-
T
I
M
E
-
-
4
-
-
9
-
1
-
1

 

 

-
9
S
P
A
C
E
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
-
-
-
-
9
-
-
+
=
10
1+0
=
1
=
1
=
1
-
-
19
-
-
-
-
-
-
9
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
9
S
P
A
C
E
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
-
7
1
3
5
-
2
-
4
5
+
=
27
2+7
=
9
=
9
=
9
-
-
-
16
1
3
5
-
20
-
13
5
+
=
63
6+3
=
9
=
9
=
9
-
9
S
P
A
C
E
-
T
I
M
E
-
-
-
-
-
--
-
-
-
-
-
-
19
16
1
3
5
-
20
9
13
5
+
=
91
9+1
=
10
1+0
1
=
1
-
-
1
7
1
3
5
-
2
9
4
5
+
=
37
3+7
=
10
1+0
1
=
1
-
9
S
P
A
C
E
-
T
I
M
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
14
9
S
P
A
C
E
-
T
I
M
E
-
-
31
-
-
9
-
37
-
28
1+4
-
-
-
-
-
-
-
-
9
-
-
-
-
3+1
-
-
-
-
3+7
-
2+8
5
9
S
P
A
C
E
-
T
I
M
E
-
-
4
-
-
9
-
10
-
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
1+0
5
9
S
P
A
C
E
-
T
I
M
E
-
-
4
-
-
9
-
1
-
1

 

6
ENERGY
74
38
2
8
ENERGIES
82
46
1

 

 

5
FORCE
47
29
2
6
FORCES
66
30
3

 

 

4
HEAT
34
16
7
5
LIGHT
56
29
2
9
Add to Reduce
90
45
9
-
Reduce to Deduce
9+0
4+5
-
9
Essence of Number
9
9
9

 

 

20
ELECTROMAGNETIC LIGHT
206
98
8
-
-
-
-
-
21
ELECTROMAGNETIC LIGHTS
-
-
-
-
E+L+E+C+T
45
18
9
-
R
18
9
9
-
O+M+A+G
36
18
9
-
N+E+T
39
12
3
-
I
9
9
9
-
C
3
3
3
-
L
12
3
3
-
I
9
9
9
-
G+H+T+S
54
18
9
21
ELECTROMAGNETIC LIGHTS
225
99
63
2+0
-
2+2+5
9+9
6+3
21
ELECTROMAGNETIC LIGHTS
9
18
9
1+0
-
-
1+8
-
21
ELECTROMAGNETIC LIGHTS
9
9
9

 

 

Q
=
8
=
7
QUANTUM
107
26
8
E
=
5
=
7
ELECTRO
78
33
6
G
=
7
=
8
DYNAMICS
88
34
7
-
-
20
-
22
First Total
273
93
21
-
-
2+0
-
2+2
Add to Reduce
2+7+3
9+3
2+1
-
-
2
-
4
Second Total
12
12
3
-
-
-
-
-
Reduce to Deduce
1+2
1+2
-
-
-
2
-
4
Essence of Number
3
3
3

 

 

E
=
5
=
7
ELECTRO
78
33
6
M
=
4
=
8
MAGNETIC
78
33
6
F
=
6
=
6
FORCES
66
30
3
-
-
15
-
22
First Total
216
93
21
-
-
1+5
-
2+1
Add to Reduce
2+1+6
9+3
2+1
-
-
6
-
3
Second Total
9
12
9
-
-
-
-
-
Reduce to Deduce
1+2
1+2
-
-
-
6
-
3
Essence of Number
9
9
9

 

 

-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
11
-
16
GEO MAGNETIC FIELD
135
81
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
-
-
18
-
3
-
27
18
18
-
-
-
-
-
-
-
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
8
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
11
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
-
36
-
8
-
72
36
36
-
-
-
-
-
-
-
-
-
-
F
=
6
12
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
13
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
L
=
3
15
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
D
=
5
16
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
27
-
5
-
36
27
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
6
8
20
12
7
8
18
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
2+0
1+2
-
-
1+8
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
6
8
2
3
7
8
9
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
17
-
16
GEO MAGNETIC FIELD
135
81
27
-
1
2
6
8
2
3
7
8
9
-
-
1+7
-
1+6
-
1+3+5
8+1
2+7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
GEO MAGNETIC FIELD
9
9
9
-
1
2
6
8
2
3
7
8
9

 

 

-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
11
-
16
GEO MAGNETIC FIELD
135
81
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
8
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
11
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
F
=
6
12
1
F
6
6
6
-
-
-
-
-
-
6
-
8
-
I
=
9
13
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
L
=
3
15
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
D
=
5
16
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
6
8
20
12
7
8
18
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
2+0
1+2
-
-
1+8
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
6
8
2
3
7
8
9
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
17
-
16
GEO MAGNETIC FIELD
135
81
27
-
1
2
6
8
2
3
7
8
9
-
-
1+7
-
1+6
-
1+3+5
8+1
2+7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
GEO MAGNETIC FIELD
9
9
9
-
1
2
6
8
2
3
7
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

5 x 4 = 40

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 4 = 20

 

-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
11
-
16
GEO MAGNETIC FIELD
135
81
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
C
=
3
11
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
15
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
D
=
5
16
1
D
4
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
7
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
8
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
F
=
6
12
1
F
6
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
I
=
9
13
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
-
1
2
6
8
20
12
7
8
18
G
=
7
=
3
GEO
27
18
9
-
-
-
-
-
2+0
1+2
-
-
1+8
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
6
8
2
3
7
8
9
F
=
6
=
5
FIELD
36
27
9
-
-
-
-
-
-
-
-
-
-
-
-
17
-
16
GEO MAGNETIC FIELD
135
81
27
-
1
2
6
8
2
3
7
8
9
-
-
1+7
-
1+6
-
1+3+5
8+1
2+7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
7
GEO MAGNETIC FIELD
9
9
9
-
1
2
6
8
2
3
7
8
9

 

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
E
=
5
=
7
ELECTRO
78
33
6
M
=
4
=
8
MAGNETIC
72
36
9
E
=
5
=
6
ENERGY
74
38
2
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8

 

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
-
-
33
-
7
-
78
33
33
-
-
-
-
-
-
-
-
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
10
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
15
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
-
36
-
8
-
72
36
36
-
-
-
-
-
-
-
-
-
-
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
17
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
19
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
20
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
21
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
38
-
6
-
74
38
38
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
4
9
4
35
6
21
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
3+5
-
2+1
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
4
9
4
8
6
3
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
4
9
4
8
6
3
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
4
9
4
8
6
3
8
9

 

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
7
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
G
=
7
10
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
15
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
16
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
17
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
18
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
R
=
9
19
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
G
=
7
20
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
Y
=
7
21
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
4
9
4
35
6
21
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
3+5
-
2+1
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
4
9
4
8
6
3
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
4
9
4
8
6
3
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
4
9
4
8
6
3
8
9

 

LETTERS TRANSPOSED INTO NUMBERS REARRANGED IN NUMERICAL ORDER

5 x 7 = 35

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 7 = 35

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
-
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
-
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
-
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
4
9
4
35
6
21
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
3+5
-
2+1
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
4
9
4
8
6
3
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
4
9
4
8
6
3
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
4
9
4
8
6
3
8
9

 

ELECTRO MAGNETIC ENERGY

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
E
=
5
=
7
ELECTRO
78
33
6
M
=
4
=
8
MAGNETIC
72
36
9
E
=
5
=
6
ENERGY
74
38
2
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8

 

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
1
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
-
-
-
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
4
2
C+T
23
3
3
-
-
-
-
-
5
-
-
-
-
-
-
-
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
7
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
-
27
18
18
-
-
-
-
-
-
-
-
-
-
-
-
-
8
2
M+A
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
10
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
-
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
12
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
13
3
T+I+C
32
14
5
-
-
-
-
-
5
-
-
-
-
-
-
-
8
-
72
36
36
-
-
-
-
-
-
-
-
-
-
-
-
-
16
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
17
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
18
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
19
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
20
1
G+Y
32
14
5
-
-
-
-
-
5
-
-
-
-
-
-
5
-
36
27
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
55
6
7
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
5+5
-
-
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
3
4
10
6
7
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
1+0
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
2
3
4
1
6
7
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
2
9
4
1
6
7
8
9

 

5 x 11 = 55

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 11 = 55

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
5
1
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
3
2
1
L
12
3
3
-
1
2
3
-
-
-
-
8
-
-
-
5
3
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
3
4
1
C+T
23
3
3
-
1
2
-
-
5
-
-
8
-
-
-
-
6
1
R
18
9
9
-
1
2
-
-
-
-
-
8
9
-
-
-
7
1
O
15
6
6
-
1
2
-
-
-
6
-
8
-
-
-
-
8
1
M+A
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
10
1
G
7
7
7
-
1
2
-
-
-
-
7
8
-
-
-
-
11
1
N
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
12
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
13
1
T+I+C
32
14
5
-
1
2
-
-
5
-
-
8
-
-
-
-
16
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
17
1
N
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
18
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
19
1
R
18
9
9
-
1
2
-
-
-
-
-
8
9
-
-
-
20
1
G+Y
32
14
5
-
1
2
-
-
5
-
-
8
-
-
5
-
36
27
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
55
6
7
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
5+5
-
-
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
3
4
10
6
7
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
1+0
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
2
3
4
1
6
7
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
2
9
4
1
6
7
8
9

 

5 x 11 = 55

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 11 = 55

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
3
2
1
L
12
3
3
-
1
2
3
-
-
-
-
8
-
-
-
5
1
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
5
3
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
3
4
1
C+T
23
3
3
-
1
2
-
-
5
-
-
8
-
-
-
-
8
1
M+A
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
11
1
N
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
12
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
13
1
T+I+C
32
14
5
-
1
2
-
-
5
-
-
8
-
-
-
-
16
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
17
1
N
14
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
18
1
E
5
5
5
-
1
2
-
-
5
-
-
8
-
-
-
-
20
1
G+Y
32
14
5
-
1
2
-
-
5
-
-
8
-
-
-
-
7
1
O
15
6
6
-
1
2
-
-
-
6
-
8
-
-
-
-
10
1
G
7
7
7
-
1
2
-
-
-
-
7
8
-
-
-
-
19
1
R
18
9
9
-
1
2
-
-
-
-
-
8
9
-
-
-
6
1
R
18
9
9
-
1
2
-
-
-
-
-
8
9
-
5
-
36
27
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
1
2
3
4
55
6
7
8
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
5+5
-
-
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
1
2
3
4
10
6
7
8
9
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
1+0
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
1
2
3
4
1
6
7
8
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
1
2
9
4
1
6
7
8
9

 

5 x 11 = 55

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 11 = 55

 

-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
3
5
6
7
9
E
=
5
=
7
ELECTRO
78
33
6
-
-
-
-
-
-
M
=
4
=
8
MAGNETIC
72
36
9
-
-
-
-
-
-
E
=
5
=
6
ENERGY
74
38
2
-
-
-
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
5
6
7
9
-
-
3
2
1
L
12
3
3
-
3
-
-
-
-
-
-
5
1
1
E
5
5
5
-
-
5
-
-
-
-
-
5
3
1
E
5
5
5
-
-
5
-
-
-
-
-
3
4
1
C+T
23
3
3
-
-
5
-
-
-
-
-
-
8
1
M+A
14
5
5
-
-
5
-
-
-
-
-
-
11
1
N
14
5
5
-
-
5
-
-
-
-
-
-
12
1
E
5
5
5
-
-
5
-
-
-
-
-
-
13
1
T+I+C
32
14
5
-
-
5
-
-
-
-
-
-
16
1
E
5
5
5
-
-
5
-
-
-
-
-
-
17
1
N
14
5
5
-
-
5
-
-
-
-
-
-
18
1
E
5
5
5
-
-
5
-
-
-
-
-
-
20
1
G+Y
32
14
5
-
-
5
-
-
-
-
-
-
7
1
O
15
6
6
-
-
-
6
-
-
-
-
-
10
1
G
7
7
7
-
-
-
-
7
-
-
-
-
19
1
R
18
9
9
-
-
-
-
-
9
-
-
-
6
1
R
18
9
9
-
-
-
-
-
9
-
5
-
36
27
27
-
-
-
-
-
-
-
-
-
-
-
ELECTRO MAGNETIC ENERGY
-
-
-
-
3
55
6
7
27
E
=
5
=
7
ELECTRO
78
33
6
-
-
5+5
-
-
2+7
M
=
4
=
8
MAGNETIC
72
36
9
-
3
10
6
7
9
E
=
5
=
6
ENERGY
74
38
2
-
-
1+0
-
-
-
-
-
14
-
21
ELECTRO MAGNETIC ENERGY
224
107
17
-
3
1
6
7
9
-
-
1+4
-
2+1
-
2+2+4
1+0+7
1+7
-
-
-
-
-
-
-
-
5
-
3
ELECTRO MAGNETIC ENERGY
8
8
8
-
9
1
6
7
9

5 x 11 = 55

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 11 = 55

 

-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
9
-
-
-
5
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
15
-
9
-
-
-
14
-
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
2
-
4
-
3
-
5
-
5
9
7
7
+
=
43
4+3
=
5
=
7
=
7
-
-
1
20
-
13
-
3
-
5
-
5
18
7
25
+
=
97
9+7
=
16
1+6
7
=
7
-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
20
15
13
9
3
-
5
14
5
18
7
25
+
=
135
1+3+5
=
9
=
9
=
9
-
-
1
2
6
4
9
3
-
5
5
5
9
7
7
+
=
63
6+3
=
9
=
9
=
9
-
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
--
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
1+2
6
-
--
--
--
--
--
--
--
--
-
-
-
-
7
7
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
37
-
-
12
-
63
-
36
-
1+2
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
3+7
-
-
1+2
-
6+3
-
3+6
8
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
10
-
-
3
-
9
-
9
-
--
1
2
6
4
9
3
-
5
5
5
9
7
7
-
-
1+0
-
-
--
-
-
-
-
8
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
1
-
-
3
-
9
-
9

 

 

12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
--
-
-
-
-
-
-
-
6
-
9
-
-
-
5
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
15
-
9
-
-
-
14
-
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
1
2
-
4
-
3
-
5
-
5
9
7
7
+
=
43
4+3
=
5
=
7
=
7
-
1
20
-
13
-
3
-
5
-
5
18
7
25
+
=
97
9+7
=
16
1+6
7
=
7
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
1
20
15
13
9
3
-
5
14
5
18
7
25
+
=
135
1+3+5
=
9
=
9
=
9
-
1
2
6
4
9
3
-
5
5
5
9
7
7
+
=
63
6+3
=
9
=
9
=
9
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
--
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
1+2
6
--
--
--
--
--
--
--
--
-
-
-
-
7
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
37
-
-
12
-
63
-
36
1+2
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
3+7
-
-
1+2
-
6+3
-
3+6
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
10
-
-
3
-
9
-
9
--
1
2
6
4
9
3
-
5
5
5
9
7
7
-
-
1+0
-
-
--
-
-
-
-
3
A
T
O
M
I
C
-
E
N
E
R
G
Y
-
-
1
-
-
3
-
9
-
9

 

 

-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
9
-
-
5
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
15
-
9
-
-
14
-
-
-
-
+
=
38
3+8
=
11
1+1
2
=
2
-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
2
-
4
-
3
5
-
5
9
7
7
+
=
43
4+3
=
5
=
7
=
7
-
-
1
20
-
13
-
3
5
-
5
18
7
25
+
=
97
9+7
=
16
1+6
7
=
7
-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
-
--
-
-
-
-
-
-
1
20
15
13
9
3
5
14
5
18
7
25
+
=
135
1+3+5
=
9
=
9
=
9
-
-
1
2
6
4
9
3
5
5
5
9
7
7
+
=
63
6+3
=
9
=
9
=
9
-
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
--
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
1+2
6
-
--
--
--
--
--
--
--
-
-
-
-
7
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
12
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
37
-
-
12
-
63
-
36
-
1+2
-
-
-
-
-
-
5
5
5
-
-
-
-
-
3+7
-
-
1+2
-
6+3
-
3+6
8
3
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
10
-
-
3
-
9
-
9
-
--
1
2
6
4
9
3
5
5
5
9
7
7
-
-
1+0
-
-
--
-
-
-
-
8
3
A
T
O
M
I
C
E
N
E
R
G
Y
-
-
1
-
-
3
-
9
-
9

 

 

S
=
1
-
9
SPLITTING
126
45
9
T
=
2
-
3
THE
33
15
6
A
=
1
-
4
ATOM
49
13
4
B
-
4
4
16
First Total
208
73
19
-
-
-
-
1+6
Add to Reduce
2+0+8
7+3
1+9
-
-
7
-
7
Second Total
10
10
10
8
-
-
-
-
Reduce to Deduce
1+0
1+0
1+0
-
-
7
-
7
Essence of Number
1
1
1

 

 

-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
38
-
1
-
-
9
-
-
9
5
-
-
-
8
-
-
-
-
6
-
+
=
38
3+8
=
11
1+1
2
=
2
83
-
19
-
-
9
-
-
9
14
-
-
-
8
-
-
-
-
15
-
+
=
74
8+3
=
11
1+1
2
=
2
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
25
-
-
7
3
-
2
2
-
-
7
-
2
-
5
-
1
2
-
4
+
=
35
3+5
=
8
=
8
=
8
79
-
-
16
12
-
20
20
-
-
7
-
20
-
5
-
1
20
-
13
+
=
134
1+3+4
=
8
=
8
=
8
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
208
-
19
16
12
9
20
20
9
14
7
-
20
8
5
-
1
20
15
13
+
=
208
2+0+8
=
10
1+0
1
=
1
73
-
1
7
3
9
2
2
9
5
7
-
2
8
5
-
1
2
6
4
+
=
73
7+3
=
10
1+0
1
=
1
-
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
``-
-
-
-
-
2
2
-
-
-
-
2
-
-
-
-
2
-
-
-
-
2
occurs
x
4
=
8
=
8
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
9
-
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
16
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
45
-
-
16
-
73
-
46
4+5
1+6
-
-
-
-
2
2
-
-
-
-
2
-
-
-
-
2
-
-
-
-
4+5
-
-
1+6
-
7+3
-
4+6
9
7
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
9
-
-
7
-
10
-
10
-
-
1
7
3
9
2
2
9
5
7
-
2
8
5
-
1
2
6
3
-
-
-
-
-
-
-
1+0
-
1+0
6
7
S
P
L
I
T
T
I
N
G
-
T
H
E
-
A
T
O
M
-
-
6
-
-
7
-
1
-
1

 

 

NUCLEAR UNCLEAR

 

 

-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
-
38
-
1
-
-
9
-
-
9
5
-
-
8
-
-
-
6
-
+
=
38
3+8
=
11
1+1
2
=
2
83
-
19
-
-
9
-
-
9
14
-
-
8
-
-
-
15
-
+
=
74
8+3
=
11
1+1
2
=
2
-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
-
25
-
-
7
3
-
2
2
-
-
7
2
-
5
1
2
-
4
+
=
35
3+5
=
8
=
8
=
8
79
-
-
16
12
-
20
20
-
-
7
20
-
5
1
20
-
13
+
=
134
1+3+4
=
8
=
8
=
8
-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
-
208
-
19
16
12
9
20
20
9
14
7
20
8
5
1
20
15
13
+
=
208
2+0+8
=
10
1+0
1
=
1
73
-
1
7
3
9
2
2
9
5
7
2
8
5
1
2
6
4
+
=
73
7+3
=
10
1+0
1
=
1
-
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
``-
-
-
-
-
2
2
-
-
-
2
-
-
-
2
-
-
-
-
2
occurs
x
4
=
8
=
8
3
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
9
-
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
16
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
45
-
-
16
-
73
-
46
4+5
1+6
-
-
-
-
2
2
-
-
-
2
-
-
-
2
-
-
-
-
4+5
-
-
1+6
-
7+3
-
4+6
9
7
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
9
-
-
7
-
10
-
10
-
-
1
7
3
9
2
2
9
5
7
2
8
5
1
2
6
3
-
-
-
-
-
-
-
1+0
-
1+0
6
7
S
P
L
I
T
T
I
N
G
T
H
E
A
T
O
M
-
-
6
-
-
7
-
1
-
1

 

 

-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
-
6
-
+
=
6
-
=
6
=
6
-
-
-
-
15
-
+
=
15
1+5
=
6
=
6
-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
1
2
-
4
+
=
7
-
=
7
=
7
-
-
1
20
-
13
+
=
34
3+4
=
7
=
7
-
4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
1
20
15
13
+
=
49
4+9
=
13
1+3
4
-
-
1
2
6
4
+
=
13
1+3
=
4
=
4
-
4
A
T
O
M
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
4
A
T
O
M
-
-
13
-
-
4
-
13
3+2
-
-
-
-
-
-
-
1+3
-
-
-
-
1+3
5
4
A
T
O
M
-
-
4
-
-
4
-
4
-
-
1
2
6
4
-
-
-
-
-
-
-
-
5
4
A
T
O
M
-
-
4
-
-
4
-
4

 

 

4
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
6
-
+
=
6
-
=
6
=
6
-
-
-
15
-
+
=
15
1+5
=
6
=
6
4
A
T
O
M
-
-
-
-
-
--
-
-
-
1
2
-
4
+
=
7
-
=
7
=
7
-
1
20
-
13
+
=
34
3+4
=
7
=
7
4
A
T
O
M
-
-
-
-
-
--
-
-
-
1
20
15
13
+
=
49
4+9
=
13
1+3
4
-
1
2
6
4
+
=
13
1+3
=
4
=
4
4
A
T
O
M
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
6
-
-
-
6
occurs
x
1
=
6
4
A
T
O
M
-
-
13
-
-
4
-
13
-
-
-
-
-
-
-
1+3
-
-
-
-
1+3
4
A
T
O
M
-
-
4
-
-
4
-
4
-
1
2
6
4
-
-
-
-
-
-
-
-
4
A
T
O
M
-
-
4
-
-
4
-
4

 

 

-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
-
-
6
-
1
+
=
7
-
=
7
=
7
-
-
-
-
15
-
19
+
=
34
3+4
=
7
=
7
-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
1
2
-
4
-
+
=
7
-
=
7
=
7
-
-
1
20
-
13
-
+
=
34
3+4
=
7
=
7
-
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
1
20
15
13
19
+
=
68
6+8
=
14
1+4
5
-
-
1
2
6
4
1
+
=
14
1+4
=
5
=
5
-
5
A
T
O
M
S
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
32
5
A
T
O
M
S
-
-
13
-
-
5
-
14
3+2
-
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
5
5
A
T
O
M
S
-
-
4
-
-
5
-
5
-
-
1
2
6
4
1
-
-
-
-
-
-
-
-
5
5
A
T
O
M
S
-
-
4
-
-
5
-
5

 

 
A
T
O
M
S
-
-
-
-
-
--
-
-
-
-
-
6
-
1
+
=
7
-
=
7
=
7
-
-
-
15
-
19
+
=
34
3+4
=
7
=
7
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
1
2
-
4
-
+
=
7
-
=
7
=
7
-
1
20
-
13
-
+
=
34
3+4
=
7
=
7
5
A
T
O
M
S
-
-
-
-
-
--
-
-
-
1
20
15
13
19
+
=
68
6+8
=
14
1+4
5
-
1
2
6
4
1
+
=
14
1+4
=
5
=
5
5
A
T
O
M
S
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
2
=
2
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
5
A
T
O
M
S
-
-
13
-
-
5
-
14
-
-
-
-
-
-
-
-
1+3
-
-
-
-
1+4
5
A
T
O
M
S
-
-
4
-
-
5
-
5
-
1
2
6
4
1
-
-
-
-
-
-
-
-
5
A
T
O
M
S
-
-
4
-
-
5
-
5

 

 

-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
-
8
-
-
-
-
6
-
+
=
14
1+4
=
5
=
5
-
-
-
8
-
-
-
-
15
-
+
=
23
2+3
=
5
=
5
-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
2
-
5
-
1
2
-
4
+
=
14
1+4
=
5
=
5
-
-
20
-
5
-
1
20
-
13
+
=
59
5+9
=
14
1+4
5
-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
20
8
5
-
1
20
15
13
+
=
82
8+2
=
10
1+0
1
-
-
2
8
5
-
1
2
6
4
+
=
28
2+8
=
10
1+0
1
-
7
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
3
-
-
-
-
-
-
--
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
7
-
-
--
--
--
--
--
--
--
-
-
7
SEVEN
7
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
19
7
T
H
E
-
A
T
O
M
-
-
26
-
-
7
-
28
1+9
-
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+8
10
7
T
H
E
-
A
T
O
M
-
-
8
-
-
7
-
10
1+0
-
2
8
5
-
1
2
6
4
-
-
-
-
-
-
-
1+0
1
7
T
H
E
-
A
T
O
M
-
-
8
-
-
4
-
1

 

 

7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
-
8
-
-
-
-
6
-
+
=
14
1+4
=
5
=
5
-
-
8
-
-
-
-
15
-
+
=
23
2+3
=
5
=
5
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
2
-
5
-
1
2
-
4
+
=
14
1+4
=
5
=
5
-
20
-
5
-
1
20
-
13
+
=
59
5+9
=
14
1+4
5
7
T
H
E
-
A
T
O
M
-
-
-
-
-
--
-
-
-
20
8
5
-
1
20
15
13
+
=
82
8+2
=
10
1+0
1
-
2
8
5
-
1
2
6
4
+
=
28
2+8
=
10
1+0
1
7
T
H
E
-
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
2
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
7
T
H
E
-
A
T
O
M
-
-
26
-
-
7
-
28
-
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+8
7
T
H
E
-
A
T
O
M
-
-
8
-
-
7
-
10
-
2
8
5
-
1
2
6
4
-
-
-
-
-
-
-
1+0
7
T
H
E
-
A
T
O
M
-
-
8
-
-
4
-
1

 

 

7
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
-
8
-
-
-
6
-
+
=
14
1+4
=
5
=
5
-
-
8
-
-
-
15
-
+
=
23
2+3
=
5
=
5
7
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
2
-
5
1
2
-
4
+
=
14
1+4
=
5
=
5
-
20
-
5
1
20
-
13
+
=
59
5+9
=
14
1+4
5
7
T
H
E
A
T
O
M
-
-
-
-
-
--
-
-
-
20
8
5
1
20
15
13
+
=
82
8+2
=
10
1+0
1
-
2
8
5
1
2
6
4
+
=
28
2+8
=
10
1+0
1
7
T
H
E
A
T
O
M
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
2
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
-
5
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
7
T
H
E
A
T
O
M
-
-
26
-
-
7
-
28
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+8
7
T
H
E
A
T
O
M
-
-
8
-
-
7
-
10
-
2
8
5
1
2
6
4
-
-
-
-
-
-
-
1+0
7
T
H
E
A
T
O
M
-
-
8
-
-
4
-
1

 

 

3
THE
33
15
6
6
ATOMIC
61
25
7
5
MINDS
59
23
5
1
I
9
9
9
15
Add to Reduce
162
72
27
1+5
Reduce to Deduce
1+6+2
7+2
2+7
8
Essence of Number
9
9
9

 

 

-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
6
-
9
-
-
-
9
5
-
1
-
9
+
=
47
4+7
=
11
1+1
2
=
2
-
-
-
8
-
-
-
-
15
-
9
-
-
-
9
14
-
19
-
9
+
=
83
8+3
=
11
1+1
2
=
2
-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
1
2
-
4
-
3
-
4
-
-
4
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
20
-
5
-
1
20
-
13
-
3
-
13
-
-
4
-
-
-
+
=
79
7+9
=
16
1+6
7
=
7
-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
1
20
15
13
9
3
-
13
9
14
4
19
-
9
+
=
162
1+6+2
=
9
=
9
=
9
-
-
2
8
5
-
1
2
6
4
9
3
-
4
9
5
4
1
-
9
+
=
63
6+3
=
9
=
9
=
9
-
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
``-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
4
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
9
occurs
x
3
=
27
 2+7
9
7
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
38
-
-
15
-
63
-
36
-
1+5
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
3+8
-
-
1+5
-
6+3
-
3+6
7
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
11
-
-
6
-
9
-
9
-
-
2
8
5
-
1
2
6
3
9
3
-
3
9
5
4
1
-
9
-
-
1+1
-
-
-
-
-
-
-
7
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
2
-
-
6
-
9
-
9

 

 

5
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
6
-
9
-
-
-
9
5
-
1
-
9
+
=
47
4+7
=
11
1+1
2
=
2
-
-
8
-
-
-
-
15
-
9
-
-
-
9
14
-
19
-
9
+
=
83
8+3
=
11
1+1
2
=
2
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
1
2
-
4
-
3
-
4
-
-
4
-
-
-
+
=
25
2+5
=
7
=
7
=
7
-
20
-
5
-
1
20
-
13
-
3
-
13
-
-
4
-
-
-
+
=
79
7+9
=
16
1+6
7
=
7
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
1
20
15
13
9
3
-
13
9
14
4
19
-
9
+
=
162
1+6+2
=
9
=
9
=
9
-
2
8
5
-
1
2
6
4
9
3
-
4
9
5
4
1
-
9
+
=
63
6+3
=
9
=
9
=
9
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
``-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
4
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
9
occurs
x
3
=
27
 2+7
9
15
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
38
-
-
15
-
63
-
36
1+5
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
3+8
-
-
1+5
-
6+3
-
3+6
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
11
-
-
6
-
9
-
9
-
2
8
5
-
1
2
6
3
9
3
-
3
9
5
4
1
-
9
-
-
1+1
-
-
-
-
-
-
-
6
T
H
E
-
A
T
O
M
I
C
-
M
I
N
D
S
-
I
-
-
2
-
-
6
-
9
-
9

 

 

5
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
6
-
9
-
-
9
5
-
1
9
+
=
47
4+7
=
11
1+1
2
=
2
-
-
8
-
-
-
15
-
9
-
-
9
14
-
19
9
+
=
83
8+3
=
11
1+1
2
=
2
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
--
-
-
-
-
-
2
-
5
1
2
-
4
-
3
4
-
-
4
-
-
+
=
25
2+5
=
7
=
7
=
7
-
20
-
5
1
20
-
13
-
3
13
-
-
4
-
-
+
=
79
7+9
=
16
1+6
7
=
7
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
--
-
-
-
-
-
20
8
5
1
20
15
13
9
3
13
9
14
4
19
9
+
=
162
1+6+2
=
9
=
9
=
9
-
2
8
5
1
2
6
4
9
3
4
9
5
4
1
9
+
=
63
6+3
=
9
=
9
=
9
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
2
=
2
=
2
``-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
4
-
-
4
-
-
4
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
9
-
-
9
occurs
x
3
=
27
 2+7
9
15
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
38
-
-
15
-
63
-
36
1+5
-
-
-
-
-
-
-
9
-
-
9
-
-
-
9
-
-
3+8
-
-
1+5
-
6+3
-
3+6
6
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
11
-
-
6
-
9
-
9
-
2
8
5
1
2
6
3
9
3
3
9
5
4
1
9
-
-
1+1
-
-
-
-
-
-
-
6
T
H
E
A
T
O
M
I
C
M
I
N
D
S
I
-
-
2
-
-
6
-
9
-
9

 

 

A
=
1
-
4
ATOM
49
13
4
C
=
3
-
4
CELL
32
14
5
S
-
4
4
8
Add to Reduce
81
27
9
-
-
-
-
-
Reduce to Deduce
8+1
2+7
-
-
-
4
-
8
Essence of Number
9
9
9

 

 

-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
-
15
-
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
-
1
2
-
4
-
3
5
3
3
+
=
21
2+1
=
3
=
3
=
3
-
-
1
20
-
13
-
3
5
12
12
+
=
66
6+6
=
12
1+2
3
=
3
-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
-
1
20
15
13
--
3
5
12
12
+
=
81
8+1
=
9
=
9
=
9
-
-
1
2
6
4
-
3
5
3
3
+
=
27
2+7
=
9
=
9
=
9
-
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
--
-
-
-
3
-
3
3
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
--
--
--
--
--
--
-
-
-
--
--
7
SEVEN
7
-
-
-
-
-
8
-
--
--
--
--
--
--
-
-
-
--
--
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
--
--
9
NINE
9
-
-
-
-
-
24
8
A
T
O
M
-
C
E
L
L
-
-
21
-
-
8
-
27
-
27
2+4
-
-
-
-
-
-
3
-
3
3
-
-
2+1
-
-
-
-
2+7
-
2+7
6
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9
--
-
1
2
6
4
-
3
5
3
3
-
-
-
-
-
--
-
-
-
-
6
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9

 

 

8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
15
-
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
1
2
-
4
-
3
5
3
3
+
=
21
2+1
=
3
=
3
=
3
-
1
20
-
13
-
3
5
12
12
+
=
66
6+6
=
12
1+2
3
=
3
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
1
20
15
13
--
3
5
12
12
+
=
81
8+1
=
9
=
9
=
9
-
1
2
6
4
-
3
5
3
3
+
=
27
2+7
=
9
=
9
=
9
8
A
T
O
M
-
C
E
L
L
-
-
-
-
-
--
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
--
-
-
-
3
-
3
3
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
8
A
T
O
M
-
C
E
L
L
-
-
21
-
-
8
-
27
-
27
-
-
-
-
-
-
-
-
-
-
-
-
2+1
-
-
-
-
2+7
-
2+7
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9
-
1
2
6
4
-
3
5
3
3
-
-
-
-
-
--
-
-
-
-
8
A
T
O
M
-
C
E
L
L
-
-
3
-
-
8
-
9
-
9

 

 

-
4
C
E
L
L
-
-
-
-
-
--
-
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
-
3
5
3
3
+
=
14
1+4
=
5
=
5
-
4
C
E
L
L
-
-
-
-
-
--
-
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
-
3
5
3
3
+
=
14
1+4
=
5
=
5
-
4
C
E
L
L
T
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-2-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
3
3
-
-
3
occurs
x
3
=
9
4
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
--
-
5
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
--
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
37
4
C
E
L
L
-
-
8
-
-
4
-
14
3+7
-
3
-
3
3
-
-
-
-
-
-
-
1+4
10
4
C
E
L
L
-
-
8
-
-
4
-
5
1+0
-
3
5
3
3
-
-
-
-
-
-
-
-
1
4
C
E
L
L
-
-
8
-
-
4
-
5

 

 

4
C
E
L
L
-
-
-
-
-
--
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
3
5
3
3
+
=
14
1+4
=
5
=
5
4
C
E
L
L
-
-
-
-
-
--
-
-
`-
3
5
12
12
+
=
32
3+2
=
5
=
5
-
3
5
3
3
+
=
14
1+4
=
5
=
5
4
C
E
L
L
T
-
-
-
-
-
-
-
-
3
-
3
3
-
-
3
occurs
x
3
=
9
--
-
5
-
-
-
-
5
occurs
x
1
=
5
4
C
E
L
L
-
-
8
-
-
4
-
14
-
3
-
3
3
-
-
-
-
-
-
-
1+4
4
C
E
L
L
-
-
8
-
-
4
-
5
-
3
5
3
3
-
-
-
-
-
-
-
-
4
C
E
L
L
-
-
8
-
-
4
-
5

 

 

-
5
C
E
L
L
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
+
=
1
-
=
1
=
1
-
`-
-
-
-
-
19
+
=
19
1+9
=
10
1+0
1
-
5
C
E
L
L
S
-
-
-
-
-
--
-
-
-
-
3
5
3
3
-
+
=
14
1+4
=
5
=
5
-
`-
3
5
12
12
-
+
=
32
3+2
=
5
=
5
-
5
C
E
L
L
S
-
-
-
-
-
--
-
-
-
`-
3
5
12
12
19
+
=
51
5+1
=
6
=
6
-
-
3
5
3
3
1
+
=
15
1+5
=
6
=
6
-
5
C
E
L
L
S
T
-
-
-
-
-
-
-
--
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-2-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
3
3
-
-
-
3
occurs
x
3
=
9
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
--
-
5
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
--
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
36
5
C
E
L
L
S
-
-
9
-
-
5
-
15
3+6
-
3
-
3
3
-
-
-
-
-
-
-
-
1+5
9
5
C
E
L
L
S
-
-
9
-
-
5
-
6
-
-
3
5
3
3
1
-
-
-
-
-
-
-
-
9
5
C
E
L
L
S
-
-
9
-
-
5
-
6

 

 

5
C
E
L
L
S
-
-
-
-
-
--
-
-
-
-
-
-
-
1
+
=
1
-
=
1
=
1
`-
-
-
-
-
19
+
=
19
1+9
=
10
1+0
1
5
C
E
L
L
S
-
-
-
-
-
--
-
-
-
3
5
3
3
-
+
=
14
1+4
=
5
=
5
`-
3
5
12
12
-
+
=
32
3+2
=
5
=
5
5
C
E
L
L
S
-
-
-
-
-
--
-
-
`-
3
5
12
12
19
+
=
51
5+1
=
6
=
6
-
3
5
3
3
1
+
=
15
1+5
=
6
=
6
5
C
E
L
L
S
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
3
-
3
3
-
-
-
3
occurs
x
3
=
9
--
-
5
-
-
-
-
-
5
occurs
x
1
=
5
5
C
E
L
L
S
-
-
9
-
-
5
-
15
-
3
-
3
3
-
-
-
-
-
-
-
-
1+5
5
C
E
L
L
S
-
-
9
-
-
5
-
6
-
3
5
3
3
1
-
-
-
-
-
-
-
-
5
C
E
L
L
S
-
-
9
-
-
5
-
6

 

 

4
MIND
40
22
4
6
MATTER
77
23
5
10
Add to Reduce
117
45
9
1+0
Reduce to Deduce
1+1+7
4+5
-
1
Essence of Number
9
9
9

 

 

-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
9
5
-
-
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
9
14
-
-
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
4
-
-
4
-
4
1
2
2
5
9
+
=
31
3+1
=
4
=
4
=
4
-
-
13
-
-
4
-
13
1
20
20
5
18
+
=
94
9+4
=
13
1+3
4
=
4
-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
13
9
14
4
-
13
1
20
20
5
18
+
=
117
1+2
=
9
=
9
=
9
-
-
4
9
5
4
-
4
1
2
2
5
9
+
=
45
1+0
=
9
=
9
=
9
-
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
2
2
-
-
-
-
2
occurs
x
2
=
4
=
4
3
-
--
--
--
--
--
--
--
--
--
--
--
-
-
3
-
-
-
-
-
-
-
-
-`
4
-
-
4
-
4
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
--
--
--
--
--
--
--
--
--
--
-
-
6
--
--
--
--
--
--
--
7
-
-
--
--
--
--
--
--
--
--
--
--
-
-
7
--
--
--
--
--
--
--
8
-
-
--
--
--
--
--
--
--
--
--
--
-
-
8
--
--
--
--
--
--
--
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
24
10
M
I
N
D
-
M
A
T
T
E
R
-
-
21
-
-
10
-
45
-
18
2+4
1+0
-
9
-
-
-
-
-
-
-
-
9
-
-
2+1
-
-
1+0
-
4+5
-
1+8
6
1
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9
-
-
4
9
5
4
-
4
1
2
2
5
9
+
=
45
1+0
=
9
=
9
=
9
6
1
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9

 

 

10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
9
5
-
-
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
9
14
-
-
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
4
-
-
4
-
4
1
2
2
5
9
+
=
31
3+1
=
4
=
4
=
4
-
13
-
-
4
-
13
1
20
20
5
18
+
=
94
9+4
=
13
1+3
4
=
4
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
13
9
14
4
-
13
1
20
20
5
18
+
=
117
1+2
=
9
=
9
=
9
-
4
9
5
4
-
4
1
2
2
5
9
+
=
45
1+0
=
9
=
9
=
9
10
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
2
2
-
-
-
-
2
occurs
x
2
=
4
=
4
-
4
-
-
4
-
4
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
10
M
I
N
D
-
M
A
T
T
E
R
-
-
21
-
-
10
-
45
-
18
1+0
-
9
-
-
-
-
-
-
-
-
9
-
-
2+1
-
-
1+0
-
4+5
-
1+8
1
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9
-
4
9
5
4
-
4
1
2
2
5
9
+
=
45
1+0
=
9
=
9
=
9
1
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
1
-
9
-
9

 

 

-
MIND MATTER
-
-
-
1
M
13
4
4
1
I
9
9
9
2
ND
18
9
9
2
MA
14
5
5
3
TTE
45
9
9
1
R
18
9
9
10
MATTER MIND
117
45
45
1+0
1+1+7
4+5
4+5
1
MIND MATTER
9
9
9

 

 

-
-
-
-
-
MATTER ANTI MATTER
-
-
-
M
=
4
-
3
MATTER
77
23
5
A
=
1
-
7
ANTI
44
17
8
M
=
4
--
5
MATTER
77
23
5
-
-
9
-
15
MATTER ANTI MATTER
198
63
18
-
-
-
-
1+5
-
1+9+8
6+3
1+8
--
--
9
--
6
MATTER ANTI MATTER
18
9
9
-
-
-
--
-
-
1+8
-
-
-
-
9
--
6
MATTER ANTI MATTER
9
9
9

 

 

-
16
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
-
-
-
-
-
-
-
+
=
14
1+4
=
5
-
5
-
5
-
-
-
-
-
-
-
-
-
-
14
-
9
-
-
-
-
-
-
-
+
=
23
2+3
=
5
-
5
-
5
-
16
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
4
1
2
2
5
9
-
1
-
2
-
-
4
1
2
2
5
9
+
=
49
4+9
=
13
1+3
4
-
4
-
-
13
1
20
20
5
18
-
1
-
20
-
-
13
1
20
20
5
18
+
=
175
1+7+5
=
13
1+3
4
-
4
-
16
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
13
1
20
20
5
18
-
1
14
20
9
-
13
1
20
20
5
18
+
=
198
1+9+8
=
18
1+8
9
9
-
-
4
1
2
2
5
9
-
1
5
2
9
-
4
1
2
2
5
9
+
=
63
6+3
=
9
-
9
9
-
16
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-`
-
1
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
-
3
-
-
-
-
2
2
-
-
-
-
-
2
-
-
-
-
2
2
-
-
-
-
2
occurs
x
5
=
10
1+0
1
3
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
3
-
-
-
-
-
-
-
-
-`
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
6
-
-
-
-
-
-
-
7
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
7
-
-
-
-
-
-
-
8
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
occurs
x
3
=
27
2+7
9
24
16
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
21
-
-
20
-
63
-
27
2+4
1+6
-
-
2
2
-
-
-
-
-
2
-
-
-
-
2
2
-
9
-
-
2+1
-
-
2+0
-
6+3
-
2+7
6
7
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
3
-
-
2
-
9
-
9
-
-
4
1
2
2
5
9
-
1
5
2
9
-
4
1
2
2
5
9
-
-
-
-
-
-
-
-
-
-
6
7
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
3
-
-
2
-
9
-
9

 

 

16
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
-
-
-
-
-
-
-
+
=
14
1+4
=
5
-
5
-
5
-
-
-
-
-
-
-
-
-
14
-
9
-
-
-
-
-
-
-
+
=
23
2+3
=
5
-
5
-
5
16
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
4
1
2
2
5
9
-
1
-
2
-
-
4
1
2
2
5
9
+
=
49
4+9
=
13
1+3
4
-
4
-
13
1
20
20
5
18
-
1
-
20
-
-
13
1
20
20
5
18
+
=
175
1+7+5
=
13
1+3
4
-
4
16
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
13
1
20
20
5
18
-
1
14
20
9
-
13
1
20
20
5
18
+
=
198
1+9+8
=
18
1+8
9
9
-
4
1
2
2
5
9
-
1
5
2
9
-
4
1
2
2
5
9
+
=
63
6+3
=
9
-
9
9
16
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
-
3
-
-
-
2
2
-
-
-
-
-
2
-
-
-
-
2
2
-
-
-
-
2
occurs
x
5
=
10
1+0
1
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
occurs
x
3
=
27
2+7
9
16
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
21
-
-
20
-
63
-
27
1+6
-
-
-
2
2
-
-
-
-
-
2
-
-
-
-
2
2
-
-
-
2+1
-
-
2+0
-
6+3
-
2+7
7
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
3
-
-
2
-
9
-
9
-
4
1
2
2
5
9
-
1
5
2
9
-
4
1
2
2
5
9
-
-
-
-
-
-
-
-
-
-
7
M
A
T
T
E
R
-
A
N
T
I
-
M
A
T
T
E
R
-
-
3
-
-
2
-
9
-
9

 

 

D
=
4
Q
4
DARK
34
16
7
M
=
4
Q
6
MATTER
77
23
5
M
=
4
Q
4
MIND
40
22
4
L
=
3
Q
5
LIGHT
56
29
2
-
-
15
-
19
First Total
207
90
18
-
-
1+5
-
1+9
Add to Reduce
1+1+1
9+0
1+8
-
-
6
Q
10
Second Total
9
9
9
-
-
-
-
1+0
Reduce to Deduce
-
-
-
-
-
6
Q
1
Essence of Number
9
9
9

 

 

-
19
D
A
R
K
-
M
A
T
T
E
R
-
M
I
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
-
-
-
9
-
8
-
+
=
31
3+1
=
4
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
14
-
-
-
9
-
8
-
+
=
40
4+0
=
4
=
4
=
4
-
19
D
A
R
K
-
M
A
T
T
E
R
-
M
I
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
4
1
9
2
-
4
1
2
2
5
9
-
4
-
-
4
-
3
-
7
-
2
+
=
59
5+9
=
14
1+4
5
=
5
-
-
4
1
18
11
-
13
1
20
20
5
18
-
13
-
-
4
-
12
-
7
-
20
+
=
167
1+6+7
=
14
1+4
5
=
5
-
19
D
A
R
K
-
M
A
T
T
E
R
-
M
I
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
4
1
18
11
-
13
1
20
20
5
18
-
13
9
14
4
-
12
9
7
8
20
+
=
207
2+0+7
=
9
=
9
=
9
-
-
4
1
9
2
-
4
1
2
2
5
9
-
4
9
5
4
-
3
9
7
8
2
+
=
90
9+0
=
9
=
9
=
9
-
19
D
A
R
K
-
M
A
T
T
E
R
-
M
I
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
2
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
4
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
4
-
-
-
-
-
-
4
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
4
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
9
occurs
x
4
=
36
3+6
9
6
19
D
A
R
K
-
M
A
T
T
E
R
-
M
I
N
D
-
L
I
G
H
T
-
-
39
-
-
19
-
90
-
45
-
1+9
-
-
9
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+9
-
9+0
-
4+5
6
10
D
A
R
K
-
M
A
T
T
E
R
-
M
I
N
D
-
L
I
G
H
T
-
-
12
-
-
10
-
9
-
9
-
1+0
4
1
9
2
-
4
1
2
2
5
9
-
4
9
5
4
-
3
9
7
8
2
-
-
1+2
-
-
1+0
-
-
-
-
6
1
D
A
R
K
-
M
A
T
T
E
R
-
M
I
N
D
-
L
I
G
H
T
-
-
3
-
-
1
-
9
-
9

 

 

-
-
-
-
-
DARK MATTER
-
-
-
D
=
4
Q
4
DARK
34
16
7
M
=
4
Q
6
MATTER
77
23
5
-
-
8
-
10
DARK MATTER
111
39
12
-
-
-
-
1+0
-
1+1+1
3+9
1+2
-
-
8
Q
1
DARK MATTER
3
12
3
-
-
-
-
-
-
-
1+2
-
-
-
8
Q
1
DARK MATTER
3
3
3

 

 

-
10
D
A
R
K
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
4
1
9
2
-
4
1
2
2
5
9
+
=
39
3+9
=
12
1+2
3
=
3
-
-
4
1
18
11
-
13
1
20
20
5
18
+
=
111
1+1+1
=
3
=
3
=
3
-
10
D
A
R
K
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
4
1
9
2
-
4
1
2
2
5
9
+
=
39
3+9
=
12
1+2
3
=
3
-
-
4
1
18
11
-
13
1
20
20
5
18
+
=
111
1+1+1
=
3
=
3
=
3
-
10
D
A
R
K
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
4
1
18
11
-
13
1
20
20
5
18
+
=
111
1+1+1
=
3
=
3
=
3
-
-
4
1
9
2
-
4
1
2
2
5
9
+
=
39
3+9
=
12
1+2
3
=
3
-
10
D
A
R
K
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
2
2
-
-
-
-
2
occurs
x
3
=
6
=
6
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
4
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
2
=
8
1+6
8
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
1+0
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
3+6
9
24
10
D
A
R
K
-
M
A
T
T
E
R
-
-
21
-
-
10
-
39
-
30
2+4
1+0
-
-
9
-
-
-
-
-
-
-
9
-
-
2+1
-
-
1+0
-
3+9
-
3+0
6
1
D
A
R
K
-
M
A
T
T
E
R
-
-
3
-
-
1
-
12
-
3
-
-
4
1
9
2
-
4
1
2
2
5
9
-
-
-
-
-
-
-
1+2
-
-
6
1
D
A
R
K
-
M
A
T
T
E
R
-
-
3
-
-
1
-
3
-
3

 

 

10
D
A
R
K
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
4
1
9
2
-
4
1
2
2
5
9
+
=
39
3+9
=
12
1+2
3
=
3
-
4
1
18
11
-
13
1
20
20
5
18
+
=
111
1+1+1
=
3
=
3
=
3
10
D
A
R
K
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
4
1
9
2
-
4
1
2
2
5
9
+
=
39
3+9
=
12
1+2
3
=
3
-
4
1
18
11
-
13
1
20
20
5
18
+
=
111
1+1+1
=
3
=
3
=
3
10
D
A
R
K
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
4
1
18
11
-
13
1
20
20
5
18
+
=
111
1+1+1
=
3
=
3
=
3
-
4
1
9
2
-
4
1
2
2
5
9
+
=
39
3+9
=
12
1+2
3
=
3
10
D
A
R
K
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
2
2
-
-
-
-
2
occurs
x
3
=
6
=
6
-
4
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
2
=
8
1+6
8
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
1+0
5
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
3+6
9
10
D
A
R
K
-
M
A
T
T
E
R
-
-
21
-
-
10
-
39
-
30
1+0
-
-
9
-
-
-
-
-
-
-
9
-
-
2+1
-
-
1+0
-
3+9
-
3+0
1
D
A
R
K
-
M
A
T
T
E
R
-
-
3
-
-
1
-
12
-
3
-
4
1
9
2
-
4
1
2
2
5
9
-
-
-
-
-
-
-
1+2
-
-
1
D
A
R
K
-
M
A
T
T
E
R
-
-
3
-
-
1
-
3
-
3

 

 

M
=
4
4
MIND
40
22
4
M
=
4
6
MATTER
77
23
5
M
=
4
6
MATTER
77
23
5
M
=
4
4
MIND
40
22
4
-
-
16
20
Add to Reduce
234
90
18
-
-
1+6
2+0
Reduce to Deduce
2+3+4
9+0
1+8
-
-
7
2
Essence of Number
9
9
9

 

 

-
20
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
-
9
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
9
14
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
14
-
+
=
46
4+6
=
10
1+0
1
=
1
-
20
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
4
-
-
4
-
4
1
2
2
5
9
-
4
1
2
2
5
9
-
4
-
-
4
+
=
62
6+2
=
8
=
8
=
8
-
-
13
-
-
4
-
13
1
20
20
5
18
-
13
1
20
20
5
18
-
13
-
-
4
+
=
188
1+8+8
=
17
1+7
8
-
8
-
20
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
13
9
14
4
-
13
1
20
20
5
18
-
13
1
20
20
5
18
-
13
9
14
4
+
=
234
2+3+4
=
9
=
9
=
9
-
-
4
9
5
4
-
4
1
2
2
5
9
-
4
1
2
2
5
9
-
4
9
5
4
+
=
90
9+0
=
9
=
9
=
9
-
20
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
2
-
-
-
-
-
2
2
-
-
-
-
-
-
-
-
-
2
occurs
x
4
=
8
=
8
3
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
3
-
-
-
-
-
-
-
-
-`
4
-
-
4
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
4
-
-
4
occurs
x
6
=
24
2+4
6
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
--
--
--
--
--
6
-
-
-
-
-
-
-
7
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
--
--
--
--
--
7
-
-
-
-
-
-
-
8
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
--
--
--
--
--
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
24
20
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
21
-
-
20
-
90
-
36
2+4
2+0
4
-
-
4
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
4
-
-
4
-
-
2+0
-
9+0
-
3+6
6
2
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
3
-
-
2
-
9
-
9
-
-
4
9
5
4
-
4
1
2
2
5
9
-
4
1
2
2
5
9
-
4
9
5
4
-
-
-
-
-
-
-
-
-
-
6
2
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
3
-
-
2
-
9
-
9

 

 

0
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
-
9
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
9
14
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
14
-
+
=
46
4+6
=
10
1+0
1
=
1
20
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
4
-
-
4
-
4
1
2
2
5
9
-
4
1
2
2
5
9
-
4
-
-
4
+
=
62
6+2
=
8
=
8
=
8
-
13
-
-
4
-
13
1
20
20
5
18
-
13
1
20
20
5
18
-
13
-
-
4
+
=
188
1+8+8
=
17
1+7
8
-
8
20
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
-
-
-
--
-
-
-
-
-
13
9
14
4
-
13
1
20
20
5
18
-
13
1
20
20
5
18
-
13
9
14
4
+
=
234
2+3+4
=
9
=
9
=
9
-
4
9
5
4
-
4
1
2
2
5
9
-
4
1
2
2
5
9
-
4
9
5
4
+
=
90
9+0
=
9
=
9
=
9
20
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
2
2
-
-
-
-
-
2
2
-
-
-
-
-
-
-
-
-
2
occurs
x
4
=
8
=
8
-
4
-
-
4
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
4
-
-
4
occurs
x
6
=
24
2+4
6
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
20
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
21
-
-
20
-
90
-
36
2+0
4
-
-
4
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
4
-
-
4
-
-
2+0
-
9+0
-
3+6
2
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
3
-
-
2
-
9
-
9
-
4
9
5
4
-
4
1
2
2
5
9
-
4
1
2
2
5
9
-
4
9
5
4
-
-
-
-
-
-
-
-
-
-
2
M
I
N
D
-
M
A
T
T
E
R
-
M
A
T
T
E
R
-
M
I
N
D
-
-
3
-
-
2
-
9
-
9

 

 

-
20
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
-
-
-
9
5
-
-
-
-
-
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
-
-
-
-
-
-
9
14
-
-
-
9
14
-
-
-
-
-
-
-
-
+
=
46
4+6
=
10
1+0
1
=
1
-
20
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
4
1
2
2
5
9
-
4
-
-
4
-
4
-
-
4
-
4
1
2
2
5
9
+
=
62
6+2
=
8
=
8
=
8
-
-
13
1
20
20
5
18
-
13
-
-
4
-
13
-
-
4
-
13
1
20
20
5
18
+
=
188
1+8+8
=
17
1+7
8
=
8
-
20
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
13
1
20
20
5
18
-
13
9
14
4
-
13
9
14
4
-
13
1
20
20
5
18
+
=
234
2+3+4
=
9
=
9
=
9
-
-
4
1
2
2
5
9
-
4
9
5
4
-
4
9
5
4
-
4
1
2
2
5
9
+
=
90
9+0
=
9
=
9
=
9
-
20
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-`
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
2
-
-
-
-
2
occurs
x
4
=
8
=
8
3
-
--
--
--
--
--
--
--
-
--
--
--
--
-
--
--
--
--
--
--
--
--
--
--
--
--
3
-
-
-
-
-
-
-
-
-`
4
-
-
-
-
-
-
4
-
-
4
-
4
-
-
4
-
4
-
-
-
-
-
-
-
4
occurs
x
6
=
24
2+4
6
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
--
--
--
--
--
--
--
-
--
--
--
--
-
--
--
--
--
--
--
--
--
--
--
--
--
6
-
-
-
-
-
-
-
7
-
--
--
--
--
--
--
--
-
--
--
--
--
-
--
--
--
--
--
--
--
--
--
--
--
--
7
-
-
-
-
-
-
-
8
-
--
--
--
--
--
--
--
-
--
--
--
--
-
--
--
--
--
--
--
--
--
--
--
--
--
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
4
=
36
3+6
9
24
20
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
21
-
-
20
-
90
-
36
2+4
2+0
4
-
-
-
-
-
-
4
-
-
4
-
4
-
-
4
-
4
-
-
-
-
-
-
-
2+1
-
-
2+0
-
9+0
-
3+6
6
2
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
2
-
9
-
9
-
-
4
1
2
2
5
9
-
4
9
5
4
-
4
9
5
4
-
4
1
2
2
5
9
-
-
-
-
-
-
-
-
-
-
6
2
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
2
-
9
-
9

 

 

20
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
-
-
-
9
5
-
-
-
-
-
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
-
-
-
-
-
-
-
9
14
-
-
-
9
14
-
-
-
-
-
-
-
-
+
=
46
4+6
=
10
1+0
1
=
1
20
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
4
1
2
2
5
9
-
4
-
-
4
-
4
-
-
4
-
4
1
2
2
5
9
+
=
62
6+2
=
8
=
8
=
8
-
13
1
20
20
5
18
-
13
-
-
4
-
13
-
-
4
-
13
1
20
20
5
18
+
=
188
1+8+8
=
17
1+7
8
=
8
20
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
13
1
20
20
5
18
-
13
9
14
4
-
13
9
14
4
-
13
1
20
20
5
18
+
=
234
2+3+4
=
9
=
9
=
9
-
4
1
2
2
5
9
-
4
9
5
4
-
4
9
5
4
-
4
1
2
2
5
9
+
=
90
9+0
=
9
=
9
=
9
20
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-`
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
2
-
-
-
-
2
occurs
x
4
=
8
=
8
`
4
-
-
-
-
-
-
4
-
-
4
-
4
-
-
4
-
4
-
-
-
-
-
-
-
4
occurs
x
6
=
24
2+4
6
-
-
-
-
-
5
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
4
=
36
3+6
9
20
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
21
-
-
20
-
90
-
36
2+0
4
-
-
-
-
-
-
4
-
-
4
-
4
-
-
4
-
4
-
-
-
-
-
-
-
2+1
-
-
2+0
-
9+0
-
3+6
2
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
2
-
9
-
9
-
4
1
2
2
5
9
-
4
9
5
4
-
4
9
5
4
-
4
1
2
2
5
9
-
-
-
-
-
-
-
-
-
-
2
M
A
T
T
E
R
-
M
I
N
D
-
M
I
N
D
-
M
A
T
T
E
R
-
-
3
-
-
2
-
9
-
9

 

 

L
=
3
5
LIGHT
56
29
2
M
=
4
4
MIND
40
22
4
M
=
4
6
MATTER
77
23
5
D
=
4
4
DARK
34
16
7
-
-
15
19
First Total
207
90
18
-
-
1+5
1+9
Add to Reduce
2+0+7
9+0
1+8
Q
-
5
10
Second Total
9
9
9
-
-
-
1+0
Reduce to Deduce
-
-
-
-
-
5
1
Essence of Number
9
9
9

 

 

-
19
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
8
-
-
-
9
5
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
31
3+1
=
4
=
4
=
4
-
-
-
9
-
8
-
-
-
9
14
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
40
4+0
=
4
=
4
=
4
--
19
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
--
-
-
-
-
-
-
3
-
7
-
2
-
4
-
-
4
-
4
1
2
2
5
9
-
4
1
9
2
+
=
59
5+9
=
14
1+4
5
=
5
-
-
12
-
7
-
20
-
13
-
-
4
-
13
1
20
20
5
18
-
4
1
18
11
+
=
167
1+6+7
=
14
1+4
5
=
5
--
19
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
--
-
-
-
-
--
-
12
9
7
8
20
-
13
9
14
4
-
13
1
20
20
5
18
-
4
1
18
11
+
=
207
2+0+7
=
9
=
9
=
9
--
-
3
9
7
8
2
-
4
9
5
4
-
4
1
2
2
5
9
-
4
1
9
2
+
=
90
9+0
=
9
=
9
=
9
-
19
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
2
-
-
-
-
-
-
2
-
-
2
occurs
x
4
=
8
=
8
-
-
3
-
-
-
-
-
-
--
--
--
-
--
--
--
--
--
--
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
4
-
4
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
4
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
--
--
--
-
--
--
--
--
--
--
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
--
--
--
-
--
--
--
--
--
--
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
--
--
--
-
--
--
--
--
--
--
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
9
occurs
x
4
=
36
3+6
9
6
19
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
39
-
-
19
-
90
-
45
-
1+9
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
3+9
-
-
1+9
-
9+0
-
4+5
6
10
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
12
-
-
10
-
9
-
9
-
1+0
3
9
7
8
2
-
4
9
5
4
-
4
1
2
2
5
9
-
4
1
9
2
-
-
1+2
-
-
1+0
-
-
-
-
6
1
L
I
G
H
T
-
M
I
N
D
-
M
A
T
T
E
R
-
D
A
R
K
-
-
3
-
-
1
-
9
-
9

 

 

L
=
3
5
LIGHT
56
29
2
E
=
5
7
ELECTRO
78
33
6
M
=
4
8
MAGNETIC
72
36
9
R
=
9
9
RADIATION
91
46
1
-
-
21
29
First Total
297
144
18
-
-
2+1
2+9
Add to Reduce
2+9+7
1+4+4
1+8
Q
-
3
11
Second Total
18
9
9
-
-
-
1+1
Reduce to Deduce
1+8
-
-
-
-
3
2
Essence of Number
9
9
9

 

 

-
21
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
-
-
-
6
-
-
-
-
5
-
-
9
-
-
-
-
-
9
-
-
9
6
5
+
=
66
6+6
=
12
1+2
3
-
3
-
`-
-
9
-
8
-
-
-
-
-
-
-
-
15
-
-
-
-
14
-
-
9
-
-
-
-
-
9
-
-
9
15
14
+
 =
102
1+0+2
=
3
-
3
-
3
-
21
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
-
3
-
7
-
2
-
5
3
5
3
2
9
-
-
4
1
7
-
5
2
-
3
-
9
1
4
-
1
2
-
-
-
+
=
78
7+8
=
15
1+2
6
-
6
-
`-
12
-
7
-
20
-
5
12
5
3
20
18
-
-
13
1
7
-
5
20
-
3
-
18
1
4
-
1
20
-
-
-
+
=
195
1+9+5
=
15
1+5
6
-
6
-
21
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
-
`-
12
9
7
8
20
-
5
12
5
3
20
18
15
-
13
1
7
14
5
20
9
3
-
18
1
4
9
1
20
9
15
14
+
=
297
2+9+7
=
18
1+8
9
-
9
-
-
3
9
7
8
2
-
5
3
5
3
2
9
6
-
4
1
7
5
5
2
9
3
-
9
1
4
9
1
2
9
6
5
+
=
144
1+4+4
=
9
-
9
-
9
-
21
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
-
-
-
--
-
-
-
-
1
-
1
-
-
-
-
-
-
1
1
-
-
-
1
-
-
1
1
-
-
-
-
-
-
-
1
-
-
1
-
-
1
-
-
-
1
occurs
x
3
=
3
-
3
2
-
-
4
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
4
-
2
-
-
-
-
-
-
-
-
2
-
-
4
-
-
2
occurs
x
4
=
8
-
8
3
-
3
-
-
-
-
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
4
=
12
-
3
4
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
-
-
-
-
-
-
-
4
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
-
8
5
-
-
-
-
5
-
-
5
-
5
5
-
-
-
-
-
-
-
5
5
5
-
5
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
3
-
2
-
-
-
-
-
-
-
6
-
-
-
-
-
3
-
2
-
-
-
-
-
2
-
-
2
6
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
3
8
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
2
-
-
-
-
-
2
-
-
2
-
-
-
-
8
occurs
x
1
=
8
-
8
9
-
-
9
-
-
-
-
9
-
-
-
9
9
-
-
9
-
-
-
-
-
9
-
-
9
-
-
9
-
-
9
-
-
-
-
9
occurs
x
6
=
54
5+4
9
45
21
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
45
-
-
21
-
144
-
54
4+5
2+1
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
9
-
-
9
-
-
9
-
-
-
-
4+5
-
-
2+1
-
1+4+4
-
5+4
9
3
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
9
-
-
3
-
9
-
9
-
-
3
9
7
8
2
-
5
3
5
3
2
9
6
-
4
1
7
5
5
2
9
3
-
9
1
4
9
1
2
9
6
5
-
-
-
-
-
-
-
-
-
-
9
3
L
I
G
H
T
-
E
L
E
C
T
R
O
-
M
A
G
N
E
T
I
C
-
R
A
D
I
A
T
I
O
N
-
-
9
-
-
3
-
9
-
9

 

 

-
10
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
--
-
-
-
-
-
-
9
-
9
-
-
+
=
18
1+8
=
9
=
9
=
9
-
10
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
9
5
3
1
2
-
4
-
2
7
+
=
33
3+3
=
6
=
6
=
6
-
-
18
5
12
1
20
-
22
-
20
25
+
=
123
1+2+3
=
6
=
6
=
6
-
10
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
18
5
12
1
20
9
22
9
20
25
+
=
141
1+4+1
=
6
=
6
=
6
-
-
9
5
3
1
2
9
4
9
2
7
+
=
51
5+1
=
6
=
6
=
6
-
10
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
--
-
-
-
-
-
2
-
-
-
2
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
3
-
-
-
--
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
-
-
7
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
14
10
R
E
L
A
T
I
V
I
T
Y
-
-
31
-``
-
10
-
51
-
33
1+4
1+0
9
-
-
-
-
9
-
9
-
-
-
-
3+1
-
-
1+0
-
5+1
-
3+3
5
1
R
E
L
A
T
I
V
I
T
Y
-
-
4
-``
-
1
-
6
-
6
-
-
9
5
3
1
2
9
4
9
2
7
-
-
-
-
-
-
-
-
-
-
5
1
R
E
L
A
T
I
V
I
T
Y
-
-
4
-
-
1
-
6
-
6

 

 

10
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
+
=
18
1+8
=
9
=
9
=
9
10
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
9
5
3
1
2
-
4
-
2
7
+
=
33
3+3
=
6
=
6
=
6
-
18
5
12
1
20
-
22
-
20
25
+
=
123
1+2+3
=
6
=
6
=
6
10
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
18
5
12
1
20
9
22
9
20
25
+
=
141
1+4+1
=
6
=
6
=
6
-
9
5
3
1
2
9
4
9
2
7
+
=
51
5+1
=
6
=
6
=
6
10
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
-
2
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
3
-
-
-
--
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
--
-
-
7
-
-
7
occurs
x
1
=
7
-
7
-
9
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
10
R
E
L
A
T
I
V
I
T
Y
-
-
31
-``
-
10
-
51
-
33
1+0
9
-
-
-
-
9
-
9
-
-
-
-
3+1
-
-
1+0
-
5+1
-
3+3
1
R
E
L
A
T
I
V
I
T
Y
-
-
4
-``
-
1
-
6
-
6
-
9
5
3
1
2
9
4
9
2
7
-
-
-
-
-
-
-
-
-
-
1
R
E
L
A
T
I
V
I
T
Y
-
-
4
-
-
1
-
6
-
6

 

 

-
25
G
E
N
E
R
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
8
-
6
-
-
-
6
-
-
-
-
-
-
-
9
-
9
-
-
+
=
43
4+3
=
7
=
7
=
7
-
-
-
-
14
-
-
-
-
-
-
8
-
15
-
-
-
15
-
-
-
-
-
-
-
9
-
9
-
-
+
=
70
7+0
=
7
=
7
=
7
-
25
G
E
N
E
R
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
5
9
1
3
-
2
-
5
-
9
7
-
-
6
-
9
5
3
1
2
-
4
-
2
7
+
=
92
9+2
=
11
1+1
2
=
2
-
-
7
5
-
5
18
1
12
-
20
-
5
-
18
25
-
-
6
-
18
5
12
1
20
-
22
-
20
25
+
=
245
2+4+5
=
11
1+1
2
=
1
-
25
G
E
N
E
R
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
7
5
14
5
18
1
12
-
20
8
5
15
18
25
-
15
6
-
18
5
12
1
20
9
22
9
20
25
+
+
351
1+8+2
=
9
-
9
=
9
-
-
7
5
5
5
9
1
3
-
2
8
5
6
9
7
-
6
6
-
9
5
3
1
2
9
4
9
2
7
+
+
135
1+3+5
=
9
-
9
=
2
-
25
G
E
N
E
R
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
``-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
2
occurs
x
3
=
6
=
6
3
``-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
5
5
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
3
=
21
2+1
3
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
5
=
45
=
9
45
25
G
E
N
E
R
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
45
-
-
25
-
135
-
54
4+5
2+5
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
-
9
-
-
-
-
4+5
-
-
2+5
-
1+3+5
-
5+4
9
7
G
E
N
E
R
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
9
-
-
7
-
9
-
9
-
-
7
5
5
5
9
1
3
-
2
8
5
6
9
7
-
6
6
-
9
5
3
1
2
9
4
9
2
7
-
-
-
-
-
-
-
-
-
-
9
7
G
E
N
E
R
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
9
-
-
7
-
9
-
9

 

 

G
=
7
7
GENERAL
62
35
8
T
=
2
6
THEORY
91
37
1
O
=
6
2
OF
21
12
3
R
=
9
10
RELATIVITY
141
51
6
-
-
24
25
Add to Reduce
315
135
18
-
-
2+4
2+5
Reduce to Deduce
3+1+5
1+3+5
1+8
-
-
6
7
Essence of Number
9
9
9

 

 

7
SPECIAL
65
29
2
6
THEORY
91
37
1
2
OF
21
12
3
10
RELATIVITY
141
51
6
25
First Total
318
129
12
2+5
Add to Reduce
3+1+8
1+2+9
1+2
7
Second Total
12
12
3
-
Reduce to Deduce
1+2
1+2
-
7
Essence of Number
3
3
3

 

 

G
=
7
7
GENERAL
62
35
8
T
=
2
6
THEORY
91
37
1
-
-
9
13
Add to Reduce
153
72
9
-
-
-
1+3
Reduce to Deduce
1+5+3
7+2
-
-
-
9
4
Essence of Number
9
9
9

 

 

T
=
2
3
THE
33
15
6
G
=
7
7
GENERAL
62
35
8
T
=
2
6
THEORY
91
37
1
O
=
6
2
OF
21
12
3
R
=
9
10
RELATIVITY
141
51
6
-
-
26
28
First Total
348
150
24
-
-
2+6
2+8
Add to Reduce
3+4+8
1+5+0
2+4
-
-
8
10
Second Total
15
6
6
-
-
-
1+0
Reduce to Deduce
1+5
-
-
-
-
8
1
Essence of Number
6
6
6

 

 

3
THE
33
15
6
7
SPECIAL
65
29
2
6
THEORY
91
37
1
2
OF
21
12
3
10
RELATIVITY
141
51
6
28
First Total
351
144
18
2+8
Add to Reduce
3+5+1
1+4+4
1+8
10
Second Total
9
9
9
1+0
Reduce to Deduce
-
-
-
1
Essence of Number
9
9
9

 

 

25
GENERAL THEORY OF RELATIVITY
315
135
9

 

 

28
THE SPECIAL THEORY OF RELATIVITY
351
144
9

 

 

-
28
T
H
E
-
S
P
E
C
I
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
1
1
-
-
-
9
-
-
-
-
8
-
6
-
-
-
6
-
-
-
-
-
-
-
9
-
9
-
-
+
=
56
5+6
=
11
1+1
2
=
2
-
-
-
8
-
-
19
-
-
-
9
-
-
-
-
8
-
15
-
-
-
15
-
-
-
-
-
-
-
9
-
9
-
-
+
=
92
9+2
=
11
1+1
2
=
2
-
28
T
H
E
-
S
P
E
C
I
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
-
7
5
3
-
1
3
-
2
-
5
-
9
7
-
-
6
-
9
5
3
1
2
-
4
-
2
7
+
=
88
8+8
=
16
1+6
7
=
7
-
-
20
-
5
-
-
16
5
3
-
1
12
-
20
-
5
-
18
25
-
-
6
-
18
5
12
1
20
-
22
-
20
25
+
=
259
2+5+9
=
16
1+6
7
=
7
-
28
T
H
E
-
S
P
E
C
I
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
19
16
5
3
9
1
12
-
20
8
5
15
18
25
-
15
6
-
18
5
12
1
20
9
22
9
20
25
+
+
351
3+5+1
=
9
-
9
=
9
-
-
2
8
5
-
1
7
5
3
9
1
3
-
2
8
5
6
9
7
-
6
6
-
9
5
3
1
2
9
4
9
2
7
+
+
144
1+4+4
=
9
-
9
=
9
218
28
T
H
E
-
S
P
E
C
I
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
2
``-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
2
occurs
x
4
=
8
=
8
3
``-
-
-
-
-
-
-
-
3
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
occurs
x
3
=
9
-
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
3
=
21
2+1
3
8
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
5
=
45
=
9
45
28
T
H
E
-
S
P
E
C
I
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
45
-
-
28
-
144
-
54
4+5
2+8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
-
9
-
-
-
-
4+5
-
-
2+8
-
1+4+4
-
5+4
9
10
T
H
E
-
S
P
E
C
I
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
9
-
-
10
-
9
-
9
-
1+0
2
8
5
-
1
7
5
3
9
1
3
-
2
8
5
6
9
7
-
6
6
-
9
5
3
1
2
9
4
9
2
7
-
-
-
-
-
1+0
-
-
-
-
9
1
T
H
E
-
S
P
E
C
I
A
L
-
T
H
E
O
R
Y
-
O
F
-
R
E
L
A
T
I
V
I
T
Y
-
-
9
-
-
1
-
9
-
9

 

 

-
14
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
1
-
-
9
5
+
=
29
2+9
=
11
1+1
2
=
2
-
`-
-
-
-
-
-
-
-
-
9
14
19
-
-
9
14
+
=
65
6+5
=
11
1+1
2
=
2
-
14
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
-
-
-
--
-
-
-
-
-
-
1
3
2
5
9
2
-
5
-
-
-
2
5
-
-
+
=
25
2+5
=
7
=
7
=
7
-
`-
1
12
2
5
18
20
-
5
-
-
-
20
5
-
-
+
=
88
8+8
=
16
1+6
7
=
7
-
14
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
-
-
-
--
-
-
-
-
-
`-
1
12
2
5
18
20
-
5
9
14
19
20
5
9
14
+
=
153
1+5+3
=
9
=
9
=
9
-
-
1
3
2
5
9
2
-
5
9
5
1
2
5
9
5
+
=
63
6+3
=
9
=
9
=
9
-
14
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-T
-T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
2
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-4
-`-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
6
-
-
-
-
-
-`-
-
-
-
-
5
-
-
-
5
-
5
-
-
5
-
5
-
-
5
occurs
x
5
=
25
2+5
7
6
-`-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
-
-
-
-
-
7
-`-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
8
-`-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-`-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
-
8
EIGHT
8
3
=
27
2+7
9
25
14
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
20
-
1
14
-
63
-
27
2+5
1+4
-
-
-
5
-
-
-
5
-
5
-
-
5
-
5
-
-
2+0
-
-
1+4
-
6+3
-
2+7
7
5
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
2
-
1
5
-
9
-
9
-
-
1
3
2
5
9
2
-
5
9
5
1
2
5
9
5
-
-
-
-
-
--
-
-
-
-
7
5
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
2
-
1
5
-
9
-
9

 

 

14
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
9
5
1
-
-
9
5
+
=
29
2+9
=
11
1+1
2
=
2
`-
-
-
-
-
-
-
-
-
9
14
19
-
-
9
14
+
=
65
6+5
=
11
1+1
2
=
2
14
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
-
-
-
--
-
-
-
-
-
1
3
2
5
9
2
-
5
-
-
-
2
5
-
-
+
=
25
2+5
=
7
=
7
=
7
`-
1
12
2
5
18
20
-
5
-
-
-
20
5
-
-
+
=
88
8+8
=
16
1+6
7
=
7
14
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
-
-
-
--
-
-
-
-
`-
1
12
2
5
18
20
-
5
9
14
19
20
5
9
14
+
=
153
1+5+3
=
9
=
9
=
9
-
1
3
2
5
9
2
-
5
9
5
1
2
5
9
5
+
=
63
6+3
=
9
=
9
=
9
14
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
2
-
-
2
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
5
-
-
-
5
-
5
-
-
5
-
5
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
-
-
9
-
-
-
9
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
14
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
20
-
1
14
-
63
-
27
1+4
-
-
-
5
-
-
-
5
-
5
-
-
5
-
5
-
-
2+0
-
-
1+4
-
6+3
-
2+7
5
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
2
-
1
5
-
9
-
9
-
1
3
2
5
9
2
-
5
9
5
1
2
5
9
5
-
-
-
-
-
--
-
-
-
-
5
A
L
B
E
R
T
-
E
I
N
S
T
E
I
N
-
-
2
-
1
5
-
9
-
9

 

 

ABCDEFGHIJKLMNOPQRSTUVWXYZ

ABCDEFGHIJKLMNOPQRSTUVWXYZ

ABCDEFGH9JKLMNOPQ9STUVWXYZ

"The most common letter in the English alphabet is E."

ABCDEFGHIJKLMNOPQRSTUVWXYZ

ABCDEFGHIJKLMNOPQRSTUVWXYZ

ABCD5FGHIJKLM5OPQRSTUV5XYZ

 

 

DOES GOD PLAY DICE

THE NEW MATHEMATICS OF CHAOS

Ian Stewart 1989

Page 1

PROLOGUE

CLOCKWORK OR CHAOS?

"YOU BELIEVE IN A GOD WHO PLAYS DICE, AND I IN COMPLETE LAW AND ORDER."

Albert Einstein, Letter to Max Born

 

-
-
-
-
-
ALBERT EINSTEIN-
-
-
-
A
=
1
-
6
ALBERT
58
22
4
E
=
5
-
8
EINSTEIN
95
41
5
-
-
6
-
14
ALBERT EINSTEI
153
63
9
-
-
-
-
1+4
-
1+5+3
6+3
1+8
-
-
6
-
5
ALBERT EINSTEI-
9
9
9

 

"YOU BELIEVE IN A GOD WHO PLAYS DICE, AND I IN COMPLETE LAW AND ORDER."

 

LOOK AT THE 5FIVE5S LOOK AT THE 5FIVE5S LOOK AT THE 5FIVE5S THE 5FIVE5S THE 5FIVE5S

5 x 12 = 60

"YOU B5LI5V5 I5 A GOD 5HO PLAYS DIC5, A5D I I5 COMPL5T5 LA5 A5D ORD5R."

 

G
=
7
-
7
GENERAL
62
35
8
T
=
2
-
6
THEORY
91
37
1
O
=
6
-
2
OF
21
12
3
R
=
9
-
10
RELATIVITY
141
51
6
-
-
24
-
25
Add to Reduce
315
135
18
-
-
2+4
-
2+5
Reduce to Deduce
3+1+5
1+3+5
1+8
-
-
6
-
7
Essence of Number
9
9
9

 

ALBERT EINSTEIN

LOOK AT THE 5FIVE5S LOOK AT THE 5FIVE5S LOOK AT THE 5FIVE5S THE 5FIVE5S THE 5FIVE5S

5 x 5 = 25

ALB5RT 5I5ST5I5

 

-
-
-
-
-
ALBERT EINSTEIN-
-
-
-
A
=
1
-
6
ALBERT
58
22
4
E
=
5
-
8
EINSTEIN
95
41
5
-
-
6
-
14
ALBERT EINSTEI
153
63
9
-
-
-
-
1+4
-
1+5+3
6+3
1+8
-
-
6
-
5
ALBERT EINSTEI-
9
9
9

 

 

-
-
-
-
-
ALBERT EINSTEIN-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
6
ALBERT
58
22
4
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
EINSTEIN
95
50
5
-
-
-
-
-
-
-
-
-
-
-
-
6
-
14
ALBERT EINSTEI
153
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALBERT
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
B
=
2
3
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
T
=
2
6
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
22
-
6
ALBERT
58
22
22
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
EINSTEIN
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
9
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
11
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
13
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
8
EINSTEIN
95
50
41
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALBERT EINSTEIN-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
6
ALBERT
58
22
4
-
2
6
3
4
25
6
7
8
27
E
=
5
-
8
EINSTEIN
95
50
5
-
-
-
-
-
2+5
-
-
-
2+7
-
-
6
-
14
ALBERT EINSTEI
153
72
9
-
2
6
3
4
7
6
7
8
9
-
-
-
-
1+4
-
1+5+3
7+2
1+8
-
-
-
-
-
-
-
-
-
-
-
-
6
-
5
ALBERT EINSTEI-
9
9
9
-
2
6
3
4
7
6
7
8
9

 

"YOU BELIEVE IN A GOD WHO PLAYS DICE, AND I IN COMPLETE LAW AND ORDER."

Albert Einstein, Letter to Max Born

 

-
-
-
-
-
ALBERT EINSTEIN-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
6
ALBERT
58
22
4
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
EINSTEIN
95
50
5
-
-
-
-
-
-
-
-
-
-
-
-
6
-
14
ALBERT EINSTEI
153
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALBERT
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
4
-
6
7
8
-
L
=
3
2
1
L
12
3
3
-
-
-
3
4
-
6
7
8
-
B
=
2
3
1
B
2
2
2
-
-
2
-
4
-
6
7
8
-
E
=
5
4
1
E
5
5
5
-
-
-
-
4
5
6
7
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
4
-
6
7
8
9
T
=
2
6
1
T
20
2
2
-
-
2
-
4
-
6
7
2
-
E
=
5
7
1
E
5
5
5
-
-
-
-
4
5
6
7
5
-
I
=
9
8
1
I
9
9
9
-
-
-
-
4
-
6
7
9
9
N
=
5
9
1
N
14
5
5
-
-
-
-
4
5
6
7
5
-
S
=
1
10
1
S
19
10
1
-
1
-
-
4
-
6
7
1
-
T
=
2
11
1
T
20
2
2
-
-
2
-
4
-
6
7
2
-
E
=
5
12
1
E
5
5
5
-
-
-
-
4
5
6
7
5
-
I
=
9
13
1
I
9
9
9
-
-
-
-
4
-
6
7
9
9
N
=
5
14
1
N
14
5
5
-
-
-
-
4
5
6
7
5
-
-
-
-
-
8
EINSTEIN
95
50
41
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALBERT EINSTEIN-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
6
ALBERT
58
22
4
-
2
6
3
4
25
6
7
8
27
E
=
5
-
8
EINSTEIN
95
50
5
-
-
-
-
-
2+5
-
-
-
2+7
-
-
6
-
14
ALBERT EINSTEI
153
72
9
-
2
6
3
4
7
6
7
8
9
-
-
-
-
1+4
-
1+5+3
7+2
1+8
-
-
-
-
-
-
-
-
-
-
-
-
6
-
5
ALBERT EINSTEI-
9
9
9
-
2
6
3
4
7
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

LOOK AT THE 5FIVE5S LOOK AT THE 5FIVE5S LOOK AT THE 5FIVE5S THE 5FIVE5S THE 5FIVE5S

5 x 5 = 25

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 5 = 25

"The most common letter in the English alphabet is E."

5 x 5 = 25

LETTERS TRANSPOSED INTO NUMBER REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
ALBERT EINSTEIN-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
6
ALBERT
58
22
4
-
-
-
-
-
-
-
-
-
-
E
=
5
-
8
EINSTEIN
95
50
5
-
-
-
-
-
-
-
-
-
-
-
-
6
-
14
ALBERT EINSTEI
153
63
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALBERT
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
4
-
6
7
8
-
S
=
1
10
1
S
19
10
1
-
1
-
-
4
-
6
7
1
-
B
=
2
3
1
B
2
2
2
-
-
2
-
4
-
6
7
8
-
T
=
2
6
1
T
20
2
2
-
-
2
-
4
-
6
7
2
-
T
=
2
11
1
T
20
2
2
-
-
2
-
4
-
6
7
2
-
L
=
3
2
1
L
12
3
3
-
-
-
3
4
-
6
7
8
-
E
=
5
4
1
E
5
5
5
-
-
-
-
4
5
6
7
8
-
E
=
5
7
1
E
5
5
5
-
-
-
-
4
5
6
7
5
-
N
=
5
9
1
N
14
5
5
-
-
-
-
4
5
6
7
5
-
E
=
5
12
1
E
5
5
5
-
-
-
-
4
5
6
7
5
-
N
=
5
14
1
N
14
5
5
-
-
-
-
4
5
6
7
5
-
R
=
9
5
1
R
18
9
9
-
-
-
-
4
-
6
7
8
9
I
=
9
8
1
I
9
9
9
-
-
-
-
4
-
6
7
9
9
I
=
9
13
1
I
9
9
9
-
-
-
-
4
-
6
7
9
9
-
-
-
-
8
EINSTEIN
95
50
41
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALBERT EINSTEIN-
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
-
6
ALBERT
58
22
4
-
2
6
3
4
25
6
7
8
27
E
=
5
-
8
EINSTEIN
95
50
5
-
-
-
-
-
2+5
-
-
-
2+7
-
-
6
-
14
ALBERT EINSTEI
153
72
9
-
2
6
3
4
7
6
7
8
9
-
-
-
-
1+4
-
1+5+3
7+2
1+8
-
-
-
-
-
-
-
-
-
-
-
-
6
-
5
ALBERT EINSTEI-
9
9
9
-
2
6
3
4
7
6
7
8
9

 

LOOK AT THJE 5FIVES LOOK AT THE 5FIVES LOOK AT THE 5FIVES THE 5FIVES THE 5FIVES

5 x 5 = 25

"The most common letter in the English alphabet is E."

5 x 5 = 25

 

-
-
-
-
-
ALBERT EINSTEIN-
-
-
-
-
1
2
3
5
9
A
=
1
-
6
ALBERT
58
22
4
-
-
-
-
-
-
E
=
5
-
8
EINSTEIN
95
50
5
-
-
-
-
-
-
-
-
6
-
14
ALBERT EINSTEI
153
63
9
-
1
2
3
5
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALBERT
-
-
-
-
1
2
3
5
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
B
=
2
3
1
B
2
2
2
-
-
2
-
-
-
T
=
2
6
1
T
20
2
2
-
-
2
-
-
-
T
=
2
11
1
T
20
2
2
-
-
2
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
5
-
E
=
5
7
1
E
5
5
5
-
-
-
-
5
-
N
=
5
9
1
N
14
5
5
-
-
-
-
5
-
E
=
5
12
1
E
5
5
5
-
-
-
-
5
-
N
=
5
14
1
N
14
5
5
-
-
-
-
5
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
9
I
=
9
8
1
I
9
9
9
-
-
-
-
-
9
I
=
9
13
1
I
9
9
9
-
-
-
-
-
9
-
-
-
-
8
EINSTEIN
95
50
41
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ALBERT EINSTEIN-
-
-
-
-
-
-
-
-
-
A
=
1
-
6
ALBERT
58
22
4
-
2
6
3
25
27
E
=
5
-
8
EINSTEIN
95
50
5
-
-
-
-
2+5
2+7
-
-
6
-
14
ALBERT EINSTEI
153
72
9
-
2
6
3
7
9
-
-
-
-
1+4
-
1+5+3
7+2
1+8
-
-
-
-
-
-
-
-
6
-
5
ALBERT EINSTEI-
9
9
9
-
2
6
3
7
9

 

 

... How Einstein Arrived at E=MC Squared

... a constant--as he had intuitively guessed--then energy and matter must be one and the same (energy equals matter times the speed of light squared). ... www.stresscure.com/hrn/einstein.html

 

DOES GOD PLAY DICE

THE NEW MATHEMATICS OF CHAOS

Ian Stewart 1989

Page 1

PROLOGUE

CLOCKWORK OR CHAOS?

"YOU BELIEVE IN A GOD WHO PLAYS DICE, AND I IN COMPLETE LAW AND ORDER."

Albert Einstein, Letter to Max Born

 

 

 

 

-
3
L
A
W
-
-
-
-
-
--
-
-
-
-
12
1
23
+
=
36
3+6
=
9
=
9
-
-
3
1
5
+
=
9
-
=
9
-
9
-
3
L
A
W
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
2
``-
-
-
-
-
-
2
-
-
-
-
-
``-
-
3
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
4
-
-
-
-
-
``-
-
-
-
5
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
36
3
L
A
W
-
-
9
-
-
3
-
9
3+6
``-
-
-
-
-
-
-
-
-
-
-
-
9
3
L
A
W
-
-
9
-
-
3
-
9
-
-
3
1
5
-
-
-
-
-
-
-
-
9
3
L
A
W
-
-
9
-
-
3
-
9

 

 

3
L
A
W
-
-
-
-
-
--
-
-
-
12
1
23
+
=
36
3+6
=
9
=
9
-
3
1
5
+
=
9
-
=
9
-
9
3
L
A
W
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
-
3
-
-
-
-
3
occurs
x
1
=
3
-
-
-
5
-
-
5
occurs
x
1
=
5
3
L
A
W
-
-
9
-
-
3
-
9
``-
-
-
-
-
-
-
-
-
-
-
-
3
L
A
W
-
-
9
-
-
3
-
9
-
3
1
5
-
-
-
-
-
-
-
-
3
L
A
W
-
-
9
-
-
3
-
9

 

 

3
THE
33
15
6
3
LAW
36
9
9
2
OF
21
12
3
5
CAUSE
49
13
4
3
AND
19
10
1
6
EFFECT
45
27
9
22
First Total
203
86
32
2+2
Add to Reduce
2+0+3
8+6
3+2
4
Second Total
5
14
5
-
Reduce to Deduce
-
1+4
-
4
Essence of Number
5
5
5

 

 

21-
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
-
-
6
-
-
-
-
-
1
-
-
-
5
-
-
-
-
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
8
-
-
-
-
-
-
15
-
-
-
-
-
19
-
-
-
14
-
-
-
-
-
-
-
-
+
=
56
5+6
=
11
1+1
2
=
2
-
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
1
5
-
-
6
-
3
1
3
-
5
-
1
-
4
-
5
6
6
5
3
2
+
=
66
6+6
=
12
1+2
3
=
3
-
-
20
-
5
-
12
1
23
-
-
6
-
3
1
21
-
5
-
1
-
4
-
5
6
6
5
3
20
+
=
147
1+4+7
=
12
1+2
3
=
3
-
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
12
1
23
-
15
6
-
3
1
21
19
5
-
1
14
4
-
5
6
6
5
3
20
+
=
203
2+0+3
=
5
=
5
=
5
-
-
2
8
5
-
3
1
5
-
6
6
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
+
=
86
8+6
=
14
1+4
5
=
5
-
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
4
=
4
=
4
-
``-
2
-
-
-`
-
-
-
-`
-
-
-`
-
-
-
-
-
-`
-
-
-
-`
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
-
-
-
-
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
16
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
29
-
-
22
-
86
-
32
1+6
2+2
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
2+9
-
-
2+2
-
8+6
-
3+2
7
4
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
11
-
-
4
-
14
-
5
-
-
2
8
5
-
3
1
5
-
6
6
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
-
-
1+1
-
-
-
-
1+4
-
-
7
4
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
2
-
-
4
-
5
-
5

 

 

22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
-
-
6
-
-
-
-
-
1
-
-
-
5
-
-
-
-
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
8
-
-
-
-
-
-
15
-
-
-
-
-
19
-
-
-
14
-
-
-
-
-
-
-
-
+
=
56
5+6
=
11
1+1
2
=
2
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
1
5
-
-
6
-
3
1
3
-
5
-
1
-
4
-
5
6
6
5
3
2
+
=
66
6+6
=
12
1+2
3
=
3
-
20
-
5
-
12
1
23
-
-
6
-
3
1
21
-
5
-
1
-
4
-
5
6
6
5
3
20
+
=
147
1+4+7
=
12
1+2
3
=
3
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
12
1
23
-
15
6
-
3
1
21
19
5
-
1
14
4
-
5
6
6
5
3
20
+
=
203
2+0+3
=
5
=
5
=
5
-
2
8
5
-
3
1
5
-
6
6
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
+
=
86
8+6
=
14
1+4
5
=
5
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
4
=
4
=
4
``-
2
-
-
-`
-
-
-
-`
-
-
-`
-
-
-
-
-
-`
-
-
-
-`
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
3
-
-
-
-
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
22
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
29
-
-
22
-
86
-
32
2+2
-
-
5
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
2+9
-
-
2+2
-
8+6
-
3+2
4
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
11
-
-
4
-
14
-
5
-
2
8
5
-
3
1
5
-
6
6
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
-
-
1+1
-
-
-
-
1+4
-
-
4
T
H
E
-
L
A
W
-
O
F
-
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
2
-
-
4
-
5
-
5

 

 

5
CAUSE
49
13
4
3
AND
19
10
1
6
EFFECT
45
27
9
14
Add to Reduce
113
50
14
1+4
Reduce to Deduce
1+1+3
5+0
1+4
5
Essence of Number
5
5
5

 

 

-
14
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
1
-
-
-
5
-
-
-
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
-
-
19
-
-
-
14
-
-
-
-
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
14
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
-
3
1
3
-
5
-
1
-
4
-
5
6
6
5
3
2
+
=
44
4+4
=
8
=
8
=
8
-
-
3
1
21
-
5
-
1
-
4
-
5
6
6
5
3
20
+
=
80
8+0
=
8
=
8
=
8
-
14
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
-
3
1
21
19
5
-
1
14
4
-
5
6
6
5
3
20
+
=
113
1+1+3
=
5
=
5
=
5
-
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
+
=
50
5+0
=
5
=
5
=
5
-
14
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-`
-
-
-
-`
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
24
14
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
21
-
-
14
-
50
-
23
2+4
1+4
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
2+1
-
-
1+4
-
5+0
-
2+3
6
5
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
3
-
-
5
-
5
-
5
-
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
-
-
-
-
-
-
-
-
-
-
6
5
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
3
-
-
5
-
5
-
5

 

 
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
-
-
-
5
-
-
-
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
-
19
-
-
-
14
-
-
-
-
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
14
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
3
1
3
-
5
-
1
-
4
-
5
6
6
5
3
2
+
=
44
4+4
=
8
=
8
=
8
-
3
1
21
-
5
-
1
-
4
-
5
6
6
5
3
20
+
=
80
8+0
=
8
=
8
=
8
14
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
--
-
-
-
-
-
3
1
21
19
5
-
1
14
4
-
5
6
6
5
3
20
+
=
113
1+1+3
=
5
=
5
=
5
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
+
=
50
5+0
=
5
=
5
=
5
14
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-`
-
-
-
-`
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
3
-
3
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
4
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
21
-
-
14
-
50
-
23
1+4
-
-
-
-
5
-
-
5
-
-
5
-
-
5
-
-
-
-
2+1
-
-
1+4
-
5+0
-
2+3
5
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
3
-
-
5
-
5
-
5
-
3
1
3
1
5
-
1
5
4
-
5
6
6
5
3
2
-
-
-
-
-
-
-
-
-
-
5
C
A
U
S
E
-
A
N
D
-
E
F
F
E
C
T
-
-
3
-
-
5
-
5
-
5

 

 

S
=
1
-
12
SCHRODINGERS
139
67
4
C
=
3
-
3
CAT
24
6
6
D
=
4
-
3
DID
17
17
8
C
=
3
-
10
CURIOUSITY
160
52
7
K
=
2
-
4
KILL
44
17
8
T
=
2
-
3
THE
33
15
6
C
=
3
-
3
CAT
24
6
6
-
-
18
4
38
First Total
441
180
45
-
-
1+8
-
3+8
Add to Reduce
4+4+1
1+8+0
4+5
-
-
9
-
11
Second Total
9
9
9
4
4
-
4
1+1
Reduce to Deduce
-
-
4
Q
-
9
5
2
Essence of Number
9
9
9

 

 

Daily Mail

Tuesday, June 1, 2010

Answers to Correspondents Compiled by Charles Legge

Page 59

QUESTION

I know the phrase 'curiosity killed the cat', but I have recently been told it continues 'satisfaction brought it back'. What is the origin of this?

ORIGINALLY 'care' killed the cat, not curiosity. That form of the expression is first found in Ben Jonson's play Every Man In His Humour, in 1598: 'Helterskelter, hang sorrow, care'll kill a cat, uptails all and a louse for the hangman.' In this sense, care meant 'worry or sorrow'. rather than the modern 'look after or provide for'. The play was first performed by the Lord Chamberlain's men, a troupe of actors of which Shakespeare was a member.

He obviously liked the line because he used it the following year in Much Ado About Nothing: 'What, courage man! What though care killed a cat, thou hast mettle in thee to kill care.'

The notion of curiosity has been frowned on, particularly by early theologians. St Augustine wrote in confessions (AD397) 'God fashioned hell for the inquisitive'', so the idea of curiosity killing the cat would seem logical.

Yet as late as 1898 the original form was still in use. Brewster's Dictionary Of Phrase And Fable had: 'Care killed the Cat. It is said that a cat has nine lives, but care would wear them all out.'

The. earliest known printed reference is in the O. Henry short story Schools And Schools from 1909: 'Curiosity can do more things than Kill a cat; and if emotions. well recognised as feminine, are inimical to feline life, then jealously would soon leave the world catless.'

The rejoinder 'satisfaction brought it back' is a curiosity in itself; the idea is obvious: if you are satisfied with your lot, you are unlikely to be curious about an alternative life.

When.the rejoinder was coined is uncertain, but it dates from the mid to late 20th century and seems to have been part of a ditty popularised
by a murderous Jack Nicholson in the movie The Shining (1980)

Curiosity killed the cat
Satisfaction brought it back
Safe and sound.
From hcad, to ground
From head.to ground
It was safe and sound.'

Jon Welham, Halifax.

 

 

THE GALACTIC CLUB

Intelligent life in outer space?

Ronald N. Bracewell 1974

Page 1

Chapter 1

ARE WE ALONE?


"Growing in size and complexity
Living things, masses of atoms, DNA, protein
Dancing a pattern ever more intricate.
Out of the cradle onto the dry land
Here it is standing
Atoms with consciousness
Matter with curiosity.
Stands at the sea
Wonders at wondering
I
A universe of atoms
An atom in the universe."

Richard P. Feynman

 

 

 

 

 

I

SAY

HAVE

I

MENTIONED DIVINE THOUGHT DIVINE CONSCIENCE

I

SAY

HAVE

I

MENTIONED

GODS

DIVINE LOVE DIVINE

HAVE

I

MENTIONED

THAT

?

I

HAVE

O

GOOD

 

 

THOSE PATENT PATIENT PATTERN MAKERS

 

 

Nature's Numbers
Ian Stewart 1995

Numerology is the easiest-and consequently the most dangerous-method for finding patterns. It is easy because anybody can do it and dangerous for the same reason. The difficulty lies in distinguishing significant numerical patterns from accidental ones. Here's a case in point. Kepler was fascinated with patterns in nature, and he devoted much of his life to looking for them in the behaviour of the planets. He devised a simple and tidy theory for the existence of precisely six planets (in his time only Mercury, Venus, Earth, Mars, Jupiter, and Saturn were known). He also discovered a very strange pattern relating the orbital period of a / planet- the time it takes to go once around the Sun-to its distance from the Sun. Recall that the square of a number is what you get when you multiply it by itself: for example, the square of 4 is 4 x 4 = 16. Similarly, the cube is what you get when you multiply it by itself twice: for example, the cube of 4 is 4 x 4 x 4 = 64. Kepler found that if you take the cube of the distance of any planet from the Sun and divide it by the square of its orbital period, you always get the same number. It was not an especially elegant number, but it was the same for all six planets.

Which of these numerological observations is the more significant? The verdict of posterity is that it is the second one, the complicated and rather arbitrary calculation with squares and cubes. This numerical pattern was one of the key steps towards Isaac Newton's theory of gravity, which has explained all sorts of puzzles about the motion of stars and planets. In contrast, Kepler's neat, tidy theory for the number of planets has been buried without trace. For a start it must have been wrong, because we now know of nine planets, not six. There could be even more, farther out from the Sun, and small enough to be undetectable But more important, we no longer expect to find a neat, tidy theory for the number of planets. We think that the Solar System condensed from a cloud of gas surrounding the Sun, and the number of planets presumably depended on the amount of matter in the gas cloud, how it was distributed, and how fast and in what directions it was moving. An equally plausible gas cloud could have given us eight planets, or eleven; the number is accidental, depending on the initial conditions of the gas cloud, rather than universal, reflecting a general law of nature"

Page 6

" The big problem with numerological pattern-seeking is that it generates millions of accidentals for each universal. Nor is it always obvious which is which. For example, there are three stars, roughly equally spaced and in a straight line, in the belt of the constellation Orion. Is that a clue to a significant law of nature?
Here's a similar question. Io, Europa, and Ganymede are three of Jupiter's larger satellites. They orbit the planet in , respectively, 1.77, 3.55, and 7.16 days. Each of these numbers is almost exactly twice the previous one. Is that a significant pattern? Three stars in a row, in terms of orbital period. Which pattern if either, is an important clue..."
    "… In addition to numerical patterns there are geometric ones…"
    "… Until recently the main shapes that appealed to mathematicians were very simple ones: triangles, squares, pen / Page 7 /tagons, hexagons, circles, ellipses, spirals, cubes, spheres, cones, and so on. All of these shapes can be found in nature, although some are far more common, or more evident, than others. The rainbow, for example, is a collection of circles, one for each colour. We don't normally see the entire circle just an arc; but rainbows seen from the air can be complete circles. You also see circles in the ripples on a pond, in the human eye, and on butterflies wings.
         Talking of ripples, the flow of fluids provides an inexhaustible supply of nature's patterns. There are waves of many different kinds-surging toward a beach in parallel ranks, spreading in a V-shape behind a moving boat, radiating outward from an underwater earthquake…"
"…There are swirling spiral whirlpools and tiny vortices. And there is the apparently structureless, random frothing of turbulent flow, one of the great enigmas of mathematics and physics. There are similar patterns in the atmosphere, too, the most dramatic being the vast spiral of a hurricane…"
    "…There are also wave patterns on land. The most strikingly mathematical landscapes on Earth are to be found in the great ergs, or sand oceans, of the Arabian and Sahara deserts. Even when the wind blows steadily in a fixed direction, sand dunes form. The simplest pattern is that of transverse dunes, which-just like ocean waves-line up in parallel straight rows at right angles to the prevailing wind direction. Sometimes the rows themselves become wavy in which case they are called barchanoid ridges; sometimes they break up into / Page 8 / innumerable shield-shaped barchan dunes. If the sand is slightly moist, and there is a little vegetation to bind it together, then you may find parabolic dunes-shaped like a U, with the rounded end pointing in the direction of the wind. These sometimes occur in clusters, and they resemble the teeth of a rake. If the wind direction is variable, other forms become possible. For example, clusters of sand shaped dunes can form, each having several irregular arms radiating from a central peak. They arrange themselves in a random pattern of spots.

Chapter 6

Page 81

"Nature's symmetries can be found on every scale, from the structure of subatomic particles to that of the entire universe. Many chemical molecules are symmetric. The methane molecule is a tetrahedron - a triangular-sided pyramid - with one carbon atom at its center and four hydrogen atoms at its corners Benzene has the sixfold symmetry of a regular hexagon. The fashionable molecule buckminsterfullerene is a truncated icosahedral cage of sixty carbon atoms. (An icosahedron is a regular solid with twenty triangular faces;
"truncated" means that the corners are cut off.) Its symmetry lends it a remarkable stability, which has opened up new possibilities for organic chemistry.
    On a slightly larger scale than molecules, we find symmetries in cellular structure; at the heart of cellular replication lies a tiny piece of mechanical engineering. Deep within each / Page 82  / living cell, there is a rather shapeless structure known as the centrosome, which sprouts long thin microtubules, basic components of the cell's internal "skeleton", like a diminutive sea urchin. Centrsomes were first discovered in 1887 and play an important role in organizing cell division. How-ever in one respect the structure of the centresome is astonishingly symmetric. Inside it has two structures, known as centrioles, positioned at right angles to each other. Each centriole is cylindrical, made from twenty-seven microtubules fused together along their lengths in threes, and arranged with perfect ninefold symmetry. The microtubules themselves also have an astonishingley regular symmetric form. They are hollow tubes, made from a perfect regular checkerboard pattern of units that contain two distinct proteins, alpha- and betatubulin. One day, perhaps, we will understand why nature chose these symmetric forms. But it is amazing to see symmetric structures at the core of a living cell. "

 

CELL = 3533 = CELL

3533 = CELL = 3533

CELL = 3533 = CELL

CELL = 5 = CELL

SEE EL EL SEE

C ELL ELL C

CIRCLE = 5 5 = CIRCLE

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

0
-
Z
=
8
-
4
ZERO
64
28
1
1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
42
-
40
Add
522
225
45
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
9
-
-
-
6
-
4
Deduce
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
-
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

 

1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
34
-
36
Add
458
197
44
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
9
-
-
-
7
4
9
Deduce
17
17
8
-
-
-
-
-
-
-
Produce
1+7
1+7
-
9
-
-
-
7
-
9
Essence
8
8
8

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
34
-
36
Add
458
197
44
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
7
4
9
Deduce
17
17
8
-
1
4
3
8
5
18
14
8
9
-
-
-
-
-
-
-
Produce
1+7
1+7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
7
-
9
Essence
8
8
8
-
1
4
3
8
5
9
5
8
9

 

 

0
-
4
ZERO
8
5
9
6
-
=
28
2+8
=
10
1+0
1
1
-
3
ONE
6
5
5
-
-
=
16
1+6
=
7
-
7
2
-
3
TWO
2
5
6
-
-
=
13
1+3
=
4
-
4
3
-
5
THREE
2
8
9
5
5
=
29
2+9
=
11
1+1
2
4
-
4
FOUR
6
6
3
9
-
=
24
2+4
=
6
-
6
5
-
4
FIVE
6
9
4
5
-
=
24
2+4
=
6
-
6
6
-
3
SIX
1
9
6
-
-
=
16
1+6
=
7
-
7
7
-
5
SEVEN
1
5
4
5
5
=
20
2+0
=
2
-
2
8
-
5
EIGHT
5
9
7
8
2
=
31
3+1
=
4
-
4
9
-
4
NINE
5
9
5
5
-
=
24
2+4
=
6
-
6
45
-
40
Add
42
70
58
43
12
-
225
-
-
63
-
45
4+5
-
4+0
-
4+2
7+0
5+8
4+3
1+2
-
2+2+5
-
-
6+3
-
4+5
9
-
4
Reduce
6
7
13
7
3
-
9
-
-
9
-
-
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
9
-
4
Deduce
6
7
4
7
3
-
9
-
-
9
-
9

 

 

O
=
6
3
ONE
34
16
7
T
=
2
3
TWO
58
13
4
T
=
2
5
THREE
56
29
2
F
=
6
4
FOUR
60
24
6
F
+
6
4
FIVE
42
24
6
S
=
1
3
SIX
52
16
7
S
=
1
5
SEVEN
65
20
2
E
=
5
5
EIGHT
49
31
4
N
=
5
4
NINE
42
24
6
-
-
39
36
-
458
197
44
-
-
3+9
3+6
-
4+5+8
1+9+7
4+4
-
-
12
9
-
17
17
8
-
-
1+2
-
-
-
-
-
-
-
3
9
-
8
8
8

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Page 32

5


To Sorcerers and Magicians number FIVE is the most powerful - five is the mark of the pentacle, a five pointed star drawn by extending the sides of a Pentagon. Five surely is in the possession of the occult. And the Pentagon is the geometric figure in which the golden ratio of classical art and architecture is found most.

 

 

THE

BALANCING

ONE TWO THREE FOUR

FIVE

NINE EIGHT SEVEN SIX

 

 

O
=
15
-
3
ONE
34
16
7
-
1
T
=
20
-
3
TWO
58
13
4
-
2
T
=
20
-
5
THREE
56
29
2
-
3
F
=
6
-
4
FOUR
60
24
6
-
4
-
-
61
-
15
Add
208
82
19
-
10
-
-
6+1
-
1+5
Reduce
2+0+8
8+2
1+9
-
1+0
-
-
7
-
6
Deduce
10
10
10
-
1
-
-
-
-
-
Produce
1+0
1+0
1+0
-
-
-
-
7
-
6
Essence
1
1
1
-
1

 

 

N
=
14
-
4
NINE
42
24
6
-
9
E
=
5
-
5
EIGHT
49
31
4
-
8
S
=
19
-
5
SEVEN
65
20
2
-
7
S
=
19
-
3
SIX
52
16
7
-
6
-
-
57
-
17
Add
208
91
19
-
30
-
-
5+7
-
1+7
Reduce
2+0+8
9+1
1+9
-
3+0
-
-
12
-
8
Deduce
10
10
10
-
3
-
-
1+2
-
-
Produce
1+0
1+0
1+0
-
-
-
-
3
-
8
Essence
1
1
1
-
3

 

 

4
FIVE
42
24
6

 

1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3 2 1

 

15
ONE TWO THREE FOUR
208
82
1
4
FIVE
42
24
6
17
NINE EIGHT SEVEN SIX
208
91
1

 

 

3
ONE
34
16
7
-
3
SIX
52
16
7
3
TWO
58
13
4
-
5
SEVEN
65
20
2
5
THREE
56
29
2
-
5
EIGHT
49
31
4
4
FOUR
60
24
6
-
4
NINE
42
24
6
15
Add
208
82
19
-
17
Add
208
91
19
1+5
Reduce
2+0+8
8+2
1+9
-
1+7
Reduce
2+0+8
9+1
1+9
6
Deduce
10
10
10
-
8
Deduce
10
10
10
-
Produce
1+0
1+0
1+0
-
-
Produce
1+0
1+0
1+0
6
Essence
1
1
1
-
8
Essence
1
1
1

 

ALWAYS BALANCING IS THAT FIVE THAT FIVE IS BALANCING ALWAYS

 

 

F
=
6
-
3
FOR
39
21
3
E
=
5
-
5
EVERY
75
30
3
A
=
1
-
6
ACTION
62
26
8
T
=
2
-
5
THERE
56
29
2
I
=
9
-
2
IS
28
19
1
A
=
1
-
2
AN
15
6
6
E
=
5
-
5
EQUAL
56
20
2
A
=
1
-
3
AND
19
10
1
O
=
6
-
8
OPPOSITE
115
43
7
R
=
9
-
8
REACTION
85
40
4
-
-
45
4
46
First Total
550
244
37
-
-
4+5
-
4+6
Add to Reduce
5+5+0
2+4+4
3+7
Q
-
9
-
10
Second Total
10
10
10
-
-
-
4
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
9
5
1
Essence of Number
1
1
1

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
5
ADDED
18
18
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
2
TO
35
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
3
ALL
25
7
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
5
MINUS
76
22
4
-
-
-
-
4
-
-
-
-
-
N
=
5
-
4
NONE
48
21
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
6
SHARED
55
28
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
10
EVERYTHING
133
61
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
10
MULTIPLIED
121
49
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
A
=
1
-
9
ABUNDANCE
65
29
2
-
-
2
-
-
-
-
-
-
-
-
-
35
-
58
First Total
626
266
59
-
1
2
3
8
5
6
14
8
18
-
-
3+5
-
5+8
Add to Reduce
6+2+6
2+6+6
5+9
-
-
-
-
-
-
-
1+4
-
1+8
-
-
8
-
13
Second Total
14
14
14
-
1
2
3
8
5
6
5
8
9
-
-
-
-
1+3
Reduce to Deduce
2+3
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Essence of Number
5
5
5
-
1
2
3
8
5
6
5
8
9

 

 

-
-
-
-
-
THE CODING
-
-
-
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CODING
52
34
7
-
-
5
-
9
THE CODING
85
49
13
-
-
-
-
-
-
8+5
4+9
1+3
-
-
5
-
9
THE CODING
13
13
4
-
-
-
-
-
-
1+3
1+3
-
-
-
5
-
9
THE CODING
4
4
4

 

 

-
-
-
-
-
THE CODING
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
-
THE CODING
33
15
15
-
-
-
-
-
-
-
-
-
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
6
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
7
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
9
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
34
-
-
THE CODING
52
34
34
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
1
2
3
4
10
6
7
8
9
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
1+0
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
8+5
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
13
13
4
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
4
4
4
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
THE CODING
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
1
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
C
=
3
4
1
C
3
3
3
-
1
-
3
-
-
-
-
-
-
O
=
6
5
1
O
15
6
6
-
1
-
-
-
-
6
-
-
-
D
=
4
6
1
D
4
4
4
-
1
-
-
4
-
-
-
-
-
I
=
9
7
1
I
9
9
9
-
1
-
-
-
-
-
-
-
9
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
-
-
G
=
7
9
1
G
7
7
7
-
1
-
-
-
-
-
7
-
-
T
=
2
-
3
THE
33
15
6
-
1
2
3
4
10
6
7
8
9
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
1+0
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
8+5
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
13
13
4
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
4
4
4
-
1
2
3
4
5
6
7
8
9

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
-
THE CODING
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
1
2
-
-
-
-
-
-
-
C
=
3
4
1
C
3
3
3
-
1
-
3
-
-
-
-
-
-
D
=
4
6
1
D
4
4
4
-
1
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
1
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
1
-
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
1
-
-
-
-
6
-
-
-
G
=
7
9
1
G
7
7
7
-
1
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
1
-
-
-
-
-
-
8
-
I
=
9
7
1
I
9
9
9
-
1
-
-
-
-
-
-
-
9
T
=
2
-
3
THE
33
15
6
-
1
2
3
4
10
6
7
8
9
C
=
3
-
6
CODING
52
34
7
-
-
-
-
-
1+0
-
-
-
-
-
-
5
-
9
THE CODING
85
49
13
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
8+5
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
13
13
4
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
THE CODING
4
4
4
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
THE CODING
-
-
-
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CODING
52
34
7
-
-
5
-
9
THE CODING
85
49
13
-
-
-
-
-
-
8+5
4+9
1+3
-
-
5
-
9
THE CODING
13
13
4
-
-
-
-
-
-
1+3
1+3
-
-
-
5
-
9
THE CODING
4
4
4

 


The Discovery of the Expanding Universe - SDSS SkyServer

https://skyserver.sdss.org › astro › universe › universe

The universe is in a constant state of change. The expanding universe, a new idea based on modern physics, laid to rest the paradoxes that troubled astronomers ...

The Expanding Universe

For thousands of years, astronomers wrestled with basic questions about the size and age of the universe. Does the universe go on forever, or does it have an edge somewhere? Has it always existed, or did it come to being some time in the past? In 1929, Edwin Hubble, an astronomer at Caltech, made a critical discovery that soon led to scientific answers for these questions: he discovered that the universe is expanding.

The ancient Greeks recognized that it was difficult to imagine what an infinite universe might look like. But they also wondered that if the universe were finite, and you stuck out your hand at the edge, where would your hand go? The Greeks' two problems with the universe represented a paradox - the universe had to be either finite or infinite, and both alternatives presented problems.

After the rise of modern astronomy, another paradox began to puzzle astronomers. In the early 1800s, German astronomer Heinrich Olbers argued that the universe must be finite. If the Universe were infinite and contained stars throughout, Olbers said, then if you looked in any particular direction, your line-of-sight would eventually fall on the surface of a star. Although the apparent size of a star in the sky becomes smaller as the distance to the star increases, the brightness of this smaller surface remains a constant. Therefore, if the Universe were infinite, the whole surface of the night sky should be as bright as a star. Obviously, there are dark areas in the sky, so the universe must be finite.

But, when Isaac Newton discovered the law of gravity, he realized that gravity is always attractive. Every object in the universe attracts every other object. If the universe truly were finite, the attractive forces of all the objects in the universe should have caused the entire universe to collapse on itself. This clearly had not happened, and so astronomers were presented with a paradox.

When Einstein developed his theory of gravity in the General Theory of Relativity, he thought he ran into the same problem that Newton did: his equations said that the universe should be either expanding or collapsing, yet he assumed that the universe was static. His original solution contained a constant term, called the cosmological constant, which cancelled the effects of gravity on very large scales, and led to a static universe. After Hubble discovered that the universe was expanding, Einstein called the cosmological constant his "greatest blunder."

At around the same time, larger telescopes were being built that were able to accurately measure the spectra, or the intensity of light as a function of wavelength, of faint objects. Using these new data, astronomers tried to understand the plethora of faint, nebulous objects they were observing. Between 1912 and 1922, astronomer Vesto Slipher at the Lowell Observatory in Arizona discovered that the spectra of light from many of these objects was systematically shifted to longer wavelengths, or redshifted. A short time later, other astronomers showed that these nebulous objects were distant galaxies.

The Discovery of the Expanding Universe

Meanwhile, other physicists and mathematicians working on Einstein's theory of gravity discovered the equations had some solutions that described an expanding universe. In these solutions, the light coming from distant objects would be redshifted as it traveled through the expanding universe. The redshift would increase with increasing distance to the object.

Edwin Hubble

In 1929 Edwin Hubble, working at the Carnegie Observatories in Pasadena, California, measured the redshifts of a number of distant galaxies. He also measured their relative distances by measuring the apparent brightness of a class of variable stars called Cepheids in each galaxy. When he plotted redshift against relative distance, he found that the redshift of distant galaxies increased as a linear function of their distance. The only explanation for this observation is that the universe was expanding.

Once scientists understood that the universe was expanding, they immediately realized that it would have been smaller in the past. At some point in the past, the entire universe would have been a single point. This point, later called the big bang, was the beginning of the universe as we understand it today.

The expanding universe is finite in both time and space. The reason that the universe did not collapse, as Newton's and Einstein's equations said it might, is that it had been expanding from the moment of its creation. The universe is in a constant state of change. The expanding universe, a new idea based on modern physics, laid to rest the paradoxes that troubled astronomers from ancient times until the early 20th Century.

The Heavy Elements

Astronomers are not only interested in the fate of the universe; they are also interested in understanding its present physical state. One question they try to answer is why the universe is primarily composed of hydrogen and helium, and what is responsible for the relatively small concentration of the heavier elements.

With the rise of nuclear physics in the 1930s and 40s, scientists started to try to explain the abundances of heavier elements by assuming they were synthesized out of primordial hydrogen in the early universe. In the late 1940s, American physicists George Gamow, Robert Herman, and Ralph Alpher realized that long ago, the universe was much hotter and denser. They made calculations to show whether nuclear reactions that took place at those higher temperatures could have created the heavy elements.

Unfortunately, with the exception of helium, they found that it was impossible to form heavier elements in any appreciable quantity. Today, we understand that heavy elements were synthesized either in the cores of stars or during supernovae, when a large dying star implodes.

Gamow, Herman, and Alpher did realize, though, that if the universe were hotter and denser in the past, radiation should still be left over from the early universe. This radiation would have a well-defined spectrum (called a blackbody spectrum) that depends on its temperature. As the universe expanded, the spectrum of this light would have been redshifted to longer wavelengths, and the temperature associated with the spectrum would have decreased by a factor of over one thousand as the universe cooled.

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
T
=
2
-
3
THE
33
15
6
E
=
5
-
9
EXPANDING
94
49
4
U
=
3
-
8
UNIVERSE
113
41
5
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
-
1+0
-
2+0
-
2+4+0
1+0+5
1+5
-
-
1
-
2
THE EXPANDING UNIVERSE
6
6
6

 

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EXPANDING
94
49
4
-
-
-
-
-
-
-
-
-
-
U
=
3
-
8
UNIVERSE
113
41
5
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
-
THE EXPANDING UNIVERSE
33
15
15
-
-
-
-
-
-
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
5
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
9
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
49
4
-
THE EXPANDING UNIVERSE
94
49
49
-
-
-
-
-
-
-
-
-
-
U
=
3
13
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
16
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
15
-
20
THE EXPANDING UNIVERSE
113
15
15
-
2
2
3
8
35
6
14
8
27
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
3+5
-
1+4
-
2+7
E
=
5
-
9
EXPANDING
94
34
7
-
2
2
3
8
8
6
5
8
9
U
=
3
-
8
UNIVERSE
113
15
6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
49
13
-
2
2
3
8
8
6
5
8
9
-
-
1+0
-
2+0
-
2+4+0
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
THE EXPANDING UNIVERSE
6
13
4
-
2
2
3
8
8
6
5
8
9

 

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EXPANDING
94
49
4
-
-
-
-
-
-
-
-
-
-
U
=
3
-
8
UNIVERSE
113
41
5
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
5
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
9
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
U
=
3
13
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
16
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
THE EXPANDING UNIVERSE
-
-
-
-
2
2
3
8
35
6
14
8
27
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
3+5
-
1+4
-
2+7
E
=
5
-
9
EXPANDING
94
34
7
-
2
2
3
8
8
6
5
8
9
U
=
3
-
8
UNIVERSE
113
15
6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
49
13
-
2
2
3
8
8
6
5
8
9
-
-
1+0
-
2+0
-
2+4+0
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
THE EXPANDING UNIVERSE
6
13
4
-
2
2
3
8
8
6
5
8
9

 

TRANSPOSED LETTERS REARRANGED IN NUMERICAL ORDER

 

-
-
-
-
20
THE EXPANDING UNIVERSE
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
E
=
5
-
9
EXPANDING
94
49
4
-
-
-
-
-
-
-
-
-
-
U
=
3
-
8
UNIVERSE
113
41
5
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
105
15
-
1
2
3
4
5
6
7
8
9
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
13
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
9
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
V
=
4
16
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
8
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
20
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
5
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
G
=
7
12
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
10
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
15
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
THE EXPANDING UNIVERSE
-
-
-
-
2
2
3
8
35
6
14
8
27
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
3+5
-
1+4
-
2+7
E
=
5
-
9
EXPANDING
94
34
7
-
2
2
3
8
8
6
5
8
9
U
=
3
-
8
UNIVERSE
113
15
6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
20
THE EXPANDING UNIVERSE
240
49
13
-
2
2
3
8
8
6
5
8
9
-
-
1+0
-
2+0
-
2+4+0
4+9
1+3
-
-
-
-
-
-
-
-
-
-
-
-
1
-
2
THE EXPANDING UNIVERSE
6
13
4
-
2
2
3
8
8
6
5
8
9

 

 

 

A PHOTON IS GOING THROUGH CUSTOMS

THE CUSTOMS OFFICER ASKS THE PHOTON WHERE ITS LUGGAGE IS

THE PHOTON ANSWERS I DON'T HAVE ANY I'M TRAVELLING LIGHT

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
I
=
9
-
2
IS
19
1
1
-
1
-
-
-
-
-
-
-
-
G
=
7
-
5
GOING
52
34
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
7
THROUGH
97
43
7
-
-
-
-
-
-
-
7
-
-
C
=
3
-
7
CUSTOMS
110
20
2
-
-
2
-
-
-
-
-
-
-
-
-
29
-
28
-
367
133
25
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
C
=
3
-
7
CUSTOMS
110
20
2
-
-
2
-
-
-
-
-
-
-
O
=
6
-
7
OFFICER
62
44
8
-
-
-
-
-
-
-
-
8
-
A
=
2
-
4
ASKS
50
14
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
W
=
5
-
5
WHERE
59
32
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
3
ITS
48
12
3
-
-
-
3
-
-
-
-
-
-
L
=
3
-
7
LUGGAGE
60
33
6
-
-
-
-
-
-
6
-
-
-
I
=
9
-
2
IS
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
19
-
44
-
562
229
49
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6
-
-
-
P
=
7
-
6
PHOTON
88
34
7
-
-
-
-
-
-
-
7
-
-
A
=
1
-
7
ANSWERS
99
27
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
-
4
DONT
53
17
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
4
HAVE
36
18
9
-
-
-
-
-
-
-
-
-
9
A
=
1
-
7
ANY
40
13
4
-
-
-
-
4
-
-
-
-
-
-
-
32
-
32
-
358
133
52
-
-
-
-
-
-
-
-
-
-
I
=
9
-
2
I'M
22
13
4
-
-
-
-
4
-
-
-
-
-
T
=
2
-
10
TRAVELLING
120
48
3
-
-
-
3
-
-
-
-
-
-
L
=
3
-
5
LIGHT
56
29
2
-
-
2
-
-
-
-
-
-
-
-
-
14
-
17
-
198
90
18
-
-
-
-
-
-
-
-
-
-
-
-
34
-
57
First Total
1485
585
252
-
3
6
6
8
10
24
35
16
27
-
-
3+4
-
5+7
Add to Reduce
1+4+8+5
5+8+5
2+5+2
-
-
-
-
-
 1+0
2+4
3+5
 1+6
2+7
-
-
7
-
12
Second Total
18
18
9
-
3
6
6
8
1
6
8
7
9
-
-
-
-
1+2
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
Third Total
9
9
9
-
3
6
6
8
1
6
8
7
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
3
Essence of Number
9
9
9
-
3
6
6
8
1
6
8
7
9

 

 

-
-
-
-
LIVING
-
-
-
L
=
3
1
L
12
3
3
I
=
9
1
I
9
9
9
V
=
4
1
V
22
4
4
I
=
9
1
I
9
9
9
N
=
5
1
N
14
5
5
G
=
7
1
G
7
7
7
-
-
37
6
LIVING
73
37
37
-
-
3+7
-
-
7+3
3+7
3+7
Q
-
10
6
LIVING
10
10
10
-
-
1+0
-
-
1+0
1+0
1+0
-
-
1
6
LIVING
1
1
1

 

 

-
6
L
I
V
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
5
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
9
-
9
14
-
+
=
32
3+2
=
5
=
5
=
5
-
6
L
I
V
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
3
-
4
-
-
7
+
=
14
1+4
=
5
=
5
=
5
-
-
12
-
22
-
-
7
+
=
41
4+1
=
5
=
5
=
5
-
6
L
I
V
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
12
9
22
9
14
7
+
+
73
7+3
=
10
1+0
1
=
1
-
-
3
9
4
9
5
7
+
+
37
3+7
=
10
1+0
1
=
1
-
6
L
I
V
I
N
G
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
8
EIGHT
9
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+7
9
17
6
L
I
V
I
N
G
-
-
28
-
-
6
-
37
-
28
1+0
-
-
9
-
9
-
-
-
-
2+8
-
-
-
-
3+7
-
2+8
8
6
L
I
V
I
N
G
-
-
10
-
-
6
-
10
-
10
-
-
3
9
4
9
5
7
-
-
1+0
-
-
-
-
1+0
-
1+0
8
6
L
I
V
I
N
G
-
-
1
-
-
6
-
1
-
1

 

 

6
L
I
V
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
5
-
+
=
23
2+3
=
5
=
5
=
5
-
-
9
-
9
14
-
+
=
32
3+2
=
5
=
5
=
5
6
L
I
V
I
N
G
-
-
-
-
-
-
-
-
-
-
-
3
-
4
-
-
7
+
=
14
1+4
=
5
=
5
=
5
-
12
-
22
-
-
7
+
=
41
4+1
=
5
=
5
=
5
6
L
I
V
I
N
G
-
-
-
-
-
-
-
-
-
-
-
12
9
22
9
14
7
+
+
73
7+3
=
10
1+0
1
=
1
-
3
9
4
9
5
7
+
+
37
3+7
=
10
1+0
1
=
1
6
L
I
V
I
N
G
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+7
9
6
L
I
V
I
N
G
-
-
28
-
-
6
-
37
-
28
-
-
9
-
9
-
-
-
-
2+8
-
-
-
-
3+7
-
2+8
6
L
I
V
I
N
G
-
-
10
-
-
6
-
10
-
10
-
3
9
4
9
5
7
-
-
1+0
-
-
-
-
1+0
-
1+0
6
L
I
V
I
N
G
-
-
1
-
-
6
-
1
-
1

 

 

BREATHE ON ME BREATH OF GOD

 

 

HOLY BIBLE

Scofield References

Page 7

GENESIS

C 2 V 7

And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
OXYGEN
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
36
-
6
OXYGEN
90
36
36
-
1
2
3
4
10
12
14
8
9
-
-
3+6
-
-
-
9+0
3+6
3+6
-
-
-
-
-
1+0
1+2
1+4
-
-
-
-
9
-
6
OXYGEN
9
9
9
-
1
2
3
4
1
3
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
5
6
7
-
-
-
-
-
OXYGEN
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
6
-
X
=
6
-
1
X
24
6
6
-
-
6
-
Y
=
7
-
1
Y
25
7
7
-
-
-
7
G
=
7
-
1
G
7
7
7
-
-
-
7
E
=
5
-
1
E
5
5
5
-
5
-
-
N
=
5
-
1
N
14
5
5
-
5
-
-
-
-
36
-
6
OXYGEN
90
36
36
-
10
12
14
-
-
3+6
-
-
-
9+0
3+6
3+6
-
1+0
1+2
1+4
-
-
9
-
6
OXYGEN
9
9
9
-
1
3
5

 

 

-
-
-
-
-
-
-
-
-
-
5
6
7
-
-
-
-
-
OXYGEN
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
5
-
-
N
=
5
-
1
N
14
5
5
-
5
-
-
O
=
6
-
1
O
15
6
6
-
-
6
-
X
=
6
-
1
X
24
6
6
-
-
6
-
Y
=
7
-
1
Y
25
7
7
-
-
-
7
G
=
7
-
1
G
7
7
7
-
-
-
7
-
-
36
-
6
OXYGEN
90
36
36
-
10
12
14
-
-
3+6
-
-
-
9+0
3+6
3+6
-
1+0
1+2
1+4
-
-
9
-
6
OXYGEN
9
9
9
-
1
3
5

 

 

A
=
1
-
1
BLACK
29
11
2
L
=
3
-
1
B
2
2
2
A
=
1
-
1
LACK
27
9
9
D
=
4
-
1
OF
21
12
3
D
=
4
-
1
LIGHT
56
29
2
4
4
27
4
7
Add to Reduce
135
54
18
-
-
2+7
-
-
Reduce to Deduce
1+3+5
2+7
1+8
-
-
9
-
7
Essence of Number
9
9
9

 

 

N
=
5
-
11
NOTHINGNESS
144
54
9
N
=
5
-
7
NOTHING
87
42
6
-
-
-
-
-
-
-
-
-
E
=
5
-
5
EMPTY
79
25
6
E
=
5
-
9
EMPTYNESS
120
39
3
-
-
-
-
-
-
-
-
-
E
=
5
-
7
EXTINCT
95
32
5
E
=
5
-
10
EXTINCTION
133
52
7
-
-
-
-
-
-
-
-
-
A
=
1
-
4
ABYSS
66
12
3
V
=
4
-
10
VOID
50
23
5
-
-
-
-
-
-
-
-
-
V
=
4
-
5
VACUUM
81
18
9
-
-
-
-
-
-
-
-
-

 

 

Higgs boson - Wikipedia
https://en.wikipedia.org/wiki/Higgs_boson

The Higgs boson is an elementary particle in the Standard Model of particle physics. First suspected to exist in the 1960s, it is the quantum excitation of the Higgs field, a fundamental field of crucial importance to particle physics theory. Unlike other known fields such as the electromagnetic field, it has a non-zero constant ...

Higgs boson
Subatomic particle

The Higgs boson is an elementary particle in the Standard Model of particle physics. First suspected to exist in the 1960s, it is the quantum excitation of the Higgs field, a fundamental field of crucial importance to particle physics theory. Wikipedia

Composition: Elementary particle

Classification: Boson

Symbol: H°

Mass: 125.09±0.21 (stat.)±0.11 (syst.) GeV/c² (CMS+ATLAS)

Electric charge: 0 e

Discovered: Large Hadron Collider (2011–2013)

Mean lifetime: 1.56×10-22 s (predicted)

 

T
=
2
-
3
THE
33
15
6
H
=
8
-
5
HIGGS
50
41
5
B
=
2
-
5
BOSON
65
29
2
-
-
12
-
13
First Total
148
85
13
-
-
1+2
-
1+3
Add to Reduce
1+4+8
8+5
-
-
-
3
-
4
Second Total
13
13
4
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
3
-
4
Essence of Number
4
4
4

 

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
THE
-
-
-
-
-
-
3
4
-
-
-
-
-
T
=
6
1
1
T
20
2
2
-
-
2
3
4
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
-
-
-
-
15
-
3
THE
33
15
15
-
-
-
3
4
-
-
-
-
-
-
-
-
-
-
HIGGS
-
-
-
-
-
-
3
4
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
3
4
-
-
-
-
9
G
=
7
6
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
S
=
1
8
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
-
-
32
-
5
HIGGS
50
41
32
-
-
-
3
4
-
-
-
-
-
-
-
-
-
-
BOSON
-
-
-
-
-
-
3
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
3
4
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
-
-
-
-
20
-
5
BOSON
65
29
20
-
-
-
3
4
-
-
-
-
-
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
3
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
3
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
3
4
1
3
5
7
9

 

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
6
1
1
T
20
2
2
-
-
2
3
4
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
3
4
-
-
-
-
9
G
=
7
6
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
S
=
1
8
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
3
4
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
-
-
-
-
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
3
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
3
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
3
4
1
3
5
7
9

 

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
8
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
3
4
-
-
-
-
-
T
=
6
1
1
T
20
2
2
-
-
2
3
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
3
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
-
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
3
4
-
6
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
3
4
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
H
=
8
4
1
H
8
8
8
-
-
-
3
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
3
4
-
-
-
-
9
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
3
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
3
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
3
4
1
3
5
7
9

 

 

-
-
-
-
-
THE HIGGS BOSON
-
-
-
-
1
2
5
6
7
8
9
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
-
T
=
6
1
1
T
20
2
2
-
-
2
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
5
-
-
-
-
N
=
5
13
1
N
14
5
5
-
-
-
5
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
6
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
-
6
-
-
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
7
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
8
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
9
-
-
67
-
13
THE HIGGS BOSON
148
85
67
-
2
4
10
12
14
16
9
6+7
-
1+3
-
1+4+8
8+5
6+7
-
-
-
1+0
1+2
1+4
1+6
-
-
-
13
-
4
THE HIGGS BOSON
13
13
13
-
2
4
1
3
5
7
9
-
-
1+3
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
4
-
4
THE HIGGS BOSON
4
4
4
-
2
4
1
3
5
7
9

 

 

H
=
8
-
5
HIGGS
50
32
5
B
=
2
-
5
BOSON
65
20
2
P
=
7
-
8
PARTICLE
84
39
3
-
-
17
-
18
First Total
199
91
10
-
-
1+7
-
1+8
Add to Reduce
1+9+9
9+1
1+0
-
-
8
-
18
Second Total
10
10
1
-
-
-
-
1+8
Reduce to Deduce
1+0
1+0
-
-
-
8
-
9
Essence of Number
1
1
1

 

 

BBC - h2g2 - Heisenberg's Uncertainty Principle www.bbc.co.uk/dna/h2g2/A408638Cached - Similar
10 Jun 2003 – Simply put, Heisenberg's Uncertainty Principle states that it is impossible to know both the exact position and the exact velocity of an object at ...

•Frequency of visible light ≈ 1014 Hz

•λ = wavelength = (c / frequency) ≈ (108 ms-1)/(1014 Hz ) ≈ 10-6 m

This is one millionth of a metre, one thousandth of a millimetre.

As the speed of light in a vacuum is constant, to reduce the wavelength of a photon, its frequency of the light must be increased. Using Energy = hf, where h is Planck's constant and f is the photon's frequency, the greater the photon's frequency, the greater the energy it carries, as h is always constant.

The wavelength of a particle is described by the DeBroglie formula as λ = (Planck's constant)/(momentum) = h/mc. Therefore, mc = h/λ

Photons have no rest mass but, when moving, have an apparent mass due to their kinetic energy (energy of motion). Using E=mc2, their apparent mass is E/c2

When one of these photons bounces off the electron, the electron's momentum will, therefore, be changed. This is similar to the way billiard balls change their trajectories when they collide.

The change in the electron's momentum (Δmv) is uncertain and will be of the same order and magnitude as the photon's momentum: Δmv ≈ (h/λ)

Since c in f = c / λ is constant, an increase in the photon's wavelength leads to a decrease in its frequency and, therefore, a decrease in the energy it carries. Therefore, the uncertainty in its momentum is smaller.

The photon of light cannot measure the electron's position (x) with perfect accuracy. Considering the photon of light as a wave, to increase the accuracy in position measurement, a photon with a smaller wavelength must be used. However, the smaller the wavelength of light, the higher its frequency and the higher its energy. Therefore, on collision with the electron, it will change its momentum a relatively large amount, meaning the momentum is less accurately determined when the position is more accurately determined. The opposite is also true - if the momentum is more accurately determined, the position must be less accurately determined.

An estimate of the position of the particle is at least one photon wavelength from the original position.

The uncertainty in position, Δx, ≥ one photon wavelength. Therefore, Δx ≥ λ

The smaller the wavelength, the greater the accuracy in the measurement of the position, but, as the wavelength of the photon gets shorter, its frequency increases. According to the equation E = hf, the greater its frequency, the greater its energy and the greater the change in momentum when it collides with a particle. That is, the momentum of the electron has greater uncertainty when using photons with smaller wavelengths.

The opposite is also true - the longer the wavelength, the lower the energy and the lower the change in momentum. However, the greater the uncertainty in the position of the electron.

Crucially, we cannot know both the exact position and momentum of a particle - we can only find an approximation to each. The better the approximation to one, the worse the approximation to the other becomes.

The equations

Since Δmv ≈ h /λ and Δx ≥ λ the two can be combined:

ΔxΔmv ≥ hλ/λ. Therefore, ΔxΔp ≥ h

--------------------------------------------------------------------------------
1 'Position' means the location of the particle and momentum is its mass multiplied by its velocity.
2 It should be noted that here photons are considered as waves, rather than particles. The wave-particle duality is described in this entry



Formally stated, Newton's third law is: For every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.

 

F
=
6
-
3
FOR
39
21
3
E
=
5
-
5
EVERY
75
30
3
A
=
1
-
6
ACTION
62
26
8
T
=
2
-
5
THERE
56
29
2
I
=
9
-
2
IS
28
19
1
A
=
1
-
2
AN
15
6
6
E
=
5
-
5
EQUAL
56
20
2
A
=
1
-
3
AND
19
10
1
O
=
6
-
8
OPPOSITE
115
43
7
R
=
9
-
8
REACTION
85
40
4
-
-
45
4
46
First Total
550
244
37
-
-
4+5
-
4+6
Add to Reduce
5+5+0
2+4+4
3+7
Q
-
9
-
10
Second Total
10
10
10
-
-
-
4
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
9
5
1
Essence of Number
1
1
1

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
F
=
6
-
3
FOR
39
21
3
-
-
-
3
-
5
-
-
-
9
E
=
5
-
5
EVERY
75
30
3
-
-
-
3
-
5
-
-
-
9
A
=
1
-
6
ACTION
62
26
8
-
-
-
-
-
5
-
-
8
9
T
=
2
-
5
THERE
56
29
2
-
-
2
-
-
5
-
-
-
9
I
=
9
-
2
IS
28
19
1
-
1
-
-
-
5
-
-
-
9
A
=
1
-
2
AN
15
6
6
-
-
-
-
-
5
6
-
-
9
E
=
5
-
5
EQUAL
56
20
2
-
-
2
-
-
5
-
-
-
9
A
=
1
-
3
AND
19
10
1
-
1
-
-
-
5
-
-
-
9
O
=
6
-
8
OPPOSITE
115
43
7
-
-
-
-
-
5
-
7
-
9
R
=
9
-
8
REACTION
85
40
4
-
-
-
-
4
5
-
-
-
9
-
-
45
4
46
First Total
550
244
37
-
2
4
6
4
5
6
7
8
9
-
-
4+5
-
4+6
Add to Reduce
5+5+0
2+4+4
3+7
-
-
-
-
-
-
-
-
-
-
Q
-
9
-
10
Second Total
10
10
10
-
2
4
6
4
5
6
7
8
9
-
-
-
4
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
9
5
1
Essence of Number
1
1
1
-
2
4
6
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
I
=
9
-
2
IS
28
19
1
-
1
-
-
-
5
-
-
-
9
A
=
1
-
3
AND
19
10
1
-
1
-
-
-
5
-
-
-
9
T
=
2
-
5
THERE
56
29
2
-
-
2
-
-
5
-
-
-
9
E
=
5
-
5
EQUAL
56
20
2
-
-
2
-
-
5
-
-
-
9
F
=
6
-
3
FOR
39
21
3
-
-
-
3
-
5
-
-
-
9
E
=
5
-
5
EVERY
75
30
3
-
-
-
3
-
5
-
-
-
9
R
=
9
-
8
REACTION
85
40
4
-
-
-
-
4
5
-
-
-
9
A
=
1
-
2
AN
15
6
6
-
-
-
-
-
5
6
-
-
9
O
=
6
-
8
OPPOSITE
115
43
7
-
-
-
-
-
5
-
7
-
9
A
=
1
-
6
ACTION
62
26
8
-
-
-
-
-
5
-
-
8
9
-
-
45
4
46
First Total
550
244
37
-
2
4
6
4
5
6
7
8
9
-
-
4+5
-
4+6
Add to Reduce
5+5+0
2+4+4
3+7
-
-
-
-
-
-
-
-
-
-
Q
-
9
-
10
Second Total
10
10
10
-
2
4
6
4
5
6
7
8
9
-
-
-
4
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
9
5
1
Essence of Number
1
1
1
-
2
4
6
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
6
7
8
I
=
9
-
2
IS
28
19
1
-
1
-
-
-
-
-
-
A
=
1
-
3
AND
19
10
1
-
1
-
-
-
-
-
-
T
=
2
-
5
THERE
56
29
2
-
-
2
-
-
-
-
-
E
=
5
-
5
EQUAL
56
20
2
-
-
2
-
-
-
-
-
F
=
6
-
3
FOR
39
21
3
-
-
-
3
-
-
-
-
E
=
5
-
5
EVERY
75
30
3
-
-
-
3
-
-
-
-
R
=
9
-
8
REACTION
85
40
4
-
-
-
-
4
-
-
-
A
=
1
-
2
AN
15
6
6
-
-
-
-
-
6
-
-
O
=
6
-
8
OPPOSITE
115
43
7
-
-
-
-
-
-
7
-
A
=
1
-
6
ACTION
62
26
8
-
-
-
-
-
-
-
8
-
-
45
4
46
First Total
550
244
37
-
2
4
6
4
6
7
8
-
-
4+5
-
4+6
Add to Reduce
5+5+0
2+4+4
3+7
-
-
-
-
-
-
-
-
Q
-
9
-
10
Second Total
10
10
10
-
2
4
6
4
6
7
8
-
-
-
4
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
9
5
1
Essence of Number
1
1
1
-
2
4
6
4
6
7
8

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
6
7
8
F
=
6
-
3
FOR
39
21
3
-
-
-
3
-
-
-
-
E
=
5
-
5
EVERY
75
30
3
-
-
-
3
-
-
-
-
A
=
1
-
6
ACTION
62
26
8
-
-
-
-
-
-
-
8
T
=
2
-
5
THERE
56
29
2
-
-
2
-
-
-
-
-
I
=
9
-
2
IS
28
19
1
-
1
-
-
-
-
-
-
A
=
1
-
2
AN
15
6
6
-
-
-
-
-
6
-
-
E
=
5
-
5
EQUAL
56
20
2
-
-
2
-
-
-
-
-
A
=
1
-
3
AND
19
10
1
-
1
-
-
-
-
-
-
O
=
6
-
8
OPPOSITE
115
43
7
-
-
-
-
-
-
7
-
R
=
9
-
8
REACTION
85
40
4
-
-
-
-
4
-
-
-
-
-
45
4
46
First Total
550
244
37
-
2
4
6
4
6
7
8
-
-
4+5
-
4+6
Add to Reduce
5+5+0
2+4+4
3+7
-
-
-
-
-
-
-
-
Q
-
9
-
10
Second Total
10
10
10
-
2
4
6
4
6
7
8
-
-
-
4
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
-
-
-
-
-
-
-
-
9
5
1
Essence of Number
1
1
1
-
2
4
6
4
6
7
8

 

 

3
THE
33
15
6
3
LAW
36
9
9
2
OF
21
12
3
7
CLOSURE
93
30
3
15
First Total
93
30
21
1+5
Add to Reduce
9+3
3+0
2+1
6
Second Total
12
3
3
-
Reduce to Deduce
1+2
-
-
6
Essence of Number
3
3
3

 

 

-
-
-
-
-
LIGHT WAVES-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
10
LIGHT WAVES-
126
54
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
6
-
-
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
6
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
6
-
8
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
6
-
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
V
=
4
8
1
V
22
4
4
-
-
-
-
4
-
6
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
-
-
45
-
10
LIGHT WAVES
126
54
45
-
2
2
3
4
10
60
7
8
9
-
-
6+5
-
1+0
-
1+2+6
5+4
5+4
-
-
-
-
-
1+0
6+0
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
LIGHT WAVES-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
-
8
-
10
LIGHT WAVES-
126
54
9
-
1
2
3
4
5
6
7
8
9
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
6
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
6
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
6
-
-
-
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
6
-
-
-
V
=
4
8
1
V
22
4
4
-
-
-
-
4
-
6
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
6
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
6
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
6
-
8
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
6
-
-
9
-
-
45
-
10
LIGHT WAVES
126
54
45
-
2
2
3
4
10
60
7
8
9
-
-
6+5
-
1+0
-
1+2+6
5+4
5+4
-
-
-
-
-
1+0
6+0
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
LIGHT WAVES-
-
-
-
-
1
2
3
4
5
7
8
9
L
=
3
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
8
-
10
LIGHT WAVES-
126
54
9
-
1
2
3
4
5
7
8
9
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
-
-
V
=
4
8
1
V
22
4
4
-
-
-
-
4
-
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
8
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
45
-
10
LIGHT WAVES
126
54
45
-
2
2
3
4
10
7
8
9
-
-
6+5
-
1+0
-
1+2+6
5+4
5+4
-
-
-
-
-
1+0
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
1
LIGHT WAVES
9
9
9
-
2
2
3
4
1
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER

RE-ARRANGED IN NUMERICAL ORDER

 

 

-
-
-
-
-
SOUND WAVES
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND WAVES
143
53
8
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
4
1
N
23
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
5
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
19
-
-
-
73
28
19
-
-
-
-
-
-
-
-
-
-
W
=
5
6
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
V
=
4
8
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
10
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
16
-
-
SOUND WAVES-
70
25
16
-
-
-
-
-
-
-
-
-
-
-
-
35
-
5
SOUND
73
28
1
-
3
2
3
8
15
6
7
8
9
-
-
3+5
-
5
WAVES
70
25
7
-
-
-
-
-
1+5
-
-
-
-
-
-
8
-
10
SOUND WAVES
143
53
8
-
3
2
3
8
6
6
7
8
9
-
-
-
-
-
-
1+4+3
5+3
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
SOUND WAVES
8
8
8
-
3
2
3
8
6
6
7
8
9

 

 

-
-
-
-
-
SOUND WAVES
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND WAVES
143
53
8
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
2
-
-
-
-
7
8
9
O
=
6
2
1
O
15
6
6
-
-
2
-
-
-
6
7
8
9
U
=
3
3
1
U
21
3
3
-
-
2
3
-
-
-
7
8
9
N
=
5
4
1
N
23
5
5
-
-
2
-
-
5
-
7
8
9
D
=
4
5
1
D
4
4
4
-
-
2
-
4
-
-
7
8
9
W
=
5
6
1
W
23
5
5
-
-
2
-
-
5
-
7
8
9
A
=
1
7
1
A
1
1
1
-
1
2
-
-
-
-
7
8
9
V
=
4
8
1
V
22
4
4
-
-
2
-
4
-
-
7
8
9
E
=
5
9
1
E
5
5
5
-
-
2
-
-
5
-
7
8
9
S
=
1
10
1
S
19
10
1
-
1
2
-
-
-
-
7
8
9
-
-
-
-
-
SOUND WAVES-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
35
-
5
SOUND
73
28
1
-
3
2
3
8
15
6
7
8
9
-
-
3+5
-
5
WAVES
70
25
7
-
-
-
-
-
1+5
-
-
-
-
-
-
8
-
10
SOUND WAVES
143
53
8
-
3
2
3
8
6
6
7
8
9
-
-
-
-
-
-
1+4+3
5+3
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
SOUND WAVES
8
8
8
-
3
2
3
8
6
6
7
8
9

 

 

-
-
-
-
-
SOUND WAVES
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
WAVES
70
25
7
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND WAVES
143
53
8
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
2
-
-
-
-
7
8
9
A
=
1
7
1
A
1
1
1
-
1
2
-
-
-
-
7
8
9
S
=
1
10
1
S
19
10
1
-
1
2
-
-
-
-
7
8
9
U
=
3
3
1
U
21
3
3
-
-
2
3
-
-
-
7
8
9
D
=
4
5
1
D
4
4
4
-
-
2
-
4
-
-
7
8
9
V
=
4
8
1
V
22
4
4
-
-
2
-
4
-
-
7
8
9
N
=
5
4
1
N
23
5
5
-
-
2
-
-
5
-
7
8
9
W
=
5
6
1
W
23
5
5
-
-
2
-
-
5
-
7
8
9
E
=
5
9
1
E
5
5
5
-
-
2
-
-
5
-
7
8
9
O
=
6
2
1
O
15
6
6
-
-
2
-
-
-
6
7
8
9
-
-
-
-
-
SOUND WAVES-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
35
-
5
SOUND
73
28
1
-
3
2
3
8
15
6
7
8
9
-
-
3+5
-
5
WAVES
70
25
7
-
-
-
-
-
1+5
-
-
-
-
-
-
8
-
10
SOUND WAVES
143
53
8
-
3
2
3
8
6
6
7
8
9
-
-
-
-
-
-
1+4+3
5+3
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
1
SOUND WAVES
8
8
8
-
3
2
3
8
6
6
7
8
9

 

LETTERS TRANSPOSED INTO NUMBER

RE-ARRANGED IN NUMERICAL ORDER

 

 

-
-
-
-
-
LIGHT SOUND-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND LIGHT
129
57
3
-
1
2
3
4
5
6
7
8
9
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
29
-
-
-
56
29
29
-
-
-
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
5
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
19
-
-
-
73
28
19
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
LIGHT SOUND-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
48
-
5
SOUND
73
28
1
-
1
2
6
4
5
6
7
8
9
-
-
4+8
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
12
-
10
SOUND LIGHT
129
57
3
-
1
2
6
4
5
6
7
8
9
-
-
1+2
-
1+0
-
1+2+9
5+7
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
LIGHT SOUND-
12
12
3
-
1
2
6
4
5
6
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
SOUND LIGHT
8
8
3
-
1
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
LIGHT SOUND-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND LIGHT
129
57
3
-
1
2
3
4
5
6
7
8
9
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
5
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
LIGHT SOUND-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
48
-
5
SOUND
73
28
1
-
1
2
6
4
5
6
7
8
9
-
-
4+8
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
12
-
10
SOUND LIGHT
129
57
3
-
1
2
6
4
5
6
7
8
9
-
-
1+2
-
1+0
-
1+2+9
5+7
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
LIGHT SOUND-
12
12
3
-
1
2
6
4
5
6
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
SOUND LIGHT
8
8
3
-
1
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
LIGHT SOUND-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
5
SOUND
73
28
1
-
-
-
-
-
-
-
-
-
-
W
=
5
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
6
-
10
SOUND LIGHT
129
57
3
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
5
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
5
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
4
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
2
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
LIGHT SOUND-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
48
-
5
SOUND
73
28
1
-
1
2
6
4
5
6
7
8
9
-
-
4+8
-
5
LIGHT
56
29
2
-
-
-
-
-
-
-
-
-
-
-
-
12
-
10
SOUND LIGHT
129
57
3
-
1
2
6
4
5
6
7
8
9
-
-
1+2
-
1+0
-
1+2+9
5+7
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
LIGHT SOUND-
12
12
3
-
1
2
6
4
5
6
7
8
9
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
1
SOUND LIGHT
8
8
3
-
1
2
6
4
5
6
7
8
9

 

 

LETTERS TRANSPOSED INTO NUMBER

RE-ARRANGED IN NUMERICAL ORDER

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Preface to the New Edition

Page 5
Twelve years ago a little boy entered my imagination as he hopped across the centuries and played with numbers. I began to see how the simple architecture of our decimal system could be constructed in secret ways — not a building project this time but an abstract one. On the surface of our arithmetic countless combinations of numbers take part in tedious and exacting calculations but underneath it all there is pattern, governed by a repeating code of integers. The Sigma Code reduces numbers to a single digit and the illusion of the many is seen to be but the reflection of a few. This is not a book on maths: this is a book for anyone who can carry out simple sums in their heads, and who won't be short-changed knowingly.
When Number 9 first came out I received mail from many who played with numbers. They chased patterns; some had special numbers and even mystical systems. I was tempted to write about numerology but resisted. I wanted to write about the intricacy of what the.. numbers actually do and leave the reader to wonder about the larger irrational that seems to hover around such constructions.
If I were writing this book today the numbers would have featured in a wider context of structuring nature's patterns, and also playing the role of animator in algorithms that create unique architectural forms and shapes. I would also include my previous research into other base systems. But this book was a first step which came from a child-like urge, like playing with building blocks, to build out of our numbers — just the simple 1, 2, 3, up to number 9.

 

RESEARCH R E SEARCH ER RESEARCH

 

www.merriam-webster.com/dictionary/algorithm

a procedure for solving a mathematical problem (as of finding the greatest common divisor) in a finite number of steps that frequently involves repetition of an ...

algorithm [ˈælgəˌrɪðəm]
n
1. (Mathematics) a logical arithmetical or computational procedure that if correctly applied ensures the solution of a problem Compare heuristic
2. (Mathematics) Logic Maths a recursive procedure whereby an infinite sequence of terms can be generated Also called algorism
[changed from algorism, through influence of Greek arithmos number]
algorithmic adj
aal·go·rithm (lg-rm)
n.
A step-by-step problem-solving procedure, especially an established, recursive computational procedure for solving a problem in a finite number of steps.
algorithmically adv

algorithm (lg-rthm)
A finite set of unambiguous instructions performed in a prescribed sequence to achieve a goal, especially a mathematical rule or procedure used to compute a desired result. Algorithms are the basis for most computer programming.

Noun 1. algorithm - a precise rule (or set of rules) specifying how to solve some problem
algorithmic program, algorithmic rule
formula, rule - (mathematics) a standard procedure for solving a class of mathematical problems; "he determined the upper bound with Descartes' rule of signs"; "he gave us a general formula for attacking polynomials"
sorting algorithm - an algorithm for sorting a list
stemming algorithm, stemmer - an algorithm for removing inflectional and derivational endings in order to reduce word forms to a common stem algorithm
any methodology for solving a certain kind of problem.
See also: Mathematics

 

Algorithm
From Wikipedia, the free encyclopedia

Flow chart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields "yes" (or true) (more accurately the number b in location B is greater than or equal to the number a in location A) THEN, the algorithm specifies B ← B − A (meaning the number b − a replaces the old b). Similarly, IF A > B, THEN A ← A − B. The process terminates when (the contents of) B is 0, yielding the g.c.d. in A. (Algorithm derived from Scott 2009:13; symbols and drawing style from Tausworthe 1977).
In mathematics and computer science, an algorithm (i/ˈælɡərɪðəm/) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning.

More precisely, an algorithm is an effective method expressed as a finite list[1] of well-defined instructions[2] for calculating a function.[3] Starting from an initial state and initial input (perhaps empty),[4] the instructions describe a computation that, when executed, will proceed through a finite [5] number of well-defined successive states, eventually producing "output"[6] and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.[7]

Though al-Khwārizmī's algorism referred to the rules of performing arithmetic using Hindu-Arabic numerals and the systematic solution of linear and quadratic equations, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability"[8] or "effective method";[9] those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.[10]

Informal definition
For a detailed presentation of the various points of view around the definition of "algorithm" see Algorithm characterizations. For examples of simple addition algorithms specified in the detailed manner described in Algorithm characterizations, see Algorithm examples.
While there is no generally accepted formal definition of "algorithm," an informal definition could be "a set of rules that precisely defines a sequence of operations."[11] For some people, a program is only an algorithm if it stops eventually; for others, a program is only an algorithm if it stops before a given number of calculation steps.[12]

A prototypical example of an algorithm is Euclid's algorithm to determine the maximum common divisor of two integers; an example (there are others) is described by the flow chart above and as an example in a later section.

Boolos & Jeffrey (1974, 1999) offer an informal meaning of the word in the following quotation:

No human being can write fast enough, or long enough, or small enough† ( †"smaller and smaller without limit ...you'd be trying to write on molecules, on atoms, on electrons") to list all members of an enumerably infinite set by writing out their names, one after another, in some notation. But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.[13]

The term "enumerably infinite" means "countable using integers perhaps extending to infinity." Thus, Boolos and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be chosen from 0 to infinity. Thus an algorithm can be an algebraic equation such as y = m + n—two arbitrary "input variables" m and n that produce an output y. But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of (for the addition example):
Precise instructions (in language understood by "the computer")[14] for a fast, efficient, "good"[15] process that specifies the "moves" of "the computer" (machine or human, equipped with the necessary internally contained information and capabilities)[16] to find, decode, and then process arbitrary input integers/symbols m and n, symbols + and = ... and "effectively"[17] produce, in a "reasonable" time,[18] output-integer y at a specified place and in a specified format.
The concept of algorithm is also used to define the notion of decidability. That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules. In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension. From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete (in some sense) and abstract usage of the term.

[edit] Formalization

Algorithms are essential to the way computers process data. Many computer programs contain algorithms that detail the specific instructions a computer should perform (in a specific order) to carry out a specified task, such as calculating employees' paychecks or printing students' report cards. Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system. Authors who assert this thesis include Minsky (1967), Savage (1987) and Gurevich (2000):

Minsky: "But we will also maintain, with Turing . . . that any procedure which could "naturally" be called effective, can in fact be realized by a (simple) machine. Although this may seem extreme, the arguments . . . in its favor are hard to refute".[19]

Gurevich: "...Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ... according to Savage [1987], an algorithm is a computational process defined by a Turing machine".[20]

Typically, when an algorithm is associated with processing information, data is read from an input source, written to an output device, and/or stored for further processing. Stored data is regarded as part of the internal state of the entity performing the algorithm. In practice, the state is stored in one or more data structures.

For some such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable).

Because an algorithm is a precise list of precise steps, the order of computation will always be critical to the functioning of the algorithm. Instructions are usually assumed to be listed explicitly, and are described as starting "from the top" and going "down to the bottom", an idea that is described more formally by flow of control.

So far, this discussion of the formalization of an algorithm has assumed the premises of imperative programming. This is the most common conception, and it attempts to describe a task in discrete, "mechanical" means. Unique to this conception of formalized algorithms is the assignment operation, setting the value of a variable. It derives from the intuition of "memory" as a scratchpad. There is an example below of such an assignment.

For some alternate conceptions of what constitutes an algorithm see functional programming and logic programming.

[edit] Expressing algorithms

Algorithms can be expressed in many kinds of notation, including natural languages, pseudocode, flowcharts, programming languages or control tables (processed by interpreters). Natural language expressions of algorithms tend to be verbose and ambiguous, and are rarely used for complex or technical algorithms. Pseudocode, flowcharts and control tables are structured ways to express algorithms that avoid many of the ambiguities common in natural language statements. Programming languages are primarily intended for expressing algorithms in a form that can be executed by a computer, but are often used as a way to define or document algorithms.

There is a wide variety of representations possible and one can express a given Turing machine program as a sequence of machine tables (see more at finite state machine, state transition table and control table), as flowcharts (see more at state diagram), or as a form of rudimentary machine code or assembly code called "sets of quadruples" (see more at Turing machine).

Representations of algorithms can be classed into three accepted levels of Turing machine description:[21]
1 High-level description:
"...prose to describe an algorithm, ignoring the implementation details. At this level we do not need to mention how the machine manages its tape or head." 2 Implementation description:
"...prose used to define the way the Turing machine uses its head and the way that it stores data on its tape. At this level we do not give details of states or transition function." 3 Formal description:
Most detailed, "lowest level", gives the Turing machine's "state table". For an example of the simple algorithm "Add m+n" described in all three levels see Algorithm examples.
[edit] Implementation

Most algorithms are intended to be implemented as computer programs. However, algorithms are also implemented by other means, such as in a biological neural network (for example, the human brain implementing arithmetic or an insect looking for food), in an electrical circuit, or in a mechanical device.

[edit] Computer algorithms

Flowchart examples of the canonical Böhm-Jacopini structures: the SEQUENCE (rectangles descending the page), the WHILE-DO and the IF-THEN-ELSE. The three structures are made of the primitive conditional GOTO (IF test=true THEN GOTO step xxx) (a diamond), the unconditional GOTO (rectangle), various assignment operators (rectangle), and HALT (rectangle). Nesting of these structures inside assignment-blocks result in complex diagrams (cf Tausworthe 1977:100,114).
In computer systems, an algorithm is basically an instance of logic written in software by software developers to be effective for the intended "target" computer(s), in order for the target machines to produce output from given input (perhaps null).

"Elegant" (compact) programs, "good" (fast) programs : The notion of "simplicity and elegance" appears informally in Knuth and precisely in Chaitin:
Knuth: ". . .we want good algorithms in some loosely defined aesthetic sense. One criterion . . . is the length of time taken to perform the algorithm . . .. Other criteria are adaptability of the algorithm to computers, its simplicity and elegance, etc"[22] Chaitin: " . . . a program is 'elegant,' by which I mean that it's the smallest possible program for producing the output that it does"[23]
Chaitin prefaces his definition with: "I'll show you can't prove that a program is 'elegant'"—such a proof would solve the Halting problem (ibid).

Algorithm versus function computable by an algorithm: For a given function multiple algorithms may exist. This will be true, even without expanding the available instruction set available to the programmer. Rogers observes that "It is . . . important to distinguish between the notion of algorithm, i.e. procedure and the notion of function computable by algorithm, i.e. mapping yielded by procedure. The same function may have several different algorithms".[24]

Unfortunately there may be a tradeoff between goodness (speed) and elegance (compactness)—an elegant program may take more steps to complete a computation than one less elegant. An example of using Euclid's algorithm will be shown below.

Computers (and computors), models of computation: A computer (or human "computor"[25]) is a restricted type of machine, a "discrete deterministic mechanical device"[26] that blindly follows its instructions.[27] Melzak's and Lambek's primitive models[28] reduced this notion to four elements: (i) discrete, distinguishable locations, (ii) discrete, indistinguishable counters[29] (iii) an agent, and (iv) a list of instructions that are effective relative to the capability of the agent.[30]

Minsky describes a more congenial variation of Lambek's "abacus" model in his "Very Simple Bases for Computability".[31] Minsky's machine proceeds sequentially through its five (or six depending on how one counts) instructions unless either a conditional IF–THEN GOTO or an unconditional GOTO changes program flow out of sequence. Besides HALT, Minsky's machine includes three assignment (replacement, substitution)[32] operations: ZERO (e.g. the contents of location replaced by 0: L ← 0), SUCCESSOR (e.g. L ← L+1), and DECREMENT (e.g. L ← L − 1).[33] Rarely will a programmer have to write "code" with such a limited instruction set. But Minsky shows (as do Melzak and Lambek) that his machine is Turing complete with only four general types of instructions: conditional GOTO, unconditional GOTO, assignment/replacement/substitution, and HALT.[34]

Simulation of an algorithm: computer (computor) language: Knuth advises the reader that "the best way to learn an algorithm is to try it . . . immediately take pen and paper and work through an example".[35] But what about a simulation or execution of the real thing? The programmer must translate the algorithm into a language that the simulator/computer/computor can effectively execute. Stone gives an example of this: when computing the roots of a quadratic equation the computor must know how to take a square root. If they don't then for the algorithm to be effective it must provide a set of rules for extracting a square root.[36]

This means that the programmer must know a "language" that is effective relative to the target computing agent (computer/computor).

But what model should be used for the simulation? Van Emde Boas observes "even if we base complexity theory on abstract instead of concrete machines, arbitrariness of the choice of a model remains. It is at this point that the notion of simulation enters".[37] When speed is being measured, the instruction set matters. For example, the subprogram in Euclid's algorithm to compute the remainder would execute much faster if the programmer had a "modulus" (division) instruction available rather than just subtraction (or worse: just Minsky's "decrement").

Structured programming, canonical structures: Per the Church-Turing thesis any algorithm can be computed by a model known to be Turing complete, and per Minsky's demonstrations Turing completeness requires only four instruction types—conditional GOTO, unconditional GOTO, assignment, HALT. Kemeny and Kurtz observe that while "undisciplined" use of unconditional GOTOs and conditional IF-THEN GOTOs can result in "spaghetti code" a programmer can write structured programs using these instructions; on the other hand "it is also possible, and not too hard, to write badly structured programs in a structured language".[38] Tausworthe augments the three Böhm-Jacopini canonical structures:[39] SEQUENCE, IF-THEN-ELSE, and WHILE-DO, with two more: DO-WHILE and CASE.[40] An additional benefit of a structured program will be one that lends itself to proofs of correctness using mathematical induction.[41]

Canonical flowchart symbols[42]: The graphical aide called a flowchart offers a way to describe and document an algorithm (and a computer program of one). Like program flow of a Minsky machine, a flowchart always starts at the top of a page and proceeds down. Its primary symbols are only 4: the directed arrow showing program flow, the rectangle (SEQUENCE, GOTO), the diamond (IF-THEN-ELSE), and the dot (OR-tie). The Böhm-Jacopini canonical structures are made of these primitive shapes. Sub-structures can "nest" in rectangles but only if a single exit occurs from the superstructure. The symbols and their use to build the canonical structures are shown in the diagram.

 

EVOLVE LOVE EVOLVE

LOVES SOLVE LOVES

EVOLVE LOVE EVOLVE

 

Algorithm - Wikipedia, the free encyclopedia en.wikipedia.org/wiki/Algorithm

In mathematics and computer science, an algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and ...

 

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-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
5
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
5
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
5
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
5
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
5
-
-
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
5
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
5
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
5
-
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
5
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
5
-
-
-
9
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
5
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
6
7
8
9
-
-
-
-
-
ALGORITHMS
-
-
-
-
-
-
-
-
-
-
-
-
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
S
=
1
10
1
S
1
1
1
-
1
-
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
L
=
3
2
1
L
12
3
3
-
-
-
3
-
-
-
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
O
=
6
4
1
O
15
6
6
-
-
-
-
-
6
-
-
-
G
=
7
3
1
G
7
7
7
-
-
-
-
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
9
-
-
50
-
10
ALGORITHMS
122
50
50
-
2
2
3
4
6
7
8
18
-
-
5+0
-
1+0
-
1+2+2
5+5
5+0
-
-
-
-
-
-
-
-
1+8
-
-
5
-
1
ALGORITHMS
5
5
5
-
2
2
3
4
6
7
8
9

 

 

M
=
4
-
4
MIND
40
22
4
S
=
1
-
6
SPIRIT
91
37
1
M
=
4
-
6
MATTER
77
23
5
-
-
9
4
16
First Total
208
82
10
-
-
-
-
1+6
Add to Reduce
2+0+8
8+2
1+0
-
-
9
-
7
Second Total
10
10
1
-
-
-
4
-
Reduce to Deduce
1+0
1+0
-
-
-
9
5
7
Essence of Number
1
1
1

 

 

.ONE TWO THREE FOUR 5 SIX SEVEN EIGHT NINE

123 4 5 6789

THE

BALANCING

 

 

-
-
-
-
-
HARMONIC
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
-
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
-
45
-
8
HARMONIC
81
45
45
-
1
2
3
4
5
6
7
8
18
-
-
4+5
-
-
-
8+1
4+5
4+5
-
-
-
-
-
-
-
-
-
1+8
-
-
9
-
8
HARMONIC
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
HARMONIC
-
-
-
-
1
2
3
4
5
6
7
8
9
H
=
8
-
1
H
8
8
8
-
-
2
-
-
-
-
7
8
-
A
=
1
-
1
A
1
1
1
-
1
2
-
-
-
-
7
-
-
R
=
9
-
1
R
18
9
9
-
-
2
-
-
-
-
7
-
9
M
=
4
-
1
M
13
4
4
-
-
2
-
4
-
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
2
-
-
-
6
7
-
-
N
=
5
-
1
N
14
5
5
-
-
2
-
-
5
-
7
-
-
I
=
9
-
1
I
9
9
9
-
-
2
-
-
-
-
7
-
9
C
=
3
-
1
C
3
3
3
-
-
2
3
-
-
-
7
-
-
-
-
45
-
8
HARMONIC
81
45
45
-
1
2
3
4
5
6
7
8
18
-
-
4+5
-
-
-
8+1
4+5
4+5
-
-
-
-
-
-
-
-
-
1+8
-
-
9
-
8
HARMONIC
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
HARMONIC
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
1
A
1
1
1
-
1
2
-
-
-
-
7
-
-
C
=
3
-
1
C
3
3
3
-
-
2
3
-
-
-
7
-
-
M
=
4
-
1
M
13
4
4
-
-
2
-
4
-
-
7
-
-
N
=
5
-
1
N
14
5
5
-
-
2
-
-
5
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
2
-
-
-
6
7
-
-
H
=
8
-
1
H
8
8
8
-
-
2
-
-
-
-
7
8
-
I
=
9
-
1
I
9
9
9
-
-
2
-
-
-
-
7
-
9
R
=
9
-
1
R
18
9
9
-
-
2
-
-
-
-
7
-
9
-
-
45
-
8
HARMONIC
81
45
45
-
1
2
3
4
5
6
7
8
18
-
-
4+5
-
-
-
8+1
4+5
4+5
-
-
-
-
-
-
-
-
-
1+8
-
-
9
-
8
HARMONIC
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
HARMONIC
-
-
-
-
1
3
4
5
6
8
9
A
=
1
-
1
A
1
1
1
-
1
-
-
-
-
-
-
C
=
3
-
1
C
3
3
3
-
-
3
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
4
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
5
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
6
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
8
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
45
-
8
HARMONIC
81
45
45
-
1
3
4
5
6
8
18
-
-
4+5
-
-
-
8+1
4+5
4+5
-
-
-
-
-
-
-
1+8
-
-
9
-
8
HARMONIC
9
9
9
-
1
3
4
5
6
8
9

 

 

HARMONIC 288

Bruce Cathie

1977

EIGHT

THE MEASURE OF LIGHT

Page 80

"THE OBELISK RISING majestically from the sandswept plain has been visible to man for many centuries. Its massive bulk and geometric simplicity of shape have caused wonder and endless speculation to countless generations of wise men throughout history. The meaning, or reason, for such a structure has been lost and those responsible for the building of an edifice such as this must have been in possession of extremely advanced scientific knowledge. Were they an advanced race of this world who destroyed themselves by unwise manipulation of their own scientific achievement? Or, so-called gods? Or, people from other worlds who left amongst us an almost indestructible repository of advanced knowledge in the mathematical complexities of the universe?
The obelisk I speak of is not the cold, black, forbidding obelisk depicted in Stanley Kubrick's movie 2001, but a pyramid of shining splendour built on a rocky mile-square plateau ten miles west of Cairo, The plateau is known as Giza; the pyramidal structure of an estimated two-and-a-half million blocks of granite and limestone, is the"Great Pyramid of Cheops",     Page 95 "The value that I calculated for length was extremely close to that of the one published in Davidson and Aldersmith's book, their value being1836 inches, and my theoretical value 1833.46 geodetic inches.
A considerable amount of time was required to calculate a satisfactory value for the length of the Gallery. I eventually found that the amount of hollowing-in at the base provided the clue. If 57.6 (the amount in inches by which the base is inset) is I divided by pi or 3.1415927, the resulting value is 18.334649. The harmonic equivalent of 1833.46 when applied to Gallery length would ensure that the wave - forms set up in the cavity were finely tuned to light frequencies.
A search of my physics books revealed that1836 was the closest approximation the scientists have calculated to the mass / Page 96 (Diagram omitted)) / Page 97 / ratio of the positive hydrogen ion, i.e. the proton, to the electron. tf we dare to assume that the value, of 1833.46 is the true geometric ratio then the wave-forms in the Gallery will also have a harmonic affinity with the structure of the atom, the building block of the universe itself. Pressing on with this train of thought I again consulted a book on atomic physics and found that the mass of the electron is given as 9.2 x 10-31 kilo- grammes. I believe that, according to the clues presented by the Pyramid, the true value of electron mass, in the harmonic sense, could be taken as a standard of 9.24184 x 10-31 kilo- grammes."

 

Formally stated, Newton's third law is: For every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.

 

 

F
=
6
-
3
FOR
39
21
3
E
=
5
-
5
EVERY
75
30
3
A
=
1
-
6
ACTION
62
26
8
T
=
2
-
5
THERE
56
29
2
I
=
9
-
2
IS
28
19
1
A
=
1
-
2
AN
15
6
6
E
=
5
-
5
EQUAL
56
20
2
A
=
1
-
3
AND
19
10
1
O
=
6
-
8
OPPOSITE
115
43
7
R
=
9
-
8
REACTION
85
40
4
-
-
45
4
46
First Total
550
244
37
-
-
4+5
-
4+6
Add to Reduce
5+5+0
2+4+4
3+7
Q
-
9
-
10
Second Total
10
10
10
-
-
-
4
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
9
5
1
Essence of Number
1
1
1

 

 

 

 

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

 

 

 

 

THE SCULPTURE OF VIBRATIONS 1971

 

 
 
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