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Evokation
  
 
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A

MAZE

IN

ZAZAZA ENTER ZAZAZA

ZAZAZAZAZAZAZAAZAZAZAZAZAZAZ

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

The God of the Mystics

Page 250

"(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."  

 

 

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

 

 

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

 

 

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

 

 

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 LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

-
ALL IS NUMBER
-
-
-
3
ALL
25
7
7
2
IS
28
10
1
6
NUMBER
73
28
1
11
ALL IS NUMBER
126
45
9
1+1
-
1+2+6
4+5
-
2
ALL IS NUMBER
9
9
9

 

 

-
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
1
-
-
-
-
-
5
-
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
14
9
-
-
-
19
-
-
-
-
-
14
-
-
-
-
-
+
=
56
5+6
=
11
1+1
2
=
2
-
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
5
9
-
1
3
-
3
1
-
7
3
1
7
5
+
=
52
5+2
=
7
=
7
=
7
-
-
21
-
-
22
5
18
-
1
12
-
12
1
-
7
21
1
7
5
+
=
133
1+3+3
=
7
=
7
=
7
-
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
21
14
9
22
5
18
19
1
12
-
12
1
14
7
21
1
7
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
-
3
5
9
4
5
9
1
1
3
-
3
1
5
7
3
1
7
5
+
=
72
7+2
=
9
=
9
=
9
-
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
1
-
-
-`
1
-
-
-
1
-
-
-
-
1
occurs
x
4
=
4
=
4
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
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
16
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
29
-
-
17
-
72
-
27
1+6
1+7
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
1+7
-
7+2
-
2+7
7
8
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
11
-
-
8
-
9
-
9
-
-
3
5
9
4
5
9
1
1
3
-
3
1
5
7
3
1
7
5
-
-
1+1
-
-
-
-
-
-
-
7
8
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
2
-
-
8
-
9
-
9

 

 

17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
1
-
-
-
-
-
5
-
-
-
-
-
+
=
20
2+0
=
2
=
2
=
2
-
-
14
9
-
-
-
19
-
-
-
-
-
14
-
-
-
-
-
+
=
56
5+6
=
11
1+1
2
=
2
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
4
5
9
-
1
3
-
3
1
-
7
3
1
7
5
+
=
52
5+2
=
7
=
7
=
7
-
21
-
-
22
5
18
-
1
12
-
12
1
-
7
21
1
7
5
+
=
133
1+3+3
=
7
=
7
=
7
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
21
14
9
22
5
18
19
1
12
-
12
1
14
7
21
1
7
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
3
5
9
4
5
9
1
1
3
-
3
1
5
7
3
1
7
5
+
=
72
7+2
=
9
=
9
=
9
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
-
-
-
-
-
-
-
-
-
-
-`
-
-
-
-
1
1
-
-
-`
1
-
-
-
1
-
-
-
-
1
occurs
x
4
=
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
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
17
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
29
-
-
17
-
72
-
27
1+7
-
-
9
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
1+7
-
7+2
-
2+7
8
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
11
-
-
8
-
9
-
9
-
3
5
9
4
5
9
1
1
3
-
3
1
5
7
3
1
7
5
-
-
1+1
-
-
-
-
-
-
-
8
U
N
I
V
E
R
S
A
L
-
L
A
N
G
U
A
G
E
-
-
2
-
-
8
-
9
-
9

 

 

-
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
1
-
5
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
-
-
9
19
-
14
-
-
-
-
-
+
=
42
4+2
=
6
=
6
=
6
-
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
3
3
-
-
-
-
-
3
4
2
5
9
+
=
30
3+0
=
3
=
3
=
3
-
-
1
12
12
-
-
-
-
-
21
13
2
5
18
+
=
84
8+4
=
12
1+2
3
=
3
-
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
12
12
-
9
19
-
14
21
13
2
5
18
+
=
126
1+2+6
=
9
=
9
=
9
-
-
1
3
3
-
9
1
-
5
3
4
2
5
9
+
=
45
4+5
=
9
=
9
=
9
-
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
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
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
21
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
24
-
-
11
-
45
-
27
2+1
1+1
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
2+4
-
-
1+1
-
4+5
-
2+7
3
2
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
6
-
-
2
-
9
-
9

 

 

11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
1
-
5
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
-
9
19
-
14
-
-
-
-
-
+
=
42
4+2
=
6
=
6
=
6
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
1
3
3
-
-
-
-
-
3
4
2
5
9
+
=
30
3+0
=
3
=
3
=
3
-
1
12
12
-
-
-
-
-
21
13
2
5
18
+
=
84
8+4
=
12
1+2
3
=
3
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
1
12
12
-
9
19
-
14
21
13
2
5
18
+
=
126
1+2+6
=
9
=
9
=
9
-
1
3
3
-
9
1
-
5
3
4
2
5
9
+
=
45
4+5
=
9
=
9
=
9
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
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
occurs
x
2
=
10
1+0
1
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
11
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
24
-
-
11
-
45
-
27
1+1
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
2+4
-
-
1+1
-
4+5
-
2+7
2
A
L
L
-
I
S
-
N
U
M
B
E
R
-
-
6
-
-
2
-
9
-
9

 

 

-
ALL IS NUMBER
-
-
-
3
ALL
25
7
7
2
IS
28
10
1
6
NUMBER
73
28
1
11
ALL IS NUMBER
126
45
9
1+1
-
1+2+6
4+5
-
2
ALL IS NUMBER
9
9
9

 

 

I
=
9
-
1
I
9
9
9
-
-
S
=
1
-
3
SEE
29
11
2
-
2
I
=
9
-
2
IT
29
11
2
-
2
A
=
1
-
3
ALL
25
7
7
-
7
N
=
5
-
3
NOW
52
16
7
-
7
S
=
1
-
4
SAID
33
15
6
-
6
T
=
2
-
3
THE
33
15
6
-
6
B
=
2
-
5
BLIND
41
23
5
-
-
M
=
4
-
3
MAN
28
10
1
-
-
-
-
34
4
27
First
279
117
45
4
30
-
-
3+4
-
2+7
Add
2+7+9
1+1+7
4+5
-
3+0
-
-
7
-
9
Second
18
9
9
-
3
-
-
-
-
-
Reduce
1+8
-
-
-
-
-
-
7
-
9
Essence
9
9
9
-
3

 

 

W
=
5
-
4
WHAT
52
16
7
O
=
6
-
3
ONE
34
16
7
W
=
5
-
5
WOULD
75
21
3
L
=
3
-
4
LOOK
53
17
8
F
=
6
-
3
FOR
30
21
3
T
=
2
-
9
THEREFORE
100
46
1
W
=
5
-
5
WOULD
75
21
3
B
=
2
-
2
BE
7
7
7
A
=
1
-
1
A
1
1
1
U
=
3
-
9
UNIVERSAL
121
40
4
L
=
3
-
8
LANGUAGE
68
32
5
-
-
41
4
53
First Total
616
238
49
-
-
4+1
-
5+3
Add to Reduce
6+1+6
2+3+8
4+9
-
-
5
-
8
Second Total
13
13
13
-
-
-
-
-
Reduce to Deduce
1+3
1+3
1+3
-
-
5
-
8
Essence of Number
4
4
4

 

 

T
=
2
-
3
THE
33
15
6
K
=
2
-
4
KIND
38
20
2
O
=
6
-
2
OF
21
12
3
L
=
3
-
8
LANGUAGE
68
32
5
T
=
2
-
4
THAT
49
13
4
W
=
5
-
5
WOULD
75
21
3
B
=
2
-
2
BE
7
7
7
C
=
3
-
14
COMPREHENSIBLE
144
72
9
T
=
2
-
2
TO
35
8
8
A
=
1
-
3
ANY
40
13
4
T
=
2
-
15
TECHNOLOGICALLY
161
71
8
A
=
1
-
2
ADVANCED
54
27
9
S
=
1
-
7
SOCIETY
96
33
6
I
=
9
-
2
IN
23
14
5
A
=
1
-
3
ANY
40
13
4
E
=
5
-
5
EPOCH
47
29
2
-
-
47
4
81
First Total
931
400
85
-
-
4+7
-
8+1
Add to Reduce
9+3+1
4+0+0
8+5
-
-
11
-
9
Second Total
13
4
13
-
-
1+5
-
-
Reduce to Deduce
1+3
-
1+3
-
-
2
-
9
Essence of Number
4
4
4

 

 

S
=
1
-
4
SUCH
51
15
6
L
=
3
-
9
LANGUAGES
87
33
6
A
=
1
-
3
ARE
24
15
6
F
=
6
-
3
FEW
34
16
7
A
=
1
-
3
AND
19
10
1
F
=
6
-
3
FAR
25
16
7
B
=
2
-
7
BETWEEN
74
29
2
B
=
2
-
3
BUT
43
7
7
M
=
4
-
11
MATHEMATICS
112
40
4
I
=
9
-
2
IS
28
10
1
O
=
6
-
3
ONE
34
16
7
O
=
6
-
2
OF
21
12
3
T
=
2
-
4
THEM
46
19
1
-
-
49
4
57
First Total
598
238
58
-
-
4+9
-
5+7
Add to Reduce
5+9+8
2+3+8
5+8
-
-
13
-
12
Second Total
22
13
13
-
-
1+3
-
1+2
Reduce to Deduce
2+2
1+3
1+3
-
-
3
-
3
Essence of Number
4
4
4

 

 

A
=
1
-
1
A
1
1
1
L
=
3
-
8
LANGUAGE
68
32
5
O
=
6
-
2
OF
21
12
3
L
=
3
-
7
LETTERS
99
27
9
A
=
1
-
3
AND
19
10
1
N
=
5
-
7
NUMBERS
73
28
1
-
-
19
4
28
First Total
299
110
20
-
-
1+9
-
2+8
Add to Reduce
2+9+9
1+1+0
2+0
-
-
10
-
10
Second Total
20
2
2
-
-
1+0
-
1+0
Reduce to Deduce
2+0
-
-
-
-
1
-
1
Essence of Number
2
2
2

 

MATHEMATICS A LANGUAGE OF LETTERS AND NUMBERS

 

W
=
5
-
4
WHAT
52
16
7
O
=
6
-
3
ONE
34
16
7
W
=
5
-
5
WOULD
75
21
3
L
=
3
-
4
LOOK
53
17
8
F
=
6
-
3
FOR
30
21
3
T
=
2
-
9
THEREFORE
100
46
1
W
=
5
-
5
WOULD
75
21
3
B
=
2
-
2
BE
7
7
7
A
=
1
-
1
A
1
1
1
U
=
3
-
9
UNIVERSAL
121
40
4
L
=
3
-
8
LANGUAGE
68
32
5
-
-
41
4
53
-
616
238
49
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
K
=
2
-
4
KIND
38
20
2
O
=
6
-
2
OF
21
12
3
L
=
3
-
8
LANGUAGE
68
32
5
C
=
3
-
4
THAT
144
72
9
T
=
2
-
5
WOULD
35
8
8
A
=
1
-
2
BE
40
13
4
T
=
2
-
14
COMPREHENSIBLE
161
71
8
A
=
1
-
2
TO
54
27
9
S
=
1
-
3
ANY
96
33
6
I
=
9
-
15
TECHNOLOGICALLY
23
14
5
A
=
1
-
2
ADVANCED
40
13
4
E
=
5
-
7
SOCIETY
48
29
2
T
=
2
-
2
IN
49
13
4
W
=
5
-
3
ANY
75
21
3
B
=
2
-
5
EPOCH
7
7
7
-
-
47
4
81
-
931
400
85
-
-
-
-
-
-
-
-
-
S
=
1
-
4
SUCH
51
15
6
L
=
3
-
9
LANGUAGES
87
33
6
A
=
1
-
3
ARE
24
15
6
F
=
6
-
3
FEW
34
16
7
A
=
1
-
3
AND
19
10
1
F
=
6
-
3
FAR
25
16
7
B
=
2
-
7
BETWEEN
74
29
2
B
=
2
-
3
BUT
43
7
7
M
=
4
-
11
MATHEMATICS
112
40
4
I
=
9
-
2
IS
28
10
1
O
=
6
-
3
ONE
34
16
7
O
=
6
-
2
OF
21
12
3
T
=
2
-
4
THEM
46
19
1
-
-
49
4
57
-
598
238
58
-
-
-
-
-
-
-
-
-
A
=
1
-
1
A
1
1
1
L
=
3
-
8
LANGUAGE
68
32
5
O
=
6
-
2
OF
21
12
3
L
=
3
-
7
LETTERS
99
27
9
A
=
1
-
3
AND
19
10
1
N
=
5
-
7
NUMBERS
73
28
1
-
-
19
4
28
-
299
110
20
-
-
-
-
-
-
-
-
-
-
-
156
-
219
First Total
2444
986
212
-
-
1+5+6
-
2+1+9
Add to Reduce
2+4+4+4
9+8+6
2+1+2
-
-
12
-
12
Second Total
14
23
5
-
-
1+2
-
1+2
Reduce to Deduce
1+4
2+3
-
-
-
3
-
3
Essence of Number
5
5
5

 

MATHEMATICS A LANGUAGE OF LETTER AND NUMBER

 

A
=
1
-
1
A
1
1
1
L
=
3
-
8
LANGUAGE
68
32
5
O
=
6
-
2
OF
21
12
3
L
=
3
-
6
LETTER
80
26
8
A
=
1
-
3
AND
19
10
1
N
=
5
-
6
NUMBER
73
28
1
S
-
19
4
26
First Total
261
108
18
-
-
1+9
-
2+6
Add to Reduce
2+6+1
1+0+8
1+8
-
-
10
-
8
Second Total
9
9
9
-
-
1+0
-
-
Reduce to Deduce
-
-
-
-
-
1
-
8
Essence of Number
9
9
9

 

 

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
-
9
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
9
-
4
Deduce
6
7
4
7
3
-
9
-
-
9
-
9

 

 

 

A
-
J
-
S
-
-
-
-
-
--
1
-
1
-
1
+
=
3
-
=
3
A
-
J
-
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
B
-
K
-
T
-
-
-
-
-
--
2
-
2
-
2
+
=
6
-
=
6
B
-
K
-
T
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
C
-
L
-
U
-
-
-
-
-
--
3
-
3
-
3
+
=
9
-
=
9
C
-
L
-
U
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
D
-
M
-
V
-
-
-
-
-
--
4
-
4
-
4
+
=
12
1+2
=
3
D
-
M
-
V
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
E
-
N
-
W
-
-
-
-
-
--
5
-
5
-
5
+
=
15
1+5
=
6
E
-
N
-
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
F
-
O
-
X
-
-
-
-
-
--
6
-
6
-
6
+
=
18
1+8
=
9
F
-
O
-
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
G
-
P
-
Y
-
-
-
-
-
--
7
-
7
-
7
+
=
21
2+1
=
3
G
-
P
-
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
H
-
Q
-
Z
-
-
-
-
-
--
8
-
8
-
8
+
=
24
2+4
=
6
H
-
Q
-
Z
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
I
-
R
-
-
-
-
-
-
-
--
9
-
9
-
-
+
=
18
1+8
=
9
I
-
R
-
-
-
-
-
-
-
--
-
-
-
-
-
-
-
126
-
-
54
-
-
-
-
-
-
-
1+2+6
-
-
5+4
-
-
-
-
-
-
-
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
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
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

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN SOME 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."

 

 

A - Z
ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE
MATHEMATICIAN
MATHEMATICS
ONE TWO THREE FOUR 6 FIVE 6 SEVEN EIGHT NINE
ONE TWO THREE FOUR
SIX SEVEN EIGHT NINE
FIVE
THREE SIX NINE
ONE, THREE, FIVE, SEVEN, NINE, EIGHT, SIX, FOUR, TWO, ZERO
THREE, SIX, NINE
ONE, SEVEN
NINE, SIX, THIRTEEN
ONE, SIX
THREE, SIX
THREE SIX
FOUR FIVE NINE
SQUARE, SQ, UA, R, E
CYLINDER, CYL, I, N, DE, R
CUBE
OBLONG
EDFU, ED, FU
TETRA HYDROCANNIBONAL
KINDRED, SPIRITS, SPIRIT
EPOPTEIA
THE, CROWING, OF, THE, COCK
THE, PERFECT, UNION, OF, OPPOSITES
MARRIAGE, OF, EQUALS
MATHEMATICS, MATH, ME, AT, I, CS
DARK, MATTER, MIND, LIGHT
EFFLUX, EF, FLUX
UNDERSTOOD
WISH, WISHED, WISHES, ISH
AMSU, MIN
HERMES, HER, ME, S
FESTIVAL, OF, EID
EID, UL, FITR
KNEPH

 

 

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

 

 

3
3
-
A+B+C
6
6
6
2
-
2
D+E
9
9
9
3
3
-
F+G+H
21
21
3
1
-
1
I
9
9
9
3
3
-
J+K+L
33
6
6
2
-
2
M+N
27
9
9
2
2
-
O+P
31
13
4
3
-
3
QRS
54
18
9
3
-
3
TUV
63
9
9
3
-
3
WXY
72
18
9
1
1
-
Z
26
8
8
26
12
14
First Total
351
126
81
2+6
1+2
1+4
Add to Reduce
3+5+1
1+2+6
8+1
8
3
5
Reduce to Deduce
9
9
9

 

 

3
A+B+C
6
6
6
-
D+E
-
-
-
3
F+G+H
21
21
3
-
I
-
-
-
3
J+K+L
33
6
6
-
M+N
-
-
-
2
O+P
31
13
4
-
QRS
-
-
-
-
TUV
-
-
-
-
WXY
-
-
-
1
Z
26
8
8
12
First Total
117
54
27
2+6
Add to Reduce
1+1+7
5+4
2+7
8
Reduce to Deduce
9
9
9

 

 

-
A+B+C
-
-
-
2
D+E
9
9
9
-
F+G+H
-
-
-
1
I
9
9
9
-
J+K+L
-
-
-
2
M+N
27
9
9
-
O+P
-
-
-
3
QRS
54
18
9
3
TUV
63
9
9
3
WXY
72
18
9
-
Z
-
-
-
14
First Total
234
72
54
1+4
Add to Reduce
2+3+4
7+2
5+4
5
Reduce to Deduce
9
9
9

 

 

4

ZERO

64

28

1
3

ONE
34
16
7
3

TWO
58
13
4
5

THREE
56
29
2
4

FOUR
60
24
6
4

FIVE
42
24
6
3

SIX
52
16
7
5

SEVEN
65
20
2
5

EIGHT
49
31
4
4

NINE
42
24
6
40
-
522
225
45
4+0
-
5+2+2
2+2+5
4+5
4
-
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
-
-
1+7
1+7
-
-
-
3
9
-
8
8
8

 

 

Z
=
8
4
ZERO
64
28
1
O
=
6
3
ONE
34
16
7
S
=
1
5
SEVEN
65
20
2
T
=
2
3
TWO
58
13
4
F
=
6
4
FOUR
60
24
6
S
=
1
3
SIX
52
16
7
T
=
2
5
THREE
56
29
2
F
=
6
4
FIVE
42
24
6
E
=
5
5
EIGHT
49
31
4
N
=
5
4
NINE
42
24
6
-
-
47
40
-
522
225
45
-
-
11
4+0
-
5+2+2
2+2+5
4+5
-
-
2
4
-
9
9
9

 

 

N
=
5
-
6
NUMBER
73
28
1
L
=
3
-
6
LETTER
80
26
8
S
-
8
4
12
Add to Reduce
153
54
9
-
-
-
-``
1+2
Reduce to Deduce
1+5+3
5+4
-
S
-
8
4
9
Essence of Number
9
9
9

 

 

-
12
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
+
=
5
-
=
5
=
5
=
5
-
-
14
-
-
-
-
-
-
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
12
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
-
3
4
2
5
9
-
3
5
2
2
5
9
+
=
49
4+9
=
13
1+3
4
=
4
-
-
-
21
13
2
5
18
-
12
5
20
20
5
18
+
=
139
1+3+9
=
13
1+3
4
=
4
-
12
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
14
21
13
2
5
18
-
12
5
20
20
5
18
+
=
153
1+5+3
=
9
=
9
=
9
-
-
5
3
4
2
5
9
-
3
5
2
2
5
9
+
=
54
5+4
=
9
=
9
=
9
-
12
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
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
-
-
-
5
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
22
12
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
23
-
-
12
-
54
-
27
2+2
1+2
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
2+3
-
-
1+2
-
5+4
-
2+7
4
3
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
5
-
-
3
-
9
-
9
-
-
5
3
4
2
5
9
-
3
5
2
2
5
9
-
-
-
-
-
-
-
-
-
-
4
3
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
5
-
-
3
-
9
-
9

 

 

12
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
+
=
5
-
=
5
=
5
=
5
-
14
-
-
-
-
-
-
-
-
-
-
-
-
+
=
14
1+4
=
5
=
5
=
5
12
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
-
3
4
2
5
9
-
3
5
2
2
5
9
+
=
49
4+9
=
13
1+3
4
=
4
-
-
21
13
2
5
18
-
12
5
20
20
5
18
+
=
139
1+3+9
=
13
1+3
4
=
4
12
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
-
-
-
--
-
-
-
-
-
14
21
13
2
5
18
-
12
5
20
20
5
18
+
=
153
1+5+3
=
9
=
9
=
9
-
5
3
4
2
5
9
-
3
5
2
2
5
9
+
=
54
5+4
=
9
=
9
=
9
12
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
5
-
-
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
12
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
23
-
-
12
-
54
-
27
1+2
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
2+3
-
-
1+2
-
5+4
-
2+7
3
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
5
-
-
3
-
9
-
9
-
5
3
4
2
5
9
-
3
5
2
2
5
9
-
-
-
-
-
-
-
-
-
-
3
N
U
M
B
E
R
-
L
E
T
T
E
R
-
-
5
-
-
3
-
9
-
9

 

 

8
LANGUAGE`
68
32
5
7
LETTERS
99
27
9
7
NUMBERS
92
29
2
3
THE
33
15
6
7
ESSENCE
70
25
7
2
OF
21
12
3
3
OUR
54
18
9
6
SEANCE
47
20
2
4
WITH
60
24
6
7
REALITY
90
36
9
3
AND
19
10
1
5
HUMAN
57
21
3
4
FORM
52
25
7

 

 

-
13
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
-
-
-
-
-
-
-
-
=
=
-
-
-
8
-
-
-
-
9
-
9
`-
5
+
=
31
3+1
=
4
=
4
=
4
=
=
-
-
-
8
-
-
-
-
9
-
9
-
14
+
=
40
4+0
=
4
=
4
=
4
-
13
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
-
-
-
-
-
-
-
-
=
=
4
1
2
-
5
4
1
2
-
3
-
1
-
+
=
23
2+3
=
5
=
5
=
5
-
=
13
1
20
-
5
13
1
20
-
3
-
1
-
+
=
77
7+7
=
14
1+4
5
=
5
-
13
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
-
-
-
-
-
-
-
-
-
-
13
1
20
8
5
13
1
20
9
3
9
1
14
+
=
117
1+1+7
=
9
=
9
=
9
-
-
4
1
2
8
5
4
1
2
9
3
9
1
5
+
=
54
5+4
=
9
=
9
=
9
-
13
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
1
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
13
13
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
32
-
-
13
-
54
-
36
1+3
1+3
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
3+2
-
-
1+3
-
5+4
-
3+6
4
4
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
5
-
-
4
-
9
-
9
--
--
4
1
2
8
5
4
1
2
9
3
9
1
5
-
-
-
-
-
--
-
-
-
-
4
4
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
5
-
-
4
-
9
-
9

 

 

13
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
-
-
-
-
-
-
-
-
=
-
-
-
8
-
-
-
-
9
-
9
`-
5
+
=
31
3+1
=
4
=
4
=
4
=
-
-
-
8
-
-
-
-
9
-
9
-
14
+
=
40
4+0
=
4
=
4
=
4
13
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
-
-
-
-
-
-
-
-
=
4
1
2
-
5
4
1
2
-
3
-
1
-
+
=
23
2+3
=
5
=
5
=
5
=
13
1
20
-
5
13
1
20
-
3
-
1
-
+
=
77
7+7
=
14
1+4
5
=
5
13
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
-
-
-
-
-
-
-
-
-
13
1
20
8
5
13
1
20
9
3
9
1
14
+
=
117
1+1+7
=
9
=
9
=
9
-
4
1
2
8
5
4
1
2
9
3
9
1
5
+
=
54
5+4
=
9
=
9
=
9
13
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
1
-
-
-
1
occurs
x
3
=
3
=
3
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
4
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
13
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
32
-
-
13
-
54
-
36
1+3
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
3+2
-
-
1+3
-
5+4
-
3+6
4
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
5
-
-
4
-
9
-
9
--
4
1
2
8
5
4
1
2
9
3
9
1
5
-
-
-
-
-
--
-
-
-
-
4
M
A
T
H
E
M
A
T
I
C
I
A
N
-
-
5
-
-
4
-
9
-
9

 

 

 

-
MATHEMATICS
-
-
-
4
MATH
42
15
6
2
ME
18
9
9
2
AT
21
3
3
1
I
9
9
9
2
CS
22
4
4
11
MATHEMATICS
112
40
31
1+1
-
1+1+2
4+0
3+1
2
MATHEMATICS
4
4
4

 

 

-
-
-
-
-
MATHEMATICS
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
8
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
2
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
40
-
11
MATHEMATICS
112
49
40
-
3
4
3
8
5
6
7
8
9
-
-
4+0
-
1+1
-
1+1+2
4+9
4+0
-
-
-
-
-
-
-
-
-
-
-
-
4
-
2
MATHEMATICS
4
13
4
-
3
4
3
8
5
6
7
8
9
-
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
2
MATHEMATICS
4
4
4
-
3
4
3
8
5
6
7
8
9

 

 

-
-
-
-
-
MATHEMATICS
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
6
7
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
6
7
-
-
S
=
1
2
1
S
19
10
1
-
1
-
-
-
-
6
7
-
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
6
7
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
6
7
-
-
C
=
3
8
1
C
3
3
3
-
-
-
3
-
-
6
7
-
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
6
7
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
6
7
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
6
7
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
6
7
8
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
6
7
-
9
-
-
40
-
11
MATHEMATICS
112
49
40
-
3
4
3
8
5
6
7
8
9
-
-
4+0
-
1+1
-
1+1+2
4+9
4+0
-
-
-
-
-
-
-
-
-
-
-
-
4
-
2
MATHEMATICS
4
13
4
-
3
4
3
8
5
6
7
8
9
-
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
2
MATHEMATICS
4
4
4
-
3
4
3
8
5
6
7
8
9

 

 

-
-
-
-
-
MATHEMATICS
-
-
-
-
1
2
3
4
5
8
9
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
-
S
=
1
2
1
S
19
10
1
-
1
-
-
-
-
-
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
C
=
3
8
1
C
3
3
3
-
-
-
3
-
-
-
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
H
=
8
4
1
H
8
8
8
-
-
-
-
-
-
8
-
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
9
-
-
40
-
11
MATHEMATICS
112
49
40
-
3
4
3
8
5
8
9
-
-
4+0
-
1+1
-
1+1+2
4+9
4+0
-
-
-
-
-
-
-
-
-
-
4
-
2
MATHEMATICS
4
13
4
-
3
4
3
8
5
8
9
-
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
-
-
4
-
2
MATHEMATICS
4
4
4
-
3
4
3
8
5
8
9

 

 

-
11
M
A
T
H
E
M
A
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
9
-
1
+
=
18
1+8
=
9
=
9
-
-
-
-
-
8
-
-
-
-
9
-
19
+
=
36
3+6
=
9
=
9
-
11
M
A
T
H
E
M
A
T
I
C
S
-
-
-
-
-
-
-
-
-
-
4
1
2
-
5
4
1
2
-
3
-
+
=
22
2+2
=
4
=
4
-
-
13
1
20
-
5
13
1
20
-
3
-
+
=
76
7+6
=
13
1+3
4
-
11
M
A
T
H
E
M
A
T
I
C
S
-
-
-
-
-
-
-
-
-
-
13
1
20
8
5
13
1
20
9
3
19
+
=
112
1+1+2
=
4
=
4
-
-
4
1
2
8
5
4
1
2
9
3
1
+
=
40
4+0
=
4
=
4
-
11
M
A
T
H
E
M
A
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
3
=
3
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
4
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
2
=
8
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
13
11
M
A
T
H
E
M
A
T
I
C
S
-
-
32
-
-
11
-
40
1+3
1+1
-
-
-
-
-
-
-
-
9
-
-
-
-
3+2
-
-
1+1
-
4+0
4
2
M
A
T
H
E
M
A
T
I
C
S
-
-
5
-
-
2
-
4
-
-
4
1
2
8
5
4
1
2
9
3
1
-
-
-
-
-
-
-
-
4
2
M
A
T
H
E
M
A
T
I
C
S
-
-
5
-
-
2
-
4

 

 

11
M
A
T
H
E
M
A
T
I
C
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
9
-
1
+
=
18
1+8
=
9
=
9
-
-
-
-
8
-
-
-
-
9
-
19
+
=
36
3+6
=
9
=
9
11
M
A
T
H
E
M
A
T
I
C
S
-
-
-
-
-
-
-
-
-
4
1
2
-
5
4
1
2
-
3
-
+
=
22
2+2
=
4
=
4
-
13
1
20
-
5
13
1
20
-
3
-
+
=
76
7+6
=
13
1+3
4
11
M
A
T
H
E
M
A
T
I
C
S
-
-
-
-
-
-
-
-
-
13
1
20
8
5
13
1
20
9
3
19
+
=
112
1+1+2
=
4
=
4
-
4
1
2
8
5
4
1
2
9
3
1
+
=
40
4+0
=
4
=
4
11
M
A
T
H
E
M
A
T
I
C
S
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
1
-
-
1
occurs
x
3
=
3
-
-
-
2
-
-
-
-
2
-
-
-
-
-
2
occurs
x
2
=
4
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
4
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
2
=
8
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
11
M
A
T
H
E
M
A
T
I
C
S
-
-
32
-
-
11
-
40
1+1
-
-
-
-
-
-
-
-
9
-
-
-
-
3+2
-
-
1+1
-
4+0
2
M
A
T
H
E
M
A
T
I
C
S
-
-
5
-
-
2
-
4
-
4
1
2
8
5
4
1
2
9
3
1
-
-
-
-
-
-
-
-
2
M
A
T
H
E
M
A
T
I
C
S
-
-
5
-
-
2
-
4

 

 

MATHEMATICS MINUS I MINUS I MATHEMATICS

 

 

11
M
A
T
H
E
M
A
T
C
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
1
+
=
18
1+8
=
9
=
9
-
-
-
-
8
-
-
-
-
-
19
+
=
36
3+6
=
9
=
9
11
M
A
T
H
E
M
A
T
C
S
-
-
-
-
-
-
-
-
-
4
1
2
-
5
4
1
2
3
-
+
=
22
2+2
=
4
=
4
-
13
1
20
-
5
13
1
20
3
-
+
=
76
7+6
=
13
1+3
4
11
M
A
T
H
E
M
A
T
C
S
-
-
-
-
-
-
-
-
-
13
1
20
8
5
13
1
20
3
19
+
=
112
1+1+2
=
4
=
4
-
4
1
2
8
5
4
1
2
3
1
+
=
40
4+0
=
4
=
4
11
M
A
T
H
E
M
A
T
C
S
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
-
-
1
occurs
x
3
=
3
-
-
-
2
-
-
-
-
2
-
-
-
-
2
occurs
x
2
=
4
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
-
4
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
2
=
8
-
-
-
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
11
M
A
T
H
E
M
A
T
C
S
-
-
32
-
-
11
-
40
1+1
-
-
-
-
-
-
-
-
-
-
-
-
3+2
-
-
1+1
-
4+0
2
M
A
T
H
E
M
A
T
C
S
-
-
5
-
-
2
-
4
-
4
1
2
8
5
4
1
2
3
1
-
-
-
-
-
-
-
-
2
M
A
T
H
E
M
A
T
C
S
-
-
5
-
-
2
-
4

 

 

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

 

 

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

 

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
Reduce
10
10
10
-
8
Reduce
10
10
10
-
Deduce
1+0
1+0
1+0
-
-
Deduce
1+0
1+0
1+0
6
Essence
1
1
1
-
8
Essence
1
1
1

 

 

-
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
+
=
31
3+1
=
4
=
4
=
4
-
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
+
=
67
6+7
=
13
1+3
4
=
4
-
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
2
5
-
-
2
-
9
5
5
-
6
-
3
9
+
=
51
5+1
=
6
=
6
=
6
-
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
+
=
141
1+4+1
=
6
=
6
=
6
-
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
15
14
5
-
20
23
15
-
20
8
18
5
5
-
6
15
21
18
+
=
208
2+0+8
=
10
1+0
1
=
1
-
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
+
=
82
8+2
=
10
1+0
1
=
1
-
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
5
occurs
x
5
=
25
2+5
7
-
-
6
-
-
-
-
-
6
-
-
-
-
-
-
-
6
6
-
-
-
-
6
occurs
x
4
=
24
2+4
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-``
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
12
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
33
-
-
15
-
82
-
37
1+2
1+5
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
3+3
-
-
1+5
-
8+2
-
3+7
3
6
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
6
-
-
6
-
10
-
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
1+0
3
6
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
6
-
-
6
-
1
-
1

 

 

15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
+
=
31
3+1
=
4
=
4
=
4
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
+
=
67
6+7
=
13
1+3
4
=
4
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
-
5
-
2
5
-
-
2
-
9
5
5
-
6
-
3
9
+
=
51
5+1
=
6
=
6
=
6
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
+
=
141
1+4+1
=
6
=
6
=
6
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
15
14
5
-
20
23
15
-
20
8
18
5
5
-
6
15
21
18
+
=
208
2+0+8
=
10
1+0
1
=
1
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
+
=
82
8+2
=
10
1+0
1
=
1
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
5
occurs
x
5
=
25
2+5
7
-
6
-
-
-
-
-
6
-
-
-
-
-
-
-
6
6
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
15
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
33
-
-
15
-
82
-
37
1+5
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
3+3
-
-
1+5
-
8+2
-
3+7
6
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
6
-
-
6
-
10
-
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
1+0
6
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
-
6
-
-
6
-
1
-
1

 

 

-
17
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
5
9
5
-
-
-
9
-
8
-
-
1
-
-
-
5
-
1
9
6
+
=
58
5+8
=
13
1+3
4
=
4
-
-
14
9
14
-
-
-
9
-
8
-
-
19
-
-
-
14
-
19
9
24
+
=
139
1+3+9
=
13
1+3
4
=
4
-
17
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
5
-
5
-
7
-
2
-
-
5
4
5
-
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
-
-
-
-
5
-
5
-
7
-
20
-
-
5
22
5
-
-
-
-
-
+
=
69
6+9
=
15
1+5
6
=
6
-
17
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
14
9
14
5
-
5
9
7
8
20
-
19
5
22
5
14
-
19
9
24
+
=
208
2+0+8
=
10
1+0
1
=
1
-
-
5
9
5
5
-
5
9
7
8
2
-
1
5
4
5
5
-
1
9
6
+
=
91
9+1
=
10
1+0
1
=
1
-
17
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
5
5
-
5
-
-
-
-
-
-
5
-
5
5
-
-
-
-
-
-
5
occurs
x
7
=
35
3+5
8
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
=
6
-
--
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
--
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
3
17
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
42
-
-
17
-
91
-
46
-
1+7
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
4+2
-
-
1+7
-
9+1
-
4+6
3
8
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
6
-
-
8
-
10
-
10
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
1+0
3
8
N
I
N
E
-
E
I
G
H
T
-
S
E
V
E
N
-
S
I
X
-
-
6
-
-
8
-
1
-
1

 

 

15
ONE TWO THREE FOUR
208
82
1
17
NINE EIGHT SEVEN SIX
208
91
1

 

 

-
4
F
I
V
E
-
-
-
-
-
--
-
-
- -
-
9
-
-
+
=
9
-
=
9
=
9
-
4
F
I
V
E
-
-
-
-
-
--
-
-
- -
6
-
4
5
+
=
15
1+5
=
6
=
6
- -
6
-
22
5
+
=
33
3+3
=
6
=
6
-
4
F
I
V
E
-
-
-
-
-
--
-
-
- -
6
9
22
5
+
=
42
4+2
=
6
=
6
- -
6
9
4
5
+
=
24
2+4
=
6
=
6
-
4
F
I
V
E
-
-
-
-
-
-
-
-
1
-
 - - - -
-
-
1
-
-
-
-
-
2
-
 - - - -
-
-
2
-
-
-
-
-
3
-
 - - - -
-
-
3
-
-
-
-
-
-
-
 -
-
4
-
-
-
4
occurs
x
1
=
4
-
-
 -
-
-
5
-
-
5
occurs
x
1
=
5
-
-
6
 - - -
-
-
6
occurs
x
1
=
6
7
-
 - - - -
-
-
7
-
-
-
-
-
8
-
 - - - -
-
-
8
-
-
-
-
-
-
-
 -
9
-
-
-
-
9
occurs
x
1
=
9
21
4
F
I
V
E
-
-
24
-
-
4
-
24
2+1
-
-
9
-
-
-
-
2+4
-
-
-
-
2+4
3
4
F
I
V
E
-
-
6
-
-
4
-
6

 

 

4
F
I
V
E
-
-
-
-
-
--
-
-
-
-
9
-
-
+
=
9
-
=
9
=
9
4
F
I
V
E
-
-
-
-
-
--
-
-
-
6
-
4
5
+
=
15
1+5
=
6
=
6
-
6
-
22
5
+
=
33
3+3
=
6
=
6
4
F
I
V
E
-
-
-
-
-
--
-
-
-
6
9
22
5
+
=
42
4+2
=
6
=
6
-
6
9
4
5
+
=
24
2+4
=
6
=
6
4
F
I
V
E
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
6
-
-
-
-
-
6
occurs
x
1
=
6
-
-
9
-
-
-
-
9
occurs
x
1
=
9
4
F
I
V
E
-
-
24
-
-
4
-
24
-
-
9
-
-
-
-
2+4
-
-
-
-
2+4
4
F
I
V
E
-
-
6
-
-
4
-
6

 

 

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

 

 

-
12
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
1
9
6
-
5
9
5
-
+
=
43
4+3
=
7
=
7
=
7
-
-
-
8
-
-
-
-
19
9
24
-
14
9
14
-
+
=
97
9+7
=
16
1+6
7
=
7
-
12
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
2
-
9
5
5
-
-
-
-
-
-
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
-`
20
-
18
5
5
-
-
-
-
-
-
-
-
5
+
=
53
5+3
=
8
=
8
=
8
-
12
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
20
8
18
5
5
-
19
9
24
-
14
9
14
5
+
=
150
1+5+0
=
6
=
6
=
6
-
-
2
8
9
5
5
-
1
9
6
-
5
9
5
5
+
=
69
6+9
=
15
1+5
6
=
6
-
12
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
-
-
5
-
5
5
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
--
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
14
12
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
31
-
-
12
-
69
-
33
1+4
1+2
-
-
9
-
-
-
-
9
-
-
-
9
-
-
-
-
3+1
-
-
1+2
-
6+9
-
3+3
5
3
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
4
-
-
3
-
15
-
6
-
-
2
8
9
5
5
-
1
9
6
-
5
9
5
5
-
-
-
-
-
-
-
1+5
=
-
5
3
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
4
-
-
3
-
6
-
6

 

 

12
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
1
9
6
-
5
9
5
-
+
=
43
4+3
=
7
=
7
=
7
-
-
8
-
-
-
-
19
9
24
-
14
9
14
-
+
=
97
9+7
=
16
1+6
7
=
7
12
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
2
-
9
5
5
-
-
-
-
-
-
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-`
20
-
18
5
5
-
-
-
-
-
-
-
-
5
+
=
53
5+3
=
8
=
8
=
8
12
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
-
-
-
--
-
-
-
-
-
20
8
18
5
5
-
19
9
24
-
14
9
14
5
+
=
150
1+5+0
=
6
=
6
=
6
-
2
8
9
5
5
-
1
9
6
-
5
9
5
5
+
=
69
6+9
=
15
1+5
6
=
6
12
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
5
5
-
-
-
-
-
5
-
5
5
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
-
-
-
-
-
-
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
12
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
31
-
-
12
-
69
-
33
1+2
-
-
9
-
-
-
-
9
-
-
-
9
-
-
-
-
3+1
-
-
1+2
-
6+9
-
3+3
3
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
4
-
-
3
-
15
-
6
-
2
8
9
5
5
-
1
9
6
-
5
9
5
5
-
-
-
-
-
-
-
1+5
=
-
3
T
H
R
E
E
-
S
I
X
-
N
I
N
E
-
-
4
-
-
3
-
6
-
6

 

 

3
ONE
34
16
7
5
THREE
56
29
2
4
FIVE
42
24
6
5
SEVEN
65
20
2
4
NINE
42
24
6
21
First Total
239
113
23
2+1
Add to Reduce
2+3+9
1+1+3
2+3
3
Second Total
14
5
5
-
Reduce to Deduce
1+4
-
-
3
Essence of Number
5
5
5
-
-
-
-
-
-
-
-
-
-
5
EIGHT
49
31
4
3
SIX
52
16
7
4
FOUR
60
24
6
3
TWO
58
13
4
15
First Total
219
84
21
1+5
Add to Reduce
2+1+9
8+4
2+1
6
Second Total
12
12
3
-
Reduce to Deduce
1+2
1+2
-
6
Essence of Number
3
3
3
-
-
-
-
-
-
-
-
-
-
4
ZERO
64
28
1

 

 

T
=
2
5
THREE
56
29
2
-
3
S
=
1
3
SIX
52
16
7
-
6
N
=
5
4
NINE
42
24
6
-
9
-
-
8
12
First Total
150
69
15
-
18
-
-
-
1+2
Add to Reduce
1+5+0
6+9
1+5
-
1+8
Q
-
8
3
Second Total
6
15
6
-
9
-
-
-
-
Reduce to Deduce
-
1+5
-
-
-
-
-
8
3
Essence of Number
6
6
6
-
9

 

 

O
=
6
3
ONE
34
16
7
-
1
S
=
1
5
SEVEN
65
20
2
-
7
-
-
7
8
First Total
99
36
9
-
8
-
-
-
-
Add to Reduce
9+9
3+6
-
-
-
Q
-
7
8
Second Total
18
9
9
-
8
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
7
8
Essence of Number
9
9
9
-
8

 

 

4
NINE
42
24
6
-
9
3
SIX
52
16
7
6
6
7
-
94
40
13
-
15
-
-
9+4
4+0
1+3
-
1+5
7
-
13
4
4
-
6
8
THIRTEEN
99
45
9
-
-

 

 

O
=
6
3
ONE
34
16
7
-
1
S
=
1
3
SIX
52
16
7
-
6
-
-
7
6
First Total
86
32
14
-
7
-
-
-
-
Add to Reduce
8+6
3+2
1+4
-
-
Q
-
7
6
Second Total
14
5
5
-
7
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
-
-
7
6
Essence of Number
5
5
5
-
7

 

 

T
=
2
5
THREE
56
29
2
-
3
S
=
1
3
SIX
52
16
7
-
6
-
-
3
8
Add to Reduce
108
45
9
-
9
-
-
-
-
Reduce to Deduce
1+0+8
4+5
-
-
-
-
-
3
8
Essence of Number
9
9
9
-
9

 

 

-
8
T
H
R
E
E
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
1
9
6
+
=
24
2+4
=
6
=
6
=
6
-
-
-
8
-
-
-
-
19
9
24
+
=
60
6+0
=
6
=
6
=
6
-
8
T
H
R
E
E
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
2
-
9
5
5
-
-
-
-
+
=
21
2+1
=
3
=
3
=
3
-
-`
20
-
18
5
5
-
-
-
-
+
=
48
4+8
=
12
1+2
3
=
3
-
8
T
H
R
E
E
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
20
8
18
5
5
-
19
9
24
+
=
108
1+0+8
=
9
=
9
=
9
-
-
2
8
9
5
5
-
1
9
6
+
=
45
4+5
=
9
=
9
=
9
-
8
T
H
R
E
E
-
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
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
-
-
-
-
-
-
-
-
--
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
14
8
T
H
R
E
E
-
S
I
X
-
-
31
-
-
8
-
45
-
27
1+4
-
-
-
9
-
-
-
-
9
-
-
-
3+1
-
-
-
-
4+5
-
2+7
5
8
T
H
R
E
E
-
S
I
X
-
-
4
-
-
8
-
9
-
9

 

 

8
T
H
R
E
E
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
1
9
6
+
=
24
2+4
=
6
=
6
=
6
-
-
8
-
-
-
-
19
9
24
+
=
60
6+0
=
6
=
6
=
6
8
T
H
R
E
E
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
2
-
9
5
5
-
-
-
-
+
=
21
2+1
=
3
=
3
=
3
-`
20
-
18
5
5
-
-
-
-
+
=
48
4+8
=
12
1+2
3
=
3
8
T
H
R
E
E
-
S
I
X
-
-
-
-
-
--
-
-
-
-
-
20
8
18
5
5
-
19
9
24
+
=
108
1+0+8
=
9
=
9
=
9
-
2
8
9
5
5
-
1
9
6
+
=
45
4+5
=
9
=
9
=
9
8
T
H
R
E
E
-
S
I
X
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
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
occurs
x
2
=
18
1+8
9
8
T
H
R
E
E
-
S
I
X
-
-
31
-
-
8
-
45
-
27
-
-
-
9
-
-
-
-
9
-
-
-
3+1
-
-
-
-
4+5
-
2+7
8
T
H
R
E
E
-
S
I
X
-
-
4
-
-
8
-
9
-
9

 

 

-
12
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
9
-
-
-
5
9
5
-
+
=
34
3+4
=
7
=
7
=
7
-
-
-
15
-
-
-
-
9
-
-
-
14
9
14
-
+
=
61
6+1
=
7
=
7
=
7
-
12
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
6
-
3
9
-
6
-
4
5
-
-
-
-
5
+
=
38
3+8
=
11
1+1
2
=
2
-
-
6
-
21
18
-
6
-
22
5
-
-
-
-
5
+
=
83
8+3
=
11
1+1
2
=
2
-
12
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
6
6
21
18
-
6
9
22
5
-
14
9
14
5
+
=
144
1+4+4
=
9
=
9
=
9
-
-
6
6
3
9
-
6
9
4
5
-
5
9
5
5
+
=
72
7+2
=
9
=
9
=
9
-
12
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
-
5
-
5
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
6
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
18
12
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
27
-
-
12
-
72
-
27
1+8
1+2
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
2+7
-
-
1+2
-
7+2
-
2+7
9
3
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
9
-
-
3
-
9
-
9

 

 

-
12
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
9
-
-
-
5
9
5
-
+
=
34
3+4
=
7
=
7
=
7
-
-
-
15
-
-
-
-
9
-
-
-
14
9
14
-
+
=
61
6+1
=
7
=
7
=
7
-
12
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
6
-
3
9
-
6
-
4
5
-
-
-
-
5
+
=
38
3+8
=
11
1+1
2
=
2
-
-
6
-
21
18
-
6
-
22
5
-
-
-
-
5
+
=
83
8+3
=
11
1+1
2
=
2
-
12
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
6
6
21
18
-
6
9
22
5
-
14
9
14
5
+
=
144
1+4+4
=
9
=
9
=
9
-
-
6
6
3
9
-
6
9
4
5
-
5
9
5
5
+
=
72
7+2
=
9
=
9
=
9
-
12
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
--
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
-
5
-
5
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
6
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
18
12
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
27
-
-
12
-
72
-
27
1+8
1+2
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
2+7
-
-
1+2
-
7+2
-
2+7
9
3
F
O
U
R
-
F
I
V
E
-
N
I
N
E
-
-
9
-
-
3
-
9
-
9

 

 

-
SQUARE
-
-
-
2
S+Q
36
18
9
2
U+A
22
4
4
1
R
18
9
9
1
E
5
5
5
6
SQUARE
81
36
27
-
-
8+1
3+6
2+7
6
SQUARE
9
9
9

 

 

-
CYLINDER
-
-
-
3
C+Y+L
40
13
4
1
I
9
9
9
1
N
14
5
5
2
D+E
9
9
9
1
R
18
9
9
8
CYLINDER
81
36
27
-
-
8+1
3+6
2+7
8
CYLINDER
9
9
9

 

 

-`
4
C
U
B
E
-
-
-
-
-
-
-
-
-
-
3
21
2
5
+
=
31
3+1
=
4
=
4
-
-
3
3
2
5
+
=
13
1+3
=
4
=
4
-
4
C
U
B
E
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
--
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
3
3
-
-
-
-
3
occurs
x
2
=
6
4
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
-
6
-
-
-
-
-
7
-
-
-
-
-
-
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
35
4
C
U
B
E
-
-
10
-``
-
4
-
13
3+5
-
-
-
-
-
-
-
1+0
-
-
-
-
1+3
8
4
C
U
B
E
-
-
1
-``
-
4
-
4

 

 

4
C
U
B
E
-
-
-
-
-
-
-
-
-
3
21
2
5
+
=
31
3+1
=
4
=
4
-
3
3
2
5
+
=
13
1+3
=
4
=
4
4
C
U
B
E
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
3
3
-
-
-
-
3
occurs
x
2
=
6
-
-
-
-
5
-
-
5
occurs
x
1
=
5
4
C
U
B
E
-
-
10
-``
-
4
-
13
-
-
-
-
-
-
-
1+0
-
-
-
-
1+3
4
C
U
B
E
-
-
1
-``
-
4
-
4

 

 

-
6
O
B
L
O
N
G
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
5
-
+
=
17
1+7
=
8
=
8
-
8
-
-
15
-
-
15
14
-
+
=
44
4+4
=
8
=
8
-
8
-
6
O
B
L
O
N
G
-
-
-
-
-
-
-
-
-
-
-
-
-
2
3
-
-
7
+
=
12
1+2
=
3
=
3
-
3
-
-
-
2
12
-
-
7
+
=
21
2+1
=
3
=
3
-
3
-
6
O
B
L
O
N
G
-
-
-
-
-
-
-
-
-
-
-
-
15
2
12
15
14
7
+
=
65
6+5
=
11
1+1
2
-
2
-
-
6
2
3
6
5
7
+
=
29
2+9
=
11
1+1
2
-
2
-
6
O
B
L
O
N
G
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
--
-
3
--
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
-
-
6
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
22
6
O
B
L
O
N
G
-
-
23
-
-
6
-
29
-
20
2+2
-
-
-
-
-
-
-
-
-
2+3
-
-
-
-
2+9
-
2+0
4
6
O
B
L
O
N
G
-
-
5
-
-
6
-
11
-
2
-`
-
6
2
3
6
5
7
-
-
-
-
-
-
-
1+1
-
-
3
6
O
B
L
O
N
G
-
-
5
-
-
6
-
2
-
2

 

 

6
O
B
L
O
N
G
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
5
-
+
=
17
1+7
=
8
=
8
-
8
-
15
-
-
15
14
-
+
=
44
4+4
=
8
=
8
-
8
6
O
B
L
O
N
G
-
-
-
-
-
-
-
-
-
-
-
-
2
3
-
-
7
+
=
12
1+2
=
3
=
3
-
3
-
-
2
12
-
-
7
+
=
21
2+1
=
3
=
3
-
3
6
O
B
L
O
N
G
-
-
-
-
-
-
-
-
-
-
-
15
2
12
15
14
7
+
=
65
6+5
=
11
1+1
2
-
2
-
6
2
3
6
5
7
+
=
29
2+9
=
11
1+1
2
-
2
6
O
B
L
O
N
G
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
--
-
3
--
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
-
6
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
6
O
B
L
O
N
G
-
-
23
-
-
6
-
29
-
20
-
-
-
-
-
-
-
-
-
2+3
-
-
-
-
2+9
-
2+0
6
O
B
L
O
N
G
-
-
5
-
-
6
-
11
-
2
-
6
2
3
6
5
7
-
-
-
-
-
-
-
1+1
-
-
6
O
B
L
O
N
G
-
-
5
-
-
6
-
2
-
2

 

 

-
EDFU
-
-
-
2
E+D
9
9
9
2
F+U
27
9
9
4
EDFU
36
18
18
-
-
3+6
1+8
1+8
4
EDFU
9
9
9

 

 

7
KINDRED
65
38
2
7
SPIRITS
110
38
2
6
SPIRIT
91
37
1

 

 

8
EPOPTEIA
87
42
6

 

 

3
THE
33
15
6
7
CROWING
89
44
8
2
OF
21
12
3
3
THE
33
15
6
4
COCK
32
14
5
19
First Total
208
100
28
1+9
Add to Reduce
2+0+8
1+0+0
2+8
10
Second Total
10
1
10
1+0
Reduce to Deduce
1+0
-
1+0
1
Essence of Number
1
1
1

 

 

3
THE
33
15
6
7
PERFECT
73
37
1
5
UNION
73
28
1
2
OF
21
12
3
9
OPPOSITES
134
44
8
26
First Total
334
136
19
2+6
Add to Reduce
3+3+4
1+3+6
1+9
8
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
8
Essence of Number
1
1
1

 

 

8
MARRIAGE
72
45
9
2
OF
21
12
3
6
EQUALS
75
21
3
16
First Total
168
78
15
1+6
Add to Reduce
1+6+8
7+8
1+5
7
Second Total
15
15
6
-
Reduce to Deduce
1+5
1+5
-
7
Essence of Number
6
6
6

 

 

MACBETH

William Shakespeare

Circa 1564 - 1616

Act 1 Scene 3

First Witch

I myself have all the other,
And the very ports they blow,
All the quarters that they know
I' the shipman's card.
I will drain him dry as hay:
Sleep shall neither night nor day
Hang upon his pent-house lid;
He shall live a man forbid:
Weary se'nnights nine times nine
Shall he dwindle, peak and pine:
Though his bark cannot be lost,
Yet it shall be tempest-tost.
Look what I have.

ALL

The weird sisters, hand in hand,
Posters of the sea and land,
Thus do go about, about:
Thrice to thine and thrice to mine
And thrice again, to make up nine.
Peace! the charm's wound up.

 

 

-
6
T
H
R
I
C
E
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
9
-
-
+
=
17
1+7
=
8
=
8
=
8
-
6
T
H
R
I
C
E
-
-
-
  
-
--
-
-
-
-
-
-
2
=
9
=
3
5
+
=
19
1+9
=
10
1+0
1
=
1
-
`-
20
-
18
-
3
5
+
=
46
4+6
=
10
1+0
1
=
1
-
6
T
H
R
I
C
E
-
-
-
  
-
--
-
-
-
-
-
`-
20
8
18
9
3
5
+
=
63
6+3
=
9
=
9
=
9
-
-
2
8
9
9
3
5
+
=
36
3+6
=
9
=
9
=
9
-
6
T
H
R
I
C
E
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
--
-
2
occurs
x
1
=
2
=
2
-
--
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-`
-
-
-
-
-
-
5
--
-
5
occurs
x
1
=
5
=
5
6
--
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
7
--
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
18
6
T
H
R
I
C
E
-
-
27
-
-
6
-
36
-
27
1+8
-
-
-
9
9
-
-
-
-
2+7
-
-
-
-
3+6
-
2+7
9
6
T
H
R
I
C
E
-
-
9
-
-
6
-
9
-
9

 

 

6
T
H
R
I
C
E
-
-
-
-
-
--
-
-
-
-
-
-
8
-
9
-
-
+
=
17
1+7
=
8
=
8
=
8
6
T
H
R
I
C
E
-
-
-
  
-
--
-
-
-
-
-
2
=
9
=
3
5
+
=
19
1+9
=
10
1+0
1
=
1
`-
20
-
18
-
3
5
+
=
46
4+6
=
10
1+0
1
=
1
6
T
H
R
I
C
E
-
-
-
  
-
--
-
-
-
-
`-
20
8
18
9
3
5
+
=
63
6+3
=
9
=
9
=
9
-
2
8
9
9
3
5
+
=
36
3+6
=
9
=
9
=
9
6
T
H
R
I
C
E
-T
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
--
-
2
occurs
x
1
=
2
=
2
--
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
5
--
-
5
occurs
x
1
=
5
=
5
-
-
8
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
6
T
H
R
I
C
E
-
-
27
-
-
6
-
36
-
27
-
-
-
9
9
-
-
-
-
2+7
-
-
-
-
3+6
-
2+7
6
T
H
R
I
C
E
-
-
9
-
-
6
-
9
-
9

 

 

6
THRICE
63
36
9
6
THRICE
63
36
9
6
THRICE
63
36
9
18
-
189
108
27
1+8
-
1+8+9
1+0+8
2+7
9
-
18
9
9
-
-
1+8
-
-
6
-
9
9
9

 

 

8
CALCULUS
-
-
-
-
-
-
-
C
3
3
3
-
-
3
-
A
1
1
1
-
1
-
-
L
12
3
3
-
-
3
-
C
3
3
3
-
-
3
-
U
21
3
3
-
-
3
-
L
12
3
3
-
-
3
-
U
21
3
3
-
-
3
-
S
19
10
10
-
1
-
8
CALCULUS
92
29
29
-
2
18
-
-
9+2
2+9
2+9
-
-
1+8
8
CALCULUS
11
11
11
-
2
9
-
-
1+1
1+1
1+1
-
-
-
8
CALCULUS
2
2
2
-
2
9

 

 

-
8
C
A
L
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
+
=
1
-
=
1
=
1
=
1
-
-
-
-
-
-
-
-
-
19
+
=
19
1+9
=
10
1+0
1
=
1
-
8
C
A
L
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
-
3
1
3
3
3
3
3
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
3
1
12
3
21
12
21
-
+
=
73
7+3
=
10
1+0
1
=
1
-
8
C
A
L
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
-
3
1
12
3
21
12
21
19
+
=
92
9+2
=
11
1+0
2
=
2
-
-
3
1
3
3
3
3
3
1
+
=
20
2+0
=
2
=
2
=
2
-
8
C
A
L
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
3
3
3
3
3
-
-
-
3
occurs
x
6
=
18
1+8
9
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
41
8
C
A
L
C
U
L
U
S
-
-
4
-
-
8
-
20
-
11
4+1
-
3
-
3
3
3
3
3
-
-
-
-
-
-
-
-
2+0
-
2+0
5
8
C
A
L
C
U
L
U
S
-
-
4
-
-
8
-
2
-
2
-
-
3
1
3
3
3
3
3
1
-
-
-
-
-
-
-
-
-
-
2
8
C
A
L
C
U
L
U
S
-
-
4
-
-
8
-
2
-
2

 

 

8
C
A
L
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
+
=
1
-
=
1
=
1
=
1
-
-
-
-
-
-
-
-
19
+
=
19
1+9
=
10
1+0
1
=
1
8
C
A
L
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
3
1
3
3
3
3
3
-
+
=
19
1+9
=
10
1+0
1
=
1
-
3
1
12
3
21
12
21
-
+
=
73
7+3
=
10
1+0
1
=
1
8
C
A
L
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
3
1
12
3
21
12
21
19
+
=
92
9+2
=
11
1+0
2
=
2
-
3
1
3
3
3
3
3
1
+
=
20
2+0
=
2
=
2
=
2
8
C
A
L
C
U
L
U
S
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
3
-
3
3
3
3
3
-
-
-
3
occurs
x
6
=
18
1+8
9
8
C
A
L
C
U
L
U
S
-
-
4
-
-
8
-
20
-
11
-
3
-
3
3
3
3
3
-
-
-
-
-
-
-
-
2+0
-
2+0
8
C
A
L
C
U
L
U
S
-
-
4
-
-
8
-
2
-
2
-
3
1
3
3
3
3
3
1
-
-
-
-
-
-
-
-
-
-
8
C
A
L
C
U
L
U
S
-
-
4
-
-
8
-
2
-
2

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN SOME AMAZE

THE

ZED ALIZ ZED

SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

AT THE THROW OF THE NINTH RAM WHEN IN CONJUNCTION SET

THE

FAR YONDER SCRIBE

MADE RECORD OF THE FALL

 

 

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.

 

I

AM THE OPPOSITE OF THE OPPOSITE

I

AM THE OPPOSITE OF OPPOSITE IS THE AM

I

ALWAYS

AM

 

 

I

THAT AM THAT

THE

PATIENT PATTERN

MAKER

THIS IS THE SEEN OF THE SCENE UNSEEN THE UNSEEN SEEN OF THE SCENE

UNSEEN

 

 

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

 

 

-
EFFLUX
 - - -
2
E+F
11
11
2
4
F+L+U+X
63
18
9
6
EFFLUX
74
29
11
-
-
7+4
2+9
1+1
6
EFFLUX
11
11
2
-
-
1+1
1+1
-
6
EFFLUX
2
2
2

 

 

10
UNDERSTOOD
135
45
9

 

 

4
WISH
59
23
5
6
WISHED
68
32
5
6
WISHES
83
38
2
3
ISH
36
18
9

 

 

4
AMSU
54
18
9
3
MIN
36
18
9

 

 

-
HERMES
 - - -
3
H+E+R
31
22
4
2
M+E
18
18
9
1
S
19
10
1
6
HERMES
-
-
-

 

 

8
FESTIVAL
94
31
4
2
OF
21
12
3
3
EID
18
18
9
13
Add to Reduce
133
61
16
1+3
Reduce to Deduce
1+3+3
6+1
1+6
4
Essence of Number
7
7
7

 

 

3
EID
18
18
9
2
UL
33
6
6
4
FITR
53
26
8
9
Add to Reduce
104
50
23
-
Reduce to Deduce
1+0+4
5+0
2+3
9
Essence of Number
5
5
5

 

 

5
KNEPH
54
27
9

 

 

-
16
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
-
9
5
-
-
-
-
5
-
-
-
-
-
1
+
=
29
2+9
=
11
1+1
2
=
2
-
-
9
-
-
-
9
14
-
-
-
-
14
-
-
-
-
-
19
+
=
65
6+5
=
11
1+1
2
=
2
-
16
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
-
4
1
7
-
-
1
9
7
-
-
3
4
2
5
9
-
+
=
52
5+2
=
9
=
9
=
9
-
-
-
13
1
7
-
-
1
18
25
-
-
21
13
2
5
18
-
+
=
124
1+2+4
=
7
=
7
=
7
-
16
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
9
13
1
7
9
14
1
18
25
-
14
21
13
2
5
18
19
+
=
189
1+8+9
=
18
1+8
9
=
9
-
-
9
4
1
7
9
5
1
9
7
-
5
3
4
2
5
9
1
+
=
81
8+1
=
9
=
9
=
9
-
16
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
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
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
9
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
4
=
36
3+6
9
14
16
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
31
-
-
16
-
81
-
36
1+4
1+6
9
-
-
-
9
-
-
9
-
-
-
-
-
-
-
9
-
-
-
3+1
-
-
1+6
-
8+1
-
3+6
5
7
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
4
-
-
7
-
9
-
9
-
-
9
4
1
7
9
5
1
9
7
-
5
3
4
2
5
9
1
-
-
-
-
-
--
-
-
-
-
5
7
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
4
-
-
7
-
9
-
9

 

 

16
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
-
-
-
--
-
-
-
-
-
9
-
-
-
9
5
-
-
-
-
5
-
-
-
-
-
1
+
=
29
2+9
=
11
1+1
2
=
2
-
9
-
-
-
9
14
-
-
-
-
14
-
-
-
-
-
19
+
=
65
6+5
=
11
1+1
2
=
2
16
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
4
1
7
-
-
1
9
7
-
-
3
4
2
5
9
-
+
=
52
5+2
=
9
=
9
=
9
-
-
13
1
7
-
-
1
18
25
-
-
21
13
2
5
18
-
+
=
124
1+2+4
=
7
=
7
=
7
16
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
-
-
-
--
-
-
-
-
-
9
13
1
7
9
14
1
18
25
-
14
21
13
2
5
18
19
+
=
189
1+8+9
=
18
1+8
9
=
9
-
9
4
1
7
9
5
1
9
7
-
5
3
4
2
5
9
1
+
=
81
8+1
=
9
=
9
=
9
16
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
-
-
-
--
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
5
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
9
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
4
=
36
3+6
9
16
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
31
-
-
16
-
81
-
36
1+6
9
-
-
-
9
-
-
9
-
-
-
-
-
-
-
9
-
-
-
3+1
-
-
1+6
-
8+1
-
3+6
7
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
4
-
-
7
-
9
-
9
-
9
4
1
7
9
5
1
9
7
-
5
3
4
2
5
9
1
-
-
-
-
-
--
-
-
-
-
7
I
M
A
G
I
N
A
R
Y
-
N
U
M
B
E
R
S
-
-
4
-
-
7
-
9
-
9

 

 

NUMBER = 534259 = 1 = 534259 NUMBER

NUMBER = 234559 NUMBER

NUMBER = 534259 = 1 = 534259 NUMBER

 

 

NUMBERS = 5342591 = 2 = 5342591 NUMBERS

SBUMNER = 1234559 = SBUMNER

NUMBERS = 5342591 = 2 = 5342591 NUMBERS

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
-
-
-
-
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
6
7
8
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
-
-
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
6
7
8
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
9
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
-
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
3
-
-
-
-
Q
NUMBERS
-
Q
Q
-
-
-
-
-
-
-
S
=
1
-
1
S
19
1
1
-
1
-
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
M
=
4
-
1
M
13
4
4
-
-
-
-
4
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
9
-
-
29
4
7
NUMBERS
92
29
29
-
1
2
3
4
10
9
-
-
2+9
Q
-
Q
9+2
2+9
2+9
-
-
-
-
-
1+0
-
Q
-
11
-
7
NUMBERS
11
11
11
-
1
2
3
4
1
9
-
-
1+1
Q
-
Q
1+1
1+1
1+1
-
-
-
-
-
-
-
Q
-
2
-
7
NUMBERS
2
2
2
-
1
2
3
4
1
9

 

 

I = 9 9 = I
ME = 9 9 = ME
BRAIN + BODY = 9 9 = BODY + BRAIN
LIGHT + DARK = 9 9 = DARK + LIGHT
ENERGY + MASS = 9 9 = MASS +ENERGY
MIND + MATTER = 9 9 = MATTER + MIND
MAGNETIC + FIELD = 9 9 = FIELD + MAGNETIC
POSITIVE + NEGATIVE = 9 9 = NEGATIVE + POSITIVE
973 OM AZAZAZAZAZAZAZAZAZZAZAZAZAZAZAZAZAZAOM 973

 

 

THE ENGLISH ALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZ

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

0 1 2 3 4 5 6 7 8 9

ZEROONETWOTHREEFOURFIVESIXSEVENEIGHTNINE

(0) ZERO = 8x5x9x6 = 2160 2+1+6+0 = 9

(1) ONE = 6x5x5 = 150 1+5+0 = 6

(2) TWO = 2x5x6 = 60 6+0 = 6

(3) THREE = 2x8x9x5x5 = 360 3+6+0 = 9

(4) FOUR = 6x6x3x9 = 972 9+7+2 = 18 1+8 = 9

(5) FIVE = 6x9x4x5 = 1080 1+0+8+0 = 9

(6) SIX = 1x9x6 = 54 5+4 = 9

(7) SEVEN = 1x5x4x5x5 = 500 5+0+0 = 5

(8) EIGHT = 5x9x7x8x2 = 5040 5+0+4+0 = 9

(9) NINE = 5x9x5x5 = 1125 1+1+2+5 = 9

0 1 2 3 4 5 6 7 8 9

ZEROONETWOTHREEFOURFIVESIXSEVENEIGHTNINE

(0) ZERO = 8x5x9x6 = 2160 2+1+6+0 = 9

(1) ONE = 6x5x5 = 150 1+5+0 = 6

(2) TWO = 2x5x6 = 60 6+0 = 6

(3) THREE = 2x8x9x5x5 = 360 3+6+0 = 9

(4) FOUR = 6x6x3x9 = 972 9+7+2 = 18 1+8 = 9

(5) FIVE = 6x9x4x5 = 1080 1+0+8+0 = 9

(6) SIX = 1x9x6 = 54 5+4 = 9

(7) SEVEN = 1x5x4x5x5 = 500 5+0+0 = 5

(8) EIGHT = 5x9x7x8x2 = 5040 5+0+4+0 = 9

 

(9) NINE = 5x9x5x5 = 1125 1+1+2+5 = 9

 

 

THE ENGLISH ALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZ

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

12345678912345678912345678

=

1+2+6

9

ZEROONETWOTHREEFOURFIVESIXSEVENEIGHTNINE

MULTIPLICATION

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. Wikipedia

 

Q
Q
66
Q
14
MULTIPLICATION
174
66
66
-
-
6+6
-
1+4
-
1+7+4
6+6
6+6
-
-
12
-
5
MULTIPLICATION
12
12
12
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
3
-
5
MULTIPLICATION
3
3
3

 

MULTIPLICATION

 

-
-
-
-
-
MULTIPLICATION
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
L
=
3
7
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
9
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
10
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
11
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
13
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
Q
Q
66
Q
14
MULTIPLICATION
174
66
66
-
1
4
12
4
5
6
7
8
27
-
-
6+6
-
1+4
-
1+7+4
6+6
6+6
-
-
-
1+2
-
-
-
-
-
2+7
-
-
12
-
5
MULTIPLICATION
12
12
12
-
1
4
3
4
5
6
7
8
9
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
MULTIPLICATION
3
3
3
-
1
4
3
4
5
6
7
8
9

 

 

-
-
-
-
-
MULTIPLICATION
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
L
=
3
7
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
C
=
3
9
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
A
=
1
10
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
11
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
13
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
Q
Q
66
Q
14
MULTIPLICATION
174
66
66
-
1
4
12
4
5
6
7
8
27
-
-
6+6
-
1+4
-
1+7+4
6+6
6+6
-
-
-
1+2
-
-
-
-
-
2+7
-
-
12
-
5
MULTIPLICATION
12
12
12
-
1
4
3
4
5
6
7
8
9
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
MULTIPLICATION
3
3
3
-
1
4
3
4
5
6
7
8
9

 

 

-
-
-
-
-
MULTIPLICATION
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
10
1
A
1
1
1
-
1
-
-
-
-
-
-
8
-
T
=
2
11
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
-
8
-
U
=
3
2
1
U
21
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
7
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
C
=
3
9
1
C
3
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
1
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
13
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
P
=
7
6
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
I
=
9
8
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
Q
Q
66
Q
14
MULTIPLICATION
174
66
66
-
1
4
12
4
5
6
7
8
27
-
-
6+6
-
1+4
-
1+7+4
6+6
6+6
-
-
-
1+2
-
-
-
-
-
2+7
-
-
12
-
5
MULTIPLICATION
12
12
12
-
1
4
3
4
5
6
7
8
9
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
5
MULTIPLICATION
3
3
3
-
1
4
3
4
5
6
7
8
9

 

 

M
=
4
14
MULTIPLICATION
174
66
3
-
-
-
-
-
-
-
-
M
=
4
8
MULTIPLY
127
38
2
-
-
-
-
-
-
-
-
M
=
4
10
MULTIPLIES
136
46
1
-
-
-
-
-
-
-
-
M
=
4
5
MULTIPLIED
121
49
4
-
-
-
-
-
-
-
-
M
=
4
14
MULTIPLE
108
36
9
-
-
-
-
-
-
-
-
M
=
4
14
MULTIPLES
127
37
1
-
-
-
-
-
-
-
-
M
=
4
5
MULTIPLICITY
169
61
7
-
-
-
-
-
-
-
-
M
=
4
5
MULTIPLYING
158
59
5

 

 

A
=
1
3
ADD
9
9
9
-
-
-
-
-
-
-
-
A
=
1
8
ADDITION
767
31
4
-
-
-
-
-
-
-
-
S
=
1
5
SHARE
51
24
6
-
-
-
-
-
-
-
-
S
=
1
7
SHARING
76
40
4
-
-
-
-
-
-
-
-
D
=
4
6
DIVIDE
53
35
8
-
-
-
-
-
-
-
-
D
=
4
6
DIVIDES
72
36
9
-
-
-
-
-
-
-
-
D
=
4
8
DIVISION
101
47
2
-
-
-
-
-
-
-
-
L
=
3
12
LONG DIVISION
149
68
5
-
-
-
-
-
-
-
-
A
=
1
7
ALGEBRA
46
28
1
-
-
-
-
-
-
-
-
E
=
5
8
EQUATION
102
39
3

 

 

NUMERICAL

NUMBERERING

NUMERACY

NUMEROLOGY

NUMEROLOGICAL PHENOMENA

 

 

PROBLEMS - PROBLEMS

 
8
PROBLEMS
100
46
1
-
1
2
3
4
5
6
7
8
9
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
B
=
2
4
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
8
9
-
-
3+7
-
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
8
9

 

 
8
PROBLEMS
100
46
1
-
1
2
3
4
5
6
7
8
9
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
B
=
2
4
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
8
9
-
-
3+7
-
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
8
9

 

 
8
PROBLEMS
100
46
1
-
1
2
3
4
5
6
7
8
9
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
B
=
2
4
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
8
9
-
-
3+7
-
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
8
9
-
-
1+0
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
8
9

 

LETTERS RE ARRANGED NUMERICALLY

 
8
PROBLEMS
100
46
1
-
1
2
3
4
5
6
7
9
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
-
B
=
2
4
1
B
2
2
2
-
-
2
-
-
-
-
-
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
-
-
M
=
4
7
1
M
13
4
4
-
-
-
-
4
-
-
-
-
E
=
5
6
1
E
5
5
5
-
-
-
-
-
5
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
9
-
-
37
-
8
PROBLEMS
100
46
37
-
1
2
3
4
5
6
7
9
-
-
3+7
-
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
-
-
-
-
10
-
8
PROBLEMS
1
10
10
-
1
2
3
4
5
6
7
9
-
-
1+0
-
-
-
-
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
1
-
8
PROBLEMS
1
1
1
-
1
2
3
4
5
6
7
9

 

LETTERS RE ARRANGED NUMERICALLY

 

SOLVE PROBLEMS SOLVE

 
7
SOLVING
98
44
8
-
1
2
3
4
5
6
7
8
9
8
PROBLEMS
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
35
-
-
-
98
44
35
-
-
-
-
-
-
-
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
37
-
-
-
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SOLVING
98
44
35
-
2
2
6
8
10
12
14
8
18
-
-
-
-
8
PROBLEMS
100
46
37
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
72
-
15
First Total
198
90
72
-
2
2
6
8
1
3
5
8
9
-
-
7+2
-
1+5
Add to Reduce
1+9+8
9+0
7+2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Second Total
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Essence of Number
9
9
9
-
2
2
6
8
1
3
5
8
9

 

 
7
SOLVING
98
44
8
-
1
2
3
4
5
6
7
8
9
8
PROBLEMS
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SOLVING
98
44
35
-
2
2
6
8
10
12
14
8
18
-
-
-
-
8
PROBLEMS
100
46
37
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
72
-
15
First Total
198
90
72
-
2
2
6
8
1
3
5
8
9
-
-
7+2
-
1+5
Add to Reduce
1+9+8
9+0
7+2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Second Total
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Essence of Number
9
9
9
-
2
2
6
8
1
3
5
8
9

 

 
7
SOLVING
98
44
8
-
1
2
3
4
5
6
7
8
9
8
PROBLEMS
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
8
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
8
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
8
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
8
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
8
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
8
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
8
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
8
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
8
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
8
9
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SOLVING
98
44
35
-
2
2
6
8
10
12
14
8
18
-
-
-
-
8
PROBLEMS
100
46
37
-
-
-
-
-
1+0
1+2
1+4
-
1+8
-
-
72
-
15
First Total
198
90
72
-
2
2
6
8
1
3
5
8
9
-
-
7+2
-
1+5
Add to Reduce
1+9+8
9+0
7+2
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Second Total
18
9
9
-
2
2
6
8
1
3
5
8
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Essence of Number
9
9
9
-
2
2
6
8
1
3
5
8
9

 

LETTERS RE ARRANGED NUMERICALLY

 
7
SOLVING
98
44
8
-
1
2
3
4
5
6
7
9
8
PROBLEMS
100
46
37
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
B
=
2
11
1
B
2
2
2
-
-
2
-
-
-
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
-
V
=
4
4
1
V
22
4
4
-
-
-
-
4
-
-
-
-
M
=
4
14
1
M
13
4
4
-
-
-
-
4
-
-
-
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
O
=
6
2
1
O
15
6
6
-
-
-
-
-
-
6
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
9
R
=
9
9
1
R
18
9
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SOLVING
98
44
35
-
2
2
6
8
10
12
14
18
-
-
-
-
8
PROBLEMS
100
46
37
-
-
-
-
-
1+0
1+2
1+4
1+8
-
-
72
-
15
First Total
198
90
72
-
2
2
6
8
1
3
5
9
-
-
7+2
-
1+5
Add to Reduce
1+9+8
9+0
7+2
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Second Total
18
9
9
-
2
2
6
8
1
3
5
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
Essence of Number
9
9
9
-
2
2
6
8
1
3
5
9

 

 

A
=
1
--
3
ALL
25
7
7
W
=
5
--
2
WE
28
10
1
A
=
1
-
3
ARE
24
15
6
S
=
1
--
6
SAYING
75
30
3
I
=
9
--
2
IS
28
10
1
-
-
17
-
16
Add to Reduce
180
72
18
--
-
1+7
1
1+6
Reduce to Deduce
1+8+0
7+2
1+8
-
--
8
-
7
Essence of Number
9
9
9

 

 

G
=
7
--
4
GIVE
43
25
7
P
=
7
--
5
PEACE
30
21
3
A
=
1
-
1
A
1
1
1
C
=
3
--
6
CHANCE
34
25
7
-
--
18
-
15
Add to Reduce
108
72
18
--
-
1+8
1
1+8
Reduce to Deduce
1+0+8
7+2
1+8
-
--
9
-
9
Essence of Number
9
9
9

 

 

THE ENGLISH ALPHABET

ROTATOR = ROTATOR

9621269 = 9621269

ROTATOR= ROTATOR

ROTATOR 9x6x2x1x2x6x9 = 11664 = 9x6x2x1x2x6x 9ROTATOR

ROTATOR = 11664 = 1x1x6x6x4 = 4x6x6x1x1 = 46611 = ROTATOR

ROTATOR = 11664 = 1x1x6x6x4 = 144 = 1+4+4 = 9 =144 = 46611 = ROTATOR

 

 

U
=
3
9
UNIVERSAL
121
40
4
T
=
2
5
TRUTH
87
24
6
-
-
5
14
First Total
208
64
10
-
-
-
1+4
Add to Reduce
2+0+8
6+4
1+0
-
-
5
5
Second Total
10
10
1
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
5
5
Essence of Number
1
1
1

 

 

9
UNIVERSAL
121
40
4
4
LIFE
32
23
5
13
Add to Reduce
153
63
9
1+3
Reduce to Deduce
1+5+3
6+3
-
4
Essence of Number
9
9
9

 

G
=
7
3
GOD
26
17
8
I
=
9
2
IS
28
19
1
U
=
3
9
UNIVERSAL
121
40
4
L
=
3
4
LIFE
32
23
5
-
-
22
18
First Total
207
99
18
-
-
2+2
1+8
Add to Reduce
2+0+7
9+9
1+8
-
-
4
9
Second Total
9
18
9
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
4
9
Essence of Number
9
9
9

 

4
GODS
45
18
9
9
UNIVERSAL
121
40
4
5
TRUTH
87
24
6

 

MIN DOTH DREAM WHAT DOTH MIN MEAN

 

EVOLVE LOVE EVOLVE

LOVE EVOLVE LOVE

EVOLVE REVOLVE EVOLVE

REVOLVE EVOLVE REVOLVE

SOLVE LOVES SOLVE

 

 

-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
8
9
1
+
=
18
1+8
=
9
-
9
-
-
-
-
-
-
8
9
19
+
=
36
3+6
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
2
4
5
7
-
-
-
+
=
18
1+8
=
9
=
9
-
-
11
13
5
16
-
-
-
+
=
45
4+5
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
11
13
5
16
8
9
19
+
=
81
8+1
=
9
=
9
-
-
2
4
5
7
8
9
1
+
=
36
3+6
=
9
=
9
-
7
K
M
E
P
H
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
``-
2
--
-
--
-
--
-
-
-
2
occurs
x
1
=
2
3
-
-
--
-
--
--
--
-
-
-
3
THREE
-
-
-
-
-
-
--
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
-
-
--
5
--
--
--
-
-
-
5
occurs
x
1
=
5
6
-
--
--
-
--
--
--
-
-
-
6
SIX
-
-
-
-
-
-
--
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
9
7
K
M
E
P
H
I
S
-
-
36
-
-
7
-
36
-
-
-
-
-
-
-
9
-
-
-
3+6
-
-
-
-
3+6
9
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9
-
-
2
4
5
7
8
9
1
-
-
-
-
-
-
-
-
9
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9

 

 

7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
8
9
1
+
=
18
1+8
=
9
-
9
-
-
-
-
-
8
9
19
+
=
36
3+6
=
9
=
9
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
2
4
5
7
-
-
-
+
=
18
1+8
=
9
=
9
-
11
13
5
16
-
-
-
+
=
45
4+5
=
9
=
9
7
K
M
E
P
H
I
S
-
-
-
-
-
--
-
-
-
11
13
5
16
8
9
19
+
=
81
8+1
=
9
=
9
-
2
4
5
7
8
9
1
+
=
36
3+6
=
9
=
9
7
K
M
E
P
H
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
``-
2
--
-
--
-
--
-
-
-
2
occurs
x
1
=
2
-
--
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
-
--
5
--
--
--
-
-
-
5
occurs
x
1
=
5
-
--
-
-
7
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
8
-
-
-
-
8
occurs
x
1
=
8
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
7
K
M
E
P
H
I
S
-
-
36
-
-
7
-
36
-
-
-
-
-
-
9
-
-
-
3+6
-
-
-
-
3+6
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9
-
2
4
5
7
8
9
1
-
-
-
-
-
-
-
-
7
K
M
E
P
H
I
S
-
-
9
-
-
7
-
9

 

 

-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
-
8
9
-
-
6
-
-
-
-
8
9
-
+
=
40
4+0
=
4
-
4
-
4
-
`-
8
9
-
-
15
-
-
-
-
8
9
-
+
=
49
4+9
=
13
1+3
4
-
4
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
9
-
7
3
7
7
-
-
3
+
=
38
3+8
=
11
1+1
2
-
2
-
`-
-
-
5
18
-
7
12
25
16
-
-
3
+
=
83
8+3
=
11
1+1
2
-
2
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
`-
8
9
5
18
15
7
12
25
16
8
9
3
+
=
135
1+3+5
=
9
-
9
-
9
-
-
8
9
5
9
6
7
3
7
7
8
9
3
+
=
81
8+1
=
9
-
9
-
9
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
--
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
7
-
7
7
-
-
-
-
-
7
occurs
x
3
=
21
=
3
-
--
8
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
7
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
38
-
-
12
-
81
-
36
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
3+8
-
-
1+2
Q
8+1
-
3+6
7
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
11
-
-
3
-
9
-
9
-
-
8
9
5
9
6
7
3
7
7
8
9
3
-
-
1+1
-
-
-
-
-
-
-
7
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
2
-
-
3
-
9
-
9

 

 

12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
8
9
-
-
6
-
-
-
-
8
9
-
+
=
40
4+0
=
4
-
4
-
4
`-
8
9
-
-
15
-
-
-
-
8
9
-
+
=
49
4+9
=
13
1+3
4
-
4
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
5
9
-
7
3
7
7
-
-
3
+
=
38
3+8
=
11
1+1
2
-
2
`-
-
-
5
18
-
7
12
25
16
-
-
3
+
=
83
8+3
=
11
1+1
2
-
2
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
--
-
-
-
-
`-
8
9
5
18
15
7
12
25
16
8
9
3
+
=
135
1+3+5
=
9
-
9
-
9
-
8
9
5
9
6
7
3
7
7
8
9
3
+
=
81
8+1
=
9
-
9
-
9
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
-
-
-
5
-
-
-
-
-
-
-
-
--
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
7
-
7
7
-
-
-
-
-
7
occurs
x
3
=
21
=
3
--
8
-
-
-
-
-
-
-
-
8
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
3
=
27
2+7
9
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
38
-
-
12
-
81
-
36
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
3+8
-
-
1+2
Q
8+1
-
3+6
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
11
-
-
3
-
9
-
9
-
8
9
5
9
6
7
3
7
7
8
9
3
-
-
1+1
-
-
-
-
-
-
-
12
H
I
E
R
O
G
L
Y
P
H
I
C
-
-
2
-
-
3
-
9
-
9

 

 

KEEPER OF GENESIS

A QUEST FOR THE HIDDEN LEGACY OF MANKIND

Robert Bauval Graham Hancock 1996

Page 254

"...Is there in any sense an interstellar Rosetta Stone?

We believe there is a common language that all technical civilizations, no matter how different, must have.

That common language is science and mathematics.

The laws of Nature are the same everywhere:..."

 

 

R
=
9
-
7
ROSETTA
98
26
8
S
=
1
-
5
STONE
73
19
1
-
-
10
-
12
Add to Reduce
171
45
9
-
-
1+0
-
1+2
Reduce to Deduce
1+7+1
4+5
-
Q
-
1
-
3
Essence of Number
9
9
9

 

 

-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
6
1
-
-
-
-
-
1
-
6
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
15
19
-
-
-
-
-
19
-
15
14
-
+
=
82
8+2
=
10
1+0
1
=
1
-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
9
-
-
5
2
2
1
-
-
2
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
-
18
-
-
5
20
20
1
-
-
20
-
-
5
+
=
89
8+9
=
17
1+7
8
=
8
-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
18
15
19
5
20
20
1
-
19
20
15
14
5
+
=
171
1+7=1
=
9
=
9
=
9
-
-
9
6
1
5
2
2
1
-
1
2
6
5
5
+
=
45
4+5
=
9
=
9
=
9
-
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
-
``-
-
-
-
-
2
2
-
-`
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
22
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
23
-
-
12
-
45
-
27
2+2
1+2
9
-``
-
-
-
-
-
-
-
-
-``
-
-
-
-
2+3
-
-
1+2
-
4+5
-
2+7
4
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9
-
-
9
6
1
5
2
2
1
-
1
2
6
5
5
-
-
-
-
-
-
-
-
-
-
4
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9

 

 

12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
6
1
-
-
-
-
-
1
-
6
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
15
19
-
-
-
-
-
19
-
15
14
-
+
=
82
8+2
=
10
1+0
1
=
1
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
9
-
-
5
2
2
1
-
-
2
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
18
-
-
5
20
20
1
-
-
20
-
-
5
+
=
89
8+9
=
17
1+7
8
=
8
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
18
15
19
5
20
20
1
-
19
20
15
14
5
+
=
171
1+7=1
=
9
=
9
=
9
-
9
6
1
5
2
2
1
-
1
2
6
5
5
+
=
45
4+5
=
9
=
9
=
9
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
``-
-
-
-
-
2
2
-
-`
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
5
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
23
-
-
12
-
45
-
27
1+2
9
-``
-
-
-
-
-
-
-
-
-``
-
-
-
-
2+3
-
-
1+2
-
4+5
-
2+7
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9
-
9
6
1
5
2
2
1
-
1
2
6
5
5
-
-
-
-
-
-
-
-
-
-
3
R
O
S
E
T
T
A
-
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9

 

 

12
R
O
S
E
T
T
A
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
6
1
-
-
-
-
1
-
6
5
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
15
19
-
-
-
-
19
-
15
14
-
+
=
82
8+2
=
10
1+0
1
=
1
12
R
O
S
E
T
T
A
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
9
-
-
5
2
2
1
-
2
-
-
5
+
=
26
2+6
=
8
=
8
=
8
-
18
-
-
5
20
20
1
-
20
-
-
5
+
=
89
8+9
=
17
1+7
8
=
8
12
R
O
S
E
T
T
A
S
T
O
N
E
-
-
-
-
-
--
-
-
-
-
-
18
15
19
5
20
20
1
19
20
15
14
5
+
=
171
1+7=1
=
9
=
9
=
9
-
9
6
1
5
2
2
1
1
2
6
5
5
+
=
45
4+5
=
9
=
9
=
9
12
R
O
S
E
T
T
A
S
T
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
1
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
``-
-
-
-
-
2
2
-
-
2
-
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
5
-
-
-
-
-
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
6
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
R
O
S
E
T
T
A
S
T
O
N
E
-
-
23
-
-
12
-
45
-
27
1+2
9
-``
-
-
-
-
-
-
-
-``
-
-
-
-
2+3
-
-
1+2
-
4+5
-
2+7
3
R
O
S
E
T
T
A
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9
-
9
6
1
5
2
2
1
1
2
6
5
5
-
-
-
-
-
-
-
-
-
-
3
R
O
S
E
T
T
A
S
T
O
N
E
-
-
5
-
-
3
-
9
-
9

 

 

Noted at 9:09 am 02 Nov 2016

The Oracle Forum at 973-Eht-Namuh-973.com
Topics An Introduction to Hyperspace by heron » 05 Apr 2016 15:57

1/2 Replies 15

Views 1836

Last post by heron View the latest post 02 Nov 2016 06:14

 

 

User avatar
heron
Posts: 18
Joined: 05 Apr 2016 15:48
Re: An Introduction to Hyperspace

Quote Postby heron » 05 Apr 2016 20:10

Creatures that drift
in the depths of the sea
are the very last
to discover the water

 

 

 

 

 

 

 

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