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Evokation
  
 
Index
  

 

 

ADVENT TABLE ADVENT

 

 

 

THE NUCLEAR FAMILY 1969

 

 

 

 

A

MAZE

IN

ZAZAZA ENTERS AZAZAZ

AZAZAZAZAZAZAZZAZAZAZAZAZAZA

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGICALALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZZYXWVUTSRQPONMLKJIHGFEDCBA

12345678910111213141516171819202122232425262625242322212019181716151413121110987654321

 

 

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

 

....

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
-
5
ADDED
18
18
9
-
-
-
-
-
-
-
-
-
9
T
=
2
-
2
TO
35
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
3
ALL
25
7
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
5
MINUS
76
22
4
-
-
-
-
4
-
-
-
-
-
N
=
5
-
4
NONE
48
21
3
-
-
-
3
-
-
-
-
-
-
S
=
1
-
6
SHARED
55
28
1
-
1
-
-
-
-
-
-
-
-
B
=
2
-
2
BY
27
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
10
EVERYTHING
133
61
7
-
-
-
-
-
-
-
7
-
-
M
=
4
-
10
MULTIPLIED
121
49
4
-
-
-
-
4
-
-
-
-
-
I
=
9
-
2
IN
23
14
5
-
-
-
-
-
5
-
-
-
-
A
=
1
-
9
ABUNDANCE
65
29
2
-
-
2
-
-
-
-
-
-
-
-
-
35
-
58
First Total
995
266
59
-
1
2
3
8
5
6
14
8
18
-
-
3+5
-
5+8
Add to Reduce
9+9+5
2+6+6
5+9
-
-
-
-
-
-
-
1+4
-
1+8
-
-
8
-
13
Second Total
23
14
15
-
1
2
3
8
5
6
5
8
9
-
-
-
-
1+3
Reduce to Deduce
2+3
1+4
 1+5
-
-
-
-
-
-
-
-
-
-
-
-
8
-
4
Essence of Number
5
5
5
-
1
2
3
8
5
6
5
8
9

 

 

A

HISTORY OF GOD

Karen Armstrong 1993

The God of the Mystics

Page 250

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

 

Page 250

THERE IS NO ATTEMPT MADE 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 THE MIND AWAY FROM THE NORMAL

CONNOTATIONS OF WORDS

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

....

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

 

 

 

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

 

 

 

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"

 

 

-
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

 

 

THE CITY OF REVELATION

John Michell 1972

Gnostic Numbers 

Page 118

"Exactly how they came by their science of numbers is not certain, but they appear to have made the discovery that the numerical code of the Hebrew cabala and those of other mystical systems throughout the world were all degenerate versions of the same once universal system of knowledge that returns within the reach of human perception at certain intervals in time. As the revealed books of the Old Testament were written in a code to be interpreted by reference to number, so were the revelations of the gnostic prophets expressed in words and phrases formed on a system of proportion, which gave life and power to the Christian myth, while allowing initiates to gain a further understanding of the balance of forces that produce the world of phenomena."  

Page 121 / How it was ever supposed that the Hebrew alphabet of twenty- two letters, together with various geometrical symbols might serve to represent the entire moving pattern of the universe is not now easy to understand; but, since all ancient philosophy, religion, magic, the arts and sciences were based on the concept of a correspondence between numbers and cosmic law, it is impossible to appreciate the history of the past without some actual experience of the fundamental truth behind this approach to cosmology. Plato gives a remarkable account in Cratylos of the origin of language and letters. The philosopher is asked whether there is any particular significance in names, for surely they are simply a matter of convention and one is more or less as good as another. After all, foreigners call things by different names and appear to manage just as well as the Greeks in this respect. The answer given is that despite appearances the matter is by no means so simple. Words are the tools of expression, and the making of these, as of any other tools, is the task of a skilled craftsman, in this case the lawgiver. Language has grown corrupt over the ages, and names have deviated from their original perfect forms, which are those used by the gods. But all names were originally formed on certain principles, through knowledge of which it is possible to discover the archetypal meaning of words in current use. 'So perhaps the man who knows about names considers their value and is not confused if some letter is added, transposed or subtracted, or even if the force of the name is expressed in quite different letters.' This is Plato's clearest reference to the mystical science of the cabala, in which letters, words and whole phrases may be substituted for others of the same numerical value. The force of a name is to be found in its number, and can be expressed through any combination of letters, provided the sum of the letters amounts to the appropriate number by gematria.

 

THE MAGIC ALPHABET

 

A
=
1
-
9
ABCDEFGHI
45
45
45
-
-
-
-
-
-
-
-
-
-
J
=
1
-
9
JKLMNOPQR
126
45
45
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
STUVWXYZ
180
45
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
351
135
126
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
B
=
2
2
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
C
=
3
3
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
4
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
6
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
45
-
-
-
45
45
45
-
-
-
-
-
-
-
-
-
-
J
=
1
10
1
J
10
1
1
-
1
-
-
-
-
-
-
-
-
K
=
2
11
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
13
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
15
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
16
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
Q
=
8
17
1
Q
17
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
45
-
-
-
126
45
45
-
-
-
-
-
-
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
21
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
22
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
W
=
5
23
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
24
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
Y
=
7
25
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
Z
=
8
26
1
Z
26
8
8
-
-
-
-
-
-
-
-
8
-
36
-
-
-
180
45
36
-
-
-
-
-
-
-
-
-
-
126
-
-
-
-
-
-
-
3
6
9
12
15
18
21
24
18
-
-
1+2+6
-
9
ABCDEFGHI
45
45
45
-
-
-
-
1+2
1+5
1+8
2+1
2+4
1+8
-
-
9
-
9
JKLMNOPQR
126
45
45
-
3
6
9
3
6
9
3
6
9
-
-
-
-
8
STUVWXYZ
180
45
36
-
-
-
-
-
-
-
-
-
-
-
-
9
-
26
ADD TO REDUCE
351
135
126
-
3
6
9
3
6
9
3
6
9
-
-
-
-
2+6
REDUCE TO DEDUCE
3+5+1
1+3+5
1+2+6
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
ESSENCE OF NUMBER
9
9
9
-
3
6
9
3
6
9
3
6
9

 

 

A
=
1
-
9
ABCDEFGHI
45
45
45
-
-
-
-
-
-
-
-
-
-
J
=
1
-
9
JKLMNOPQR
126
45
45
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
STUVWXYZ
180
45
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
351
135
126
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
B
=
2
2
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
C
=
3
3
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
4
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
6
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
J
=
1
10
1
J
10
1
1
-
1
-
-
-
-
-
-
-
-
K
=
2
11
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
13
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
15
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
16
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
Q
=
8
17
1
Q
17
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
21
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
22
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
W
=
5
23
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
24
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
Y
=
7
25
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
Z
=
8
26
1
Z
26
8
8
-
-
-
-
-
-
-
-
8
-
126
-
-
-
-
-
-
-
3
6
9
12
15
18
21
24
18
-
-
1+2+6
-
9
ABCDEFGHI
45
45
45
-
-
-
-
1+2
1+5
1+8
2+1
2+4
1+8
-
-
9
-
9
JKLMNOPQR
126
45
45
-
3
6
9
3
6
9
3
6
9
-
-
-
-
8
STUVWXYZ
180
45
36
-
-
-
-
-
-
-
-
-
-
-
-
9
-
26
ADD TO REDUCE
351
135
126
-
3
6
9
3
6
9
3
6
9
-
-
-
-
2+6
REDUCE TO DEDUCE
3+5+1
1+3+5
1+2+6
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
ESSENCE OF NUMBER
9
9
9
-
3
6
9
3
6
9
3
6
9

 

 

A
=
1
-
9
ABCDEFGHI
45
45
45
-
-
-
-
-
-
-
-
-
-
J
=
1
-
9
JKLMNOPQR
126
45
45
-
-
-
-
-
-
-
-
-
-
S
=
1
-
8
STUVWXYZ
180
45
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
351
135
126
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
J
=
1
10
1
J
10
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
19
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
B
=
2
2
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
K
=
2
11
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
C
=
3
3
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
12
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
U
=
3
21
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
4
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
M
=
4
13
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
V
=
4
22
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
14
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
W
=
5
23
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
6
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
15
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
X
=
6
24
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
7
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
P
=
7
16
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
25
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
8
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
Q
=
8
17
1
Q
17
8
8
-
-
-
-
-
-
-
-
8
-
Z
=
8
26
1
Z
26
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
126
-
-
-
-
-
-
-
3
6
9
12
15
18
21
24
18
-
-
1+2+6
-
9
ABCDEFGHI
45
45
45
-
-
-
-
1+2
1+5
1+8
2+1
2+4
1+8
-
-
9
-
9
JKLMNOPQR
126
45
45
-
3
6
9
3
6
9
3
6
9
-
-
-
-
8
STUVWXYZ
180
45
36
-
-
-
-
-
-
-
-
-
-
-
-
9
-
26
ADD TO REDUCE
351
135
126
-
3
6
9
3
6
9
3
6
9
-
-
-
-
2+6
REDUCE TO DEDUCE
3+5+1
1+3+5
1+2+6
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
ESSENCE OF NUMBER
9
9
9
-
3
6
9
3
6
9
3
6
9

 

 

LETTERS TRANSPOSED INTO NUMBER

RE-ARRANGED IN NUMERICAL ORDER

 

S
=
1
-
8
STUVWXYZ
180
36
36
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
19
1
S
19
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
20
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
21
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
22
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
W
=
5
23
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
X
=
6
24
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
Y
=
7
25
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
Z
=
8
26
1
Z
26
8
8
-
-
-
-
-
-
-
-
8
-
36
-
8
STUVWXYZ
180
36
36
-
1
2
3
4
5
6
7
8
9
-
-
3+6
-
-
-
1+8+0
3+6
3+6
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
STUVWXYZ
9
9
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
STUVWXYZ
9
9
9
-
1
2
3
4
5
6
7
8
9

 

STUVWXYZ 180 ZYXWVUTS

STUVWXYZ 36 ZYXWVUTS

STUVWXYZ 9 ZYXWVUTS

 

 

JUST SIX NUMBERS

Martin Rees

1
999

OUR COSMIC HABITAT

PLANETS STARS AND LIFE

Page 24

A

proton

is

1,836 times heavier than an electron, and the number 1,836

would have the same connotations to any 'intelligence'

Page 24 / 25
"A manifestly artificial signal- even if it were as boring as lists of prime numbers, or the digits of 'pi' - would imply that 'intelli- gence' wasn't unique to the Earth and had evolved elsewhere. The nearest potential sites are so far away that signals would take many years in transit. For this reason alone, transmission would be primarily one-way. There would be time to send a measured response, but no scope for quick repartee!
Any remote beings who could communicate with us would have some concepts of mathematics and logic that paralleled our own. And they would also share a knowledge of the basic particles and forces that govern our universe. Their habitat may be very different (and the biosphere even more different) from ours here on Earth; but they, and their planet, would be made of atoms just like those on Earth. For them, as for us, the most important particles would be protons and electrons: one electron orbiting a proton makes a hydrogen atom, and electric currents and radio transmitters involve streams of electrons. A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' "able and motivated to transmit radio signals. All the basic forces and natural laws would be the same. Indeed, this uniformity - without which our universe would be a far more baffling place - seems to extend to the remotest galaxies that astronomers can study. (Later chapters in this book will, however, speculate about other 'universes', forever beyond range of our telescopes, where different laws may prevail.)
Clearly, alien beings wouldn't use metres, kilograms or seconds. But we could exchange information about the ratios of two masses (such as thc ratio of proton and electron masses) or of two lengths, which are 'pure numbers' that don't depend on what units are used: the statement that one rod is ten times as long as another is true (or false) whether we measure lengths / in feet or metres or some alien units

 

A

proton

is

1,836 times heavier than an electron, and the number 1,836

would have the same connotations to any 'intelligence'

 

E
=
5
-
8
EIGHTEEN
73
46
1
T
=
2
-
9
THIRTYSIX
152
53
8
-
-
7
4
17
First Total
225
99
9
-
-
-
-
1+7
Add to Reduce
2+2+5
9+9
-
Q
-
7
-
8
Second Total
9
18
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
Q
-
7
-
8
Essence of Number
9
9
9

 

 

3
SUN
54
9
9
5
EARTH
52
25
7
4
MOON
57
21
3
12
First Total
163
55
19
1+2
Add to Reduce
1+6+3
5+5
6+2
3
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
3
Essence of Number
1
1
1

 

 

1
I
9
9
9
3
SAY
45
9
9
7
DECODER
54
36
9
6
DECODE
36
27
9
4
CODE
27
18
9
-
-
-
-
-
-
-
-
-
-
5
CODED
31
22
4
5
CODES
46
19
1

 

 

-
CODE
--
-
-
2
C+O
18
9
9
2
D+E
9
9
9
-
DECODE
--
-
-
2
D+E
9
9
9
2
C+O
18
9
9
2
D+E
9
9
9
-
DECODER
--
-
-
2
D+E
9
9
9
2
C+O
18
9
9
2
D+E
9
9
9
1
R
18
9
9

 

CODE DE CODE

C+O D+E D+E C+O D+E

9+9+9+9+9

C+O D+E D+E C+O D+E

CODE DE CODE

 

10
CODE DE CODE
67
13
4
6
C+O
18
9
9
4
D+E
9
9
9
4
D+E
9
9
9
6
C+O
18
9
9
4
D+E
9
9
9
10
CODE DE CODE
63
36
36
1+0
-
6+3
3+6
3+6
1
CODE DE CODE
9
9
9

 

 

8
QUO VADIS
108
36
9
6
VOX POP
108
36
9
11
SORROW
108
36
9
8
INSTINCT
108
36
9
11
DESCENDANTS
108
36
9
8
STARTING
108
36
9
9
NARRATIVE
108
36
9
9
SEQUENCES
108
36
9
9
TANTALIZE
108
36
9
9
COMPLETES
108
36
9
9
AMBIGUOUS
108
36
9
7
JOURNEY
108
36
9

 

 

 

THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY

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

AS THOUGH WRITING A BOOK BUT LANGUAGE ENTIRELY TRANSFORMED

THE MESSAGE OF CREATION IS CLEAR EACH LETTER OF

THE

ALPHABET

IS

GIVEN

A

NUMERICAL

VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS

REARRANGING THEM IN ENDLESS CONFIGURATIONS

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

 

....

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

2
IS
28
10
1
9
UNIVERSAL
121
40
4
4
MIND
40
22
4
3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
33
First Total
378
162
27
3+3
Add to Reduce
3+7+8
1+6+2
2+7
6
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
6
Essence of Number
9
9
9

 

 

9
UNIVERSAL
121
40
4
4
MIND
40
22
4
2
IS
28
10
1
3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
33
First Total
378
162
27
3+3
Add to Reduce
3+7+8
1+6+2
2+7
6
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
6
Essence of Number
9
9
9

 

 

E
=
5
-
2
EX
11
2
2
U
=
3
-
6
UMBRIS
82
28
1
E
=
5
-
2
ET
25
7
7
I
=
9
-
10
IMAGINIBUS
104
50
5
I
=
9
-
2
IN
23
14
5
V
=
4
-
9
VERITATEM
113
41
5
-
-
35
-
31
First Total
358
142
25
-
-
3+5
-
3+1
Add to Reduce
3+5+8
1+4+2
2+5
-
-
8
-
4
Second Total
16
7
7
-
-
-
-
-
Reduce to Deduce
1+6
-
-
-
-
8
-
4
Essence of Number
7
7
7

 

 

O
=
6
-
3
OUT
56
11
2
O
=
6
-
2
OF
21
12
3
S
=
1
-
7
SHADOWS
89
26
8
A
=
1
-
3
AND
82
28
1
P
=
7
-
9
PHANTASMS
111
30
3
I
=
9
-
4
INTO
58
22
4
T
=
2
-
5
TRUTH
87
24
6
-
-
32
-
33
Add to Reduce
441
135
27
-
-
3+2
-
3+3
Reduce to Deduce
4+4+1
1+3+5
2+7
-
-
5
-
6
Essence of Number
9
9
9

 

 

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

 

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN

SWIFT REPEAT SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

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

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

Searching out patterns is a pure delight.

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

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

 

 

FINGERPRINTS OF THE GODS

A QUEST FOR THE BEGINNING AND THE END

Graham Hancock 1995

Chapter 32

Speaking to the Unborn

Page 285

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

A message in the bottle of time"

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

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

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

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

"WRITTEN IN THE ETERNAL LANGUAGE OF MATHEMATICS"

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

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

 

 

MATHEMATICS AND THE IMAGINATION

Edward Kasner and James Newman

1940

Assorted Geometries-Plane and Fancy 

Page 124

"Analytical four-dimensional Eu-clidean geometry is the system formed by theorems de-rived from these definitions.
Note that nothing has been said in either of these defini-tions about space; neither the space of our sense percep-tions, nor the space of the physicist, nor that of the philos-opher. All that we have done is to define two systems of mathematics which are logical and self-consistent, which may be played like checkers, or charades, according to stated rules. Anyone who finds a resemblance between his game of checkers or charades and the physical reality of his experience is privileged to point morals and to make capital of his suggestion.
But having established that we are in the realm of pure conception, beyond the most elastic bounds of imagina-tion, who is satisfied? Even the mathematician would like / Page 125 / to nibble the forbidden fruit, to glimpse what it would be like if he could slip for a moment into a fourth dimension. It's hard to grub along like moles down here below, to hear someone tell of a fourth dimension, to make careful note of it, and then to plow along, giving it no further thought. To make matters worse, books on popular sci-ence have made everything so ridiculously simple-rela-tivity, quanta, and what not-that we are shamed by our inability to picture a fourth dimension as something more concrete than time.
Graphic representations of four-dimensional figures have been attempted: it cannot be said these efforts have been crowned with any great success. Fig. 31(diagram omitted) illustrates" the four-dimensional analogue of the three-dimensional cube, a hypercube or tesseract: Our difficulties in drawing this figure are in no way diminished by the fact that a three-dimensional figure can only be drawn in perspective on a two-dimensional surface-such as this page-, while the four-dimensional object on a two dimensional page is only a perspective of a "perspective."
Yet since a2 equals the area of a square, a3 the volume / Page 126 / of a cube, we feel certain that a4 describes something, whatever that something may be. Only by analogy can we reason that that "something" is the hypervolume (or content) of a tesseract. Reasoning further, we infer that the tesseract is bounded by 8 cubes (or cells), has 16 vertices, 24 faces and 32 edges. But visualization of the tesseract is another story.
Fortunately, without having to rely on distorted dia-grams, we may use other means, using familiar objects to help our limping imagination to depict a fourth dimen-sion.
The two triangles A and B in Fig. 32 are exactly alike. Fig 32 ( triangles diagram omitted).
Geometrically, it is said they are congruent, * meaning that by a suitable motion, one may be perfectly super-posed on the other. Evidently, that motion can be carried out in a plane, i.e., in two dimensions, simply by sliding triangle A on top of triangle B.** But what about the two triangles C and D in Fig. 33?
One is the mirror image of the other. There seems to be no reason why by sliding or turning in the plane, C / Page Page 127 / cannot be superimposed on D. Strangely enough, this cannot be done. C or D must be lifted out of the plane, from two dimensions into a third, to effect superposition. Lift C up, turn it over, put it back in the plane, and then it can be slid over D.
Now, if a third dimension is essential for the solution of certain two-dimensional problems, a fourth dimension would make possible the solution of otherwise unsolvable problems of three dimensions. To be sure, we are in the Fig.33.(triangles diagram omitted) realm of fancy, and it need hardly be pointed out that a fourth dimension is not at hand to make Houdinis of us all. Yet, in theoretical inquiries, a fourth dimension / Page  128 / is of signal importance, and part of the warp and woof of modern theoretical physics and mathematics. Ex-amples chosen from these subjects are quite difficult and would be out of place, but some simpler ones in the lower dimensions may prove amusing.
If we lived in a two-dimensional world, so graphically described by Abbott in his famous romance, Flatland, our house would be a plane figure, as in Fig. 34.(Figure omitted) Entering through the door at A, we would be safe from our friends and enemies once the door was closed, even though there were no roof over our head, and the walls and windows were merely lines. To climb over these lines would mean getting out of the plane into a third dimension, and of course, no one in the two-dimensional world would have
any better idea of how to do that than we know how to escape from a locked safe..deposit vault by means of a fourth dimension. A three-dimensional cat might peek at a two-dimensional king, but he would never be the wiser.
When winter comes to Flatland, its inhabitants wear gloves. Three-dimensional hands look like this: ( Page 129 diagrams omitted )

Page 130

Modern science has as yet devised no relief for the man who finds himself with two right gloves instead of a right and a left. In Flatland, the same problem would exist. But there, Gulliver, looking down at its inhabitants from the eminence of a third dimensionl would see at once that, just as in the case of the two triangles on page 127, all that is necessary to turn a right glove into a left
one is to lift it up and turn it over. Of course, no one in Flatland would or could lift a finger to do that, since it involves an extra dimension.
If then, we could be transported into a fourth dimen-sion, there is no end to the miracles we could perform-starting with the rehabilitation of all ill-assorted pairs of gloves. Lift the right glove from three-dimensional space into a fourth dimension, turn it around, bring it back and it becomes a left glove. No prison cell could hold the four-dimensional Gulliver-far more of a men-ace than a mere invisible man. Gulliver could take a knot and untie it without touching the ends or breaking it, merely by transporting it into a fourth dimension and slipping the solid cord through the extra loophole.
Or he might take two links of a chain apart without breaking them. All, this and much' more would seem absurdly simple to him, and he would regard our help lessness with the same amusement and pity as we look upon the miserable creatures of Flatland.
                                    
Our romance must end. If it has aided some readers in making a fourth dimension more real and has satisfied a common anthropomorphic thirst, it has served its pur-pose. For our own part, we confess that the fables have never made the facts any clearer.
An idea originally associated with ghosts and spirits / Page 131 / needs, if it is to serve science, to be as far removed as possible from fuzzy thinking. It must be clearly and courageously faced if its true essence is to be discovered. But it is even more stupid to reject and deride than to glorify and enshrine it. No concept that has come out of our heads or pens marked a greater forward step in our thinking, no idea of religion, philosophy, or science broke. more sharply with tradition and commonly accepted knowledge, than the idea of a fourth dimension.
Eddington has put it very well: 6
However successful the theory of a four-dimensional world may be, it is difficult to ignore a voice inside us which whispers: "At the back of your mind, you know that a fourth dimension is all nonsense." I fancy that voice must often have had a busy time in the past history of physics. What nonsense to say that this solid table on which I am writing is a collection of electrons moving with prodigious speed in empty spaces, which relatively to electronic dimensions are as wide as the spaces between the planets in the solar system! What nonsense to say that the thin air is trying to crush my body with a load of 14lbs. to the square inch! What nonsense that the star cluster which I see through the telescope, obviously there now, is a glimpse into a past age 50,000 years ago! Let us not be beguiled by this voice. It is discredited. . . .
We have found a strange footprint on the shores of the un- known. We have devised profound theories, one after another to account for its origin. At last, we have succeeded in recon-structing the creature that made the footprint. And lo! It is our own.

Page 127

( Fig 34.- This is no blueprint but an actual house in Flatland.diagram omitted) 

Notes page 126 *See the chapter on paradoxes for an exact definition.
**Actually, "sliding on top or' would be impossible in a physical two-dimensional world.

 

 

THE MAGIC MOUNTAIN

Thomas Mann

1875 1955

Page 10

"Number 34"

 

 

A RANDOM WALK IN SCIENCE

An Anthology compiled by RL Weber 1973

Flatland: a romance of many dimensions

"From Nature [An anonymous letter entitled 'Euclid, Newton, and Einstein,' published in Nature on February12, 1920, called attention to a little book by Edwin Abbott Abbott (1838-1926), best known for his scholarly Shakespearian Grammar, his life of Francis Bacon and a number of theological discussions.]
Some thirty or more years ago, a little jeu d'esprit was written by Dr Edwin Abbott, entitled 'Flatland.' At the time of its pulication it did not attract as much attention as it deserved. Dr Abbott pictures intelligent beings whose whole experience is confined to a plane, or other space of two dimensions, who have no faculties by which they can become conscious of anything outside that space and no means of moving off the surface on which they live. He then asks the reader, who has the consciousness of the third dimension, to imagine a sphere descending upon the plane of Flatland and passing through it. How will the inhabitants regard this phenomenon? They will not see the approaching sphere and will have no conception of its solidity. They will only be conscious of the circle in which it cuts their plane. This circle, at first a point, will gradually increase in diameter, driving the inhabitants of Flatland outwards from its circumference, and this will go on until half the sphere has passed through the plane, when the circle will gradually contract to a point and then vanish, leaving the Flatlanders in undisturbed possession of their country.
Their experience will be that of a circular obstacle gradually expanding or growing, and then contracting, and they will attribute to growth in time what the external observer in three dimensions assigns to motion in the third dimension, through three-dimensional space. Assume the past and future of the universe to be all depicted in four-dimensional space and visible to any being who has consci-ousness of the fourth dimension. If there is motion of our three- dimensional space relative to the fourth dimension, all the changes we experience and assign to the flow of time will be due simply to this movement, the whole of the future as well as the past always existing in the fourth dimension.

From Edwin A Abbott Flatland A Romance of Many Dimensions (New York: Barnes and Noble) 1963 

 

[In a vision the narrator, a native of Flatland, has been indoctrinated by Abbott, Flatland. Sphere to carry the Gospel of Three Dimensions to his blind benighted countrymen in Flatland.]
I. 'Pardon me, 0 Thou Whom I must no longer address as the Perfection of all Beauty; but let me beg thee to vouchsafe thy
servant a sight of thine interior.'
Sphere. 'My what?' Page 94

I. 'Thine interior: thy stomach, thy intestines.'
Sphere. 'Whence this ill-timed impertinent request? . . .'
 I. 'But my Lord has shewn me the intestines of all my countrymen in the Land of Two Dimensions by taking me with him into the Land of Three. What therefore more easy than now to take his servant on a second journey into the blessed region of the Fourth Dimension, where I shall look down with him once more upon this land of Three Dimensions, and see the inside of every three- dimensional house, the secrets of the solid earth, the treasures of the mines in Spaceland, and the intestines of every solid living creature, even of the noble and adorable Spheres'.
Sphere. 'But where is this land of Four Dimensions?'

I. 'I know not: but doubtless my Teacher knows'.
Sphere. 'Not I. There is no such land. The very idea of it is utterly inconceivable. . . . Men are divided in opinion as to the facts. And even granting the facts, they explain them in different ways. And in any case, however great may be the number of different explanations, no one has adopted or suggested the theory of a Fourth Dimension. Therefore, pray have done with this trifling, and let us return to business.' "

 

THE FLATLANDS

 

T
=
2
-
3
THE
33
15
6
F
=
6
-
9
FLATLANDS
89
35
8
-
-
8
-
12
Add to Reduce
122
50
14
-
-
-
-
1+2
Reduce to Deduce
1+2+2
5+0
1+4
-
-
8
-
3
Essence of Number
5
5
5

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1875 - 1955

Page 711

"These were the moments when the "Seven-Sleeper," not knowing what had happened, was slowly stirring himself in the grass, before he sat up, rubbed his eyes - yes, let us carry the figure to the end, in order to do justice to the movement of our hero's mind: he drew up his legs, stood up, looked about him. He saw himself released, freed from enchantment-not of his own motion; he was fain to confess, but by the operation of exterior powers, of whose activities his own liberation was a minor incident Indeed! Yet though his tiny destiny fainted to nothing in the face of the general, was there not some hint of a personal mercy and grace for him, a manifestation of divine goodness and justice? Would Life receive again her erring and " delicate " child-not by a cheap and easy slipping back to her arms, but sternly, solemnly, peni-entially - perhaps not even among the living, but only with three salvoes fired over the grave of him a sinner? Thus might he return. He sank on his knees, raising face and hands to a heaven that howsoever dark and sulphurous was no longer the gloomy grotto of his state of sin."

 

PLATO

THE REPUBLIC

Translated with an introduction by

Desmond Lee

1953

Page 316

PART SEVEN [BOOK SIX] .
§ 7. THE SIMILE OF THE CAVE

"This is a more graphic presentation of the truths presented in the analogy of the Line,' in particular, it tells us more about the two states of mind called in the Line analogy Belief and Illusion. We are shown the ascent of the mind from illusion to pure philosophy, and the difficulties which accompany its progress. And the philosopher, when he has achieved the supreme vision, is required to return to the cave and serve his fellowls, his very unwillingness to do so being his chief qualification.

As Cornford pointed out, the best llIay to understand the simile is to replace' the clumsier apparatus' of the cave by the cinema, though today television is an even better comparison. It is the moral and intellectual condition of the average man from llIhich Plato starts; and though clearlY the ordinary man knollls the difference between substance and ShadO1ll in the physical llIorld, the simile suggests that his moral and intellectual opinions often bear as little relation to the tntth as the average film or television programme does to real life.

1 The words used for 'belief' and 'illusion' do not (with the possible exception of a use of pistis in Book X; see p. 430) occur elsewhere in Plato in the sense in which they are used here. Pistis, 'belief', conveys overtones of assurance and trustworthiness: 'commonsense assurance' (Cross and WoozIey,p. 226). Eikasia, 'illusion', is a rare word whose few occurrences elsewhere in Greek literature give us little guidance. It can mean 'conjecture', 'guesswork', and some prefer so to translate it here.
But 'illusion' is perhaps more appropriate for a 'state of mind '.

Page 317

THE PHILOSOPHER RULER

'I want you to go on to picture the enlightenment or ignorance of our human condition somewhat as follows.

Imagine an underground chamber like a cave, with a long entrance open to the daylight and as wide as the cave. In this chamber are men who have been prisoners there since they were children, their legs and necks being so fastened that they can only look straight ahead of them and cannot turn their heads. Some way off, behind and higher up, a fire is burn-ing, and between the fire and the prisoners and above them runs a road, in front of which a curtain-wall has been built, like the screen at puppet shows between the operators and their audience, above which they show their puppets.'
'I see.'
'Imagine further that there are men carrying all sorts of gear along behind the curtain-wall, projecting above it and including figures of men and animals made of wood and, stone and all sorts of other materials, and that some of these  men, as you would expect, are talking and some not.'
An odd picture and an odd sort of prisoner.'
'They are drawn from life,'1 I replied.' For, tell me, do you think our prisoners could see anything of themselves or their fellows except the shadows thrown by the fire on the wall of the cave opposite them?'
'How could they see anything else if they were prevented from moving their heads all their lives?' 
'And would they see anything more of the objects carried along the road?'
'Of course not.'
'Then if they were able to talk to each other, would they not assume that the shadows they saw were the real things?' 'Inevitably.'
And if the wall of their prison opposite them reflected / Page 318 /  sound, don't you think that they would suppose, whenever one of the passers-by on the road spoke, that the voice be- longed to the shadow passing before them?'
'They would be bound to think so.'
' And so in every way they would believe that the shadows of the objects we mentioned were the whole truth.'1
'Yes, inevitably.'
'Then think what would naturally happen to them if they were released from their bonds and cured of their delusions. Suppose one of them were let loose, and suddenly compelled to stand up and turn his head and look and walk towards the fire; all these actions would be painful and he would be too dazzled to see properly the objects of which he used to see the shadows. What do you think he would say if he was told that what he used to see was so much empty nonsense and that he was now nearer reality and seeing more correctly, because he was turned towards objects that were more real, and if on top of that he were compelled to say what each of the passing objects was when it was pointed out to him? Don't you think he would be at a loss, and think that what he used to see was far truer2 than the objects now being pointed out to him?'
'Yes, far truer.'
I ' And if he were made to look directly at the light of the fire, it would hurt his eyes and he would turn back and retreat to the things which he could see properly, which he would think really clearer than the things being shown him.
'Yes.'
'And if,' I went on, 'he were forcibly dragged up the steep and rugged ascent and not let go till he had been dragged out into the sunlight, the process would be a painful one, to which he would much object, and when he emerged into the light his eyes would be so dazzled by the glare of it that he wouldn't be able to see a single one of the things he was now told were real.'3
Page 319

'Certainly not at first,' he agreed.
'Because, of course, he wo'uld need to grow accustomed to the light before he could see things in the upper world outside the cave. First he would find it easiest to look at shadows, next at the reflections of men and other objects in water, and later on at the objects themselves. After that he would find it easier to observe the heavenly bodies and the
sky itself at night, and to look at the light of the moon and b stars rather than at the sun and its light by day.'
'Of course.'
'The thing he would be able to do last would be to look directly at the sun itself, and gaze at it without using reflec- tions in water or any other medium, but as it is in itself.'
'That must come last.'
'Later on he would come to the conclusion that it is the sun that produces the changing seasons and years and con-trols everything in the visible world, and is in a sense, responsible for everything that he and his fellow-prisoners used to see.'
'That is the conclusion which he would obviously reach.' , And when he thought of his first home and what passed for wisdom there, and of his fellow-prisoners, don't you think he would congratulate himself on his good fortune and be sorry for them?'
'Very much so.'
'There was probably a certain amount of. honour and glory to be won among the prisoners, and prizes for keen- sightedness for those best able to remember the order of sequence among the passing shadows and so be best able to divine their future appearances. Will our released prisoner hanker after these prizes or envy this power or honour? Won't he be more likely to feel, as Homer says, that he would far rather be "a serf in the house of some landless man ",l or indeed anything else in the world, than hold the opinions and live the life that they do? '
'Yes,' he replied, 'he would prefer anything to a life like, theirs.'
'Then what do you think would happen,' I asked, 'if he / Page 320 / went back to sit in his old seat in the cave? Wouldn't his eyes be blinded by the darkness, because he had come in suddenly out of the sunlight?'
'Certainly.'
'And if he had to discriminate between the shadows, in competition with the other prisoners, while he was still blinded and before his eyes got used to the darkness - a process that would take some time - wouldn't he be likely to make a fool of himself? And they would say that his visit to the upper world had ruined his sight, and that the ascent was not worth even attempting. And if anyone tried to release them and lead them up, they would kill him if they could lay hands on him.'
'They certainly would.'
'Now, my dear Glaucon,' I went on, 'this simile must be connected throughout with what preceded it.l The realm revealed by sight corresponds to the prison, and the light of the fire in the prison to the power of the sun. And you won't go wrong if you connect the ascent into the upper world / Page 321 / and the sight of the objects there with the upward progress of the mind into the intelligible region. That at any rate is my interpretation, which is what you are anxious to hear; the truth of the matter is, after all, known only to god.1 But in my opinion, for what it is worth, the final thing to be perceived in the intelligible region, and perceived only with difficulty, is the form of the good; once seen, it is inferred to be responsible for whatever is right and valuable in anything, producing in the visible region light and the source of light, and being in the intelligible region itself controlling source of truth and intelligence. And anyone who is going to act rationally either in public or private life must have sight of it.'
'I agree,' he said, 'so far as I am able to understand you.' 'Then you will perhaps also agree with me that it won't be surprising if those who get so far are unwilling to involve themselves in human affairs, and if their minds long to remain in the realm above. That's what we should expect if our simile holds good again.'
'Yes, that's to be expected.'
'Nor will you think it strange that anyone who descends from contemplation of the divine to human life and its ills should blunder and make a fool of himself, if, while still blinded and unaccustomed to the surrounding darkness, he's forcibly put on trial in the law-courts or elsewhere about the shadows of justice or the figures2 of which they are shadows and made to dispute about the notions of them held by men, who have never seen justice itself.'
'There's nothing strange in that.' 'But anyone with any sense,' I said, 'will remember that the eyes may be unsighted in two ways, by a transition either from light to darkness or from darkness to light, and will recognize that the same thing applies to the mind. So when he sees a mind confused and unable to see clearly he will not laugh without thinking, but will ask himself whether it has come from a clearer world and is confused by the unaccus-tomed darkness, or whether it is dazzled by the stronger light of the clearer world to which it has escaped from its / Page 322 / previous ignorance, The first condition of life is a reason for congratulation, the second for sympathy, though if one wants to laugh at it one can do so with less absurdity than at the mind that has descended from the daylight of the upper world,'
'You put it very reasonably,'
'If this is true,' I continued, 'we must reject the concep-tion of education professed by those who say that they can put into the mind knowledge that was not there before - rather as if they could put sight into blind eyes..
'It is a claim that is certainly made,' he said,
'But our argument indicates that the capacity for know-ledge is innate in each man's mind, and that the organ by which he learns is like an eye which cannot be turned from darkness to light unless the whole body is turned; in the same way the mind as a whole must be turned away from the world of change until its eye can bear to look straight at reality, and at the brightest of all realities which is what we call the good. Isn't that so?'
'Yes,'
'Then this turning around of the mind itself might be made a subject of professional skill,' which would effect the conversion as easily and effectively as possible, It would not be concerned to implant sight, but to ensure that someone who had it already was not either turned in the wrong direction or looking the wrong way.'
'That may well be so,'
'The rest, therefore, of what are commonly called excel-lences2 of the mind perhaps resemble those of the body, in that they are not in fact innate, but are implanted by sub-sequent training and practice; but knowledge, it seems, must surely have a diviner quality, something which never loses its power, but whose effects are useful and salutary or again useless and harmful according to the direction in which it is turned, Have you never noticed how shrewd is the glance of the type of men commonly called bad but clever? They have small minds. but their sight is sharp and piercing enough in / Page 323 / matters that concern them; it's not that their sight is weak, but that they are forced to serve evil, so that the keener their sight the more effective that evil is,'
'That's true.'
'But suppose,' I said, 'that such natures were cut loose, when they were still children, from all the dead weights natural to this world of change and fastened on them by sensual indulgences like gluttony, which twist their minds' vision to lower things, and suppose that when so freed they were turned towards the truth, then this same part of these same individuals would have as keen a vision of truth as it has of the objects on which it is at present turned,'
'Very likely,'
'And is it not also likely, and indeed a necessary conse- quence of what we have said, that society will never be properly governed either by the uneducated, who have no knowledge of the truth, or by those who are allowed to t spend all their lives in purely intellectual pursuits? The un-educated have no single aim in life to which all their actions, public and private, are to be directed; the intellectuals will take no practical action of their own accord, fancying them-selves to be out of this world in some kind of 'eartWy paradise,'
'True.'
'Then our job as lawgivers is to compel the best minds to attain what we have called the highest form of knowledge, and to ascend to the vision of the good as we have described, and when they have achieved this and see well enough, a' prevent them behaving as they are now allowed to,'
'What do you mean by that?'
'Remaining in the upper world, and refusing to return again to the prisoners in the cave below and share their labours and rewards, whether trivial or serious.'
'But surely,' he protested, 'that will not be fair, We shall be compelling them to live a poorer life than they might live,'
'The object of our legislation,' I reminded him again, 'is, not the special welfare of any particular class in our society, / Page 324 / but of the society as a whole;I and it uses persuasion or compulsion to unite all citizens and make them share together the benefits which each individually can confer on the community; and its purpose in fostering this attitude is not to leave everyone to please himself, but to make each man a link in the unity of the whole.'
'You are right; I had forgotten,' he said.
'You see, then, Glaucon,' I went on, 'we shan't be unfair to our philosophers, but shall be quite fair in what we say when we compel them to have some care and responsibility for others. We shall tell them that philosophers born in other states can reasonably refuse to take part in the hard work of politics; for society produces them quite involun-tarily and unintentionally, and it is only just that anything that grows up on its own should feel it has nothing to repay for an upbringing which it owes to no one. "But," we shall say, "we have bred you both for your own sake and that of the whole community to act as leaders and king-bees in a hive; you are better and more fully educated than the rest and better qualified to combine the practice of philosophy and politics. You must therefore each descend in turn and live with your fellows in the cave and get used to seeing in the dark; once you get used to it you will see a thousand times better than they do and will distinguish the various shadows, and know what they are shadows of, because you have seen the truth about things admirable and just and good. And so our state and yours will be really awake, and not merely dreaming like most societies today, with their shadow battles and their struggles for political power, which they treat as some great prize. The truth is quite different: the state whose prospective rulers come to their duties with least enthusiasm is bound to have the best and most tranquil government, and the state whose rulers are eager to rule the worst." '2
'I quite agree.'

Page325 (number omitted)

'Then will our pupils, when they hear what we say, dissent and refuse to take their share of the hard work of government, even though spending the greater part of their time together in the pure air above?'
They cannot refuse, for we are making a just demand of  just men. But of course, unlike present rulers, they will approach the business of government as an unavoidable necessity.'
'Yes, of course,' I agreed. 'The truth is that if you want a well-governed state to be possible, you must find for your future rulers some way of life they like better than govern-ment; for only then will you have government by the truly rich, those, that is, whose riches consist not of gold, but of the true happiness of a good and rational life. If you get, in public affairs, men whose life is impoverished and desti-tute of personal satisfactions, but who hope to snatch some compensation for their own inadequacy from a political career, there can never be good government. They start fighting for power, and the consequent internal and domestic conflicts ruin both them and society.'
'True indeed.'
'Is there any life except that of true philosophy which looks down on positions of political power?'
'None whatever.'
'But what we need is that the only men to get power should be men who do not love it, otherwise we shall have rivals' quarrels.'
'That is certain.'
Who else, then, will you compel to undertake the responsibilities of Guardians of our state, if it is not to be those who know most about the principles of good govern- ment and who have other rewards and a better life than the politician's ?'
'There is no one else.'..."

Note 1 page 317

I. Lit: 'like us'. How 'like' has been a matter of controversy. Plato can hardly have meant that the ordinary man cannot distinguish between shadows and real things. But he does seem to be saying, with a touch of caricature (we must not take him too solemnly), that the ordinary man is often very uncritical in his beliefs, which are little more than a 'careless acceptance of appearances , (Crombie).

Notes page 318

1. Lit: 'regard nothing else as true but the shadows'. The Greek word alethes (true) carries an implication of genuinenes, and some
translators render it here as 'real'.
2. Or 'more real'. 3. Or 'true', 'genuine'.

Note page 319 Odyssey, XI, 489.

Note Page 320

1. I.e. the similes of the Sun and the Line (though pp. 267-76 must surely also be referred to). The detailed relations between the three similes have been much disputed, as has the meaning of the word here translated 'connected'. Some interpret it to mean a detailed corre-spondence ('every feature. . . is meant to fit' - Cornford), others to mean, more loosely, 'attached' or 'linked to'. That Plato intended some degree of 'connection' between the three similes cannot be in doubt in view of the sentences which follow. But we should remember that they are similes, not scientific descriptions, and it would be a mistake to try to find too much detailed precision. Plato has just spoken of the prisoners 'getting their hands' on their returned fellow and killing him. How could they do that if fettered as described at the opening Of the simile (p. 317)? But Socrates was executed, so of course they must.
This translation assumes the following main correspondences:
Tied prisoner in the cave' illusion
Freed prisoner in the cave Belief
Looking at shadows and reflections in the world outside the cave and the ascent thereto Reason
Looking at real things in the world outside the cave Intelligence
Looking at the sun Vision of the form of the good.

Note 1 page 321 1. a. footnote 4, p.133 

Note 1 page 322 1. Techne., Arete,

Note 1 page 324 1. cr. 420b and 4660 above, pp. 18fand 252.
2. Socrates takes up here a point made to Thrasymachus at 347b, p.89.

 

 

R
=
9
-
5
RENEW
65
29
2
H
=
8
-
8
HARMONIC
81
45
9
C
=
3
-
13

INTERCONNECTEDNESS
206
98
8
-
-
29
-
31
First Total
352
172
19
-
-
2+9
-
3+1
Add to Reduce
3+5+2
1+7+2
1+0
-
-
11
-
4
Second Total
10
10
1
-
-
1+0
-
-
Reduce to Deduce
1+0
1+0
-
-
-
1
-
4
Essence of Number
1
1
1

 

 

-
RENEW
-
-
-
-
-
-
-
-
1
R
18
9
9
-
-
-
-
9
1
E
5
5
5
-
-
-
5
-
1
N
14
5
5
-
-
-
5
-
1
E
5
5
5
-
-
-
5
-
1
W
23
5
5
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
8
HARMONIC
81
45
9
-
-
-
-
9
-
INTERCONNECTEDNESS
-
-
-
-
-
-
-
-
1
I
9
9
9
-
-
-
-
9
1
N
14
5
5
-
-
-
5
-
1
T
20
2
2
-
2
-
-
-
1
E
5
5
5
-
-
-
5
-
1
R
18
9
9
-
-
-
-
9
1
C
3
3
3
-
3
-
-
-
1
O
15
4
4
-
-
4
-
-
1
N
14
5
5
-
-
-
5
-
1
N
14
5
5
-
-
-
5
-
1
E
5
5
5
-
-
-
5
-
1
C
3
3
3
-
3
-
-
-
1
T
20
2
2
-
2
-
-
-
1
E
5
5
5
-
-
-
5
-
1
D
4
4
4
-
-
4
-
-
1
N
14
5
5
-
-
-
5
-
1
E
5
5
5
-
-
-
5
-
1
S
19
10
1
-
2
-
-
-
1
S
19
10
1
-
2
-
-
-
31
FIRST TOTAL
352
172
118
-
4
4
65
45
3+1
ADD TO REDUCE
3+5+2
1+7+2
1+1+8
-
-
-
6+5
4+5
4
SECOND TOTAL
10
10
10
-
4
4
11
9
-
REDUCE TO DEDUCE
1+0
1+0
1+0
-
-
-
1+1
-
4
ESSENCE OF NUMBER
1
1
1
-
4
4
2
9

 

 

R
=
9
-
5
RENEW
65
29
2
H
=
8
-
8
HARMONIC
81
45
9
C
=
3
-
13

INTERCONNECTEDNESS
206
98
8
-
-
29
-
31
First Total
352
172
19
-
-
2+9
-
3+1
Add to Reduce
3+5+2
1+7+2
1+0
-
-
11
-
4
Second Total
10
10
1
-
-
1+0
-
-
Reduce to Deduce
1+0
1+0
-
-
-
1
-
4
Essence of Number
1
1
1

 

 

-
-
-
-
-
RENEW
-
-
-
-
1
2
3
4
5
6
7
8
9
R
=
9
1
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
W
=
5
5
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
-
29
-
5
RENEW
65
29
29
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HARMONIC
-
-
-
-
-
-
-
-
-
-
-
-
-
H
=
8
6
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
-
45
-
-
HARMONIC
81
45
45
-
-
-
-
-
-
-
-
-
-
-
-
-
-
INTERCONNECTEDNESS
-
-
-
-
-
-
-
-
-
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
19
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
O
=
6
20
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
21
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
22
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
23
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
C
=
3
24
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
T
=
2
25
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
26
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
27
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
N
=
5
28
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
29
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
30
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
31
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
80
-
-
INTERCONNECTEDNESS
206
98
80
-
3
4
9
8
65
12
7
8
45
-
-
154
-
-
-
-
-
-
-
-
-
-
-
6+5
1+2
-
-
4+5
-
-
1+5+4
-
5
RENEW
65
29
2
-
3
4
9
8
11
3
7
8
9
-
-
10
-
8
HARMONIC
81
45
9
-
-
-
-
-
1+1
-
-
-
-
-
-
1+0
-
18
INTERCONNECTEDNESS
140
98
5
-
-
-
-
-
-
-
-
-
-
-
-
10
-
31
First Total
352
172
19
-
3
4
9
8
2
3
7
8
9
-
-
1+0
-
3+1
Add to Reduce
3+5+2
1+7+4
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
4
Second Total
10
10
1
-
3
4
9
8
2
3
7
8
9
-
-
-
-
-
Add to Reduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
4
Essence of Number
10
10
1
-
3
4
9
8
2
3
7
8
9

 

RENEW HARMONIC INTERCONNECTEDNESS

 

-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
R
=
9
1
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
W
=
5
5
1
W
23
5
5
-
-
-
-
-
5
-
7
-
-
H
=
8
6
1
H
8
8
8
-
-
-
-
-
-
-
7
8
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
7
-
-
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
7
-
9
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
-
7
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
7
-
9
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
C
=
3
19
1
C
3
3
3
-
-
-
3
-
-
-
7
-
-
O
=
6
20
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
N
=
5
21
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
22
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
23
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
C
=
3
24
1
C
3
3
3
-
-
-
3
-
-
-
7
-
-
T
=
2
25
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
E
=
5
26
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
D
=
4
27
1
D
4
4
4
-
-
-
-
4
-
-
7
-
-
N
=
5
28
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
29
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
S
=
1
30
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
S
=
1
31
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
-
-
154
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5+4
-
5
RENEW
65
29
2
-
3
4
9
8
65
12
7
8
45
-
-
10
-
8
HARMONIC
81
45
9
-
-
-
-
-
6+5
1+2
-
-
4+5
-
-
1+0
-
18
INTERCONNECTEDNESS
140
98
5
-
3
4
9
8
11
3
7
8
9
-
-
10
-
31
First Total
352
172
19
-
-
-
-
-
1+1
-
-
-
-
-
-
1+0
-
3+1
Add to Reduce
3+5+2
1+7+4
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
4
Second Total
10
10
1
-
3
4
9
8
2
3
7
8
9
-
-
-
-
-
Add to Reduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
4
Essence of Number
10
10
1
-
3
4
9
8
2
3
7
8
9

 

RENEW HARMONIC INTERCONNECTEDNESS

 

-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
7
-
-
S
=
1
30
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
S
=
1
31
1
S
19
10
1
-
1
-
-
-
-
-
7
-
-
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
T
=
2
25
1
T
20
2
2
-
-
2
-
-
-
-
7
-
-
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
-
7
-
-
C
=
3
19
1
C
3
3
3
-
-
-
3
-
-
-
7
-
-
C
=
3
24
1
C
3
3
3
-
-
-
3
-
-
-
7
-
-
M
=
4
9
1
M
13
4
4
-
-
-
-
4
-
-
7
-
-
D
=
4
27
1
D
4
4
4
-
-
-
-
4
-
-
7
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
W
=
5
5
1
W
23
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
11
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
21
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
22
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
23
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
26
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
N
=
5
28
1
N
14
5
5
-
-
-
-
-
5
-
7
-
-
E
=
5
29
1
E
5
5
5
-
-
-
-
-
5
-
7
-
-
O
=
6
10
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
O
=
6
20
1
O
15
6
6
-
-
-
-
-
-
6
7
-
-
H
=
8
6
1
H
8
8
8
-
-
-
-
-
-
-
7
8
-
R
=
9
1
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
R
=
9
8
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
7
-
9
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
7
-
9
R
=
9
18
1
R
18
9
9
-
-
-
-
-
-
-
7
-
9
-
-
154
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5+4
-
5
RENEW
65
29
2
-
3
4
9
8
65
12
7
8
45
-
-
10
-
8
HARMONIC
81
45
9
-
-
-
-
-
6+5
1+2
-
-
4+5
-
-
1+0
-
18
INTERCONNECTEDNESS
140
98
5
-
3
4
9
8
11
3
7
8
9
-
-
10
-
31
First Total
352
172
19
-
-
-
-
-
1+1
-
-
-
-
-
-
1+0
-
3+1
Add to Reduce
3+5+2
1+7+4
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
4
Second Total
10
10
1
-
3
4
9
8
2
3
7
8
9
-
-
-
-
-
Add to Reduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
4
Essence of Number
10
10
1
-
3
4
9
8
2
3
7
8
9

 

LETTERS TRANSPOSED INTO NUMERICAL ORDER REARRANGED IN NUMERICAL ORDER

 

 

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
ZERO
-
-
-
-
-
-
-
-
-
-
-
-
-
Z
=
8
-
1
Z
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
-
-
28
-
4
ZERO
64
28
28
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ONE
-
-
-
-
-
-
-
-
-
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
16
-
3
ONE
34
16
16
7
-
-
-
-
-
-
-
-
-
-
-
-
-
TWO
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
W
=
5
-
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
-
-
13
-
3
TWO
58
13
13
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THREE
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
29
-
5
THREE
56
29
29
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
FOUR
-
-
-
-
-
-
-
-
-
-
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
24
-
4
FOUR
60
24
24
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
FIVE
-
-
-
-
-
-
-
-
-
-
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
24
-
4
FIVE
42
24
24
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SIX
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
-
-
16
-
3
SIX
52
25
16
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
SEVEN
-
-
-
-
-
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
20
-
5
SEVEN
65
29
20
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
EIGHT
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
31
-
5
EIGHT
49
31
31
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
NINE
-
-
-
-
-
-
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
24
-
4
NINE
42
24
24
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
45
-
40
First Total
522
243
225
-
2
6
3
8
70
42
7
24
63
-
-
4+5
-
4+0
Add to Reduce
5+2+2
2+4+3
2+2+5
-
-
-
-
-
7+0
4+2
-
2+4
6+3
-
-
9
-
4
Second Total
9
9
9
-
2
6
3
8
7
6
7
6
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
4
Essence of Number
9
9
9
-
2
6
3
8
7
6
7
6
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
=
8
-
1
Z
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
W
=
5
-
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
45
-
40
First Total
522
243
225
-
2
6
3
8
70
42
7
24
63
-
-
4+5
-
4+0
Add to Reduce
5+2+2
2+4+3
2+2+5
-
-
-
-
-
7+0
4+2
-
2+4
6+3
-
-
9
-
4
Second Total
9
9
9
-
2
6
3
8
7
6
7
6
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
4
Essence of Number
9
9
9
-
2
6
3
8
7
6
7
6
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
W
=
5
-
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
1
Z
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
45
-
40
First Total
522
243
225
-
2
6
3
8
70
42
7
24
63
-
-
4+5
-
4+0
Add to Reduce
5+2+2
2+4+3
2+2+5
-
-
-
-
-
7+0
4+2
-
2+4
6+3
-
-
9
-
4
Second Total
9
9
9
-
2
6
3
8
7
6
7
6
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
4
Essence of Number
9
9
9
-
2
6
3
8
7
6
7
6
9

 

 

1
occurs
x
2
=
2
=
2
2
occurs
x
3
=
6
=
6
3
occurs
x
1
=
3
=
3
4
occurs
x
2
=
8
=
8
5
occurs
x
14
=
70
7+0
7
6
occurs
x
7
=
42
4+2
6
7
occurs
x
1
=
7
=
7
8
occurs
x
3
=
24
2+4
6
9
occurs
x
7
=
63
6+3
9
45
-
-
40
-
225
-
54
4+5
-
-
4+0
-
2+2+5
-
5+4
9
-
-
4
-
9
-
9

 

 

Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
8
-
-
6
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
-
1
9
6
-
1
-
-
-
5
-
-
9
-
8
-
-
5
9
5
-
112
26
-
-
15
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
-
19
9
24
-
19
-
-
-
14
-
-
9
-
8
-
-
14
9
14
-
256
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
5
9
-
-
-
-
5
-
2
5
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
-
-
-
-
-
-
5
4
5
-
-
5
-
7
-
2
-
-
-
-
5
113
-
5
18
-
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
-
-
-
-
-
-
5
22
5
-
-
5
-
7
-
20
-
-
-
-
5
266
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
26
5
18
15
-
15
14
5
-
20
23
15
-
20
8
18
5
5
-
6
15
21
18
-
6
9
22
5
-
19
9
24
-
19
5
22
5
14
-
5
9
7
8
20
-
14
9
14
5
522
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
225
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
-
-
-
--
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
5
-
5
5
5
-
-
-
6
-
6
-
-
-
-
--
6
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
9
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
45
-
5
-
-
-
--
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
5
5
-
-
-
-
5
4+5
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
9
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
-
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
9

 

 

1
occurs
x
2
=
2
=
2
2
occurs
x
3
=
6
=
6
3
occurs
x
1
=
3
=
3
4
occurs
x
2
=
8
=
8
5
occurs
x
14
=
70
7+0
7
6
occurs
x
7
=
42
4+2
6
7
occurs
x
1
=
7
=
7
8
occurs
x
3
=
24
2+4
6
9
occurs
x
7
=
63
6+3
9
45
-
-
40
-
225
-
54
4+5
-
-
4+0
-
2+2+5
-
5+4
9
-
-
4
-
9
-
9

 

 

Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
8
-
-
6
6
5
-
-
-
6
-
8
-
-
-
-
6
-
-
-
9
-
-
1
9
6
1
-
-
-
5
-
9
-
8
-
5
9
5
-
112
26
-
-
15
15
14
-
-
-
15
-
8
-
-
-
-
15
-
-
-
9
-
-
19
9
24
19
-
-
-
14
-
9
-
8
-
14
9
14
-
256
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
-
5
9
-
-
-
5
2
5
-
2
-
9
5
5
6
-
3
9
6
-
4
5
-
-
-
-
5
4
5
-
5
-
7
-
2
-
-
-
5
113
-
5
18
-
-
-
5
20
23
-
20
-
18
5
5
6
-
21
18
6
-
22
5
-
-
-
-
5
22
5
-
5
-
7
-
20
-
-
-
5
266
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
26
5
18
15
15
14
5
20
23
15
20
8
18
5
5
6
15
21
18
6
9
22
5
19
9
24
19
5
22
5
14
5
9
7
8
20
14
9
14
5
522
8
5
9
6
6
5
5
2
5
6
2
8
9
5
5
6
6
3
9
6
9
4
5
1
9
6
1
5
4
5
5
5
9
7
8
2
5
9
5
5
225
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
5
-
-
--
5
5
-
5
-
-
-
-
5
5
-
-
-
-
-
-
-
5
-
-
-
-
5
-
5
5
5
-
-
-
-
5
-
5
5
5
-
-
-
6
6
-
-
-
--
6
-
-
-
-
-
6
6
-
-
6
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
9
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
9
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
45
-
5
-
-
--
5
5
-
5
-
-
-
-
5
5
-
-
-
-
-
-
-
5
-
-
-
-
5
-
5
5
5
-
-
5
5
-
-
-
5
4+5
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
9
8
5
9
6
6
5
5
2
5
6
2
8
9
5
5
6
6
3
9
6
9
4
5
1
9
6
1
5
4
5
5
5
9
7
8
2
5
9
5
5
-
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
-
-
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
2
3
4
5
6
7
8
9
0
-
Z
=
8
1
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
F
=
6
2
5
FIRST
72
27
9
-
-
-
-
-
-
-
-
-
9
2
-
S
=
1
3
6
SECOND
60
24
6
-
-
-
-
-
-
6
-
-
-
3
-
T
=
2
4
5
THIRD
59
32
5
-
-
-
-
-
5
-
-
-
-
4
-
F
=
6
5
6
FOURTH
88
34
7
-
-
-
-
-
-
-
7
-
-
5
-
F
=
6
6
5
FIFTH
49
31
4
-
-
-
-
4
-
-
-
-
-
6
-
S
=
1
7
5
SIXTH
80
26
8
-
-
-
-
-
-
-
-
8
-
7
-
S
=
1
8
7
SEVENTH
93
30
3
-
-
-
3
-
-
-
-
-
-
8
-
E
=
5
9
6
EIGHTH
57
39
3
-
-
-
3
-
-
-
-
-
-
9
-
N
=
5
10
5
NINTH
65
29
2
-
-
2
-
-
-
-
-
-
-
45
-
-
-
41
-
54
Add
687
300
48
-
1
2
6
4
5
6
7
8
9
4+5
-
-
-
4+1
-
5+4
Reduce
6+8+7
3+0+0
4+8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
5
-
9
Deduce
21
3
12
-
1
2
6
4
5
6
7
8
9
-
-
-
-
-
-
-
Reduce
2+1
-
1+2
-
-
-
-
-
-
-
-
-
-
9
-
-
-
5
-
9
Essence
3
3
3
-
1
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
0
-
Z
=
8
1
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
9
-
N
=
5
10
5
NINTH
65
29
2
-
-
2
-
-
-
-
-
-
-
7
-
S
=
1
8
7
SEVENTH
93
30
3
-
-
-
3
-
-
-
-
-
-
8
-
E
=
5
9
6
EIGHTH
57
39
3
-
-
-
3
-
-
-
-
-
-
5
-
F
=
6
6
5
FIFTH
49
31
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
4
5
THIRD
59
32
5
-
-
-
-
-
5
-
-
-
-
2
-
S
=
1
3
6
SECOND
60
24
6
-
-
-
-
-
-
6
-
-
-
4
-
F
=
6
5
6
FOURTH
88
34
7
-
-
-
-
-
-
-
7
-
-
6
-
S
=
1
7
5
SIXTH
80
26
8
-
-
-
-
-
-
-
-
8
-
1
-
F
=
6
2
5
FIRST
72
27
9
-
-
-
-
-
-
-
-
-
9
45
-
-
-
41
-
54
Add
687
300
48
-
1
2
6
4
5
6
7
8
9
4+5
-
-
-
4+1
-
5+4
Reduce
6+8+7
3+0+0
4+8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
5
-
9
Deduce
21
3
12
-
1
2
6
4
5
6
7
8
9
-
-
-
-
-
-
-
Reduce
2+1
-
1+2
-
-
-
-
-
-
-
-
-
-
9
-
-
-
5
-
9
Essence
3
3
3
-
1
2
6
4
5
6
7
8
9

 

NUMBERS RE-ARRANGED IN NUMERICAL ORDER

 

 

 

-
-
-
-
-
ENLIGHTENMENT
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
1
-
-
-
5
6
-
-
-
N
=
5
2
1
N
14
5
5
-
1
-
-
-
5
6
-
-
-
L
=
3
3
1
L
12
3
3
-
1
-
3
-
-
6
-
-
-
I
=
9
4
1
I
9
9
9
-
1
-
-
-
-
6
-
-
9
G
=
7
5
1
G
7
7
7
-
1
-
-
-
-
6
7
-
-
H
=
8
6
1
H
8
8
8
-
1
-
-
-
-
6
-
8
-
T
=
2
7
1
T
20
2
2
-
1
2
-
-
-
6
-
-
-
E
=
5
8
1
E
5
5
5
-
1
-
-
-
5
6
-
-
-
N
=
5
9
1
N
14
5
5
-
1
-
-
-
5
6
-
-
-
M
=
4
10
1
M
13
4
4
-
1
-
-
4
-
6
-
-
-
E
=
5
11
1
E
5
5
5
-
1
-
-
-
5
6
-
-
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
6
-
-
-
T
=
2
13
1
T
20
2
2
-
1
2
-
-
-
6
-
-
-
-
-
65
-
13
ENLIGHTENMENT
146
65
65
-
1
4
3
4
30
6
7
8
9
-
-
6+5
-
1+3
-
1+4+6
6+5
6+5
-
-
-
-
-
3+0
-
-
-
-
-
-
11
-
4
ENLIGHTENMENT
11
11
11
-
1
4
3
4
3
6
7
8
9
-
-
1+1
-
-
-
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
4
ENLIGHTENMENT
2
2
2
-
1
4
3
4
3
6
7
8
9

 

 

-
-
-
-
-
ENLIGHTENMENT
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
7
1
T
20
2
2
-
1
2
-
-
-
6
-
-
-
T
=
2
13
1
T
20
2
2
-
1
2
-
-
-
6
-
-
-
L
=
3
3
1
L
12
3
3
-
1
-
3
-
-
6
-
-
-
M
=
4
10
1
M
13
4
4
-
1
-
-
4
-
6
-
-
-
E
=
5
1
1
E
5
5
5
-
1
-
-
-
5
6
-
-
-
N
=
5
2
1
N
14
5
5
-
1
-
-
-
5
6
-
-
-
E
=
5
8
1
E
5
5
5
-
1
-
-
-
5
6
-
-
-
N
=
5
9
1
N
14
5
5
-
1
-
-
-
5
6
-
-
-
E
=
5
11
1
E
5
5
5
-
1
-
-
-
5
6
-
-
-
N
=
5
12
1
N
14
5
5
-
1
-
-
-
5
6
-
-
-
G
=
7
5
1
G
7
7
7
-
1
-
-
-
-
6
7
-
-
H
=
8
6
1
H
8
8
8
-
1
-
-
-
-
6
-
8
-
I
=
9
4
1
I
9
9
9
-
1
-
-
-
-
6
-
-
9
-
-
65
-
13
ENLIGHTENMENT
146
65
65
-
1
4
3
4
30
6
7
8
9
-
-
6+5
-
1+3
-
1+4+6
6+5
6+5
-
-
-
-
-
3+0
-
-
-
-
-
-
11
-
4
ENLIGHTENMENT
11
11
11
-
1
4
3
4
3
6
7
8
9
-
-
1+1
-
-
-
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
4
ENLIGHTENMENT
2
2
2
-
1
4
3
4
3
6
7
8
9

 

LETTERS TRANSCRIBED INTO NUMBERS

IONE1 TO 9NINE

REARRANGED NUMERICALLY.

 

-
-
-
-
-
ENLIGHTENMENT
-
-
-
-
2
3
4
5
7
8
9
T
=
2
7
1
T
20
2
2
-
2
-
-
-
-
-
-
T
=
2
13
1
T
20
2
2
-
2
-
-
-
-
-
-
L
=
3
3
1
L
12
3
3
-
-
3
-
-
-
-
-
M
=
4
10
1
M
13
4
4
-
-
-
4
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
-
5
-
-
-
N
=
5
2
1
N
14
5
5
-
-
-
-
5
-
-
-
E
=
5
8
1
E
5
5
5
-
-
-
-
5
-
-
-
N
=
5
9
1
N
14
5
5
-
-
-
-
5
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
5
-
-
-
N
=
5
12
1
N
14
5
5
-
-
-
-
5
-
-
-
G
=
7
5
1
G
7
7
7
-
-
-
-
-
7
-
-
H
=
8
6
1
H
8
8
8
-
-
-
-
-
-
8
-
I
=
9
4
1
I
9
9
9
-
-
-
-
-
-
-
9
-
-
65
-
13
ENLIGHTENMENT
146
65
65
-
4
3
4
30
7
8
9
-
-
6+5
-
1+3
-
1+4+6
6+5
6+5
-
-
-
-
3+0
-
-
-
-
-
11
-
4
ENLIGHTENMENT
11
11
11
-
4
3
4
3
7
8
9
-
-
1+1
-
-
-
1+1
1+1
1+1
-
-
-
-
-
-
-
-
-
-
2
-
4
ENLIGHTENMENT
2
2
2
-
4
3
4
3
7
8
9

 

ENLIGHTENS

 

-
-
-
-
-
ENLIGHTENS
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
-
-
-
4
5
6
-
-
-
N
=
5
2
1
N
14
5
5
-
-
-
-
4
5
6
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
4
-
6
-
-
-
I
=
9
4
1
I
9
9
9
-
-
-
-
4
-
6
-
-
9
G
=
7
5
1
G
7
7
7
-
-
-
-
4
-
6
7
-
-
H
=
8
6
1
H
8
8
8
-
-
-
-
4
-
6
-
8
-
T
=
2
7
1
T
20
2
2
-
-
2
-
4
-
6
-
-
-
E
=
5
8
1
E
5
5
5
-
-
-
-
4
5
6
-
-
-
N
=
5
9
1
N
14
5
5
-
-
-
-
4
5
6
-
-
-
S
=
1
10
1
S
19
10
2
-
1
-
-
4
-
6
-
-
-
-
-
50
-
10
ENLIGHTENS
113
59
50
-
1
2
3
4
20
6
7
8
9
-
-
5+0
-
1+0
-
1+1+3
5+9
5+0
-
-
-
-
-
2+0
-
-
-
-
-
-
5
-
1
ENLIGHTENS
5
14
5
-
1
2
3
4
2
6
7
8
9
-
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
1
ENLIGHTENS
5
5
2
-
1
2
3
4
2
6
7
8
9

 

LETTERS TRANSCRIBED INTO NUMBERS

IONE1 TO 9NINE

REARRANGED NUMERICALLY

 

-
-
-
-
-
ENLIGHTENS
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
7
1
S
19
10
2
-
1
-
-
4
-
6
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
4
-
6
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
4
-
6
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
-
4
5
6
-
-
-
N
=
5
2
1
N
14
5
5
-
-
-
-
4
5
6
-
-
-
E
=
5
8
1
E
5
5
5
-
-
-
-
4
5
6
-
-
-
N
=
5
9
1
N
14
5
5
-
-
-
-
4
5
6
-
-
-
G
=
7
5
1
G
7
7
7
-
-
-
-
4
-
6
7
-
-
H
=
8
6
1
H
8
8
8
-
-
-
-
4
-
6
-
8
-
I
=
9
4
1
I
9
9
9
-
-
-
-
4
-
6
-
-
9
-
-
50
-
10
ENLIGHTENS
113
59
50
-
1
2
3
4
20
6
7
8
9
-
-
5+0
-
1+0
-
1+1+3
5+9
5+0
-
-
-
-
-
2+0
-
-
-
-
-
-
5
-
1
ENLIGHTENS
5
14
5
-
1
2
3
4
2
6
7
8
9
-
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
1
ENLIGHTENS
5
5
2
-
1
2
3
4
2
6
7
8
9

 

 

-
-
-
-
-
ENLIGHTENS
-
-
-
-
1
2
3
5
7
8
9
S
=
1
7
1
S
19
10
2
-
1
-
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
-
5
-
-
-
N
=
5
2
1
N
14
5
5
-
-
-
-
5
-
-
-
E
=
5
8
1
E
5
5
5
-
-
-
-
5
-
-
-
N
=
5
9
1
N
14
5
5
-
-
-
-
5
-
-
-
G
=
7
5
1
G
7
7
7
-
-
-
-
-
7
-
-
H
=
8
6
1
H
8
8
8
-
-
-
-
-
-
8
-
I
=
9
4
1
I
9
9
9
-
-
-
-
-
-
-
9
-
-
50
-
10
ENLIGHTENS
113
59
50
-
1
2
3
20
7
8
9
-
-
5+0
-
1+0
-
1+1+3
5+9
5+0
-
-
-
-
2+0
-
-
-
-
-
5
-
1
ENLIGHTENS
5
14
5
-
1
2
3
2
7
8
9
-
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
5
-
1
ENLIGHTENS
5
5
2
-
1
2
3
2
7
8
9

 

ENLIGHTEN

 

-
-
-
-
-
ENLIGHTEN
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
1
E
5
5
5
-
1
-
-
4
5
6
-
-
-
N
=
5
2
1
N
14
5
5
-
1
-
-
4
5
6
-
-
-
L
=
3
3
1
L
12
3
3
-
1
-
3
4
-
6
-
-
-
I
=
9
4
1
I
9
9
9
-
1
-
-
4
-
6
-
-
9
G
=
7
5
1
G
7
7
7
-
1
-
-
4
-
6
7
-
-
H
=
8
6
1
H
8
8
8
-
1
-
-
4
-
6
-
8
-
T
=
2
7
1
T
20
2
2
-
1
2
-
4
-
6
-
-
-
E
=
5
8
1
E
5
5
5
-
1
-
-
4
5
6
-
-
-
N
=
5
9
1
N
14
5
5
-
1
-
-
4
5
6
-
-
-
-
-
50
-
9
ENLIGHTEN
94
49
50
-
1
2
3
4
20
6
7
8
9
-
-
5+0
-
-
-
9+4
4+9
5+0
-
-
-
-
-
2+0
-
-
-
-
-
-
5
-
9
ENLIGHTEN
13
13
5
-
1
2
3
4
2
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
ENLIGHTEN
4
4
2
-
1
2
3
4
2
6
7
8
9

 

LETTERS TRANSCRIBED INTO NUMBERS

IONE1 TO 9NINE

REARRANGED NUMERICALLY

 

-
-
-
-
-
ENLIGHTEN
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
7
1
T
20
2
2
-
1
2
-
4
-
6
-
-
-
L
=
3
3
1
L
12
3
3
-
1
-
3
4
-
6
-
-
-
E
=
5
1
1
E
5
5
5
-
1
-
-
4
5
6
-
-
-
N
=
5
2
1
N
14
5
5
-
1
-
-
4
5
6
-
-
-
E
=
5
8
1
E
5
5
5
-
1
-
-
4
5
6
-
-
-
N
=
5
9
1
N
14
5
5
-
1
-
-
4
5
6
-
-
-
G
=
7
5
1
G
7
7
7
-
1
-
-
4
-
6
7
-
-
H
=
8
6
1
H
8
8
8
-
1
-
-
4
-
6
-
8
-
I
=
9
4
1
I
9
9
9
-
1
-
-
4
-
6
-
-
9
-
-
50
-
9
ENLIGHTEN
94
49
50
-
1
2
3
4
20
6
7
8
9
-
-
5+0
-
-
-
9+4
4+9
5+0
-
-
-
-
-
2+0
-
-
-
-
-
-
5
-
9
ENLIGHTEN
13
13
5
-
1
2
3
4
2
6
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
9
ENLIGHTEN
4
4
2
-
1
2
3
4
2
6
7
8
9

 

 

-
-
-
-
-
ENLIGHTEN
-
-
-
-
2
3
5
7
8
9
T
=
2
7
1
T
20
2
2
-
2
-
-
-
-
-
L
=
3
3
1
L
12
3
3
-
-
3
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
2
1
N
14
5
5
-
-
-
5
-
-
-
E
=
5
8
1
E
5
5
5
-
-
-
5
-
-
-
N
=
5
9
1
N
14
5
5
-
-
-
5
-
-
-
G
=
7
5
1
G
7
7
7
-
-
-
-
7
-
-
H
=
8
6
1
H
8
8
8
-
-
-
-
-
8
-
I
=
9
4
1
I
9
9
9
-
-
-
-
-
-
9
-
-
50
-
9
ENLIGHTEN
94
49
50
-
2
3
20
7
8
9
-
-
5+0
-
-
-
9+4
4+9
5+0
-
-
-
2+0
-
-
-
-
-
5
-
9
ENLIGHTEN
13
13
5
-
2
3
2
7
8
9
-
-
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
5
-
9
ENLIGHTEN
4
4
2
-
2
3
2
7
8
9

 

 

-
-
-
-
-
EN- LIGHT-EN
-
-
-
E
=
5
-
1
E
5
5
5
N
=
5
-
1
N
14
5
5
L
=
3
-
5
LIGHT
56
29
2
E
=
5
-
1
E
5
5
5
N
=
5
-
1
N
14
5
5
-
-
23
-
9
EN- LIGHT-EN
94
49
22
-
-
2+3
-
-
-`
9+4
4+9
2+2
-
-
5
-
9
EN- LIGHT-EN
13
13
4
-
-
2+3
-
-
-`
1+3
1+3
-
-
-
5
-
9
EN- LIGHT-EN
4
4
4

 

 

WISE W IS E WISE

WISE W IS E WISE

5IS5 5 IS 5 5IS5

WISE W IS E WISE

WISE W IS E WISE

1234 5 6789

 

-
WISE
-
-
-
1
W
23
5
5
-
IS
-
-
-
1
E
5
5
5
2
WISE
28
10
10
-
-
2+8
2+0
1+0
2
WISE
10
1
1
-
-
1+0
-
-
2
WISE
1
1
1

 

 

4
WISE
-
-
-
-
W
23
5
5
-
IS
28
10
1
-
E
5
5
5
4
WISE
56
20
11
-
-
5+6
2+0
1+1
4
WISE
11
2
2
-
-
1+1
-
-
4
WISE
2
2
2

 

 

-
4
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
9
1
-
+
=
10
1+0
=
1
=
1
=
1
-
-
-
9
19
-
+
=
28
2+8
=
10
1+0
1
=
1
-
4
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
+
=
10
1+0
=
1
=
1
=
1
-``
-
23
-
-
5
+
=
28
2+8
=
10
1+0
1
=
1
-
4
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
-
23
9
19
5
+
=
56
5+6
=
11
1+1
2
=
2
-
-
5
9
1
5
+
=
20
2+0
=
2
=
2
=
2
-
4
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
20
4
W
I
S
E
-
-
15
-
-
6
-
20
-
20
2+0
-
-
9
-
-
-
-
1+5
-
-
-
-
2+0
-
1+1
2
4
W
I
S
E
-
-
6
-
-
6
-
2
-
2
-
-
5
9
1
5
-
-
-
-
-
-
-
-
-
-
2
4
W
I
S
E
-
-
6
-
-
6
-
2
-
2

 

 

4
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
-
9
1
-
+
=
10
1+0
=
1
=
1
=
1
-
-
9
19
-
+
=
28
2+8
=
10
1+0
1
=
1
4
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
+
=
10
1+0
=
1
=
1
=
1
-
23
-
-
5
+
=
28
2+8
=
10
1+0
1
=
1
4
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
23
9
19
5
+
=
56
5+6
=
11
1+1
2
=
2
-
5
9
1
5
+
=
20
2+0
=
2
=
2
=
2
4
W
I
S
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
4
W
I
S
E
-
-
15
-
-
6
-
20
-
20
-
-
9
-
-
-
-
1+5
-
-
-
-
2+0
-
1+1
4
W
I
S
E
-
-
6
-
-
6
-
2
-
2
-
5
9
1
5
-
-
-
-
-
-
-
-
-
-
4
W
I
S
E
-
-
6
-
-
6
-
2
-
2

 

 

4
WISE
-
-
-
-
W
23
5
5
-
IS
28
10
1
-
E
5
5
5
4
WISE
56
20
11
-
-
5+6
2+0
1+1
4
WISE
11
2
2
-
-
1+1
-
-
4
WISE
2
2
2

 

 

-
4
W
-
I
S
-
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
1
-
-
+
=
10
1+0
=
1
=
1
=
1
-
-
-
-
9
19
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
4
W
-
I
S
-
E
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
+
=
10
1+0
=
1
=
1
=
1
-``
-
23
-
-
-
-
5
+
=
28
2+8
=
10
1+0
1
=
1
-
4
W
-
I
S
-
E
-
-
-
-
-
-
-
-
-
-
-
-
23
-
9
19
-
5
+
=
56
5+6
=
11
1+1
2
=
2
-
-
5
-
9
1
-
5
+
=
20
2+0
=
2
=
2
=
2
-
4
W
-
I
S
-
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
20
4
W
-
I
S
-
E
-
-
15
-
-
6
-
20
-
20
2+0
-
-
-
9
-
-
-
-
-
1+5
-
-
-
-
2+0
-
1+1
2
4
W
-
I
S
-
E
-
-
6
-
-
6
-
2
-
2
-
-
5
-
9
1
-
5
-
-
-
-
-
-
-
-
-
-
2
4
W
-
I
S
-
E
-
-
6
-
-
6
-
2
-
2

 

 

4
W
-
I
S
-
E
-
-
-
-
-
-
-
-
-
-
-
-
-
9
1
-
-
+
=
10
1+0
=
1
=
1
=
1
-
-
-
9
19
-
-
+
=
28
2+8
=
10
1+0
1
=
1
4
W
-
I
S
-
E
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
+
=
10
1+0
=
1
=
1
=
1
-
23
-
-
-
-
5
+
=
28
2+8
=
10
1+0
1
=
1
4
W
-
I
S
-
E
-
-
-
-
-
-
-
-
-
-
-
23
-
9
19
-
5
+
=
56
5+6
=
11
1+1
2
=
2
-
5
-
9
1
-
5
+
=
20
2+0
=
2
=
2
=
2
4
W
-
I
S
-
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
5
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
4
W
-
I
S
-
E
-
-
15
-
-
6
-
20
-
20
-
-
-
9
-
-
-
-
-
1+5
-
-
-
-
2+0
-
1+1
4
W
-
I
S
-
E
-
-
6
-
-
6
-
2
-
2
-
5
-
9
1
-
5
-
-
-
-
-
-
-
-
-
-
4
W
-
I
S
-
E
-
-
6
-
-
6
-
2
-
2

 

 

4
WISE
-
-
-
-
W
23
5
5
-
IS
28
10
1
-
E
5
5
5
4
WISE
56
20
11
-
-
5+6
2+0
1+1
4
WISE
11
2
2
-
-
1+1
-
-
4
WISE
2
2
2

 

WISE W IS E WISE

WISE W IS E WISE5IS5 5 IS 5 5IS5

WISE W IS E WISE

WISE W IS E WISE

 

-
WISE
-
-
-
1
W
23
5
5
-
IS
-
-
-
1
E
5
5
5
2
WISE
28
10
10
-
-
2+8
2+0
1+0
2
WISE
10
1
1
-
-
1+0
-
-
2
WISE
1
1
1

 

1234 5 6789

 

-
WISDOM
-
-
-
1
W
23
5
5
-
IS
-
-
-
3
D+O+M
32
14
5
4
WISDOM
55
19
10
-
-
5+5
1+9
1+0
4
WISDOM
10
10
1
-
-
1+0
1+1
1+1
4
WISDOM
1
1
1

 

WISDOM W IS DOM WISDOM

WISDOM W IS DOM WISDOM

5IS5 5 IS 5 5IS5

WISDOM W IS DOM WISDOM

WISDOM W IS DOM WISDOM

 

6
WISDOM
-
-
-
-
W
23
5
5
-
IS
28
10
1
-
D+O+M
32
14
5
6
WISDOM
83
29
10
-
-
8+3
2+9
2+0
6
WISDOM
11
11
2
-
-
1+1
1+1
1+1
6
WISDOM
2
2
2

 

 

6
WISDOM
-
-
-
-
W
23
5
5
-
I
9
9
9
-
S+D+O+M
51
15
6
6
WISDOM
83
29
20
-
-
8+3
2+9
2+0
6
WISDOM
11
11
2
-
-
1+1
1+1
1+1
6
WISDOM
2
2
2

 

 

-
6
W
I
S
D
O
M
-
-
-
-
-
-
-
-
-
-
-
9
1
-
6
-
+
=
16
1+6
=
7
=
7
-
-
-
9
19
-
15
-
+
=
43
4+3
=
7
=
7
-
6
W
I
S
D
O
M
-
-
-
-
-
-
-
-
-
-
5
-
-
4
-
4
+
=
13
1+3
=
4
=
4
-``
-
23
-
-
4
-
13
+
=
40
4+0
=
4
=
4
-
6
W
I
S
D
O
M
-
-
-
-
-
-
-
-
-
-
23
9
19
4
15
13
+
=
83
8+3
=
11
1+1
2
-
-
5
9
1
4
6
4
+
=
29
2+9
=
11
1+1
2
-
6
W
I
S
D
O
M
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
4
-
4
-
-
4
occurs
x
2
=
8
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
20
6
W
I
S
D
O
M
-
-
25
-
-
6
-
29
2+0
-
-
9
-
-
-
-
-
-
2+5
-
-
-
-
2+9
2
6
W
I
S
D
O
M
-
-
7
-
-
6
-
11
-
-
5
9
1
4
6
4
-
-
-
-
-
-
-
1+1
2
6
W
I
S
D
O
M
-
-
7
-
-
6
-
2

 

 

6
W
I
S
D
O
M
-
-
-
-
-
-
-
-
-
-
9
1
-
6
-
+
=
16
1+6
=
7
=
7
-
-
9
19
-
15
-
+
=
43
4+3
=
7
=
7
6
W
I
S
D
O
M
-
-
-
-
-
-
-
-
-
5
-
-
4
-
4
+
=
13
1+3
=
4
=
4
-
23
-
-
4
-
13
+
=
40
4+0
=
4
=
4
6
W
I
S
D
O
M
-
-
-
-
-
-
-
-
-
23
9
19
4
15
13
+
=
83
8+3
=
11
1+1
2
-
5
9
1
4
6
4
+
=
29
2+9
=
11
1+1
2
6
W
I
S
D
O
M
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
4
-
4
-
-
4
occurs
x
2
=
8
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
-
-
9
-
-
-
-
-
-
9
occurs
x
1
=
9
6
W
I
S
D
O
M
-
-
25
-
-
6
-
29
-
-
9
-
-
-
-
-
-
2+5
-
-
-
-
2+9
6
W
I
S
D
O
M
-
-
7
-
-
6
-
11
-
5
9
1
4
6
4
-
-
-
-
-
-
-
1+1
6
W
I
S
D
O
M
-
-
7
-
-
6
-
2

 

 

1234 5 6789

WISDOM W IS DOM WISDOM

WISDOM W IS DOM WISDOM

5IS5 5 IS 5 5IS5

WISDOM W IS DOM WISDOM

WISDOM W IS DOM WISDOM

1234 5 6789

 

-
WISDOM
-
-
-
1
W
23
5
5
-
IS
-
-
-
3
D+O+M
32
14
5
4
WISDOM
55
19
10
-
-
5+5
1+9
1+0
4
WISDOM
10
10
1
-
-
1+0
1+1
1+1
4
WISDOM
1
1
1

 

 

1234 5 6789

WISE W IS E WISE

WISE W IS E WISE

5IS5 5 IS 5 5IS5

WISE W IS E WISE

WISE W IS E WISE

1234 5 6789

 

-
WISE
-
-
-
1
W
23
5
5
-
IS
-
-
-
1
E
5
5
5
2
WISE
28
10
10
-
-
2+8
2+0
1+0
2
WISE
10
1
1
-
-
1+0
-
-
2
WISE
1
1
1

 

 

PLUTARCH

MORALIA

Edited by G. P. Goold 1936

Page 194

"THE E AT DELPHI"

 

T
=
2
-
3
THE
33
15
6
E
=
5
-
1
E
5
5
5
A
=
1
-
2
AT
21
3
3
D
=
4
-
6
DELPHI
54
36
9
-
-
12
-
12
First Total
113
59
23
-
-
1+2
-
1+2
Add to Reduce
1+1+3
5+9
2+3
Q
-
3
-
3
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
=
-
-
3
-
3
Essence of Number
5
5
5

 

THE 5 AT DELPHI

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Page 32

5


To Sorcerers and Magicians number FIVEis 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

 

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

 

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

 

 

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

 

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

 

 

 

T
=
2
-
3
THE
33
15
6
E
=
5
-
1
E
5
5
5
A
=
1
-
2
AT
21
3
3
D
=
4
-
6
DELPHI
54
36
9
-
-
12
-
12
First Total
113
59
23
-
-
1+2
-
1+2
Add to Reduce
1+1+3
5+9
2+3
Q
-
3
-
3
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
=
-
-
3
-
3
Essence of Number
5
5
5

 

 

T
=
2
-
3
THE
33
15
6
E
=
5
-
1
E
5
5
5
A
=
1
-
2
AT
21
3
3
D
=
4
-
6
DELPHI
54
36
9
-
-
12
-
12
First Total
113
59
23
-
-
1+2
-
1+2
Add to Reduce
1+1+3
5+9
2+3
Q
-
3
-
3
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
=
-
-
3
-
3
Essence of Number
5
5
5

 

THE E AT DELPHI

THE 5 AT DELPHI

THE E AT DELPHI

 

T
=
2
-
3
THE
33
15
6
E
=
5
-
1
E
5
5
5
A
=
1
-
2
AT
21
3
3
D
=
4
-
6
DELPHI
54
36
9
-
-
12
-
12
First Total
113
59
23
-
-
1+2
-
1+2
Add to Reduce
1+1+3
5+9
2+3
Q
-
3
-
3
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
=
-
-
3
-
3
Essence of Number
5
5
5

 

 

PLUTARCH

MORALIA

VOLUME

LCL 306 V

With an English Traslation by Frank Cole Babbitt 1999

Page 194

INTRODUCTION

"PLUTARCH, in this essay on the E at Delphi, tells us that beside the well-known inscriptions at Delphi there was also a representation of the letter E, the fifth letter of the Greek alphabet. The Greek name for this letter was El, and this diphthong, in addition to being used in Plutarch's time as the name of E (which denotes the number five), is the Greek word for" if," and also the word for the second person singular of the verb" to be " (thou art).
In searching for an explanation of the unexplain­able it is only natural that the three meanings of El (" five," "if," "thou art") should be examined to see if any hypothesis based on anyone of them might possibly yield a rational explanatiqn; and these hypotheses constitute the skeleton about which is built the body of Plutarch's essay. From it we gain
some interesting delineations of character and an engaging portrayal of the way in which a philosopher acts, or reacts, when forced unwillingly to face the unknowable.
Plutarch puts forward seven possible explanations
of the letter: .
(1) It was dedicated by the Wise Men, as a protest against interlopers, to show that their number was actually five and not seven (El = E, five). ' / Page 195

(2) El is the second vowel, the Sun is the second planet, and Apollo is identified with the sun (El = R, the vowel).
(3) El means" if": people ask the oracle IF they shall succeed, or IF they shall do this or that (El = " if ").
(4) El is used in wishes or prayers to the god, often in the combination €tO€ or d yap (El =" if" or " if only").
(5) El, " if," is an indispensable word in logic for
the construction of a syllogism (El = " if ").
(6) Five is a most important number in mathematics, physiology, philosophy, and music (El = E, " five ").
(7) El means" thou art" and is the address of the consultant to Apollo, to indicate that the god has eternal being (El =" thou art "). a
Attempts to explain the letter have been also made in modern times by Gottling, Berichte der Sachs. Gesell. der Wiss. I. (1846-47) pp. 311 ff., and by Schultz in Philologus (1866), pp. 214 ff. Roscher, in Philologus (1900), pp. 21 ff.; (1901), pp. 81 ff.; (1902), pp. 513 ff. ; Hermes (1901), pp. 470 ff. (<;omment also by C. Robert in the same volume, p. 490), and the Philo­logische Wochenschrift (1922), col. 1211, maintains that El is an imperative from €lfLL, " go," addressed to the person who came to consult the oracle, and that it means" go on," " continue" into the temple. The value of this explanation is somewhat doubtful, since El in this word (€llu) is a true diphthong, and so is not generally spelled with simple E except in the Corinthian alphabet. Although a This explanation is accepted by Poulsen (Delphi, p. 149), but is open to very serious objections

 

 

T
=
2
-
3
THE
33
15
6
E
=
5
-
1
E
5
5
5
A
=
1
-
2
AT
21
3
3
D
=
4
-
6
DELPHI
54
36
9
-
-
12
-
12
First Total
113
59
23
-
-
1+2
-
1+2
Add to Reduce
1+1+3
5+9
2+3
Q
-
3
-
3
Second Total
5
14
5
-
-
-
-
-
Reduce to Deduce
-
1+4
=
-
-
3
-
3
Essence of Number
5
5
5

 

 

ISIS HORUS OSIRIS

THAT

CHRISTOS OF SPIRIT THAT SPIRIT OF CHRISTOS

 

 

EUS USE USE EUS

ODYSSEUS

PERSEUS

ZEUS

THESEUS

ORPHEUS

PROMETHEUS

EUS USE USE EUS

5+3+1 3+5+1 3+5+1 5+3+1

 

 

-
ODYSSEUS
-
-
-
-
O+D+Y+S+S
82
19
1
-
E
5
5
5
-
U
21
3
3
-
S
19
1
1
8
ODYSSEUS
127
28
19
-
-
1+2+7
2+8
1+9
8
ODYSSEUS
10
10
10
-
-
1+0
1+0
1+0
8
ODYSSEUS
1
1
1

 

PERSEUS PURSUES

 

-
PERSEUS
-
-
-
-
P+E+R+S
58
22
4
-
E
5
5
5
-
U
21
3
3
-
S
19
1
1
7
PERSEUS
103
31
22
-
-
1+0+3
3+1
2+2
7
PERSEUS
13
4
4
-
-
1+3
-
-
7
PERSEUS
4
4
4

 

 

-
PERSEUS
-
-
-
2
PE
21
12
3
1
R
18
9
9
2
SE
24
6
6
1
U
21
3
3
1
S
19
1
1
7
PERSEUS
103
31
22
-
-
1+0+3
3+1
2+2
7
PERSEUS
13
4
4
-
-
1+3
-
-
7
PERSEUS
4
4
4

 

 

-
THESEUS
-
-
-
-
THES
52
16
7
-
E
5
5
5
-
U
21
3
3
-
S
19
1
1
7
THESEUS
97
25
16
-
-
9+7
2+5
1+6
7
THESEUS
16
7
7
-
-
1+6
-
-
7
THESEUS
7
7
7

 

 

-
ORPHEUS
-
-
-
-
ORPH
57
30
3
-
E
5
5
5
-
U
21
3
3
-
S
19
1
1
7
ORPHEUS
102
39
17
-
-
1+0+2
3+9
1+7
7
ORPHEUS
3
12
3
-
-
-
1+2
-
7
ORPHEUS
3
3
3

 

 

-
PROMETHEUS
-
-
-
-
PROMETH
95
41
5
-
E
5
5
5
-
U
21
3
3
-
S
19
1
1
10
PROMETHEUS
71
17
17
1+0
-
7+1
1+7
1+7
1
PROMETHEUS
8
8
8

 

 

-
HERCULES
-
-
-
-
HERCU
55
28
1
-
L
12
3
3
-
E
5
5
5
-
S
19
1
1
8
HERCULES
97
25
16
-
-
9+7
2+5
1+6
8
HERCULES
16
7
7
-
-
1+6
-
-
8
HERCULES
7
7
7

 

 

-
ACHILLES
-
-
-
-
ACHIL
33
24
6
-
L
12
3
3
-
E
5
5
5
-
S
19
1
1
8
ACHILLES
97
25
16
-
-
9+7
2+5
1+6
8
ACHILLES
16
7
7
-
-
1+6
-
-
8
ACHILLES
7
7
7

 

 

-
ZEUS
-
-
-
-
Z
26
8
8
-
EUS
45
9
9
5
ZEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ODYSSEUS
-
-
-
-
ODYSS
82
19
1
-
EUS
45
9
9
8
ODYSSEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
PERSEUS
-
-
-
-
PERS
58
22
4
-
EUS
45
9
9
7
PERSEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THESEUS
-
-
-
-
THES
52
16
7
-
EUS
45
9
9
7
THESEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ORPHEUS
-
-
-
-
ORPH
57
30
3
-
EUS
45
9
9
7
ORPHEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
PROMETHEUS
-
-
-
-
PROMETH
95
41
5
-
EUS
45
9
9
10
PROMETHEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HERCULES
-
-
-
-
HERCU
55
28
1
-
LES
36
9
9
8
HERCULES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ACHILLES
-
-
-
-
ACHIL
55
28
1
-
LES
36
9
9
8
ACHILLES
-
-
-

 

 

-
ZEUS
-
-
-
-
Z
-
-
-
-
EUS
45
9
9
5
ZEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ODYSSEUS
-
-
-
-
ODYSS
-
-
-
-
EUS
45
9
9
8
ODYSSEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
PERSEUS
-
-
-
-
PERS
-
-
-
-
EUS
45
9
9
7
PERSEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THESEUS
-
-
-
-
THES
-
-
-
-
EUS
45
9
9
7
THESEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ORPHEUS
-
-
-
-
ORPH
-
-
-
-
EUS
45
9
9
7
ORPHEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
PROMETHEUS
-
-
-
-
PROMETH
-
-
-
-
EUS
45
9
9
10
PROMETHEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
HERCULES
-
-
-
-
HERCU
-
-
-
-
LES
36
9
9
8
HERCULES
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ACHILLES
-
-
-
-
ACHIL
-
-
-
-
LES
36
9
9
8
ACHILLES
-
-
-

 

 

-
ZEUS
E
U
S
-
Z
-
-
-
-
EUS
5
3
1
5
ZEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ODYSSEUS
-
-
-
-
ODYSS
-
-
-
-
EUS
5
3
1
8
ODYSSEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
PERSEUS
-
-
-
-
PERS
-
-
-
-
EUS
5
3
1
7
PERSEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
THESEUS
-
-
-
-
THES
-
-
-
-
EUS
5
3
1
7
THESEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
ORPHEUS
-
-
-
-
ORPH
-
-
-
-
EUS
5
3
1
7
ORPHEUS
-
-
-
-
-
-
-
-
-
-
-
-
-
-
PROMETHEUS
-
-
-
-
PROMETH
-
-
-
-
EUS
5
3
1
10
PROMETHEUS
-
-
-

 


4
GODS
45
18
9
5
HUMAN
57
21
3
7
DESTINY
96
33
6
9
GREATNESS
108
36
9
25
Add to Reduce
306
108
27
2+5
Reduce to Deduce
2+6+1
9+0
2+7
7
Essence of Number
9
9
9

 

 

IN

THE

BEGINNING

WAS THE WORD AND THE WORD WAS

WITH

GOD AND THE WORD WAS GOD

THE

SAME WAS IN THE BEGINNING WITH

GOD ALL THINGS WERE MADE BY GOD AND WITHOUT GOD

WAS

NOT

ANYTHING

MADE THAT WAS MADE

IN

GOD

WAS LIFE AND THE LIFE WAS

THE

LIGHT

OF

HUMANKIND

AND

THE LIGHT SHINETH IN THE DARKNESS AND THE DARKNESS COMPREHENDED IT NOT

 

 

I

AM

ALPHA AND OMEGA

THE BEGINNING AND THE END THE FIRST AND THE LAST

I

AM

THE ROOT AND THE OFFSPRING

OF

DAVID

AND

THE BRIGHT AND MORNING STAR

AND

THE SPIRIT AND THE BRIDE SAY COME

AND

LET THEM THAT HEARETH SAY COME

AND

LET THEM THAT IS ATHIRST COME

AND

WHOSOEVER WILL LET THEM TAKE THE WATER OF LIFE FREELY

 

 
 
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