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Evokation
  
 
Index
  

 

A

MAZE

IN

ZAZAZA ENTER ZAZAZA

ZAZAZAZAZAZAZAAZAZAZAZAZAZAZ

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGIKALALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZZYXWVUTSRQPONMLKJIHGFEDCBA

 12345678910111213141516171819202122232425262625242322212019181716151413121110987654321

 

 

WORK DAYS OF GOD

Herbert W Morris D.D.circa 1883

Page 22

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

 

 

LIGHT AND LIFE

Lars Olof Bjorn 1976

Page 197

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

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

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

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

 

 

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

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

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

 

 

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

 

 

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 Upside Down of the Downside Up

 

 

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

 

 

 

O
=
6
-
3
OUT
56
11
2
O
=
6
-
2
OF
21
12
3
Z
=
8
-
4
ZERO
64
28
1
C
=
3
-
6
COMETH
64
28
1
O
=
6
-
3
ONE
34
16
7
Q
Q
29
Q
18
Q
239
95
14
-
-
2+9
-
1+8
-
2+3+9
9+5
1+4
-
-
11
-
9
-
14
14
5
-
-
1+1
-
-
-
1+4
1+4
-
-
-
2
-
9
-
5
5
5

 

 

-
18
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
8
-
-
6
-
-
6
-
-
-
8
-
6
5
-
+
=
51
5+1
=
6
=
6
=
6
-
-
15
-
-
-
15
-
-
26
-
-
15
-
-
15
-
-
-
8
-
15
14
-
+
=
123
1+2+3
=
6
=
6
=
6
-
18
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
3
2
-
-
6
-
-
5
9
-
-
3
-
4
5
2
-
-
-
-
5
+
=
44
4+4
=
8
=
8
=
8
-
-
-
21
20
-
-
6
-
-
5
18
-
-
3
-
13
5
20
-
-
-
-
5
+
=
116
1+1+6
=
8
=
8
=
8
-
18
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
15
21
20
-
15
6
-
26
5
18
15
-
3
15
13
5
20
8
-
15
14
5
+
=
239
2+3+9
=
14
1+4
5
=
5
-
-
6
3
2
-
6
6
-
8
5
9
6
-
3
6
4
5
2
8
-
6
5
5
+
=
95
9+5
=
14
1+4
5
=
5
-
18
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
-
6
6
-
-
-
-
6
-
-
6
-
-
-
-
-
6
-
-
-
-
6
occurs
x
6
=
36
3+6
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
8
18
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
37
-
-
18
-
95
-
41
-
1+8
6
-
-
-
6
6
-
-
-
-
6
-
-
6
-
-
-
-
-
6
-
-
-
-
3+7
-
-
1+8
-
9+5
-
4+1
8
9
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
4-
10
-
-
9
-9
14
-
5
-
-
6
3
2
-
6
6
-
8
5
9
6
-
3
6
4
5
2
8
-
6
5
5
-
-
1+0
-
-
-
-
1+4
-
-
8
9
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
1
-
-
9
-
5
-
5

 

 

18
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
-
8
-
-
6
-
-
6
-
-
-
8
-
6
5
-
+
=
51
5+1
=
6
=
6
=
6
-
15
-
-
-
15
-
-
26
-
-
15
-
-
15
-
-
-
8
-
15
14
-
+
=
123
1+2+3
=
6
=
6
=
6
18
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
3
2
-
-
6
-
-
5
9
-
-
3
-
4
5
2
-
-
-
-
5
+
=
44
4+4
=
8
=
8
=
8
-
-
21
20
-
-
6
-
-
5
18
-
-
3
-
13
5
20
-
-
-
-
5
+
=
116
1+1+6
=
8
=
8
=
8
18
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
15
21
20
-
15
6
-
26
5
18
15
-
3
15
13
5
20
8
-
15
14
5
+
=
239
2+3+9
=
14
1+4
5
=
5
-
6
3
2
-
6
6
-
8
5
9
6
-
3
6
4
5
2
8
-
6
5
5
+
=
95
9+5
=
14
1+4
5
=
5
18
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
6
-
-
-
6
6
-
-
-
-
6
-
-
6
-
-
-
-
-
6
-
-
-
-
6
occurs
x
6
=
36
3+6
9
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
18
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
37
-
-
18
-
95
-
41
1+8
6
-
-
-
6
6
-
-
-
-
6
-
-
6
-
-
-
-
-
6
-
-
-
-
3+7
-
-
1+8
-
9+5
-
4+1
9
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
4-
10
-
-
9
-9
14
-
5
-
6
3
2
-
6
6
-
8
5
9
6
-
3
6
4
5
2
8
-
6
5
5
-
-
1+0
-
-
-
-
1+4
-
-
9
O
U
T
-
O
F
-
Z
E
R
O
-
C
O
M
E
T
H
-
O
N
E
-
-
1
-
-
9
-
5
-
5

 

 

-
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
6
-
6
5
-
-
9
1
+
=
35
1+5
=
8
=
8
=
8
-
-
26
-
-
15
-
15
14
-
-
9
19
+
=
98
9+8
=
17
1+7
8
=
8
-
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
-
5
-
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
5
18
-
-
-
-
5
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
-
-
-
-
-
-
-
26
5
18
15
-
15
14
5
-
9
19
+
=
126
1+2+6
=
9
=
9
=
9
-
-
8
5
9
6
-
6
5
5
-
9
1
+
=
54
5+4
=
9
=
9
=
9
-
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
-
-
-
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
6
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
16
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
29
-
-
9
-
54
-
27
1+6
-
-
-
9
-
-
-
-
-
-
9
-
-
-
2+9
-
-
-
-
5+4
-
2+7
7
9
Z
E
R
O
-
O
N
E
-
I
S
-
4-
11
-
-
9
-9
9
-
9
-
-
8
5
9
6
-
6
5
5
-
9
1
-
-
1+1
-
-
-
-
-
-
-
7
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
2
-
-
9
-
9
-
9

 

 

9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
-
-
-
-
-
-
8
-
-
6
-
6
5
-
-
9
1
+
=
35
1+5
=
8
=
8
=
8
-
26
-
-
15
-
15
14
-
-
9
19
+
=
98
9+8
=
17
1+7
8
=
8
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
-
5
-
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
5
18
-
-
-
-
5
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
-
-
-
-
-
-
26
5
18
15
-
15
14
5
-
9
19
+
=
126
1+2+6
=
9
=
9
=
9
-
8
5
9
6
-
6
5
5
-
9
1
+
=
54
5+4
=
9
=
9
=
9
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
5
-
-
-
-
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
29
-
-
9
-
54
-
27
-
-
-
9
-
-
-
-
-
-
9
-
-
-
2+9
-
-
-
-
5+4
-
2+7
9
Z
E
R
O
-
O
N
E
-
I
S
-
4-
11
-
-
9
-9
9
-
9
-
8
5
9
6
-
6
5
5
-
9
1
-
-
1+1
-
-
-
-
-
-
-
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
2
-
-
9
-
9
-
9

 

1 6 3 8 1836 8 3 6 1

 

9
Z
E
R
O
O
N
E
I
S
-
-
-
-
-
-
-
-
-
-
-
8
-
-
6
6
5
-
9
1
+
=
35
1+5
=
8
=
8
=
8
-
26
-
-
15
15
14
-
9
19
+
=
98
9+8
=
17
1+7
8
=
8
9
Z
E
R
O
O
N
E
I
S
-
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
5
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
5
18
-
-
-
5
-
-
+
=
28
2+8
=
10
1+0
1
=
1
9
Z
E
R
O
O
N
E
I
S
-
-
-
-
-
-
-
-
-
-
-
26
5
18
15
15
14
5
9
19
+
=
126
1+2+6
=
9
=
9
=
9
-
8
5
9
6
6
5
5
9
1
+
=
54
5+4
=
9
=
9
=
9
9
Z
E
R
O
O
N
E
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
5
-
-
-
5
5
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
6
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
9
Z
E
R
O
O
N
E
I
S
-
-
29
-
-
9
-
54
-
27
-
-
-
9
-
-
-
-
9
-
-
-
2+9
-
-
-
-
5+4
-
2+7
9
Z
E
R
O
O
N
E
I
S
-
4-
11
-
-
9
-9
9
-
9
-
8
5
9
6
6
5
5
9
1
-
-
1+1
-
-
-
-
-
-
-
9
Z
E
R
O
O
N
E
I
S
-
-
2
-
-
9
-
9
-
9

 

 

G
=
7
-
3
GOD
26
17
8
I
=
9
-
2
IS
28
10
1
Z
=
8
-
4
ZERO
64
28
1
O
=
6
-
3
ONE
34
16
7
I
=
9
-
2
IS
28
10
1
-
-
39
4
14
Add to Reduce
180
81
18
-
-
12
-
1+4
Reduce to Deduce
1+8+0
8+1
1+8
-
-
3
-
5
Essence of Number
9
9
9

 

 

-
ZERO IS ONE
-
-
-
-
ZERO
-
-
-
1
Z
26
8
8
1
E
5
5
5
1
R
18
9
9
1
O
15
6
6
4
ZERO
64
28
28
-
IS
-
-
-
1
I
9
9
9
1
S
19
10
1
2
IS
28
19
10
-
ONE
-
-
-
1
O
15
6
6
1
N
14
5
5
1
E
5
5
5
3
ONE
34
16
16
9
ZERO IS ONE
126
63
54
-
-
1+2+6
6+3
5+4
9
ZERO I S ONE
9
9
9

 

 

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

 

 

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

 

 

KEEPER OF GENESIS

A

QUEST

FOR THE HIDDEN LEGACY OF MANKIND

Robert Bauval Graham Hancock

1996

Return to the Beginning

Page 283

"I stand before the masters who witnessed the genesis, who were the authors of their own forms, who walked the dark, circuitous passages of their own becoming. . .

I stand before the masters who witnessed the transformation of the body of a man into the body in spirit, who were witnesses to resurrection when the corpse of Osiris entered the mountain and the soul of Osiris walked out shining. . . when he came forth from death, a shining thing, his face white with heat. . .

I stand before the masters who know the histories of the dead, who decide which tales to hear again, who judge the books of lives as either full or empty, who are themselves authors of truth. And they are Isis and Osiris, the divine intelligences. And when the story is written and the end is good and the soul of a man is perfected, with a shout they lift him into heaven. . .'

Ancient Egyptian Book of the Dead (Norrnandi Ellis translation)

 

 

IN SEARCH OF THE MIRACULOUS

Fragments of an Unknown Teaching

P. D. Oupensky 1878 - 1947 (Gurdjieff quote)

Page 217

'A man may be born, but in order to be born he must first die, and in order to die he must first awake.'
'When a man awakes he can die; when he dies he can be born'

 

 

I AM THE OPPOSITE OF THE OPPOSITE I AM THE OPPOSITE OF OPPOSITE IS THE AM I ALWAYS AM

 

 

ZEROREZ

 

 

1
N
14
5
5
6
NOUGHT
85
31
4
5
OUGHT
71
26
8

 

 

4
ZERO
64
28
1
5
OUGHT
71
26
8
9
Add to Reduce
135
54
9
-
Reduce to Deduce
1+3+5
5+4
-
9
Essence of Number
9
9
9

 

 

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

 

 

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

 

 

-
5
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
6
-
-
8
-
+
=
14
1+4
=
5
=
5
-
-
15
-
-
8
-
+
=
23
2+3
=
5
=
5
-
5
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
3
7
-
2
+
=
12
1+2
=
3
=
3
-
-
-
21
7
-
20
+
=
48
4+8
=
12
1+2
3
-
5
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
15
21
7
8
20
+
=
71
7+1
=
8
=
8
-
-
6
3
7
8
2
+
=
26
2+6
=
8
=
8
-
5
O
U
G
H
T
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
-
4
FOUR
1
-
-
-
5
-
-
-
-
-
-
-
-
5
FIVE
1
-
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
9
-
-
-
-
-
-
-
-
9
NINE
1
-
-
-
19
5
O
U
G
H
T
-
-
26
-
-
5
-
26
1+9
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+6
10
5
O
U
G
H
T
-
-
8
-
-
5
-
8
1+0
-
6
3
7
8
2
-
-
-
-
-
--
-
-
1
5
O
U
G
H
T
-
-
8
-
-
5
-
8

 

 

5
O
U
G
H
T
-
-
-
-
-
--
-
-
-
6
-
-
8
-
+
=
14
1+4
=
5
=
5
-
15
-
-
8
-
+
=
23
2+3
=
5
=
5
5
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
3
7
-
2
+
=
12
1+2
=
3
=
3
-
-
21
7
-
20
+
=
48
4+8
=
12
1+2
3
5
O
U
G
H
T
-
-
-
-
-
--
-
-
-
15
21
7
8
20
+
=
71
7+1
=
8
=
8
-
6
3
7
8
2
+
=
26
2+6
=
8
=
8
5
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
5
O
U
G
H
T
-
-
26
-
-
5
-
26
-
-
-
-
-
-
-
-
2+6
-
-
-
-
2+6
5
O
U
G
H
T
-
-
8
-
-
5
-
8
-
6
3
7
8
2
-
-
-
-
-
--
-
-
5
O
U
G
H
T
-
-
8
-
-
5
-
8

 

 

-
9
Z
E
R
O
-
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
6
-
6
-
-
8
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
26
-
-
15
-
15
-
-
8
-
+
=
64
6+4
=
10
1+0
1
=
1
-
9
Z
E
R
O
-
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
-
5
9
-
-
-
3
7
-
2
+
=
26
2+6
=
8
=
8
=
8
-
-
-
5
18
-
-
-
21
7
-
20
+
=
71
7+1
=
8
=
8
=
8
-
9
Z
E
R
O
-
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
26
5
18
15
-
15
21
7
8
20
+
=
135
1+3+5
=
9
=
9
=
9
-
-
8
5
9
6
-
6
3
7
8
2
+
=
54
5+4
=
9
=
9
=
9
-
9
Z
E
R
O
-
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
6
-
6
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
5
9
Z
E
R
O
-
O
U
G
H
T
-
-
40
-
-
9
-
54
-
36
-
-
-
-
9
-
-
-
-
-
-
-
-
-
4+0
-
-
-
-
5+4
-
3+6
5
9
Z
E
R
O
-
O
U
G
H
T
-
-
4
-
-
9
-
9
-
9
-
-
8
5
9
6
-
6
3
7
8
2
-
-
-
-
-
-
-
-
-
-
5
9
Z
E
R
O
-
O
U
G
H
T
-
-
4
-
-
9
-
9
-
9

 

 

9
Z
E
R
O
-
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
8
-
-
6
-
6
-
-
8
-
+
=
28
2+8
=
10
1+0
1
=
1
-
26
-
-
15
-
15
-
-
8
-
+
=
64
6+4
=
10
1+0
1
=
1
9
Z
E
R
O
-
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
5
9
-
-
-
3
7
-
2
+
=
26
2+6
=
8
=
8
=
8
-
-
5
18
-
-
-
21
7
-
20
+
=
71
7+1
=
8
=
8
=
8
9
Z
E
R
O
-
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
26
5
18
15
-
15
21
7
8
20
+
=
135
1+3+5
=
9
=
9
=
9
-
8
5
9
6
-
6
3
7
8
2
+
=
54
5+4
=
9
=
9
=
9
9
Z
E
R
O
-
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
6
-
6
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
8
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
9
Z
E
R
O
-
O
U
G
H
T
-
-
40
-
-
9
-
54
-
36
-
-
-
9
-
-
-
-
-
-
-
-
-
4+0
-
-
-
-
5+4
-
3+6
9
Z
E
R
O
-
O
U
G
H
T
-
-
4
-
-
9
-
9
-
9
-
8
5
9
6
-
6
3
7
8
2
-
-
-
-
-
-
-
-
-
-
9
Z
E
R
O
-
O
U
G
H
T
-
-
4
-
-
9
-
9
-
9

 

 

-
THOUGHT
-
-
-
2
TH
28
10
1
2
OU
36
9
9
3
GHT
35
17
8
7
THOUGHT
99
36
18
-
-
9+9
3+6
1+8
7
THOUGHT
18
9
9
-
-
1+8
-
-
7
THOUGHT
9
9
9

 

 

-
7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
-
8
6
-
-
8
-
+
=
22
2+2
=
4
=
4
=
4
-
-
-
8
15
-
-
8
-
+
=
31
3+1
=
4
=
4
=
4
-
7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
2
-
-
3
7
-
2
+
=
14
1+4
=
5
=
5
=
5
-
-
20
-
-
21
7
-
20
+
=
68
6+8
=
14
1+4
5
=
5
-
7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
20
8
15
21
7
8
20
+
=
99
9+9
=
18
1+8
9
=
9
-
-
2
8
6
3
7
8
2
+
=
36
3+6
=
9
=
9
=
9
-
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
19
7
T
H
O
U
G
H
T
-
-
26
-
-
7
-
36
-
27
1+9
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
3+6
-
2+7
10
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9
1+0
-
2
8
6
3
7
8
2
-
-
-
-
-
--
-
-
-
-
1
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9

 

 

7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
8
6
-
-
8
-
+
=
22
2+2
=
4
=
4
=
4
-
-
8
15
-
-
8
-
+
=
31
3+1
=
4
=
4
=
4
7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
2
-
-
3
7
-
2
+
=
14
1+4
=
5
=
5
=
5
-
20
-
-
21
7
-
20
+
=
68
6+8
=
14
1+4
5
=
5
7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
20
8
15
21
7
8
20
+
=
99
9+9
=
18
1+8
9
=
9
-
2
8
6
3
7
8
2
+
=
36
3+6
=
9
=
9
=
9
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
7
T
H
O
U
G
H
T
-
-
26
-
-
7
-
36
-
27
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
3+6
-
2+7
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9
-
2
8
6
3
7
8
2
-
-
-
-
-
--
-
-
-
-
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9

 

 

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

 

 

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

 

 

-
3
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
6
5
-
+
=
11
1+1
=
2
=
2
=
2
-
-
15
14
-
+
=
29
2+9
=
11
1+1
2
=
2
-
3
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
-
3
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
15
14
5
+
=
34
3+4
=
7
=
7
=
7
-
-
6
5
5
+
=
16
1+6
=
7
=
7
=
7
-
3
O
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
ONE
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
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
34
3
O
N
E
-
-
11
-
-
3
-
16
-
7
3+4
-
-
-
-
-
-
1+1
-
-
-
-
1+6
-
-
7
3
O
N
E
-
-
2
-
-
3
-
7
-
7

 

 

3
O
N
E
-
-
-
-
-
--
-
-
-
-
-
6
5
-
+
=
11
1+1
=
2
=
2
=
2
-
15
14
-
+
=
29
2+9
=
11
1+1
2
=
2
3
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
5
+
=
5
-
=
5
=
5
=
5
3
O
N
E
-
-
-
-
-
--
-
-
-
-
-
15
14
5
+
=
34
3+4
=
7
=
7
=
7
-
6
5
5
+
=
16
1+6
=
7
=
7
=
7
3
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
6
-
-
-
-
6
occurs
x
1
=
6
=
6
3
O
N
E
-
-
11
-
-
3
-
16
-
7
-
-
-
-
-
-
1+1
-
-
-
-
1+6
-
-
3
O
N
E
-
-
2
-
-
3
-
7
-
7

 

 

-
7
Z
E
R
O
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
6
-
6
5
-
+
=
25
2+5
=
7
=
7
=
7
-
-
26
-
-
15
-
15
14
-
+
=
70
7+0
=
7
=
7
=
7
-
7
Z
E
R
O
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
5
9
-
-
-
-
5
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
5
18
-
-
-
-
5
+
=
28
2+8
=
10
1+0
1
=
1
-
7
Z
E
R
O
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
26
5
18
15
-
15
14
5
+
=
98
9+8
=
17
1+7
8
=
8
-
-
8
5
9
6
-
6
5
5
+
=
44
4+4
=
8
=
8
=
8
-
7
Z
E
R
O
-
O
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
-
-
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
6
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
17
7
Z
E
R
O
-
O
N
E
-
-
28
-
-
7
-
44
-
26
1+7
-
-
-
9
-
-
-
-
-
-
-
2+8
-
-
-
-
4+4
-
2+6
8
7
Z
E
R
O
-
O
N
E
-
-
10
-
-
7
-
8
-
8
-
-
8
5
9
6
-
6
5
5
-
-
1+0
-
-
-
-
-
-
-
8
7
Z
E
R
O
-
O
N
E
-
-
1
-
-
7
-
8
-
8

 

 

7
Z
E
R
O
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
8
-
-
6
-
6
5
-
+
=
25
2+5
=
7
=
7
=
7
-
26
-
-
15
-
15
14
-
+
=
70
7+0
=
7
=
7
=
7
7
Z
E
R
O
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
5
9
-
-
-
-
5
+
=
19
1+9
=
10
1+0
1
=
1
-
-
5
18
-
-
-
-
5
+
=
28
2+8
=
10
1+0
1
=
1
7
Z
E
R
O
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
26
5
18
15
-
15
14
5
+
=
98
9+8
=
17
1+7
8
=
8
-
8
5
9
6
-
6
5
5
+
=
44
4+4
=
8
=
8
=
8
7
Z
E
R
O
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
7
Z
E
R
O
-
O
N
E
-
-
28
-
-
7
-
44
-
26
-
-
-
9
-
-
-
-
-
-
-
2+8
-
-
-
-
4+4
-
2+6
7
Z
E
R
O
-
O
N
E
-
-
10
-
-
7
-
8
-
8
-
8
5
9
6
-
6
5
5
-
-
1+0
-
-
-
-
-
-
-
7
Z
E
R
O
-
O
N
E
-
-
1
-
-
7
-
8
-
8

 

 

 

 

4
ZERO
64
28
1
3
ONE
34
16
7
-
-
-
-
-
-
-
-
-
-
3
TEN
39
12
3

 

 

-
10
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
6
-
-
5
-
-
6
5
-
+
=
30
3+0
=
3
=
3
=
3
-
-
26
-
-
15
-
-
14
-
-
15
14
-
+
=
84
8+4
=
12
1+2
3
=
3
-
10
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
5
9
-
-
1
-
4
-
-
-
5
+
=
24
2+4
=
6
=
6
=
6
-
-
-
5
18
-
-
1
-
4
-
-
-
5
+
=
33
3+3
=
6
=
6
=
6
-
10
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
26
5
18
15
-
1
14
4
-
15
14
5
+
=
117
1+1+7
=
9
=
9
=
9
-
-
8
5
9
6
-
1
5
4
-
6
5
5
+
=
54
5+4
=
9
=
9
=
9
-
10
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
-
5
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
12
10
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
33
-
-
10
-
54
-
27
1+2
1+0
-
-
9
-
-
-
-
-
-
-
-
-
-
-
3+3
-
-
1+0
-
5+4
-
2+7
3
1
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
6
-
-
7
-
8
-
8
-
-
8
5
9
6
-
1
5
4
-
6
5
5
-
-
-
-
-
-
-
-
-
-
3
1
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
6
-
-
7
-
8
-
8

 

 

0
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
8
-
-
6
-
-
5
-
-
6
5
-
+
=
30
3+0
=
3
=
3
=
3
-
26
-
-
15
-
-
14
-
-
15
14
-
+
=
84
8+4
=
12
1+2
3
=
3
10
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
-
5
9
-
-
1
-
4
-
-
-
5
+
=
24
2+4
=
6
=
6
=
6
-
-
5
18
-
-
1
-
4
-
-
-
5
+
=
33
3+3
=
6
=
6
=
6
10
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
-
-
-
--
-
-
-
-
-
26
5
18
15
-
1
14
4
-
15
14
5
+
=
117
1+1+7
=
9
=
9
=
9
-
8
5
9
6
-
1
5
4
-
6
5
5
+
=
54
5+4
=
9
=
9
=
9
10
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
-
-
5
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
33
-
-
10
-
54
-
27
1+0
-
-
9
-
-
-
-
-
-
-
-
-
-
-
3+3
-
-
1+0
-
5+4
-
2+7
1
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
6
-
-
7
-
8
-
8
-
8
5
9
6
-
1
5
4
-
6
5
5
-
-
-
-
-
-
-
-
-
-
1
Z
E
R
O
-
A
N
D
-
O
N
E
-
-
6
-
-
7
-
8
-
8

 

 

3
ONE
34
16
7
3
AND
19
10
1
4
ZERO
64
28
1
10
Add to Reduce
117
54
9
1+0
Reduce to Deduce
1+1+7
5+4
-
1
Essence of Number
9
9
9

 

 

-
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
6
-
6
5
-
-
9
1
+
=
35
3+5
=
8
=
8
=
8
-
-
26
-
-
15
-
15
14
-
-
9
19
+
=
98
9+8
=
17
1+7
8
=
8
-
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
--
-
-
-
-
-
-
-
5
9
-
-
-
-
5
-
-
-
+
=
18
1+9
=
10
1+0
1
=
1
-
-
-
5
18
-
-
-
-
5
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
--
-
-
-
-
-
-
26
5
18
15
-
15
14
5
-
9
19
+
=
126
1+2+6
=
9
=
9
=
9
-
-
8
5
9
6
-
6
5
5
-
9
1
+
=
54
5+4
=
9
=
9
=
9
-
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
-
-
-
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
6
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
16
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
29
-
-
9
-
54
-
27
1+6
-
-
-
9
-
-
-
-
-
-
9
-
-
-
2+9
-
-
-
-
5+4
-
2+7
7
9
Z
E
R
O
-
O
N
E
-
I
S
-
4-
11
-
-
9
-9
9
-
9
-
-
8
5
9
6
-
6
5
5
-
9
1
-
-
1+1
-
-
-
-
-
-
-
7
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
2
-
-
9
-
9
-
9

 

 

9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
--
-
-
-
-
-
8
-
-
6
-
6
5
-
-
9
1
+
=
35
3+5
=
8
=
8
=
8
-
26
-
-
15
-
15
14
-
-
9
19
+
=
98
9+8
=
17
1+7
8
=
8
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
--
-
-
-
-
-
-
5
9
-
-
-
-
5
-
-
-
+
=
18
1+9
=
10
1+0
1
=
1
-
-
5
18
-
-
-
-
5
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
--
-
-
-
-
-
26
5
18
15
-
15
14
5
-
9
19
+
=
126
1+2+6
=
9
=
9
=
9
-
8
5
9
6
-
6
5
5
-
9
1
+
=
54
5+4
=
9
=
9
=
9
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
-
5
-
-
-
-
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
9
-
-
-
9
occurs
x
2
=
18
1+8
9
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
29
-
-
9
-
54
-
27
-
-
-
9
-
-
-
-
-
-
9
-
-
-
2+9
-
-
-
-
5+4
-
2+7
9
Z
E
R
O
-
O
N
E
-
I
S
-
4-
11
-
-
9
-9
9
-
9
-
8
5
9
6
-
6
5
5
-
9
1
-
-
1+1
-
-
-
-
-
-
-
9
Z
E
R
O
-
O
N
E
-
I
S
-
-
2
-
-
9
-
9
-
9

 

 

G
=
7
-
3
GOD
26
17
8
I
=
9
-
2
IS
28
10
1
Z
=
8
-
4
ZERO
64
28
1
O
=
6
-
3
ONE
34
16
7
I
=
9
-
2
IS
28
10
1
-
-
39
4
14
Add to Reduce
180
81
18
-
-
12
-
1+4
Reduce to Deduce
1+8+0
8+1
1+8
-
-
3
-
5
Essence of Number
9
9
9

 

 

-
ZERO IS ONE
-
-
-
-
ZERO
-
-
-
1
Z
26
8
8
1
E
5
5
5
1
R
18
9
9
1
O
15
6
6
4
ZERO
64
28
28
-
IS
-
-
-
1
I
9
9
9
1
S
19
10
1
2
IS
28
19
10
-
ONE
-
-
-
1
O
15
6
6
1
N
14
5
5
1
E
5
5
5
3
ONE
34
16
16
9
ZERO IS ONE
126
63
54
-
-
1+2+6
6+3
5+4
9
ZERO I S ONE
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
-
-
-
-
-
-
-
-
-
-
8
-
-
6
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
-
1
9
6
-
1
-
-
-
5
-
-
9
-
8
-
-
5
9
5
-
+
=
112
1+1+2
=
4
-
4
-
4
26
-
-
15
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
-
19
9
24
-
19
-
-
-
14
-
-
9
-
8
-
-
14
9
14
-
+
=
256
2+5+6
=
13
1+3
4
-
4
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
1+1+3
=
5
-
5
-
5
-
5
18
-
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
-
-
-
-
-
-
5
22
5
-
-
5
-
7
-
20
-
-
-
-
5
+
=
266
2+6+6
=
14
1+4
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
-
-
-
-
-
-
-
-
-
-
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
5+2+2
=
9
-
9
-
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
+
=
225
2+2+5
=
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
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
+
=
2
occurs
x
3
=
6
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
4
occurs
x
2
=
8
-
8
-
5
-
-
-
-
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
5
-
5
5
+
=
5
occurs
x
14
=
70
7+0
7
-
-
-
6
  
6-
-
-
-
-
-
6
  
-
-
-
-
-
  
6
6
-
-
-
6
-
-
-
  
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
  
-
-
-
-
+
=
6
occurs
x
7
=
42
4+2
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
+
=
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
+
=
8
occurs
x
3
=
24
2+4
6
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
+
=
9
occurs
x
7
=
63
6+3
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
-
-
40
-
225
-
54
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
4+5
-
-
4+0
-
2+2+5
-
5+4
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
-
-
4
-
9
-
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
-
-
4
-
9
-
9

 

 

-
3
-
-
3
-
-
-
-
5
-
-
-
-
-
4
-
-
  
-
4
-
-
  
3
-
-
-
-
5
-
-
-
  
-
5
-
-
-
-
4
-
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
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
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
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
5
-
5
5
6-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
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
6
-
-
-
-
-
6
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
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
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
13
=
65
6+5
=
11
1+1
=
2
6
occurs
x
6
=
36
3+6
=
9
-
-
9
7
occurs
x
1
=
7
-
-
-
-
-
7
8
occurs
x
2
=
16
1+6
=
7
-
-
7
9
occurs
x
6
=
54
5+4
=
9
-
-
9
45
-
-
36
-
197
-
-
-
-
-
53
4+5
-
-
3+6
-
1+9+7
-
-
-
-
-
5+3
9
-
-
9
-
17
-
-
-
-
-
8
-
-
-
-
-
1+7
-
-
-
-
-
-
9
-
-
9
-
8
-
-
-
-
-
8

 

 

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

 

 

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

 

 

THE

BALANCING

ONE TWO THREE FOUR

FIVE

NINE EIGHT SEVEN SIX

 

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

 

 

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

 

 

4 FIVE 42 24 6

 

1 2 3 4 5 6 7 8 9

9 8 7 6 5 4 3 2 1

 

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

 

 

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

 

 

WATCHING THE TREE

Adeline Yen Mah

A Chinese daughter reflects on happiness spiritual beliefs and universal wisdom

Page 156

..." Turn your paper around and look at the word che from a different angle. Does it not look like a cart with a wheel on each side and an axle running down the middle?
'In future, when you look at any Chinese word, keep in mind the phrase Zi xing cang li (Chinese symbols omitted) (Hidden logic within the shape of words). Li means logic, reason, truth and principle. Dissect each word and search for the li represented by the characters.
'For example, how we Chinese regard the ant might be seen by looking at the word for "ant" (omitted) (yi). On the left is (omitted) which means "insect". On the right is (omitted) which means "justice, loyalty, relationship and unselfishness".'
Of all the animals, only we humaus are endowed with the ability to communicate through language. Described by philos­ophers as a 'mirror of man's mind', language reflects the essence of our perceptions and concepts. We use it to clarify our thoughts, fee!ings or ideas and express them to others.
Ideas define how we perceive reality. At first glance, having ideas may seem to be a natural function separate from the domain of language. Indeed, in some instances, it is. Although it is mainly through words that we express our ideas, it is by no means the only way.
Emotional and spiritual concepts are probably best conveyed by music, art, meditation or physical disciplines such as dance, qi gong, tai chi or yoga. A skilful artist is able to erase the boundary between observation, feeling and expression, thereby creating a conduit directly to the mind of the beholder.

Page 156

Ideas in mathematics, however, are better interpreted by a special numerical 'alphabet' that is able to represent an infinite variety of concepts with a small and simple assemblage of symbols. Galileo wrote,

Philosophy is written in that great book which ever lies before our eyes - I mean the universe. But we cannot understand it [the universe 1 if we do not first learn the languagc and grasp the symbols in which it is written. This book [of the universe] is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single word of it, without which one wanders in vain through a dark labyrinth

The way in which we think - and the degree of sophistication of the culture we create - is highly dependent on our vocabulary. The importance of mathematics in the development of science was recognised by the Chincse only relatively recently, and the Hindu-Arabic number system was not adopted or taught at schools in China until the twentieth century. Yet according to Lconardo da Vinci, 'a science is perfect to the degree that it is mathcmatical'. In the 1880s, when my grandfather was a boy, numbers were still being written in Chinese characters with a brush. Besides being cumbersome and time-consuming, the traditional Chinese method of recording numbers lacked two vital components: positional value and the symbol zero.

When my son Roger was seven years old, I gave him a record called Multiplication Rock, which he loved. Morning, noon and night he would play it over and ovcr, driving our whole / Page 157 / family crazy with the same tunes, same beat, same words. One of the songs was named 'My Hero Zero'. It went something like this:

My hero Zero,
When you stand to the right of the number one
The number becomes ten;
When you stand to the right of the number ten
The number beeomes one hundred;
When you stand to the right of the number one hundred The number becomes one thousand.

Roger loved the song so much that, for his eighth birthday, I wrote him a short story featuring his hero Zero (dressed in a bright red military uniform) coming to the rescue of all the other nine numbers which had moeked and belittled him for being of no value.
In a way, this story symbolises the reason why China fell behind the west in mathematics and science. The symbol zero,
invented in India in the ninth century and adopted as part of the Hindu-Arabic number system, is indeed very much a hero. However, zero's value was never truly recognized by my Chinese ancestors before the twentieth century.
For one thing, zero is different from any other number. Like the mysterious, ineffable tao in Lao Zi's Tao Te Ching, zero

. . . resembles an empty bowl

Which, while being used, can never be filled.

Bottomless, it seems to be the source of everything.

Blunting all sharpness, / Page 58 /

Unravelling all complications,

Harmonising all glare,

Uniting the world into common dust.

Hidden and invisible,

Yet it appears to exist.

I know not whose offspring it is;

It looks like the ancestor of all.

Before its invention, zero played a hidden role as a blank space on the abacus. Its incarnation as a symbol (and its establishment as a place-holder) is what gave zero its unique power aud status. I have been fascinated by zero ever sincc I studied it as a schoolgirl in Hong Kong. Trying to discover the logic hidden within its shape (zi xing cang li), [ became bewitched and enchanted. I was taught that adding a number to zero or subtracting zero from a number changcd nothing. In such cases, zero counted for naught. however, any number multiplied by zero became zero itself, whereas any number divided by zero became infinity. I remember being thrilled by zero's paradoxical powers, seemingly so insignificant. To me at the age of twelve, zero and infinity, like yin and yang, or nothing and eternity, appeared to represent the two opposite ends of the universe. Between them, they held all the secrets of a magical world.
My feelings towards zero have not changed over the years. Like the tao, zero will always remain enigmatic and beautiful.
Indian astronomical tables were first translated into Arabic in Baghdad and later into Latin. The great scholar and intellectual Pope Silvester II (who was pontiff for only four years. from AD 999 to 1003 was one of tbe earliest proponents of these numbers. but it was Leonardo Fibonacci of Pisa (1170-1230) who, in his book Liber Abace. first pointed out zero's / Page 160 / unique significance. He also noted that the ten Hindu-Arabic numbers (987654321 and zero) possess the ability to express an infinite variety of numbers.
Four centuries later. Leibniz. while reading the I Ching. recognised that instead of using ten numbers. any number can also be written by using only zero and 1. This is the binary (base 2) system of mathematics that is used in computers today. To Leibniz. one stood for God. zero stood for the void and binary mathematics symbolised the creation of the universe out of nothing (Creation ex nihila). In 1703 he published an article in the French Academy of Sciences discussing the relationship between binary mathematics and the I Ching. His correspondence with the Jesuit missionaries Bouvet. Foucquet and Gaubil showed an intense desire to learn from Chinese thought and philosophy.
The advantages of using Hindu-Arabic numerals were so manifest that they gradually replaced all other number systems. They have now been accepted internationally as the basic 'alphabet' in the language of mathematics, called by some the 'one and only truly universal language' . Though the same numbers and mathematical symbols are pronounced differently in different countries, their meanings remain the same throughout the world. This has greatly facilitated the advancement and exchange of scientific knowledge.
As mentioned before. the invention of zero simultaneously introduced the other key concept that produced such a revol­ution in mathematical thought. That concept is known as 'position'.
The great eighteenth-century mathematician Laplace said of position, 'The idea is so simple that this very simplicity is the reason for our not being sulliciently aware how much admiration it deserves.'
160

unique significance. He also noted that the ten Hindu-Arabic numbers (987654321 and zero) possess the ability to express an infinite variety of numbers.
Four centuries later, Leibniz, while reading the I Chiny, recognised that, instead of using ten numbers, any number can also be written by using only zero and 1. This is the binary (base 2) system of mathematics that is used in com­puters today. To Leibniz, one stood for God, zero stood for the void and binary mathematics symbolised the creation of the universe out of nothing (Creation ex nibilo). In 1703 he published an article in the French Academy of Sciences dis­cussing the relationship between binary mathematics and the I Chiny, His correspondence with the Jesuit missionaries Bouvet, Foucquet and Gaubil showed an intense desire to learn from Chinese thought and philosophy,
The advantages of using Hindu-Arabic numerals were so manifest that they gradually replaced all other number systems. They have now been accepted internationally as the basic 'alphabet' in the language of mathematics, called by some the 'one and only truly universal language'. Though the same numbers and mathematical symbols are pronounced differently in different countries, their meanings remain the same throughout the world. This has greatly facilitated the advancement and exchange of scientific knowledge.
As mentioned before. the invention of zero simultaneously introduced the other key concept that produced such a revol­ution in mathematical thought. That concept is known as 'position' .
The great eighteenth-century mathematician Laplace said of position, 'The idea is so simple that this very simplicity is the reason for our not being sufliciently aware how much admiration it deserves,'
160

These two inventions (positional value of a digit and the symbol for zero) are considered by many to be among the most important developments in mathematics in the last 3000 years. Zero allows every number to be put in its rightful place. The number 2 in front of three zeros (2000) has an entirely difTerent value from the same number 2 in front of six (2.000,000) or nine (2,000,000,000) zeros. Each given number could be considered to have two values: a fundamen­tal value indicated by the isolated numeral itself. and a place value dependent on the numeral's location within the sequence of digits used to express a particular number.
China invented the abacus (swm pal! ~~) or counting board in the sixth century BC and continued to use it for the next 2500 years. There is an implied understanding of both positional value and the concept of zero whenever a number is 'registered' on the abacus. For instance, the number lOO}
involves placing a single disc in the fourth box from the right, leaving the third and second boxes empty to signify zeros. and putting another single disc in the first box. However. when this same number was written down as Chinese charac­ters, it was transcribed as yi qial! yi - 'f - (onc thousand one).
But like old Roman numerals. the three words yi (lian yi possess neither place value nor the symbol for zero. This meant that Chinese mathematicians were unable to transpose numbers on to paper quickly and easily for accurate calcu­lation. Mathematical thought lacked an adequate alphabet for expression. progression or development. As a result, calcu­lus was never invented, the development of science was hin­dered and China fell behind the west in technology.*
. Note: According to Robert Temple in Tile Cm;us of CIIi/1lI (l9X6), the zero symhol orst appeared in print in China in 1247. However. the Chinese were secretive and seldom puhlished their work. It was also traditional not to reveal step-by-step calculations in solving mathematical problems.
J61

If one compares the writings of Marco Polo (1254-1324), describing the Yuan dynasty, with those of Matteo Ricci (1552-1610), who was in China during the Ming dynasty,
the differences are astonishing. Marco Polo's The Book of
Marco Polo is tilled with the might, power and marvels (print­ing, paper money, grand canals) of a rich and amazingly advanced country, while Matteo Ricc!' s China in the Sixteenth Century describes a nation ignorant of physics, geometry and astronomy; one whose people suffered from illiteracy and superstition and practised foot-binding and female infanticide. Far from being in awe of his host-country, Ricci was attracting potential converts (including some of the best and brightest scholar-mandarins) by dazzling them with Euro­pean clocks, prisms, telescopes, globes, maps, paintings and books on mathematics and astronomy. In a period of less than 300 years the west had caught up with and surpassed China in science and technology.
During the summer of 1951, when I was thirteen, my stepmother allowed me to come home for a few days to recuperate from pnellmonia (see page 9°). My brother James had just escaped from China to Hong Kong and was sharing a room with my grandfather. They placed a eot bebNeen their two beds and the three of us would talk deep into the night, with Jamcs and me bombarding Ye Ye with questions about his past. His life as a boy in the city of Nantao, Shanghai, during the Qing dynasty fascinated me.
'V/hat was it like, wearing a queue?' I asked one night.
'My older brothers used to tease me by tying my queue to
a bed post when I was sleeping. I always hated my hairstyle but the queue was mandated by the Qing emperors and dis­
162

obedicnce meant dcath by bchcading. The only permitted ;dlcrnativc was to shave off all the hair on my head and I soon did so.'
'What was Father like as a young man?' James said.
'He was so intelligent! I remember when he first joined my
finn, Hwa Chong Hong, at eighteen. He had just come to Tianjin from Shanghai and was with us for barely three months when our boss, K. C. Li, called me into his office. "This son of yours is rcally something!" he exclaimed. "In less than three months he has already cleared up our messy accounts and caught the thief in our midst."
'In those days, accounts werc added, subtracted, multiplied or dividcd only by nsing the abacus. ':' Now the abacus is a wonderful instrument, but there is no written record of the steps a person goes throngh in arriving at his final number. In fact, it is traditional in China not to write down the sequence of calculations one goes through in solving mathcmatical prob­lems. What your father did was to teach everyone the foreigners' number system and insist that everyone write down his calcu­lations on paper one step at a time.
'For over two thousand years additions, subtractions, multi­plications and divisions involving large numbers could only be carried out on the abacus because written Chinese numbers contain neithcr zcro nor position. After learning the Hindu­Arabic numbers, young c1erks at our firm were successfully challenging traditional abacists [those using the abacus] in their daily calculations. Not only were they fast and accurate, these
, It is possible, but highly cumbersome. to do mathematical calculations on paper while using Chinese characters alone. Until the adoption of the Hindu-Arabic number system. almost all calculations were carried out on the abacus in China out of necessity. not preference.
163

 

 

-
11
T
H
E
 -
H
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 -
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A
M
E
-
-
-
-
-
--
-
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-
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8
-
 -
8
6
-
-
 -
5
-
-
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+
=
27
2+7
=
9
=
9
=
9
- -
-
8
-
 -
8
15
-
-
 -
14
-
-
-
+
=
45
4+5
=
9
=
9
=
9
-
11
T
H
E
 -
H
O
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Y
 -
N
A
M
E
-
-
-
-
-
--
-
-
-
-
- -
2
-
5
 -
-
-
3
7
 -
-
1
4
5
+
=
27
2+7
=
9
=
9
=
9
- -
20
-
5
 -
-
-
12
25
 -
-
1
13
5
+
=
81
8+1
=
9
=
9
=
9
--
11
T
H
E
 -
H
O
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Y
 -
N
A
M
E
-
-
-
-
-
--
-
-
-
-
- -
20
8
5
 -
8
15
12
25
 -
14
9
14
5
+
=
126
1+2+6
=
9
=
9
=
9
- -
2
8
5
 -
8
6
3
7
 -
5
9
5
5
+
=
54
5+4
=
9
=
9
=
9
-
11
T
H
E
 -
H
O
L
Y
 -
N
A
M
E
-
-
-
-
-
-
-
-
-
-
-
 - -
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
 -
-
-
-
-
--
3
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
 - -
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
=
4
-
-
 -
-
5
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
- - -
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
 -
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
 -
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
11
T
H
E
 -
H
O
L
Y
 -
N
A
M
E
-
-
36
-
-
11
-
54
-
36
-
1+1
 -
-
-
 -
-
-
-
-
 -
-
9
-
-
-
-
3+6
-
-
1+1
-
5+4
-
3+6
9
2
T
H
E
 -
H
O
L
Y
 -
N
A
M
E
-
-
9
-
-
2
-
9
-
9

 

 

YOU ARE GOING ON A JOURNEY A VERY SPECIAL JOURNEY DO HAVE A PLEASANT JOURNEY DO

 

 
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