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Evokation
  
 
Index
  

 

 

 

 

THE ACT OF CREATION

 

 

 

 

 

 

 

 

 

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

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

 

 

THE

ENGLISH ALPHABET

ADD
TO
REDUCE REDUCE
TO
DEDUCE

THE NUMERICAL ROOT VALUE OF THE

ENGLISH ALPHABET

 

 

 

 

A TO Z

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

First Total = 351 and 3+5+1 = 9

 

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

Second total 126 and 1 + 2 + 6 = 9

 

12
SUPERNATURAL
166
49
4
12
SUPERSTITION
185
59
5
24
Add to Reduce
351
108
9
2+4
Reduce to Deduce
3+5+1
1+0+8
-
6
Essence of Number
9
9
9

 

 

 

 

 

THE

MAGIKALALPHABET

THE

ENGLISH LANGUAGE

TRANSMUTED INTO NUMBER

IS

ONE OF THE MAIN CONDUITS

THROUGH WHICH APPEAR CLEARER UNDERSTANDING

OF

THOSE REFRACTED PATTERNS AND SENSIBILITIES APPARENTLY RANDOM

DESCRIBING ENERGIES WHICH INTERMINGLED WITHIN THE GREAT HERE AND NOW

ARE

CONSIDERED

THE

CREATIVE LIVING EXPERIENCE

OF

REALITY

 

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

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

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

Searching out patterns is a pure delight.

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

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

 

 

THE GUINNESS ENCYCLOPEDIA

John Foley

1993

ALPHABETOLOGY

SIGNS AND SYMBOLS

Page 22

The most commonly used numerical symbols throughout the modern World; the so-called Arabic numerals

1 2 3 4 5 6 7 8 9

derive ultimately from a system developed by the Hindus in India sometime between the 3rd Century B,C. and 6th Century A.D.

The more rounded Western Arabic numerals were introduced into Spain by the Moors in the 10th Century.

The first European to take serious note of the new numeration was the French scholar Gerbert of Aurilliac (Pope Sylvester II from 999 to 1003) who had studied the system in Spain

The Hindus are also credited with the invention at some unknown date of the symbol for zero, which was first written as a small circle and later reduced to a large dot.

The nine Indian figures are : 9 8 7 6 5 4 3 2 1

With these nine figures and with the sign O any number may be written.

Leonardo of Pisa

Liber abaci

 

1234 5 6789

 

 

THE DEATH OF GODS IN ANCIENT EGYPT

Jane B. Sellars 1992

Page 204

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

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

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

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

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

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

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

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

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

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

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

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

AN IMPORTANT POSTSCRIPT

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

Page 206

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

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

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

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

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

Page 207

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

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

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

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

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

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

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

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

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

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

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

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

 

 

STRIKE A LIGHT

LUCIFER MEETS ITS MATCH

 

 

OSIRIS

SO IRIS IS

 

 

ENTERS THE NETERS

 

 

THE ELEMENTS OF EGYPTIAN WISDOM

Naomi Ozaniec 1994

THE SACRED SCRIPT - THE MEDU NETERS

Page 80 / The logical mind begins to reel / Page 81 / Language as evocation is immensely powerful. Word play is not finished; Neith can also be written by spelling the 't' with the sign for land, ta, in combination with the sign for water, 'n'. This particular hieroglyph represents ruffled water. By spelling the same name in a different way, we are presented with a different set of ideas. Here is Neith as 'the primeval water which gave birth to the land,' a theologically familiar concept. Once again a brief word encapsulates both divine name and divine function.

Hieroglyphic omitted

Schwaller de Lubicz reminds us repeatedly that we do need to look for a convoluted symbolism. The Medu Neters were chosen in such a way as to really signify all the qualities and functions implicit in the image. We are of course removed from the direct observation of vulture and ibis, crocodile and falcon, It is hard for us to understand the subtleties of movement, habit or life cycle which prompted a recognition deep in the Egyptian mind. It is well known that the humble dung beetle was raised to a sacred status from its simple egg-laying habit. The young emerged from the ball of dung as new life unbegotten. It is less well known that the scarab resembles the human skull, its two wing cases being reminiscent of the two halves of the human skull.

The ability to find the cosmic In the mundane through a correspondence is the hallmark of a mind sensitized through symbolic training. Any contemporary Qabalist recognizes this function for what it is, the inner workings of an esoteric system. These brief examples serve to illustrate the workings of both the Egyptian mind and the Egyptian tradition. Each letter had its own secret; all sacred alphabets are constructed in this way. Moreover a sacred language always serves a double purpose, a written double entendre. To the uninitiated there is no secret to hide. The language functions perfectly well at a purely practical level. To the initiated there exists another level of inner meaning as opposed to the apparent meaning. The inner meaning requires no elaborate subterfuge. It is there all the time, open and blatant. 'It / Page 82 / is hidden from view only because it represents a higher non-cerebral consciousness which simply evades the logical mind.

The Egyptians preserved this double function with astonishing brilliance and clarity over an immensely long period of time. Hebrew still functions as a sacred alphabet.. Each of its letters signifies ideas, numbers and cosmic principles.. A word becomes a code for an abstraction, a metaphysical concept, an esoteric teaching. An outsider cannot penetrate into the labyrinthine maze of meanings without becoming lost in ideas and distracted by elusive possibilities. A guide is always required in such matters - scribal training took place through an apprenticeship system. It is a mistake to think that we might uncover how the scribes viewed individual hieroglyphs by simply applying any meaning that springs to our mind. It is Clear that individual signs and arrangements carried a precise range of corresponding symbols.

Schwaller de Lubicz acts as our guide into the intricacies of an individual hieroglyph in the book Her-Bak.

The letter r is written in the lenticular shape of a half open mouth. Now look. for the ideas, qualities and functions this sign represents. First, its nature. The mouth, ra, is the upper opening of the body, an entrance that communicates by two channels with the lungs and stomach; that is why this hieroglyph is also the generic word for an entrance, ra. The mouth opens and shuts to eat, breathe and speak, as the eye, ar.t, opens and shuts to receive or refuse light. The mouth's function is dual, passive and active, it receives air and food, emits breath and voice. The eye's function is dual, likewise 'the reception of light and expression of organic and emotional response. The mouth's shape changes by the separation of the lips for the performance of its function. Opening, it widens or narrows like the shadow thrown on a disc by another disc which gradually eclipses it. In the partially occulted disc, the lentil or dark mouth is the complement of the crescent still visible. This gradual change of shape produces portions of different size that represents parts of the occulted disc. The characteristic has given the name ra to parts of a whole such as numerical fractions, chapters and so forth.

Page 83

These profound thoughts revolve around a single letter majestic insights might we discover if only someone would serve as our guide through all the hieroglyphic combinations! Here is a way of thinking quite unlike our own, a mind set removed from our utilitarian use of language. This totally symbolic thinking produced completely practical applications, as we see through Egypt's many lasting achievements there is no grounds whatsoever for thinking that this symbolic system produced woolly mindedness. On the contrary it gave rise to a mind that was both extensive and focused, deep and creative, traditonal yet original.

 

 

T
=
2
-
3
THE
33
15
6
C
=
3
-
5
CYCLE
48
21
3
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CIRCLE
50
32
5
-
-
16
-
19
First Total
185
95
23
-
-
1+6
-
1+9
Add to Reduce
1+8+5
9+5
2+3
-
-
7
-
10
Second Total
14
14
5
-
-
-
-
1+0
Reduce to Deduce
1+4
1+4
-
-
-
7
-
1
Essence of Number
5
5
5

 

 

ESOTERIC = 4 = ESOTERIC

ESOTERIC

I

SECRET

O

ESOTERIC

ESOTERIC = 4 = ESOTERIC

 

 

-
ESOTERIC
-
-
-
1
I
9
9
9
6
SECRET
70
34
7
1
O
15
6
6
8
ESOTERIC
94
49
22
-
-
9+4
4+9
2+2
8
ESOTERIC
13
13
4
-
-
1+3
1+3
-
8
ESOTERIC
4
4
4

 

 

-
ESOTERIC
-
-
-
1
O
15
6
6
6
SECRET
70
34
7
1
I
9
9
9
8
ESOTERIC
94
49
22
-
-
9+4
4+9
2+2
8
ESOTERIC
13
13
4
-
-
1+3
1+3
-
8
ESOTERIC
4
4
4

 

 

T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CIRCLE
50
32
5
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
C
=
3
-
5
CYCLE
48
21
3
-
-
16
-
19
First Total
185
95
23
-
-
1+6
-
1+9
Add to Reduce
1+8+5
9+5
2+3
-
-
7
-
10
Second Total
14
14
5
-
-
-
-
1+0
Reduce to Deduce
1+4
1+4
-
-
-
7
-
1
Essence of Number
5
5
5

 

 

LOVE DIVINE DIVINE LOVE

9 9 9 9 9 9 9 9 9 6 6 6 6 6 6 6 6 6

THAT LIGHT THAT

THAT LOVE THAT

THAT DIVINE LOVE LIGHT THAT

 

 

LIGHT AND LIFE
Lars Olof Bjorn 1976

Page197


BY
WRITING
THE
26
LETTERS

OF

THE ENGLISH ALPHABET

IN A CERTAIN ORDER ONE MAY PUT DOWN ALMOST ANY MESSAGE

 

 

I
=
9
-
3
I
9
9
9
M
=
4
-
2
ME
18
18
9
E
=
5
-
4
EGO
27
18
9
O
=
6
-
3
OGRE
45
27
9
C
=
3
-
2
CENTRIC
72
27
9
C
=
3
-
3
CONSCIENCE
90
45
9
G
=
7
-
2
GODS
45
18
9
D
=
4
-
4
DIVINE
63
36
9
T
=
1
-
3
THOUGHT
99
36
9

 

 

THE
MAGIKALALPHABET
ROOT
VALUE OF THE WORDS
I = 9 9 = I
ME = 9 9 = ME
EGO = 9 9 = EGO
CONSCIENCE = 9 9 = CONSCIENCE
DIVINE =9 9 = DIVINE
THOUGHT = 9 9 = THOUGHT
OUR = 9 9 = OUR
LOVE = 9 9 = LOVE
REAL = 9 9 = REAL
REALITY = 9 9 = REALITY
SUN = 9 9 = SUN
EARTH = 7 7 = EARTH
MOON = 3 3 = MOON
JUPITER = 9 9 = JUPITER
MAGNETIC = 9 9 = MAGNETIC
FIELD = 9 9 = FIELD
PHYSICS = 9 9 = PHYSICS
ORIONIS = 9 9 = ORIONIS ASCENSION = 9 9 = ASCENSION ORIONIS = 9 9 = ORIONIS
973 GOD OF NAMES 99 NAMES OF GOD = 9 9 9 9 = GOD OF NAMES 99 NAMES OF GOD 973

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

FOREWORD

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

 

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

Page 15

The Nine Billion Names of God

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

Page16

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

 

I = 9 9 = I

R = 9 9 = R

 

OF

T9ME AND STA9S

A9thu9 C. Cla9ke,1972

Page 15

THE N9NE B9LL9ON NAMES OF GOD

'Th9s 9s a sl9ghtly unusual 9equest,'sa9d D9 Wagne9, w9th what he hoped was commendable 9est9a9nt.' As fa9 as 9 know, 9t's the f99st t9me anyone's been asked to supply a T9betan monaste9y with an Automat9c Sequence Compute9. 9 don't w9sh to be 9nqu9s9t9ve, but 9 should ha9dly have thought that you9- ah - establ9shment had much use for such a mach9ne.Could you expla9n just what you 9ntend to do w9th 9t?'

'Gladly,' 9epl9ed the lama, 9eadjust9ng h9s s9lk 9obes and ca9efully putting away the sl9de 9ule he had been us9ng fo9 cu99ency conve9s9ons. 'You9 Ma9k V Compute9 can ca99y out any 9out9ne mathemat9cal ope9at9on 9nvolv9ng up to ten d9g9ts. Howeve9, for ou9 wo9k we a9e 9nte9ested 9n lette9s, not numbe9s. As we w9sh you to mod9fy the output c9rcu9ts,the mach9ne w9ll be p99nt9ng wo9ds not columns of f9gu9es.'

'9 dont qu9te unde9stand…'

'Th9s 9s a p9oject on wh9ch we have been work9ng fo9 the last th9ee centu99es - s9nce the lamase9y was founded, 9n fact.9t 9s somewhat al9en to you9 way of thought, so9 hope you w9ll l9sten with an open m9nd wh9le 9 expla9n 9t

'Natu9ally.'

'9t 9s 9eally qu9te s9mple.We have been comp9l9ng a l9st wh9ch shall conta9n all the poss9ble names of God'

'9 beg you9 pa9don?' / Page16 / 'We have 9eason to bel9eve' cont9nued the lama 9mpe9tu9bably, ' that all such names can be w99tten with not mo9e than n9ne lette9s 9n an alphabet we have dev9sed,'

'And you have been do9ng th9s for three centu99es?

'Yes: we expected9t would take us about f9fteen thousand yea9s to complete the task.'

'Oh, Dr Wagne9 looked a l9ttle dazed. 'Now9 see why you wanted to h99e one of ou9 mach9nes. But what exactly9s the pu9pose of th9s p9oject ?

'The lama hes9tated fo9 a f9act9on of a second, and Wagne9 wonde9ed9f he had offended h9m.9f so the9e was no t9ace of annoyance9n the 9eply.

'Call9t 99tual, 9f you l9ke, but 9t's a fundamental pa9t of ou9 bel9ef. All the many names of the Sup9eme Be9ng - God , Jehova , Allah , and so on - they a9e only man made labels. The9e 9s a ph9losoph9cal p9oblem of some d9ff9culty he9e, wh9ch9 do not p9opose to d9scuss, but somewhe9e among all the poss9ble comb9nat9ons of lette9s that can occu9 a9e what one may call the 9eal names of God. By systemat9c pe9mutat9on of lette9s, we have been t9y9ng to l9st them all'

9 see. You've been sta9t9ng at AAAAAAA… and wo9k-9ng up to ZZZZZZZZ …'

'Exactly - though we use a spec9al alphabet of ou9 own. Mod9fy9ng the elect9omat9c typew99te9s to deal w9th th9s 9s of cou9se t99v9al. A 9athe9 mo9e 9nte9est9ng p9oblem 9s that of dev9s9ng su9table c99cu9ts to el9m9nate 9 9d9culous comb9nat9ons. Fo9 example, no lette9 must occu9 mo9e than th9ee t9mes 9n sucess9on.'

'Th9ee? Su9ely you mean two.'

'Th9ee 9s co99ect; 9 am af9a9d 9t would take too long to expla9n why , even 9f you unde9stood ou9 language.'/ Page 17 / '9'm su9e 9t would,' sa9d Wagne9 hast9ly. 'Go on.'

'Luck9ly, 9t w9ll be a s9mple matte9 to adapt you9 Automat9c Sequence Compute9 fo9 th9s wo9k, s9nce once 9t has been p9og9ammed p9ope9ly 9t w9ll pe9mute each lette9 9n tu9n and p99nt the 9esult. What would have taken us f9fteen thousand years 9t w9ll be able to do 9n a hund9ed days.'

'Dr Wagne9 was sca9cely consc9ous of the fa9nt sounds f9om the Manhatten st9eets fa9 below. He was 9n a d9ffe9ent wo9ld, a wo9ld of natu9al, not man-made mounta9ns. H9gh up 9n the99 9emote ae99es these monks had been pat9ently at wo9k gene9at9on afte9 gene9at9on, comp9l9ng the99 l9sts of mean9ngless wo9ds. Was the9e any l9m9ts to the foll9es of mank9nd ? St9ll, he must g9ve no h9nt of h9s 9nne9 thoughts. The custome9 was always 99ght…"

 

 

OF

T9ME AND STA9S

A9thu9 C. Cla9ke,1972

Page 68

Into the Comet


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

 

 

-
-
-
-
-
ABACUS
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
B
=
2
2
1
B
2
2
2
-
-
2
-
4
5
6
7
8
9
A
=
1
3
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
C
=
3
4
1
C
3
3
3
-
-
-
3
4
5
6
7
8
9
U
=
3
5
1
U
21
3
3
-
-
-
3
4
5
6
7
8
8
S
=
1
6
1
S
19
10
1
-
1
-
-
4
5
6
7
8
9
-
-
11
-
6
ABACUS
47
20
11
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
4+7
2+0
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
11
2
2
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
2
2
2
-
3
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
ABACUS
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
A
=
1
3
1
A
1
1
1
-
1
-
-
4
5
6
7
8
9
S
=
1
6
1
S
19
10
1
-
1
-
-
4
5
6
7
8
9
B
=
2
2
1
B
2
2
2
-
-
2
-
4
5
6
7
8
9
C
=
3
4
1
C
3
3
3
-
-
-
3
4
5
6
7
8
9
U
=
3
5
1
U
21
3
3
-
-
-
3
4
5
6
7
8
8
-
-
11
-
6
ABACUS
47
20
11
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
4+7
2+0
1+1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
11
2
2
-
3
2
6
4
5
6
7
8
9
-
-
1+1
-
-
-
1+1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
6
ABACUS
2
2
2
-
3
2
6
4
5
6
7
8
9

 

 

A
=
1
-
1
A
1
1
1
C
=
3
-
8
COUNTING
103
40
4
T
=
2
-
5
TABLE
40
13
4
-
-
6
-
14
Add to Reduce
144
54
9
-
-
-
-
1+4
Reduce to Deduce
1+4+4
5+4
1+6
-
-
6
-
5
Essence of Number
9
9
9

 

 

Abacus - Wikipedia
https://en.wikipedia.org/wiki/Abacus

The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system. The exact origin of the abacus is still unknown.

The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system. The exact origin of the abacus is still unknown. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone, or metal.
Abaci come in different designs. Some designs, like the bead frame consisting of beads divided into tens, are used mainly to teach arithmetic, although they remain popular in the post-Soviet states as a tool. Other designs, such as the Japanese soroban, have been used for practical calculations even involving several digits. For any particular abacus design, there usually are numerous different methods to perform a certain type of calculation, which may include basic operations like addition and multiplication, or even more complex ones, such as calculating square roots. Some of these methods may work with non-natural numbers (numbers such as 1.5 and ?3/4).
Although today many use calculators and computers instead of abaci to calculate, abaci still remain in common use in some countries. Merchants, traders and clerks in some parts of Eastern Europe, Russia, China and Africa use abaci, and they are still used to teach arithmetic to children.[1] Some people who are unable to use a calculator because of visual impairment may use an abacus.

Etymology[edit]

The use of the word abacus dates before 1387 AD, when a Middle English work borrowed the word from Latin to describe a sandboard abacus. The Latin word came from Greek ?ßa? abax which means something without base, and improperly, any piece of rectangular board or plank.[2][3][4] Alternatively, without reference to ancient texts on etymology, it has been suggested that it means "a square tablet strewn with dust",[5] or "drawing-board covered with dust (for the use of mathematics)"[6] (the exact shape of the Latin perhaps reflects the genitive form of the Greek word, ßao? abakos). Whereas the table strewn with dust definition is popular, there are those that do not place credence in this at all and in fact state that it is not proven.[7][nb 1] Greek ?ßa? itself is probably a borrowing of a Northwest Semitic, perhaps Phoenician, word akin to Hebrew ?abaq (???), "dust" (or in post-Biblical sense meaning "sand used as a writing surface").[8]

The preferred plural of abacus is a subject of disagreement, with both abacuses[9] and abaci[9] in use. The user of an abacus is called an abacist.[10]

 

 

R
=
9
-
-
RIVER
-
-
-
-
-
-
-
1
R
18
9
9
-
-
-
-
1
I
9
9
9
-
-
-
-
2
V+E
27
9
9
-
-
-
-
1
R
18
9
9
R
=
9
-
5
RIVER
72
36
36
-
-
-
-
-
-
7+2
3+6
3+6
R
=
9
-
5
RIVER
9
9
9

 

 

THE SPLENDOUR THAT WAS EGYPT

Margaret A. Murray

Appendix

4

The New Year of God

Cornhill Magazine 1934

Page 231/233

"Three o'clock and a still starlight night in mid-September in Upper Egypt. At this hour the village is usually asleep, but to-night it is a stir for this is Nauruz Allah, the New Year of God, and the narrow streets are full of the soft sound of bare feet moving towards the Nile. The village lies on a strip of ground; one one side is the river, now swollen to its height, on the other are the floods of the inundation spread in a vast sheet of water to the edge of the desert. On a windy night the lapping of wavelets is audible on every hand; but to-night the air is calm and still, there is no sound but the muffled tread of unshod feet in the dust and the murmur of voices subdued in the silence of the night.

In ancient times throughout the whole of Egypt the night of High Nile was a night of prayer and thanks giving to the great god , the Ruler of the river, Osiris himself. Now it is only in this Coptic village that the ancient rite is preserved, and here the festival is still one of prayer and thanksgiving. In the great cities the New Year is a time of feasting and processions, as blatant and uninteresting as a Lord Mayor's Show, with that additional note of piercing vulgarity peculiar to the East.

In this village, far from all great cities, and-as a Coptic community-isolated from and therefore uninfluenced either by its Moslem neighbours or by foreigners, the festival is one of simplicity and piety. The people pray as of old to the Ruler of the river, no longer Osiris, but Christ; and as of old they pray for a blessing upon their children and their homes.

There are four appointed places on the river bank to which the village women go daily to fill their water-jars and to water their animals. To these four places the villagers are now making their way, there to keep the New Year of God.

The river gleams coldly pale and grey; Sirius blazing in the eastern sky casts a narrow path of light across the mile-wide waters. A faint glow low on the horizon shows where the moon will rise, a dying moon on the last day of the last quarter.

The glow gradually spreads and brightens till the thin crescent, like a fine silver wire, rises above the distant palms. Even in that attenuated form the moonlight eclipses the stars and the glory of Sirius is dimmed. The water turns to the colour of tarnished silver, smooth and glassy; the palm-trees close at hand stand black against the sky, and the distant shore is faintly visible. The river runs silently and without a ripple in the windless calm; the palm fronds, so sensitive to the least movement of the air, hang motionless and still; all Nature seems to rest upon this holy night.

The women enter the river and stand knee-deep in the running stream praying; they drink nine times, wash the face and hands, and dip themselves in the water. Here is a mother carrying a tiny wailing baby; she enters the river and gently pours the waternine times over the little head. The wailing ceases as the water cools the little hot face. Two anxious women hasten down the steep bank, a young boy between them; they hurriedly enter the water and the boy squats down in the river up to his neck, while the mother pours the water nine times with her hands over his face and shaven head. There is the sound of a little gasp at the first shock of coolness, and the mother laughs, a little tender laugh, and the grandmother says something under her breath, at which they all laugh softly together. After the ninth washing the boy stands up, then squats down again and is again washed nine times, and yet a third nine times; then the grandmother takes her turn and she also washes him nine times. Evidently he is very precious to the hearts of those two women, perhaps the mother's last surviving child. Another sturdy urchin refuses to sit down in the water, frightened perhaps, for a woman's voice speaks encouragingly, and presently a faint splashing and a little gurgle of childish laughter shows that he too is receiving the blessing of the Nauruz of God.

A woman stands alone, her slim young figure in its wet clinging garments silhouetted against the steel-grey water. Solitary she stands, apart from the happy groups of parents and children; then, stooping , she drinks from her once, pauses and drinks again; and so drinksnine times with a short pause between every drink and a longer pause between every three. Except for the movement of her hand as she lifts the water to her lips, she stands absolutely still, her body tense with the earnestness of her prayer, the very atmosphere round her charged with the agony of her supplication. Throughout the whole world there is only one thing which causes a woman to pray with such intensity, and that one thing is children. " This may be a childless woman praying for a child, or it may be that, in this land where Nature is as careless and wasteful of infant life as of all else, this a mother praying for the last of her little brood, feeling assured that on this festival of mothers and children her prayers must perforce be heard. At last she straightens herself, beats the water nine times with the corner of her garment, goes softly up the bank, and disappears in the darkness.

Little family parties come down to the river, a small child usually riding proudly on her father's shoulder. The men often affect to despise the festival as a woman's affair, but with memories in their hearts of their own mothers and their own childhood they sit quietly by the river and drink nine times. A few of the rougher young men fling themselves into the water and swim boisterously past, but public feeling is against them, for the atmosphere is one of peace and prayer enhanced by the calm and silence of the night.

Page 232 and 233 Continued.

For thousands of years on the night of High Nile the mothers of Egypt have stood in the great river to implore from the God of the Nile a blessing upon their children; formerly from a God who Himself has memories of childhood and a Mother. Now, as then, the stream bears on its broad surface the echo of countless prayers, the hopes and fears of human hearts; and in my memory remains a vision of the darkly flowing river, the soft murmur of prayer, the peace and calm of the New Year of God.

Abu Nauruz hallal.

 

THE WORD "NINE" OCCURS x 9 AND "NINTH" x 1

 

Page 231/233

"Three o'clock and a still starlight night in mid-September in Upper Egypt. At this hour the village is usually asleep, but to-night it is a stir for this is Nauruz Allah, the New Year of God

 

N
=
5
-
6
NAURUZ
101
29
2
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"Three o'clock and a still starlight night in mid-September in Upper Egypt. At this hour the village is usually asleep, but to-night it is a stir for this is Nauruz Allah, the New Year of God

 

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Abacus - Wikipedia
https://en.wikipedia.org/wiki/Abacus

The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system. The exact origin of the abacus is still unknown.

The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system. The exact origin of the abacus is still unknown. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone, or metal.
Abaci come in different designs. Some designs, like the bead frame consisting of beads divided into tens, are used mainly to teach arithmetic, although they remain popular in the post-Soviet states as a tool. Other designs, such as the Japanese soroban, have been used for practical calculations even involving several digits. For any particular abacus design, there usually are numerous different methods to perform a certain type of calculation, which may include basic operations like addition and multiplication, or even more complex ones, such as calculating square roots. Some of these methods may work with non-natural numbers (numbers such as 1.5 and ?3/4).
Although today many use calculators and computers instead of abaci to calculate, abaci still remain in common use in some countries. Merchants, traders and clerks in some parts of Eastern Europe, Russia, China and Africa use abaci, and they are still used to teach arithmetic to children.[1] Some people who are unable to use a calculator because of visual impairment may use an abacus.

Etymology[edit]

The use of the word abacus dates before 1387 AD, when a Middle English work borrowed the word from Latin to describe a sandboard abacus. The Latin word came from Greek ?ßa? abax which means something without base, and improperly, any piece of rectangular board or plank.[2][3][4] Alternatively, without reference to ancient texts on etymology, it has been suggested that it means "a square tablet strewn with dust",[5] or "drawing-board covered with dust (for the use of mathematics)"[6] (the exact shape of the Latin perhaps reflects the genitive form of the Greek word, ?ßa?o? abakos). Whereas the table strewn with dust definition is popular, there are those that do not place credence in this at all and in fact state that it is not proven.[7][nb 1] Greek ?ßa? itself is probably a borrowing of a Northwest Semitic, perhaps Phoenician, word akin to Hebrew ?abaq (???), "dust" (or in post-Biblical sense meaning "sand used as a writing surface").[8]

The preferred plural of abacus is a subject of disagreement, with both abacuses[9] and abaci[9] in use. The user of an abacus is called an abacist.[10]

History[edit]

Mesopotamian[edit]

The period 2700–2300 BC saw the first appearance of the Sumerian abacus, a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.[11]

Some scholars point to a character from the Babylonian cuneiform which may have been derived from a representation of the abacus.[12] It is the belief of Old Babylonian[13] scholars such as Carruccio that Old Babylonians "may have used the abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations".[14]

Egyptian[edit]

The use of the abacus in Ancient Egypt is mentioned by the Greek historian Herodotus, who writes that the Egyptians manipulated the pebbles from right to left, opposite in direction to the Greek left-to-right method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument have not been discovered.[15]

Persian[edit]

During the Achaemenid Empire, around 600 BC the Persians first began to use the abacus.[16] Under the Parthian, Sassanian and Iranian empires, scholars concentrated on exchanging knowledge and inventions with the countries around them – India, China, and the Roman Empire, when it is thought to have been exported to other countries.

Greek[edit]

An early photograph of the Salamis Tablet, 1899. The original is marble and is held by the National Museum of Epigraphy, in Athens.
The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC.[17] Also Demosthenes (384 BC–322 BC) talked of the need to use pebbles for calculations too difficult for your head.[18][19] A play by Alexis from the 4th century BC mentions an abacus and pebbles for accounting, and both Diogenes and Polybius mention men that sometimes stood for more and sometimes for less, like the pebbles on an abacus.[19] The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus saw use in Achaemenid Persia, the Etruscan civilization, Ancient Rome and, until the French Revolution, the Western Christian world.

A tablet found on the Greek island Salamis in 1846 AD (the Salamis Tablet), dates back to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble 149 cm (59 in) long, 75 cm (30 in) wide, and 4.5 cm (2 in) thick, on which are 5 groups of markings. In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semicircle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.[20] Also from this time frame the Darius Vase was unearthed in 1851. It was covered with pictures including a "treasurer" holding a wax tablet in one hand while manipulating counters on a table with the other.[18]

Chinese[edit]

Main article: Suanpan

A Chinese abacus (suanpan) (the number represented in the picture is 6,302,715,408)

Abacus

Chinese
??

Literal meaning
"calculating tray"

[show]Transcriptions

The earliest known written documentation of the Chinese abacus dates to the 2nd century BC.[21]

The Chinese abacus, known as the suanpan (??, lit. "counting tray"), is typically 20 cm (8 in) tall and comes in various widths depending on the operator. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. If you move them toward the beam, you count their value. If you move away, you don't count their value.[22] The suanpan can be reset to the starting position instantly by a quick movement along the horizontal axis to spin all the beads away from the horizontal beam at the center.

Suanpan can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed. There are currently schools teaching students how to use it.

In the long scroll Along the River During the Qingming Festival painted by Zhang Zeduan during the Song dynasty (960–1297), a suanpan is clearly visible beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao).

The similarity of the Roman abacus to the Chinese one suggests that one could have inspired the other, as there is some evidence of a trade relationship between the Roman Empire and China. However, no direct connection can be demonstrated, and the similarity of the abaci may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern Korean and Japanese) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2. (Incidentally, this allows use with a hexadecimal numeral system, which was used for traditional Chinese measures of weight.) Instead of running on wires as in the Chinese, Korean, and Japanese models, the beads of Roman model run in grooves, presumably making arithmetic calculations much slower.

Another possible source of the suanpan is Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a place holder. The zero was probably introduced to the Chinese in the Tang dynasty (618–907) when travel in the Indian Ocean and the Middle East would have provided direct contact with India, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians.

Roman[edit]

Main article: Roman abacus

Copy of a Roman abacus
The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles (calculi) were used. Later, and in medieval Europe, jetons were manufactured. Marked lines indicated units, fives, tens etc. as in the Roman numeral system. This system of 'counter casting' continued into the late Roman empire and in medieval Europe, and persisted in limited use into the nineteenth century.[23] Due to Pope Sylvester II's reintroduction of the abacus with very useful modifications, it became widely used in Europe once again during the 11th century[24][25] This abacus used beads on wires, unlike the traditional Roman counting boards, which meant the abacus could be used much faster.[26]

Writing in the 1st century BC, Horace refers to the wax abacus, a board covered with a thin layer of black wax on which columns and figures were inscribed using a stylus.[27]

One example of archaeological evidence of the Roman abacus, shown here in reconstruction, dates to the 1st century AD. It has eight long grooves containing up to five beads in each and eight shorter grooves having either one or no beads in each. The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives –five units, five tens etc., essentially in a bi-quinary coded decimal system, obviously related to the Roman numerals. The short grooves on the right may have been used for marking Roman "ounces" (i.e. fractions).

Indian[edit]

There is no clear evidence for use of the abacus in India. The decimal number system invented in India replaced the abacus in Western Europe.[28]

The Abhidharmakosabha?ya of Vasubandhu (316-396), a Sanskrit work on Buddhist philosophy, says that the second-century CE philosopher Vasumitra said that "placing a wick (Sanskrit vartika) on the number one (eka?ka) means it is a one, while placing the wick on the number hundred means it is called a hundred, and on the number one thousand means it is a thousand". It is unclear exactly what this arrangement may have been. Around the 5th century, Indian clerks were already finding new ways of recording the contents of the Abacus.[29] Hindu texts used the term sunya (zero) to indicate the empty column on the abacus.[30]

Japanese[edit]

Main article: Soroban

Japanese soroban

In Japanese, the abacus is called soroban (??, ????, lit. "Counting tray"), imported from China in the 14th century.[31] It was probably in use by the working class a century or more before the ruling class started, as the class structure did not allow for devices used by the lower class to be adopted or used by the ruling class.[32] The 1/4 abacus, which is suited to decimal calculation, appeared circa 1930, and became widespread as the Japanese abandoned hexadecimal weight calculation which was still common in China. The abacus is still manufactured in Japan today even with the proliferation, practicality, and affordability of pocket electronic calculators. The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation. Using visual imagery of a soroban, one can arrive at the answer in the same time as, or even faster than, is possible with a physical instrument.[33]

Korean[edit]

The Chinese abacus migrated from China to Korea around 1400 AD.[18][34][35] Koreans call it jupan (??), supan (??) or jusan (??).[36]

Native American[edit]

Representation of an Inca quipu

A yupana as used by the Incas.
Some sources mention the use of an abacus called a nepohualtzintzin in ancient Aztec culture.[37] This Mesoamerican abacus used a 5-digit base-20 system.[38] The word Nepohualtzintzin [nepo?wa?'t?sint?sin] comes from Nahuatl and it is formed by the roots; Ne – personal -; pohual or pohualli ['po?wal?i] – the account -; and tzintzin ['t?sint?sin] – small similar elements. Its complete meaning was taken as: counting with small similar elements by somebody. Its use was taught in the Calmecac to the temalpouhqueh [tema?'po?ke?], who were students dedicated to take the accounts of skies, from childhood.

The Nepohualtzintzin was divided in two main parts separated by a bar or intermediate cord. In the left part there were four beads, which in the first row have unitary values (1, 2, 3, and 4), and in the right side there are three beads with values of 5, 10, and 15 respectively. In order to know the value of the respective beads of the upper rows, it is enough to multiply by 20 (by each row), the value of the corresponding account in the first row.

Altogether, there were 13 rows with 7 beads in each one, which made up 91 beads in each Nepohualtzintzin. This was a basic number to understand, 7 times 13, a close relation conceived between natural phenomena, the underworld and the cycles of the heavens. One Nepohualtzintzin (91) represented the number of days that a season of the year lasts, two Nepohualtzitzin (182) is the number of days of the corn's cycle, from its sowing to its harvest, three Nepohualtzintzin (273) is the number of days of a baby's gestation, and four Nepohualtzintzin (364) completed a cycle and approximate a year (1
1/ 4
days short). When translated into modern computer arithmetic, the Nepohualtzintzin amounted to the rank from 10 to the 18 in floating point, which calculated stellar as well as infinitesimal amounts with absolute precision, meant that no round off was allowed.

The rediscovery of the Nepohualtzintzin was due to the Mexican engineer David Esparza Hidalgo,[39] who in his wanderings throughout Mexico found diverse engravings and paintings of this instrument and reconstructed several of them made in gold, jade, encrustations of shell, etc.[40] There have also been found very old Nepohualtzintzin attributed to the Olmec culture, and even some bracelets of Mayan origin, as well as a diversity of forms and materials in other cultures.

George I. Sanchez, "Arithmetic in Maya", Austin-Texas, 1961 found another base 5, base 4 abacus in the Yucatán Peninsula that also computed calendar data. This was a finger abacus, on one hand 0, 1, 2, 3, and 4 were used; and on the other hand 0, 1, 2 and 3 were used. Note the use of zero at the beginning and end of the two cycles. Sanchez worked with Sylvanus Morley, a noted Mayanist.

The quipu of the Incas was a system of colored knotted cords used to record numerical data,[41] like advanced tally sticks – but not used to perform calculations. Calculations were carried out using a yupana (Quechua for "counting tool"; see figure) which was still in use after the conquest of Peru. The working principle of a yupana is unknown, but in 2001 an explanation of the mathematical basis of these instruments was proposed by Italian mathematician Nicolino De Pasquale. By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for the different fields in the instrument. Using the Fibonacci sequence would keep the number of grains within any one field at a minimum.[42]

Russian[edit]

Russian abacus
The Russian abacus, the schoty (?????), usually has a single slanted deck, with ten beads on each wire (except one wire, usually positioned near the user, with four beads for quarter-ruble fractions). Older models have another 4-bead wire for quarter-kopeks, which were minted until 1916. The Russian abacus is often used vertically, with wires from left to right in the manner of a book. The wires are usually bowed to bulge upward in the center, to keep the beads pinned to either of the two sides. It is cleared when all the beads are moved to the right. During manipulation, beads are moved to the left. For easy viewing, the middle 2 beads on each wire (the 5th and 6th bead) usually are of a different color from the other eight beads. Likewise, the left bead of the thousands wire (and the million wire, if present) may have a different color.

As a simple, cheap and reliable device, the Russian abacus was in use in all shops and markets throughout the former Soviet Union, and the usage of it was taught in most schools until the 1990s.[43][44] Even the 1874 invention of mechanical calculator, Odhner arithmometer, had not replaced them in Russia and likewise the mass production of Felix arithmometers since 1924 did not significantly reduce their use in the Soviet Union.[45] The Russian abacus began to lose popularity only after the mass production of microcalculators had started in the Soviet Union in 1974. Today it is regarded as an archaism and replaced by the handheld calculator.

The Russian abacus was brought to France around 1820 by the mathematician Jean-Victor Poncelet, who served in Napoleon's army and had been a prisoner of war in Russia.[46] The abacus had fallen out of use in western Europe in the 16th century with the rise of decimal notation and algorismic methods. To Poncelet's French contemporaries, it was something new. Poncelet used it, not for any applied purpose, but as a teaching and demonstration aid.[47] The Turks and the Armenian people also used abaci similar to the Russian schoty. It was named a coulba by the Turks and a choreb by the Armenians.[48]

School abacus[edit]

Early 20th century abacus used in Danish elementary school.

A twenty bead rekenrek
Around the world, abaci have been used in pre-schools and elementary schools as an aid in teaching the numeral system and arithmetic.

In Western countries, a bead frame similar to the Russian abacus but with straight wires and a vertical frame has been common (see image). It is still often seen as a plastic or wooden toy.

The wire frame may be used either with positional notation like other abaci (thus the 10-wire version may represent numbers up to 9,999,999,999), or each bead may represent one unit (so that e.g. 74 can be represented by shifting all beads on 7 wires and 4 beads on the 8th wire, so numbers up to 100 may be represented). In the bead frame shown, the gap between the 5th and 6th wire, corresponding to the color change between the 5th and the 6th bead on each wire, suggests the latter use.

The red-and-white abacus is used in contemporary primary schools for a wide range of number-related lessons. The twenty bead version, referred to by its Dutch name rekenrek ("calculating frame"), is often used, sometimes on a string of beads, sometimes on a rigid framework.[49]

 

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-
8
COUNTING
103
40
4
T
=
2
-
5
TABLE
40
13
4
-
-
6
-
14
Add to Reduce
144
54
9
-
-
-
-
1+4
Reduce to Deduce
1+4+4
5+4
1+6
-
-
6
-
5
Essence of Number
9
9
9

 

 

LOOK AT THE THREES LOOK AT THE THREES LOOK AT THE THREES THE THREES THE THREES

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
THREES
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
3
1
R
9
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
4
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
30
-
6
THREES
75
39
30
-
1
2
3
4
10
6
7
8
9
-
-
3+0
-
-
-
7+5
3+9
3+0
-
-
-
-
-
1+0
-
-
-
-
-
-
3
-
6
THREES
12
12
3
-
1
2
3
4
1
6
7
8
9
-
-
3+0
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
6
THREES
3
3
3
-
1
2
3
4
1
6
7
8
9

 

3THREE TO THINE AND 3THREE TO MINE AND 3THREE TIMES 3THREE AS MAKE UP 9NINE

 

 

11
CALCULATION
-
-
-
-
-
-
-
C
3
3
3
-
-
3
-
A
1
1
1
-
1
-
-
L
12
3
3
-
-
3
-
C
3
3
3
-
-
3
-
U
21
3
3
-
-
3
-
L
12
3
3
-
-
3
-
A+T
21
3
3
-
-
3
-
I
9
9
9
-
-
-
-
O+N
29
11
2
-
2
-
11
CALCULATION
111
39
30
-
3
18
1+1
-
1+1+1
3+9
3+0
-
-
1+8
2
CALCULATION
3
12
3
-
3
9
-
-
-
1+2
-
-
-
-
2
CALCULATION
3
3
3
-
3
9

 

 

12
CALCULATIONS
130
40
4
8
CALCULUS
92
20
2

 

 

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

 

 

-
-
-
-
-
CALCULATING
-
-
-
-
1
2
3
4
5
6
7
8
9
C
=
3
1
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
U
=
3
5
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
8
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
10
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
-
-
40
-
11
CALCULATING
103
40
40
-
2
2
15
4
5
6
7
8
9
-
-
4+0
-
1+1
-
1+0+3
4+0
4+0
-
-
-
1+5
-
-
-
-
-
-
-
-
4
-
2
CALCULATING
4
4
4
-
2
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
CALCULATING
-
-
-
-
1
2
3
4
5
6
7
8
9
C
=
3
1
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
A
=
1
2
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
L
=
3
3
1
L
12
3
3
-
-
-
3
4
-
6
-
8
-
C
=
3
4
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
U
=
3
5
1
U
21
3
3
-
-
-
3
4
-
6
-
8
-
L
=
3
6
1
L
12
3
3
-
-
-
3
4
-
6
-
8
-
A
=
1
7
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
T
=
2
8
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
I
=
9
9
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
N
=
5
10
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
G
=
7
11
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
-
-
40
-
11
CALCULATING
103
40
40
-
2
2
15
4
5
6
7
8
9
-
-
4+0
-
1+1
-
1+0+3
4+0
4+0
-
-
-
1+5
-
-
-
-
-
-
-
-
4
-
2
CALCULATING
4
4
4
-
2
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
CALCULATING
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
7
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
A
=
1
2
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
T
=
2
8
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
C
=
3
1
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
L
=
3
3
1
L
12
3
3
-
-
-
3
4
-
6
-
8
-
C
=
3
4
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
U
=
3
5
1
U
21
3
3
-
-
-
3
4
-
6
-
8
-
L
=
3
6
1
L
12
3
3
-
-
-
3
4
-
6
-
8
-
N
=
5
10
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
G
=
7
11
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
I
=
9
9
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
40
-
11
CALCULATING
103
40
40
-
2
2
15
4
5
6
7
8
9
-
-
4+0
-
1+1
-
1+0+3
4+0
4+0
-
-
-
1+5
-
-
-
-
-
-
-
-
4
-
2
CALCULATING
4
4
4
-
2
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
CALCULATING
-
-
-
-
1
2
3
5
7
9
A
=
1
7
1
A
1
1
1
-
1
-
-
-
-
-
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
T
=
2
8
1
T
20
2
2
-
-
2
-
-
-
-
C
=
3
1
1
C
3
3
3
-
-
-
3
-
-
-
L
=
3
3
1
L
12
3
3
-
-
-
3
-
-
-
C
=
3
4
1
C
3
3
3
-
-
-
3
-
-
-
U
=
3
5
1
U
21
3
3
-
-
-
3
-
-
-
L
=
3
6
1
L
12
3
3
-
-
-
3
-
-
-
N
=
5
10
1
N
14
5
5
-
-
-
-
5
-
-
G
=
7
11
1
G
7
7
7
-
-
-
-
-
7
-
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
9
-
-
40
-
11
CALCULATING
103
40
40
-
2
2
15
5
7
9
-
-
4+0
-
1+1
-
1+0+3
4+0
4+0
-
-
-
1+5
-
-
-
-
-
4
-
2
CALCULATING
4
4
4
-
2
2
6
5
7
9

 

 

-
CALCULATING
-
-
-
-
1
2
3
4
5
6
7
8
9
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
2
A+T
21
3
3
-
-
-
3
-
-
-
-
-
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
2
N+G
21
3
3
-
-
-
3
-
-
-
-
-
-
11
CALCULATING
103
40
40
-
1
2
21
4
5
6
7
8
9
1+1
-
1+0+3
4+0
4+0
-
-
-
2+1
-
-
-
-
-
-
2
CALCULATING
4
4
4
-
1
2
3
4
5
6
7
8
9

 

 

-
CALCULATING
-
-
-
-
1
3
9
1
C
3
3
3
-
-
3
-
1
A
1
1
1
-
1
-
-
1
L
12
3
3
-
-
3
-
1
C
3
3
3
-
-
3
-
1
U
21
3
3
-
-
3
-
1
L
12
3
3
-
-
3
-
2
A+T
21
3
3
-
-
3
-
1
I
9
9
9
-
-
-
9
2
N+G
21
3
3
-
-
3
-
11
CALCULATING
103
40
40
-
1
21
9
1+1
-
1+0+3
4+0
4+0
-
-
2+1
-
2
CALCULATING
4
4
4
-
1
3
9

 

 

10
CURRICULUM
-
-
-
-
C
3
3
3
-
U
21
3
3
-
R
18
9
9
-
R
18
9
9
-
I
9
9
9
-
C
3
3
3
-
U
21
3
3
-`
L
12
3
3
-
U
21
12
3
-
M
13
4
4
10
CURRICULUM
139
58
49
1+0
-
1+3+9
5+8
4+9
1
CURRICULUM
13
13
13
-
-
1+3
1+3
1+3
1
CURRICULUM
4
4
4

 

 

10
CURRICULUM
--
-
-
-
-
-
-
-
C
3
3
3
-
3
-
-
-
U
21
3
3
-
3
-
-
-
R
18
9
9
-
-
-
9
-
R
18
9
9
-
-
-
9
-
I
9
9
9
-
-
-
9
-
C
3
3
3
-
3
-
-
-
U
21
3
3
-
3
-
-
-
L
12
3
3
-
3
-
-
-
U
21
3
3
-
3
-
-
-
M
13
4
4
-
-
4
-
10
CURRICULUM
139
49
49
-
18
4
27
1+0
-
1+3+9
4+9
4+9
-
1+8
-
2+7
1
CURRICULUM
13
13
13
-
9
4
9
-
-
1+3
1+3
1+3
-
-
-
-
1
CURRICULUM
4
4
4
-
9
4
9

 

 

G
=
7
-
4
GODS
45
27
9
U
=
3
-
9
UNIVERSAL
121
49
4
M
=
4
-
5
MINDS
59
32
5
I
=
9
-
1
I
9
9
9
-
-
14
-
19
First Total
234
117
27
-
-
1+4
-
1+9
Add to Reduce
2+3+4
1+1+7
2+7
-
-
5
-
10
Second Total
9
9
9
-
-
-
-
1+0
Reduce to Deduce
-
-
-
-
-
5
-
1
Essence of Number
9
9
9

 

 

-
-
-
-
A
-
-
-
-
-
-
-
-
T
-
-
-
-
-
-
-
-
O
-
-
-
-
-
-
-
-
N
-
-
-
-
A
T
O
N
E
M
E
N
T
-
-
-
-
M
-
-
-
-
-
-
-
-
E
-
-
-
-
-
-
-
-
N
-
-
-
-
-
-
-
-
T
-
-
-
-

 

 

-
-
-
-
-
A
-
-
-
-
-
-
-
-
-
-
B
-
-
-
-
-
-
-
-
-
-
R
-
-
-
-
-
-
-
-
-
-
A
-
-
-
-
-
-
-
-
-
-
C
-
-
-
-
-
A
B
R
A
C
A
D
A
B
R
A
-
-
-
-
-
D
-
-
-
-
-
-
-
-
-
-
A
-
-
-
-
-
-
-
-
-
-
B
-
-
-
-
-
-
-
-
-
-
R
-
-
-
-
-
-
-
-
-
-
A
-
-
-
-
-

 

 

A
-
-
-
A
-
-
-
-
A
-
B
-
-
-
B
-
-
-
R
-
-
-
R
-
-
R
-
-
B
-
-
-
-
-
A
-
A
-
A
-
-
-
-
-
-
-
C
C
D
-
-
-
-
A
B
R
A
C
A
D
A
B
R
A
-
-
-
-
C
D
D
-
-
-
-
-
-
-
A
-
A
-
A
-
-
-
-
-
R
-
-
B
-
-
B
-
-
-
B
-
-
-
R
-
-
-
R
-
A
-
-
-
A
-
-
-
-
A

 

 

-
ABRACADABRA
-
-
-
2
AB
3
3
3
1
R
18
9
9
4
A+C+A+D
9
9
9
2
A+B
3
3
3
1
R
18
9
9
1
A
1
1
1
11
ABRACADABRA
52
34
34
1+1
-
5+2
3+4
3+4
2
ABRACADABRA
7
7
7

 

 

-
ABRACADABRA
-
-
-
4
A+R+A+B
22
4
4
3
C+A+D
8
8
8
4
A+R+A+B
22
4
4
11
ABRACADABRA
52
34
34
1+1
-
5+2
3+4
3+4
2
ABRACADABRA
7
7
7

 

 

-
ABRACADABRA
-
-
-
4
A+R+A+B
22
4
4
1
C
3
3
3
1
A
1
1
1
1
D
4
4
4
4
A+R+A+B
22
4
4
11
ABRACADABRA
52
34
34
1+1
-
5+2
3+4
3+4
2
ABRACADABRA
7
7
7

 

World Wide Words: Abracadabra
19 Dec 2005 ... The origin of the mystical phrase 'abracadabra', much beloved of conjurors, is explained.
www.worldwidewords.org/qa/qa-abr1.htm

[Q] From Speranza Spiratos: Can you shed some magical clarity on the word abracadabra please?

[A] Let me wave my wand ... Ah, a brief sputter, then nothing. It seems the origin isn’t known for certain.

These days it’s just a joking conjuror’s incantation with no force behind it, like hocus pocus and other meaningless phrases. But the word is extremely ancient and originally was thought to be a powerful invocation with mystical powers.

What we know for sure is that it was first recorded in a Latin medical poem, De medicina praecepta, by the Roman physician Quintus Serenus Sammonicus in the second century AD. It’s believed to have come into English via French and Latin from a Greek word abrasadabra (the change from s to c seems to have been through a confused transliteration of the Greek). Serenus Sammonicus said that to get well a sick person should wear an amulet around the neck, a piece of parchment inscribed with a triangular formula derived from the word, which acts like a funnel to drive the sickness out of the body:

A B R A C A D A B R A
A B R A C A D A B R
A B R A C A D A B
A B R A C A D A
A B R A C A D
A B R A C A
A B R A C
A B R A
A B R
A B
A

However, it seems likely that abracadabra is older and that it derives from one of the Semitic languages, though nobody can say for sure, because there is no written record before Serenus Sammonicus. For what it’s worth, here are some theories:

•It’s from the Aramaic phrase avra kehdabra, meaning “I will create as I speak”.
•The source is three Hebrew words, ab (father), ben (son), and ruach acadosch (holy spirit).
•It’s from the Chaldean abbada ke dabra, meaning “perish like the word”.
•It originated with a Gnostic sect in Alexandria called the Basilidians and was probably based on Abrasax, the name of their supreme deity (Abraxas in Latin sources).
Fans of the Harry Potter books will know the killing curse, Avada Kedavra, in which J K Rowling seems to have combined the supposed Aramaic source of abracadabra with the Latin cadaver, a dead body.

 

“I will create as I speak”

 

I
=
9
-
1
I
9
9
9
W
=
5
-
4
WILL
56
20
2
C
=
3
-
6
CREATE
52
25
7
A
=
1
-
2
AS
20
11
2
I
=
9
-
1
I
9
9
9
S
=
1
-
5
SPEAK
52
25
7
-
-
28
4
19
First Total
198
99
36
-
-
2+8
1
1+9
Add to Reduce
1+9+8
9+9
3+6
-
-
10
-
10
Second Total
18
18
9
-
-
1+0
4
1+0
Reduce to Deduce
1+8
1+8
-
-
-
1
-
1
Essence of Number
9
9
9

 

 

-
-
-
-
-
ABRACADABRA
-
-
-
-
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
-
-
-
-
-
-
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
4
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
C
=
3
5
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
6
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
-
-
34
-
11
ABRACADABRA
52
34
34
-
5
4
3
4
5
6
7
8
18
-
-
3+4
-
1+1
-
5+2
3+4
3+4
-
-
-
-
-
-
-
-
-
1+8
-
-
7
-
2
ABRACADABRA
7
7
7
-
5
4
3
4
5
6
7
8
9

 

 

-
-
-
-
-
ABRACADABRA
-
-
-
-
1
2
3
4
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
B
=
2
2
1
B
2
2
2
-
-
2
-
-
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
9
A
=
1
4
1
A
1
1
1
-
1
-
-
-
-
C
=
3
5
1
C
3
3
3
-
-
-
3
-
-
A
=
1
6
1
A
1
1
1
-
1
-
-
-
-
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
9
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
34
-
11
ABRACADABRA
52
34
34
-
5
4
3
4
18
-
-
3+4
-
1+1
-
5+2
3+4
3+4
-
-
-
-
-
1+8
-
-
7
-
2
ABRACADABRA
7
7
7
-
5
4
3
4
9

 

 

 

-
-
-
-
-
ABRACADABRA
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
5
6
7
8
-
B
=
2
2
1
B
2
2
2
-
-
2
-
-
5
6
7
8
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
5
6
7
8
9
A
=
1
4
1
A
1
1
1
-
1
-
-
-
5
6
7
8
-
C
=
3
5
1
C
3
3
3
-
-
-
3
-
5
6
7
8
-
A
=
1
6
1
A
1
1
1
-
1
-
-
-
5
6
7
8
-
D
=
4
7
1
D
4
4
4
-
-
-
-
4
5
6
7
8
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
5
6
7
8
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
5
6
7
8
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
5
6
7
8
9
A
=
1
11
1
A
1
1
1
-
1
-
-
-
5
6
7
8
-
-
-
34
-
11
ABRACADABRA
52
34
34
-
5
4
3
4
5
6
7
8
18
-
-
3+4
-
1+1
-
5+2
3+4
3+4
-
-
-
-
-
-
-
-
-
1+8
-
-
7
-
2
ABRACADABRA
7
7
7
-
5
4
3
4
5
6
7
8
9

 

 

-
-
-
-
-
ABRACADABRA
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
5
6
7
8
-
A
=
1
4
1
A
1
1
1
-
1
-
-
-
5
6
7
8
-
A
=
1
6
1
A
1
1
1
-
1
-
-
-
5
6
7
8
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
5
6
7
8
-
A
=
1
11
1
A
1
1
1
-
1
-
-
-
5
6
7
8
-
B
=
2
2
1
B
2
2
2
-
-
2
-
-
5
6
7
8
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
5
6
7
8
-
C
=
3
5
1
C
3
3
3
-
-
-
3
-
5
6
7
8
-
D
=
4
7
1
D
4
4
4
-
-
-
-
4
5
6
7
8
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
5
6
7
8
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
5
6
7
8
9
-
-
34
-
11
ABRACADABRA
52
34
34
-
5
4
3
4
5
6
7
8
18
-
-
3+4
-
1+1
-
5+2
3+4
3+4
-
-
-
-
-
-
-
-
-
1+8
-
-
7
-
2
ABRACADABRA
7
7
7
-
5
4
3
4
5
6
7
8
9

 

 

-
-
-
-
-
ABRACADABRA
-
-
-
-
1
2
3
4
9
A
=
1
1
1
A
1
1
1
-
1
-
-
-
-
A
=
1
4
1
A
1
1
1
-
1
-
-
-
-
A
=
1
6
1
A
1
1
1
-
1
-
-
-
-
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
-
B
=
2
2
1
B
2
2
2
-
-
2
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
C
=
3
5
1
C
3
3
3
-
-
-
3
-
-
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
R
=
9
3
1
R
18
9
9
-
-
-
-
-
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
9
-
-
34
-
11
ABRACADABRA
52
34
34
-
5
4
3
4
18
-
-
3+4
-
1+1
-
5+2
3+4
3+4
-
-
-
-
-
1+8
-
-
7
-
2
ABRACADABRA
7
7
7
-
5
4
3
4
9

 

 

“I will create as I speak”

 

I
=
9
-
1
I
9
9
9
W
=
5
-
4
WILL
56
20
2
C
=
3
-
6
CREATE
52
25
7
A
=
1
-
2
AS
20
11
2
I
=
9
-
1
I
9
9
9
S
=
1
-
5
SPEAK
52
25
7
-
-
28
4
19
First Total
198
99
36
-
-
2+8
1
1+9
Add to Reduce
1+9+8
9+9
3+6
-
-
10
-
10
Second Total
18
18
9
-
-
1+0
4
1+0
Reduce to Deduce
1+8
1+8
-
-
-
1
-
1
Essence of Number
9
9
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
-
W
=
5
-
4
WILL
56
20
2
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CREATE
52
25
7
-
-
-
-
-
-
-
-
-
-
A
=
1
-
2
AS
20
11
2
-
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SPEAK
52
25
7
-
-
-
-
-
-
-
-
-
-
-
-
28
4
19
First Total
198
99
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
I
=
9
1
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
W
=
5
2
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
L
=
3
4
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
8
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
10
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
P
=
7
16
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
18
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
K
=
2
19
1
K
11
2
2
-
-
2
-
-
-
-
-
-
-
-
-
81
-
6
-
198
99
81
-
5
4
9
4
20
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+0
-
-
-
2+7
I
=
9
-
1
I
9
9
9
-
5
4
9
4
2
6
7
8
9
W
=
5
-
4
WILL
56
20
2
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CREATE
52
25
7
-
5
4
9
4
2
6
7
8
9
A
=
1
-
2
AS
20
11
2
-
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
5
4
9
4
2
6
7
8
9
S
=
1
-
5
SPEAK
52
25
7
-
-
-
-
-
-
-
-
-
-
-
-
28
-
19
First Total
198
99
36
-
5
4
9
4
2
4
7
8
9
-
-
2+8
-
1+9
Add to Reduce
1+9+8
9+9
3+6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
10
Second Total
18
18
9
-
5
4
9
4
2
4
7
8
9
-
-
1+0
-
1+0
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
Essence of Number
9
9
9
-
5
4
3
4
2
4
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
-
W
=
5
-
4
WILL
56
20
2
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CREATE
52
25
7
-
-
-
-
-
-
-
-
-
-
A
=
1
-
2
AS
20
11
2
-
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SPEAK
52
25
7
-
-
-
-
-
-
-
-
-
-
-
-
28
4
19
First Total
198
99
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
I
=
9
1
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
W
=
5
2
1
W
23
5
5
-
-
-
-
4
5
6
-
8
-
I
=
9
3
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
L
=
3
4
1
L
12
3
3
-
-
-
3
4
-
6
-
8
-
L
=
3
5
1
L
12
3
3
-
-
-
3
4
-
6
-
8
-
C
=
3
6
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
R
=
9
7
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
E
=
5
8
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
A
=
1
9
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
T
=
2
10
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
A
=
1
12
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
S
=
1
13
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
I
=
9
14
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
S
=
1
15
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
P
=
7
16
1
P
16
7
7
-
-
-
-
4
-
6
7
8
-
E
=
5
17
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
A
=
1
18
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
K
=
2
19
1
K
11
2
2
-
-
2
-
4
-
6
-
8
-
-
-
81
-
6
-
198
99
81
-
5
4
9
4
20
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+0
-
-
-
2+7
I
=
9
-
1
I
9
9
9
-
5
4
9
4
2
6
7
8
9
W
=
5
-
4
WILL
56
20
2
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CREATE
52
25
7
-
5
4
9
4
2
6
7
8
9
A
=
1
-
2
AS
20
11
2
-
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
5
4
9
4
2
6
7
8
9
S
=
1
-
5
SPEAK
52
25
7
-
-
-
-
-
-
-
-
-
-
-
-
28
-
19
First Total
198
99
36
-
5
4
9
4
2
4
7
8
9
-
-
2+8
-
1+9
Add to Reduce
1+9+8
9+9
3+6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
10
Second Total
18
18
9
-
5
4
9
4
2
4
7
8
9
-
-
1+0
-
1+0
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
Essence of Number
9
9
9
-
5
4
3
4
2
4
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
-
W
=
5
-
4
WILL
56
20
2
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CREATE
52
25
7
-
-
-
-
-
-
-
-
-
-
A
=
1
-
2
AS
20
11
2
-
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
5
SPEAK
52
25
7
-
-
-
-
-
-
-
-
-
-
-
-
28
4
19
First Total
198
99
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
9
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
A
=
1
12
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
S
=
1
13
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
S
=
1
15
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
A
=
1
18
1
A
1
1
1
-
1
-
-
4
-
6
-
8
-
T
=
2
10
1
T
20
2
2
-
-
2
-
4
-
6
-
8
-
K
=
2
19
1
K
11
2
2
-
-
2
-
4
-
6
-
8
-
L
=
3
4
1
L
12
3
3
-
-
-
3
4
-
6
-
8
-
L
=
3
5
1
L
12
3
3
-
-
-
3
4
-
6
-
8
-
C
=
3
6
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
W
=
5
2
1
W
23
5
5
-
-
-
-
4
5
6
-
8
-
E
=
5
8
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
E
=
5
17
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
P
=
7
16
1
P
16
7
7
-
-
-
-
4
-
6
7
8
-
I
=
9
1
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
I
=
9
3
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
R
=
9
7
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
I
=
9
14
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
81
-
6
-
198
99
81
-
5
4
9
4
20
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+0
-
-
-
2+7
I
=
9
-
1
I
9
9
9
-
5
4
9
4
2
6
7
8
9
W
=
5
-
4
WILL
56
20
2
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CREATE
52
25
7
-
5
4
9
4
2
6
7
8
9
A
=
1
-
2
AS
20
11
2
-
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
5
4
9
4
2
6
7
8
9
S
=
1
-
5
SPEAK
52
25
7
-
-
-
-
-
-
-
-
-
-
-
-
28
-
19
First Total
198
99
36
-
5
4
9
4
2
4
7
8
9
-
-
2+8
-
1+9
Add to Reduce
1+9+8
9+9
3+6
-
-
-
-
-
-
-
-
-
-
-
-
10
-
10
Second Total
18
18
9
-
5
4
9
4
2
4
7
8
9
-
-
1+0
-
1+0
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
Essence of Number
9
9
9
-
5
4
3
4
2
4
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
5
7
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
W
=
5
-
4
WILL
56
20
2
-
-
-
-
-
-
-
C
=
3
-
6
CREATE
52
25
7
-
-
-
-
-
-
-
A
=
1
-
2
AS
20
11
2
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
S
=
1
-
5
SPEAK
52
25
7
-
-
-
-
-
-
-
-
-
28
4
19
First Total
198
99
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
5
7
9
A
=
1
9
1
A
1
1
1
-
1
-
-
-
-
-
A
=
1
12
1
A
1
1
1
-
1
-
-
-
-
-
S
=
1
13
1
S
19
10
1
-
1
-
-
-
-
-
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
-
A
=
1
18
1
A
1
1
1
-
1
-
-
-
-
-
T
=
2
10
1
T
20
2
2
-
-
2
-
-
-
-
K
=
2
19
1
K
11
2
2
-
-
2
-
-
-
-
L
=
3
4
1
L
12
3
3
-
-
-
3
-
-
-
L
=
3
5
1
L
12
3
3
-
-
-
3
-
-
-
C
=
3
6
1
C
3
3
3
-
-
-
3
-
-
-
W
=
5
2
1
W
23
5
5
-
-
-
-
5
-
-
E
=
5
8
1
E
5
5
5
-
-
-
-
5
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
5
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
5
-
-
P
=
7
16
1
P
16
7
7
-
-
-
-
-
7
-
I
=
9
1
1
I
9
9
9
-
-
-
-
-
-
9
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
9
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
9
-
-
81
-
6
-
198
99
81
-
5
4
9
20
7
27
-
-
-
-
-
-
-
-
-
-
-
-
-
2+0
-
2+7
I
=
9
-
1
I
9
9
9
-
5
4
9
2
7
9
W
=
5
-
4
WILL
56
20
2
-
-
-
-
-
-
-
C
=
3
-
6
CREATE
52
25
7
-
5
4
9
2
7
9
A
=
1
-
2
AS
20
11
2
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
5
4
9
2
7
9
S
=
1
-
5
SPEAK
52
25
7
-
-
-
-
-
-
-
-
-
28
-
19
First Total
198
99
36
-
5
4
9
2
7
9
-
-
2+8
-
1+9
Add to Reduce
1+9+8
9+9
3+6
-
-
-
-
-
-
-
-
-
10
-
10
Second Total
18
18
9
-
5
4
9
2
7
9
-
-
1+0
-
1+0
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
1
-
1
Essence of Number
9
9
9
-
5
4
3
2
7
9

 

 

11
A
B
R
A
C
A
D
A
B
R
A
-
-
-
-
-
-
1
2
18
1
3
1
4
1
2
18
1
+
=
52
5+2
7
-
1
2
9
1
3
1
4
1
2
9
1
+
=
34
3+4
7
11
A
B
R
A
C
A
D
A
B
R
A
-
-
-
-
-
-
A
-
-
-
-
-
-
-
-
-
A
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
+
=
2
=
2
-
-
B
-
-
-
-
-
-
-
R
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
9
-
+
=
11
1+1
2
-
-
-
R
-
-
-
-
-
B
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
2
-
-
+
=
11
1+1
2
-
-
-
-
A
-
-
-
A
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
+
=
2
=
2
-
-
-
-
-
C
-
D
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
4
-
-
-
-
+
=
7
=
7
-
-
-
-
-
-
A
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
=
1
11
A
B
R
A
C
A
D
A
B
R
A
-
-
34
-
16
1+1
-
-
9
-
-
-
-
-
-
9
-
-
-
3+4
-
1+6
2
A
B
R
A
C
A
D
A
B
R
A
-
-
7
-
7
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
-
11
A
B
R
A
C
A
D
A
B
R
A
-
-
1
-
7

 

 

12
B
U
R
I
A
L
-
R
I
T
U
A
L
n
-
-
-
-
--
-
-
-
-
9
-
-
-
-
9
-
-
-
-
+
=
18
1+8
=
9
12
B
U
R
I
A
L
-
R
I
T
U
A
L
n
-
-
-
-
--
-
2
3
9
-
1
3
-
9
-
2
3
1
3
+
=
36
3+6
=
9
-
2
21
18
-
1
12
-
18
-
20
21
1
12
+
=
126
1+2+6
=
9
12
B
U
R
I
A
L
-
R
I
T
U
A
L
n
-
-
-
-
--
-
2
21
18
9
1
3
-
18
9
20
21
1
12
+
=
144
1+4+4
=
9
-
2
3
9
9
1
3
-
9
9
2
3
1
3
+
=
45
4+5
=
9
12
B
U
R
I
A
L
-
R
I
T
U
A
L
-
-
-
-
-
-
-
B
-
-
-
-
-
-
-
-
-
-
-
L
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
3
+
=
5
-
-
5
-
-
U
-
-
-
-
-
-
-
-
-
A
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
1
-
+
=
4
---
-
4
-
-
-
R
-
-
-
-
-
-
-
U
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
3
-
-
+
=
12
1+2
=
3
-
-
-
-
I
-
-
-
-
-
T
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
2
-
-
-
+
=
11
1+1
=
2
-
-
-
-
-
A
-
-
-
I
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
9
-
-
-
-
+
=
10
1+0
=
1
-
-
-
-
-
  
L
-
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
9
-
-
-
-
-
+
=
12
1+2
=
3
12
B
U
R
I
A
L
-
R
I
T
U
A
L
-
-
54
-
-
18
1+2
-
-
-
-
-
-
-
9
9
-
-
 -
-
-
-
5+4
-
-
1+8
3
B
U
R
I
A
L
-
R
I
T
U
A
L
-
-
9
-
-
9

 

ZERO = 1 = ZERO

 

 

I
=
9
-
1
I
9
9
9
T
=
2
-
4
THAT
49
13
4
A
=
1
-
2
AM
14
5
5
T
=
2
-
4
THAT
20
11
2
T
=
2
-
4
TIME
49
13
4
E
=
5
-
5
EMITS
66
30
3
-
-
21
4
20
First Total
234
90
27
-
-
2+1
1
2+0
Add to Reduce
2+3+4
9+0
3+6
-
-
3
-
2
Second Total
9
9
9
-
-
-
-
-
Reduce to Deduce
1+8
1+8
1+0
-
-
3
-
2
Essence of Number
9
9
9

 

 

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

 

 

GODS HOST GODS HOST

THE HOLY GHOST

 

T
=
2
-
3
THE
33
15
6
H
=
8
-
4
HOLY
42
24
6
G
=
7
-
5
GHOST
69
33
6
-
-
17
4
12
Add to Reduce
144
72
18
-
-
1+7
1
1+3
Reduce to Deduce
1+4+4
7+2
1+8
-
-
8
-
4
Essence of Number
9
9
9

 

 

THE

HOLY SPIRIT

SPIRIT I TRIPS

THE

LIFE FILE

 

 

SEVEN I'M IN HEAVEN

THE SO EVEN SEVEN

SEVEN EVENS

HEADS I WIN TAILS YOU LOSE

 

8
HEBDOMAD
-
-
-
1
H
8
8
8
2
E+B
7
7
7
-
D+O
19
10
1
2
M+A+D
18
9
9
8
HEBDOMAD
52
34
25
-
-
5+2
3+4
2+5
8
HEBDOMAD
7
7
7

 


Origin of hebdomad. Latin hebdomas hebdomad- the number seven from Greek from hebdomos seventh from hepta seven ;

see sept&mlowring; in Indo-European roots.

Hebdomad dictionary definition | hebdomad defined - YourDictionary
www.yourdictionary.com/hebdomad

Hebdomad | Definition of Hebdomad by Merriam-Webster
https://www.merriam-webster.com/dictionary/hebdomad

Definition of hebdomad. 1 :a group of seven. 2 :a period of seven days :week.

Hebdomad - Wikipedia
https://en.wikipedia.org/wiki/Hebdomad
Hebdomad (Ancient Greek: ?ßd?µ??) may refer to: On Hebdomads, a work of the Hippocratic Corpus; Hebdomad, a term used by Neoplatonist philosophers ...
Hebdomad (Ancient Greek: ?ßd?µ??) may refer to:
On Hebdomads, a work of the Hippocratic Corpus
Hebdomad, a term used by Neoplatonist philosophers such as Iamblichus and Proclus in reference to the intellect
The Hebdomad, the seven world-creating archons in most Gnostic systems: see Archon (Gnosticism)#Hebdomad
On Hebdomads (De hebdomadibus), a work of the Neoplatonist Boethius commented upon by Thomas Aquinas, in which the hebdomads are common mental conceptions or axioms
The Celestial Hebdomad, the archons who make up the ruling council of Mount Celestia in Dungeons & Dragons

 

-
HEBDOMAD
--
-
-
5
H+E+B+D+O
34
25
7
3
M+A+D
18
9
9
8
HEBDOMAD
52
34
16
-
-
5+2
3+4
1+6
8
HEBDOMAD
7
7
7

 

 

THE

BALANCING

ONE TWO THREE FOUR

FIVE

NINE EIGHT SEVEN SIX

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

1234 5 6789

 

 

ZERO = 64 = ZERO

ZERO = 28 = ZERO

ZERO = 10 = ZERO

ZERO = 1 = ZERO

 

 

prime number - Whatis Techtarget
https://whatis.techtarget.com/definition/prime-number
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

 


Prime number - Wikipedia
https://en.wikipedia.org/wiki/Prime_number

The first 25 prime numbers (all the prime numbers less than 100) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 (sequence A000040 in the OEIS).
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 6 is composite because it is the product of two numbers (2 × 3) that are both smaller than 6. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.

There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen number being prime is inversely proportional to its number of digits, that is, to its logarithm.
Several historical questions regarding prime numbers are still unsolved. These include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes having just one even number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals.

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. There are several proofs of the theorem.

 

Prime numbers
www-groups.dcs.st-and.ac.uk/history/HistTopics/Prime_numbers.html
Euclid also showed that if the number 2n - 1 is prime then the number 2n-1(2n - 1) is a perfect number. The mathematician Euler (much later in 1747) was able to ...
Prime numbers

Number theory index History Topics Index

Version for printing

Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians.
The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers.
A perfect number is one whose proper divisors sum to the number itself. e.g. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has divisors 1, 2, 4, 7 and 14 and 1 + 2 + 4 + 7 + 14 = 28.
A pair of amicable numbers is a pair like 220 and 284 such that the proper divisors of one number sum to the other and vice versa.
You can see more about these numbers in the History topics article Perfect numbers.

By the time Euclid's Elements appeared in about 300 BC, several important results about primes had been proved. In Book IX of the Elements, Euclid proves that there are infinitely many prime numbers. This is one of the first proofs known which uses the method of contradiction to establish a result. Euclid also gives a proof of the Fundamental Theorem of Arithmetic: Every integer can be written as a product of primes in an essentially unique way.

Euclid also showed that if the number 2n - 1 is prime then the number 2n-1(2n - 1) is a perfect number. The mathematician Euler (much later in 1747) was able to show that all even perfect numbers are of this form. It is not known to this day whether there are any odd perfect numbers.

In about 200 BC the Greek Eratosthenes devised an algorithm for calculating primes called the Sieve of Eratosthenes.

There is then a long gap in the history of prime numbers during what is usually called the Dark Ages.

 

PRIME NUMBERS

 

P
=
2
-
5
PRIME
61
34
7
N
=
2
-
7
NUMBERS
92
38
2
-
-
17
-
12
Add to Reduce
153
72
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
8
-
3
Essence of Number
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
34
-
11
-
61
34
34
-
-
-
-
-
-
-
-
-
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
29
-
10
-
92
38
29
-
1
2
3
8
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
6
7
8
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
6
7
8
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
6
7
8
-
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
6
-
8
9
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
6
-
8
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
6
-
8
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
6
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
6
-
8
-
-
-
-
-
-
-
-
-
-
-
1
2
3
8
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
6
7
8
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
6
7
8
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
6
-
8
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
6
-
8
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
6
-
8
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
6
-
8
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
6
-
8
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
6
-
8
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
6
7
8
-
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
6
-
8
9
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
6
-
8
9
-
-
-
-
-
-
-
-
-
-
1
2
3
8
15
6
7
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
6
7
8
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
6
7
8
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
6
7
8
9

 

6 +8 = 14 1+4 = 5

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
9
P
=
2
-
5
PRIME
61
34
7
-
-
-
-
-
-
-
-
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
9
S
=
1
12
1
S
19
10
1
-
1
-
-
-
-
-
-
B
=
2
9
1
B
2
2
2
-
-
2
-
-
-
-
-
U
=
3
7
1
U
21
3
3
-
-
-
3
-
-
-
-
M
=
4
8
1
M
13
4
4
-
-
-
-
4
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
N
=
5
6
1
N
14
5
5
-
-
-
-
-
5
-
-
E
=
5
10
1
E
5
5
5
-
-
-
-
-
5
-
-
P
=
7
1
1
P
16
7
7
-
-
-
-
-
-
7
-
I
=
9
3
1
I
9
9
9
-
-
-
-
-
-
-
9
R
=
9
2
1
R
18
9
9
-
-
-
-
-
-
-
9
R
=
9
11
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
1
2
3
8
15
7
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+5
-
2+7
P
=
2
-
5
PRIME
61
34
7
-
1
2
3
8
6
7
9
N
=
2
-
7
NUMBERS
92
38
2
-
-
-
-
-
-
-
-
-
-
17
-
12
Add to Reduce
153
72
9
-
1
2
3
8
6
7
9
-
-
1+7
-
1+2
Reduce to Deduce
1+5+3
7+2
-
-
-
-
-
-
-
-
-
-
-
8
-
3
Essence of Number
9
9
9
-
1
2
3
8
6
7
9

 

 

-
THE SUNS ENERGY
-
-
-
3
THE
33
15
6
4
SUNS
73
28
1
6
ENERGY
74
38
2
10
THE SUNS ENERGY
180
81
9
1+0
-
1+8+0
8+1
-
1
THE SUNS ENERGY
9
12
3
-
-
1+2
1+2
-
1
THE SUNS ENERGY
9
9
3

 

 

T
=
2
3
THE
33
15
6
W
=
5
5
WATER
67
22
4
O
=
6
2
OF
21
12
3
L
=
3
4
LIFE
32
23
5
-
-
16
14
Add to Reduce
153
72
18
-
-
1+6
1+4
Reduce to Deduce
1+5+3
7+2
1+8
-
-
7
5
Essence of Number
9
9
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
R
=
1
-
11
RENAISSANCE
108
63
36
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0+8
6+3
3+6
-
-
-
-
-
-
-
-
-
-
R
=
1
-
11
RENAISSANCE
9
9
9
-
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
-
-
-
-
A
=
1
4
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
7
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
N
=
5
9
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
C
=
3
10
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
43
-
11
RENAISSANCE
108
63
36
-
4
2
3
4
20
6
7
8
18
-
-
4+3
-
1+1
-
1+0+8
6+3
3+6
-
-
-
-
-
2+0
-
-
-
1+8
-
-
7
-
2
RENAISSANCE
9
9
9
-
4
2
3
4
2
6
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
3
5
9
-
-
-
-
11
RENAISSANCE
108
63
36
-
-
-
-
-
-
-
-
-
-
-
1+0+8
6+3
3+6
-
-
-
-
-
-
-
-
-
11
RENAISSANCE
9
9
9
-
1
3
5
9
A
=
1
4
1
A
1
1
1
-
1
-
-
-
S
=
1
6
1
S
19
10
1
-
1
-
-
-
S
=
1
7
1
S
19
10
1
-
1
-
-
-
A
=
1
8
1
A
1
1
1
-
1
-
-
-
C
=
3
10
1
C
3
3
3
-
-
3
-
-
E
=
5
2
1
E
5
5
5
-
-
-
5
-
N
=
5
3
1
N
14
5
5
-
-
-
5
-
N
=
5
9
1
N
14
5
5
-
-
-
5
-
E
=
5
11
1
E
5
5
5
-
-
-
5
-
R
=
9
1
1
R
18
9
9
-
-
-
-
9
I
=
9
5
1
I
9
9
9
-
-
-
-
9
-
-
43
-
11
RENAISSANCE
108
63
36
-
4
3
20
18
-
-
4+3
-
1+1
-
1+0+8
6+3
3+6
-
-
-
2+0
1+8
-
-
7
-
2
RENAISSANCE
9
9
9
-
4
3
2
9

 

 

I
=
9
-
1
I
9
9
9
T
=
2
-
5
THINK
62
26
8
T
=
2
-
9
THEREFORE
100
55
1
I
=
9
-
1
I
9
9
9
A
=
1
-
2
AM
14
5
5
-
-
21
-
18
First Total
194
104
32
-
-
2+1
-
1+8
Reduce to Deduce
1+9+4
1+0+4
3+2
-
-
21
-
9
First Total
14
5
5
-
-
2+1
-
-
Reduce to Deduce
1+4
-
-
-
-
3
-
9
Essence of Number
5
5
5

 

 

I
=
9
-
1
I
9
9
9
T
=
2
-
5
THINK
62
26
8
T
=
2
-
9
THEREFORE
100
55
1
I
=
9
-
1
I
9
9
9
A
=
1
-
2
AM
14
5
5
N
=
5
-
3
NOT
49
13
4
-
-
28
-
21
First Total
243
117
36
-
-
2+8
-
2+1
Reduce to Deduce
2+4+3
1+1+7
3+6
-
-
10
-
3
First Total
9
9
9
-
-
1+0
-
-
Reduce to Deduce
-
-
-
-
-
1
-
3
Essence of Number
9
9
9

 

 

entropy

1.

Physics
a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system. "the second law of thermodynamics says that entropy always increases with time"

noun: entropy; plural noun: entropies; symbol: S

2.

lack of order or predictability; gradual decline into disorder.
"a marketplace where entropy reigns supreme"

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
ENTROPY
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
2
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
3
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
R
=
9
4
1
R
9
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
6
1
P
7
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
7
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
41
-
7
ENTROPY
113
41
41
-
1
2
3
4
10
6
14
8
9
-
-
4+1
-
-
-
1+1+3
4+1
4+1
-
-
-
-
-
1+0
-
1+4
-
-
-
-
5
-
7
ENTROPY
5
5
5
-
1
2
3
4
1
6
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
ENTROPY
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
3
1
T
20
2
2
-
1
2
2
3
-
-
-
8
-
E
=
5
1
1
E
5
5
5
-
1
-
2
3
5
-
-
8
-
N
=
5
2
1
N
14
5
5
-
1
-
2
3
5
-
-
8
-
O
=
6
5
1
O
15
6
6
-
1
-
2
3
-
6
-
8
-
P
=
7
6
1
P
7
7
7
-
1
-
2
3
-
-
7
8
-
Y
=
7
7
1
Y
25
7
7
-
1
-
2
3
-
-
7
8
-
R
=
9
4
1
R
9
9
9
-
1
-
2
3
-
-
-
8
9
-
-
41
-
7
ENTROPY
113
41
41
-
1
2
3
4
10
6
14
8
9
-
-
4+1
-
-
-
1+1+3
4+1
4+1
-
-
-
-
-
1+0
-
1+4
-
-
-
-
5
-
7
ENTROPY
5
5
5
-
1
2
3
4
1
6
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
2
5
6
7
9
-
-
-
-
-
ENTROPY
-
-
-
-
-
-
-
-
-
T
=
2
3
1
T
20
2
2
-
2
-
-
-
-
E
=
5
1
1
E
5
5
5
-
-
5
-
-
-
N
=
5
2
1
N
14
5
5
-
-
5
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
6
-
-
P
=
7
6
1
P
7
7
7
-
-
-
-
7
-
Y
=
7
7
1
Y
25
7
7
-
-
-
-
7
-
R
=
9
4
1
R
9
9
9
-
-
-
-
-
9
-
-
41
-
7
ENTROPY
113
41
41
-
2
10
6
14
9
-
-
4+1
-
-
-
1+1+3
4+1
4+1
-
-
1+0
-
1+4
-
-
-
5
-
7
ENTROPY
5
5
5
-
2
1
6
5
9

 

 

-
-
-
-
THERMODYNAMICS
-
-
-
T
=
2
6
THERMO
79
34
7
D
=
4
8
DYNAMICS
88
34
7
-
-
6
14
THERMODYNAMICS
167
68
14
-
-
-
1+4
-
1+6+7
6+8
1+4
-
-
6
5
THERMODYNAMICS
14
14
5
-
-
-
-
-
1+4
1+4
-
-
-
6
5
THERMODYNAMICS-
5
5
5

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
-
-
-
14
THERMODYNAMICS
167
68
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+4
-
1+6+7
6+8
-
-
-
-
-
-
-
-
-
-
-
S
-
-
-
5
THERMODYNAMICS
14
14
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
S
-
-
-
5
THERMODYNAMICS
5
5
5
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
4
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
M
=
4
5
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
O
=
6
6
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
Y
=
7
8
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
N
=
5
9
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
A
=
1
10
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
M
=
4
11
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
14
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
-
68
-
14
THERMODYNAMICS
167
77
68
-
2
2
3
12
10
6
7
8
18
-
-
6+8
-
1+4
-
1+6+7
7+7
6+8
-
-
-
-
1+2
1+0
-
-
-
1+8
-
-
14
-
5
THERMODYNAMICS
14
14
14
-
2
2
3
3
1
6
7
8
9
-
-
1+4
-
-
-
1+4
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
THERMODYNAMICS
5
5
5
-
2
2
3
3
1
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
-
-
-
14
THERMODYNAMICS
167
68
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+4
-
1+6+7
6+8
-
-
-
-
-
-
-
-
-
-
-
S
-
-
-
5
THERMODYNAMICS
14
14
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
S
-
-
-
5
THERMODYNAMICS
5
5
5
-
1
2
3
4
5
6
7
8
9
A
=
1
10
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
14
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
C
=
3
13
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
M
=
4
5
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
M
=
4
11
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
9
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
6
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
Y
=
7
8
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
4
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
12
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
68
-
14
THERMODYNAMICS
167
77
68
-
2
2
3
12
10
6
7
8
18
-
-
6+8
-
1+4
-
1+6+7
7+7
6+8
-
-
-
-
1+2
1+0
-
-
-
1+8
-
-
14
-
5
THERMODYNAMICS
14
14
14
-
2
2
3
3
1
6
7
8
9
-
-
1+4
-
-
-
1+4
1+4
1+4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
5
THERMODYNAMICS
5
5
5
-
2
2
3
3
1
6
7
8
9

 

 

T
=
2
3
THE
33
15
6
L
=
3
3
LAW
36
9
9
O
=
6
2
OF
21
12
3
T
=
2
14
THERMODYNAMICS
167
68
5
-
-
13
22
First Total
257
104
23
-
-
1+3
2+2
Add to Reduce
2+5+7
1+0+4
2+3
-
-
4
4
Second Total
14
5
5
-
-
-
-
Reduce to Deduce
1+4
-
-
-
-
4
4
Essence of Number
5
5
5

 

 

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

 

 

E
=
5
-
-
ENERGY
-
-
-
-
-
-
-
1
E
5
5
5
-
-
-
-
1
N
14
5
5
-
-
-
-
1
E
5
5
5
-
-
-
-
1
R
18
9
9
-
-
-
-
2
G+Y
32
14
5
E
=
5
-
6
ENERGY
74
38
29
-
-
-
-
-
-
7+4
3+8
2+9
E
=
5
4
6
ENERGY
11
11
11
-
-
-
-
-
-
1+1
1+1
1+1
E
=
5
4
6
ENERGY
2
2
2

 

 

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

 

 

https://en.wikipedia.org/wiki/Synergetics

Synergetics can refer to: Synergetics (Fuller), a study of systems behavior suggested by BuckminsterFuller;

Synergetics (Haken), a school of thought on ...

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
-
-
-
11
SYNERGETICS
144
72
54
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+4+4
7+2
3+6
-
-
-
-
-
-
-
-
-
-
S
-
-
-
11
SYNERGETICS
9
9
9
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
Y
=
7
2
1
Y
25
7
7
-
-
-
-
4
-
6
7
8
-
N
=
5
3
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
E
=
5
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
G
=
7
6
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
E
=
5
7
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
T
=
2
8
1
T
2
2
2
-
-
2
-
4
-
6
-
8
-
I
=
9
9
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
C
=
3
10
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
S
=
1
11
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
-
-
54
-
11
SYNERGETICS
144
72
54
-
2
2
3
4
15
6
14
8
18
-
-
5+4
-
1+1
-
1+4+4
7+2
3+6
-
-
-
-
-
1+5
-
1+4
-
1+8
-
-
9
-
2
SYNERGETICS
9
9
9
-
2
2
3
4
6
6
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
-
-
-
11
SYNERGETICS
144
72
54
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+4+4
7+2
3+6
-
-
-
-
-
-
-
-
-
-
S
-
-
-
11
SYNERGETICS
9
9
9
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
S
=
1
11
1
S
19
10
1
-
1
-
-
4
-
6
-
8
-
T
=
2
8
1
T
2
2
2
-
-
2
-
4
-
6
-
8
-
C
=
3
10
1
C
3
3
3
-
-
-
3
4
-
6
-
8
-
N
=
5
3
1
N
14
5
5
-
-
-
-
4
5
6
-
8
-
E
=
5
4
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
E
=
5
7
1
E
5
5
5
-
-
-
-
4
5
6
-
8
-
Y
=
7
2
1
Y
25
7
7
-
-
-
-
4
-
6
7
8
-
G
=
7
6
1
G
7
7
7
-
-
-
-
4
-
6
7
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
4
-
6
-
8
9
I
=
9
9
1
I
9
9
9
-
-
-
-
4
-
6
-
8
9
-
-
54
-
11
SYNERGETICS
144
72
54
-
2
2
3
4
15
6
14
8
18
-
-
5+4
-
1+1
-
1+4+4
7+2
3+6
-
-
-
-
-
1+5
-
1+4
-
1+8
-
-
9
-
2
SYNERGETICS
9
9
9
-
2
2
3
4
6
6
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
5
7
9
S
-
-
-
11
SYNERGETICS
144
72
54
-
-
-
-
-
-
-
-
-
-
-
-
-
1+4+4
7+2
3+6
-
-
-
-
-
-
-
S
-
-
-
11
SYNERGETICS
9
9
9
-
1
2
3
5
7
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
S
=
1
11
1
S
19
10
1
-
1
-
-
-
-
-
T
=
2
8
1
T
2
2
2
-
-
2
-
-
-
-
C
=
3
10
1
C
3
3
3
-
-
-
3
-
-
-
N
=
5
3
1
N
14
5
5
-
-
-
-
5
-
-
E
=
5
4
1
E
5
5
5
-
-
-
-
5
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
5
-
-
Y
=
7
2
1
Y
25
7
7
-
-
-
-
-
7
-
G
=
7
6
1
G
7
7
7
-
-
-
-
-
7
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
9
I
=
9
9
1
I
9
9
9
-
-
-
-
-
-
9
-
-
54
-
11
SYNERGETICS
144
72
54
-
2
2
3
15
14
18
-
-
5+4
-
1+1
-
1+4+4
7+2
3+6
-
-
-
-
1+5
1+4
1+8
-
-
9
-
2
SYNERGETICS
9
9
9
-
2
2
3
6
5
9

 

 

https://en.wikipedia.org/wiki/Synergetics
Synergetics can refer to: Synergetics (Fuller), a study of systems behavior suggested by Buckminster Fuller; Synergetics (Haken), a school of thought on ...

 

Synergetics (Fuller) - Wikipedia
https://en.wikipedia.org/wiki/Synergetics_(Fuller)

Synergetics is the empirical study of systems in transformation, with an emphasis on total system behavior unpredicted by the behavior of any isolated ...
?Definition · ?Tetrahedral accounting · ?Starting with Universe · ?Intuitive geometry
Synergetics is the empirical study of systems in transformation, with an emphasis on total system behavior unpredicted by the behavior of any isolated components, including humanity's role as both participant and observer.

Since systems are identifiable at every scale from the quantum level to the cosmic, and humanity both articulates the behavior of these systems and is composed of these systems, synergetics is a very broad discipline, and embraces a broad range of scientific and philosophical studies including tetrahedral and close-packed-sphere geometries, thermodynamics, chemistry, psychology, biochemistry, economics, philosophy and theology. Despite a few mainstream endorsements such as articles by Arthur Loeb and the naming of a molecule "buckminsterfullerene", synergetics remains an iconoclastic subject ignored by most traditional curricula and academic departments.

Buckminster Fuller (1895-1983) coined the term and attempted to define its scope in his two volume work Synergetics.[1][2][3] His oeuvre inspired many researchers to tackle branches of synergetics. Three examples: Haken explored self-organizing structures of open systems far from thermodynamic equilibrium, Amy Edmondson explored tetrahedral and icosahedral geometry, Stafford Beer tackled geodesics in the context of social dynamics, and Nystrom proposed a theory of computational cosmography.[4] Many other researchers toil today on aspects of Synergetics, though many deliberately distance themselves from Fuller's broad all-encompassing definition, given its problematic attempt to differentiate and relate all aspects of reality including the ideal and the physically realized, the container and the contained, the one and the many, the observer and the observed, the human microcosm and the universal macrocosm.
"Synergetics" is defined by R. Buckminster Fuller (1895-1983) in his two books Synergetics: Explorations in the Geometry of Thinking and Synergetics 2: Explorations in the Geometry of Thinking as:

A system of mensuration employing 60-degree vectorial coordination comprehensive to both physics and chemistry, and to both arithmetic and geometry, in rational whole numbers ... Synergetics explains much that has not been previously illuminated ... Synergetics follows the cosmic logic of the structural mathematics strategies of nature, which employ the paired sets of the six angular degrees of freedom, frequencies, and vectorially economical actions and their multi-alternative, equi-economical action options ... Synergetics discloses the excruciating awkwardness characterizing present-day mathematical treatment of the interrelationships of the independent scientific disciplines as originally occasioned by their mutual and separate lacks of awareness of the existence of a comprehensive, rational, coordinating system inherent in nature.[5]

Other passages in Synergetics that outline the subject are its introduction (The Wellspring of Reality) and the section on Nature's Coordination (410.01). The chapter on Operational Mathematics (801.00-842.07) provides an easy to follow, easy to build introduction to some of Fuller's geometrical modeling techniques. So this chapter can help a new reader become familiar with Fuller's approach, style and geometry. One of Fuller's clearest expositions on "the geometry of thinking" occurs in the two part essay "Omnidirectional Halo" which appears in his book No More Secondhand God.[6]

Amy Edmondson describes synergetics "in the broadest terms, as the study of spatial complexity, and as such is an inherently comprehensive discipline." [7] In her PhD study, Cheryl Clark synthesizes the scope of synergetics as "the study of how nature works, of the patterns inherent in nature, the geometry of environmental forces that impact on humanity."[8]

Here's an abridged list of some of the discoveries Fuller claims for Synergetics again quoting directly:
The rational volumetric quantation or constant proportionality of the octahedron, the cube, the rhombic triacontahedron, and the rhombic dodecahedron when referenced to the tetrahedron as volumetric unity.
The trigonometric identification of the great-circle trajectories of the seven axes of symmetry with the 120 basic disequilibrium LCD triangles of the spherical icosahedron. (See Sec. 1043.00.)
The rational identification of number with the hierarchy of all the geometries.
The A and B Quanta Modules.
The volumetric hierarchy of Platonic and other symmetrical geometricals based on the tetrahedron and the A and B Quanta Modules as unity of coordinate mensuration.
The identification of the nucleus with the vector equilibrium.
Omnirationality: the identification of triangling and tetrahedroning with second- and third-powering factors.
Omni-60-degree coordination versus 90-degree coordination.
The integration of geometry and philosophy in a single conceptual system providing a common language and accounting for both the physical and metaphysical.[9]

Significance[edit]
Several authors have tried to characterize the importance of synergetics. Amy Edmonson asserts that "Experience with synergetics encourages a new way of approaching and solving problems. Its emphasis on visual and spatial phenomena combined with Fuller's holistic approach fosters the kind of lateral thinking which so often leads to creative breakthroughs.".[10] Cheryl Clark points out that "In his thousands of lectures, Fuller urged his audiences to study synergetics, saying 'I am confident that humanity's survival depends on all of our willingness to comprehend feelingly the way nature works.'"[11]

 

S
=
1
-
-
11
SYNERGETICS
144
72
54
-
-
-
-
-
1+1
-
1+4+4
7+2
3+6
S
=
1
-
-
2
SYNERGETICS
9
9
9

 

 

SYNERGY

synergy | Definition of synergy in English by Oxford Dictionaries
https://en.oxforddictionaries.com/definition/synergy

The interaction or cooperation of two or more organizations, substances, or other agents to produce a combined effect greater than the sum of their separate effects.

Syzygy | Definition of Syzygy by Merriam-Webster

www.merriam-webster.com/dictionary/syzygy
the nearly straight-line configuration of three celestial bodies (as the sun, moon, and earth during a solar or lunar eclipse) in a gravitational system. Editor's note: ...

 

SYZYGY 178777 SYZYGY

SYZYGY 127 SYZYGY

SYZYGY 37 SYZYGY

SYZYGY 10 SYZYGY

SYZYGY 1 SYZYGY

SYZYGY 178777 SYZYGY

 

Syzygy | Define Syzygy at Dictionary.com

www.dictionary.com/browse/syzygy

noun (pl) -gies. 1. either of the two positions (conjunction or opposition) of a celestial body when sun, earth, and the body lie in a straight line: the moon is at syzygy when full. 2. (in classical prosody) a metrical unit of two feet.

 

syzygy - definition of syzygy in English | Oxford Dictionaries

https://www.oxforddictionaries.com/definition/english/syzygy

1Astronomy. A conjunction or opposition, especially of the moon with the sun. 'the planets were aligned in syzygy' 'In case you didn't know, Earth, the Moon, and the Sun are in syzygy every time they line up in space.' 'Maximum gravitation force occurs when a syzygy and perigee occur on the same day as perihelion.'

 

syzygy

/'s?z?d?i/
noun
noun: syzygy; plural noun: syzygies

1. Astronomy
a conjunction or opposition, especially of the moon with the sun.
"the planets were aligned in syzygy"
2. a pair of connected or corresponding things.

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
SYZYGY
-
-
-
-
-
2
3
4
5
6
-
-
9
S
=
1
-
1
S
19
10
1
-
1
2
3
4
5
6
-
-
9
Y
=
7
-
1
Y
25
7
7
-
-
2
3
4
5
6
7
-
9
Z
=
8
-
1
Z
26
8
8
-
-
2
3
4
5
6
-
8
9
Y
=
7
-
1
Y
25
7
7
-
-
2
3
4
5
6
7
-
9
G
=
7
-
1
G
7
7
7
-
-
2
3
4
5
6
7
-
9
Y
=
7
-
1
Y
25
7
7
-
-
2
3
4
5
6
7
-
9
-
-
37
-
6
SYZYGY
127
46
37
-
1
2
3
4
5
6
28
8
9
-
-
3+7
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
2+8
-
-
-
10
-
6
SYZYGY
1
10
10
-
1
2
3
4
5
6
10
8
9
-
-
1+0
-
-
-
1+0
1+0
-
-
-
-
-
-
-
1+0
-
-
-
1
-
6
SYZYGY
1
1
1
-
1
2
3
4
5
6
1
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
7
8
-
-
-
-
-
SYZYGY
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
Y
=
7
-
1
Y
25
7
7
-
-
7
-
Z
=
8
-
1
Z
26
8
8
-
-
-
8
Y
=
7
-
1
Y
25
7
7
-
-
7
-
G
=
7
-
1
G
7
7
7
-
-
7
-
Y
=
7
-
1
Y
25
7
7
-
-
7
-
-
-
37
-
6
SYZYGY
127
46
37
-
1
28
8
-
-
3+7
-
-
1+0+0
4+6
3+7
-
-
2+8
-
-
10
-
6
SYZYGY
1
10
10
-
1
10
8
-
-
1+0
-
-
-
1+0
1+0
-
-
1+0
-
-
1
-
6
SYZYGY
1
1
1
-
1
1
8

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
SYZYGY
-
-
-
-
-
2
3
4
5
6
-
-
9
S
=
1
-
1
S
19
10
1
-
1
2
3
4
5
6
-
-
9
Y
=
7
-
1
Y
25
7
7
-
-
2
3
4
5
6
7
-
9
Y
=
7
-
1
Y
25
7
7
-
-
2
3
4
5
6
7
-
9
G
=
7
-
1
G
7
7
7
-
-
2
3
4
5
6
7
-
9
Y
=
7
-
1
Y
25
7
7
-
-
2
3
4
5
6
7
-
9
Z
=
8
-
1
Z
26
8
8
-
-
2
3
4
5
6
-
8
9
-
-
37
-
6
SYZYGY
127
46
37
-
1
2
3
4
5
6
28
8
9
-
-
3+7
-
-
1+0+0
4+6
3+7
-
-
-
-
-
-
-
2+8
-
-
-
10
-
6
SYZYGY
1
10
10
-
1
2
3
4
5
6
10
8
9
-
-
1+0
-
-
-
1+0
1+0
-
-
-
-
-
-
-
1+0
-
-
-
1
-
6
SYZYGY
1
1
1
-
1
2
3
4
5
6
1
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
7
8
-
-
-
-
-
SYZYGY
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
Y
=
7
-
1
Y
25
7
7
-
-
7
-
Y
=
7
-
1
Y
25
7
7
-
-
7
-
G
=
7
-
1
G
7
7
7
-
-
7
-
Y
=
7
-
1
Y
25
7
7
-
-
7
-
Z
=
8
-
1
Z
26
8
8
-
-
-
8
-
-
37
-
6
SYZYGY
127
46
37
-
1
28
8
-
-
3+7
-
-
1+0+0
4+6
3+7
-
-
2+8
-
-
10
-
6
SYZYGY
1
10
10
-
1
10
8
-
-
1+0
-
-
-
1+0
1+0
-
-
1+0
-
-
1
-
6
SYZYGY
1
1
1
-
1
1
8

 

 

Synergy | Define Synergy at Dictionary.com
www.dictionary.com/browse/synergy
the interaction of elements that when combined produce a total effect that is greater than the sum of the individual elements, contributions, etc.; synergism. ... “Synergy is the creation of a whole that is greater than the sum of its parts.“. ... The interaction of two or more agents

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
SYNERGY
-
-
-
-
-
2
3
4
-
6
-
8
-
S
=
1
-
1
S
19
10
1
-
1
2
3
4
-
6
-
8
-
Y
=
7
-
1
Y
25
7
7
-
-
2
3
4
-
6
7
8
-
N
=
5
-
1
N
14
5
5
-
-
2
3
4
5
6
-
8
-
E
=
5
-
1
E
5
5
5
-
-
2
3
4
5
6
-
8
-
R
=
9
-
1
R
18
9
9
-
-
2
3
4
-
6
-
8
9
G
=
7
-
1
G
7
7
7
-
-
2
3
4
-
6
7
8
-
Y
=
7
-
1
Y
25
7
7
-
-
2
3
4
-
6
7
8
-
-
-
41
-
7
SYNERGY
113
50
41
-
1
2
3
4
10
6
21
8
9
-
-
4+1
-
-
1+1+3
5+0
4+1
-
-
-
-
-
1+0
-
2+1
-
-
-
5
-
7
SYNERGY
5
5
5
-
1
2
3
4
1
6
3
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
5
7
9
-
-
-
-
-
SYNERGY
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
7
-
N
=
5
-
1
N
14
5
5
-
-
5
-
-
E
=
5
-
1
E
5
5
5
-
-
5
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
9
G
=
7
-
1
G
7
7
7
-
-
-
7
-
Y
=
7
-
1
Y
25
7
7
-
-
-
7
-
-
-
41
-
7
SYNERGY
113
50
41
-
1
10
21
9
-
-
4+1
-
-
1+1+3
5+0
4+1
-
-
1+0
2+1
-
-
5
-
7
SYNERGY
5
5
5
-
1
1
3
9

 

 

BREATHE ON ME BREATH OF GOD

 

 

HOLY BIBLE

Scofield References

Page 7

GENESIS

C 2 V 7

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

 

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

 

 

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

 

 

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

 

 

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

 

-
INTERCONNECTEDNESS
-
-
-
-
-
1
I
9
9
9
-
-
1
N
14
5
5
-
5
1
T
20
2
2
-
-
1
E
5
5
5
-
5
1
R
18
9
9
-
-
2
CO
18
9
9
-
-
1
N
14
5
5
-
5
1
N
14
5
5
-
5
1
E
5
5
5
-
5
2
CT
23
5
5
-
5
1
E
5
5
5
-
5
1
D
4
4
4
-
-
1
N
14
5
5
-
5
1
E
5
5
5
-
5
2
SS
38
20
2
-
-
18
INTERCONNECTEDNESS
206
98
80
-
45
1+8
-
2+0+6
9+8
8+0
-
4+5
9
INTERCONNECTEDNESS
8
17
8
-
9
-
-
-
1+7
3+5
-
-
9
INTERCONNECTEDNESS
8
8
8
-
9

 

 

-
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
2
CO
18
9
9
-
-
-
-
9
1
N
14
5
5
-
-
-
5
-
1
N
14
5
5
-
-
-
5
-
1
E
5
5
5
-
-
-
5
-
2
CT
23
5
5
-
-
-
5
-
1
E
5
5
5
-
-
-
5
-
1
D
4
4
4
-
-
4
-
-
1
N
14
5
5
-
-
-
5
-
1
E
5
5
5
-
-
-
5
-
2
SS
38
20
2
-
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
I
=
9
-
5
INTER
66
30
3
C
=
3
-
13
CONNECTEDNESS
140
50
5
-
-
21
-
23
First Total
271
109
10
-
-
2+1
-
2+3
Add to Reduce
2+7+1
1+0+9
1+0
-
-
3
-
5
Second Total
10
10
1
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
3
-
6
Essence of Number
1
1
1

 

 

T
=
2
-
3
THE
33
15
6
L
=
3
-
5
LORDS
68
32
5
P
=
7
-
6
PRAYER
83
38
2
-
-
12
-
14
First Total
184
85
13
-
-
1+2
-
1+4
Add to Reduce
1+8+4
8+5
1+3
-
-
3
-
5
Second Total
13
13
4
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
3
-
5
Essence of Number
4
4
4

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
L
=
3
-
5
LORDS
68
32
5
-
-
-
-
-
-
-
-
-
-
P
=
7
-
6
PRAYER
83
38
2
-
-
-
-
-
-
-
-
-
-
-
-
12
-
14
First Total
184
85
13
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
15
-
3
-
33
15
15
-
-
-
-
-
-
-
-
-
-
L
=
3
4
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
-
23
-
5
-
68
32
23
-
-
-
-
-
-
-
-
-
-
P
=
7
9
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
14
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
38
-
6
-
83
38
38
-
2
2
3
4
10
6
14
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
1+4
-
2+7
-
-
76
-
3
THE
33
15
6
-
2
2
3
4
1
6
5
8
9
-
-
7+6
-
5
LORDS
68
32
5
-
-
-
-
-
-
-
-
-
-
-
-
13
-
6
PRAYER
83
38
2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
14
First Total
184
85
13
-
2
2
3
4
1
6
5
8
9
-
-
-
-
1+4
Add to Reduce
1+8+4
8+5
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
Second Total
13
13
4
-
2
2
3
4
1
6
5
8
9
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
Essence of Number
4
4
4
-
2
2
3
4
1
6
5
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
L
=
3
-
5
LORDS
68
32
5
-
-
-
-
-
-
-
-
-
-
P
=
7
-
6
PRAYER
83
38
2
-
-
-
-
-
-
-
-
-
-
-
-
12
-
14
First Total
184
85
13
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
L
=
3
4
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
P
=
7
9
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
14
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
2
2
3
4
10
6
14
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
1+4
-
2+7
-
-
76
-
3
THE
33
15
6
-
2
2
3
4
1
6
5
8
9
-
-
7+6
-
5
LORDS
68
32
5
-
-
-
-
-
-
-
-
-
-
-
-
13
-
6
PRAYER
83
38
2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
14
First Total
184
85
13
-
2
2
3
4
1
6
5
8
9
-
-
-
-
1+4
Add to Reduce
1+8+4
8+5
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
Second Total
13
13
4
-
2
2
3
4
1
6
5
8
9
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
Essence of Number
4
4
4
-
2
2
3
4
1
6
5
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
L
=
3
-
5
LORDS
68
32
5
-
-
-
-
-
-
-
-
-
-
P
=
7
-
6
PRAYER
83
38
2
-
-
-
-
-
-
-
-
-
-
-
-
12
-
14
First Total
184
85
13
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
8
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
11
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
4
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
13
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
5
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
9
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
Y
=
7
12
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
6
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
10
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
14
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
2
2
3
4
10
6
14
8
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+0
-
1+4
-
2+7
-
-
76
-
3
THE
33
15
6
-
2
2
3
4
1
6
5
8
9
-
-
7+6
-
5
LORDS
68
32
5
-
-
-
-
-
-
-
-
-
-
-
-
13
-
6
PRAYER
83
38
2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
14
First Total
184
85
13
-
2
2
3
4
1
6
5
8
9
-
-
-
-
1+4
Add to Reduce
1+8+4
8+5
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
Second Total
13
13
4
-
2
2
3
4
1
6
5
8
9
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
Essence of Number
4
4
4
-
2
2
3
4
1
6
5
8
9

 

 

3
THE
33
15
6
4
LAST
52
7
7
6
SUPPER
95
32
5
13
Add to Reduce
180
54
18
1+3
Reduce to Deduce
1+8+0
5+4
1+8
4
Essence of Number
9
9
9

 

 

T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LAST
52
7
7
S
=
1
-
6
SUPPER
95
32
5
-
-
6
-
13
Add to Reduce
180
54
18
-
-
-
-
1+3
Reduce to Deduce
1+8+0
5+4
1+8
-
-
6
-
4
Essence of Number
9
9
9

 

 

 

THE LAST SUPPER 1977

 

 

T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LAST
52
7
7
J
=
1
-
9
JUDGEMENT
99
36
9
-
-
6
-
16
First Total
184
58
22
-
-
-
-
1+6
Add to Reduce
1+8+4
5+8
2+2
-
-
6
-
7
Second Total
13
13
4
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
6
-
7
Essence of Number
4
4
4

 

 

THE LAST JUDGEMENT

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LAST
52
16
7
-
-
-
-
-
-
-
-
-
-
J
=
1
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
-
-
6
-
16
-
184
67
22
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
6
-
-
9
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
6
-
8
9
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
6
-
-
9
-
15
-
3
-
33
15
15
-
-
-
-
-
-
-
-
-
-
L
=
3
4
1
L
12
3
3
-
-
-
3
-
-
6
-
-
9
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
6
-
-
9
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
6
-
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
6
-
-
9
-
7
-
4
-
52
16
7
-
-
-
-
-
-
-
-
-
-
J
=
1
8
1
J
10
1
1
-
1
-
-
-
-
6
-
-
9
U
=
3
9
1
U
21
3
3
-
-
-
3
-
-
6
-
-
9
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
6
-
-
9
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
6
7
-
9
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
6
-
-
9
M
=
4
13
1
M
13
4
4
-
-
-
-
4
-
6
-
-
9
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
6
-
-
9
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
6
-
-
9
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
6
-
-
9
36
-
9
-
99
36
36
-
3
6
6
8
20
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+0
-
-
-
-
-
-
58
-
3
THE
33
15
6
-
3
6
6
8
2
6
7
8
9
-
-
5+8
-
4
LAST
52
16
7
-
-
-
-
-
-
-
-
-
-
-
-
13
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
-
-
4
-
16
First Total
184
67
22
-
3
6
6
8
2
6
7
8
9
-
-
-
-
1+6
Add to Reduce
1+8+4
6+7
2+2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
7
Second Total
13
13
4
-
3
6
6
8
2
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
7
Essence of Number
4
4
4
-
3
6
6
8
2
6
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LAST
52
16
7
-
-
-
-
-
-
-
-
-
-
J
=
1
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
-
-
6
-
16
-
184
67
22
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
6
-
-
9
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
6
-
8
9
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
6
-
-
9
L
=
3
4
1
L
12
3
3
-
-
-
3
-
-
6
-
-
9
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
6
-
-
9
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
6
-
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
6
-
-
9
J
=
1
8
1
J
10
1
1
-
1
-
-
-
-
6
-
-
9
U
=
3
9
1
U
21
3
3
-
-
-
3
-
-
6
-
-
9
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
6
-
-
9
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
6
7
-
9
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
6
-
-
9
M
=
4
13
1
M
13
4
4
-
-
-
-
4
-
6
-
-
9
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
6
-
-
9
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
6
-
-
9
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
6
-
-
9
-
-
-
-
-
-
-
-
-
-
3
6
6
8
20
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+0
-
-
-
-
-
-
58
-
3
THE
33
15
6
-
3
6
6
8
2
6
7
8
9
-
-
5+8
-
4
LAST
52
16
7
-
-
-
-
-
-
-
-
-
-
-
-
13
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
-
-
4
-
16
First Total
184
67
22
-
3
6
6
8
2
6
7
8
9
-
-
-
-
1+6
Add to Reduce
1+8+4
6+7
2+2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
7
Second Total
13
13
4
-
3
6
6
8
2
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
7
Essence of Number
4
4
4
-
3
6
6
8
2
6
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LAST
52
16
7
-
-
-
-
-
-
-
-
-
-
J
=
1
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
-
-
6
-
16
-
184
67
22
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
6
-
-
9
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
6
-
-
9
J
=
1
8
1
J
10
1
1
-
1
-
-
-
-
6
-
-
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
6
-
-
9
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
6
-
-
9
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
6
-
-
9
L
=
3
4
1
L
12
3
3
-
-
-
3
-
-
6
-
-
9
U
=
3
9
1
U
21
3
3
-
-
-
3
-
-
6
-
-
9
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
6
-
-
9
M
=
4
13
1
M
13
4
4
-
-
-
-
4
-
6
-
-
9
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
6
-
-
9
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
6
-
-
9
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
6
-
-
9
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
6
-
-
9
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
6
7
-
9
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
6
-
8
9
-
-
-
-
-
-
-
-
-
-
3
6
6
8
20
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+0
-
-
-
-
-
-
58
-
3
THE
33
15
6
-
3
6
6
8
2
6
7
8
9
-
-
5+8
-
4
LAST
52
16
7
-
-
-
-
-
-
-
-
-
-
-
-
13
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
-
-
4
-
16
First Total
184
67
22
-
3
6
6
8
2
6
7
8
9
-
-
-
-
1+6
Add to Reduce
1+8+4
6+7
2+2
-
-
-
-
-
-
-
-
-
-
-
-
4
-
7
Second Total
13
13
4
-
3
6
6
8
2
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
7
Essence of Number
4
4
4
-
3
6
6
8
2
6
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
8
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
L
=
3
-
4
LAST
52
16
7
-
-
-
-
-
-
-
-
J
=
1
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
6
-
16
-
184
67
22
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
8
A
=
1
5
1
A
1
1
1
-
1
-
-
-
-
-
-
S
=
1
6
1
S
19
10
1
-
1
-
-
-
-
-
-
J
=
1
8
1
J
10
1
1
-
1
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
T
=
2
7
1
T
20
2
2
-
-
2
-
-
-
-
-
T
=
2
16
1
T
20
2
2
-
-
2
-
-
-
-
-
L
=
3
4
1
L
12
3
3
-
-
-
3
-
-
-
-
U
=
3
9
1
U
21
3
3
-
-
-
3
-
-
-
-
D
=
4
10
1
D
4
4
4
-
-
-
-
4
-
-
-
M
=
4
13
1
M
13
4
4
-
-
-
-
4
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
E
=
5
12
1
E
5
5
5
-
-
-
-
-
5
-
-
E
=
5
14
1
E
5
5
5
-
-
-
-
-
5
-
-
N
=
5
15
1
N
14
5
5
-
-
-
-
-
5
-
-
G
=
7
11
1
G
7
7
7
-
-
-
-
-
-
7
-
H
=
8
2
1
H
8
8
8
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
3
6
6
8
20
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2+0
-
-
-
-
58
-
3
THE
33
15
6
-
3
6
6
8
2
7
8
-
-
5+8
-
4
LAST
52
16
7
-
-
-
-
-
-
-
-
-
-
13
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
4
-
16
First Total
184
67
22
-
3
6
6
8
2
7
8
-
-
-
-
1+6
Add to Reduce
1+8+4
6+7
2+2
-
-
-
-
-
-
-
-
-
-
4
-
7
Second Total
13
13
4
-
3
6
6
8
2
7
8
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
4
-
7
Essence of Number
4
4
4
-
3
6
6
8
2
7
8

 

 

LAST JUDGEMENT

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
4
LAST
52
16
7
-
-
-
-
-
-
-
-
-
-
J
=
1
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
-
-
4
-
13
Add to Reduce
151
52
16
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
6
-
8
9
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
6
-
8
9
S
=
1
3
1
S
19
10
1
-
1
-
-
-
-
6
-
8
9
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
6
-
8
9
J
=
1
5
1
J
10
1
1
-
1
-
-
-
-
6
-
8
9
U
=
3
6
1
U
21
3
3
-
-
-
3
-
-
6
-
8
9
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
6
-
8
9
G
=
7
8
1
G
7
7
7
-
-
-
-
-
-
6
7
8
9
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
6
-
8
9
M
=
4
10
1
M
13
4
4
-
-
-
-
4
-
6
-
8
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
9
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
6
-
8
9
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
6
-
8
9
-
-
-
-
-
-
-
-
-
-
3
4
6
8
15
6
7
8
9
-
-
43
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
-
-
-
5+8
-
4
LAST
52
16
7
-
3
4
6
8
6
6
7
8
9
-
-
13
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
-
-
4
-
13
Add to Reduce
151
52
16
-
3
4
6
8
6
6
7
8
9
-
-
-
-
1+3
Reduce to Deduce
1+5+1
5+2
1+6
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
Essence of Number
7
7
7
-
3
4
6
8
6
6
7
8
9

 

 

LAST JUDGEMENT

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
4
LAST
52
16
7
-
-
-
-
-
-
-
-
-
-
J
=
1
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
-
-
4
-
13
Add to Reduce
151
52
16
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
6
-
8
9
S
=
1
3
1
S
19
10
1
-
1
-
-
-
-
6
-
8
9
J
=
1
5
1
J
10
1
1
-
1
-
-
-
-
6
-
8
9
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
6
-
8
9
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
6
-
8
9
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
6
-
8
9
U
=
3
6
1
U
21
3
3
-
-
-
3
-
-
6
-
8
9
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
6
-
8
9
M
=
4
10
1
M
13
4
4
-
-
-
-
4
-
6
-
8
9
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
6
-
8
9
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
6
-
8
9
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
6
-
8
9
G
=
7
8
1
G
7
7
7
-
-
-
-
-
-
6
7
8
9
-
-
-
-
-
-
-
-
-
-
3
4
6
8
15
6
7
8
9
-
-
43
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
-
-
-
5+8
-
4
LAST
52
16
7
-
3
4
6
8
6
6
7
8
9
-
-
13
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
-
-
-
4
-
13
Add to Reduce
151
52
16
-
3
4
6
8
6
6
7
8
9
-
-
-
-
1+3
Reduce to Deduce
1+5+1
5+2
1+6
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
Essence of Number
7
7
7
-
3
4
6
8
6
6
7
8
9

 

 

LAST JUDGEMENT

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
L
=
3
-
4
LAST
52
16
7
-
-
-
-
-
-
-
J
=
1
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
4
-
13
Add to Reduce
151
52
16
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
7
A
=
1
2
1
A
1
1
1
-
1
-
-
-
-
-
S
=
1
3
1
S
19
10
1
-
1
-
-
-
-
-
J
=
1
5
1
J
10
1
1
-
1
-
-
-
-
-
T
=
2
4
1
T
20
2
2
-
-
2
-
-
-
-
T
=
2
13
1
T
20
2
2
-
-
2
-
-
-
-
L
=
3
1
1
L
12
3
3
-
-
-
3
-
-
-
U
=
3
6
1
U
21
3
3
-
-
-
3
-
-
-
D
=
4
7
1
D
4
4
4
-
-
-
-
4
-
-
M
=
4
10
1
M
13
4
4
-
-
-
-
4
-
-
E
=
5
9
1
E
5
5
5
-
-
-
-
-
5
-
E
=
5
11
1
E
5
5
5
-
-
-
-
-
5
-
N
=
5
12
1
N
14
5
5
-
-
-
-
-
5
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
3
4
6
8
15
7
-
-
43
-
-
-
-
-
-
-
-
-
-
-
1+5
-
-
-
5+8
-
4
LAST
52
16
7
-
3
4
6
8
6
7
-
-
13
-
9
JUDGEMENT
99
36
9
-
-
-
-
-
-
-
-
-
4
-
13
Add to Reduce
151
52
16
-
3
4
6
8
6
7
-
-
-
-
1+3
Reduce to Deduce
1+5+1
5+2
1+6
-
-
-
-
-
-
-
-
-
4
-
4
Essence of Number
7
7
7
-
3
4
6
8
6
7

 

 

LAST JUDGEMENT

 

B
=
2
-
5
BLACK
29
11
2
B
=
2
-
1
B
2
2
2
L
=
3
-
4
LACK
27
9
9
O
=
6
-
2
OF
21
12
3
L
=
3
-
5
LIGHT
56
29
2
B
=
2
-
2
BE
7
7
7
-
-
18
-
19
First Total
142
70
25
-
-
1+8
-
1+9
Add to Reduce
1+4+2
7+0
2+5
-
-
9
-
10
Second Total
7
7
7
-
-
-
-
1+0
Reduce to Deduce
-
-
-
-
-
9
-
1
Essence of Number
7
7
7

 

 

The Island Where Time Stands Still (Gregory Sallust Book 9)
by Dennis Wheatley 1936

 

T
=
2
-
3
THE
33
15
6
I
=
9
-
6
ISLAND
59
23
5
W
=
4
-
5
WHERE
59
32
5
T
=
2
-
4
TIME
47
20
2
S
=
1
-
6
STANDS
77
14
5
S
=
1
-
5
STILL
72
18
9
-
-
19
-
29
First Total
347
122
32
-
-
1+9
-
2+9
Add to Reduce
3+4+7
1+2+2
3+2
-
-
10
-
11
Second Total
14
5
5
-
-
1+0
-
1+1
Reduce to Deduce
1+4
-
-
-
-
1
-
2
Essence of Number
5
5
5

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
M
=
4
-
4
MIND
40
22
4
-
-
-
-
4
-
-
-
-
-
B
=
2
-
4
BORN
49
22
4
-
-
-
-
4
-
-
-
-
-
S
=
1
-
4
SONS
67
13
4
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
5
THOSE
67
22
4
-
-
-
-
4
-
-
-
-
-
P
=
7
-
6
PATENT
76
22
4
-
-
-
-
4
-
-
-
-
-
P
=
7
-
7
PATIENT
85
31
4
-
-
-
-
4
-
-
-
-
-
P
=
7
-
8
PATENTED
85
31
4
-
-
-
-
4
-
-
-
-
-
P
=
7
-
7
PATTERN
94
31
4
-
-
-
-
4
-
-
-
-
-
M
=
4
-
6
MAKERS
67
22
4
-
-
-
-
4
-
-
-
-
-
-
-
41
-
51
Add to Reduce
630
216
36
-
1
2
3
36
3
3
9
9
9
-
-
4+1
-
5+1
Reduce to Deduce
6+3+0
2+1+6
3+6
-
-
-
-
3+6
-
-
-
-
-
-
5
-
6
Essence of Number
9
9
9
-
1
2
3
9
3
3
5
7
9

 

MIND BORN SONS

THOSE PATENT PATIENT PATENTED PATTERN MAKERS

 

 

-
NINETEEN
-
-
-
1
N
14
5
5
1
I
9
9
9
1
N
14
5
5
1
E
5
5
5
1
T
20
2
2
1
E
5
5
5
1
E
5
5
5
1
N
14
5
5
8
NINETEEN
-
-
-

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
NINETEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
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
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
41
-
8
NINETEEN
86
41
41
-
1
2
3
4
30
6
7
8
9
-
-
4+1
-
-
8+6
4+1
4+1
-
-
-
-
-
3+0
-
-
-
-
-
5
-
8
NINETEEN
14
5
5
-
1
2
3
4
3
6
7
8
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
8
NINETEEN
5
5
5
-
1
2
3
4
3
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
2
5
9
-
-
-
-
-
NINETEEN
-
-
-
-
-
-
-
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
-
T
=
2
-
1
T
20
2
2
-
2
-
-
E
=
5
-
1
E
5
5
5
-
-
5
-
E
=
5
-
1
E
5
5
5
-
-
5
-
N
=
5
-
1
N
14
5
5
-
-
5
-
-
-
41
-
8
NINETEEN
86
41
41
-
2
30
9
-
-
4+1
-
-
8+6
4+1
4+1
-
-
3+0
-
-
5
-
8
NINETEEN
14
5
5
-
2
3
9
-
-
-
-
-
-
1+4
-
-
-
-
-
-
-
5
-
8
NINETEEN
5
5
5
-
2
3
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
INBETWEEN
-
-
-
-
-
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
B
=
2
-
1
B
2
2
2
-
-
2
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
W
=
5
-
1
W
23
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
-
-
-
-
-
-
43
-
9
INBETWEEN
97
43
43
-
1
4
3
4
30
6
7
8
9
-
-
4+3
-
-
9+7
4+3
4+3
-
-
-
-
-
3+0
-
-
-
-
-
7
-
9
INBETWEEN
16
7
7
-
1
4
3
4
3
6
7
8
9
-
-
-
-
-
-
1+6
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
9
INBETWEEN
7
7
7
-
1
4
3
4
3
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
2
5
9
-
-
-
-
-
INBETWEEN
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
5
-
B
=
2
-
1
B
2
2
2
-
2
-
-
E
=
5
-
1
E
5
5
5
-
-
5
-
T
=
2
-
1
T
20
2
2
-
2
-
-
W
=
5
-
1
W
23
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
-
-
-
43
-
9
INBETWEEN
97
43
43
-
4
30
9
-
-
4+3
-
-
9+7
4+3
4+3
-
-
3+0
-
-
7
-
9
INBETWEEN
16
7
7
-
4
3
9
-
-
-
-
-
-
1+6
-
-
-
-
-
-
-
7
-
9
INBETWEEN
7
7
7
-
4
3
9

 

 

THE

BALANCING

OF

BETWEEN IN BETWEEN

 

 

-
BETWEEN
-
-
-
1
B
2
2
2
1
E
5
5
5
1
T
20
2
2
1
W
23
5
5
1
E
5
5
5
1
E
5
5
5
1
N
14
5
5
7
BETWEEN
74
29
29
-
-
7+4
2+9
2+9
7
BETWEEN
11
11
11
-
-
1+1
1+1
1+1
7
BETWEEN
2
2
2

 

 

BETWEEN IN BETWEEN

2+5+2+5+5+5+5 +9+5 +2 5 2 5 5 5 5

9

2222

5 5 5 5 5 5 5 5 5 5 5

2+5+2+5+5+5+5 +9+5 +2 5 2 5 5 5 5

BETWEEN IN BETWEEN

 

 

-
BETWEEN
-
-
-
1
B
2
2
2
1
E
5
5
5
1
T
2
2
2
4
WEEN
5
5
5
7
BETWEEN
74
29
29
-
-
7+4
2+9
2+9
7
BETWEEN
11
11
11
-
-
1+1
1+1
1+1
7
BETWEEN
2
2
2

 

 

-
BETWEEN
-
-
-
1
B
2
2
2
1
E
5
5
5
1
T
20
2
2
1
W
23
5
5
1
E
5
5
5
1
E
5
5
5
1
N
14
5
5
-
BETWEEN
-
-
-
2
IN
23
14
5
-
BETWEEN
-
-
-
1
B
2
2
2
1
E
5
5
5
1
T
20
2
2
1
W
23
5
5
1
E
5
5
5
1
E
5
5
5
1
N
14
5
5
-
BETWEEN
-
-
-
16
Add to Reduce
171
72
63
1+6
Reduce to Deduce
1+7+1
7+2
6+3
7
Essence of Number
9
9
9

 

 

-
INBETWEEN
-
-
-
2
IN
23
14
5
7
BETWEEN
74
29
2
9
INBETWEEN
97
43
7
-
-
9+7
4+3
-
9
INBETWEEN
16
7
7
-
-
1+6
-
-
9
INBETWEEN
7
7
7

 

 

THE

INBETWEENERS

Inbetweener's | Define Inbetweener's at Dictionary.com
www.dictionary.com/browse/inbetweener-s
noun, Also, in-betweener. 1. a person or thing that is between two extremes, two contrasting conditions, etc.: yeses, noes, and in-betweens; a tournament for professional, amateur, and in-between. 2.

 

THE

INBETWEENERS 952525555591 INBETWEENERS

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
I
=
9
-
12
INBETWEENERS
68
32
5
-
-
-
-
-
-
-
-
-
-
-
-
12
-
15
First Total
184
85
13
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
3
4
-
6
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
6
7
8
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
6
7
-
-
I
=
9
4
1
I
9
9
9
-
-
-
3
4
-
6
7
-
9
N
=
5
5
1
N
14
5
5
-
-
-
3
4
5
6
7
-
-
B
=
2
6
1
B
2
2
2
-
-
2
3
4
-
6
7
-
-
E
=
5
7
1
E
5
5
5
-
-
-
3
4
5
6
7
-
-
T
=
2
8
1
T
20
2
2
-
-
2
3
4
-
6
7
-
-
W
=
5
9
1
W
23
5
5
-
-
-
3
4
5
6
7
-
-
E
=
5
10
1
E
5
5
5
-
-
-
3
4
5
6
7
-
-
E
=
5
11
1
E
5
5
5
-
-
-
3
4
5
6
7
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
6
7
-
-
E
=
5
12
1
E
5
5
5
-
-
-
3
4
5
6
7
-
-
R
=
9
14
1
R
18
9
9
-
-
-
3
4
-
6
7
-
9
S
=
1
15
1
S
19
10
1
-
1
-
3
4
-
6
7
-
-
-
-
73
-
9
-
172
82
73
-
1
6
3
4
40
6
7
8
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4+0
-
-
-
1+8
-
-
73
-
3
THE
33
15
6
-
1
6
3
4
4
6
7
8
9
-
-
7+3
-
12
INBETWEENERS
139
67
4
-
-
-
-
-
-
-
-
-
-
-
-
10
-
15
First Total
172
82
10
-
1
6
3
4
4
6
7
8
9
-
-
1+0
-
1+5
Add to Reduce
1+7+2
8+2
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
6
Second Total
10
10
1
-
1
6
3
4
4
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
6
Essence of Number
1
1
1
-
1
6
3
4
4
6
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
I
=
9
-
12
INBETWEENERS
68
32
5
-
-
-
-
-
-
-
-
-
-
-
-
12
-
15
First Total
184
85
13
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
15
1
S
19
10
1
-
1
-
3
4
-
6
7
-
-
T
=
2
1
1
T
20
2
2
-
-
2
3
4
-
6
7
-
-
B
=
2
6
1
B
2
2
2
-
-
2
3
4
-
6
7
-
-
T
=
2
8
1
T
20
2
2
-
-
2
3
4
-
6
7
-
-
E
=
5
3
1
E
5
5
5
-
-
-
3
4
5
6
7
-
-
N
=
5
5
1
N
14
5
5
-
-
-
3
4
5
6
7
-
-
E
=
5
7
1
E
5
5
5
-
-
-
3
4
5
6
7
-
-
W
=
5
9
1
W
23
5
5
-
-
-
3
4
5
6
7
-
-
E
=
5
10
1
E
5
5
5
-
-
-
3
4
5
6
7
-
-
E
=
5
11
1
E
5
5
5
-
-
-
3
4
5
6
7
-
-
N
=
5
13
1
N
14
5
5
-
-
-
3
4
5
6
7
-
-
E
=
5
12
1
E
5
5
5
-
-
-
3
4
5
6
7
-
-
H
=
8
2
1
H
8
8
8
-
-
-
3
4
-
6
7
8
-
I
=
9
4
1
I
9
9
9
-
-
-
3
4
-
6
7
-
9
R
=
9
14
1
R
18
9
9
-
-
-
3
4
-
6
7
-
9
-
-
73
-
9
-
172
82
73
-
1
6
3
4
40
6
7
8
18
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4+0
-
-
-
1+8
-
-
73
-
3
THE
33
15
6
-
1
6
3
4
4
6
7
8
9
-
-
7+3
-
12
INBETWEENERS
139
67
4
-
-
-
-
-
-
-
-
-
-
-
-
10
-
15
First Total
172
82
10
-
1
6
3
4
4
6
7
8
9
-
-
1+0
-
1+5
Add to Reduce
1+7+2
8+2
1+0
-
-
-
-
-
-
-
-
-
-
-
-
1
-
6
Second Total
10
10
1
-
1
6
3
4
4
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
6
Essence of Number
1
1
1
-
1
6
3
4
4
6
7
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
5
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
I
=
9
-
12
INBETWEENERS
68
32
5
-
-
-
-
-
-
-
-
12
-
15
First Total
184
85
13
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
5
8
9
S
=
1
15
1
S
19
10
1
-
1
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
B
=
2
6
1
B
2
2
2
-
-
2
-
-
-
T
=
2
8
1
T
20
2
2
-
-
2
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
5
-
-
N
=
5
5
1
N
14
5
5
-
-
-
5
-
-
E
=
5
7
1
E
5
5
5
-
-
-
5
-
-
W
=
5
9
1
W
23
5
5
-
-
-
5
-
-
E
=
5
10
1
E
5
5
5
-
-
-
5
-
-
E
=
5
11
1
E
5
5
5
-
-
-
5
-
-
N
=
5
13
1
N
14
5
5
-
-
-
5
-
-
E
=
5
12
1
E
5
5
5
-
-
-
5
-
-
H
=
8
2
1
H
8
8
8
-
-
-
-
8
-
I
=
9
4
1
I
9
9
9
-
-
-
-
-
9
R
=
9
14
1
R
18
9
9
-
-
-
-
-
9
-
-
73
-
9
-
172
82
73
-
1
6
40
8
18
-
-
-
-
-
-
-
-
-
-
-
-
4+0
-
1+8
-
-
73
-
3
THE
33
15
6
-
1
6
4
8
9
-
-
7+3
-
12
INBETWEENERS
139
67
4
-
-
-
-
-
-
-
-
10
-
15
First Total
172
82
10
-
1
6
4
8
9
-
-
1+0
-
1+5
Add to Reduce
1+7+2
8+2
1+0
-
-
-
-
-
-
-
-
1
-
6
Second Total
10
10
1
-
1
6
4
8
9
-
-
-
-
-
Reduce to Deduce
1+0
1+0
-
-
-
-
-
-
-
-
-
1
-
6
Essence of Number
1
1
1
-
1
6
4
8
9

 

 

C
=
3
-
6
CAUGHT
60
24
6
B
=
2
-
7
BETWEEN
74
29
2
A
=
1
-
1
A
1
1
1
R
=
9
-
4
ROCK
47
20
2
A
=
1
-
3
AND
19
10
1
A
=
1
-
1
A
1
1
1
H
=
8
-
4
HARD
31
22
4
P
=
7
-
5
PLACE
37
19
1
-
-
32
-
31
Add to Reduce
270
126
18
-
-
3+2
-
2+2
Reduce to Deduce
2+7+0
1+0+4
1+8
-
-
5
-
4
Essence of Number
9
9
9

 

 

KEEPER OF GENESIS  
Robert Bauval Graham Hancock 1996

Page 254

Professor Sagan then offers a comparison that is highly apposite to our present inquiry. 'Today,' he says:
we are again seeking messages from an ancient and exotic civilization, this time hidden from us not only in time, but in space. If we should receive a radio message from an extraterrestrial civilization, how could it possibly be understood? Extraterrestrial intelligence will be elegant, complex, internally consistent and utterly alien. Extraterrestrials would, of course, wish to make a message sent to us as comprehensible as possible. But how could they? Is there in any sense an interstellar Rosetta Stone? We believe there is a common language that all technical civilizations, no matter how different, must have. That common language is science and mathematics. The laws of Nature are the same everywhere.3

Extraterrestrial intelligence will be elegant, complex, internally consistent and utterly alien.

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
16
EXTRATERRESTRIAL
213
78
6
-
-
-
-
-
-
6
-
-
-
I
=
9
2
12
INTELLIGENCE
115
61
7
-
-
-
-
-
-
-
7
-
-
W
=
5
3
4
WILL
56
20
2
-
-
2
-
-
-
-
-
-
-
B
=
2
4
2
BE
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
5
7
ELEGANT
64
28
1
-
1
-
-
-
-
-
-
-
-
C
=
3
6
7
COMPLEX
88
34
7
-
-
-
-
-
-
-
7
-
-
I
=
9
7
10
INTERNALLY
130
49
4
-
-
-
-
4
-
-
-
-
-
C
=
3
8
10
CONSISTENT
138
57
3
-
-
-
3
-
-
-
-
-
-
A
=
1
9
3
AND
19
10
1
-
1
-
-
-
-
-
-
-
-
U
=
3
10
7
UTTERLY
121
31
4
-
-
-
-
4
-
-
-
-
-
O
=
6
11
5
ALIEN
41
23
5
-
-
-
-
-
5
-
-
-
-
-
-
51
-
83
First Total
992
398
47
-
2
2
3
8
5
6
21
8
9
-
-
5+1
-
8+3
Add to Reduce
9+9+2
3+9+8
4+7
-
-
-
-
-
-
-
2+1
-
-
-
-
6
-
11
Second Total
20
20
11
-
2
2
3
8
5
6
3
8
9
-
-
-
-
1+1
Reduce to Deduce
2+0
2+0
1+1
-
-
-
-
-
-
-
-
-
-
-
-
6
-
2
Essence of Number
2
2
2
-
2
2
3
8
5
6
3
8
9

 

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
1
16
EXTRATERRESTRIAL
213
78
6
-
-
-
-
-
-
6
-
8
9
I
=
9
2
12
INTELLIGENCE
115
61
7
-
-
-
-
-
-
-
7
8
9
W
=
5
3
4
WILL
56
20
2
-
-
2
-
-
-
-
-
8
9
B
=
2
4
2
BE
7
7
7
-
-
-
-
-
-
-
7
8
9
E
=
5
5
7
ELEGANT
64
28
1
-
1
-
-
-
-
-
-
8
9
C
=
3
6
7
COMPLEX
88
34
7
-
-
-
-
-
-
-
7
8
9
I
=
9
7
10
INTERNALLY
130
49
4
-
-
-
-
4
-
-
-
8
9
C
=
3
8
10
CONSISTENT
138
57
3
-
-
-
3
-
-
-
-
8
9
A
=
1
9
3
AND
19
10
1
-
1
-
-
-
-
-
-
8
9
U
=
3
10
7
UTTERLY
121
31
4
-
-
-
-
4
-
-
-
8
9
O
=
6
11
5
ALIEN
41
23
5
-
-
-
-
-
5
-
-
8
9
-
-
51
-
83
First Total
992
398
47
-
2
2
3
8
5
6
21
8
9
-
-
5+1
-
8+3
Add to Reduce
9+9+2
3+9+8
4+7
-
-
-
-
-
-
-
2+1
-
-
-
-
6
-
11
Second Total
20
20
11
-
2
2
3
8
5
6
3
8
9
-
-
-
-
1+1
Reduce to Deduce
2+0
2+0
1+1
-
-
-
-
-
-
-
-
-
-
-
-
6
-
2
Essence of Number
2
2
2
-
2
2
3
8
5
6
3
8
9

 

RE 95 RE

REARRANGED NUMERICALLY REARRANGED

RE 95 RE

 
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
E
=
5
5
7
ELEGANT
64
28
1
-
1
-
-
-
-
-
-
8
9
A
=
1
9
3
AND
19
10
1
-
1
-
-
-
-
-
-
8
9
W
=
5
3
4
WILL
56
20
2
-
-
2
-
-
-
-
-
8
9
C
=
3
8
10
CONSISTENT
138
57
3
-
-
-
3
-
-
-
-
8
9
I
=
9
7
10
INTERNALLY
130
49
4
-
-
-
-
4
-
-
-
8
9
U
=
3
10
7
UTTERLY
121
31
4
-
-
-
-
4
-
-
-
8
9
O
=
6
11
5
ALIEN
41
23
5
-
-
-
-
-
5
-
-
8
9
E
=
5
1
16
EXTRATERRESTRIAL
213
78
6
-
-
-
-
-
-
6
-
8
9
I
=
9
2
12
INTELLIGENCE
115
61
7
-
-
-
-
-
-
-
7
8
9
B
=
2
4
2
BE
7
7
7
-
-
-
-
-
-
-
7
8
9
C
=
3
6
7
COMPLEX
88
34
7
-
-
-
-
-
-
-
7
8
9
-
-
51
-
83
First Total
992
398
47
-
2
2
3
8
5
6
21
8
9
-
-
5+1
-
8+3
Add to Reduce
9+9+2
3+9+8
4+7
-
-
-
-
-
-
-
2+1
-
-
-
-
6
-
11
Second Total
20
20
11
-
2
2
3
8
5
6
3
8
9
-
-
-
-
1+1
Reduce to Deduce
2+0
2+0
1+1
-
-
-
-
-
-
-
-
-
-
-
-
6
-
2
Essence of Number
2
2
2
-
2
2
3
8
5
6
3
8
9

 

 

KEEPER OF GENESIS

A QUEST FOR THE HIDDEN LEGACY OF MANKIND

Robert Bauval Graham Hancock 1996

Page 254

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

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

That common language is science and mathematics.

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

 

 

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

 

 

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

 

 

THE MAGIC MOUNTAIN


Thomas Mann 1875-1955

Page 417

"I preach mathematics."

 

I
=
9
-
1
I
9
9
9
S
=
1
-
6
PREACH
51
33
6
R
=
9
-
11
MATHEMATICS
112
40
4
-
-
19
-
18
First Total
172
91
19
-
-
1+9
-
1+8
Add to Reduce
1+7+2
9+1
1+9
Q
-
10
-
9
Second Total
10
10
10
-
-
1+0
-
-
Reduce to Deduce
1+0
1+0
1+0
Q
-
1
-
9
Essence of Number
1
1
1

 

 

G
=
7
-
3
GOD
26
17
8
I
=
9
-
2
IS
28
19
1
A
=
1
-
1
A
1
1
1
M
=
4
-
13
MATHEMATICIAN
117
54
9
-
-
21
-
19
First Total
172
91
19
-
-
2+1
-
1+9
Add to Reduce
1+7+2
9+1
1+9
Q
-
3
-
10
Second Total
10
10
10
-
-
-
-
1+0
Reduce to Deduce
1+0
1+0
1+0
Q
-
3
-
1
Essence of Number
1
1
1

 

 

N
=
5
-
5
NAMES
52
25
7
O
=
6
-
2
OF
21
12
3
G
=
7
-
3
GOD
26
17
8
-
-
18
-
10
First Total
99
54
18
-
-
1+8
-
 1+0
Add to Reduce
9+9
5+4
1+8
Q
-
9
-
1
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
Q
-
9
-
1
Essence of Number
9
9
9

 

 

THE BIBLE CODE
Michael Drosnin 1997
Chapter Four
THE SEALED BOOK

Page 70

"The astronomer Carl Sagan once noted that if there was other intelligent life in the universe some of it would have certainly evolved far earlier than we did, and had thousands, or hundreds of thousands, or millions, or hundreds of millions of years to develop the advanced technology that we are only now beginning to develop.
'After billions of years of biological evolution - on their planet and ours - an alien civilization cannot be in technological lockstep with us,' wrote Sagan.
'There 'have been humans for more than twenty thousand centuries, but we've had radio only for about one century,' wrote Sagan. 'If alien civilizations are behind us, they're likely to be too far behind us to have radio. And if they're ahead of us, they're likely to be far ahead of us. Think of the technical advances on our world over just the last few centuries. What is for us technologically difficult or impossible, what might seem to us like magic, might for them be trivially easy.'
The author of 2001, Arthur C. Clarke - who envisioned a mysterious black monolith that reappears at successive stages of human evolution, each time we are ready to be taken to a higher level - made a similar observation:

'Any sufficiently advanced technology is indistinguishable from magic.'

 

 

KEEPER OF GENESIS  
Robert Bauval Graham Hancock 1996

Page 252

Chapter 16
Message in a Bottle?
'We have reached this fascinating point in
our evolution. . . we have reached the time
when we know we can talk to each other
across the distances between the stars. . . '
Dr John Billingham, NASA Ames Research Center, 1995

"Together with the ancient texts and rituals that are linked to them, could the vast monuments of the Giza necropolis have been designed to transmit a message from one culture to another - a message not across space, but across time?
Egyptologists reply to such questions by rolling their eyes and hooting derisively, Indeed they would not be 'Egyptologists' (or at any rate they could not long remain within that profession) if they reacted with anything other than scorn and disbelief to suggestions that the necropolis might be more than a cemetery, that the Great Sphinx might significantly predate the epoch of 2500 BC, and that the Pyramids might not be just 'royal tombs'. By the same token, no self- respecting Egyptologist would be prepared to consider, even for a moment, the outlandish possibility that some sort of mysterious 'message' might have been encoded into the monuments.
So whom should we turn to for advice when confronted by what we suspect may be a message from a civilization so far distant from us in time as to be almost unknowable?
Anti-cipher
The only scientists actively working on such problems today are those involved in the Search for Extraterrestrial Intelligence - SETI for / Page 253 / short. They endlessly sweep the heavens for messages from distant civilizations and they have therefore naturally had to give some thought to what might happen if they ever did identify such a message. According to Dr Philip Morisson of the Massachusetts Institute of Technology:
To begin with we would know very little about it. If we received it we would not understand what we're getting. But we would have an unmistakable signal, full of structure, full of challenge. The best people would try to decode it, and it will be easy to do because those who have constructed it would have made it easy to decode, otherwise there's no point. This is anti-cryptography: 'I want to make a message for you, who never got in touch with any symbols of mine, no key no clue, nevertheless you'll be able to read it . . .' I would have to fill it full of clues and unmistakable clever devices. . .1
In his book, Cosmos, Professor Carl Sagan of Cornell University makes much the same point - and does so, curiously enough, with reference to the ancient Egyptian hieroglyphic system. He explains that the 'Egyptian hieroglyphics are, in significant part, a simple substitution cipher. But not every hieroglyph is a letter or syllable. Some are pictographs. . .' When it came to translation, this 'mix of letters and pictographs caused some grief for interpreters. . .' In the early nineteenth century, however, a breakthrough was made by the French scholar Champollion who deciphered the famous 'Rosetta Stone', a slab of black basalt bearing identical inscriptions in Egyptian hieroglyphics and in Greek. Since Champollion could read the Greek, all he needed was some kind of 'key' to relate specific hieroglyphs to specific Greek words or letters. This key was provided by the constant repetition in the Greek text of the name of Pharaoh Ptolemy V and an equal number of repetitions in the Egyptian text of a distinctive oblong enclosure - known as a cartouche - containing a repeated group of hieroglyphs. As Sagan comments:
The cartouches were the key. . . almost as though the Pharaohs of Egypt had circled their own names to make the going easier for Egyptologists two thousand years in the future. . . What a joy it must have been [for Champollion] to open this one-way communication channel with another civilization, to permit a culture that had been / Page 254 / mute for millennia to speak of its history, magic, medicine, religion, politics and philosophy.2
Professor Sagan then offers a comparison that is highly apposite to our present inquiry. 'Today,' he says:
we are again seeking messages from an ancient and exotic civilization, this time hidden from us not only in time, but in space. If we should receive a radio message from an extraterrestrial civilization, how could it possibly be understood? Extraterrestrial intelligence will be elegant, complex, internally consistent and utterly alien. Extraterrestrials would, of course, wish to make a message sent to us as comprehensible as possible. But how could they? Is there in any sense an interstellar Rosetta Stone? We believe there is a common language that all technical civilizations, no matter how different, must have. That common language is science and mathematics. The laws of Nature are the same everywhere.3
It seems to us that if there is indeed a very ancient 'message' at Giza then it is likely to be expressed in the language of science and mathematics that Sagan identifies - and for the same reason. Moreover, given its need to continue 'transmitting' coherently across thousands of years (and chasms of cultural change), we think that the composer of such a message would be likely to make use of the Precession of the Equinoxes, the one particular 'law of Nature' that can be said to govern, and measure - and identify - long periods of terrestrial time.
Durable vehicles
The Pyramids and the Great Sphinx at Giza are, above all else, as elegant, as complex, as internally consistent and as utterly 'alien' as the extraterrestrial intelligence that Sagan envisages (alien in the sense of the tremendous, almost superhuman scale of these structures and of their uncanny - and in our terms apparently unnecessary - precision).
Moreover, returning briefly to Dr Philip Morisson's remarks quoted earlier, we think that the Giza necropolis also qualifies rather well for the description 'packed full of clues and unmistakable clever devices'.4 Indeed, it seems to us that a truly astonishing quantum of / Page 255 / ingenuity was invested by the Pyramid builders to ensure that the four fundamental aspects of an 'unmistakable' message were thoroughly elaborated here:
1 the creation of durable, unequivocal markers which could serve as beacons to inflame the curiosity and engage the intelligence of future generations of seekers;
2 the use of the 'common language' of precessional astronomy;
3 the use of precessional co-ordinates to signal specific time- referents linking past to present and present to future;
4 Cunningly concealed store-rooms, or 'Halls of Records' that could only be found and entered by those who were fully initiated in the 'silent language' and thus could read and follow its clues.
In addition, though the monuments are enabled to 'speak' from the moment that their astronomical context is understood, we have also to consider the amazing profusion of funerary texts that have come down to us from all periods of Egyptian history - all apparently emanating from the same very few common sources.5 As we have seen, these texts operate like 'software' to the monuments' 'hardware', charting the route that the Horus-King (and all other future seekers) must follow.
We recall a remark made by Giorgio de Santillana and Hertha von Dechend in Hamlet's Mill to the effect that the great strength of myths as vehicles for specific technical information is that they are capable of transmitting that information independently of the knowledge of individual story-tellers.6 In other words as long as a myth continues to be told true, it will also continue to transmit any higher message that may be concealed within its structure - even if neither the teller nor the hearer understands that message.
So, too, we suspect, with the ancient Egyptian funerary texts. We would be surprised if the owners of many of the coffins and tomb walls onto which they were copied had even the faintest inkling that specific astronomical observations and directions were being dupli- cated at their expense. What motivated them was precisely what the texts offered - the lure of immortal life. Yet by taking that lure did they not in fact guarantee a kind of immortality for the texts themselves? Did they not ensure that so many faithful copies would / Page 256 / be made that some at least would be bound to survive for many thousands of years?
We think that there were always people who understood the true 'science of immortality' connected to the texts, and who were able to read the astronomical allegories in which deeper secrets, not granted to the common herd, lay concealed. We presume that these people were once called the 'Followers of Horus', that they operated as an invisible college behind the scenes in Egyptian prehistory and history, that their primary cult centre was at Giza-Heliopolis, and that they were responsible for the initiation of kings and the realization of blueprints. We also think that the timetables they worked to - and almost everything of significance that they did - was in one way or another written in the stars.
Hints and memories
The powerfully astronomical character of the Giza necropolis, although ignored by Egyptologists, has been recognized by open- minded and intuitive researchers throughout history. The Hermetic Neoplatonists of Alexandria, for example, appear to have been acutely sensitive to the possibility of a 'message' and were quick to discern the strong astral qualities of the textual material and the monuments.' 7 The scholar Proclus (fifth century AD) also acknowledged that the Great Pyramid was astronomically designed - and with certain specific stars in mind. Indeed, in his commentary on Plato's Timaeus (which deals with the story of the lost civilization of 'Atlantis'), Proclus reported strangely that 'the Great Pyramid was used as an observation for Sirius'.8
Vague memories of an astronomically constructed 'message' at Giza appear to have filtered down to the Middle Ages. At any rate the Arab chroniclers in this period spoke of the Great Pyramid as 'a temple to the stars' and frequently connected it to the Biblical 'Flood' which they dated to circa 10,300 BC.9 Also of relevance is a report written by the Arab geographer Yakut al Hamawi (eleventh century AD) to the effect that the star-worshippers of Harran, the Sabians (whose 'holy books' were supposedly the writings ofThoth-Hermes) came at that time on special pilgrimages to the Pyramids at Giza.10 It / Page 257 / has also been pointed out that the very name of the Sabians - in Arabic Sa' Ba - almost certainly derived from the ancient Egyptian word for star, i.e. Sba..11 And the reader will recall from Part I that as far back as the early second millennium BC - i.e. almost three thousand years before Yakut al Hamawi left us his report connecting the Sabians to the Pyramids - pilgrims from Harran are known to have visited the Sphinx which they worshipped as a god under the name Hwl.12
In the seventeenth century, the British mathematician Sir Isaac Newton became deeply interested in the Great Pyramid and wrote a dissertation on its mathematical and geodetic qualities based on data that had been gathered at Giza by Dr John Greaves, the Savillian Professor of Astronomy at Oxford.13 Later, in 1865 the Astronomer Royal of Scotland, Charles Piazzi Smyth, launched an investigation into the Great Pyramid which he was convinced was an instrument of prophecy that incorporated a Messianic 'message'. It was Piazzi Smyth who first accurately measured and demonstrated the intense polar and meridional alignments of the monument, the precision of which he assigned to sightings of the ancient Pole star, Alpha Draconis.14
In the first half of the twentieth century, a succession of eminent astronomers - such as Richard Proctor, Eugene Antoniadi, Jean Baptiste Biot and Norman Lockyer - made persistent attempts to draw attention to the astronomical qualities of the Giza monuments. Their efforts, however, had little impact on professional Egyptolo-gists who by this time felt that they had got the whole intellectual business of the necropolis 'wrapped up' (it was a cemetery), did not understand astronomy at all (and claimed that the ancient Egyptians didn't either), and routinely ganged up to debunk, deride or simply ignore any astronomical 'theories' which diverged from their consensus.
Despite this hostile intellectual climate, we are of the opinion at the end of our own research that the big question is no longer whether the monuments of Giza were designed to express key astronomical and mathematical principles, but why.
Once again, the clue may lie in the narrow star-shafts of the Great Pyramid.

Page 258

The language of the stars

The first major breakthrough in understanding the function of the Great Pyramid's shafts was made in. the summer of 1963 by the American astronomer Virginia Trimble and the Egyptologist-architect, Dr Alexander Badawy. It came about because they decided to follow up Badawy's 'hunch' that the shafts might not be 'ventilation channels' as Egyptologists supposed, 15 but might instead prove to have a symbolic function related to the astral rituals of the Pyramid builders. Virginia Trimble was able to buttress her colleague's intuition by showing that the shafts from the King's Chamber had pointed, in the epoch of 2500 BC, to major star systems that were of crucial importance to the Pyramid builders. As readers will recall from Part I, the northern shaft had been targeted on Alpha Draconis - the Pole Star in the Pyramid Age - and the southern shaft had been targeted on Orion's belt.16
Today Virginia Trimble is a senior professor of astronomy at UCLA and the University of Maryland and is also the Vice-President of the American Astronomical Society. Her views, as well as being enlightened by a comprehensive grasp of astronomy, accord fully with common sense:
Which constellations the Egyptians saw in the sky is still something of a mystery. . . but they had one constellation that was an erect standing man, Osiris, the god. And the one constellation that looks like a standing man to everyone is Orion, and the identification between a deceased Pharaoh and the god Osiris made Orion immediately a candidate for a shaft whose sole purpose was to enable the soul of the Pharaoh to communicate between earth and sky. . .17
When we met Virginia Trimble we immediately realized we were in the presence of an acute and formidable thinker. Alexander Badawy had passed away in the late 1980s yet she remained undaunted. She had concluded that the shafts were astronomically aligned, she said, and that they had an astronomical function, because logic and evidence dictated that this was the case.
Trimble's views have won general acceptance amongst senior astronomers. To give one recent example, Dr Mary Bruck of Edinburgh, writing in the Journal of the British Astronomical / Page 259 / Association in 1995, had this to say about the shafts: 'Their alignments are ... compatible with the hypothesis that they indicate the culmination of certain important stars around the 25th century BC . . . The addition of a Sirius shaft [southern shaft of the Queen's Chamber] to the Orion one strongly supports the claim that they have an astronomical significance.' 18

Thought-tools

We suggest that one of the major objectives of the unseen academy, whose members were known as the 'Followers of Horus', was to 'fix' the epoch of 2500 BC (i.e. 4500 years before the present) by using the Great Pyramid, its precisely angled shafts, and the stars of Orion's belt. We suggest that they envisaged those stars rather like the gauge of a gigantic sliding scale set across the south meridian. Once this 'thought-tool' was in place all they needed to do in order to determine a date either in the past or in the future was mentally to 'slide' the belt up or down the meridian from the 'zero point' targeted by the southern shaft of the King's Chamber.
We also suggest that a second and somewhat similar 'thought-tool' was attached to the ecliptic (the apparent annual path of the sun through the twelve constellations of the zodiac). Here the gauge was the vernal point. By mentally sliding it to the left (east) or to the right (west) of a 'fixed' marker on the ecliptic the 'Followers of Horus' would once again have been able to determine and denominate either a past date or a date in the future. . .
In our own epoch, circa AD 2000, the vernal point is poised to enter the sign or 'Age' of Aquarius. For a little over 2000 years it has been passing through Pisces (160 BC to AD 2000) and before that it was in Aries (2320 BC to 160 BC).ln the Pyramid Age the vernal point slowly swept through Taurus (4480 BC to 2320 BC). Going further back we reach the 'Ages' of Gemini (6640 BC to 4480 BC) and then Cancer (8800 BC to 6640 BC). After six 'Great Months' we reach the Age of Leo (10,960BC to 8800 BC).
Now imagine that we find an ancient document at Giza which states that it was composed when the vernal point was in the sign of the Ram - i.e. when the sun on the spring equinox rose against the / Page 260 / stellar background of the constellation of Aries. Armed with this information all that we can do is roughly bracket the document's date as being somewhere between 2320 BC and 160 BC. What we need in order to arrive at a more precise chronology is some means to 'fine-tune' the vernal point. It is here that the specific utility of the sliding scale at the meridian becomes apparent because if the ancient document not only stated which zodiacal sign housed the vernal point but also advised that the lowest star of Orion's belt crossed the meridian at an altitude of 50 degrees above the horizon then we would be able, using precession, to calculate with great accuracy that the date in question must be very near 1400 BC.19
The Pyramid Age occurred when the vernal point was in Taurus and, as we have seen, the fine-tuning permitted by the 45-degree angle of the Great Pyramid's 'Orion shaft' draws particular attention to the date of 2500 BC. With this date, 4500 years before the present, we can use precession to calculate the exact position of the vernal point - which, as the reader will recall, was near the head of the Hyades-Taurus at that time, close to the right (i.e. west) bank of the Milky Way.
The reader will also not have forgotten that this is the 'address' given in the Pyramid Texts as the starting point for the cosmic journey of the solar Horus-King. It is here that he receives his instructions to board the solar-bark and 'sail' across the Milky Way towards the 'horizon' to meet up with Horakhti. His direction of travel is, therefore, eastwards, i.e. to the left of the vernal point. In terms of the chronology of the 'Great Year' of precession (as distinct from the solar year), this means that the Horus-King is now poised to travel back in time towards the age of Leo-Horakhti and to a specific spot on the ecliptic path - 'The Splendid Place of the "First Time" ', . . . 'the place more noble than any place'.20
But where is that place? How is the Horus-King (initiate, seeker) to find it in the 2160-year, 30-degree swathe that the constellation of Leo occupies on the ecliptic?
The answer is that he would have to use the gauge of Orion's belt at the meridian to fine-tune the exact place of the vernal point and hence also to arrive at an exact date. In his mind's eye he would have to slide / Page 261 / the belt 'down' the meridian to its 'First Time' and then see how far to the east that operation had 'pushed' the vernal point along the ecliptic.
Wherever that place was would be the celestial destination that the 'Followers of Horus' were urging him to reach.
And it would, of course, have its counterpart on the ground at Giza, in the vicinity of the lion-bodied Sphinx. "

 

THE

LIONS IN HIS LOINS

THE

HOURS OF HORUS

 

 

 

 

MIN DOTH DREAM WHAT DOTH MIN MEAN

 

-
MIND
-
-
-
3
M+I+N
36
18
9
1
D
4
4
4
4
MIND
40
22
13
-
-
4+0
2+2
1+3
4
MIND
4
4
4

 

 

 

 

 

THE SCULPTURE OF VIBRATION 1971

 

 

 
 
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