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A

MAZE

IN

ZAZAZA ENTER ZAZAZA

ZAZAZAZAZAZAZAAZAZAZAZAZAZAZ

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGICALALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZZYXWVUTSRQPONMLKJIHGFEDCBA

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WORK DAYS OF GOD

Herbert W Morris D.D.circa 1883

Page 22

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

 

 

LIGHT AND LIFE

Lars Olof Bjorn 1976

Page 197

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

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

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

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

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

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A

HISTORY OF GOD

Karen Armstrong

The God of the Mystics

Page 250

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

 

 

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THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY

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

AS THOUGH WRITING A BOOK BUT LANGUAGE ENTIRELY TRANSFORMED

THE MESSAGE OF CREATION IS CLEAR EACH LETTER OF

THE

ALPHABET

IS

GIVEN

A

NUMERICAL

VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS

REARRANGING THEM IN ENDLESS CONFIGURATIONS

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

 

 

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FINGERPRINTS OF THE GODS

A QUEST FOR THE BEGINNING AND THE END

Graham Hancock 1995

Chapter 32

Speaking to the Unborn

Page 285

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

A message in the bottle of time"

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

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

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

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

"WRITTEN IN THE ETERNAL LANGUAGE OF MATHEMATICS"

 

 

 

 

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THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

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

AT THE THROW OF THE NINTH RAM WHEN IN CONJUNCTION SET

THE

FAR YONDER SCRIBE

MADE RECORD OF THEIR FALL

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

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

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

Searching out patterns is a pure delight.

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

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

 

 

HAMLET'S MILL

AN ESSAY INVESTIGATING THE ORIGINS OF HUMAN KNOWLEDGE

AND ITS TRANSMISSION THROUGH MYTH

Giorgio De Santillana and Hertha Von Dechend 1969

Intoduction

Page 1 (number omitted)

"The unbreakable fetters which bound down the Great Wolf Fenrir had been cunningly forged by Loki from these: the footfall of a cat, the roots of a rock, the beard of a woman, the breath of a fish, the spittle of a bird. The Edda

Toute vue des choses qui n'est pas estrange est fausse. VALERY

THIS IS meant to be only an essay. It is a first reconnaissance of a realm well-nigh unexplored and uncharted. From whichever way onc enters it, one is caught in the same bewildering circular complexity, as in a labyrinth, for it has no deductive order in the abstract sense, but instead resembles an organism tightly closed in itself, or even better, a monumental "Art of the Fugue."

The figure of Hamlet as a favorable starting point came by chance. Many other avenues offered themselves, rich in strange symbols and beckoning with great images, but the choice went to Hamlet because he led the mind on a truly inductive quest through a familiar landscape-and one which has the merit of its literary setting. Here is a character deeply present to our awareness, in whom ambiguities and uncertainties, tormented self-questioning and dispassionate insight give a presentiment of the modern mind. His personal drama was that he had to be a hero, but still try to avoid the role Destiny assigned him. His lucid intellect remained above the conflict of motives-in other words, his was and is a truly con­/ Page 2 / temporary consciousness. And yet this character whom the poet made one of us, the first unhappy intellectual, concealed a past as a legendary being, his features predetermined, preshaped by long­standing myth. There was a numinous aura around him, and many clues led up to him. But it was a surprise to find behind the mask an ancient and all-embracing cosmic power-the original master of the dreamed-of first age of the world.
Yet in all his guises he remained strangely himself. The original Amlodhi, * as his name was in Icelandic legend, shows the same characteristics of melancholy and high intellect. He, too, is a son dedicated to avenge his father, a speaker of cryptic but inescapable truths, an elusive carrier of Fate who must yield once his mission is accomplished and sink once more into concealment in the depths of time to which he belongs: Lord of the Golden Age, the Once and Future King.

This essay will follow the figure farther and farther afield, from the Northland to Rome, from there to Finland, Iran, and India; he will appear again unmistakably in Polynesian legend. Many other Dominations and Powers will materialize to frame him within the proper order.

Amlodhi was identified, in the crude and vivid imagery of the Norse, by the ownership of a fabled mill which, in his own time, ground out peace and plenty. Later, in decaying times, it ground out salt; and now finally, having landed at the bottom of the sea, it is grinding rock and sand, creating a vast whirlpool, the Maelstrom (i.e., the grinding stream, from the verb mala, "to grind"), which is supposed to be a way to the land of the dead. This imagery stands, as the evidence develops, for an astronomical process, the secular shifting of the sun through the signs of the zodiac which determines world-ages, each numbering thousands of years. Each age brings a World Era, a Twilight of the Gods. Great structures collapse; pillars topple which supported the great fabric; floods and cataclysms herald the shaping of a new world.
The image of the mill and its owner yielded elsewhere to more / Page 3 / sophisticated ones, more adherent to celestial events. In Plato's powerful mind, the figure stood out as the Craftsman God, the Demiurge, who shaped the heavens; but even Plato did not escape the idea he had inherited, of catastrophes and the periodic rebuilding of the world.

Tradition will show that the measures of a new world had to be procured from the depths of the celestial ocean and tuned with the measures from above, dictated by the "Seven Sages," as they are often cryptically mentioned in India and elsewhere. They turn out to be the Seven Stars of Ursa, which are normative in all cosmological alignments on the starry sphere. These dominant stars of the Far North are peculiarly but systematically linked with those which are considered the operative powers of the cosmos, that is, the planets as they move in different placements and configurations along the zodiac. The ancient Pythagoreans, in their conventional language, called the two Bears the Hands of Rhea (the Lady of Turning Heaven), and called the planets the Hounds of Persephone, Queen of the Underworld. Far away to the south, the mysterious ship Argo with its Pilot star held the depths of the past; and the Galaxy was the Bridge out of Time. These notions appear to have been common doctrine in the age before history-all over the belt of high civilizations around our globe. They also seem to have been born of the great intellectual and technological revolution of the late Neolithic period.

The intensity and richness, the coincidence of details, in this cumulative thought have led to the conclusion that it all had its origin in the Near East. It is evident that this indicates a diffusion of ideas to an extent hardly countenanced by current anthropology. But this science, although it has dug up a marvelous wealth of details, has been led by its modern evolutionary and psychological bent to forget about the main source of myth, which was astronomy -the Royal Science. This obliviousness is itself a recent turn of events-barely a century old. Today expert philologists tell us that Saturn and Jupiter are names of vague deities, subterranean or atmospheric, superimposed on the planets at a "late" period; they neatly sort out folk origins and "late" derivations, all unaware that planetary periods, sidereal and synodic, were known and rehearsed / Page 4 / in numerous ways by celebrations already traditional in archaic times. If a scholar has never known those periods even from elementary science, he is not in the best position to recognize them when they come up in his material.

Ancient historians would have been aghast had they been told that obvious things were to become unnoticeable. Aristotle was proud to state it as known that the gods were originally stars, even if popular fantasy had later obscured this truth. Little as he believed in progress, he felt this much had been secured for the future. He could not guess that W. D. Ross, his modern editor, would condescendingly annotate: "This is historically untrue." Yet we know that Saturday and Sabbath had to do with Saturn, just as Wednesday and Mercredi had to do with Mercury. Such names are as old as time; as old, certainly, as the planetary heptagram of the Har­ranians. They go back far before Professor Ross' Greek philology. The inquiries of great and meticulous scholars such as Ideler, Lep­sius, Chwolson, BoIl and, to go farther back, of Athanasius Kircher and Petavius, had they only been read carefully, and noted, would have taught several relevant lessons to the historians of culture, but interest shifted to other goals, as can be seen from current anthro­pology, which has built up its own idea of the "primitive" and what came after.

One still reads in that most unscientific of records, the Bible, that God disposed all things by number, weight and measure; ancient Chinese texts say that "the calendar and the pitch pipes have such a close fit, that you could not slip a hair between them." People read it, and think nothing of it. Yet such hints might reveal a world of vast and firmly established complexity, infinitely different from ours. But the experts now are benighted by the current folk fantasy, which is the belief that they are beyond all this-critics without nonsense and extremely wise.

In 1959 I wrote:
The dust of centuries had settled upon the remains of this great world-wide archaic construction when the Greeks came upon the scene. Yet something of it survived in traditional rites, in myths and fairy tales no longer understood. Taken verbally, it matured the / Page 5 / bloody cults intended to procure fertility, based on the belief in a dark universal force of an ambivalent nature, which seems now to monopolize our interest. Yet its original themes could flash out again, preserved almost intact, in the later thought of the Pythagoreans and of Plato.

But they are tantalizing fragments of a lost whole. They make one think of those "mist landscapes" of which Chinese painters are masters, which show here a rock, here a gable, there the tip of a tree, and leave the rest to imagination. Even when the code shall have yielded, when the techniques shall be known, we cannot expect to gauge the thought of those remote ancestors of ours, wrapped as it is in its symbols.

Their words are no more heard again Through lapse of many ages. . .

We think we have now broken part of that code. The thought behind these constructions of the high and far-off times is also lofty, even if its forms are strange. The theory about "how the world began" seems to involve the breaking asunder of a harmony, a kind of cosmogonic "original sin" whereby the circle of the ecliptic (with the zodiac) was tilted up at an angle with respect to the equator, and the cycles of change came into being.

This is not to suggest that this archaic cosmology will show any great physical discoveries, although it required prodigious feats of concentration and computing. What it did was to mark out the unity of the universe, and of man's mind, reaching out to its farthest limits. Truly, man is doing the same today.

Einstein said: "What is inconceivable about the universe, is that it should be at all conceivable." Man is not giving up. When he discovers remote galaxies by the million, and then those quasi-stellar radio sources billions of light-years away which confound his speculation, he is happy that he can reach out to those depths. But he pays a terrible price for his achievement. The science of astro­physics reaches out on a grander and grander scale without losing its footing. Man as man cannot do this. In the depths of space he loses himself and all notion of his significance. He is unable to fit himself into the concepts of today's astrophysics short of schizophrenia. Modern man is facing the nonconceivable. Archaic man, however, kept a firm grip on the conceivable by framing within his cosmos / Page 6 / an order of time and an eschatology that made sense to him and reserved a fate for his soul. Yet it was a prodigiously vast theory, with no concessions to merely human sentiments. It, too, dilated the mind beyond the bearable, although without destroying man's role in the cosmos. It was a ruthless metaphysics.

Not a forgiving universe, not a world of mercy. That surely not. Inexorable as the stars in their courses, miserationis parcissimae, the Romans used to say. Yet it was a world somehow not unmindful of man, one in which there was an accepted place for everything, rightfully and not only statistically, where no sparrow could fall unnoted, and where even what was rejected through its own error would not go down to eternal perdition; for the order of Number and Time was a total order preserving all, of which all were members, gods and men and animals, trees and crystals and even absurd errant stars, all subject to law and measure.

This is what Plato knew, who could still speak the language of archaic myth. He made myth consonant with his thought, as he built the first modern philosophy. We have trusted his clues as landmarks even on occasions when he professes to speak "not quite seriously." He gave us a first rule of thumb; he knew what he was talking about.

Behind Plato there stands the imposing body of doctrine attributed to Pythagoras, some of its formulation uncouth, but rich with the prodigious content of early mathematics, pregnant with a sci­ence and a metaphysics that were to flower in Plato's time. From it come such words as "theorem," "theory," and "philosophy." This in its turn rests on what might be called a proto-Pythagorean phase, spread all over the East but with a focus in Susa. And then there was something else again, the stark numerical computing of Baby­Ion. From it all came that strange principle: "Things are numbers."

Once having grasped a thread going back in time, then the test of later doctrines with their own historical developments lies in their congruence with tradition preserved intact even if half under­stood. For there are seeds which propagate themselves along the jetstream of time.

Page 7

And universality is in itself a test when coupled with a firm design. When something found, say, in China turns up also in Babyionian astrological texts, then it must be assumed to be relevant, for it reveals a complex of uncommon images which nobody could claim had risen independently by spontaneous generation.

Take the origin of music. Orpheus and his harrowing death may be a poetic creation born in more than one instance in diverse places. But when characters who do not play the lyre but blow pipes get themselves flayed alive for various absurd reasons, and their identical end is rehearsed on several continents, then we feel we have got hold of something, for such stories cannot be linked by internal sequence. And when the Pied Piper turns up both in the medieval German myth of Hamelin and in Mexico long before Columbus, and is linked in both places with certain attributes like the color red, it can hardly be a coincidence. Generally, there is little that finds its way into music by chance.

Again, when one finds numbers like 108, or 9 x 13, reappearing under several multiples in the Vedas, in the temples of Angkor, in Babylon, in Heraclitus' dark utterances, and also in the Norse Valhalla, it is not accident.

There is one way of checking signals thus scattered in early data, in lore, fables and sacred texts. What we have used for sources may seem strange and disparate, but the sifting was considered, and it had its reasons. Those reasons will be given later in the chapter on method. I might call it comparative morphology. The reservoir of myth and fable is great, but there are morphological "markers" for what is not mere storytelling of the kind that comes naturally. There is also wonderfully preserved archaic material in "secondary" primitives, like American Indians and West Africans. Then there are courtly stories and annals of dynasties which look like novels: the Feng Shen Yen I, the Japanese Nihongi, the Hawaiian Kumulipo. These are not merely fantasy-ridden fables.

In hard and perilous ages, what information should a well-born man entrust to his eldest son? Lines of descent surely, but what else? The memory of an ancient nobility is the means of preserving the / Page 8 / arcana imperii, the arcana legis and the arcana mundi, just as it was in ancient Rome. This is the wisdom of a ruling class. The Polynesian chants taught in the severely restricted Whare-wananga were mostly astronomy. That is what a liberal education meant then.

Sacred texts are another great source. In our age of print one is tempted to dismiss these as religious excursions into homiletics, but originally they represented a great concentration of attention on material which had been distilled for relevancy through a long period of time and which was considered worthy of being committed to memory generation after generation. The tradition of Celtic Druidism was delivered not only in songs, but also in tree-lore which was much like a code. And in the East, out of complicated games based on astronomy, there developed a kind of shorthand which became the alphabet.

As we follow the clues-stars, numbers, colors, plants, forms, verse, music, structres-a huge framework of connections is re­vealed at many levels. One is inside an echoing manifold where everything responds and everything has a place and a time assigned to it. This is a true edifice, something like a mathematical matrix, a World-Image that fits the many levels, and all of it kept in order by strict measure. It is measure that provides the countercheck, for there is much that can be identified and redisposed from rules like the old Chinese saying about the pitch pipes and the calendar. When we speak of measures, it is always some form of Time that provides them, starting from two basic ones, the solar year and the octave, and going down from there in many periods and intervals, to actual weights and sizes. What modern man attempted in the merely conventional metric system has archaic precedents of great complexity. Down the centuries there comes an echo of Al-Biruni's wondering a thousand years ago, when that prince of scientists discovered that the Indians, by then miserable astronomers, calculated aspects and events by means of stars-and were not able to show him anyone star that he asked for. Stars had become items for them, as they were to become again for Leverrier and Adams, who never troubled to look at Neptune in their life although they had computed and discovered it in 1847. The Mayas and the Aztecs in their / Page 9 / unending calculations seem to have had similar attitudes. The connections were what counted. Ultimately so it was in the archaic universe, where all things were signs and signatures of each other, inscribed in the hologram, to be divined subtly. And Number dominated them all (appendix # I ).

This ancient world moves a little closer if one recalls two great transitional figures who were simultaneously archaic and modern in their habits of thought. The first is Johannes Kepler, who was of the old order in his unremitting calculations and his passionate devotion to the dream of rediscovering the "Harmony of the Spheres." But he was a man of his own time, and also of ours, when this dream began to prefigure the polyphony that led up to Bach. In somewhat the same way, our strictly scientific world view has its counterpart in what John Hollander, the historian of music, has described as "The Untuning of the Sky." The second transitional figure is no less a man than Sir Isaac Newton, the very inceptor of the rigorously scientific view. There is no real paradox in mentioning Newton in this connection. John Maynard Keynes, who knew Newton as well as many of our time, said of him:

Newton was not the first of the Age of Reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual world rather less than 10,000 years ago. . . Why do I call him a magician? Because he looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying pure thought to certain evidence, certain mystic clues which God had laid about the world to allow a sort of philosopher's treasure hunt to the esoteric brother­hood. He believed that these clues were to be found partly in the evidence of the heavens and in the constitution of elements (and that is what gives the false suggestion of his being an experimental natural philosopher), but also partly in certain papers and traditions handed down by the brethren in an unbroken chain back to the original cryptic revelation in Babylonia. He regarded the universe as a cryptogram set by the Almighty-just as he himself wrapt the discovery of the calculus in a cryptogram when he communicated with Leibniz. By pure thought, by concentration of mind, the riddle, he believed, would be revealed to the initiate.1

Page 10

Lord Keynes' appraisal, written ca. 1942, remains both unconventional and profound. He knew, we all know, that Newton failed. Newton was led astray by his dour sectarian preconceptions. But his undertaking was truly in the archaic spirit, as it begins to appear now after two centuries of scholarly search into many cultures of which he could have had no idea. To the few clues he found with rigorous method, a vast number have been added. Still, the wonder remains, the same that was expressed by his great predecessor Galileo:

But of all other stupendous inventions, what sublimity of mind must have been his who conccived how to communicate his most secret thoughts to any othcr person, though very far distant either in time or place, speaking with those who are in the In dies, speaking to those who are not yet born, nor shall be this thousand or ten thousand years) And with no greater difficulty than the various arrangement of two dozcn little signs upon paper? Let this be the seal of all the admirable inventions of man.

'Way back in the 6th century A.D., Gregoire de Tours was writing: "The mind has lost its cutting edge, we hardly understand the Ancicnts." So much more today, despite our wallowing in mathematics for the million and in sophisticated technology.
It is undeniable that, notwithstanding our Classics Departments' labors, the wilting away of classical studies, the abandonment of any living familiarity with Greek and Latin has cut the ompha­loessa, the umbilical cord which connected our cultUre-at least at its top level-with Greece, in the same manner in which men of the Pythagorean and Orphic tradition were tied up through Plato and a few others with the most ancient Near East. It is beginning to appear that this destruction is leading into a very up-to-date Middle Ages, much worse than the first. People will sneer: "Stop the World, I want to get off." It cannot be changed, however; this is the way it goes when someone or other tampers with the reserved knowledge that science is, and was meant to represent.
But, as Goethe said at the very onset of the Progressive Age, "Noch ist es Tag, da ruhre sich der Mann! Die Nacht tritt ein, wo niemand wirken kann." ("It is still day, let men get up and / Page 11 / going-the night creeps in, when there is nothing doing.") There might come once more some kind of "Renaissance" out of the hopelessly condemned and trampled past, when certain ideas come to life again, and we should not deprive our grandchildren of a last chance at the heritage of the highest and farthest-off times. And if, as looks infinitely probable, even that last chance is passed up in the turmoil of progress, why then one can still think with Poliziano, who was himself a master humanist, that there will be men whose minds find a refuge in poetry and art and the holy tradition "which alone make men free from death and turn them to eternity, so long as the stars will go on, still shining over a world made for­ever silent." Right now, there is still left some daylight in which to undertake this first quick reconnaissance. It will necessarily leave out great and significant areas of material, but even so, it will in­vestigate many unexpected byways and crannies of the past."

Page 2 Note *. The indulgence of specialists is asked for the form of certain transliterations throughout the text; for example, Amlodhi instead of Amlodi, Grotte instead of Grotti, etc. (Ed.)

Page 9 Note 1 1 "Newton the Man," in The Royal Society. Newton Tercentenary Celebrations (1947), p. 29.

 

 

-
CODE
-
-
-
2
CO
18
9
9
2
DE
9
9
9
4
CODE
27
18
18
-
-
2+7
1+8
1+8
4
CODE
9
9
9

 

 

HAMLET'S MILL

AN ESSAY INVESTIGATING THE ORIGINS OF HUMAN KNOWLEDGE

AND ITS TRANSMISSION THROUGH MYTH

Giorgio De Santillana and Hertha Von Dechend 1969

Page 162

"Finally, there is one remarkable and disturbing coincidence from the same direction. It is known that in the final battle of the gods, the massed legions on the side of "order" are the dead warriors, the "Einherier" who once fell in combat on earth and who have been transferred by the Valkyries to reside with Odin in Valhalla-a theme much rehearsed in heroic poetry. On the last day, they issue forth to battle in martial array. Says the Grimnismal (23): "Five hundred gates and forty more-are in the mighty building of Wal­halla-eight hundred 'Einherier' come out of each one gate-on the time they go out on defence against the Wolf."
That makes 432,000 in all, a number of significance from of old.
This number must have had a very ancient meaning, for it is also the number of syllables in the Rigveda. But it goes back to the basic figure 10,800, the number of stanzas in the Rigveda (40 syllables to a stanza) which, together with 108, occurs insistently in Indian tradition. 10,800 is also the number which has been given by Heraclitus for the duration of the Aion, according to Censorinus (De die natali 18), whereas Berossos made the Babylonian Great Year to last 432,000 years. Again, 10,800 is the number of bricks of the Indian fire-altar (Agnicayana). 32
"To quibble away such a coincidence," remarks Schroder, "or to ascribe it to chance, is in my opinion to drive skepticism beyond its limits."33 Shall one add Angkor to the list? It has five gates, and to each of them leads a road, bridging over that water ditch which surrounds the whole place. Each of these roads is bordered by a row of huge stone figures, 108 per avenue, 54 on each side, altogether 540 statues of Deva and Asura, and each row carries a huge Naga / Page 163 / serpent with nine heads. Only, they do not "carry" that serpent, they are shown to "pull" it, which indicates that these 540 statues are churning the Milky Ocean, represented (poorly, indeed) by the water ditch,34 using Mount Mandara as a churning staff, and Vasuki, the prince of the Nagas, as their drilling rope. (Just to prevent misunderstanding: Vasuki had been asked before, and had agreeably consented, and so had Vishnu's tortoise avatar, who was going to serve as the fixed base for that "incomparably mighty churn," and even the Milky Ocean itself had made it clear that it was willing to be churned.) The whole of Angkor thus turns out to be a colossal model set up for "alternative motion" with true Hindu fantasy and incongruousness to counter the idea of a continuous one-way Precession from west to east."

 

 

CITY OF REVELATION

John Michell 1972

Page 77

CHAPTER SEVEN

3168, The Perimeter of the Temple

"If the numbers of the sacred principles, mentioned by St John in connection with the New Jerusalem, are obtained from the Greek text by the cabalistic method of gematria, it is found that they correspond to the dimensions of the city, set out in Fig 16. (Figure omitted) For example, the perimeter of a hexagon contained within the circle representing the earth, 7920 feet in diameter, measures 2376 feet, and 2376 is the number of (Greek text omitted), the twelve apostles of the Lamb (Revelation 21.14). 2376 x 2 feet is equal to 1746 MY, and 1745 = (Greek text omitted), the twelve apostles. The names of the apostles are said to be in the twelve foundations of the wall of the city. The wall is the circle of diameter 7920 feet and 14,400 cubits in circumference, and the foundations are the twelve corners of the double hexagon inscribed within it, fonowing the customary pattern of an astrological chart. The position of the twelve apostles in the scheme is thus clearly defined.
Of all the canonical numbers the most notable is 3168. The New Jerusalem measures 48,000 furlongs or 31,680,000 feet round the perimeter of its four sides; the mean perimeter of the Stonehenge sarsen circle is 316.8 feet; the perimeter of the square 12 hides of Glastonbury is 31,680 feet; the significance of 31,680 in the canon of cosmology is illustrated in Fig.11, and we shall also find this number set round the border of Plato's mystical city, described in Laws.
Obviously the number 3168 had an important symbolic meaning, the Christian interpretation of which is provided in New Testament
gematria. The most sacred name of Christianity is (Greek text omitted);
(Greek text omitted), Lord Jesus Christ, and the number of these three words together is 3168. (Greek text omitted) is an astrological term meaning the ruler or dominant influence.
Another sacred phrase from the New Testament, (Greek text omitted) the Power of Christ (2 Corinthians 12.9) has the value 3168 if the alternative spelling of Christos, (Greek text omitted) is adopted.

Page 78

The perimeter of the temple is 3168, Lord Jesus Christ, when the temple is measured by the foot, the most sacred unit of ancient metrology. In terms of the megalithic yard (2.72 feet), however, the perimeter measures 1164, because 3168 feet = 1164 MY. Yet this makes no difference to the symbolic interpretation by gematria, for 1164 is the number of another name of Christ, (Greek text omitted) Son of God.

As a geodetic or earth-measuring number, 3168 also demonstrates the antiquity and sacred origin of British metrology, for
31,680 inches = half a mile

31,680 ft. = 6 miles.

31,680 furlongs = 3960 miles = radius of the earth.

31,680 miles = perimeter of square containing the terrestrial sphere.

31,680 miles = circumference of circle drawn on the combined diameters of the earth and moon (10,080 miles)

Other cosmological correspondences of 3168 are given on page 109.

The Stonehenge sarsen circle with circumference of 316.8 feet
contains an area of 888 square yards, 888 being the number of Jesus, which is equal to 1080 square MY. The circle contained within a square of perimeter 316.8 feet, corresponding to the bluestone circle at Stonehenge, has an area of 666 square MY. Thus the two stone circles at Stonehenge have areas of 1080 and 666 square MY, these two numbers representing the opposite poles of lunar and solar or negative and positive energy.
The number 144 or 122 is characteristic of the New Jerusalem scheme, and 3168 demonstrates the value of (pi symbol 22/7 omitted) in terms of this number, for 144 x 7 = 1008 and 144 x 22 = 3168.

3168 in Plato's city
A remarkable use of the number 3168 occurs in Plato's account in Book V of.Laws of the mystical dimensions of the perfect city. Throughout his work Plato makes guarded reference to a secret canon of numbers that applies universally to every aspect of human life and activity, including government, astronomy, acoustics, kinetics, plane and solid geometry and divination. Linear measurements, areas and volumes are obviously incommensurable, but Plato declares that there are certain numbers that link these with each other and with all phenomena capable of being measured. As an example of these numbers, the study of which Plato recommends as the most sanctifying of all pursuits, he gives 5040. This is the ideal number of citizens in the state and serves other purposes in con­/ Page 79 / nection with the framing of laws and standards. The reason why it is most suitable for all matters of division is that for its size it has the greatest number of divisors, 60 in all, including the entire decad, the numbers 1 - 10. Another property of the number 5040 is that it is the radius of a circle with circumference 31,680. Further examina­tion of the numerical foundations of Plato's state shows that the scheme to which he refers is the ancient plan of the cosmic temple.
The lawgivers in Plato's state are reminded that the perfect human society would be one in which all possessions, wives, children, land and chattels were held in common, where all the citizens were of one mind and acted together so harmoniously that it were as if eyes, ears and hands were also common property. To keep this ideal alive is the function of the prophet. Human nature and conditioning, however, demand a more practical alternative, 'very near to the first in immortality and second to it in merit'. This is provided in Laws V.
Plato's state is arranged in a manner that can scarcely be under­stood literally, and is obviously intended, like the New Jerusalem, as a geometer's allegory. The land is all divided into twelve parts, each dedicated to one of the twelve gods and populated by one of the twelve tribes of the 5040 households. The city is similarly divided, forming a microcosm of the state as a whole. In the centre of the city is the acropolis and 'from this centre he must divide up the city itself and the whole country into twelve parts. The twelve parts must be equalised by making those of good land small and those of inferior land greater. He must mark off 5040 allotments, and each of these he must cut in two and join two pieces to form the allotments, so that each contains a near piece and a distant piece - joining the piece next to the city with the piece furthest off, the second nearest with the second furthest, and so on with the rest.'
The only way in which this division can be represented is by a circle of radius 5040, a hundred times larger than that of Stonehenge measured in feet; the perimeter of this circle is 31 ,680. In Fig. 24 (Figure 24 omitted) the radius of the circle should be divided equally into 5040 parts to produce 5040 concentric circles. These are bisected into 10,080 semi­circles by the diameter and positioned out in Plato's manner into 5040 double allotments, each of equal area.
In this scheme 31,680 is not only the circumference of the circular state, but also the area of each of its 2520 pairs of rings, proving Plato's assertion that linear and area pleasurements can be made / Page 80 / (Figure 24 omitted) commensurable by number. The entire circle is divided into two halves, each containing 39,916,800 square units of land. These numbers, which are inherent in the New Jerusalem scheme, have the following significance:
31,680 is divisible by all the numbers1-12 with the exception of 7

5040 = 1 x 2 x 3 x 4 x 5 x 6 x 7

39,916,800 = 1 x 2 x 3 x 4 x 5x 6 x 7 x 8 x 9 x.10 x 11

5040, the radius of the circular city, is the product of the numbers1 - 7; 7920, the side of the square city, is the product of numbers 8 - 11. In each case the perimeter of the city is 31,680. In Plato's Republic is the famous, cryptic reference to the 'marriage number', which should be consulted by the guardians of the state in all matters relating to the seasonal union of male and female. There appear to be two numbers involved, adding up to a third, but the riddle is so obscure that no firm solution has been reached despite the vast literature on the subject. For various reasons the number 12,960,000 or 36002 is most commonly proposed, and this would seem appropriate, for 12,960 = 5040 + 7920. 12,960 therefore represents the union of square and circle, symbol of the sacred marriage, and the gematria is also appropriate, for 1296 = (Greek text omitted) Mary mother of Jesus.

FIGURE 24 (Figure omitted) Plato's city divided into 5040 rings, Perimeter = 31,680, Areas: A + a = B + b = C + c = 31,680.

 

 

-
FIFTY FOUR
-
-
-
1
F
6
6
6
1
I
9
9
9
1
F
6
6
6
2
TY
45
9
9
1
F
6
6
6
2
OUR
54
18
9
9
FIFTY FOUR
126
54
45
-
-
1+2+6
5+4
4+5
9
FIFTY FOUR
9
9
9

 

 

-
FIFTY FOUR
-
-
-
1
F
6
6
6
1
I
9
9
9
1
F
6
6
6
2
TY
45
9
9
1
F
6
6
6
2
OU
36
9
9
1
R
18
9
9
9
FIFTY FOUR
126
54
45
-
-
1+2+6
5+4
4+5
9
FIFTY FOUR
9
9
9

 

 

--
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
-
-
-
-
6
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
9
-
-
-
-
-
15
-
-
+
=
24
2+4
=
6
=
6
=
6
--
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
6
-
6
2
7
-
6
-
3
9
+
=
39
3+9
=
12
1+2
3
=
3
-
-
6
-
6
20
25
-
6
-
21
18
+
=
102
1+0+2
=
3
=
3
=
3
--
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
6
9
6
20
25
-
6
15
21
18
+
=
126
1+2+6
=
9
=
9
=
9
-
-
6
9
6
2
7
-
6
6
3
9
+
=
54
5+4
=
9
=
9
=
9
-
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
2
-
--
-
--
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
--
-
--
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
6
-
-
-
6
6
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
-
7
--
-
-
--
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
--
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
18
9
F
I
F
T
Y
-
F
O
U
R
-
-
27
-
-
9
-
54
-
27
1+8
-
-
9
-
-
-
--
-
-
-
9
-
-
2+7
-
-
-
-
5+4
-
2+7
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9
-
-
6
9
6
2
7
--
6
6
3
9
-
-
-
-
-
-
-
-
-
-
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9

 

 

--
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
-
-
-
-
6
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
9
-
-
-
-
-
15
-
-
+
=
24
2+4
=
6
=
6
=
6
--
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
6
-
6
2
7
-
6
-
3
9
+
=
39
3+9
=
12
1+2
3
=
3
-
-
6
-
6
20
25
-
6
-
21
18
+
=
102
1+0+2
=
3
=
3
=
3
--
9
F
I
F
T
Y
--
F
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
6
9
6
20
25
-
6
15
21
18
+
=
126
1+2+6
=
9
=
9
=
9
-
-
6
9
6
2
7
-
6
6
3
9
+
=
54
5+4
=
9
=
9
=
9
-
9
F
I
F
T
Y
-
F
O
U
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
--
-
--
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
6
-
6
-
-
-
6
6
-
-
-
-
6
occurs
x
4
=
24
2+4
6
-
-
-
-
-
-
7
--
-
-
--
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
9
-
-
-
-
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
9
18
9
F
I
F
T
Y
-
F
O
U
R
-
-
27
-
-
9
-
54
-
27
1+8
-
-
9
-
-
-
--
-
-
-
9
-
-
2+7
-
-
-
-
5+4
-
2+7
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9
-
-
6
9
6
2
7
--
6
6
3
9
-
-
-
-
-
-
-
-
-
-
9
9
F
I
F
T
Y
-
F
O
U
R
-
-
9
-
-
9
-
9
-
9

 

 

2
FIFTY FOUR
126
54
9
1
FORTYFIVE
126
54
9

 

 

1
I
9
9
9
4
PLAY
54
18
9
5
PLATO
64
19
1
5
CHESS
54
18
9

 

 

9
FIFTY FOUR
126
54
9

 

 

2
FIFTY FOUR
126
54
9
1
FORTYFIVE
126
54
9

 

 

-
FIVE FOUR NINE
-
-
-
1
F
6
6
6
1
I
9
9
9
2
VE
9
9
9
1
F
6
6
6
2
OU
36
9
9
1
R
18
9
9
1
N
14
5
5
1
I
9
9
9
1
N
14
5
5
1
E
5
5
5
12
FIVE FOUR NINE
144
72
72
1+2
-
1+4+4
7+2
7+2
3
FIVE FOUR NINE
9
9
9

 

 

-
FIVE FOUR NINE
-
-
-
1
F
6
6
6
1
I
9
9
9
2
VE
9
9
9
1
F
6
6
6
2
OU
36
9
9
1
R
18
9
9
1
NINE
42
24
6
12
FIVE FOUR NINE
144
72
72
1+2
-
1+4+4
7+2
7+2
3
FIVE FOUR NINE
9
9
9

 

 

-
FIVE FOUR NINE
-
-
-
1
F
6
6
6
2
IVE
36
18
9
1
F
6
6
6
2
OUR
54
18
9
1
NINE
42
24
6
12
FIVE FOUR NINE
144
72
72
1+2
-
1+4+4
7+2
7+2
3
FIVE FOUR NINE
9
9
9

 

 

-
FIVE FOUR NINE
-
-
-
1
FIVE
42
24
6
1
FOUR
60
24
6
1
NINE
42
24
6
12
FIVE FOUR NINE
144
72
72
1+2
-
1+4+4
7+2
7+2
3
FIVE FOUR NINE
9
9
9

 

 

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

 

 

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

 

 

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

 

 

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

 

 

-
SUN
-
-
-
1
S
19
10
1
1
U
21
3
3
1
N
14
5
5
3
SUN
54
18
9
-
5+4
1+8
-
3
SUN
9
9
9

 

 

-
3
S
U
N
-
-
-
-
-
-
-
-
-
-
1
-
5
+
=
6
-
=
6
=
6
-
-
19
-
14
+
=
33
3+3
=
6
=
6
-
3
S
U
N
-
-
-
-
-
-
-
-
-
-
-
3
-
+
=
3
-
=
3
=
3
-
`-
-
21
-
+
=
21
2+1
=
3
=
3
-
3
S
U
N
-
-
-
-
-
-
-
-
-
`-
19
21
14
+
=
54
5+4
=
9
=
9
-
-
1
3
5
+
=
9
-
=
9
=
9
-
3
S
U
N
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
6
-
-
-
-
-
-
6
SIX
6
-
-
-
7
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
9
NINE
9
-
-
-
36
3
S
U
N
-
-
9
-
-
3
-
9
3+6
-
-
-
-
-
-
-
-
-
-
-
-
9
3
S
U
N
-
-
9
-
-
3
-
9

 

 

3
S
U
N
-
-
-
-
-
--
-
-
-
1
-
5
+
=
6
-
=
6
=
6
-
19
-
14
+
=
33
3+3
=
6
=
6
3
S
U
N
-
-
-
-
-
--
-
-
-
-
3
-
+
=
3
-
=
3
=
3
`-
-
21
-
+
=
21
2+1
=
3
=
3
3
S
U
N
-
-
-
-
-
--
-
-
`-
19
21
14
+
=
54
5+4
=
9
=
9
-
1
3
5
+
=
9
-
=
9
=
9
3
S
U
N
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
3
-
-
-
3
occurs
x
1
=
3
-
-
-
5
-
-
5
occurs
x
1
=
5
3
S
U
N
-
-
9
-
-
3
-
9
-
-
-
-
-
-
-
-
-
-
-
-
3
S
U
N
-
-
9
-
-
3
-
9

 

 

3

SUN

54
9
9
5

EARTH

52
25
7
4

MOON

57
21
3
12
First Total
163
55
19
1+2
Add to Reduce
1+6+3
5+5
1+9
3
Second Total
10
10
10

-

Reduce to Deduce
1+0

1+0

1+0

3
Final Total
1
1
1

 

 

PLATO A PLOT A PLOT A PLATO

 

 

-
5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
-
7
3
1
2
-
+
=
13
1+3
=
4
=
4
-
-
16
12
1
20
-
+
=
49
4+9
=
13
1+3
4
-
5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
-
16
12
1
20
15
+
=
64
6+4
=
10
1+0
1
-
-
7
3
1
2
6
+
=
19
1+9
=
10
1+0
1
-
5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
26
5
P
L
A
T
O
-
-
19
-
-
5
-
19
2+6
-
-
-
-
-
-
-
-
1+9
-
-
-
-
1+9
8
5
P
L
A
T
O
-
-
10
-
-
5
-
10
-
-
7
3
1
2
6
-
-
1+0
-
-
-
-
1+0
8
5
P
L
A
T
O
-
-
1
-
-
5
-
1

 

 

5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
-
15
+
=
15
1+5
=
6
=
6
5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
7
3
1
2
-
+
=
13
1+3
=
4
=
4
-
16
12
1
20
-
+
=
49
4+9
=
13
1+3
4
5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
16
12
1
20
15
+
=
64
6+4
=
10
1+0
1
-
7
3
1
2
6
+
=
19
1+9
=
10
1+0
1
5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
5
P
L
A
T
O
-
-
19
-
-
5
-
19
-
-
-
-
-
-
-
-
1+9
-
-
-
-
1+9
5
P
L
A
T
O
-
-
10
-
-
5
-
10
-
7
3
1
2
6
-
-
1+0
-
-
-
-
1+0
5
P
L
A
T
O
-
-
1
-
-
5
-
1

 

 

THE ANANGA RANGA OF KALYANA MALLA

Translated By Sir Richard Burton and F. F. Arbuthnot

and

THE SYMPOSIUM OF PLATO

Translated By Benjamin Jowett

Edition 1963

Page 9

THE PLATONIC AND HINDU ATTITUDES TO LOVE AND SEX

by

Kenneth Walker

"PLATO, who was born in 428-7 B.C., devoted four of his dialogues mainly to the questions of love and sexual pleasure, the Lysis, the Symposium, the Phaedrus and the Philebus, qf which the Symposium and the Phaedrus are by far the most important. The opening words of the Philebus state in the clearest possible form the opposing points of view of the popular pursuit of pleasure and the sterner Platonic attitude:

"Philebus was saying that enjoyment and pleasure and delight, and the class of feelings akin to them, are a good to every living being, whereas I contend, that not these, but wisdom and intelligence and memory, and their kindred, right opinion and true reasoning, are better and more desirable than pleasure for all who are able to partake of them, and that to all such who are or ever will be they are the most advantageous of all things. Have I not given, Philebus, a fair statement of the two sides of the argument? "
Although in the Lysis and the Symposium the treatment is poetical and romantic, in the latter dialogue the inferiority of physical love is considerably stressed. /Page 10/ The seeker for truth is advised to proceed step by step, from the love of human forms to the virtually mystical contemplation of the abstract ideal of beauty itself. This is summarised at the conclusion of Socrates' famous speech:

"He who has been instructed thus far in the things of love, and who has learned to see the beautiful in due order and succession, when he comes toward the end will suddenly perceive a nature of wondrous beauty-a nature which in the first place is ever­lasting, not growing and decaying, or waxing and waning; secondly, not fair in one point of view and foul in another, or at one time or in one relation or at one place fair, at another time or in another relation or at another place foul, as if fair to some and ioul to others, or in the likeness of a face or hands or any other part of the bodily frame, or in any form of speech or knowledge, or existing in any other being, as for example, in an animal, or in heaven, or in earth, or in any other place; but beauty absolute separate simple and everlasting, which without diminution and without increase, or any change, is imparted to the ever-growing and perishing beauties of all other things. He who from these ascending under the influence of true love, begins to perceive that beauty, is not far from the end. And the true order of going, or being led by another, to the things of love, is to begin from the beauties of earth and mount upwards for the sake of that other beauty, using these as steps only, and from one going on to two, and from two to all fair forms, and from fair arms to fair practices, and from fair practices to fair notions, until from fair notions he arrives at the /Page 11/absolute beauty, and at last knows what the essence of beauty is ... In that communion only, beholding beauty with the eye of the mind, he will be enabled to bring forth, not images of beauty, but realities (for he has hold not of an image but of a reality), and bringing forth and nourishing true virtue to become the friend of god and be immortal, if mortal man may."

The Phaedrus was written in Athens in the fourth century B.C. and probably in Plato's middle years. The opening theme of the work is the art of rhetoric and this leads to a discussion of love. There follows the memorable allegory of the charioteer, Reason, and his two horses, representing the moral and con­cupiscent elements in human nature. This formulation of the tripartite nature. of the soul has been fundamental to Western philosophy. Here is the distinction which is reflected in the warring of the flesh and the spirit, of which St. Paul and so many later Christian teachers speak. Plato, it is true, did not make an absolute separation of these two aspects of the soul, aware as he was of the ease with which the higher passes into the lower or the lower can be "tamed and humbled, and follow the will of the charioteer". Such concepts are common in the strains of Christian mysticism. St. Francis would gladly have echoed th sentiment of the great final prayer of this work: "Beloved Pan, and all ye other gods who haunt this place, give me beauty in the inward soul: and may the outward and the inward man be at one". But it is undoubted that from the denigration of the senses, clearly laid down in Plato's last work, the Laws, and which is certainly implicit in the Phaedrus, 'stems the tenacious tradition in the /Page 12/ West that the body and its desires should be treated with severe discipline, as unworthy of the higher nature of man and tending to deprive him of true happiness and harmony."

 

 

THE ANANGA RANGA OF KALYANA MALLA

Translated By Sir Richard Burton and F. F. Arbuthnot

and

THE SYMPOSIUM OF PLATO

Translated By Benjamin Jowett

Edition 1963

Page 9

THE PLATONIC AND HINDU ATTITUDES TO LOVE AND SEX

by

Kenneth Walker

"Beloved Pan, and all ye other gods who haunt this place, give me beauty in the inward soul: and may the outward and the inward man be at one". But it is undoubted that from the denigration of the senses, clearly laid down in Plato's last work, the Laws, and which is certainly implicit in the Phaedrus, 'stems the tenacious tradition in the /Page 12/ West that the body and its desires should be treated with severe discipline, as unworthy of the higher nature of man and tending to deprive him of true happiness and harmony."

 

"BELOVED PAN AND ALL YE OTHER GODS WHO HAUNT THIS PLACE, GIVE ME BEAUTY IN THE INWARD SOUL:

AND MAY THE OUTWARD AND THE INWARD MAN BE AT ONE"

 

B
=
2
-
7
BELOVED
65
29
2
P
=
7
-
3
PAN
31
13
4
A
=
1
-
3
AND
19
10
1
A
=
1
-
3
ALL
25
7
7
Y
=
7
-
2
YE
30
12
3
O
=
6
-
5
OTHER
66
30
3
G
=
7
-
4
GODS
45
18
9
W
=
5
-
3
WHO
46
19
1
H
=
8
-
5
HAUNT
64
19
1
T
=
2
-
4
THIS
56
20
2
P
=
7
-
5
PLACE
37
19
1
-
-
53
-
44
-
484
196
34
-
-
-
-
-
-
-
-
-
G
=
7
-
4
GIVE
43
25
7
M
=
4
-
2
ME
18
9
9
B
=
2
-
6
BEAUTY
74
20
2
I
=
9
-
2
IN
23
14
5
T
=
2
-
3
THE
33
15
6
I
=
9
-
6
INWARD
69
33
6
S
=
1
-
4
SOUL
67
13
4
-
-
34
-
27
-
327
129
39
-
-
-
-
-
-
-
-
-
A
=
1
-
3
AND
19
10
1
M
=
4
-
3
MAY
39
12
3
T
=
2
-
3
THE
33
15
6
O
=
6
-
7
OUTWARD
102
30
3
A
=
1
-
3
AND
19
10
1
T
=
2
-
3
THE
33
15
6
I
=
9
-
6
INWARD
69
33
6
M
=
4
-
3
MAN
28
10
1
B
=
2
-
2
BE
7
7
7
A
=
1
-
2
AT
21
3
3
O
=
6
-
3
ONE
34
16
7
-
-
38
-
38
-
404
161
44
-
-
-
-
-
-
-
-
-
-
-
125
-
109
First Total
1215
486
117
Q
-
1+2+5
-
1+0+9
Add to Reduce
1+2+1+5
4+8+6
1+1+7
-
-
8
-
10
Second Total
9
9
9
-
-
-
-
1+0
Reduce to Deduce
-
-
-
-
-
8
-
1
Essence of Number
9
9
-

 

 

Humanitites Institute Colloquium: Redefining Nature's Boundaries ... - 10:37pm
Plato wrote of his teacher Socrates invoking a prayer in a grove of Attica to Pan, god of nature: “Beloved Pan, and all ye other gods who haunt this place, ...
www.bucknell.edu/x31103.xml -

Plato wrote of his teacher Socrates invoking a prayer in a grove of Attica to Pan, god of nature: “Beloved Pan, and all ye other gods who haunt this place, give me beauty in the inward soul; and may the outward and inward man be at one.” A few centuries later, the writer Plutarch described the announcement of the death of Pan in the heyday of the Roman Empire. Thamus, an Egyptian pilot called by a mysterious voice while at sea, is told to announce the death of the god. “Looking toward the land, he said the words as he had heard them: ‘Great Pan is dead.’ Even before he had finished there was a great cry of lamentation, not of one person, but of many, mingled with exclamations of amazement.”

 

Pan (mythology) - Wikipedia, the free encyclopedia
The god, still infatuated, took some of the reeds, because he could not identify ... When you reach Palodes, take care to proclaim that the great god Pan is dead. .... Vinci, Leo (1993), Pan: Great God Of Nature, Neptune Press, London ... en.wikipedia.org/wiki/Pan_(mythology)

 

The Death of Pan


Pan, Mikhail Vrubel 1900.If one were to believe the Greek historian Plutarch (in "The Obsolescence of Oracles" (Moralia, Book 5:17)), Pan is the only Greek god who is dead. During the reign of Tiberius (A.D. 14-37), the news of Pan's death came to one Thamus, a sailor on his way to Italy by way of the island of Paxi. A divine voice hailed him across the salt water, "Thamus, are you there? When you reach Palodes,[17] take care to proclaim that the great god Pan is dead." Which Thamus did, and the news was greeted from shore with groans and laments.

Robert Graves (The Greek Myths) suggested that the Egyptian Thamus apparently misheard Thamus Pan-megas Tethnece 'the all-great Tammuz is dead' for 'Thamus, Great Pan is dead!' Certainly, when Pausanias toured Greece about a century after Plutarch, he found Pan's shrines, sacred caves and sacred mountains still very much frequented.

 

GREAT PAN IS NOT DEAD

 

 

 

 

B
=
2
-
7
BELOVED
65
29
2
P
=
7
-
3
PAN
31
13
4
A
=
1
-
3
AND
19
10
1
A
=
1
-
3
ALL
25
7
7
Y
=
7
-
2
YE
30
12
3
O
=
6
-
5
OTHER
66
30
3
G
=
7
-
4
GODS
45
18
9
W
=
5
-
3
WHO
46
19
1
H
=
8
-
5
HAUNT
64
19
1
T
=
2
-
4
THIS
56
20
2
P
=
7
-
5
PLACE
37
19
1
-
-
53
4
44
First Total
484
196
34
-
-
5+3
-
4+4
Add to Reduce
4+8+4
1+9+6
3+4
Q
-
8
-
8
Second Total
16
16
7
-
-
-
-
-
Reduce to Deduce
1+6
1+6
-
-
-
8
-
8
Essence of Number
7
7
7

 

 

G
=
7
-
4
GIVE
43
25
7
M
=
4
-
2
ME
18
9
9
B
=
2
-
6
BEAUTY
74
20
2
I
=
9
-
2
IN
23
14
5
T
=
2
-
3
THE
33
15
6
I
=
9
-
6
INWARD
69
33
6
S
=
1
-
4
SOUL
67
13
4
-
-
34
4
27
First Total
327
129
39
-
-
3+4
-
2+7
Add to Reduce
3+2+7
1+2+9
3+9
Q
-
7
-
9
Second Total
12
12
12
-
-
-
-
-
Reduce to Deduce
1+2
1+2
1+2
-
-
7
-
9
Essence of Number
3
3
3

 

 

A
=
1
-
3
AND
19
10
1
M
=
4
-
3
MAY
39
12
3
T
=
2
-
3
THE
33
15
6
O
=
6
-
7
OUTWARD
102
30
3
A
=
1
-
3
AND
19
10
1
T
=
2
-
3
THE
33
15
6
I
=
9
-
6
INWARD
69
33
6
M
=
4
-
3
MAN
28
10
1
B
=
2
-
2
BE
7
7
7
A
=
1
-
2
AT
21
3
3
O
=
6
-
3
ONE
34
16
7
-
-
38
4
38
First Total
404
161
44
-
-
3+8
-
3+8
Add to Reduce
4+0+4
1+6+1
4+4
Q
-
11
-
11
Second Total
8
8
8
-
-
1+1
-
1+1
Reduce to Deduce
-
-
-
-
-
2
-
2
Essence of Number
8
8
8

 

 

P
=
7
-
5
PLATO
64
19
1
P
=
7
-
8
PHAEDRUS
92
38
2
-
-
14
4
13
First Total
156
57
3
-
-
1+4
-
1+3
Add to Reduce
1+5+6
5+7
-
Q
-
5
-
4
Second Total
12
12
3
-
-
-
-
-
Reduce to Deduce
1+2
1+2
-
-
-
5
-
4
Essence of Number
3
3
3

 

 

1
I
9
9
9
-
REMEMBER
-
-
-
1
R
18
9
9
2
EM
18
9
9
2
EM
18
9
9
2
BE
7
7
7
1
R
18
9
9
8
REMEMBER
79
43
43
-
-
7+9
4+3
4+3
8
REMEMBER
16
7
7
-
-
1+6
-
-
8
REMEMBER
7
7
7

 

MANY TIMES ARJUNA YOU AND I HAVE BEEN BORN I REMEMBER THEM ALL THOU DOST NOT

 

1
I
9
9
9
-
REMEMBERED
-
-
-
1
R
18
9
9
2
EM
18
9
9
2
EM
18
9
9
2
BE
7
7
7
1
R
18
9
9
2
ED
18
9
9
8
REMEMBERED
79
43
43
-
-
7+9
4+3
4+3
8
REMEMBERED
16
7
7
-
-
1+6
-
-
8
REMEMBERED
7
7
7

 

 

1
I
9
9
9
4
THAT
49
13
4
2
AM
14
5
5
7
-
72
27
18
-
-
7+2
2+7
1+8
7
-
9
9
9
-
-
-
-
-
-
-
-
-
-
-
REMEMBERING
-
-
-
1
R
18
9
9
2
EM
18
9
9
2
EM
18
9
9
2
BE
7
7
7
1
R
18
9
9
1
I
9
9
9
2
NG
21
12
3
11
REMEMBERING
109
64
55
1+1
-
1+0+9
6+4
5+5
2
REMEMBERING
10
10
10
-
-
1+0
1+0
1+0
2
REMEMBERING
1
1
1

 

 

THE

ZED ALIZ ZED

AGAIN IMAGES JUST THE RIGHT AMOUNT OF MAGI MAGIC

 

 

 

3
THE
33
15
6
4
FIVE
42
24
6
8
PLATONIC
90
36
9
6
SOLIDS
78
24
6
21
First Total
243
99
27
2+1
Add to Reduce
2+4+3
9+9
2+7
3
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
3
Essence of Number
9
9
9

 

 

21
T
H
E
-
F
I
V
E
-
P
L
A
T
O
N
I
C
-
S
O
L
I
D
S
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
9
-
-
-
-
-
-
-
6
5
9
-
-
1
6
-
9
-
1
+
=
54
5+4
=
9
-
9
-
9
-
-
8
-
-
-
9
-
-
-
-
-
-
-
15
14
9
-
-
19
15
-
9
-
19
+
=
117
1+1+7
=
9
-
9
-
9
21
T
H
E
-
F
I
V
E
-
P
L
A
T
O
N
I
C
-
S
O
L
I
D
S
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
6
-
4
5
-
7
3
1
2
-
-
-
3
-
-
-
3
-
4
-
+
=
45
4+5
=
9
-
9
-
9
-
20
-
5
-
6
-
22
5
-
16
12
1
20
-
-
-
3
-
-
-
12
-
4
-
+
=
126
1+2+6
=
9
-
9
-
9
21
T
H
E
-
F
I
V
E
-
P
L
A
T
O
N
I
C
-
S
O
L
I
D
S
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
6
9
22
5
-
16
12
1
20
15
14
9
3
-
19
15
12
9
4
19
+
=
243
2+4+3
=
9
=
9
-
9
-
2
8
5
-
6
9
4
5
-
7
3
1
2
6
5
9
3
-
1
6
3
9
4
1
+
=
99
9+9
=
18
1+8
9
-
9
21
T
H
E
-
F
I
V
E
-
P
L
A
T
O
N
I
C
-
S
O
L
I
D
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
``-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
21
T
H
E
-
F
I
V
E
-
P
L
A
T
O
N
I
C
-
S
O
L
I
D
S
-
-
45
-
-
21
-
99
-
36
2+1
-
-
-
-
-
9
-
-
-
-
-
-
-
-``
-
9
-
-``
-
-``
-
9
-
-
-
-
4+5
-
-
2+1
-
9+9
-
3+6
3
T
H
E
-
F
I
V
E
-
P
L
A
T
O
N
I
C
-
S
O
L
I
D
S
-
-
9
-
-
3
-
18
-
9
-
2
8
5
-
6
9
4
5
-
7
3
1
2
6
5
9
3
-
1
6
3
9
4
1
-
-
-
-
-
-
-
1+8
-
-
3
T
H
E
-
F
I
V
E
-
P
L
A
T
O
N
I
C
-
S
O
L
I
D
S
-
-
9
-
-
3
-
9
-
9

 

 

 

3
THE
33
15
6
4
FIVE
42
24
6
8
PLATONIC
90
36
9
6
SOLIDS
78
24
6
21
First Total
243
99
27
2+1
Add to Reduce
2+4+3
9+9
2+7
3
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
3
Essence of Number
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
-
-
-
-
P
=
7
-
8
PLATONIC
90
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SOLIDS
78
24
6
-
-
-
-
-
-
-
-
-
-
-
-
16
-
21
First Total
243
99
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
9
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
16
-
3
-
33
15
15
-
-
-
-
-
-
-
-
-
-
F
=
6
4
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
6
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
24
-
4
-
42
24
24
-
-
-
-
-
-
-
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
L
=
3
9
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
10
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
11
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
13
1
N
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
15
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
-
-
36
-
8
-
90
36
36
-
-
-
-
-
-
-
-
-
-
S
=
1
16
1
S
19
1
1
-
1
-
-
-
-
-
-
-
-
O
=
6
17
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
L
=
3
18
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
19
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
20
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
21
1
S
19
1
1
-
1
-
-
-
-
-
-
-
-
-
-
24
-
6
-
78
24
24
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
3
4
9
8
15
18
7
8
27
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
1+5
1+8
-
-
2+7
P
=
7
-
8
PLATONIC
90
36
9
-
3
4
9
8
6
9
7
8
9
S
=
1
-
6
SOLIDS
78
24
6
-
-
-
-
-
-
-
-
-
-
-
-
16
-
21
First Total
243
99
27
-
3
4
9
8
6
9
7
8
9
-
-
1+6
-
2+1
Add to Reduce
1+8+0
9+9
2+7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
9
Second Total
9
18
9
-
3
4
9
8
6
9
7
8
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
9
Essence of Number
9
9
9
-
3
4
9
8
6
9
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
-
-
-
-
P
=
7
-
8
PLATONIC
90
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SOLIDS
78
24
6
-
-
-
-
-
-
-
-
-
-
-
-
16
-
21
First Total
243
99
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
9
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
4
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
6
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
L
=
3
9
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
A
=
1
10
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
11
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
13
1
N
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
15
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
S
=
1
16
1
S
19
1
1
-
1
-
-
-
-
-
-
-
-
O
=
6
17
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
L
=
3
18
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
I
=
9
19
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
D
=
4
20
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
S
=
1
21
1
S
19
1
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
3
4
9
8
15
18
7
8
27
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
1+5
1+8
-
-
2+7
P
=
7
-
8
PLATONIC
90
36
9
-
3
4
9
8
6
9
7
8
9
S
=
1
-
6
SOLIDS
78
24
6
-
-
-
-
-
-
-
-
-
-
-
-
16
-
21
First Total
243
99
27
-
3
4
9
8
6
9
7
8
9
-
-
1+6
-
2+1
Add to Reduce
1+8+0
9+9
2+7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
9
Second Total
9
18
9
-
3
4
9
8
6
9
7
8
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
9
Essence of Number
9
9
9
-
3
4
9
8
6
9
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
-
-
-
-
P
=
7
-
8
PLATONIC
90
36
9
-
-
-
-
-
-
-
-
-
-
S
=
1
-
6
SOLIDS
78
24
6
-
-
-
-
-
-
-
-
-
-
-
-
16
-
21
First Total
243
99
27
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
A
=
1
10
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
16
1
S
19
1
1
-
1
-
-
-
-
-
-
-
-
S
=
1
21
1
S
19
1
1
-
1
-
-
-
-
-
-
-
-
T
=
2
1
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
11
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
L
=
3
9
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
C
=
3
15
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
L
=
3
18
1
L
12
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
6
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
D
=
4
20
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
3
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
7
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
13
1
N
5
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
4
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
12
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
17
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
P
=
7
8
1
P
16
7
7
-
-
-
-
-
-
-
7
-
-
H
=
9
2
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
5
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
14
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
19
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
T
=
2
-
3
THE
33
15
6
-
3
4
9
8
15
18
7
8
27
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
1+5
1+8
-
-
2+7
P
=
7
-
8
PLATONIC
90
36
9
-
3
4
9
8
6
9
7
8
9
S
=
1
-
6
SOLIDS
78
24
6
-
-
-
-
-
-
-
-
-
-
-
-
16
-
21
First Total
243
99
27
-
3
4
9
8
6
9
7
8
9
-
-
1+6
-
2+1
Add to Reduce
1+8+0
9+9
2+7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
9
Second Total
9
18
9
-
3
4
9
8
6
9
7
8
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
9
Essence of Number
9
9
9
-
3
4
9
8
6
9
7
8
9

 

 

11
TETRAHEDRON
128
56
2
10
OCTAHEDRON
103
49
4
11
ICOSAHEDRON
111
57
3
10
HEXAHEDRON
102
57
3
12
DODECAHEDRON
96
60
6
54
-
540
279
18

Page 78

"Plato declares that there are certain numbers that link these with each other and with all phenomena capable of being measured. As an example of these numbers, the study of which Plato recommends as the most sanctifying of all pursuits, he gives 5040."

 

11
TETRAHEDRON
128
56
2
10
OCTAHEDRON
103
49
4
11
ICOSAHEDRON
111
57
3
10
HEXAHEDRON
102
57
3
12
DODECAHEDRON
96
60
6
54
First Total
540
279
18
5+4
Add to Reduce
5+4+0
2+7+9
1+8
9
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
9
Essence of Number
9
9
9

Page78

"As an example of these numbers, the study of which Plato recommends as the most sanctifying of all pursuits, he gives 5040."

 

9
FIFTY FOUR
126
54
9

 

 

THE DIVINE PROPORTION

A STUDY IN MATHEMATICAL BEAUTY

H. E. Huntley 1970

Page 31

THE FIVE PLATONIC SOLIDS

The Greeks took a mystical view of the five regular solids. This is hardly surprising for the forms are beautiful in themselves. No mathematical sophistication is needed for the appreciation of the charm of their outward appearance: that is the given element of their beauty. By contrast, that which is acquired by training and education demands considerable mental effort.
The five regular solids were treated by Euclid in Book XIII of the Elements but are associated with the name of Plato because of his efforts to relate them to the important entities of which he supposed the world to be made. The aura of mysticism with which the Greek geometers surrounded them persisted until the dawn in the sixteenth century of the scientific era. But the aesthetic appeal of what are still known as the Platonic solids is undiminished. Next to the writer's chair, for some years past, there has stood a small dodecahedron of white china!
We are now confronted with our first example of beauty in mathematics. The facts have been common knowledge among mathematicians for 2000 years. Much evidence of their aesthetic appeal in the past is on record
The first point to note about the regular Platonic solids shown in figure 2.6 (Page 32 Figures omitted) is that they are precisely five in number. A little thought shows that, while an infinite number of polygons may be
drawn on a plane surface, it is not possible to construct more than five regular polyhedra in three-dimensional space. The surface of a regular polyhedron is bounded by congruent regular polygons. The simplest polygons. that can form the surface are the equilateral triangle, the square and the pentagon. It is clear from figure 2.6 ( Page 32 Figures omitted) that we cannot form the corner of a polyhedron with fewer than three faces and that a corner may be formed by joining three, four, or five equilateral triangles. With six such triangles, the corner flattens into a plane. The same will happen if four squares are united. Similarly, three regular pentagons at a corner is a maximum. But hexagons, and polygons with more than five sides are all ruled out. This argument for the limitation to five regular / Page 33 / solids is the source of Euler's formula V + F = E + 2, where the letters stand for the number of vertices, faces, and edges respectively.
The second point of interest is that two pairs of the Platonic solids are reciprocal and the fifth is self reciprocating in this sense: if the face centers of the cube are joined, an octahedron is formed, while the joins of the centroids of the octahedron surfaces form a cube. Similar relationship holds between the icosahedron and the dodecahedron., The join of the four centroids of the tetrahedron's faces makes another tetrahedron.
Fig. 2.7. Icosahedron (Figures omitted)
The third noteworthy feature is the relationship of the two pairs of reciprocal polyhedra to the golden rectangle (Figs. 2.7 and 2.8).(Figures omitted)
The Icosahedron. The twelve vertices of a regular icosahedron are divisible into three coplanar groups of four. These lie at the corners of three golden rectangles which are symmetrically situated with respect to each other, being mutually perpendicular, their one common point being the centroid of the icosahedron (Fig. 2.7).
The Octahedron. An icosahedron can be inscribed in an octahedron so that each vertex of the former divides an edge of the latter in the golden section.
The Dodecahedron. The centroids of the twelve pentagonal faces of a dodecahedron are divisible into three coplanar groups of / Page 34 / four. These quadrads lie at the corners of three mutually perpendicular, symmetrically placed golden rectangles, their one common point being the centroid of the dodecahedron (Fig. 2.8).
The aesthetic appeal of the topics of this chapter cannot be doubted. Whether we can explain it or not, the fact that they have been enjoyed by sixty generations of men is good evidence.

Fig. 2.8. Dodecahedron (Figures omitted)

It should be realized that we have only examined the surface of the subject. One of the ingredients of beauty in mathematics is its depth. Even in these familiar waters, "full many a gem of purest ray serene" awaits discovery by the explorer. There appears to be no limit, as Sir Edwin Arnold affirms in The Light of Asia:

Shall any gazer see with mortal eyes
Or any searcher know with mortal min
Veil after veil will lift-but there must be
Veil after veil behind
.

Page 32 (Figures omitted)

 

 

11
TETRAHEDRON
128
56
2
10
OCTAHEDRON
103
49
4
11
ICOSAHEDRON
111
57
3
10
HEXAHEDRON
102
57
3
12
DODECAHEDRON
96
60
6
54
First Total
540
279
18

 

"Plato declares that there are certain numbers that link these with each other and with all phenomena capable of being measured. As an example of these numbers, the study of which Plato recommends as the most sanctifying of all pursuits, he gives 5040."

 

 

1
THE
33
15
6
1
FIVE
42
24
6
2
PLATONIC
90
36
9
1
SOLIDS
78
24
6
6
First Total
243
99
27
-
Add to Reduce
2+4+3
9+9
2+7
6
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
6
Essence of Number
9
9
9

 

 

11
TETRAHEDRON
128
56
2
10
OCTAHEDRON
103
49
4
11
ICOSAHEDRON
111
57
3
10
HEXAHEDRON
102
57
3
12
DODECAHEDRON
96
60
6
54
First Total
540
279
18
5+4
Add to Reduce
5+4+0
2+7+9
1+8
9
Second Total
9
18
9
-
Reduce to Deduce
-
1+8
-
9
Essence of Number
9
9
9

 

 

 

-
TETRAHEDRON
-
-
-
3
T+E+T
45
9
9
1
R
18
9
9
2
A+H
9
9
9
2
E+D
9
9
9
1
R
18
9
9
2
O+N
29
11
2
11
TETRAHEDRON
128
56
47
1+1
-`
1+2+8
5+6
4+7
2
TETRAHEDRON
11
11
11
-
-`
1+1
1+1
1+1
2
TETRAHEDRON
2
2
2

 

 

 

-
OCTAHEDRON
-
-
-
3
OC
18
9
9
1
T
20
2
2
2
A+H
9
9
9
2
E+D
9
9
9
1
R
18
9
9
2
O+N
29
11
2
11
OCTAHEDRON
103
49
47
1+1
-`
1+0+3
4+9
4+7
2
OCTAHEDRON
4
13
11
-
-`
4
1+3
1+1
2
OCTAHEDRON
4
4
4

 

 

 

-
ICOSAHEDRON
-
-
-
1
I
9
9
9
2
C+O
18
9
9
1
S
19
1
1
2
A+H
9
9
9
2
E+D
9
9
9
1
R
18
9
9
2
O+N
29
11
2
11
ICOSAHEDRON
111
57
48
1+1
-`
1+1+1
5+7
4+8
2
ICOSAHEDRON
3
12
12
-
-`
-
1+2
1+2
2
ICOSAHEDRON
3
3
3

 

 

 

-
HEXAHEDRON
-
-
-
3
H+E+X
37
19
1
2
A+H
9
9
9
2
E+D
9
9
9
1
R
18
9
9
2
O+N
29
11
2
10
HEXAHEDRON
102
57
30
1+0
-`
1+0+2
5+7
3+0
1
HEXAHEDRON
3
12
3
-
-`
-
1+2
-
1
HEXAHEDRON
3
3
36

 

 

 

-
DODECAHEDRON
-
-
-
1
D
4
4
4
6
O+D+E+C+A+H
36
27
9
2
E+D
9
9
9
1
R
18
9
9
2
O+N
29
11
2
12
DODECAHEDRON
96
60
33
1+2
-`
9+6
6+0
3+3
3
DODECAHEDRON
15
6
6
-
-`
1+5
-
-
3
DODECAHEDRON
6
6
6

 

 

 

-
ICOSAHEDRON
-
-
-
1
I
9
9
9
2
C+O
18
9
9
1
S
19
1
1
2
A+H
9
9
9
2
E+D
9
9
9
1
R
18
9
9
2
O+N
29
11
2
11
ICOSAHEDRON
111
57
48
1+1
-`
1+1+1
5+7
4+8
2
ICOSAHEDRON
3
12
12
-
-`
-
1+2
1+2
2
ICOSAHEDRON
3
3
3

 

 

-
-
-
-
-
-
-
ICOSAHEDRON
-
-
-
-
1
2
3
4
5
6
7
8
9
I
=
9
-
1
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
C
=
3
-
2
-
1
C
3
3
3
-
-
-
3
-
-
-
-
-
-
O
=
6
-
3
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
S
=
1
-
4
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
A
=
1
-
5
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
-
H
=
8
-
6
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
-
7
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
D
=
4
-
8
-
1
D
4
4
4
-
-
-
-
4
-
-
-
-
-
R
=
9
-
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
10
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
-
11
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
57
-
-
-
11
ICOSAHEDRON
111
66
57
-
2
2
3
4
10
12
7
8
18
-
-
5+7
-
-
-
1+1
-
1+1+1
6+6
5+7
-
-
-
-
-
1+0
1+2
-
-
1+8
-
-
12
-
-
-
2
ICOSAHEDRON
3
12
12
-
2
2
3
4
1
3
7
8
9
-
-
1+2
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
2
ICOSAHEDRON
3
3
3
-
2
2
3
4
1
3
7
8
9

 

 

-
-
-
-
-
-
-
ICOSAHEDRON
-
-
-
-
1
3
4
5
6
7
8
9
I
=
9
-
1
-
1
I
9
9
9
-
-
-
-
-
-
-
-
9
C
=
3
-
2
-
1
C
3
3
3
-
-
3
-
-
-
-
-
-
O
=
6
-
3
-
1
O
15
6
6
-
-
-
-
-
6
-
-
-
S
=
1
-
4
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
A
=
1
-
5
-
1
A
1
1
1
-
1
-
-
-
-
-
-
-
H
=
8
-
6
-
1
H
8
8
8
-
-
-
-
-
-
-
8
-
E
=
5
-
7
-
1
E
5
5
5
-
-
-
-
5
-
-
-
-
D
=
4
-
8
-
1
D
4
4
4
-
-
-
4
-
-
-
-
-
R
=
9
-
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
9
O
=
6
-
10
-
1
O
15
6
6
-
-
-
-
-
6
-
-
-
N
=
5
-
11
-
1
N
14
5
5
-
-
-
-
5
-
-
-
-
-
-
57
-
-
-
11
ICOSAHEDRON
111
66
57
-
2
3
4
10
12
7
8
18
-
-
5+7
-
-
-
1+1
-
1+1+1
6+6
5+7
-
-
-
-
1+0
1+2
-
-
1+8
-
-
12
-
-
-
2
ICOSAHEDRON
3
12
12
-
2
3
4
1
3
7
8
9
-
-
1+2
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
2
ICOSAHEDRON
3
3
3
-
2
3
4
1
3
7
8
9

 

 

-
-
-
-
-
-
-
ICOSAHEDRON
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
4
-
1
S
19
10
1
-
1
2
-
-
-
-
7
-
-
A
=
1
-
5
-
1
A
1
1
1
-
1
2
-
-
-
-
7
-
-
C
=
3
-
2
-
1
C
3
3
3
-
-
2
3
-
-
-
7
-
-
D
=
4
-
8
-
1
D
4
4
4
-
-
2
-
4
-
-
7
-
-
E
=
5
-
7
-
1
E
5
5
5
-
-
2
-
-
5
-
7
-
-
N
=
5
-
11
-
1
N
14
5
5
-
-
2
-
-
5
-
7
-
-
O
=
6
-
3
-
1
O
15
6
6
-
-
2
-
-
-
6
7
-
-
O
=
6
-
10
-
1
O
15
6
6
-
-
2
-
-
-
6
7
-
-
H
=
8
-
6
-
1
H
8
8
8
-
-
2
-
-
-
-
7
8
-
I
=
9
-
1
-
1
I
9
9
9
-
-
2
-
-
-
-
7
-
9
R
=
9
-
9
-
1
R
18
9
9
-
-
2
-
-
-
-
7
-
9
-
-
57
-
-
-
11
ICOSAHEDRON
111
66
57
-
2
2
3
4
10
12
7
8
18
-
-
5+7
-
-
-
1+1
-
1+1+1
6+6
5+7
-
-
-
-
-
1+0
1+2
-
-
1+8
-
-
12
-
-
-
2
ICOSAHEDRON
3
12
12
-
2
2
3
4
1
3
7
8
9
-
-
1+2
-
-
-
-
-
-
1+2
1+2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
2
ICOSAHEDRON
3
3
3
-
2
2
3
4
1
3
7
8
9

 

 

 

1
I
9
9
9
4
PLAY
54
18
9
5
PLATO
64
19
1
5
CHESS
54
18
9

 

 

-
PLATO
-
-
-
2
PL
28
10
1
3
ATO
36
9
9
5
PLATO
64
19
10
-
--
6+4
1+9
1+0
5
PLATO
10
10
1
-
-
1+0
1+0
-
5
PLATO
1
1
1

 

 

5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
7
3
1
2
-
+
=
13
1+3
=
4
=
4
-
16
12
1
20
-
+
=
49
4+9
=
13
1+3
4
5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
-
-
1
+
=
1
-
=
1
-
1
-
-
-
A
-
-
-
-
-
-
-
-
-
-
-
-
3
-
2
-
+
=
5
=
5
-
5
-
-
L
-
T
-
-
-
-
-
-
-
-
-
-
7
-
-
-
6
+
=
13
1+3
=
4
-
4
-
P
-
-
-
O
-
-
-
-
-
-
-
-
5
P
L
A
T
O
-
-
-
-
-
--
-
-

 

 

-
5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
-
7
3
1
2
-
+
=
13
1+3
=
4
=
4
-
-
16
12
1
20
-
+
=
49
4+9
=
13
1+3
4
-
5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
-
16
12
1
20
15
+
+
64
6+4
=
10
1+0
1
-
-
7
3
1
2
6
+
+
19
1+9
=
10
1+0
1
-
5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
26
5
P
L
A
T
O
-
-
19
-
-
5
-
19
2+6
-
-
-
-
-
-
-
-
1+9
-
-
-
-
1+9
8
5
P
L
A
T
O
-
-
10
-
-
5
-
10
-
-
7
3
1
2
6
-
-
1+0
-
-
-
-
1+0
8
5
P
L
A
T
O
-
-
1
-
-
5
-
1

 

 

5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
15
+
=
15
1+5
=
6
=
6
5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
7
3
1
2
-
+
=
13
1+3
=
4
=
4
-
16
12
1
20
-
+
=
49
4+9
=
13
1+3
4
5
P
L
A
T
O
-
-
-
-
-
--
-
-
-
16
12
1
20
15
+
+
64
6+4
=
10
1+0
1
-
7
3
1
2
6
+
+
19
1+9
=
10
1+0
1
5
P
L
A
T
O
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
occurs
x
1
=
1
-
-
-
-
2
-
-
-
2
occurs
x
1
=
2
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
7
-
-
-
-
-
-
7
occurs
x
1
=
7
5
P
L
A
T
O
-
-
19
-
-
5
-
19
-
-
-
-
-
-
-
-
1+9
-
-
-
-
1+9
5
P
L
A
T
O
-
-
10
-
-
5
-
10
-
7
3
1
2
6
-
-
1+0
-
-
-
-
1+0
5
P
L
A
T
O
-
-
1
-
-
5
-
1

 

PLATO

 

Sacred Geometry is the theory of dimensional evolution which assumes the ... door to his academy stating,

"Let no one unacquainted with geometry enter here.". ...
ezinearticles.com/?An-Overview-Of-Sacred-Geometry

 

AN OVERVIEW OF SACRED GEOMETRY

Gregg Hall

Sacred Geometry is the theory of dimensional evolution which assumes the universe is a living system kept together by the existence of a sacred geometry that encompasses the entire cosmos and makes for the blueprint for the manifestation of what we know as our material universe and in addition organizes the context through which all love evolves.

Our universe was designed to be highly efficient and is capable of performing a wide range of multiple functions at the same time. The very same geometry which provides structure to physical reality also allows for the perceptual environments that people and civilizations must move through as part of a systematic learning process on the path towardsevolution.

Each dimension of this sacred geometry holds a unique place of perceptual space and a context of learning both for personal and social evolution. As each new dimension appears a new set of perceptions and potentials is awakened which we are free to accept and actualize or ignore. It is in understanding the dimensional structure which exists all around us that allows us to be able to understand the path and direction of personal and social evolution.

Even though our modern science generally believes there is nothing of deeper meaning to the dimensional geometry of the universe other than the actual physical aspects, there is a view that is almost diametrically opposed to this that began with the Greek philosopher Pythagoras in 500 B.C. Pythagoras believed and taught the theory or belief that all of the mathematical patterns in the universe were actually expressions of divine intelligence and signified a divine intention.

According to Pythagoras, we are surrounded by organizational intelligence that is shown in its purest from through mathematical formulas and musical harmonies and allowing ourselves to be at the center of our experience; we can know and share the organizing patterns and principles that pervade the universe. This is a thought that was even held by Albert Einstein, who stated that he received his greatest breakthroughs after praying and sleeping. The answers to the questions he was seeking came to him from the Universe while he slept! This is also the way that it can be explained for someone who is blind to be able to sculpt and for a deaf person, such as Beethoven to be able to compose intricate musical scores.

Plato, who taught over a hundred years after Pythagoras, continued in the teachings of Pythagorean thought in espousing that the universe or cosmos as Pythagoras termed it was a place of "harmonious and beautiful order" and placed such a high regard on geometry that he placed a sign above the door to his academy stating, "Let no one unacquainted with geometry enter here."

 

 

the aims of studying plane geometry and how to attain them - Jstor
https://www.jstor.org/stable/27949586

by EP Sisson - 1908
Plato had written over the porch of his famous school,

"Let no one who is unacquainted with geometry enter here."

 

 

The Cyclopædia, Or, Universal Dictionary of Arts, Sciences, and ...

Abraham Rees - 1819 - ?Encyclopedias and dictionaries
But to these arguments it has been replied, 1. ... he placed this inscription, Ovcel; 2) souárpolo; a`To

“Let no one, who is unacquainted with geometry, enter here.

 

 

A history of elementary mathematics -

Page 61

C. Florian - 1914 - History

Let no one who is unacquainted with geometry enter here,” was inscribed over the entrance to his school.

Likewise Xenocrates, a successor of Plato, as teacher ...

 

 

A History of Mathematics

Page 26

Florian Cajori - 1999 - Mathematics
Like them, he sought in arithmetic and geometry the key to the universe. ...

inscription over his porch, "Let no one who is unacquainted with geometry enter here".

 

 

"Let no one enter here who is unacquainted with geometry."

 

L
=
3
3
LET
37
10
1
N
=
5
2
NO
29
11
2
O
=
6
3
ONE
34
16
7
E
=
5
5
ENTER
62
26
8
H
=
8
4
HERE
36
27
9
W
=
5
3
WHO
46
19
1
I
=
9
2
IS
28
19
1
U
=
3
11
UNAQUAINTED
127
46
1
W
=
5
4
WITH
60
24
6
G
=
7
8
GEOMETRY
108
45
9
-
-
56
45
First Total
567
243
45
-
-
5+6
4+5
Add to Reduce
5+6+7
2+4+3
4+5
-
-
11
9
Second Total
18
9
9
-
-
1+1
-
Reduce to Deduce
1+8
-
-
-
-
2
9
Essence of Number
9
9
9

 

"Let no one enter here who is unacquainted with geometry."

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
1
-
3
LET
37
10
1
-
1
-
-
-
-
-
-
-
-
N
=
5
-
2
-
2
NO
29
11
2
-
-
2
-
-
-
-
-
-
-
O
=
6
-
3
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
4
-
5
ENTER
62
26
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
5
-
4
HERE
36
27
9
-
-
-
-
-
-
-
-
-
9
W
=
5
-
6
-
3
WHO
46
19
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
7
-
2
IS
28
19
1
-
1
-
-
-
-
-
-
-
-
U
=
3
-
8
-
11
UNAQUAINTED
127
46
1
-
1
-
-
-
-
-
-
-
-
W
=
5
-
9
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
G
=
7
-
10
-
8
GEOMETRY
108
45
9
-
-
-
-
-
-
-
-
-
9
-
-
56
-
-
-
45
First Total
567
243
45
-
4
2
3
4
5
6
7
8
18
-
-
5+6
-
-
-
4+5
Add to Reduce
5+6+7
2+4+3
4+5
-
-
-
-
-
-
-
-
-
1+8
-
-
11
-
-
-
9
Second Total
18
9
9
-
4
2
3
4
5
6
7
8
9
-
-
1+1
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
9
Essence of Number
9
9
9
-
4
2
3
4
5
6
7
8
9

 

"Let no one enter here who is unacquainted with geometry."

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
1
-
3
LET
37
10
1
-
1
-
-
-
-
-
-
-
-
W
=
5
-
6
-
3
WHO
46
19
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
7
-
2
IS
28
19
1
-
1
-
-
-
-
-
-
-
-
U
=
3
-
8
-
11
UNAQUAINTED
127
46
1
-
1
-
-
-
-
-
-
-
-
N
=
5
-
2
-
2
NO
29
11
2
-
-
2
-
-
-
-
-
-
-
W
=
5
-
9
-
4
WITH
60
24
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
3
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
E
=
5
-
4
-
5
ENTER
62
26
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
5
-
4
HERE
36
27
9
-
-
-
-
-
-
-
-
-
9
G
=
7
-
10
-
8
GEOMETRY
108
45
9
-
-
-
-
-
-
-
-
-
9
-
-
56
-
-
-
45
First Total
567
243
45
-
4
2
3
4
5
6
7
8
18
-
-
5+6
-
-
-
4+5
Add to Reduce
5+6+7
2+4+3
4+5
-
-
-
-
-
-
-
-
-
1+8
-
-
11
-
-
-
9
Second Total
18
9
9
-
4
2
3
4
5
6
7
8
9
-
-
1+1
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
9
Essence of Number
9
9
9
-
4
2
3
4
5
6
7
8
9

 

"Let no one enter here who is unacquainted with geometry."

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
1
-
3
LET
37
10
1
-
1
-
3
4
5
-
-
-
-
W
=
5
-
6
-
3
WHO
46
19
1
-
1
-
3
4
5
-
-
-
-
I
=
9
-
7
-
2
IS
28
19
1
-
1
-
3
4
5
-
-
-
-
U
=
3
-
8
-
11
UNAQUAINTED
127
46
1
-
1
-
3
4
5
-
-
-
-
N
=
5
-
2
-
2
NO
29
11
2
-
-
2
3
4
5
-
-
-
-
W
=
5
-
9
-
4
WITH
60
24
6
-
-
-
3
4
5
6
-
-
-
O
=
6
-
3
-
3
ONE
34
16
7
-
-
-
3
4
5
-
7
-
-
E
=
5
-
4
-
5
ENTER
62
26
8
-
-
-
3
4
5
-
-
8
-
H
=
8
-
5
-
4
HERE
36
27
9
-
-
-
3
4
5
-
-
-
9
G
=
7
-
10
-
8
GEOMETRY
108
45
9
-
-
-
3
4
5
-
-
-
9
-
-
56
-
-
-
45
First Total
567
243
45
-
4
2
3
4
5
6
7
8
18
-
-
5+6
-
-
-
4+5
Add to Reduce
5+6+7
2+4+3
4+5
-
-
-
-
-
-
-
-
-
1+8
-
-
11
-
-
-
9
Second Total
18
9
9
-
4
2
3
4
5
6
7
8
9
-
-
1+1
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
9
Essence of Number
9
9
9
-
4
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
6
7
8
9
L
=
3
-
1
-
3
LET
37
10
1
-
1
-
-
-
-
-
W
=
5
-
6
-
3
WHO
46
19
1
-
1
-
-
-
-
-
I
=
9
-
7
-
2
IS
28
19
1
-
1
-
-
-
-
-
U
=
3
-
8
-
11
UNAQUAINTED
127
46
1
-
1
-
-
-
-
-
N
=
5
-
2
-
2
NO
29
11
2
-
-
2
-
-
-
-
W
=
5
-
9
-
4
WITH
60
24
6
-
-
-
6
-
-
-
O
=
6
-
3
-
3
ONE
34
16
7
-
-
-
-
7
-
-
E
=
5
-
4
-
5
ENTER
62
26
8
-
-
-
-
-
8
-
H
=
8
-
5
-
4
HERE
36
27
9
-
-
-
-
-
-
9
G
=
7
-
10
-
8
GEOMETRY
108
45
9
-
-
-
-
-
-
9
-
-
56
-
-
-
45
First Total
567
243
45
-
4
2
6
7
8
18
-
-
5+6
-
-
-
4+5
Add to Reduce
5+6+7
2+4+3
4+5
-
-
-
-
-
-
1+8
-
-
11
-
-
-
9
Second Total
18
9
9
-
4
2
6
7
8
9
-
-
1+1
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
9
Essence of Number
9
9
9
-
4
2
6
7
8
9

 

 

PYTHAGORAS

THE

MISSING

NUMBERS

EGYPT PYTHAGORAS EGYPT

THREE FOUR FIVE - FIVE FOUR THREE

PYTHAGORAS OURABORUS PYTHAGORAS

 

 

10
PYTHAGORAS
130
49
4
8
OURABORUS
130
31
4
5
SAMOS
67
13
4
7
MILETUS
99
27
9
8
THIRTEEN
99
45
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
L
=
3
-
1
-
3
LET
37
10
1
-
1
-
3
4
5
-
-
-
-
W
=
5
-
6
-
3
WHO
46
19
1
-
1
-
3
4
5
-
-
-
-
I
=
9
-
7
-
2
IS
28
19
1
-
1
-
3
4
5
-
-
-
-
U
=
3
-
8
-
11
UNAQUAINTED
127
46
1
-
1
-
3
4
5
-
-
-
-
N
=
5
-
2
-
2
NO
29
11
2
-
-
2
3
4
5
-
-
-
-
W
=
5
-
9
-
4
WITH
60
24
6
-
-
-
3
4
5
6
-
-
-
O
=
6
-
3
-
3
ONE
34
16
7
-
-
-
3
4
5
-
7
-
-
E
=
5
-
4
-
5
ENTER
62
26
8
-
-
-
3
4
5
-
-
8
-
H
=
8
-
5
-
4
HERE
36
27
9
-
-
-
3
4
5
-
-
-
9
G
=
7
-
10
-
8
GEOMETRY
108
45
9
-
-
-
3
4
5
-
-
-
9
-
-
56
-
-
-
45
First Total
567
243
45
-
4
2
3
4
5
6
7
8
18
-
-
5+6
-
-
-
4+5
Add to Reduce
5+6+7
2+4+3
4+5
-
-
-
-
-
-
-
-
-
1+8
-
-
11
-
-
-
9
Second Total
18
9
9
-
4
2
3
4
5
6
7
8
9
-
-
1+1
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
9
Essence of Number
9
9
9
-
4
2
3
4
5
6
7
8
9

 

 

THE WORLD IS BUILT UPON THE POWER OF NUMBERS

"Pythagoras, the old master philosopher and mathematician, who lived in the sixth century BC, propounded the theory that nothing in the universe could exist without numbers. He established a Mystery School in Italy when he was 52 years old. He was born in Greece and lived between 582 and 507 BC, much of his life spent in study and travel. His Mystery School taught esoteric knowledge, which included the secret of number and vibration."

“The World is built upon the power of Numbers” ...Pythagoras – 6th century BC.

 

THE WORLD IS BUILT UPON THE POWER OF NUMBERS

 

T
=
2
Q
3
THE
33
15
6
W
=
5
-
5
WORLD
72
27
9
I
=
9
-
2
IS
28
10
1
B
=
2
Q
5
BUILT
64
19
1
U
=
3
-
4
UPON
66
21
3
T
=
2
Q
3
THE
33
15
6
P
=
7
Q
5
POWER
77
32
5
O
=
6
-
2
OF
21
12
3
N
=
5
-
7
NUMBERS
92
29
2
-
-
41
-
36
First Total
486
180
36
-
-
4+1
-
3+6
Add to Reduce
2+7+9
1+8+0
3+6
-
-
5
-
9
Second Total
18
9
9
-
-
-
-
-
Reduce to Deduce
1+8
-
-
-
-
5
-
9
Essence of Number
9
9
9

 

 

I

ME

NUMBERS

EGYPTPYTHAGORAS EGYPT

THREE FOUR FIVE - FIVE FOUR THREE

PYTHAGORAS OURABORUS PYTHAGORAS

 

 

THE GROWTH OF SCIENCE

A.P. Rossiter 1939

Page 15

"The Egyptians,…" "…made good observations on the stars and were able to say when the sun or moon would become dark in an eclipse (a most surprising event even in our times), and when the land would be covered by the waters of the Nile: they were expert at building and made some discoveries about the relations of lines and angles - among them one very old rule for getting a right-angle by stretching out knotted cords with 5, 4 And 3 units between the knots."

 

"...among them one very old rule for getting a right-angle by stretching out knotted cords with

5, 4 And 3 units between the knots."

 

 

CIVILIZATION, SCIENCE AND RELIGION

A. D. RITCHIE 1945

THE ART OF THINKING

Page 39

"The Egyptians could set out a right-angle on the ground,

for building or for land surveying,

by means of a cord knotted at intervals of

3, 4 and 5 units of length."

 

 

-
-
-
-
-
PYTHAGORAS
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
P
=
7
-
1
P
16
7
7
-
-
-
3
4
5
-
7
-
-
Y
=
7
-
1
Y
25
7
7
-
-
-
3
4
5
-
7
-
-
T
=
2
-
1
T
20
2
2
-
-
2
3
4
5
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
3
4
5
-
-
8
-
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
3
4
5
-
7
-
-
O
=
6
-
1
O
15
6
6
-
-
-
3
4
5
6
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
3
4
5
-
-
-
9
A
=
1
-
1
A
1
1
1
-
1
-
3
4
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
3
4
5
-
-
-
-
-
-
49
-
10
PYTHAGORAS
130
58
49
-
3
2
3
4
5
6
21
8
9
-
-
4+9
-
1+0
-
1+3+0
5+8
4+9
-
-
-
-
-
-
-
2+1
-
-
-
-
13
-
1
PYTHAGORAS
4
13
13
-
3
2
3
4
5
6
3
8
9
-
-
1+3
-
-
-
-
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
4
-
1
PYTHAGORAS
4
4
4
-
3
2
3
4
5
6
3
8
9

 

 

-
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
-
15
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
4
5
2
9
25
+
=
39
3+9
=
12
1+2
3
=
3
-
-
7
5
-
13
5
20
18
7
+
=
93
9+3
=
12
1+2
3
=
3
-
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
13
5
20
18
25
+
=
108
1+0+8
=
9
=
9
=
9
-
-
7
5
6
4
5
2
9
7
+
=
45
4+5
=
9
=
9
=
9
-
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
5
-
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
12
8
G
E
O
M
E
T
R
Y
-
-
33
-
-
8
-
45
-
27
1+2
-
-
-
-
-
-
-
9
-
-
-
3+3
-
-
-
-
4+5
-
2+7
3
8
G
E
O
M
E
T
R
Y
-
-
6
-
-
8
-
9
-
9

 

 

8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
-
-
+
=
6
-
=
6
=
6
=
6
-
-
-
15
-
-
-
-
-
+
=
15
1+5
=
6
=
6
=
6
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
7
5
-
4
5
2
9
25
+
=
39
3+9
=
12
1+2
3
=
3
-
7
5
-
13
5
20
18
7
+
=
93
9+3
=
12
1+2
3
=
3
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
7
5
15
13
5
20
18
25
+
=
108
1+0+8
=
9
=
9
=
9
-
7
5
6
4
5
2
9
7
+
=
45
4+5
=
9
=
9
=
9
8
G
E
O
M
E
T
R
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
5
-
-
-
6
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
7
-
-
-
-
-
-
7
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
=
9
8
G
E
O
M
E
T
R
Y
-
-
33
-
-
8
-
45
-
27
-
-
-
-
-
-
-
9
-
-
-
3+3
-
-
-
-
4+5
-
2+7
8
G
E
O
M
E
T
R
Y
-
-
6
-
-
8
-
9
-
9

 

 

-
-
-
-
-
GEOMETRY
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
1
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
E
=
5
2
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
M
=
4
4
1
M
13
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
6
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
Y
=
7
8
1
Y
25
7
7
-
-
-
-
-
-
-
7
-
-
-
-
45
-
7
GEOMETRY
108
45
45
-
1
2
3
4
18
6
14
8
18
-
-
4+5
-
-
-
1+0+8
4+5
4+5
-
-
-
-
-
1+8
-
1+4
-
1+8
-
-
9
-
7
GEOMETRY
9
9
9
-
1
2
3
4
9
6
5
8
9

 

 

-
-
-
-
-
GEOMETRY
-
-
-
-
1
2
3
4
5
6
7
8
9
G
=
7
1
1
G
7
7
7
-
1
-
3
-
-
-
7
8
-
E
=
5
2
1
E
5
5
5
-
1
-
3
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
1
-
3
-
-
6
-
8
-
M
=
4
4
1
M
13
4
4
-
1
-
3
4
-
-
-
8
-
E
=
5
5
1
E
5
5
5
-
1
-
3
-
5
-
-
8
-
T
=
2
6
1
T
20
2
2
-
1
2
3
-
-
-
-
8
-
R
=
9
7
1
R
18
9
9
-
1
-
3
-
-
-
-
8
9
Y
=
7
8
1
Y
25
7
7
-
1
-
3
-
-
-
7
8
-
-
-
45
-
7
GEOMETRY
108
45
45
-
1
2
3
4
10
6
14
8
18
-
-
4+5
-
-
-
1+0+8
4+5
4+5
-
-
-
-
-
1+0
-
1+4
-
1+8
-
-
9
-
7
GEOMETRY
9
9
9
-
1
2
3
4
1
6
5
8
9

 

 

-
-
-
-
-
GEOMETRY
-
-
-
-
1
2
3
4
5
6
7
8
9
T
=
2
6
1
T
20
2
2
-
1
2
3
-
-
-
-
8
-
M
=
4
4
1
M
13
4
4
-
1
-
3
4
-
-
-
8
-
E
=
5
2
1
E
5
5
5
-
1
-
3
-
5
-
-
8
-
E
=
5
5
1
E
5
5
5
-
1
-
3
-
5
-
-
8
-
O
=
6
3
1
O
15
6
6
-
1
-
3
-
-
6
-
8
-
G
=
7
1
1
G
7
7
7
-
1
-
3
-
-
-
7
8
-
Y
=
7
8
1
Y
25
7
7
-
1
-
3
-
-
-
7
8
-
R
=
9
7
1
R
18
9
9
-
1
-
3
-
-
-
-
8
9
-
-
45
-
7
GEOMETRY
108
45
45
-
1
2
3
4
10
6
14
8
18
-
-
4+5
-
-
-
1+0+8
4+5
4+5
-
-
-
-
-
1+0
-
1+4
-
1+8
-
-
9
-
7
GEOMETRY
9
9
9
-
1
2
3
4
1
6
5
8
9

 

 

-
-
-
-
-
GEOMETRY
-
-
-
-
2
4
5
6
7
9
T
=
2
6
1
T
20
2
2
-
2
-
-
-
-
-
M
=
4
4
1
M
13
4
4
-
-
4
-
-
-
-
E
=
5
2
1
E
5
5
5
-
-
-
5
-
-
-
E
=
5
5
1
E
5
5
5
-
-
-
5
-
-
-
O
=
6
3
1
O
15
6
6
-
-
-
-
6
-
-
G
=
7
1
1
G
7
7
7
-
-
-
-
-
7
-
Y
=
7
8
1
Y
25
7
7
-
-
-
-
-
7
-
R
=
9
7
1
R
18
9
9
-
-
-
-
-
-
9
-
-
45
-
7
GEOMETRY
108
45
45
-
2
4
10
6
14
18
-
-
4+5
-
-
-
1+0+8
4+5
4+5
-
-
-
1+0
-
1+4
1+8
-
-
9
-
7
GEOMETRY
9
9
9
-
2
4
1
6
5
9

 

 

-
11
G
E
O
M
E
T
R
I
C
A
L
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
-
-
9
-
-
-
+
=
15
1+5
=
6
=
6
=
6
-
-
-
-
15
-
-
-
-
9
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
11
G
E
O
M
E
T
R
I
C
A
L
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
4
5
2
9
-
3
1
3
+
=
39
3+9
=
12
1+2
3
=
3
-
-
7
5
-
13
5
20
18
-
3
1
12
+
=
84
8+4
=
12
1+2
3
=
3
-
11
G
E
O
M
E
T
R
I
C
A
L
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
13
5
20
18
9
3
1
12
+
=
108
1+0+8
=
9
=
9
=
9
-
-
7
5
6
4
5
2
9
9
3
1
3
+
=
54
5+4
=
9
=
9
=
9
-
11
G
E
O
M
E
T
R
I
C
A
L
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
3
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
5
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
11
G
E
O
M
E
T
R
I
C
A
L
-
-
37
-
-
11
-
54
-
36
-
1+1
-
-
-
-
-
-
9
9
-
-
-
-
-
3+7
-
-
1+1
-
5+4
-
3+6
8
2
G
E
O
M
E
T
R
I
C
A
L
-
-
10
-
-
2
-
9
-
9
-
-
7
5
6
4
5
2
9
9
3
1
3
-
-
1+0
-
-
--
-
-
-
-
8
2
G
E
O
M
E
T
R
I
C
A
L
-
-
1
-
-
2
-
9
-
9

 

 

-
3
G
E
O
-
-
-
-
-
--
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
3
G
E
O
-
-
-
-
-
--
-
-
-
-
7
5
-
+
=
12
1+2
=
3
=
3
-
3
G
E
O
-
-
-
-
-
--
-
-
-
-
7
5
15
+
=
27
2+7
=
9
=
9
-
-
7
5
6
+
=
18
1+8
=
9
=
9
-
3
G
E
O
-
-
-
-
-
--
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
-
-
-
3
-
-
-
-
-
-
3
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
-
-
-
6
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
8
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
27
3
G
E
O
-
-
18
-
-
3
-
18
2+7
-
-
-
-
-
-
1+8
-
-
-
-
1+8
9
3
G
E
O
-
-
9
-
-
3
-
9

 

 

3
G
E
O
-
-
-
-
-
--
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
15
+
=
15
1+5
=
6
=
6
3
G
E
O
-
-
-
-
-
--
-
-
-
7
5
-
+
=
12
1+2
=
3
=
3
3
G
E
O
-
-
-
-
-
--
-
-
-
7
5
15
+
=
27
2+7
=
9
=
9
-
7
5
6
+
=
18
1+8
=
9
=
9
3
G
E
O
-
-
-
-
-
--
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
-
-
-
6
-
-
6
occurs
x
1
=
6
-
7
-
-
-
-
7
occurs
x
1
=
7
3
G
E
O
-
-
18
-
-
3
-
18
-
-
-
-
-
-
1+8
-
-
-
-
1+8
3
G
E
O
-
-
9
-
-
3
-
9

 

 

-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
5
-
-
9
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
15
-
-
14
-
-
9
-
+
=
38
3+8
=
11
1+1
2
=
2
-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
3
5
-
2
9
-
3
+
=
34
3+4
=
7
=
7
=
7
-
-
7
5
-
3
5
-
20
18
-
3
+
=
61
6+1
=
7
=
7
=
7
-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
3
5
14
20
18
9
3
+
=
99
9+9
=
18
1+8
9
=
9
-
-
7
5
6
3
5
5
2
9
9
3
+
=
54
5+4
=
9
=
9
=
9
-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
-
-
5
5
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
9
occurs
x
2
=
18
1+8
9
13
10
G
E
O
C
E
N
T
R
I
C
-
-
32
-
-
10
-
54
-
36
1+3
1+0
-
-
-
-
-
-
-
9
9
-
-
-
3+2
-
-
1+0
-
5+4
-
3+6
4
1
G
E
O
C
E
N
T
R
I
C
-
-
5
-
-
1
-
9
-
9

 

 

10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
5
-
-
9
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
15
-
-
14
-
-
9
-
+
=
38
3+8
=
11
1+1
2
=
2
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
7
5
-
3
5
-
2
9
-
3
+
=
34
3+4
=
7
=
7
=
7
-
7
5
-
3
5
-
20
18
-
3
+
=
61
6+1
=
7
=
7
=
7
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
7
5
15
3
5
14
20
18
9
3
+
=
99
9+9
=
18
1+8
9
=
9
-
7
5
6
3
5
5
2
9
9
3
+
=
54
5+4
=
9
=
9
=
9
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
3
-
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
-
-
5
-
-
5
5
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
9
9
-
-
-
9
occurs
x
2
=
18
1+8
9
10
G
E
O
C
E
N
T
R
I
C
-
-
32
-
-
10
-
54
-
36
1+0
-
-
-
-
-
-
-
9
9
-
-
-
3+2
-
-
1+0
-
5+4
-
3+6
1
G
E
O
C
E
N
T
R
I
C
-
-
5
-
-
1
-
9
-
9

 

 

G
=
7
3
GEO
27
18
9
G
=
7
8
GEOMETRY
108
45
9
G
=
7
11
GEOMETRICAL
108
54
9
G
=
7
10
GEOCENTRIC
99
54
9

 

 

-
11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
-
9
-
11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
5
3
3
3
-
4
+
=
18
1+8
=
9
-
9
-
-
5
21
3
12
-
4
+
=
45
4+5
=
9
-
9
-
11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
5
21
3
12
9
4
+
=
54
5+4
=
9
-
9
-
-
5
3
3
3
9
4
+
=
27
2+7
=
9
-
9
-
11
E
U
C
L
I
D
-
-
-
-
-
-
-
-
1
-
-
--
-
--
--
-
--
--
1
--
--
--
--
--
2
-
-
--
-
--
--
-
--
--
2
--
--
--
--
--
-
-
-
3
3
3
-
-
-
-
3
occurs
x
3
=
9
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
6
-
-
--
-
--
-
-
--
--
6
--
--
--
--
--
7
-
-
--
-
-
-
-
--
--
7
--
--
--
--
--
8
-
-
--
-
-
-
-
--
--
8
--
--
--
--
--
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
24
11
E
U
C
L
I
D
-
-
21
-
-
6
-
27
2+4
1+1
-
-
-
-
9
-
-
-
2+1
-
-
-
-
2+7
6
2
E
U
C
L
I
D
-
-
3
-
-
6
-
9
-
-
5
3
3
3
9
4
-
-
-
-
-
-
-
-
6
2
E
U
C
L
I
D
-
-
3
-
-
6
-
9

 

 

11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
-
9
11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
5
3
3
3
-
4
+
=
18
1+8
=
9
-
9
-
5
21
3
12
-
4
+
=
45
4+5
=
9
-
9
11
E
U
C
L
I
D
-
-
-
-
-
--
-
-
-
5
21
3
12
9
4
+
=
54
5+4
=
9
-
9
-
5
3
3
3
9
4
+
=
27
2+7
=
9
-
9
11
E
U
C
L
I
D
-
-
-
-
-
-
-
-
-
-
3
3
3
-
-
-
-
3
occurs
x
3
=
9
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
-
5
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
11
E
U
C
L
I
D
-
-
21
-
-
6
-
27
1+1
-
-
-
-
9
-
-
-
2+1
-
-
-
-
2+7
2
E
U
C
L
I
D
-
-
3
-
-
6
-
9
-
5
3
3
3
9
4
-
-
-
-
-
-
-
-
2
E
U
C
L
I
D
-
-
3
-
-
6
-
9

 

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

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

 

 

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

 

 

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

 

.....

 

 

0
-

4

ZERO

64

28

1
1
-
3

ONE

34
16
7
2
-
3

TWO

58
13
4
3
-
5

THREE

56
29
2
4
-
4

FOUR

60
24
6
5
-
4

FIVE

42
24
6
6
-
3

SIX

52
16
7
7
-
5

SEVEN

65
20
2
8
-
5

EIGHT

49
31
4
9
-
4

NINE

42
24
6
45
-
40
-
522
225
45
4+5
-
4+0
-
5+2+2
2+2+5
4+5
9
-
4
-
9
9
9

 

 

Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
8
-
-
6
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
-
1
9
6
-
1
-
-
-
5
-
-
9
-
8
-
-
5
9
5
-
+
=
112
1+1+2
=
4
-
4
-
4
26
-
-
15
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
-
19
9
24
-
19
-
-
-
14
-
-
9
-
8
-
-
14
9
14
-
+
=
256
2+5+6
=
13
1+3
4
-
4
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
5
9
-
-
-
-
5
-
2
5
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
-
-
-
-
-
-
5
4
5
-
-
5
-
7
-
2
-
-
-
-
5
+
=
113
1+1+3
=
5
-
5
-
5
-
5
18
-
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
-
-
-
-
-
-
5
22
5
-
-
5
-
7
-
20
-
-
-
-
5
+
=
266
2+6+6
=
14
1+4
5
-
5
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
26
5
18
15
-
15
14
5
-
20
23
15
-
20
8
18
5
5
-
6
15
21
18
-
6
9
22
5
-
19
9
24
-
19
5
22
5
14
-
5
9
7
8
20
-
14
9
14
5
+
=
522
5+2+2
=
9
-
9
-
9
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
+
=
225
2+2+5
=
9
-
9
-
9
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
+
=
2
occurs
x
3
=
6
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
3
occurs
x
1
=
3
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
+
=
4
occurs
x
2
=
8
-
8
-
5
-
-
-
-
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
5
-
5
5
+
=
5
occurs
x
14
=
70
7+0
7
-
-
-
6
 
6-
-
-
 
-
-
6
 
-
-
-
-
-
 
6
6
-
-
-
6
-
-
-
 
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
 
-
-
-
-
+
=
6
occurs
x
7
=
42
4+2
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
+
=
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
+
=
8
occurs
x
3
=
24
2+4
6
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
+
=
9
occurs
x
7
=
63
6+3
9
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
45
-
-
40
-
225
-
54
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
4+5
-
-
4+0
-
2+2+5
-
5+4
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
9
-
-
4
-
9
-
9
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
-
-
-
-
-
-
-
-
-
-
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
9
-
-
4
-
9
-
9

 

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

A
=
1
-
-
-
-
-
-
A
=
1
occurs
x
0
=
-
-
-
=
-
-
B
=
2
-
-
-
-
-
-
B
=
2
occurs
x
0
=
-
-
-
=
-
-
C
=
3
-
-
-
-
-
-
C
=
3
occurs
x
0
=
-
-
-
=
-
-
D
=
4
-
-
-
-
-
-
D
=
4
occurs
x
0
=
-
-
-
=
-
-
E
=
-
5
-
5
-
5
-
E
=
5
occurs
x
9
=
45
4+5
=
9
-
9
F
=
-
6
-
6
-
6
-
F
=
6
occurs
x
2
=
12
-
-
3
-
3
G
=
-
7
-
7
-
7
-
G
=
7
occurs
x
1
=
7
-
-
7
-
7
H
=
-
8
-
8
-
8
-
H
=
8
occurs
x
2
=
16
1+6
-
7
-
7
I
=
-
9
-
9
-
9
-
I
=
9
occurs
x
4
=
36
3+6
=
9
-
9
J
=
10
-
-
-
-
-
-
J
=
10
occurs
x
0
=
-
-
-
-
-
-
K
=
11
-
-
-
-
-
-
K
=
11
occurs
x
0
=
-
-
-
-
-
-
L
=
12
-
-
-
-
-
-
L
=
12
occurs
x
0
=
-
-
-
-
-
-
M
=
13
-
-
-
-
-
-
M
=
13
occurs
x
0
=
-
-
-
-
-
-
N
=
-
14
1+4
5
-
5
-
N
=
14
occurs
x
4
=
56
5+6
=
11
1+1
1
O
=
-
15
1+5
6
-
6
-
O
=
15
occurs
x
4
=
60
6+0
=
6
-
6
P
=
16
-
-
-
-
-
-
P
=
16
occurs
x
0
=
-
-
-
-
-
-
Q
=
17
-
-
-
-
-
-
Q
=
17
occurs
x
0
=
-
-
-
-
-
-
R
=
-
18
1+8
9
-
9
-
R
=
18
occurs
x
3
=
54
5+4
=
9
-
9
S
=
-
19
1+9
10
1+0
1
-
S
=
19
occurs
x
2
=
38
3+8
=
11
1+1
1
T
=
-
20
2+0
2
-
2
-
T
=
20
occurs
x
3
=
60
6+0
=
6
-
6
U
=
-
21
2+1
3
-
3
-
U
=
21
occurs
x
1
=
21
2+1
=
3
-
3
V
=
-
22
2+2
4
-
4
-
V
=
22
occurs
x
2
=
44
4+4
=
8
-
8
W
=
-
23
2+3
5
-
5
-
W
=
23
occurs
x
1
=
23
2+3
=
5
-
5
X
=
-
24
2+4
6
-
6
-
X
=
24
occurs
x
1
=
24
2+4
=
6
-
6
Y
=
25
-
-
-
-
-
-
Y
=
25
occurs
x
0
=
-
-
-
-
-
-
Z
=
-
26
2+6
8
-
8
-
Z
=
26
occurs
x
1
=
26
2+6
=
8
-
8
-
-
114
237
-
84
-
-
-
-
-
351
-
-
40
-
522
-
-
108
-
45
-
-
1+1+4
2+3+7
-
8+4
-
-
-
-
-
3+5+1
-
-
4+0
-
5+2+2
-
-
1+0+8
-
4+5
-
-
6
12
-
12
-
-
-
-
-
9
-
-
4
-
9
-
-
9
-
9
-
-
-
1+2
-
1+2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
3
-
3
-
-
-
-
-
9
-
-
4
-
4
-
-
9
-
9

 

NINE EIGHT SEVEN SIX FIVE FOUR THREE TWO ONE ZERO

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN SWIFT REPEAT SCATTER THE NINE NUMBERS AMONGST THE LETTERS OF THEIR PROGRESS

AT THE THROW OF THE NINTH ARM WHEN IN CONJUNCTION SET

THE

FAR YONDER SCRIBE

MADE RECORD OF THE FALL

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

The essence of mathematics is to look for patterns.
Our minds seem to be organised to search for relationships and sequences. We look for hidden orders.
These intuitions seem to be more important than the facts themselves, for there is always the thrill at finding something, a pattern, it is a discovery - what was unknown is now revealed. Imagine looking up at the stars and finding the zodiac!
Searching out patterns is a pure delight.
Suddenly the counters fall into place and a connection is found, not necessarily a geometric one, but a relationship between numbers, pictures of the mind, that were not obvious before. There is that excitement of finding order in something that was otherwise hidden.
And there is the knowledge that a huge unseen world lurks behind the facades we see of the numbers themselves.

 

 

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

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Page 32

5


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

 

 

THE

BALANCING

ONE TWO THREE FOUR

FIVE

NINE EIGHT SEVEN SIX

 

 

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

 

 

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

 

 

4 FIVE 42 24 6

 

1 2 3 4 5 6 7 8 9

9 8 7 6 5 4 3 2 1

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

 

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

 

 

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

 

 

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

 

 

 

The Upside Down of the Downside Up

 

 

 

 

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 THE NINE NUMBERS AMONGST THE LETTERS OF THEIR PROGRESS

AT THE THROW OF THE NINTH RAM WHEN IN CONJUNCTION SET

THE

FAR YONDER SCRIBE

MADE RECORD OF THE FALL

 

 

ABCDEFGHIJKLMNOPQRSTUVWXYZ

 

8
ABCDEFGH
36
36
9
1
I
9
9
9
8
JKLMNOPQ
108
36
9
1
R
18
18
9
8
STUVWXYZ
180
36
9
26
Add to Reduce
351
126
72
2+6
Reduce to Deduce
3+5+1
1+2+6
7+2
8
Essence of Number
9
9
9

 

ZYXWVUTSRQPONMLKJIHGFEDCBA

ABRACADABRA

ARBADACARBA

ABCDEFGHIJKLMNOPQRSTUVWXYZ

 

3
ABC
6
6
6
2
DE
9
9
9
2
FG
13
13
4
3
HIJ
27
18
9
2
KL
23
5
5
2
MN
27
9
9
2
OP
31
13
4
3
QRS
54
18
9
2
TU
41
5
5
2
VW
45
9
9
3
XYZ
75
21
3
26
-
351
126
72
2+6
-
3+5+1
1+2+6
7+2
8
-
9
9
9

 

ZYXWVUTSRQPONMLKJIHGFEDCBA

ARBADACARBA

ABRACADABRA

 

 

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 inust 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 Cronus 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 Sattun'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 honouured 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 existted 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 ofthe 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 reflets, 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 kn to the ancient world, that is, Saturn, Jupiter, Mars, Venus Mercury.

Graves suggests a religious mystery bound up with two an cient 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 n umbers he points out that the aggregate number of letter strokes for the complete 22-letter Ogham alphabet that he is studying isf 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. maxium eastern elongation 'to inferior conjunction and mazimum western elongation'.13

Page 207

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

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

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

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

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

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

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

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

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

 

OSIRIS SO IRIS IS

 

 

 

 
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