THE NEW MATHEMATICS OF CHAOS

Ian Stewart 1989

Page 1

PROLOGUE

CLOCKWORK OR CHAOS?

"YOU BELIEVE IN A GOD WHO PLAYS DICE, AND I IN COMPLETE LAW AND ORDER."

Albert Einstein, Letter to Max Born

EVERY BREATH YOU TAKE

Every breath you take Every move you make Every bond you break Every step you take

Ill be watching you

Every single day Every word you say Every game you play Every night you stay

Ill be watching you

Oh, cant you see You belong to me How my poor heart aches With every step you take

Every move you make Every vow you break Every smile you fake Every claim you stake

Ill be watching you

Since youve gone I been lost without a trace I dream at night I can only see your face

I look around but its you I cant replace I feel so cold and I long for your embrace I keep crying baby, baby, please...

Oh, cant you see You belong to me How my poor heart aches With every breath you take

Every move you make Every vow you break Every smile you fake Every claim you stake

Ill be watching you

Every move you make Every step you take

Ill be watching you Ill be watching you Ill be watching you Ill be watching you Ill be watching you

Every breath you take Every move you make Every bond you break Every step you take Ill be watching you Every single day Every word you say ... www.lyricsfreak.com/p/police/every+breath+you+take

CITY OF REVELATION

John Michell 1972

CHAPTER ELEVEN

Gnostic Numbers

Page 115

The names of the gods vary with languages; but it was formerly possible for an adept to recognise the corresponding principles in each system by arithmomancy, the science of theological interpretation by number. Every ancient god had a number which determined the value of the letters in his name and also, according to Hocart, decided the number of syllables in the verses addressed to him. No doubt the priests of Stonehenge had their own names for the deities known to the Greeks as Zeus 612, Hermes 353, (Greek letters omitted) 1080 etc., whose numbers appear in the dimensions of the temple, but these are long forgotten. The numbers however may still be discovered as the values by gematria of the names given in the Greek language to the sacred principles of Christianity. Obvious examples include Jesus 888, Christos 1480, The Holy Spirit i o8o, Lord Jesus Christ 3168, Son of God 1164, Saviour 1408 etc.; and related to these are the symbolic phrases of the New Testament, as a grain of mustard seed 1746 (666 + 1080), a grain of wheat 2220, one pearl of great price and the Ark of the Covenant, both 2178, and many others.
How it comes about that the holy names of Christianity are formed on the same numerical system as the ancient cosmic temple is the deepest of mysteries, and the established Church has always been concerned that it should remain so. It is known that several early Christian teachers, including the great gnostic masters Marcus and Valentinus, demonstrated the eternal values behind the new religion by means of arithmomancy, comparing the names and numbers of Christian cosmology with those recognised by initiates of the traditional schools. Their followers were called gnostics because they claimed to have the gnosis or knowledge through direct experience and considered it idle and superstitious to accept the unsupported word of others in matters which could be explored through personal investigation in the light of revelation. The name is generally applied to the scholars of Alexandria at the beginning of the Christian era who, with the benefit of the great library with its vast collection of /Page 116/ manuscripts drawn from every part of the ancient world, reconciled the tradition of Greek philosophy with the Hebrew cabala and the hermetic doctrines of Egypt and the East to produce the logos of the new age. It was not until the second century, when the hard party men took control of the newly organised church, that gnosticism became a heresy, but so thoroughly were their proscribed works and memorials destroyed, that information about the beliefs and practices of the Christian gnostics has been virtually limited to the evidence of the Church Fathers such as Irenaeus, Tertullian and Hippolytus, who set out to discredit them.
The most informative of these is St Irenaeus in his five books, Against Heresies. This worthy Church Father, Bishop of Lyons in the second century, acquired a superficial knowledge of gnostic practices, and may have been rejected from one of their societies, for he writes that the gnostics call him ignorant, an accusation of which he claims to be proud. Irenaeus's books are abusive and scarcely rational, written in the manner of a Sunday newspaper journalist, who `exposes' other people by presenting a selective version of their beliefs and activities in such a way as to make them appear ridiculous. This approach is typified in the charges which Irenaeus brings against the gnostics: that they seduce women, corrupt and swindle their pupils, and attach more importance to their own personal experience of truth than to the exhortations of authority. People like St Irenaeus have the trick of misrepresenting others by describing literally certain of their practices, while giving no indication of the meaning behind them. It was to frustrate this menace that the gnostics preferred to keep their teaching a secret, particularly that part which related to their numerical cosmology. Irenaeus therefore saw it his duty to expose the gnostics' use of number in order to show that their methods " were vain and meaningless, claiming also that they were a powerful inducement to heresy and to the acquisition of forbidden knowledge. These scarcely compatible objections are revived by the witch-hunters in every generation. Nevertheless, although he was obviously justified in boasting of his essential ignorance in such matters, Irenaeus gives several examples of the numerical system used by the gnostics, which, they claimed, was an inheritance from the days of Homer and the ancient philosophers.
The cosmic order, the gnostics' Pleroma, was made up of 30 aeons, representing the hierarchy of power and the stages in creation. The aeons were divided into three groups of 8, 10 and 12, of which the first, containing the 8 aeons of the primeval creation, was known as the Ogdoad. According to Irenaeus, the gnostics found in the name, /Page 117/ Jesus, a reference to the Ogdoad, for the value by gematria of (Greek letters omitted) Jesus, is 888. Since it contains six letters, the name Jesus was also associated with the number 6, and the number 888 may also be reduced to 6, for 8 + 8 + 8 = 24; 2 + 4 = 6. Again the number 888 was taken to correspond with the numerical values of the twenty-four letters of the Greek alphabet, of which there are 8 units, 8 tens, and 8 hundreds.

The following is a quotation from Irenaeus about the gnostics' convention of relating words to numbers:

`But the local positions of the three hundred and sixty-five heavens they distribute in the same way as the mathematicians, for they have taken their theorems and applied them to their own kind of learning. And their head, they say, is Abraxas, therefore he has in himself the three hundred and sixty-five numbers.'

The significance of this passage is that the value of the word Abraxas, written in Greek (Greek letters omitted) is 365, and Abraxas was god of the 365 days of the solar year, corresponding to (Greek letters omitted) Mithras, whose number is also 365. From such examples it is evident that gnostic numerology was the reconstitution of a much earlier system, applied to various orders of the gods throughout the ancient world, and adopted by early Christian scholars as the canon, by which the new sacred names were constructed to represent the same eternal principles as were recognised in the past. One of the charges brought against the gnostics was that from a numerical interpretation of the scriptures, they drew certain conclusions about the Christian Saviour and his recurrent appearance in accordance with the procession of the aeons, which contradicted the new doctrine within the Church, that the coming of Jesus was the one and only appearance of the Son of God on earth, and that the true religion was first made known at the time of his birth. According to Irenaeus, they considered that Jesus had given proof of his divinity when he spoke the words, 'I am Alpha and Omega', because the sum of the Greek letters, alpha = and omega = 800 is 801, and 801 is the number of (Greek letters omitted), a dove. 801 is also the width of a vesica about 1385 in length, and 1385 is the number of (Greek letters omitted) It is the Lord (John 21.7). Thus they believed that the divine spirit, represented by the dove, entered into Jesus, the man, at his baptism, while the Church held that the spirit and the body of Jesus Christ were indivisible, and looked forward to a bodily resurrection. The seemingly unimportant differences in the positions of the two sides veiled the eternal chasm that separates the rival principles, represented by the prophet and the priest; on /Page 118/ the one hand the fertilising, disruptive spirit of the scientist, magician and philosopher, and on the other, the rule of Caesar's law. The gnostics were concerned to examine the traditions of ancient cosmology, brought to life again in the Christian revelation. Exactly how they came by their science of numbers is not certain, but they appear to have made the discovery that the numerical code of the Hebrew cabala and those of other mystical systems throughout the world were all degenerate versions of the same once universal system of knowledge that returns within the reach of human perception at certain intervals in time. As the revealed books of the Old Testament were written in a code to be interpreted by reference to number, so were the revelations of the gnostic prophets expressed in words and phrases formed on a system of proportion, which gave.life and power to the Christian myth, while allowing initiates to gain a further understanding of the balance of forces that produce the world of phenomena.
Gematria, the science of relating words to numbers, must be extremely old. Its origins are probably coeval with the first use of writing, its purely numerical aspect being much earlier, for numbers precede literature, the introduction of which has always been regarded as, at the best, a mixed blessing. Plato in Phaedrus repeats the legend of Thoth, the Egyptian god, who discovered the use of letters and went to King Thamus to show off his invention, claiming that it would be an aid to memory and an incentive to wisdom. The king told him that the opposite would be the case, 'for this invention will encourage forgetfulness in the minds of those who learn it, because they will neglect to cultivate memory. You have invented an aid not to memory but to reminding. You offer your pupils the appearance instead of the reality of wisdom, for they will read many things without instruction, and will seem knowledgeable when they are for the most part ignorant and troublesome associates, thinking themselves wise, instead of being so.' Neither the art of language nor the use of letters is a natural human attribute, and in some ways the effect of their introduction has been to inhibit communication. Both have been invented or • received, and both may have been lost and rediscovered at various periods of history. Writing was formerly reserved for sacred and divinatory purposes. Its use in secular affairs coincided with and accelerated the decline of the ancient world.
To the objections raised by King Thamus may be added another: that our sense of history has been seriously distorted by the widespread use of writing, to the extent that we are now able to understand only the inscribed records of contemporary events. to the ex / Page 119 /elusion of that greater part of the human tradition concerned with pre-literary times. In this respect the illiterate members of primitive societies are to some extent better informed than ourselves about the true history of creation and the early adventures of the human race. Among the South Sea islanders, the natives of Australia and the tribes of Africa and North America, there are still those who preserve their own scholarly institutions of oral history, transmitted through generations of priests and shamans and continually reinvoked in myth and ritual. Thus the early traditions are not only kept alive by inheritance, but are also directly experienced in the ceremonial structure of tribal life.
There are, or have been until very recently, several primitive societies in which the creation myths and popular histories are further interpreted for the benefit of initiates by means of a secret magical alphabet, based on a divinely revealed system of numbers. In northern Nigeria is a sacred grove where the Creator is said to have ordered the world according to an arrangement of letters which he laid out in a circle around him, and this type of legend recurs at many esoteric centres throughout the world. The mystic in a climatic vision penetrates into the world behind phenomena and perceives the interaction between the various forces of the cosmos. Certain rhythms, notes and geometrical forms are repeated, suggesting the idea of an alphabet in which letters or numbers represent corresponding symbols, sounds and creative influences. Thus the art of writing derives from a metaphysical code of symbols, the gift of revelation.
The Chinese I Ching, in which the cosmic order is represented in 64 hexagrams, each of six lines symbolising various combinations of negative and positive forces, has had an influence on Chinese civilisation similar to that of the Hebrew cabala in European history. Both systems are of great and indefinite antiquity; both originated as revelations and have been continually renewed from the same source. The fundamental diagram of the cabala is the Tree of Life, an arrangement of ten points or centres, linked by twenty-two paths, the whole figure laid out to represent the body of a man, Adam Kadmon, the universal macrocosm. The twenty-two paths correspond to the twenty-two letters of the Hebrew alphabet, also to the twenty-two trumps of the Tarot pack, and these letters express different aspects of cosmic energy according as they are related to the ten centres or archetypes. These ten, the sephiroth, are emanations from the one source, reflecting the stages of organic development in the creation of the universe from the primeval seed. The cabalistic diagram and the traditional teaching associated with it / Page 120 / provide a most comprehensive account of the order manifest in nature, while omitting any dogmatic assertions as to the form or nature of a supreme creative principle, questions on which no one has ever known very much, nor ever will.
Of all the surviving mystical languages, the Hebrew cabala remains the most complete and accessible to western scholars, for the Jews have been extremely tenacious of their ancient traditions and their convention of scriptural interpretation, by the use of gematria, has never entirely lapsed. They have, however, a tendency to exaggerate their own claims to antiquity at the expense of other races and pretend that the Greek cabala, the instrument of the Pythagoreans and of the neo-Platonists at Alexandria, was simply an adaptation of the Hebrew. In fact, it appears that both systems had a common source in Egyptian and Babylonian cosmology, or, more likely, that these and all the other related traditions of Europe and the East were fragments of a more perfect and universal science, disintegrated through gradual decay or sudden change. The evidence of Stonehenge shows the existence of a system of knowledge among the pre-Celtic British identical with that held by the Greeks and Hebrews. The same myths, monuments and even the same standards of measurement are found all over the world; so is the institution of the cosmic temple with the solar king and his dependent hierarchy drawn up by reference to a sacred canon that is everywhere said not to have been invented, but revealed by the gods. The conclusion is obvious. Unfortunately, the academic world flourishes on the proliferation of different categories of study, and minor variations in style are regarded as more significant than the essential similarities between the first civilised traditions of all people, however degenerate they may since have become. The prevailing faith in progress is founded on the nineteenth-century creation myth, taken from the sacred books of the Darwinians, according to which human intelligence has gradually evolved and grows ever brighter, each generation contributing towards the general advancement of civilisation. This idea has now been established as a religious belief and is therefore, to the faithful, proof against all the evidence of fact, reason and tradition which seems to the unconverted totally to discredit it. Theories of ancient history are debated with great fury because of their influence on current ideas, arousing the same passions as did matters of theology in previous centuries, and it is now considered best that the question of human origins should be settled by reference to a doctrine sufficiently vague to conceal the fact that this is another of those subjects on which no one really knows anything. / Page 121 / How it was ever supposed that the Hebrew alphabet of twenty-two letters, together with various geometrical symbols might serve to represent the entire moving pattern of the universe is not now easy to understand; but, since all ancient philosophy, religion, magic, the arts and sciences were based on the concept of a correspondence between numbers and cosmic law, it is impossible to appreciate the history of the past without some actual experience of the fundamental truth behind this approach to cosmology. Plato gives a remarkable account in Cratylos of the origin of language and letters. The philosopher is asked whether there is any particular significance in names, for surely they are simply a matter of convention and one is more or less as good as another. After all, foreigners call things by different names and appear to manage just as well .as the Greeks in this respect. The answer given is that despite appearances the matter is by no means so simple. Words are the tools of expression, and the making of these, as of any other tools, is the task of a skilled craftsman, in this case the lawgiver. Language has grown corrupt over the ages, and names have deviated from their original perfect forms, which are those used by the gods. But all names were originally formed on certain principles, through knowledge of which it is possible to discover the archetypal meaning of words in current use. 'So perhaps the man who knows about names considers their value and is not confused if some letter is added, transposed or subtracted, or even if the force of the name is expressed in quite different letters.' This is Plato's clearest reference to the mystical science of the cabala, in which letters, words and whole phrases may be substituted for others of the same numerical value. The force of a name is to be found in its number, and can be expressed through any combination of letters,. provided the sum of the letters amounts to the appropriate number by gematria. The matter becomes even more intriguing when Plato indicates the principles on which names are created. Each letter of the alphabet stands for a particular state or type of motion, and thus a word, being composed of individual letters, represents a certain balance of forces. Several examples are given. The letter `r.' conveys the meaning of hurry, rushing, running rapidly; 'l' suggests a sliding, flowing, slipping, gliding motion, and 'g' is found in words that mean sweet and sticky such as sugary and gummy. It is certainly remarkable that the Greek words used by Plato to demonstrate this idea should have English equivalents containing the same characteristic letters, and the fact that it is so may be taken as evidence that letters do have a certain autonomous existence as archetypal symbols. From this point of view it is but a logical step to give. numerical / Page 122 / values to the letters so that the relationship between two words can be expressed as a mathematical ratio. Even if the logic be denied, it remains a fact that this was the practice of the cabalists, the leading scholars of their time. Those who are now attracted by codes, anagrams, word games and crossword puzzles, the solution of which is largely a matter of intuition, are the natural cabalists deprived of their sacred role.
It is well known that the architects of the Italian Renaissance followed the example of Vitruvius and the ancients in drawing up plans and elevations in accordance with a Pythagorean canon of proportion, which was based on the intervals of musical harmony, on the principle that `the numbers by means of which the agreement of sounds affects our ears with delight, are the very same which please our eyes and our minds'. Not only did they use the simple musical proportions, octaves (1 : 2), fourths (1 : 4) and fifths (2 : 3), but also the dynamic ratios of canonical geometry such as i : -V2, the relationship between the side of a square and its diagonal. Professor Thom found evidence of the same practice in the groundplans of British stone circles of around 2000 BC. The stones are arranged in accordance with geometrical designs, based on Pythagorean triangles, a feature which could not be appreciated other than by the initiated. These facts are inexplicable without some recognition of the magical significance which in ancient times was attributed to the science of proportions. According to the Egyptian book of magic, the Asclepius of Hermes Trismegistos, certain statues in the Egyptian temples were cunningly contrived to become animated by cosmic forces. The interpretation of this phenomenon by the sixteenth-century cabalist, Giulio Camillo, is quoted by Frances Yates in The Art of Memory as follows:

`I have read, I believe in Merenvius Trismegistus, that in Egypt there were such excellent makers of statues that when they had brought some statue to the perfect proportions, it was found to be animated with an angelic spirit: for such perfection could not be without a soul. Similar to such statues I find a composition of words, the office of which is to hold all words in a proportion grateful to the ear . . . which words, as soon as they are put into their proportion, are found when pronounced to be as it were animated with a harmony.'

From this it appears that the power of the Egyptian statues lay in the magical effect of their divine proportions. Similarly in rhetoric, an art to which the cabalists devoted a great deal of attention, the influence of a perfectly balanced sentence transcends its obvious literal meaning to such an extent it becomes a powerful instru- / Page 123 / ment of control and communication. Just as there was a canon of ritual, of architecture, of painting and of musical harmony, taught in the mystery schools and in part revived at the Renaissance, so there was also a secret canon of rhetoric and literary composition. All the arts and sciences were based on the same cosmic truths expressed in number, and the sacred numbers were the ratios in a revealed world order, drawn from the experience of mystics and confirmed by precise measurements of the solar system.
It is impossible to exaggerate the respect in which these numbers were held by those who had knowledge and experience of their potential influence on human thought and actions. Though every master craftsman was acquainted with the canon of his particular trade, the inner mysteries of the numerical cosmology were known only to the initiated ministers of the temple, who were forbidden to disclose them and considered it in no one's interest that they should do so. Neither Plato nor any other ancient writer whose works survive gives an explicit demonstration of the science of gematria, and the reason is obvious. It is impossible to communicate the idea of a basic law of proportion inherent in nature to anyone who has not_ already begun to realise this fact for himself through his own observations. To attempt to do so is to provoke the resentment of those who find the idea contrary to the rationalised assumptions and prejudices in which they have been educated, and which they prefer to the evidence of their own poetic intuition. Yet those who deride the notion of the cosmic Temple as a primitive aberration, are often the very people who construct the great temple follies and the images of their own fantasy gods on earth. A system of knowledge, which in the-possession of enlightened men can produce a prosperous and well balanced society, may also be used as a diabolic instrument of tyranny. The Christian gnostics were discredited not by the works of their great masters, though these perished with the rest, but by the obscenities and absurdities of the fanatics, petty magicians and false or deluded prophets among their followers. It is easy to condemn the repressive attitude of the Church towards the gnostics and their magical science. However, as a former Bishop of Exeter observed to a clergyman, who applied to him for a licence to exorcise a ghost, the Church has for the most part given up her spiritual prerogatives on the grounds of their abuse. The decline of the old world order removed the authority which had made it possible for the secrets of the Temple to remain in the exclusive possession of initiates who could be trusted to keep alive the spirit behind its visible forms. Like all laws, the law of geometrical proportion, if applied without / Page 124 / understanding, burdens the soul and violates the function of life. Even in Plato's time, as he records, there were many who considered all scientific enquiry to be an offence against God, who had arranged things so far beyond the comprehension of men, that it was vain to seek any further guidance than may be provided by orthodox common sense and the inspiration of the moment. On the other hand, there will always be those who believe with Plato himself that 'a man who knows of a study which he finds sublime, true, beneficial to society and perfectly acceptable to God, simply cannot refrain from calling attention to it'.

(Greek letters omitted)

The Basic Mathematical Principals of Numerology

Numerology uses the “Fadic System” (sometimes referred to as natural addition) to reduce multiple-digit numbers to a single digit. With this style of addition, you continue to add together two digits until you arrive at a single number.

Numerology is based on the idea that everything in the universe is both made up of and affected by numbers.

Numerology is relatively simple to understand and implement, largely because it only involves addition. The method of addition used in numerology, however, is a bit different than the addition you are most likely used to.

Numerology uses the “Fadic System” (sometimes referred to as natural addition) to reduce multiple-digit numbers to a single digit. With this style of addition, you continue to add together two digits until you arrive at a single number. So for example, rather than seeing the number 23 as twenty-three, it is seen as its separate parts of a 2 and a 3. With natural addition, you would add together the two numbers to come up with a single digit:

Once you have mastered the concept of natural addition, the calculations are very simple.

Applying this to Numerology

Translating Letters into Numbers.

Pythagorean Numerology

The Pythagorean Number Values

The following chart shows the numbers assigned to each letter in Pythagorean numerology and is the basis for many numerology readings. To read the chart, find the letter you are looking for and look at the corresponding number at the top of the column containing the letter. For example, the letter A would be 1, the letter B would be 2, the letter C would be 3, etc.

To begin with, write down your full name (first, middle and last). In Pythagorean numerology, it is important that you use your name as it appears on your birth certificate. Then assign a number to each letter in your name. To do that, locate the letter in the above chart, and then look at the number at the top of the column containing that letter. That number is the number you would assign to that letter. Do that for each of the letters in your full name. For our example, we will use a fictional character named John Alan Smith.

J O H N A L A N S M I T H
1 6 8 5 1 3 1 5 1 4 9 2 8

The next step is to add up all these numbers and then reduce the result to a single digit. You will want to be sure to add each name separately, then add those sums together to get the total for the whole name, then if necessary reduce to a single digit. We add the parts of the name separately instead of adding the whole name straight across because not only does the total number for the name have meaning, but each part of the name also has some bearing on who we are.

John = 1+6+8+5 = 20 = 2+0 = 2

Alan = 1+3+1+5 = 10 = 1+0 = 1

Smith = 1+4+9+2+8 = 24 = 2+4 = 6

Adding those totals together we get:

2+1+6 = 9

This means that in our example, John’s birthname reduces to a 9.

To begin with, write down the name you are known by. Then assign a number to each letter in your name. To do that, locate the letter in the above chart, and then look at the number at the top of the column containing that letter. That number is the number you would assign to that letter. Do that for each of the letters in your full name. For our example, we will use a fictional character named John Alan Smith. Since everyone knows our character just as John Smith, that is the name we will use for our calculations.

J O H N S M I T H
1 7 5 5 3 4 1 4 5

The next step is to add up all these numbers and then reduce the result to a single digit. Be sure to add each name separately, then add together those sums to get a total for the whole name.

John = 1+7+5+5 = 18 = 1+8 = 9

Smith = 3+4+1+4+5 = 17 = 1+7 = 8

9+8 = 17

This number would then be further reduced to wind up with a single digit number:

17 = 1 + 7 = 8

It is vitally important that you understand how to translate letters into numbers in order to use numerology.

In Chaldean numerology the number 9 is considered sacred.

One big difference between Chaldean and Pythagorean numerology is that while in Pythagorean numerology you use the name that is on your birth certificate, in Chaldean numerology you use the name that you are most known by. This could be a nickname, a married name, or just your regular name if that is what you are known by.

HURRAH FOR RAH FOR RAH FOR RAH HURRAH

I

HAVE

COME

153 x 12 = 1836 1836 = 12 x 153

I

INVOKE THEE BELOVED ISIS QUEEN OF THE NIGHT COME WEAVE THY WEB OF RAINBOW LIGHT

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. Orpheusand 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 systemhas 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 Aztecsin 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 Newtonfailed. 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.

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 fortymore-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, 108per 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 Angkorthus 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."

Page 36 3 + 6 = 18 1 + 8 = 9 3 x 6 = 18 1 + 8 = 9

" St Augustine in The City of God also writes of the perfection of number 6, for 'in this did God make perfect all his works. Wherefore this number is not to be despised, but has the esteem apparently con-firmed by many places of scripture. Nor was it said in vain of God's works: "Thou madest all things in number, weight and measure." ' It is the unique property of number 6, on account of which it was held perfect, that it is both the sum and the product of all its factors excluding itself, for 1 + 2 + 3 = 6 and 1 x 2 x 3 = 6.
6 is the number of the cosmos, and the Greek word,..." "...sig-nifying the cosmic order, has the value by gematria of 600. The ancient astronomers adopted the mile as the unit which measures the cosmic intervals in terms of the number 6, and procured the following sacred numbers:

.

.

Diameter of sun	=	864,000 miles ( 12 x 12 x 6000 )
Diameter of moon	=	2160 miles ( 6 x 6 x 60 )
Diameter of earth	=	7920 miles ( 12 x 660 )
Mean circumference of earth	=	24,883.2 miles (12 x 12 x 12 x 12 x 1.2)
Speed of earth round sun	=	66,600 miles per hour
Distance between earth and moon	=	6 x 60 x 660 miles or 60 x earth's radius

The Fingerprints Of The Gods

Page 153 1 + 5 + 3 = 9

"In Egypt's early dynastic period, more than 45 00 years ago, an 'Ennead' of nine omnipotent deities was particularly adored by the priesthood at Heliopolis. 5 Likewise in central America both the Aztecs and the Mayas believed in an all-powerful system of nine deities."

the Pan book of

ASTRONOMY

James Muirden 1964

Page 63 6 + 3 = 9

CITY OF REVELATION

John Michell 1972

Page 77

CHAPTER SEVEN

3168, The Perimeter of the Temple

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 circumferenceof the circular state, but also the area of each of its 2520 pairs of rings, proving Plato's assertion that linear and area measurements 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.