***New Sites - SYNDEX1 and SYNDEX2
Syndex I & II are about the spiritual and universal beauty of numbers. They reflect the order and beauty of nature, but also of psyche. According to Jung, number unifies the physical and psychic (as in "realm of the psyche", not fortunetelling) worlds through synchronicity. Jung's basic ideas about the unity of knowledge and existence are in principle synonymous with the Platonic tradition, alchemy, Qabala and Gnosticism. Plato treated the end product of the evolution of mathematical concepts, (a fixed system of idealized objects), as an independent beginning point of the evolution of the "world of things." Syndex graphically displays formerly undiscovered symmetries in the natural number sequence and distribution of primes. It is based on a series of circular unities (self-contained objects), the results of prime number multiplexing, from whose factors cascade the whole panoply of ancient “sacred numbers” of many diverse cultures.
to the Philosophical and Scientific Background
"Number makes its appearance in this context as the vinculum amoris, the bond of love which unites the two principles [psyche and matter] by jointly ordering them. In its profoundest sense number thus possesses the significance of an all-uniting Eros, although it connotes something different from the usual sense of the words love and Eros...Because there seems to exist such a clear spiritual "objective" order at the base of Eros, it is expressed in the seemingly abstract, feelingless, impersonal order of numbers, as a clear, immutable factor free from illusions...this cosmic ordering of the Self constitutes the ultimate mystery behind all human desire and behavior, an unfathomable and fearsome mystery."
M.L. von Franz, Number and Time, p292-3
"The unexpectedness of a mathematical result gives us the feeling that it is not our own creation, that the world of number exists in its own right, while its necessity and symmetry are balm after the ragged edges of life, or pure joy to those who do not yet know them. The appeal of mathematical form reaches deep into human character."
L. L. Whyte
"Very vigorous applause your very intelligent, scientifically systematic synchrograph evolved elucidations binomial symmetries, tantalizing manifestations...which to me clearly related several fundamentals...Your cyclic synchrographing work clarifies and simplifies this whole matter to an epochal degree...your work fills me with joy."
B. Fuller letter to Bob Marshall, 3/3/81
NUMBER MYSTICISM & ALPHANUMERIC WRITING
Number mysticism reached a zenith in ancient Greece, since the Greeks were fascinated with the essence of the integers themselves to the point of worshipful devotion. The relation between numbers (and number words) and magic remained alive throughout the ages. It is visible in Pythagorean and Platonic philosophy, the Qabala, and various other forms of religious mysticism.
The Pythagoreans believed that numbers were the key to understanding the order of the universe, and to them numbers meant whole numbers or integers. They believed that the soul could ascend through the spheres, to eventual union with God, by means of mathematics. This peculiar fascination with numbers as individuals created an obstacle to developing a collective theory of numbers, i.e. arithmetic.
The main thread of the number concept in the crossroads cultures passed from Sumeria-Akkadia-Babylonia to Phoenicia to Hellenistic (and Hebrew), to Indian to Islamic to European cultures. Key numbers, cosmic cycles, and divine numbers permeate the number concepts of all these cultures. The Greeks and Hebrews had alphanumeric systems which developed into numerology and numberword mysticism.
Number mystics from the Pythagoreans onward considered number 'one' as the Infinite God, the First Cause, the One who transcends all multiplicity. To the Greeks, numbers were divine concepts, ideas in the mind the god who had fashioned the world. God was a great mathematician. In the Hebrew Qabala, the world is made with numbers and letters. In more accurate terms, the characters representing manifestation were alphanumeric.
Whether 'one' was actually a number at all was answered by the concept that it is the essence or underlying principle of number. All the numbers are made of it. In the West, ten (10) is the number of completion and perfection which returns the essential numbers back to unity. In China, eleven is the number of Tao, but not in the quantitative sense of ten plus one, but signifying the unity of the decade in its wholeness.
Jung echoes these ancient sentiments in Memories, Dreams, and Reflections (pp. 287 f.) by stating:
One, as the first numeral, is unity. But it is also "The unity,": the One, All-oneness, individuality and non-duality--not a numeral but a philosophical concept, an archetype and attribute of God, the monad.
In Number and Time, M.L. von Franz carries this thought further:
The number one possesses these unique qualities to a particular degree...it does not multiply by itself, or reduce itself by division because it is a divisor of all other numbers...It is the first triangular and also the first square number...it has no predecessor. In this sense it does not yet "count"; if it did it would be the first uneven prime number...in mathematics the number one is not reckoned among prime numbers.
This is supported by experimentation: "dealing with the wave configurations of sand vibrations on thin plates of metal, all prime numbers figure with the exception of the one."
Influenced by Pythagorean ideas and Qabala, in which 10 Sephiroth (Spheres) emanate from God, the occult tradition asserts that the succession of numbers 1 through 10 symbolizes and is, in fact, identical with the emanation of the manifest Universe. The 22 letters of the alphanumeric Hebrew alphabet contained and created the secret structure of all things.
The SEFIR YETZIRAH, the Book of Creation or Formation (300-600 AD) describes how God created the manifest universe by means of letters and numbers which are the foundation of all things. The letters are part of 'one body,' the alphabet which is an extension of God's own being. All created things, made by means of the letters, are also parts of the one body which is God.
True being for the Hebrew is the 'word,' dabhar, which comprises all Hebraic realities: word, deed, and concrete object. Non-being, nothing (no thing) is signified correspondingly by 'not word,' lo dabhar.
In European magical tradition, the most important of all alphanumeric alphabets is the Hebrew which had 22 letters, all of which were consonants. Vowels were inferred from context. Contemplation (theory) and application (practice) is the mystical tradition of Qabala. In this alphabet there are no vowels (our a,e,i,o, and u) represented. The same is true of the older Phoenician (Canaanite) alphabet, from which our own alphabet is descended--by way of the Greek, Etruscan, and Latin alphabets.
All over the ancient orient, in Assyria and Babylonia, as well as Egypt, the word and particularly the word of God, was not only nor even primarily an expression of thought; it was a mighty and dynamic force. The Assyrians and Babylonians conceived of the divine word under the image of a physical-cosmic power.
In Egypt, the power of creating and sustaining everything was traced back to the divine word, the ever-active fluid or ethereal divine substance proceeding out of the mouth of divinity. For example, in Memphis, Ptah is the Creator of the world. The specific organ of creation is 'the mouth which named all things.'
All things nameable can be recorded or counted by symbols for things. Writing (like naming) is an ancient, magical art, assumed to have been invented by the gods. Emerging around 3200 B.C., writing contained mysterious, hidden, even divine Wisdom, for those contemporary minds. The archaic history of writing records its evolution from pictographs and ideograms, to phonetic and syllabic cuneiform, and the alphabetic form, whose sequential letters are also used as numbers.
Certain milestones in the development of alphanumeric characters have been documented archaeologically. Interaction along trade routes in crossroads cultures contributed both to the development (from syllabic hieroglyphics and phonetic cuneiform), and dispersal of a letter sequence which could be adapted to the phonetics of local dialects.
A tablet has been found from the 14th Century B.C. showing Ugaritic letters arranged opposite a column of known Babylonian syllabic signs, which supplied the sounds for the characters a, be, ga---and so on---in basically the same order and roughly the same sounds that would appear 300 years later in the Phoenician alphabet. By 1000 B.C., the Phoenician alphabet had come to full flower.
According to Isaac Asimov (1989), this is why the alphabet was never invented independently by any other society:
"Between the Egyptians and the Babylonians were the Canaanites, inhabiting the eastern shore of the Mediterranean Sea, (the Greeks called them the Phoenicians). They were traders who acted among other things, as intermediaries between the Egyptians and Babylonians. It was necessary for such traders to know both the Egyptian and Babylonian languages, and that was a hard chore indeed."
"It occurred to some nameless Canaanite to simplify writing by adopting a kind of shorthand. Why not give a separate symbol to each of the common sounds made by human beings in speaking a language? You could then build up any words of any language by using those sound-symbols. Sound-symbols had, in fact, been used by the Egyptians, but they also preserved symbols for syllables and for whole words. The Canaanite inventor had the notion that the sound symbols should be used exclusively and that words should be built up out of them."
That same alphabet could be used as numerals.
(scan alphanumeric table)
The Ancient Development of Alphanumeric Characters:
2800-2600 BC Sumerian cuneiform; pictographs, ideograms
2500 BC Cuneiform spreads through Near East; adapted
Sumerian signs to the
phonetics of local languages (Akkadian 2300-2150)
2100-1300 BC Syllabic cuneiform (Semitic style 2500-2000)
1800-1600 BC Old Babylonia
1500-1400 BC Ugaritic cuneiform of 30 characters; first ABC letter sequence;
phonetics of a Canaanite dialect corresponding with
Babylonian syllabic signs; precedes alphabetic cuneiform
1400-1300 BC ALPHABETIC CUNEIFORM from Babylon
1100- 900 BC Phoenicians spread precursor of modern alphabets; script of 22
characters, no vowels; rise of Assyria
800 BC Greeks and Hebrews adopt Phoenician alphabet;
Greeks add first vowels;
Babylon rebuilt; ALPHABETIC NUMERALS
500 BC Sanskrit alphabet and grammar codified
1000 AD Hindu-Arabic numerals and decimal system introduced into
Europe by Pope Sylvester II
It is now generally agreed that all existing alphabets as well as those no longer used, derived from one original alphabet (Paleo-Sinatic, Syria and Palestine 1750-1500 BC). There is obviously a real advantage in the use of single symbols for single sounds, compared with thousands of symbols for representing things or ideas (pictograms). The simplicity of alphabetic writing removed the monopoly on learning. The alphabet expanded literacy.
But all alphabets are inherently flawed, or at least limited. The shortcoming is that it lacks the delicate variations necessary to indicate all the subtleties of the human voice. So perfection has eluded any alphabet for that would mean the accurate rendering of every speech-sound.
In an ideal alphabet each sound would have to be represented by a single letter, and each letter would be limited to one sound. Every alphabet so far has omitted symbols for some sounds, and most have contained redundant letters. The adaption of a script to a language is not easy when it contains sounds not occuring in the speech from which it was borrowed.
In any event, the prototype of alphabetic writing was spread by the Phoencians. Local scribes embellished it, or pared it down and evolved local variations. Historians and linguists cite four main branches of the Original:
1) North Semitic, included Canaanite, ancient Sinatic Hebrew, and Phoenician;
2) Aramaic includes Persian, Syriac, Mongolian, Armenian, Georgian alphabets, and the Indian main branch with 200 offshoots of Sanskrit; also the square Hebrew alphabet;
3) South Semitic is mainly Arabic;
4) Greek main branch includes all European alphabets: Etruscan, Cyrillic, Slavonic.
Romans adopted only 21 letters from the early Etruscan alphabet, as well as their
names for letters, which were different from the ones Greeks derived from Semitic
It made writing far easier to learn with its economy of symbols, and its direct relationship to the sounds of spoken languages and numbers. Literacy spread dramatically.
COSMIC CYCLES OF CREATION & DESTRUCTION
THE HINDU DOCTRINE OF YUGAS
After the burning and plundering of the Hellenistic Library at Alexandria, Egypt, the exact science of ancient mathematics was lost to the west. The vanguard of mathematical discovery passed to medieval India.
Hindu mathematicians had little direct influence on Europe. But it is certain that the Arabs got their arithmetic and algebra from Brahmin knowledge. Caliphs entertained Indian mathematicians in the ninth and tenth centuries. Both Sansrit and Greek classics of science were avidly translated into Arabic during the Moslem Empire.
The Crusaders were exposed to this Arab knowledge in the Holy Land, and their knowledge gradually penetrated Europe also through Islamic Spain (Toledo). This led directly to a revival of European learning after the Middle Ages.
Therefore, we attribute our present system of so-called Arabic numerals to those near-eastern cultures which preserved them through Europe's Dark Ages. However, this decimal system of numeration originated in India and was one of the many kinds of knowledge translated into Arabic during the cultural flowering of that area. The numerical characters and such notions as the zero and place valuation came directly into modern society from India, even though they had been tentatively used in older societies.
Prior to the introduction of Hindu numerals, the alphanumeric characters developed by the Phoenicians predominated. Numbers were represented by the letters of an alphabet in their spoken succession. Both the Greeks (800 B.C.) and the Hebrews adopted this principle. Not only the alphabet, but the sounds of the letters were retained.
This adoption of an alphanumeric model led to the mathematical backwater of Gematria where every sum was a word or many words, and every word had a numerical equivalent. Number mysticism then concerned itself with various cryptographic messages and numerical codes. While good for mysticism and possibly promoting superstition, it was no favor to the advancement of mathematics. The old Phoenician "acrophonic" numerals were abbreviations of number words. Alphanumerics permeated the crossroads cultures.
Cultural concepts of time, real and divine, differ dramatically and underlie and condition each culture's worldview. The background of Hindu cosmology and science has its roots in the crossroads cultures. It involves notions of time and history, astronomy, and the idea of the Divine Word.
Ethnopsychology, psychology of language, philosophy of language, logic of language, semantics and comparative linguistics show that, relatively speaking, Hebrew thinking is dynamic and temporal, while Greek thinking is static and spatial--even the Greek conception of time is spatial--boundless.
The concept of number can be understood either as spatially quantitative or dynamically qualitative quantities. For the temporally-oriented Jews, there is an inner connection between plurality and intensity. Hebrew thinking moves in time, while the Greeks employ space as their thought-form. Hebrews used a lunar calendar, while Greeks used the solar year.
Both Indo-European and Semitic languages reveal a cross-cultural ambiguity when using spatial expressions to designate tempral notions. "Before" and "behind" can mean "future" and "past." This double temporal meaning of the same words reveals two different notions of time, as eternal rhythms. In Semitic languages, the notion of recurrence coincides with that of duration. Time is the stream of events, the historical content of occurrence.
The European sense of time is a confused mixture of time and space, a legacy of Greek thought. The Indo-Germanic framework of past, present, future is foreign to Semitic thinking where tense comes principally from the dynamic of completed or incomplete action.
Our modern concept of time is spatialized. For us actions are oriented objectively, impersonally and spatially; the ancient Hebrews thought subjectively, personally, and temporally. Europeans got both space/time views mixed together as Bible cosmology.
These notions came down ambiguously because the Hebrews had no notions of firm boundaries to objects, while the Greeks delighted in thinking geometrically. They relate to quantity and number as spatially quantitative (Greek) and dynamically qualitative quantities (Hebrew).
The Hebrew language has no expressions for the simplest geometric figures such as the triangle, quadrilateral, or square, nor the corresponding adjectives. Numbers are distinguished qualitatively as rhythms, each with its own peculiarity.
The form and syntax of the Hebrew numbers two to ten indicate that the smallest and basic numbers were thought of as qualitatively different totalities. From there it was just a step further to the conception of holy numbers...concrete numerical gestalts, an intuitive quality adhering to a totally unarticulated general impression of quantity. Hebrew plural forms are preferably designated as intensive.
God revealed himself to Israel in History, not Ideas. Therefore, the Israelites developed no mathematical science, though it flourished in neighboring Phoenician and Mesopotamian cultures.
The mathematical ideas of the Greeks cannot be comprehended without bringing geometry into the inquiry. The Greek Ideas were geometrical basic forms, the eternal blueprint of reality.
Space perception is the given thought-form of the Greeks, and the visible form of things occupied their attention. Geometry for them was the most important branch of mathematics.
The Greeks, including Euclid, thought geometrically even when they dealt with numbers. The square was a visual representation of the second power and the cube of the third. For the Greeks, the concept of large, quantity (largeness) was mostly a spatial idea.
The Indian concept of time has differences and similarities with the Greek and Hebrew notions revealed by linguistics of their respective languages. Language (syntax, grammar, verb tenses, etc.) displays the basic worldview of a culture, notions about how real-time experiences are processed and conditioned by the basic philosophy of a culture. Linguistic perculiarities come from the underlying assumptions about existence in time and space, perception, being and becoming, active/passive, etc.
Like the Greeks, the Indian view of time is static, that is it is conceived statically rather than dynamically, as the Jews also do. The early Greek, Heraclitus posits that flux and becoming aloneare real, permanence and constancy are merely apparent. The Hindus believe the exact opposite.
Indians recognize, of course, that the things of this world are always moving and changing. But the substance of things is seen as basically unchanging; its underlying reality is unaffected by the ceaseless flux. Indian thought places a high value on universality, and the connection between this, and the static conception of phenomena, is of course not accidental. "The one remains, the many change and flee."
The static conception of time permeates Indian thought. It could hardly fail to do so, for it is present in the very forms of language itself, conditioning all philosophical thinking. In classical Indian languages, there are no words corresponding to the concept "to become." "To become" is "to exist."
"Being born" and "existing" come from the same root. So to become is to be born. Indians express change at all as "being otherwise." Becoming is expressed in terms of being; dynamic is seen as a phase of static. This point of view permeates the language and conditions the philosophy.
The classic Western expression of the sense of flux uses a vivid and specific verb: "All things flow." The corresponding idea in India is expressed in Sanskrit as sarvan anityam, "all existences are impermanent." It always directs the attention away from the action to the stable state of the actor, from the changing aspect of the action to the unchanging universal: "to appear" does not equal "appearance;" nothing can disappear or arise. The adverb isn't even a part of speech in Sanskrit.
In Indian philosophy, the Absolute is a Being beyond all temporal appearances. These exist and change in time; the Absolute is essentially static. The great unborn Self is imperishable, incorruptible, eternal, fearless Brahman, which is coequivalent with Atman.
Indian philosophers replaced the concept of Becoming with three aspects of temporal existence: Appearance, Extinction and Continuance, which are fundamentals in their cosmology. All three states are clearly conceived as static.
Here is a similarity to Platonic thought: Plato formulated the antithesis between Being and Becoming with the true essence of reality consisting of changeless, timeless Forms. This is why geometry was important, but Greek physical sciences only developed statics. Modern scientific thought, in contrast is concerned with kinetics, dynamics, synergetics.
Preoccupied with a more metaphysical time-sense, the numbness to the passage and flow of specific events makes non-Indians regard Indians as lacking in common sense. They simply do not seem to have a clear awareness of discrimination of "real time," historical time, and it shows in their language through the discrimination of tense. Children in India will ask you, "What is time?," not "what time is it?"
The difference between absolute past and relative past is not clearly made in the Indian language. Terms can be determined only through context. They don't grasp time quantitatively, and with historical accuracy. They exist through multiple lives repeated in limitless time: appearance, extinction, continuance, over and over through cosmic cycles of creation and destruction.
According to the Indian worldview, the universe, the world and social order are eternal. The personal is fleeting, and the basic assumption of transmigration is pervasive in language, thought, and philosophy. So, passing phenomena have no real significance, and no importance is given to providing them with accurate dates. In quasi-historical fashion they resort to hyperbole, idealization, and exaggerate to astronomical proportions. Therefore, much of Indian so-called history is confabulated, the product of pure imagination.
They are more interested in religion and poetry than historical documentation. Proper observance of ancient precepts is stronger than the regard for historical accuracy. They contemplate eternal paradigms of human experience which are by their nature timeless and in that sense, outside history.
This is a contemplative orientation and worldview, expressed in the forms of Sanskrit itself. In sanskrit, it is "effect and cause" syntactically, rather than the Western "cause and effect." The Western order of thought is to proceed temporally from cause to effect; the relationship is seen in time.
In Sanskrit, progressive phenomena are seen as already complete. Rather than "the relation of the knower and the knowable," it is "the relation of the knowable and the knower."
This way of thinking is retrospective and different from the approach which starts from the cause. Things are evaluated in terms of a final cause or aim, a teleological relation. But Indians do have a concept of abstract time and changing phases of the world. They just adhere to the universal principle that whatever is subject to organization is subject also to destruction, in lesser or greater duration.
There is no substance which abides forever. All matter is force; all substance is motion; every individual is unstable; all things pass away. Modern physics, the bastion of science's "cause and effect" confirms this curiously enough through inductive and deductive reasoning which would be alien to Indian thought.
All this is the essential background on Indian language, thought, and philosophy which provides the fertile matrix from which their cosmology of cosmic cycles of creation and destruction arose. In fact, the philosophy conditioned the language and vice versa.
And the nutshell of this philosophy and language is contained in the divine rootsyllable, the sacred numberword AUM, the sound of the mystery of the Word everywhere, whose personal realization is a peak experience.
Joseph Campbell explains AUM in THE POWER OF MYTH(1988):
AUM is a word that represents to our ears that sound of the energy of the universe of which all things are manifestations. You start in the back of the mouth "ahh," and then "oo," you fill the mouth, and "mm," closes the mouth. When you pronounce this properly, all vowel sounds are included in the pronunciation. AUM. Consonants are here regarded as interrutions of the essential vowel sound. All words are thus fragments of AUM, just as all images are fragments of the Form of forms. AUM is a symbolic sound that puts you in touch with that resounding being that is the universe. To be in touch with that and to get the sense of that is the peak experience of all.
A-U-M. The birth, the coming into being, and the dissolution that cycles back. AUM is called the "four-element syllable." What is the fourth element? The silence out of which AUM arises, and back into which it goes, and which underlies it. My life is the AUM, but there is silence underlying it too. That is what we would call the Immortal.
As well as philosophy, Hindu cosmology also mixed space and time concepts derived from astronomical and geodetic measurements. They were influenced by the ancient Sumerian lunar reckoning which came with the Aryan invasion, and is, in fact, the legacy of all neolithic cultures. Later Hellenistic notions permeated their astronomy.
The figure the ancients used to define the circumference of the earth came from their foot and their cubit. These two numbers, 1296 and 864, are basic to many ancient systems of measure.
Is it a coincidence that a circle of 1,296,000 units has a radius of 206,265 units, the length of both an English and Egyptian cubit? The Hebrew shekel weighs 129.6 grams, and the English guinea 129.6 grains. The measure of the Holy of Holies in Solomon's Temple was 1296 inches.
129600 is the numeric basis for astronomical measures and played a role in Plato's mystic symbolism. Multiples and submultiples of 12960 are easily memorized: 1728, 864, 720, 432, 360, 216, 180, 90, 40, 36, 20, 16, 10, 8, 5, 4, 2. These sacred numbers were used everywhere in the building of sacred temples. The Babylonian Tablet (Igi-Gal-Bi) uses all of them, plus 144, 162, and 810.
In IDEAL METROLOGY, W. H. Wood points out the meaning of these figures in the East: "In the law of the yoga, all periodic actions developed under the inspiration of The Invisible are measured by ideal cycles, expressed in geometric form by the number 1296 in thousands or thousands of thousands. The third stage of Yoga is represented by the third of 1296 or 432, which is considered the symbol of consecration, or standing in harmony with nature's beauty and order. The exalted life of a disciple of Buddha called for a cycle of 4320 million years."
In his classic, THE BOOK, Alan Watts points to the Hindu myth which says that as time goes on, life in the world gets worse and worse until at last the destructive aspect of the Self, the god Shiva dances a terrible dance which consumes everything in fire. There follows, says the myth 4,320,000 years of total peace during which the Self abides in itself and does not play or hide. Then the game begins again in a universe of perfect splendour which begins to deteriorate only after 1,728,000 years.
In ANCIENT CULTURAL ANTHROPOLOGY, Dr. Charles Muses wrote on the origin of certain Babylonian numbers. He noticed embedded in cosmic structure certain deeply fundamental numbers, which constitute an "alphabet" of sacred numbers. Among those still used today are 360 degrees of a circle; 60 minutes for an hour; 60 seconds for a minute and 24 hours for a day; 7 days a week; 12 months a year. Muses makes a list of 1, 3, 4, 5, 7, 12, 24, 60, and 360. He proceeds to show how all these numbers are related to patterns of circular arrangement.
Twofold twelveness, or 24 comes from uniting the 12 signs of the Zodiac with 12 hours of the day. Thus, from 360, 60 and 24 came a circle of time of 24 x 60 x 60 or 86,400 seconds. And a circle for space of 360 x 60 x 60 or 1,296,000 seconds.
Another research project of mathematician Dr. Muses is even more stunning in its results. He discovered that the roots an ancient Tantric lunar meditation practices were timed to certain anomolies in the moon's orbit. The Satapatha Brahmana and the Taittireya Sanhita recount the proceedures for a Tantric Lunar Resonance Meditation, associated with the Indo-European soma saccrifice. They are linked to the phases of the moon, but not the obvious points. The practice specifically divided the lunar month into 9 special days in both the waxing and waning halves, a cycle composed of 18 days total.
There is a striking correspondence between the two-fold cycle of lunar phases (9 + 9 = 18) each month and the hypernumber w, a lunar elliptic orbit function developed by NASA for the space program.
This hypernumber w and it's phases of the elliptical orbits provide the only available mathematical paradigm corresponding to the anomolies distinct to the waxing and waning lunar fortnights. It is amazing that they could be known through some unknown form of calculation in pre-Vedic times.
It is not necessary to describe the source and functions of hypernumbers here. It is enought to know that the hypernumber w has the remarkable property that, when multiplied successively by itself, all the resulting numbers lie on a certain ellipse. The number resulting from multiplying the square root of w successively by itself also lie on the very same ellipse. Exactly 12 distinct points are generated by both these processes.
There are three principle irregularities in the lunar orbit known since Ptolemy of Alexandria, but this cannot be the Vedic source, since it came later. Together these irregularities furnish a set of eight places in the lunar orbit where these reflecting configurations of force are maximum. These eight places map on the eight points furnished by the integer powers of the hypernumber w. W was conceived by 20th century mathematicians to describe these irregulartities of the lunar orbit.
In ancient Indo-Iranian tradition the holiest time of the month is the dark of the moon, where it is conjoined by the sun itself.
The sun travels through the celestial sphere of 360 degrees. Multiples of 360 reveal a cascade of ancient sacred numbers, which are instrumental in the arithmetical construction of Divine Ages of the Hindus.
1 x 360 = 360
2 x 360 = 720
3 x 360 = 1080 - OM
4 x 360 = 1440
5 x 360 = 1800 - half circle
6 x 360 = 2160; age of years
7 x 360 = 2520; Auric Key
8 x 360 = 2880
9 x 360 = 3240; x 2 sum of ages 6480
10 x 360 = 3600; Sumerian sar
11 x 360 = 3960
12 x 360 = 4320 Maha Yuga div by 4 = 1080
x 2 = 8640 (4320 + 6480) Yugas + Ages
Hindu cosmology mixed time-space concepts derived from solar and lunar calendars with holy number words. The Hindus had their own numberwords, called mantras. These words held mystical and numerical values. They were based on metrological and cosmological constants as well as ancient mythology, and therein lay their sacredness or divinity.
Yogananda and other Hindu sources cite #108 as a divine number, "the number of the Universe." It is said to be the number of AUM, or OM, the universal sound which underlies all creation. OM or AUM is the Word of the creator of universe, Brahman, who is associated with number 43200.
This notion is fundamental in two Hindu astro-calendaric systems, the Ages and the Yugas, which delineate the number of divine years in different Epochs. Both the so-called Ages and Yugas are all multiples of #108 (see Tables which follow).
The Hindu religion is a vast ocean of religious thought, springing as it does from the earliest time, long before the dawn of history. It comprises in its multi-colored texture shade after shade, an endless variety of design and pattern as it grew in the human mind, from animism to Nature worship to number mysticism.
FOUR YUGAS FOUR AGES
Kali 432 (108 x 4) Iron 648 (108 x 6)
Dvapara 864 x8) Copper 1296 x 12)
Treta 1296 x12) Silver 1944 x 18)
Krita 1728 x16) Gold 2592 x 24)
Maha Yuga 4320 x40) Sum 6480 x60)
36 x 3 = 108
36 x 36 = 1296
1296 x 2 = 2592 - 4 = 648
10800 x 4 = 43200
CREATION OF THE WORLD
According to Hindu cosmology, the world is created from an embryo, a "center," which also implies the construction of cosmic Time. This center concept is the root notion behind the mandala, a term which itself means "a circle."
Like our Synchrographs, the mandala represents a whole series of circles, concentric or otherwise, inscribed within a square. It is a symbol of the rite of penetration, which places the neophyte in a sort of labyrinth as an initiatory process. Mandalas clearly have a labyrinthine character, and so do mandalogs if viewed from that perspective. They help us to concentrate and find our own center in the microcosm.
This can lead directly to a more authentic and deeper personal experience and understanding, if traditional ritual has become fossilized; the need of a personal experience is for reactivating certain primordial symbols in our consciousness. The purely mental constructions act as a support for meditation.
The Hindu notion of deep time is revealed when Indra hears from the mouth of Vishnu the true story of the eternal creation and destruction of worlds, the Great Time, mythic time in which we find the true source of all beings and of all cosmic events. This helps us pierce the veil of illusion created by profane time and our own history, and like Indra cures us of our pride and ignorance. It is a redemptive function.
To transcend profane time and re-enter into mythical Great Time is equivalent to a revelation of ultimate reality--the reality which is strictly metaphysical, and can be approached in no other way than through myths and symbols.
The conception of cyclic and infinite Time, Presented by Vishnu is the general Indian conception of cosmic cycles. Though this belief is found in all archaic societies, it is first espoused in the Atharva Veda.
India elaborated the doctrine of cosmic cycles by amplifying the number of periodic creations and destructions of the Universe to ever more terrifying proportions. The transition of each age marks the beginning of a regression. The decreasing length of each yuga marks this durational degeneration toward the present Kali Yuga. It is so called for the "black" goddess Kali or (Shakti, the Great Goddess), whose name is akin to the Sanskrit kala, or "time." She is the personification of time.
Number 108 is also said to be the number of names of the great Mother Goddess.
The 12,000 years of one mahayuga has been counted as "divine years" of 360 each, which gives a total of 4,320,000 years for a single cosmic cycle. This is all we need to retain with the cyclic character of cosmic time. The life of Brahma comprises 2,560,000 of these mahayugas, each going through the same stages concluding with a pralaya, and grand dissolution.
THE HINDU CONCEPT OF NUMBER
Indian Philosophy, Cosmology, and Science
"The Hindu traditions were brought to the Indian subcontinent by 'Aryan' migrants from the shores of the Caspian Sea, cousins of the Indo-Europeans who were the Hittites of Asia Minor (today's Turkey) and of the Hurrians of the upper Euphrates River, through whom Sumerian knowledge and beliefs were transmitted to the Indo-Europeans. The Aryan migrations are believed to have taken place in the 2nd millenium BC and the Vedas were held to be 'not of human origin,' having been composed by the gods themselves in a previous age. In time the various components of the Vedas and the auxilliary literature that derived from them (the Mantras, Brahmanas, etc.) were augmented by the non-Vedic Puranas, and the great epic tales of the Mahabharata and Ramayana. In them, ages deriving from multiples of 3600 also predominate, [and the Divine Cycle of 432,000]."
Zecharia Sitchen, When Time Began
In the Bronze Age, the Indus Valley of Pakistan and Northwestern India was one of the cradles of civilization. Their lost language was proto-Dravidian. The Vedas were written in the Indo-European predecessor of the Indian root-tongue Sanskrit.
The two main cities were Mohenjo-Daro in Sind, and Harappa in the Punjab. Its original civilization, the Harappan, emerged about 2500 B.C. This was a sophisticated urban society with pictographic systems of writing and measurement (metrology). A thousand years later, Aryans brought cultural influences from the north with rituals that formed the foundation of Hinduism. These traditions apparently included number mysticism, but one of astronomical numbers, not integers..
Beginning with the Brahmanas, and even the Puranas, the Indians developed the doctrine of the four Yugas, the four Ages of the World. The essence of this theory is the cyclical creation and destruction of the World and the belief in "the perfection of the beginnings." As the Buddhists and Jains hold the same views, this doctrine of the eternal creation and destruction of the Universe is a pan-Indian idea.
In Indian cosmogony, the complete cycle is terminated by a dissolution (pralaya), with a great dissolution (mahapralaya) at the end of the thousandth cycle.
The names of the four Yugas first appear in the Aitareya Brahmana, VII, 14. In India, time is not a measure of quantity, but a means of expressing universal relationships. This doctrine of ages is a variation on the Myth of the Eternal Return, a primal conception of periodic renewal of the World.
In Hinduism, man plays no part in this re-creation, but desires to escape from the cosmic cycle. There is no final End of the World, just intervening annihilations of one Universe and the appearance of others.
In every age there is a turning-point, a new way of seeing and asserting the coherence of the world. Each culture tries to fix its visionary moment, when it was transformed by a new conception either of nature or man.
When seeking the roots of ancient sciences, it is important to remember that a language system may persist in the religious or sacred arena long after it is superceded by a more popular dialect. This has been the fate of Sumerian (which ceased to be spoken around 2000 BC), but was the language of sacred liturgy and divine knowledge for fifteen more centuries.
Other liturgical languages with a similar destiny include Sanskrit, Hebrew, and Latin, (as well as Old Slavic). The Akkadians preserved old Sumerian religious structure of a supreme Triad, and this reflected into India as Brahma/Vishnu/Shiva and the west as the Trinity.
The Akkadians promoted the Sun god over the Supreme Triad, and the Triad gradually lost cult supremacy to the sun as unrivaled universal divinity whose primary quality is the emanation of numinous light.
Another creation of Akkadian religious thought is divination. They multiplied magical practices and developed occult disciplines including astrology, which later became popular throughout the Asiatic and Mediterranean world. They added the personal experience to religious life and exalted certain divinities to supreme rank.
Astrology, a late development, was originally practiced primarily by the royal entourage. Over time, the ideas, beliefs and other techniques of Mesopotamian origin circulated from the western Mediterranean to the Hindu Kush. The Mesopotamian discoveries always emphasized a direct correspondence between heaven and earth, or macrocosm and microcosm. Contact with Sumerian culture mutated other civilizations, including the Egyptian.
The first cities of India, the indigenous Harappan civilization, were overrun by the Aryan warlords, who deplored writing and had no cities of their own. Their characteristic feature, before they settled down, was oral tradition, since after their encounter with the Near Eastern civilizations, they prohibited using writing.
This mixing of cultures led to a religious syncretism or mixing of the mental concepts of both groups, which very shortly spread Hinduism through the subcontinent. The Harappan religion provided the prototype of the Mother Goddess and her consort, the phallic Shiva (Shiva/Shakti). They echo Mesopotamian mythology.
Around 1750 BC, the Indus civilization was on its deathbed, and the Indo-Aryans gave it a mortal blow. But this happened progressively, over centuries of intermingling. Aryanization of the Punjab launched the movement of the synthesis that became Hinduism.
In the west, the Hellenic culture and religion was the result of the symbiosis between the Mediterranean substratum and the Indo-European conquerers from the north. Then Hellenism sent its roots into Egypt and Asia on the tide of Mycenaean conquerors.
Despite symbiosis with countless pre-Hellenic traditions, the Aryan-speaking conquerors succeeded in imposing their pantheon and in maintaining their specific religious style. The original home of the Indo-Europeans is the region north of the Black Sea between the Carpathians and the Caucasus.
The Indo-Europeans had elaborated a specific mythology and theology (pantheon headed by a storm god and Mother Goddess). They practiced sacrifices and knew the magico-religious value of the Word and of chanting.
They possessed concepts of rituals that enabled them to consecrate space to "cosmicize" the territories in which they settled, and enabled them to "periodically renew the world." 10800 bricks in the fire altar = recreating universe in a ritual imitation of creation.
The Indo-European tribes called themselves Aryan, "noble man." They progressively assimilated the survivors of the Dravidian Indus civilization, as shown by language. Vedic Sanskrit has a series of phonemes, especially the cerebral consonants, which are found in no other Indo-European idiom, not even in Iranian. Very probably these consonants reflect the pronunciation of the aborigines trying to learn the language of their masters. Similarly, the Vedic vocabulary preserves a large number of non-Aryan words.
The time of the Asuras preceded the present epoch, ruled by the Devas. In India as in a number of archaic and traditional religions, the passage from a primordial epoch to the present epoch is expressed in cosmogonic terms: passage from a state of chaos to an organized world, a cosmos.
The agnicayana ritual was an imitation of the creation which sacralized a locality, making it the local center of the universe. The altar was built with 10,800 bricks piled up in five courses, sometimes taking the form of a bird, symbolizing the sacrificer's mystical ascent to heaven.
Originally, it involved human sacrifice, repeating the self-sacrifice of Prajapati. The building of the altar symbolized the creation of the universe, which consecrates any land. The cosmologies, like so many other religious ideas and beliefs, represent a heritage transmitted from prehistory everywhere in the ancient world. The Indians revalorized and reinterpreted many cosmogonic myths.
In the most famous hymn of the Rig Veda, the cosmogony is presented as a metaphysics, revealing how Being came out of Non-being. There was an undifferentiated principle called "One" (neuter): "The One breathed from its own impulse, without there being any breath." Aside from that "nothing else existed."
Heat gave birth to the "One" potential and this potential developed desire which became Consciousness. The first seed then divided itself into genders, and the gods were born afterwards. The "One" transcended both Gods and Creation. The One precedes the universe and creates the world by emanation from his own being. Both consciousness and the universe are the product of procreative desire.
The Rig Veda's notion of the "One" is continued in the identity of Purusha/Prajapati. In the beginning Prajapati was the nonmanifested Unity-Totality.
The triple identification of Prajapati with the universe, with cyclic time (the year) and with the fire altar constitutes the great novelty of the Brahmanic theory of sacrifice.
They contain the thought that the world and life exhaust themselves by their very duration. Satapatha Brahmana states that, "This Prajapati, the Year, is made up of 720 days and nights; that is why the altar comprises 360 enclosing stones and 360 bricks." In short, every sacrifice repeats the primodial act of creation and guarantees the continuity of the world for the following year.
In the Brahmanas, sacrifice recreates the cosmos that has been exhausted by cyclic time (the year). This later becomes the conceptual basis of creating the atman, or indestructible spiritual being.
The self (atman) is equated with Brahman. The Brahman knows the structure and origin of the universe, because he knows the Word that expresses all that; for Vac, the Logos, can transform any person into a Brahman.
The identity atman-Brahman leads to the experience of "inner light." This spiritual exercise reflects the Vedic tradition that the sun and light are regarded as epiphanies of Being, of Spirit, of immortality and procreation. According to the Rig Veda 1.115.1, the sun is the life or atman--the Self--of all things. The atman is a form of "light in the heart." That Immortal, fearless being is atman. That is Brahman.
The identity brahman-atman constitutes the most important discovery of the Upanishads.
The MAHABHARATA, with 90,000 verses is the longest epic in world history. It recounts the conflict between two lines of Bharatas. By the fifth book of the series, they are preparing for battle, which is recounted in the sixth book--the Bhagavad Gita.
This monstrous war was decided upon by Brahma, to relieve the earth of a population that did not cease to multiply. Therefore, Brahma convinced a certain number of gods and demons to become incarnate in order to provoke a terrifying war of extermination.
Thus, the MAHABHARATA describes the end of a world (pralaya), followed by the emergence of a new world. The poem has an eschatological structure revealing a gigantic battle between good and evil. There is destruction on a cosmic scale followed by the resurgence of a new and pure world. It is the conclusion of a cosmic age.
The cyclical theory was popular from the earliest times of the Puranas. The eschatological myth is older than Hinduism; it is archaic and widely disseminated among crossroad cultures. The myth of the end of the world was known by the Indo-Europeans.
Even though the eschatological myth is not documented in the Vedic period, this doesn't prove that it did not exist. The Mahabharata contains Vedic and pre-Vedic notions. It is an epic transposition of an eschatological crisis, which Hindu mythology called the end of a yuga. It is a grandiose synthesis, much richer than the Indo-European prototype. In this cycle of the eternal return, Krishna reveals himself to Arjuna as an incarnation of Vishnu.
Vishnu is the author of catastrophic destructions and resurrections. This is as much to say that Vishnu, as a supreme being, is the ultimate reality. He governs both the creation and destruction of worlds. He is beyond good and evil, like all the gods.
But the poem also glorifies the complementarity of Shiva and Vishnu, the Aryan/Harappan synthesis. These gods, together with the Great Goddess (Shakti, Kali, Durga) have dominated Hinduism from the first centuries of our era to the present. Understanding the creative/destructive aspect of divinity is equivalent to a revelation and also constitutes a model to follow in obtaining deliverance.
Deliverance involves comprehension of the relations between the two modes of the real: immediate--that is, historically conditioned--reality and ultimate reality.
Curiously, this paradoxical work about a frightening war of extermination and the end of a yuga is the exemplary model for every spiritual synthesis achieved in Hinduism, especially the tendency to reconcile contraries. It justifies a certain mode of existing in time; it valorizes the historicity of the human condition. Arjuna's existential crisis ends with his exemplary revelation concerning the human condition and the "ways" of deliverance.
Like the Greeks and the Jews, the Hindus faced the dilemma of time's meaning:
In the History of Religious Ideas, Eliade puts it succinctly:
"How is it possible to resolve the paradoxical situation created by the twofold fact that man, on the one hand, finds himself existing in time, condemned to history, and, on the other hand, know that he will be 'damned" if he allows himself to be exhausted by temporality and by his own historicity, and that consequently, he must at all costs find in the world a way that leads to a transhistorical and atemporal plane."
Since the whole univese is the creation, (or even the epiphany of Krishna-Vishnu), to live in the world, to participate in its structures, does not constitute an evil act. The "evil act" is to believe that the world and time and history posses an independent reality of their own, that is, to believe that nothing else exists outside of the world and temporality. The idea is certainly pan-Indian, but it is in the Bhagavad Gita that it received its most consistent expression.
It is still Vishnu who periodically destroys the universe, at the end of each cosmic cycle. All is created and governed by God. Cosmic life, individual existence and history receive a religious meaning. The periodic destruction of the universe is a theophany...the resacralization of life and human existence.
In Hinduism, man plays no part in this re-creation, but desires to escape from the cosmic cycle. There is no final End of the World, just intervening annihilations of one Universe and the appearance of others.
In every age there is a turning-point, a new way of seeing and asserting the coherence of the world. Each culture tries to fix its visionary moment, when it was transformed by a new conception either of nature or man.
Hindi Baseten Numerals
The history of our base ten system emerges from this Hindu cosmogony and astronomy. Hindi-Arabic numerals penetrated into Europe beginning in the 12th Century. A unique property of Hindu numerals is that (unlike Hebrew, Greek, Roman, Mayan, Chinese, or other characters) the numerals are REVERSABLE and hold place value.
Without resorting to graphic depiction to reveal inherent symmetry and rhythms, they allow for the symbolic representation of palindromes and transpalindromes, the emergence of classes of numbers.
This is a singular property of this base ten system of notation, even though the Hindus were influenced by Hellenistic culture as well. Greece and the Near East still employed alphabetic numerals, with no place values. With the advent of positional numeration and its universal acceptance, the decimal cryptogram of a number automatically provided it with a name.
According to the Hindu view, all the aspects of the manifest world spring from similar principles. There is a correspondence or equivalence between sounds, forms, numbers, colors, ideals, as there is also between the abstractions of subtle and metaphysical worlds on one side and the forms of the perceptible universe on the other. Astronomical phenomena form the basic symbols of universal principles.
According to the Nondual Principle, the Supreme Cause must be beyond Number, otherwise Number would be the First Cause. But one is considered a number just like two, or three, or ten, or a million. If "God" is one, he is not beyond number any more than if he is two, three, or a million. But, although a million is not any nearer to infinity than any number, it seems to be so. The number one is in a way the number farthest removed from infinity, so divinity is best represented by an immense number of different gods.
In the Puranas, it says, "The nature of illusion (maya) is [represented by] the number one."
To speak of the manifest force of a unique God implies a confusion between different orders. God manifest cannot be one, nor can the number one apply to an unmanifest causal aspect. At no stage can unity be taken as the cause of anything, since the existence implies a relation and unity would mean existence without relation.
Divinity as ultimate essence, is neither one, nor two (dual), nor many. The nondual principle transcends all forms of manifest divinity. This nondual Immensity is the Brahman, on a plane different from that of existence. Existence is multiplicity.
The identity of the macrocosm and microcosm can be observed in the permanence of the relations found as the substratum of all the aspects of the perceptible universe. These relations can best be expressed in terms of number. Hence NUMBER is easily seen as the common element of all forms, the all-pervading unity of all substance. Modern physics reflects and confirms this philosophy.
The creative or revealed Word of Brahm in the Vedas is AUM, or OM. It is the first manifestation of articulate language, the root monosyllable, which includes all language and meaning. It is the seed syllable of all human speech, a nutshell containing the whole of wisdom. The four Vedas are merely comments on and amplifications of this infintely meaningful syllable. It is more than past, present, and future; it is an indestructible Immensity
AUM is said to issue through a process of MULTIFOLD REFLECTION.
Taken as a symbol of divinity, AUM appears as the form from which the universe develops; the first thought-form of Brahman, the Creator. From this basic syllable spring forth all the elemental sounds, the roots of manifestation, keys of all language.
The number 4,320,000 (108 x 40) has a very ancient symbolic or "divine" meaning. It came to India with the Aryan migration and became codified in the Rigveda, Book of Sacred Verses. Among other things, it is the number of syllables in the Rigveda, which has 40 syllables per stanza, (10800 stanzas x 40 syllables = 432,000).
Hindu tradition associated the "divine" number 432,000 with the Brahman and the Yugas and Ages. This number of the catayuga divided by four yields ages of diminishing length.
Golden Age = 4 x 4,320,000 = 1,728,000
Age of Knowledge = 3x =1,296,000
Age of Sacrifice = 2x =864,000
Age of Discord = 1x =432,000
Ten eons = 1000 cycles of caturyuga = 4,320,000,0000 years; "Day of Lord Brahman," This is a close estimate to the age of the Solar System, 4.5 billion years..
These are divine, not human years...the corresponding duration for the Kali Yuga is 36,000 mortal years. 32 x 12.
Indian Science and Cosmology
The Golden Age of Indian science came to medieval India during the Gupta Empire (320-647 AD) when culture and the arts flourished. The most famous scientist of the period was the astronomer and mathematician Aryabhata. He discussed, in verse, quadratic equations, sinces, the value of pi, eclipses, solstices, and equinoxes, and the spherical shape of the earth, and its daily revolution on its axis. His successor, Brahmagupta, systematized the astronomic knowledge of India.
Other Indian astronomers made up a calendar of 12 month, each of 30 days, each day of 30 hours, inserting an intercalary month every five years. The Buddhists still use a lunar calendar. They also predicted eclipses accurately, calculated the moon's diameter, and expounded the theory of gravity.
Indian astronomy and mathematics were unequaled (except in geometry) by those of any ancient western people. Our Arabic numerals and decimal system which come from them are far more fluid and versatile than any before them. The numerals can be found on the rock edicts of Asoka (256 BC), while the scientists used the decimals system long before the Arbs, Syrians, and Chinese had a chance to borrow them. The mathematicians also created the concept of a negative quantity (without which algebra could not exist), and found the square root of 2, and solved complicated equations.
The discovery sometime in the first centuries of our era of the Principle of Position became a world-wide event. It was a radical departure in method, which in Syndex Theory makes reciprocity possible. Without this principle of position no progress in arithmetic was possible.
Place position probably was inspired by the use of counting boards. ZERO was probably conceived this way also from an empty column, and became the Indian SUNYA. It reprents a turning point for modern science, industry, and commerce. It paved the way to a generalized number concept, and plays a fundamental role in nearly every branch of mathematics. It is one of the single greatest achievements of human thought.
There is an ancient code of numbers and proportion based on metrological standards of measure. Such constants as astronomical Precession, and geodetic measures such as polar diameter provided the basic context. Fractions of the earth's principle dimensions mirrored numerical patterns in the appearance and movement of nature.
These numbers are the vestiges of the Sumerian sexagesimal system and calendar. Earlier measures of astronomy, astrology, and cosmology were usually in units of 12, as were various ancient units of measurement of time.
Mankind counted days and the changing of the moon and seasons for millennia before recorded history. As early as 3760 BC, the Sumerians created a lunar calendar. By 2800 B.C., they had worked our a cycle of 19 years which kept it synchronized with the solar year and seasons. Certain years had 12 lunar months, while others had thirteen. This lunar calendar was adapted by the Akkadians, Babylonians, Assyrians, Greeks and Jews. The Nippur calendar is still the basis of Jewish religious ceremonies.
Sumerian astronomy included the concept of "deep time," as recounted in the Enuma Elish, the Epic of Creation. Ancient texts known as the Sumerian King Lists describe the settling of the divine Anunnaki on Earth before the deluge. They list the governorships of the first 10 leaders which lasted a total of 120 sars, or 432,000 Earth-years.
This is a direct source for divine eras in Hindu lore, but they expand the vastness to an overall time span of 4,320,000, and then to a Divine Year or Day of Lord Brahma--4,320,000,000--a thousandfold great yugas. The Sumerian formula is echoed in the Hindu traditions.
From Sumeria comes the ubiquitous concept of a sky divided into 360 degrees of Latitude, 60 minutes of 3600 seconds; 12 month years beginning on Spring Equinox; 12 hours of day and night (2x12=24); 12 signs of the Zodiac, etc.
Sumerian fractions were geared to the principle of repeated halving. Whole unit or natural fractions are important in arranging metrological units. The system based on 60 is evenly divisibly by 2,3,4,5,6,10,15, and 30 eliminating the frequent need of fractions. This naturally leads to grouping higher units in 12, 30, or 60. All these ratios occur in one or another of the parallel systems of units in Mesopotamian metrology. 4320 is one such number; so is 108000.
The Greek astronomers adopted this system, and so did their followers in India, the Islamic Empire, and Europe. Much of the mathematical knowledge commonly ascribed to the early Greek philosophers was already known to the Egyptians and Mesopotamians centuries before the rise of Greek civilization. However, the Greeks preserved and spread this knowledge. They were the first to consider mathematical concepts as abstractions not part of the real world, but of the idealized "sacred space" of the human mind.
There is some evidence of ancient India having direct contact with Sumeria around 2500 B.C. This is difficult to document, but not to deduce. However, nevertheless, Hindus contributed the final step to mathematical astronomy, namely, the use of the place value notation for the smaller decimal units. This is where we get our divisions of 60, 24, 12, and 2.
AS WE HAVE SHOWN ELSEWHERE, THESE ARE CLOSELY ALLIED TO THE HOLOTOMIC SEQUENCE: 12 - 24 - 72 - 360 - 2520, ETC.
These numbers are the vestiges of the Sumerian sexagesimal system and calendar.
THE NUMBER CONCEPT IN INDIA
2500-1500 BC Contact with ancient Sumerians. Indus civilization; proto-Dravidian language; pictographic script; no firm evidence of separate numerals. Pre-Vedic PURANAS, "Ancient Writings."
1500-1001 BC UPANISHADS: Vedic period begins; RIGVEDA, Sacred Book of Verses.
1000-801 BC Pantheistic religion develops; Brahmanism; astronomy; lunar year adjusted to correspond with solar year; In Greece, alphabetic number system.
700-600 BC Indian VEDAS completed; doctrine of transmigration.
585 BC In Greece, Thales uses Babylonian methods to predict eclipse of sun.
500 BC Era of Buddha; Sanskrit alphabet and grammar codified.
500-451 BC RAMAYANA text.
326 BC Alexander invades India; Greco-Indian kingdoms established; Greek influence on art and science. Hellenistic culture flourishes. Barrier between East and West broken.
300 BC MAHABHARATA text.
250 BC In Greece Erathosthenes sieve reveals distribution of primes among first 100 integers.
Early centuries AD Invention of the Zero (Sunya) & negative numbers in India.
150 AD In Greece, Ptolemy's ALMAGEST, a unified method for representing celestial phenomena, circular cycles and epicycles.
300-400 AD Christians vandalize Library at Alexandria, Egypt.
375-413 AD Astronomical and mathematical advances of medieval India; Aryabhata,
400 AD SURYA SIDDHANTA, classical astronomical text; spherical geometry; epicycles; formula for length of day; solar velocity; earliest place value; #108 = numberword AUM (OM) = Universe.
500 AD Aryabhata argues for a moveable and rotating earth.
505 AD PANCA SIDDHANTA, by Viraha Mihira, summary of five classical astronomical treatises; sine tables.
595 AD Powers and roots of numbers; first recorded decimal reckoning.
600-700 AD Moslem Empire; Moslems burn Alexandria Library, ancient exact science lost to west.
760 AD Hindu numerals known in Bagdad; Arabs bring decimal system from India.
810 AD Al-Khwarizmi uses zero and positional notation to create algebra.
814 AD Arabs adopt Indian numerals, including zero to multiply by 10.
850 AD Mahavir, Indian mathematician; Pythagorean triplet construction known in India.
975 AD Present arithmetical notation taken into Europse by Arabs, Jews, and Crusaders; penetrates by 12th century.
1000 AD Sridhara recognizes the importance of zero; present version of SURYA SIDDHANTA.
1030 AD al-Biruni's report on Hindu astronomy and astrology derived from Viraha Mihira.
1100 AD Europe begins adopting Hindu-Arabic numeral system from Jewish scholars who learned it in Babylon, Jerusalem and Islamic Spain. First brought to Europe by Moors; introduced by Gerbert of Aurillac (Pope Sylvester II), about 1000 AD.
1202 AD Liber Abaci (Book of the Abacus) written by Italian mathematician
Leonardo Fibonacci, who derived it from Al-Khwarizmi during his North African travels. Introduced Arabic-Hindu numerals to Europe in Latin translation.