Ancient Metrology & Precession
Iona Miller's EARTH WORKS SERIES: Ancient Metrology
See e-books SYNDEX 1 and SYNDEX 2 online, links here
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." This concrete form of philosophy was determined by the nature of Greek mathematics.
PROTO-METROLOGY Ancient cultures and alphanumerics. The Hindu divine numberword Om/108, is called the number of the Universe. The graphic enspiralment of the natural number continuum into a mandala or mandalog (based on 108 axes) forms a crucial tool for investigation of hidden properties of numbers. Multiples of 108 form the basis of Indian time measurement, the Yugas and Ages. Synchrograph C is a graphic spiral of rhythmic symmetries. On this number wheel, natural numbers are spiralled 60 times around a radial array of 108 increments to the number 6480. Contemplating the C-Graph revealed the Holotomic Sequence: 12, 24, 72, 360, 2520, 27720, 360360, 6126120, etc., created by prime number multiplexing, and the exemplary 9/11 wavecycle (a +4, -4 basewave). ****
Ancient cultures and alphanumerics. The Hindu divine numberword Om/108, is called the number of the Universe. The graphic enspiralment of the natural number continuum into a mandala or mandalog (based on 108 axes) forms a crucial tool for investigation of hidden properties of numbers. Multiples of 108 form the basis of Indian time measurement, the Yugas and Ages. Synchrograph C is a graphic spiral of rhythmic symmetries. On this number wheel, natural numbers are spiralled 60 times around a radial array of 108 increments to the number 6480. Contemplating the C-Graph revealed the Holotomic Sequence: 12, 24, 72, 360, 2520, 27720, 360360, 6126120, etc., created by prime number multiplexing, and the exemplary 9/11 wavecycle (a +4, -4 basewave).
Earth’s Measure is the Golden Key to Precession
By Iona Miller, 2009
There is a lost wisdom whose traces are found in ancient natural sciences, including cosmology. The Precession of the Equinoxes is a measure of Earth’s rotational axis (celestial pole) in space. Earth moves around in its orbit and rotates on its axis. But that axis creates a third motion of the Earth, relative to the fixed stars. The stars move across the sky at the rate of about one degree per 72 years.
The modern measure of one such cyclic span or period is 25,771.5 years but there are many variables in the calculation. After one full cycle of 25,771.5 years, the positions of the seasons relative to the orbit are "back where they started."
But other effects -- including wobble, torque, magnitude of the Earth’s tilt and gravitational forces of other heavenly bodies -- also slowly change the shape and orientation of the Earth's orbit. These, in combination with precession, create various cycles of slightly differing periods.
Written history does not encompass even one such cycle as mythological history is less than 10,000 years old. Metrology is perhaps 5000 years old but mankind has been systematically observing the sky for at least 50,000 years. Legendary numbers seem to have originated in Sumerian culture as the result of geodesic and cosmological measurements discovered millennia ago, in the mists of prehistory.
The Sumerians mythologized “divine” numbers as time portals. Metrology and chronology go together as soon as we try to take Earth’s measure in the cosmos. It appears the system was observed or discovered through simple arithmetic, rather than contrived. Precession was the ideal prototype, the vast cosmic standard by which all other things were measured.
Mankind has an inherent love of measuring which is the natural basis of metrology. It has pragmatic survival and social value. Ancient metrology is the science whose evidence is encoded and mirrored in the sacred dimensions of the Pyramids, Stonehenge, and other earthly monuments oriented to the heavens. The numerical code lies behind the layouts of temples and cities and systems of measuring time from megalithic Britain to China and even in the Americas. (Scherz)
Measurement was a sacred system of knowledge established in prehistory, based on observations of cosmic cycles. Standards of measure were framed upon universal principles of number and the geophysical dimensions of the ever-turning Earth. There is no starting nor ending point. Celestial time is virtually inconceivable without the Great Cycle.
Precession is the gradual shift in the orientation of the Earth's axis of rotation, which, like a wobbling top, traces out a conical shape in a cycle of approximately 26,000 years as it maps the heavens. The Sumerian calendar was based on the 25,920 Precession cycles. The Platonic Year was based on the divine number 2160 (1080 x 2). Plato mentions another divine number in his Republic -- 5040 (2520 x 2).
12 x 2160 = 25920
20 x 108 = 2160
36 x 60 = 2160
2160 + 360 = 2520
2160 + 432 = 2592
The key to the comprehensive analysis of general number behavior is found in the concept of "circular unity." Circular unity is an idea demonstrated by the harmonious interaction of the first six numbers. SIX is the first perfect number, being the sum of its first three digits, or 1 + 2 + 3 = 6.
1 x 2 x 3 = 6; 62 = 36; 36 x 3 = 108; 362 =1296 x 2 = 2592.
The Precession of the Equinoxes was first noticed as a slow but steady slippage through the Zodiac of 1 degree every 72 years. A full cycle was a journey of Earth through all the signs of the Zodiac. The equinoxes move westward along the ecliptic relative to the fixed stars, opposite to the motion of the Sun along the ecliptic.
To complete one cycle of the zodiac--a "Great" or Platonic Year--requires 25,920 years. Dividing this sum by 360 yields the number 432, the root of the mythological count of 432,000 years. However, it is not only mythological, or archetypal--it was discovered by centuries of controlled astronomical observation, even prior to written record-keeping.
Cosmology, horizon-based astronomy, astrology, architecture, navigation, geography, geometry, mathematics, timekeeping, writing, proportion in art, and musical notation were all related to numerical canon. The ancients encoded their knowledge of the world in their sacred monuments and texts as an esoteric code of numbers, formulas, and proportion.
There are cross-cultural links in units of measure related to sexagesimal fractions of meridian degree. All relate fractionally to the Sumerian cubit. Although no measuring devices survive from Sumeria, the varying values of the Sumerian cubit have been accurately established from the dimensions of buildings, the measurement of bricks, and from cuneiform tablets that record these dimensions.
The most widely acknowledged value of the cubit is taken from that of the half-cubit represented as a rule on the statue of Gudea from Lagash, and given as 248mm. The cubit usually divided sexagesimally into 30 fingers is at times divided into 24 fingers as in the rest of the ancient world. This 24th division of the Sumerian cubit is the Megalithic inch. Obviously this digit is the Sumerian value, 24 to that cubit, 25 to the royal Egyptian and 40 to the Megalithic yard. Units were kept standard in the dimensions of permanent stone monuments. (Neal, 2003)
“The sacred Jewish cubit, that of Moses and Ezekiel, expressed as "a cubit and a hands breadth" refers to the royal Egyptian as the basic cubit. Since a hands breadth is 5 digits, the implication is that 5 such hands comprise the royal Egyptian and 6 the sacred Jewish, this digit is therefore the Megalithic "inch": 15 to the "common" Greek foot, 24 to the Sumerian cubit, 25 to the royal Egyptian cubit, 30 to the sacred Jewish cubit and 40 to the Megalithic yard. There is little doubt that we are regarding a single organization of measurement in what has previously been viewed as quite separate systems.” (Neal)
Ancient religions had pronounced astrological elements, which have defined precessional ages from Taurus through Pisces, and the imminent age of Aquarius. Ancient state temples may have functioned as permanent repositories of standards of measures. Gods, (to whom the temples were dedicated) had characteristic numbers, from which they were indistinguishable.
The exemplar number, 108, is known as the number of the Universe. It also corresponds with the god Brahma, and the seed-syllable AUM or OM. Numbers expressed qualities, not just quantities. Prime numbers figure prominently in the measuring and numerical canons of ancient and modern times.
In the old beliefs, this code, (whose true source is lost in prehistoric antiquity), is always alleged to have a divine origin, from the gods or a god-like man. Lore relating to sacred words or phrases arose, because letters and numbers were interchangable or alphanumeric. The code arises naturally from the inherent structure of arithmetic. This golden code emphasized certain key numbers, which were seized upon by different cultures.
Metrology was the basis for development of both philosophic and scientific attitudes. The divine order of the universe was the central idea of the ancient world, and all belief-systems were enmeshed with it. Metrology provided the foundation of the systematic rational vision of the world. Cosmic order embodied in metrology was the fundamental aspect of ancient thought. Number mysticism was the essential basis of most of their knowledge.
Of course, information about the Universe has always been there, but its availability is limited to those prepared to receive or decode it. Ancient cosmologies were not only models of the physical universe, but representations of a universal mathematical archetype. The numerical canon revealed correspondences between different orders of natural phenomena. Metrology included sacred units for measuring the Universe, units of time, space, weight, and mass (or volume).
The ancient sacred units of measure come from the principle dimensions of the earth (geodesic or geodetic) and astronomical (or cosmological) constants, such as the Precession of the Equinoxes, and the orbital periods of the observable planets.
Land was measured in Mesopotamia and Egypt by the same “statute foot” we use today. The “geographic foot” is related to the length of a minute of arc at a latitude which corresponds to that found in lands such as northern Egypt. By definition, there are 6000 geographic feet in a nautical mile (one minute of latitude arc on the surface of the earth). 1/10 of a nautical mile is an ancient land measure called the "geographic stade"--600 geographic feet, or 606 (600 + 6) of our common feet. (Stecchini; Scherz)
Geography developed from metrology. Traders and navigators needed to calculate distances and time for travel. This link between measures of length and time united metrology and astronomy, and led to astronomical navigation. Ancient navigators used a sexigesimal method of dividing the horizon, using six (rather than four) cardinal directions.
Ancient linear measures expressed fractions of the earth's dimensions (polar diameter, circumference, radius, meridian circumference), generally in units of 12. Thus, we have 360 degrees of latitude, each of 60 minutes of 3600 seconds.
Cross-culturally, ancient units of measure relate proportionately to each other, because the old units (whether Mesopotamian, Greek, Egyptian, Roman, Chinese, etc.) represent fractions of the earth's dimensions. Russian archaeologist Bieliaev, points out that the same weights with the same subdivisions are found in early Rome and India of the third millennium B.C. He traced connecting links to Sumer and Egypt, and found the same units used in medieval Russia.
In ancient times, the Universe meant the observable Universe. For Pythagorean and Platonist thinkers, the patterns of numerical relationships which occur in the processes of arithmetic and geometry were considered the formative influences behind all of nature's phenomena. Numerical patterns were detected in the manifestations and dynamics of nature. Behind this is a philosophy of numbers which express universal relationships.
Although usually superceded by practical arithmetic, there is much to learn from the study of the relationship of number and form. The essence of all matter is dynamic relationships. Number is the 'first paradigm,' the basic ordering principle of nature.
Transient, Eternal or Cyclic?
Many so-called "key numbers of the Solar System" are involved, because key numbers have always stood out for their unique properties. The ancients discovered them through aeons of empirical observations of cosmic cycles. They were capable of observing long-term effects, (such as the precessional cycle), with horizon-based astronomy. Their observations of the divine order were central to the core of their civilizations.
Ancient metrology does provide a clue to what numbers might be interesting to investigate. Syndex II (Miller) follows the clues by using direct observation of natural number behavior displayed in a spiral, rather than interpretation of what is there to be seen. Certain numbers graphically call attention to themselves. It requires no ancient, alien, or mystical source, no occult doctrine or arcane secret, no ideology. It predicts no "end time." It is simply a graphically revealed "truth."
#108 as the Hindu number of the Universe is a circular totality which encodes the structure of Epochs or Divine Ages. Since the incremental 'numbers of the ages' are multiples of #108, when enspiralled along 108 axes, the characters 0 - 6480 all align along the zero/108 axis -- they naturally share the same neighborhood when displayed as "Mandalogs" or "Holotomes". (Miller & Marshall, Syndex I)
By starting with 6 (the first perfect number) and multiplying by the primes in their natural order, we get the sequence 12, 24, 72, 360, 2520, 27720, 360360, 6126120, etc. Each of these numbers forms a geometrical entity, a circular unity, (Holotome). These numbers just happen to be the exact sequence of minimal sums that accomodate the maximal amount of factors of division. Their synergetic qualities have remained unnoticed in classical number theory.
The synchrographic structure of the two ancient Hindu modules of circular unity disclose that the Yugas fall into a perfect tertiary symmetry. The Ages assume a perfect quadric symmetry when spiralled along 108 axes of a number field, array, or matrix. The final number of this synchrograph is 6480. The number of zeros at the end of any astronomical Hindu number is nearly arbitrary. The glyph unifies the two ancient systems.
In antiquity, knowledge of an alphanumerical canon spread throughout the Middle East, to Greece and India, back to the Moslem Empire, and from there into medieval Europe to catalyze the Renaissance. India raised mathematics to a high art with its most revered number 108, the number of OM and the Universe, the number of Brahma.
This number formed the basis of the Ages and Yugas, which are all multiples of this sacred numberword. Yugas include 432, 864, 1296, 1728 and add to 4320. Ages include 648, 1296, 1944, 2592 and add to 6480.
108 is itself 3 x 36--part of the Sumerian sar, 3600, also dubbed the number of the Universe, a unit of Divine Time, a year of the gods (3,600 earth-years). The number of zeros tacked on the end of these cosmological numbers is almost irrelevant, and merely emphasizes their vast importance.
Since 108 is 3 x 36 and both systems mutually include the square of 36 (1296), it becomes evident that the classic 360 degree circular unity is the common denominator of these separate systems (360 degrees of 60 minutes or 3600 seconds each).
According to Neugebauer (1952), "the division of the circumference of a circle into 360 parts originated in Babylonian astronomy of the last centuries B.C. The sexagesimal number system as such is many centuries older and has nothing to do with astronomical concepts."
However, in a far newer work, Sumerian scholar Zecharia Sitchen (1993) differs in opinion, attributing both mathematical astronomy and 360 circular unity to the Sumerians, based on his own cuneiform translations. He also refers to "the role that the key number 12 played in Sumerian science," and the "celestial 72," which comes from the precessional shift of 1 degree. He notes that 120 sars equals 432,000 earth-years. This is the number of the Great Yuga.
The key to Sumerian metrology is not as simple as the sexigesimal 6 x 60 = 360. Even in Sumeria, the sexigesimal system (60-division) was only applied in strictly mathematical and astronomical contexts. The sexagesimal numerical system had a decimal substratum (36 x 10 = 360). In other matters they used 24-division, 12-division, 10-division, and 2-division.
The real key involves the sequence in which prime numbers naturally occur in the baseten continuum. This is demonstated by multipling the third and fourth Holotomes together: 72 x 360 = 25920, a number given for the Precession of the Equinoxes in Sumerian cuneiform records. Clearly, this number relates directly to Yugas and Ages.
72 x 36 = 25920 divided by 2 = 12960;
divided by 3 = 8640
by 4 = 6480; by 6 = 4320
72 + 360 = 432
Contemplation of the numberwheel 108 discloses the complete menagery of "sacred numbers." 864 is 12 x 72, holotomes A and C; 1728 is 24 x 72, holotomes B and C.
Both systems share 362 = 1296.
Contemplation of this number wheel discloses the complete menagery of "sacred numbers." The key numbers of ancient metrology and the Holotomic Sequence are found in positions of perfect symmetry (such as the quadratic array of the four-digit palindromic sequence: 1881, 2772, 3663, 4554) where only chaos exists in classical number theory. Nature's behaviors coincide with the most crucial divisions of the synergetic continuum of baseten number.
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.
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.'
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.
Constants of Nature
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. The Hebrew year in 2009 is 5769.
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 rooted in Precession cycles and natural number dynamics.
Berriman, A.E. (1953) Historical Metrology
Knorr, W. R. (1985), The geometer and the archaeoastronomers: on the prehistoric origins of mathematics. Review of: Geometry and algebra in ancient civilizations [Springer, Berlin, 1983; MR: 85b:01001] by B. L. van der Waerden. British J. Hist. Sci. 18 (1985), no. 59, part 2, 197--212. SC: 01A10, MR: 87k:01003.
Michell, J. (1981), Ancient Metrology,
Miller, Iona and Robert Marshall (1998), SYNDEX II, A synergetic revisioning of number dynamics in light of ancient metrology and modern cosmography www.geocities.com/numeronom...dexii.html
Scherz, Old World Units of Measure Found in the Layout Geometry of Prehistoric Earthworks at Newark, Ohio By Dr James P Scherz www.midwesternepigraphic.org/scherz.html
Sitchen, Zecharia (1997), When Time Began, Avon; New York.
THE AURIC KEY: SYNDEX I and SYNDEX II by Iona Miller and Robert "Bob" Marshall
These philosophies seek to reconcile the actual condition with a hypothetical distant ideal, which expansively incorporates both personal and universal dimensions. It is an inward-oriented epistemology. By intuitive perception we can consciously reiterate the laws of Nature and mind which are equivalent to the archetypes themselves. Belief in the essential aspect of the mathematical as a real world, a "last reality" underlies the surprising efficiency of mathematics in the natural sciences and technology.
But are numbers really abstract entities existing independently of the human mind? What is the nature of mathematical truth, and how is it translated into mathematical knowledge? If it exists in another "ideal world", how can we know anything at all about the subject-matter of mathematics? What collective criteria determines the nature, terms and rules of this world?
In the Jungian view, numbers (like other archetypes of the collective unconscious) are contents and patterns of behavior which are not personally acquired in experience but are inborn. The Platonic Forms are the objects of knowledge, which is regarded as innate. They can emerge dynamically as well as imagistically. The essential nature of the Forms is dual: unity and multiplicity, finitude and infinitude. "The One" is the origin of Forms in the same way that the psyche is the origin of the archetypes.
Because they form a primary conceptual language, numbers have heavily influenced the development of culture, philosophy and myth as well as sciences such as cosmology. 'Number is All' was the Pythagorean motto. Numbers were symbols representing cosmic principles. The whole philosophy of numbers came from distinctions created by the primordial division of the One into multiplicity. Because of their archetypal essence, their mode of articulation is essentially mythic and radically symbolic.
Mathematics, by the very nature of its method, is an essentially Platonic pursuit. Mathematicians treat the objects of their investigations as real objects in a hypostasized space, as if they existed independently in some pure world of their own. Thus, they reason that the amount of prime numbers is "infinite." Discussing the amount of prime numbers, mathematicians believe that they are discussing objects as real as collections of things in their everyday life.
We use numbers casually and rigorously as a language to order space. Since ancient times, their archetypal dynamics have been the foundation of philosophy, religious, and artistic thought. Patterns of dynamic energy in numbers reflect patterns of nature--the order of the universe. Whether they actually form the basis of the universe is the subject of ongoing debate among many schools of mathematicians. The qualitative distinctions we make between phenomena are fundamentally numerical. We still don't know why the universe appears to follow mathematical laws. However, as Hilbert has suggested, we do know that the idea of the Infinite deviates significantly from the situation in the physical Universe.
Are numbers and functions the inventions of mathematicians, or do they exist independently of us? Just because a mathematical object can possibly exist doesn't mean it actually does exist. Yet, mathematicians imagine they are talking about real objects, when they may be talking about stabilized concepts. The new direction in the philosophy of mathematics is a "quasi-empirical approach that treats mathematics as just another messy experimental science." A partially unconscious process of idealization ends in the stable concept of numbers, points, lines, spheres.
When working in geometry, a mathematician does not investigate the relations of real things. He investigates some idealized, fixed notion of these relations. This notion is subjectively treated as "reality" without any fundamental reality behind it. It can, therefore, arguably be considered art as well as science. In practice, mathematicians jump to conclusions, and after the jump has been made begin the labor of proving the theorem or constructing a coherent theory. This involves subconscious reasoning, tenacity, focus, judgement, concentration, elementary intuition, free association, and conceptual visualization.
Some say mathematics is a purely human construct, an artifact of our nervous systems and culture. Others attest that even chimps and infants are hard-wired by evolution for arithmetic to deal with real objects in the real world. Numbers are not Platonic ideals but neurological creations. Integers, like colors, are artifacts of our sensory processing mechanisms.
Dehaene traces the arithmetical model to the inferior parietal cortex. This poorly understood location is where visual, auditory, tactile signals, and language processing converge. Mathematics, or at least mathematical notation, is another human languge. It also appears to be the language of nature, and therefore physical reality. Of the infinite range of mathematical creations, scientists keep those that help explain and predict reality.
The concept of natural numbers is a fixed model, an idealization of quantitative relations which ends in stable concepts of numbers. The dynamics of those numbers are described in number theory. Number theory, one of the oldest branches of pure mathematics, concerns elementary properties of primes, divisibility among integers, the existence of greatest common divisors, the study of specific families of numbers, simple recurrent relations, factorization, and more. Syndex addresses these aspects with easy to state conjectures which can be understood and observed in graphics without any particular mathematical training.
Mathematical Platonism concerns the investigation of fixed or self-contained models. The Platonic Idea or Form is essentially an unchangeable form. As symbols, numbers express the particular in the universal, the eternal in the finite. They express the ordering function of their archetypal nature. The Neoplatonists assumed an a priori structure of knowledge grounded in archetypal forms and directed toward a unification of the ultimate principle of "the One" with the diverse phenomena of "the Many." This could also apply to the number field.
We contend that the Holotomes are such self-contained models of holistic, self-reflective, finite portions of the number continuum. Holotomes are geometrically symmetrical, modular unities, based on the minimal numbers divisible by the the maximal factors of division. Each holotome adds an additional factor of divisibility to its circular unity. All base digits are captured by the number 2520.
2520 -- THE AURIC KEY
Every subsequent holotome retains a copy of the initial data plus an additional factor. Each holotome contains a rational section of a complete cycle. In these geometrical entities, the prime numbers are distributed in perfect radial symmetry within the context of every holotome. Such closed loops of causation are 'objective,' i.e. considered legitimate objects of scientific scrutiny.
Number and geometry are two ways of expressing the same set of ratios or relationships. The Exemplary 9/11 Basewave (Cycloflex) is also a synergetic, dynamic representation of objective closed loops of causation. They can not only be described, but also graphically displayed. This is a reflexive +4, -4 ambidirectional base wave with a ninth null event, (as per Buckminster Fuller), forming a series of octaves running through the continuum.
This octave is a cyclic function. This base wave can be faithfully mapped into a single coherent syntactic time frame. The base wave is highlighted by palindromes and transpalindromes (the reverse identity of any number over a single digit, i.e. 16 - 61). Syntactic objects, which clearly exist represent similarly "real" objects--objects of investigation.
Syndex is a method of mapping number structure and dynamic, synergetic behavior making number theory visibly coherent It geometrically paraphrases the elements of numeric progression. Syndex reveals the self-reflexive, synergetic properties of the base-10 natural number continuum or field. It simply exists at the level of nodes and mappings in the Syndex diagrams.
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.
These sacred numbers come from the ancient wisdom traditions, including those of Sumeria, Babylonia, Egypt, the Bible, Plato, Pythagoras, ancient India, Stonehenge, the Mayans, and Qabala. Their importance to human culture echoes down to us from the past, not in any occult way, but by disclosing an ancient number canon that conceals and reveals inherent rhythms in the base-10 continuum. It reveals a synergetic relationship between number and geometry, which can be displayed graphically and easily understood even by the nonmathematical.
These circularities are based on prime number multiplexing. Within each circular number wheel, the primes are dispersed in rational, symmetrical deployment. This mandalic science helps us visualize facts about dynamic aspects of the interaction of numbers and their families. This fact remains undiscovered in classical number theory, and is discussed under the rubric of the prime number enigma.
The Auric Key to this enigma is the rediscovery of the original program of the alphanumeric system of notation and the fundamental platform of general science, the history of which began with horizon-based astronomy and cosmology in Sumeria. The Auric Key excavates many vital properties of numbers.
Classical cultures are characterized by certain basic ideas, of which metrology is foremost. Ancient metrology was a system of interlinked measures, numeration, astronomical cycles, and geodetic standards. We can find the most often cited numbers of ancient metrology extrapolating out of a certain numerical sequence, (The Holotomic Sequence).
We begin with the question of why some unknown and ancient geometer selected 360 degrees for dividing the celestial sphere and the circle. The division of 360 by 12 produced one of the first historical cosmologies--the Zodiac. The basis of this standard of circular unity can be deduced.
360 is divisible by all eight base digits except the number 7. To include 7 as a divisor, the prime circular module must be raised to 2520, the Auric Key, the lowest number divisible by all base digits. From this clue, we can destrapolate and extrapolate an essential sequence, a family of numbers.
It turns out that 360 is but one in a strategic series of circular unities based on prime number multiplexing. Numbers 2, 3, 5, 7, 11, and 13 are the first primes. By starting with 6 (the first perfect number) and multiplying by the primes in their natural order, we get the sequence 12, 24, 72, 360, 2520, 27720, 360360, 6126120, etc. Each of these numbers forms a geometrical entity, a circular unity, (Holotome). These numbers just happen to be the exact sequence of minimal sums that accomodate the maximal amount of factors of division. Their synergetic qualities have remained unnoticed in classical number theory.
This minimalism is reflected in Syndex number theory. The first concern of Syndex method is to encode the maximum information expressed through minimal graphic elements. Therefore, we employ correspondences between numbers, colors, and frequencies of divisibility to integrate the system.
The number 2520 is the Auric Key. It, not 360, is the first number divisible by all nine base digits. It is exactly twice the number 1260, a number referred to cabalistically five times in the Book of Revelations (12:6 and 12:4). It is half of the number 5040, which figures prominently in Plato’s “Laws” regarding his ideal city/state.
This number 2520, more than 360, captures nature’s cyclic behaviors. And the graphic number wheel (synchrograph or mandalog) based on this number reverses to form a mirror image of itself at the midpoint of 1260. The real key involves the sequence in which prime numbers naturally occur in the base-10 continuum.
This synergetic effect is demonstrated by multiplying the third and fourth Holotomes together: 72 x 360 = 25920, a number given for the Precession of the Equinoxes in Sumerian cuneiform records. In Sumeria, mathematics was based on a sexagesimal system (60s) with a decimal substrate (10s). The Sumerian sar was based on multiples of 36, 360, 3600; it was known as the number of the Universe (36 x 10 = 360). Imagine a circle for space of 360 degrees x 60 minutes x 60 seconds = 1,296,000 seconds.
The real key to this system involves the sequence in which prime numbers naturally occur in the base-10 continuum:
72 x 360 = 25920 divided by 2 = 12960; divided by 3 = 8640; divided by 4 = 6480; divided by 6 = 4320. 72 + 360 = 432.
The precessional number, 25920, can also be arrived at by 432 x 60 = 25920, employing the Sumerian sexagesimal system. This number relates directly to ancient Hindu cosmology and divine time measurement as the Ages and Yugas. Their numbers (without the cosmological zeros) include 432, 864, 1296, 1728, 4320 for the Yugas, and 648, 1296, 1944, 2592, 6480 for the Ages. Both Ages and Yugas share the number 1296 (362).
The Hindu systems are based on multiples of #108 (3 x 36), the divine numberword OM, also known as the number of the Universe. The Yugas and Ages can also be generated on multiples of 36. Multiply by 12, 24, 36, and 48 for the Yugas; and 18, 36, 54, and 72 for the Ages.
12960 (half the Precessional cycle) is a numerical basis for astronomical measures and played a role in Plato's mystic symbolism: 12 x 2160 (Platonic Month) = 25920 (Platonic Year). In all cases, the historical precedent for this system comes from Sumeria, and its ancient cosmology inspired by horizon-based astronomy. These numbers and their importance come from direct observation of the precessional cycle and orbital times of the planets.
Ancient India raised mathematics and astronomy to a fine art. In medieval times, it gave the west its system of so-called Arabic numerals, the base-10 system, place value, and the zero, and created a Renaissance in art and science. It is within this system of mathematical notation that the +4, -4 basewave inherent in the continuum can most easily be seen through the mechanism of palindromes and transpalindromes.
SYNDEX I identifies and demonstrates the various properties of the base-10 number field, such as the symmetrical distribution of prime numbers. The continuum can be viewed as both progressive and regressive, or self-reflexive. The key to the comprehensive analysis of general number behavior is found in the concept of "circular unity." The graphic importance of the Holotomic Sequence is that circular symmetry is being conserved and may be enlisted as the fundamental reference key in the graphic investigations of number behavior. The primes are deployed in symmetrical interface only within these specific Holotomic domains.
Synchrographics regards symmetry as a primary analytical reference, making the Syndex archetypal system of number classes possible. The foundation of this system is palindromes and transpalindromes, yielding 12 classes of number. Palindromes, or binomial reflection numbers are neither purely accidental nor without significance. Transpalindromes are the reversal of any particular number exceeding a single digit.
Numeronomy, the laws relating to the essential structure and dynamics of number, is a new word for an extremely ancient science. This science, (based on the knowledge that the continuum contains a definite structural order with general laws that describe the nature of that order), has laws that relate to the general behavior of nature itself. Each number has both a geometrical and numerical identity. The outcome of Synchrographics is that numbers speak for themselves through structure and synergetic behavior.
All Syndex mandalogs (number wheels) are the product of the systematic generation of the exact sequence of minimax factorization. They have the perfect retrograde feature by which the patterns generated in the first half of the spiral are reversed at midpoint and are reflected as a mirrored image in the second half of the spiral. Revisioning the number continuum with the concept of simultaneous counterflow yields a more accurate picture. This revisioning is also happening in post-quantum physics under the rubric of quantum backflow.
With large spans of numbers, the complex interrelationships become difficult to visualize without good graphics. Because of the octave nature of the base cycle, there cannot be more than four consecutive transpalindromic pairs in a single symmetrical sequence, regardless of the amount of digits in each individual number. The Holotomic Sequence consists of a series of key numbers or circular unities in the rhythmic wave.
Buckminster Fuller was very excited and "filled with joy" over these revelations, when the Syndex discoveries were shared with him before his death. He wanted to publish them in a subsequent edition of Synergetics. And why not, since they shed light on old enigmas. After all, numbers are what they are, not what we wish them to be. They will not do what they cannot do, i.e. show symmetries where none exist.
SYNDEX II is about the process of discovering synergetic, rhythmic symmetries on a graphic enspiralment called Synchrograph C. It is based on the Hindu number of the Universe, 108. On this number wheel, the natural numbers are spiralled 60 times around a radial array of 108 increments to the number 6480. Contemplating the C-Graph over the years has produced several revelations, including the Holotomic Sequence, created by prime number multiplexing, and the exemplary 9/11 wave cycle (a +4, -4 base wave).
On Synchrograph C all the numbers that represent the two Hindu astrocalendaric systems fall in the same zero axis. The sum of the Yugas falls at 2/3 of this axis. 6480 divided by 3 = 2160, the Platonic Month; 12 x 2160 = 25920, Platonic Year. On this graph the four-digit palindromic sequence (1881, 2772, 3663, 4554) appears in quadratic array, where only chaos exists in classical number theory.
Jung asserted that number forms the particular element which unites the realms of psyche and matter. It is real in an archetypal, qualitative sense and a quantitative sense, uniting the imaginal and the physically knowable. The psychic dynamics of the concept of number appear archetypally as its "transgressive" aspect in the realm of matter. Numbers above the threshold of consciousness appear as quantitative discontinuities and qualitative individual numbers. But according to the Jungians, in the unconscious they interpermeate and overlap participating in the one continuum that runs through them all.
Thus, we find certain synchronicities in the Syndex numberwheel mandalas, creating metaphysical and empirical harmonies. Certain authentic mathematical structures can originate in the unconscious even though Western number theory has traditionally followed a very different path, using its accepted, formalized rules. On rare occasions graphical architecture combines with the data content to yield a uniquely spectacular graphic. Such entities caqn be described and admired but there are no compositional principles on how to create that one wonderful graphic in a million.
The ultimate Platonic ideal was that of Beauty. The most beautiful graphics do not traffic with the trivial. Graphical elegance is often found in simplicity of design and complexity of data. Visually attractive graphics also gather their power for content and interpretations beyond the immediate display of some numbers. The best graphics are about the useful and important, about life and death, about the universe.
Click here to go to SYNDEX I : contains more on Synergetics and Qabala, magick, Stonehenge, ancient insight. The Diamond Body: Buckminster Fuller and the Qabala; N = 50, V = 6; Music of the Spheres; Number and Jung's Transformational Process; The Auric Key; Numeronomy and Synchrographics.
Click here to go to SYNDEX II : number mysticism and alphanumeric writing; cosmic cycles of creation and destruction (Yugas and Ages); ancient Hindu mathematics & astronomy; mandalog #108; the Sumerian legacy; models of sacred space; milestones in the evolution of the number concept; Syndex number theory; metrology; cosmography.
©2009 Iona Miller is a nonfiction writer for the academic and popular press, hypnotherapist (ACHE) and multimedia artist. She is a participant, not just commentator. Her conspirituality work is an omni-sensory fusion of intelligence, science-art, new physics and emergent paradigm shift, melding many social issues into a new view of society. She is interested in the effects of doctrines from religion, science, psychology, and the arts. Website: http://ionamiller.iwarp.com