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SCIENCE IN ANCIENT ARTWORK Extract No.9Computers and the Ancient Reckoning SystemByCharles William JohnsonElectronic computers of this century continue to amaze most of us regarding their performance in dazzling images and number-crunching on the screen. One of the first works that this author has published was run on a then (ca. 1968) modernday card-punch IBM computer. The understanding of how card-punch data manipulation worked was relatively easy to attain when one realized the computer mechanically read the presence/absence of holes in the cards. Today's ultrathin microprocessors and laser-reading devices have blown away the concept of those tiny rectangular holes on paper cards. Alongwith the mechanical and electronic advancements in computer engineering and design, have come an avalanche of numbers combined with letters (eg., 512k, 128Kbps, 2GB, 32MB). Anyone attempting to buy an electronic computer must dominate the numbers; the first question that comes to mind is precisely what do all of those numbers and letters mean. That in itself can be frustrating; buying a computer and then finding out that it will not perform the way one needs it to because there are not enough large numbers in the computer's configuration is commonplace. There is another question that relates to our work in analyzing the ancient reckoning systems. One wonders why some of those numbers reflect the numbers of the ancient reckoning system. One would think that there should be no obvious relationship. Given that most of us today harbor the idea that our presentday civilization is more advanced than past societies, surely there is little resemblance between today's technology and that of yesterday. Yet, in one of the computer dictionaries the word abacus appears with this definition: "A device for performing calculations by sliding beads or counters along rods. An early (3000B.C.) form of digital calculator (biquinary)." [Charles J. Sippl, Computer Dictionary, 1985.]. Not only is the author attempting to translate this concept into our contemporary language, but it would appear that there is praise in his words. The ancient reckoning systems of the world are the basis of much of what we do today, even though some might not wish to recognize what the author of this dictionary has rightly stated. Let us offer some common configurations advertised for electronic computers today:
The reason for being for each of these numbers would require a lengthy essay, but what becomes obvious at once is the fact that the ancient method of duplatio/mediatio (doubling/halving) of numbers is present, alongwith adding progressions of numbers. In previous Earth/matriX essays we have seen how these methods were employed by the ancients in their reckoning systems: mediatio/duplatio: addition of 4: addition of 48: The interesting point is to observe the presence of the maya fractals 14.4 and 28.8 in these computer numbers, alongwith the progressions of the natural numbers. Contemporary computer science employs the same kind of reckoning or computing system of numbers that the ancients employed. We doubt that the contemporary computer science engineers consciously repeated the numbers of the ancient reckoning system in honor of the ancient astronomers. Yet, the numbers are there for all to observe and compare. One wonders why would a highly advanced, technologically based society like ours develope a computing system of numbers similar to the numbers of the ancient past. One suspects that the answer lies in the way in which matter and energy behave in relation to mathematical computation. It is doubtful that in either case the numbers were arbitrarily chosen by the scientists doing the computing. In a certain sense, the numbers are obligated to perform the way they do because of the manner in which matter and energy exist and the corresponding mathematics obtain thereof. In a sense the scientists have no choice but to choose these numbers established by reality itself. In our studies we have been attempting to discern the computational math behind the reckoning system and the geometrical designs related to past cultures. In the ancient reckoning systems, we have seen how the constant number series exist as of the natural numbers (eg., 1, 2, 4, 8, 16, 32, 64...; 3, 6, 12, 24, 48, 96...; 3, 6, 9, 12, 15, 18, 21...;etc.); and, as of the maya long count numbers/fractals (i.e., 36, 72, 144, 288, 576, 1152, 2304, etc.). Other historically significant series of numbers/fractals exist as well (eg., 13, 26, 52, 104, 208, 416, etc.; 27, 54, 108, 216, 432, etc.). One obtains the impression, however, that there is a much more systematic treatment of the specific manner in which the numbers may perform in the ancient reckoning system, than in the realm of electronic computers. The manipulation of numbers/fractals is evidently not due to the exact, same rules, yet the computational math behind the rules remains the same. Therefore, certain numbers/fractals appear common to both systems. In electronic computers, one is dealing with bits (a binary digit), nibbles (a 4-bit word), and bytes (an 8-bit word), and the transference of these to other devices at specific quantities and rates of speed/time. In the ancient reckoning system, one is also dealing with similar events, but regarding the planetary bodies and their relationships to one another throughout the cosmos. In both cases, we are talking about matter and energy and how they behave. So, the numbers/fractals shall be similar if the events are apprehended in a scientifically exact manner. One could say that the contemporary field of electronic computers has come to discover the numbers/fractals of the ancient reckoning system without knowing it. These numbers/fractals appear at all levels:
Even the fractal 1152 (kinchiltun) appears often in computer language; although, we have not seen the calbatun fractal (576), but certainly it must exist, as midpoint between 1152 and 288. [Even the maya tun (360) exists in the model number of the IBM 360, a curiously random choice.] But, otherwise, one can safely say that the numbers/fractals of the ancient reckoning system appear in the numbers relating to contemporary electronic computers. In order to explore the reasons for this, one would have to examine the combination of relations, such as, 12 x 192 = 2304, based on the above example, which differs from the maya procedure (1152 x 2). Obviously the numbers reflect distinct relationships, such as the configuration of computer components and astronomical events. What is surprising is the fact that today's computer field happened upon numbers/fractals that make their appearance in the ancient reckoning systems. Consider module memory 4k, 8k, 12k, 16k or more words
where k is 1024
The use of the combination of maya numbers/fractals and the constant numbers registered in the contemporary electronic computer's configuration is as infinite as that of the ancient rekoning system. This particular system of counting (bits, bytes, nibbles, megabytes, etc.) reflects similar procedures in the methods of computation employed by the ancients. Both are employing a constant number (eg., 1024) times a constant series of numbers (times 4, 8, 16, 32, 64, etc.; and times 9, 18, 36, 72, 144, 288, etc.). Two series are prevelant: a) 1024 is a natural progression of numbers times itself: since, 1024 is part of the series 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 12288, 16384, etc.; and, b) the maya long count numbers/fractals 36, 72, 144, 288, 576, 1152, 2304, etc. represent those same maya long count numbers times the natural number series. The contemporary engineers have discovered obviously what the ancients discovered as well. That the nature of things reflects certain relationships which, when quantified, translate into a mathematics and geometry proper to the very laws of how matter and energy exist. The coincidence of numbers, then, is not a mere coincidence of choice, but determined by the behavior of reality itself. As we have seen throughout these essays, no matter which level we concern ourselves with, the particular kinds of numbers/fractals appear; be it the minute level of the elements as listed on the periodic table (Cfr., Earth/matriX Nos. 61 & 62), or be it the level of the cosmos and the distances travelled, for example by the Sun and the planetary bodies (Cfr., Earth/matriX Nos. 36, 37, & 40). The relationship of the maya long count numbers/fractals and the constant progression of numbers/fractals exists at all of these levels of reality, with the corresponding appearance of similar numbers to the ones analyzed in this extract. Many scholars enjoy believing that our society is like none other before it; and that can be a noble idea full of pride in what humankind has been able to accomplish. We should not, however, have these feelings of pride overflow into thinking that the past is worthless. For by doing that we shall have to rediscover things past. Because, we are the product of a long line of studious beings, who dedicated themselves to observing and recording events around them. The ancient reckoning systems coming out of the field of astronomy and astrology share common characteristics of the procedures that we have followed today in the field of electronic computers. If we study the ancient reckoning systems as sources of knowledge, setting aside our own belief that they may represent mere systems of belief and superstition, then we may learn something that might assist us in our own knowledge. By knowing the past, we may save time in the present, and not have to discover things in an empirical manner, but more from a theoretical standpoint, such as knowing the limits of the computers. The numbers might tell us that in their own geometrically progressive terms. Consider, for example, how from the perspecive of numbers, the next fax/modem should have been one of 57.6 kbps, instead of a 56k model. Where 56 x 1024 = 57344, and 57.6 x 1024 = 58982.4; furthermore, 58982.4 - 57344 = 1638.4, a difference which is 1/10th of 16384 (16 x 1024). Even the difference between 56 and 57.6 is significant in historically determined numbers of the maya: 56/57.6 = .972; an historically significant series 972, 1944, 3888, 7776, 15552, 31104. Now, consider further the fact that the maya employed a series not used by computer science today: 13 x 1024 = 13312 (i.e., 13312, 6656, 3328, 1664, 832, 416, 208, 104, 52, 26, 13). But, then, that is simply a question of numbers. And, even the numbers do not tell the entire story; consider the fact that according to tests, a 200MHz processor in reality functions at the rate of around 180MHz. That should help us in understanding what is significant and what is not. In our view, the fact that today's computer science employs a system of mathematical computation similar to that used by the ancients millenia ago is significant and requires further study. Reproduction prohibited without written consent of the author.
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