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SCIENCE IN ANCIENT ARTWORK AND SCIENCE TODAY SERIES
A Method of Reckoning
Table of Contents
A Method of Reckoning Charles William Johnson We began our studies of ancient reckoning in search of the logic of numbers. Upon examining the historically significant numbers coming out of the ancient reckoning systems of time, we considered the possibility of finding the method of computation behind the numbers. There are many historically significant numbers in the different ancient reckoning systems of time coming from many different cultures. Many of these numbers can be easily related through the method of doubling or trebling the numbers, or by dividing those numbers by twos or threes. Early on in our studies, we suggested that the possibility may exist of finding the methods of computations by simply reviewing the historically significant numbers themselves. No one apparently knows how the ancients reckoned time. Numbers like 1366560, 1385540, 1959552 have elicited surprise and wonder for years. And, because of the fact that no one knows exactly how such numbers were achieved or chosen to be significant, scholars resist in assigning them too much scientific value; if any at all. Basically, it is thought that much of the ancient reckoning was based on myth and superstition, and not any knowledge of reality. To speak, then, of there existing a possible logic of numbers would appear as a misnomer. For it is generally thought that such numbers were not even the result of human reasoning and study. To suggest that the numbers may reflect theoretical considerations of mathematics, geometry or trigonometry, as we have offered in previous essays in the Earth/matriX series, is simply erroneous to some. Nonetheless, without wishing to ignore the vast historical legacy left by the ancient peoples, we have attempted to discern the logic of numbers reflected in the historically significant numbers. And, finally, we may suggest the possibility is strong that the ancients knew much more theoretical math than most people are willing to admit or concede. After having analyzed the concept of the radian and the anti-radian (Cfr., Earth/matriX Extracts Nos. 47 and 48), we now consider the possibility that the ancient reckoning system may have been based precisely on these concepts. The historically significant numbers would appear to respond and perform in exact accordance with the characteristics of a circle and the rules regarding their construction and existence. For a couple of centuries now, debates have concentrated on whether the ancients knew the concept of pi, the relation of the diameter of a circle to its circumference, and to what particular decimal point it was known or suspected. Most chronological tables cite the Babylonians (ca. 2000 BC)as having devised pi to the amount of 3 1/8ths at best. The Egyptians supposedly used only 3.1605 or 16/9ths. And, it was not until a couple of thousand years later that pi was known to be around 3.14163 by the Greeks. All chronological tables written in modern or contemporary times generally show a slow progression of improvement regarding the precise identification of the concept of pi. Hardly anyone recognizes the ancients as having actually discovered pi to any precise decimal place close to the number that we employ today, 3.141592654, or any similar expression. To think that the ancients may have reckoned with a precise knowledge of the concept of pi is simply something not accepted in academic writing of any worth. And, yet, as we shall illustrate below, the historically significant numbers of the different ancient reckoning systems of time reflect and suggest just such a precise knowledge of not only pi, but of the radian (57.29577951) and the anti-radian (302.7042205). To even suggest that the ancients knew such characteristics of the circle to this degree of precision would make even the want-to-be believers show surprise. Nevertheless, numbers are difficult to manipulate; and, generally, the manipulation is often discerned and disclosed. In the analysis that follows, there is no manipulation of data. We simply employ the basics of addition, subtraction, multiplication and division. There is nothing complicated in the perceived method of reckoning time. The historically significant numbers and fractals easily fall into place and into relationship with one another and with the general theoretical posits and axioms of mathematics and geometry, and even trigonometry. In a sense, we consider that our research has revealed the logic of numbers behind the ancient reckoning systems and the different day/year and cycle counts. This obtains from the obvious fact that we can easily and readily effect the computations of the different counts in relation to one another and in relation to the general rules governing mathematics, geometry and trigonometry. The historically significant numbers and fractals enter into relationships that at first hand seemed to be coincidental, and now may be easily predicted. Predicting and reproducing knowledge is generally an essential part of what is termed today to represent science with a capital letter S. We like to think that what we have discerned from the ancient numbers and fractals simply represents one possibility of what the ancients may have achieved long ago. In this essay, we shall examine how one may visualize and derive the concepts of pi, the radian, and the anti-radian from knowledge about the circle. Within this realm of inquiry, we shall use examples based on the historically significant numbers and fractals coming out of the ancient systems of reckoning. The ancient system may have been extremely dynamic. Basic ideas regarding pi, the radian and the anti-radian seem to have been well-known from a theoretical point of view. Yet, aside from these constant relationships, depending upon what particular event was being analyzed, the numbers and counts changed in relationship to one another. In this sense, the natural numbers coming out of the behavior and performance of mathematics and geometry are established on the one hand, while the distinct day/year counts and cycle counts were devised on the other. At times, there appears to have been a theoretically grounded basis for some of the day-counts, while other counts may have been chosen for reasons relating to a specific case. Without entering into examples, let us simply begin our analysis by illustrating the different aspects of a circle, as we know them today in relation to some of the historically significant counts.
Pi, the Radian, and the Anti-Radian
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