The subject of ancient reckoning of time and space can only be inferred from the logic of numbers, with very few exceptions of data in the historical record. Many historically significant numbers exist in the historical record of different ancient cultures. But, the method for computing those numerical results remains a theme of speculation. Many of the ancient Babylonian clay tablets that exist reflect specific mathematical and geometrical problems, much like a school textbook of today. However, notebooks of the scientists who computed the astronomical meandering of the bodies in our solar system have yet to be found.

Our analyses of the historically significant numbers coming out of the ancient reckoning systems are based on speculation about the logic of numbers; how the numbers might relate to one another through elementary mathematical methods. Numbers that appear in the ancient maya system are compared to the numbers that appear in the ancient kemi system. Such a comparison allows us to visualize the significance of intermediary numbers. The ancient day-counts of 260, 360, 364, and 365 days are taken into consideration in this light, along with other day-counts relating, for example, to the cycles of other planetary bodies in our solar system. In this manner, one is almost able to distinguish the possibility that the 365c day-count came about before the 260c day-count. Scholars believe the 260c day-count to be the older calendrical system, but the math of the numbers suggests otherwise.

In this manner, strange appearing numbers in the historical record, such as 756, 819, 151840, 1366560, among many others, suddenly reveal unsuspecting interrelationships. For example, the k'awil count, identified as the 819c day-count, appears to mediate computations between the 360c and the 364c day-counts. Further, one begins to distinguish the possible use of the mediatio/duplatio method of computation, whereby the ancients may have not only doubled numbers, but also trebled them. In this manner, one arrives at a table of squares and cubes of the whole numbers. Numbers that at first glance appear to be unrelated are thus revealed to lie on the same number series representing a multiple of one another. The maya long count is a more obvious case in representing a doubling of its terms (36, 72, 144, 288, 576, 1152 and 2304).

In the book The Geometry of Ancient Sites, we examine some of the numbers in terms of the side measurements of the pyramids and regarding geometrical figures. The ancient sites upon which pyramidal structures have been built reflect a relational significance with the great river basins of the world. Other authors have attempted to discern an interconnectedness among the different sites from the perspective of the mathematical expression of numbers. Beyond this, many of the numbers pertaining to right triangles and perfect right triangles would appear to harbor some kind of relationship in design. By graphing the numbers relating to specific perfect right triangles, and then comparing these graphs to the layout of the pyramidal structures at different sites, we are able to discern a possible relationship among the varied ancient cultures. It were as though one site were complementary to all the other sites.

If the numbers/fractals appear to represent a match, then most certainly one would expect a match in the geometrical expression of those numbers. Based upon the designs graphed from the measurements of perfect right triangles, one can in fact account for the smallest pyramidal structure at these sites. It appears that every structure within a pyramidal site shares a common meaning with the rest of the site's structures. The placement of the structures therefore would appear to be the result of a very detailed conscious design. The design appears to reflect the relations of equivalency in the numbers of perfect right triangles. And, these numbers are significant in that they reflect the possibility of accounting for the day-counts of the ancient reckoning system.

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Copyrighted © 1995, 1996, 1997, 1998, and 1999 by Charles William Johnson. All rights reserved. Reproduction prohibited. Printed in the United States of America. Published simultaneously in Mexico. This publication, or parts thereof, may not be reproduced in any form of photographic, electrostatic, mechanical, or any other method, for any use or purpose, including information storage or retrieval, without written permission from the author, except for the inclusion of brief quotations in a review.

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