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 Binary System. we examine different possibilities for creating binary systems other than the one in existence today. We show how the ancients utilized similar computations based on the numbers that accompany the maya long count. Different number series exist, and in that sense it is possible to create different binary expressions. However, the number series (1, 2, 4, 8, 16, 32, 64..., etc.) that we have chosen today for the construction of our binary system, just happens to be the same number series that the ancient maya chose for their long count. The maya long count (36, 72, 144, 72, 144..., etc.) runs parallel and in relation to the 1, 2, 4, 8, 16, 32..., number series. The reason for choosing this particular number series concerns the fact that it is the only number series of multiples of the natural numbers that allows for creating a binary system that would be able to express any number from zero to infinity. Most undoubtedly the ancient maya chose this system for the same scientific reason that we chose it today.