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 Anti-Radian, we review the nature of right triangles and perfect right triangles, and that of the circle. Our contemporary concept of the circle conceives of the circle as only consisting of 360 degrees. We examine the idea that the ancients may have conceived of the circle with varying numbers of degrees. In this work we present a review of a 378-degree circle. With a more dynamic concept of the nature of the circle, we may also consider the idea that the ancients not only conceived of the radian of the circle, but possibly placed emphasis on the anti-radian (that part of the circle not including the radian).