In the otherwise excellent Magicians of the Gods, a significant error exists that can use attention. By kind invitation of the author this article aims to expand and detail this claim.
Specifically, while the text of Figure 59 makes mathematical sense, the illustration taken as a whole does not.
First a few facts presented as uncontroversial. The Great Pyramid stands H = 280 cubits (builder cubits) high and B = 440 cubits along each side.
If this height were to be interpreted as the radius of a circle, the circumference of that circle would be
2 pi H = 2 pi 280 = 1760 cubits.
Note that the sum of all four sides of the Great Pyramid also equals this value.
4 * B = 4*440 = 1760 cubits.
Further note the Great Pyramid has a base/height ratio of pi/2.
4 * B = 2 pi H
B/H = pi/2
Multiplying these values by the constant scale factor K = 43200 gives a remarkably good approximation to the physical dimensions of our planet. This observation is of course spelled out in the text that accompanies Figure 59 and thus is also presented as relatively uncontroversial.
However in the illustration of Figure 59 one side of a pyramid is shown, inscribed in a circle in which the height equals a radius (X) and the base equals a diameter (Y). This is a trivial identification since Y = 2X always for every circle. And since there are four sides per pyramid, the entire perimeter would be eight times the radius.
Such a pyramid would have a base/height ratio of 2, markedly different from our Great Pyramid. Such a pyramid could be made, with its base in proper proportion to the scaled earth model, but not its height. Similarly another pyramid could be made with its height in proper proportion, but not its base.
A Figure 59 pyramid with the same base as ours (440cubits) would have a height of 220 cubits, different from the height of ours (280cubits). A Figure 59 pyramid with the same height as ours would be much larger along the base, 560 cubits.
No doubt the builders could have created any of these alternatives had they so chosen. They had to make choices about how best to model a globe, about how to encode specific physical data using the specifications of the Great Pyramid they were to actualize.
Modeled to first order as a sphere with uniform radius, only one variable – that radius – needs encoding for later retrieval.
A pyramid offers two immediate physical measurements to encode information, base (side) and height. Used to model a scaled sphere, either variable – height or base – could be used.
Note that a higher base/height ratio is easier to construct, using less stone. With its higher base/height ratio a Figure 59 pyramid could encode using the base only, and save a sizeable fraction of stonework elevating the structure to a shorter height.
Instead the builders took a more difficult path, since the actual Great Pyramid would be harder to build than a Figure 59 pyramid. All things equal, therefore, had it been an option to the builders, they could have and would have chosen it. They did not.
By building up, taking the difficult path, they could encode the radius using both the base and the height. This improves transmission efficiency with “magicians” yet to come, as the encoded variable can be duplicated, scaled accordingly, into both pyramid variables.
Using whatever method is convenient later, measuring either the height or the base would allow the magician to extract the desired value. Measuring both allows cross-referencing.
In addition, understanding the unnecessary difficulty makes the globe modelling even more obvious. This was not a coincidental choice.
In conclusion, the builders had good reasons for their decision. Those reasons – knowing the structure as it was meant to be – is the best motive for highlighting the issue with Figure 59, and making a request to correct it.
It mattered to the builders so it should matter to us.
Doug Keenan was born in Indiana and received his degree in electrical engineering from the Rose-Hulman Institute of Technology. For more than twenty years he enjoyed a career in the consumer electronics field and holds several patents including the multi-brand universal remote control. A computer programmer, botanist and entrepreneur, his work now focuses on pyramids.