Woodhenge Math 2: Geekery I confess I was a math geek as a child. I memorized pi to 50 decimal places in 7th grade, and have never forgotten it. I’m sure that kids now have another word for geek, but I wouldn’t know that because I am a math geek. This is relevant because it takes a geek to know a geek, and I can tell you that the Adena were math geeks big time. This has been apparent since Bill Romain’s masterful study of geometric earthwork relationships and since the precise lunar alignments of the octagons at High Bank and Newark were discovered by Hively and Horn in the 1990s, but the nature and extent of Adena geekery has not been appreciated, and has defied analysis up until now. Multiple pseudoscience authors have characterized Adena mathematics (using the H-word) as extensions of Egyptian, Greek, or Kabbalistic mystery cults, but these efforts, polluted by large dollops of hucksterism, not only fail on the facts (the Adena were obviously not employing Old World mathematics), but end up underestimating American Indians, whose mathematics surpassed those of the eastern Mediterranean region in important ways. In short, there is no evidence that the Adena employed the Greek golden ratio or that they ever developed algebraic notation. However, the Adena employed a more expansive definition of what we call Pythagorean triples than their Mediterranean counterparts, resulting in a larger toolkit of architectural triangles. The Adena developed more sophisticated geometric ways to represent mathematical relationships, and they had more precise means of measuring angles than any ancient civilization of the Old World. They also used a base-20 number system, whereas all of the Mediterranean cultures used base-10 – a fundamental incompatibility that rules out diffusion theories. The newly discovered woodhenge at the North Fork site adds significantly to this picture of difference. It had, as extrapolated, 108 evenly spaced posts, a number that would never appear prominently in any Egyptian or Greek construction. I have previously written that 108 is part of the mathematical series 36, 72, 108, 144, 180 – a set that reveals use of a 360-degree circle. But I left out the next number in that series intentionally because it merits special treatment. That is the double of 108, the magic number 216. You could make a movie about the mystical attributes of the number 216. In fact it’s been done – the film Pi by David Aronofsky. 216 is the cube of 6 (6 x 6 x 6), suspected of becoming associated in New Testament numerology with “the Mark of the Beast” for the same reason that other symbols of pagan mysticism, like the Pentagram, also were inverted in value by the Christian church. The New Age charlatan David Icke has linked Barack Obama to the numbers 216 and 666 as a sign of the Apocalypse. But the magic of 216 goes way beyond that flim-flam. It is the only perfect cube that is the sum of three consecutive cubes: 3^3 + 4^3 + 5^3 = 6^3 or 27 + 64 + 125 = 216. This can be expressed geometrically as the cube or three-dimensional representation of a 3-4-5 triangle – among other things the favorite triangle of the Adena. Like 72, 216 is a magic precession number since 216 x 120 = 25, 920, a good approximation of the number of years in the precession cycle, considered by the ancients as the long calendar cycle of the cosmos. Since 120 is 6 times 20, 216 encodes the precession cycle on the basis of the number 6 (6^3 x 6 x 20). This is especially evident in base-20 number systems, where the number of years in the precession cycle can be expressed simply as 6^4 x 20. 216 is also six tenths of 360. The ancient Kabbalists recognized the magic of 216 and enshrined it into a formula for the true name of God that is 216 letters long, broken into 72 sets of three-letter stems. This is really not so mysterious; it simply reflects the realization that 216 seems to encode the grand order of the cosmos. And don’t get any funny ideas about the Adena taking their math from the Kabbalists, because the Kabbalists came later. Half of 216, or 108, with which this inquiry began, has other special properties not previously mentioned. A regular pentagon has angles of 108 degrees. One of the Platonic solids, a dodecahedron, is comprised of twelve pentagonal sides, meaning that there are 6,480 degrees in all of the sixty 108-degree angles of a dodecahedron, which is one fourth of the number of years in one precession cycle, making the dodecahedron a model of the precession cycle. This might be considered highly abstract and irrelevant, if not for the fact that an artifact in the shape of a dodecahedron was discovered in Marietta, Ohio, in the early 20th century. Long dismissed as a hoax for the simple reason that no archaeologist can explain it, the possibility that this was a genuine artifact should be reconsidered, in light of new evidence that the Adena expressed a fondness for the number 108 – the number of degrees in every angle of a dodecahedron. Plus, what huckster would even think of making a dodecahedron? An ancient Roman dodecahedron that is clearly genuine has also defied archaeological explanation. Make an isosceles triangle with an angle of 108 degrees and the two remaining angles will each be 36 degrees. This is recognized as a very special triangle, called a Golden Triangle, because its sides will have the proportions 1-1-phi, phi being the magic irrational number of the golden ratio. Oops, I previously said that there was no evidence of the Adena employing the golden ratio in architecture. That is true, and I’ll stick to that, though they seem to have been playing with the angles necessary to generate the golden ratio. Discovery of the magic properties of 216 does not require diffusion, it will occur to any school of mathematicians that advances far enough into geekery. Not just the new woodhenge, but many Adena constructions are based on the mathematical series 36, 72, 108, 144, 180, 216 – including length measures, angle measures, and absolute numbers as in numbers of posts. And there is that spooky Shawnee sacred number 6, unusual if not unique among Native American sacred numbers. We may be close to the real secret of Adena mathematics.
Posted on: Sun, 29 Jun 2014 20:50:59 +0000
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