Date: Thu, 19 Mar 2020 16:24:58
To: Marie aux Bois
From Thomas Yaeger
Marie,
Re: the paper on the mathematics of the megalithic yard - there's been a lot of movement since I wrote it in the middle of February, and I will write several other articles on the back of it. One of the objections to the argument will be that arriving at Euler's number would have been impossibly complicated for them to do (quite apart from the general case I'm making as to the sense it made for them to want do this). But it isn't true that this is complicated to do, particularly if you work it out geometrically, and use the right kind of exponentiating series (i.e., ones which arrive at the limit of the series in the shortest number of steps). I've already drafted this one.
The argument of the article is fine I think, but at various points it trades on what I know, and what I've written about elsewhere. So I'm going to write another article which brings the relevant information together.
I can make a list of the most significant things in the article:
1. It brings together concepts which were present in Greek civilization and philosophy, as well as in Mesopotamia. So the same ideas are going on in their heads, even if on the face of things the cultures are quite different. For the neolithic case, they are writing in terms of number and geometry.
2 If this argument is sound, it pushes the development of sophisticated mathematical and geometric thought back to the middle to late 4th millennium (3500 -3200 BCE).
3. The argument shows that, on the basis of the mathematics and geometry in the stone circles, that the builders had the same general concept of the existence of a transcendent level of reality which we know for certain the Greeks had. Indeed, historians of ideas pick the Greeks as the originators of the idea of a transcendent level of reality, and behave as if all the other religions in the world did not, before this time.
4 This transcendent level of reality was in fact infinity itself. They came to this conclusion in the Neolithic on the same basis as the Greeks did much later. Which is that the version of reality we inhabit isn't reality at all, but a poor copy of it (I echo Plato's words here). This was established on purely logical grounds, and on the basis of puzzling things about the physical universe (why is there something rather than nothing? If reality itself is necessarily one, otherwise it breaches its nature, how is it possible that there is multiplicity?)
5. And how is it that there are irrational numbers? Again, historians of ideas argue that before the Greeks, and the Pythagoreans in particular, people had no knowledge or understanding of irrational numbers, and when the Pythagoreans discovered their existence, they tried to keep this secret. In fact *the entire basis of Pythagorean thought, both in Greece, and the protoPythagorean megalithic culture was based on the existence and significance of irrational numbers.* I've talked around this issue both in SHB, and in "Understanding Ancient Thought", firstly by discussion of how ancient people conceived that commerce between the Gods and Man was possible, and by discussion of the logical modality that Plato discusses in the "Timaeus", which is based on irrationals.
6. The esoteric core of ancient religion was often kept secret. We know this for sure about the Pythagoreans, the Spartans, the Athenians, and also the ancient Romans. Plus the Assyrians and Babylonians. Modern historians assume that a transcendentalism isn't involved, but rather a doctrine which serves societal and political functions. But what if the esoteric core is too difficult and too dangerous to convey outside a tight circle of those who understand?
7. Plato discusses how the disagreements about the nature of reality in antiquity might be resolved, in more than one place in "The Sophist". The position which must be accepted (he says) is that *Reality is both One and Many at the same time*. In other words, the esoteric core of religion, based on the consideration of natural puzzles and the reality of irrational numbers, is that transcendent reality is necessarily paradoxical in nature.
8. Hence the common representation of the transcendent reality as *the inversion of ours* (look up 'Seahenge'). It is the same as this one, but it has different properties. In that transcendent reality, all things are commensurate.
9. Finally, this argument offers the possibility of proving that transcendental thought did exist at the close of the 4th millennium around a number of cultures. If transcendental thought about the nature of reality was expressed mathematically and geometrically, and necessarily involved irrational numbers, we should be able to find such references to transcendentalism in many of the architectural and engineering achievements of the ancient world. These have been noticed already in a number of structures, long before I started pursuing this question, but (for example) the golden section, clearly present in a number of Egyptian structures, is written off as a coincidence, or as consequence of the way the structure was laid out in practical terms, and that the builders had no knowledge of its presence, and did not think the proportion had any significance in itself.
We know the measures the Egyptians used. Scope I think for a nifty little computer programme to number crunch all of these, to look for the presence of Euler's number, and other irrationals.
Best, Thomas
The paper 'The Mathematical Origins of the Meglalithic Yard' is at: https://shrineinthesea.blogspot.com/2020/02/the-mathematical-origins-of-megalithic.html
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