Thomas Yaeger's Blog: Mathematics and Calculation in Antiquity (letter to a Cambridge Scholar)

Tuesday, 8 December 2020

Mathematics and Calculation in Antiquity (letter to a Cambridge Scholar)

Date: Sun, 06 Dec 2020 12:56:04 +0000
To: .............cam.ac.uk
From: thomas yaeger
Subject: Mathematics and Calculation in Antiquity

Dear........,

I’m supplying here the address of an article which may be of interest to you, since a) you are interested in early examples of sophisticated human cognition, and also b) in examples of ideas, languages and cultures being transmitted west to east in deep antiquity. This article addresses both of these areas.

The article took seven years before it assumed its current form. It started off as a relatively minor component in a project on the presence of abstract ideas in the ANE and the Levant before the Greeks, which resulted in my book, ‘The Sacred History of Being’ (2015).

What the article argues is that the mathematics which can be found in the vast majority of megalithic rings in Britain, France and elsewhere, show that builders had a grasp of infinite series and Euler’s number from very early on (late 4^th mill. BCE onwards, up until around 1400 BCE, which is when they seem to have stopped constructing them).

The pattern of their distribution around Europe and the Mediterranean suggests the original builders travelled westwards, and then north to Britain.

One of the reasons why no-one has considered the presence of Euler’s number in these structures (2.72, supposedly first discovered by Bernoulli), is of course, why would they know this number? It is also assumed that the number would have been too hard to calculate in such ancient times, even if they did have a loose grasp of infinite series.

This is not actually the case – it can be established geometrically with a relatively small number of iterations (less than a dozen). Interestingly the procedure for doing this can be found in the Rhind Papyrus, which dates from around the 17^th century BCE, but was originally compiled earlier. In a publication issued by the British Museum in the late eighties, Gay Robins and her husband identified that the Egyptians were working with an understanding of infinite series. And showed the Egyptian diagram, illustrating how it was done.

The geometric process for establishing Euler’s number can be done on the ground, using small stones. I explored the Avebury complex pretty thoroughly in 2001 and 2002, and noticed brickish sized stones collected together, on the edge of one of the circles, almost lost in the grass. I had no idea why they might be there at the time, but they may have been what they used in the geometric construction . Effectively, the small stones are telling us what the whole structure is for.