On Non-Euclidian Geometry

I have been catching up with Hannah Fry’s BBC 4 series, Magic Numbers, which is a history of mathematics. Today I watched the second episode in which Hannah touched on some of the revolutions in mathematical thinking that took place at the end of the 19th Century. One of those revolutions was the development of non-Euclidian geometry, which is a perfectly respectable field of mathematical study. I, of course, started to think of something else.

These days we tend to think of Lovecraft as a horror writer, but I suspect that he saw himself as much more of a science fiction writer. Many of his stories involved aliens, and he seemed to keep up with what was happening in science, and in maths. He was very much disturbed by the way in which the foundations of human knowledge, which had been accepted for hundreds of years, were being eroded.

Euclid’s geometric theorems had been the basis of much of mathematical thought since the time of Classical Greece. They still hold good today, but only in certain circumstances. Because the Earth is so large we can approximate living on it to living on a flat surface. On such a surface, if you follow a path that turns through four right-angles, with equal distances between each turn, you get back to where you started. But, as Fry demonstrated in the program, that’s not the case if you live on the surface of a cube. In that case you only have to turn through three right-angles to get back where you started. That’s very weird.

The program also touched on the story of the German Mathematician, Georg Cantor. He was responsible for the development of Set Theory, as part of which he discovered that some infinities are bigger than others. This too is very weird. In the latter part of his life Cantor had very poor mental health and was institutionalised on several occasions. You can just imagine the tabloid headlines: “Famous mathematician driven mad by contemplating infinity!”

If you then throw in the development of quantum physics, which was also happening around the time that Lovecraft was writing, it is easy to see how one might come to the conclusion that unravelling the mysteries of the universe might drive men mad.

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