The Higher Dimensions Series — Part Four: The Probability Theory Connection

Welcome to Part Four of the Higher Dimensions Series, where we explore some of the strange and delightful curiosities of higher dimensional space. Currently, I have completed Parts <a href="https://medium.com/@chris.lloyd.rowe/the-higher-dimensions-series-part-one-distance-to-the-origin-3378d9118950?sk=28a592af9f4a528c3d8e40da94fea9e9" rel="noopener">One</a>, <a href="https://medium.com/@chris.lloyd.rowe/the-higher-dimensions-series-part-2-the-cube-inside-the-ball-4e13a574e240?sk=bc3c76e9e4e81898a083f6c4d38773e8" rel="noopener">Two</a>, <a href="https://chrislrowe.medium.com/the-higher-dimensions-series-part-three-the-distance-between-points-b284576582f4?sk=15314406a21f7a4d4bb5c469a077f6d8" rel="noopener">Three</a>, Four, and <a href="https://chrislrowe.medium.com/the-higher-dimensions-series-part-five-the-land-of-no-neighbors-5da13b0c5211" rel="noopener">Five</a>, with hopefully more to come. If you have not already done so, I encourage you to read the earlier parts before continuing on with our current expedition. Today we will be entering the world of probability theory to try and shed a bit of light on some of the bewildering phenomena we have encountered in earlier parts of the series. My mind was completely blown the first time I was introduced to the the relationship between these higher dimensional wonders and some fundamental concepts in probability theory. In truth, the links between higher dimensional space and probability theory are very deep, highly technical, and mostly beyond my current intellectual reach. However, by introducing some relatively simple concepts in probability theory and relating them to scenarios we’ve already explored together, we can get a tiny glimpse as to why some things behave as they do in higher dimensions. <a href="https://chrislrowe.medium.com/the-higher-dimensions-series-part-four-the-probability-theory-connection-d55a60eb4712">Website</a>