High dimensions are indeed very, what shall I say, non-intuitive. Bellman introduced, or perhaps popularized, the term 'curse of dimensionality'. High dimension

High dimensions are indeed very, what shall I say, non-intuitive. Bellman introduced, or perhaps popularized, the term 'curse of dimensionality'. High dimensions may also comes with its blessing, 'concentration of measure' a phenomenon where randomness concentrates into events of certainty in high dimensions. I checked out their Wikipedia pages, while the former has a lucid description, the page on the latter is quite technical. Both these notions play a significant role in topics like machine learning, statistics, function approximations etc. Its sometimes a delight sometimes sheer frustration to see these two phenomena play it out.