The Banach Tarski paradox - is it nonsense? | Sociology and Pure Mathematics | N J Wildberger

One of the famous "paradoxes" of 20th century pure mathematics is the assertion that it is possible to subdivide a solid ball of radius 1 in three dimensional space into 5 disjoint pieces, take those five pieces and subject them to rigid motions, that is rotations and translations, to obtain the subdivision of a solid ball of radius 2. If it sounds crazy, no problem, we can't let reality intrude into the dreamings of us pure mathematicians. Even if our theories end up disconnected from reality and from common sense.

Is it time that we stopped paying lip service to logical nonsense -- even if it is supported by all kinds of "axiomatics" - in this case the modern pure mathematician's favourite: the "Axiom of Choice"?

Here is the blog from which the first part of the video is read: you can check out quite a few more math related discussions: https://njwildberger.com/2015/12/03/the-banach-tarski-paradox-is-it-nonsense/

Видео The Banach Tarski paradox - is it nonsense? | Sociology and Pure Mathematics | N J Wildberger канала Insights into Mathematics