Grasping Infinity

Slides for this presentation

Mankind has grappled with the idea of infinity for millennia but it only got a solid mathematical foundation at the end of the 19th Century, mostly due to the work of Georg Cantor. His ideas were revolutionary, shook the world of mathematics and drove him mad. David hilbert famously said “No one shall expel us from the Paradise that Cantor has created”, this talk is a whirlwind tour of that paradise, you will find out how mathematicians wrangle with infinity - are there different kinds, can you do arithmetic with them, what it means to divide by 0, extensions to the real number line, the hyperreals, the superreals and the surreals, what infinitely many monkeys can do in a hotel with infinitely many rooms containing infinitely many typewriters (and how one cleaner can clean the hotel in a finite amount of time), infinity in physics, the Vast (but finite) Library Of Babel envisioned by Jorge Luis Borges and anything else I can squeeze in the finite time allocated.

Corrections to the video:

  • 20:30-22:20
  • The Successor function is not the powerset! Really sorry, the slides are correct from 2 = {0,1} = {{},{{}}} but the brain-fart in the earlier slide makes me misspeak, no wonder you didnt follow it! The successor function is the set of all previous numbers, I say it correctly at 24:00.
  • 0 = {} (which has cardinality 0)
  • 1 = S(0) = {0} = {{}} (which has cardinality 1)
  • 2 = S(1) = {0,1} = {{},{{}}} (which has cardinality 2)
  • etc