In this Wireless Philosophy video, Jonathan Weisberg (University of Toronto) explains Bertrand's Paradox, a famous paradox in probability theory. Beginning with the square factory example, he'll talk about how Bertrand's Paradox reveals a puzzling problem for the principle of indifference and the implications of this paradox for scientific reasoning.
Part 1 of a pair. Agustin teaches us about some weird properties of infinity, using an example due to mathematician David Hilbert called 'Hilbert's Hotel'. He shows us a result proved by another mathematician, Georg Cantor: that many infinite collections of things are the same size. Things that are the same size include: the natural numbers, the natural number plus one, the natural numbers plus the natural numbers, and as many copies of the natural numbers as there are natural numbers! Amazing!
Part 2 of a pair. After part 1, you might have thought that all different infinite collections of things are the same size. Not so! In this video, Agustin shows us another of Georg Cantor’s results: that for every size of infinity, there is a bigger one! An example: there are way more real numbers than there are natural numbers.
A Toolkit for Building a Better Mind.