A conversation about infinity inspired by The Library of Babel by Jorge Luis Borges. Presented by Katie Steckles and Peter Rowlett.
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“You Can’t Polish a Nerd” is the latest in a run of live stage shows from science/maths comedy trio Festival of the Spoken Nerd. Consisting of friends of the Aperiodical Matt Parker, Steve Mould and Helen Arney, FOTSN is a mixture of comedy, science, music and live demos, and they’ve sent us a copy of their latest show to review.
Here’s a tale of a rational (or irrational?) legal battle from the 1990s re: Cantor’s diagonal argument.
Cantor’s diagonal argument from 1891 was truly revolutionary: an ingenious way to demonstrate that no matter what proposed list of all real numbers (or, say, just those between $0$ and $1$) is put forth, it’s easy to find a number which is definitely missing from the list. ((One has to pay close attention to realise that the same proof doesn’t also establish that the rationals are uncountable, bearing in mind that the Cantor pairing function shows that the rationals most certainly are countable. See http://en.wikipedia.org/wiki/Countable_set))
In a nutshell, Cantor was the first to show that some infinities are bigger than others.
Cantor’s diagonalisation argument for the reals is watertight, and has proved to be a model of elegance and simplicity in the century plus that has passed since it first appeared.
That didn’t stop engineer William Dilworth publishing A correction in set theory, in which he refutes Cantor’s argument, in the Transactions of the Wisconsin Academy of Sciences in 1974.