Monthly Archives: December 2020

Hilbert’s Hotel and Gödel’s Freezer

A friend of mine, Flavien Hirsch, invented a fascinating paradox in probability, called Hilbert’s Hotel and Gödel’s Freezer. Technically speaking it is the same thing as the Sleeping Beauty problem, which I’ve written about here, but I find it much … Continue reading

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Beautiful angles with beautiful cosines

I’ve recently proved a theorem that is probably well-known to anyone that studied number theory. I didn’t know it before, though, and it was a lot of fun, so I decided to write it up here in case there are … Continue reading

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Implementing impossible functions via tomography

A long time ago I had a conversation with Daniel Nagaj about the following problem: given access to an unknown unitary gate $U$, is it possible to build the gate control-$U$ out of it? Nagaj argued that it was impossible, … Continue reading

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