Fun reddit thread about 'Junk Theorems'; mathematical statements that are only true because of the way we encode them in terms of set theory.

For example, 'An element of an integer is a topolgical space if and only if that integer is the graph of the successor function'.

Lang's paper pentasia:

The kite and dart Penrose tiling lifts to a surface in 3d with two equilateral triangles per tile, overhanging for the darts. Robert Lang made these nice physical models. Explanations at (Barry Cipra on the 1993 discovery of this surface with Conway) and (Lang and Barry Hayes, also on a related 3d surface for the rhombic Penrose tiling).

Me: Can I have a random point, uniformly distributed over the plane?
Probablility theory: Sorry, there's no such thing.
Me: Can I have infinitely many of them?
Probability theory: Oh yah, no problem

The traditional images aren't of the Hilbert curve, but of one of the approximations that tend to it in the limit.

Show thread

Hilbert's space filling curve evaluated at 2048 uniformly random points.


The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!