March 2021 Links
Also contains links from February.
Ansuz: What color are your bits? What do the notions of “random number” and “copyrighted music” have in common? They’re not about the specific bits under consideration, but about their color.
I was very taken with Lucy Greer’s blog drossbucket in general, and I particularly enjoyed this recent post: Speedrun: “Sensemaking”, where she tries find out as much as she can about this nebulous term in one hour. Seems like a cool thing to emulate!
Higman’s embedding theorem states that a finitely generated group can be embedded as a subgroup of a finitely presented group precisely if there is a presentation where the relations are recursively enumerable, i.e there is a computer program that generates them one after the other. Of course this statement makes sense if you replace “group” here by any single-sorted algebraic theory (i.e Lawvere theory) - The Boone Conjecture is the conjecture that it’s always true. This is now known to be false in general, but of course the problem of characterizing those algebraic theories which have this property remains. I find this extremely cool because it reduces a question about computability theory - which seems to require a lot of essentially arbitrary choices about how powerful the model of computation should be, etc - to a purely algebraic question.