Want to wade into the snowy surf of the abyss? Have a sneer percolating in your system but not enough time/energy to make a whole post about it? Go forth and be mid: Welcome to the Stubsack, your first port of call for learning fresh Awful you’ll near-instantly regret.
Any awful.systems sub may be subsneered in this subthread, techtakes or no.
If your sneer seems higher quality than you thought, feel free to cut’n’paste it into its own post — there’s no quota for posting and the bar really isn’t that high.
The post Xitter web has spawned soo many “esoteric” right wing freaks, but there’s no appropriate sneer-space for them. I’m talking redscare-ish, reality challenged “culture critics” who write about everything but understand nothing. I’m talking about reply-guys who make the same 6 tweets about the same 3 subjects. They’re inescapable at this point, yet I don’t see them mocked (as much as they should be)
Like, there was one dude a while back who insisted that women couldn’t be surgeons because they didn’t believe in the moon or in stars? I think each and every one of these guys is uniquely fucked up and if I can’t escape them, I would love to sneer at them.
(Last substack for 2025 - may 2026 bring better tidings. Credit and/or blame to David Gerard for starting this.)
One important nuance is that there are, broadly speaking, two ways to express a formal proof: it can either be fairly small but take exponential time to verify, or it can be fairly quick to verify but exponentially large. Most folks prefer to use the former sort of system. However, with extension by definitions, we can have a polynomial number of polynomially-large definitions while still verifying quickly. This leads to my favorite proof system, Metamath, whose implementations measure their verification speed in kiloproofs/second. If you give me a Metamath database then I can quickly confirm any statement in a few moments with multiple programs and there is programmatic support for looking up the axioms associated with any statement; I can throw more compute at the problem. While LLMs do know how to generate valid-looking Metamath in context, it’s safe to try to verify their proofs because Metamath’s kernel is literally one (1) string-handling rule.
This is all to reconfirm your impression that e.g. Lean inherits a “mediocre software engineering” approach. Junk theorems in Lean are laughably bad due to type coercions. The wider world of HOL is more concerned with piles of lambda calculus than with writing math proofs. Lean as a general-purpose language with I/O means that it is no longer safe to verify untrusted proofs, which makes proof-carrying Lean programs unsafe in practice.
@[email protected] you might get a laugh out of this too. FWIW I went in the other direction: I started out as a musician who learned to code for dayjob and now I’m a logician.
Thank you for the links
Those look suspicious… I mean when you consider that the set of propositions is given a topology and an order, “The set
{z : ℝ | z ≠ 0}is a continuous, non-monotone surjection.” doesn’t seem so ridiculous after all. Similarly the determinant of logical operations gains meaning on a boolean algebra. Zeta(1) is also by design. It does start getting juicy around “2 - 3 = +∞” and the nontransitive equality and the integer interval.This is darkly funny.