niplav @niplav@schelling.pt
- Website
- https://niplav.site/index.html
- Pronouns
- they/them
I operate by Crocker's rules[1].
Joined Aug 2021
Tryonics
niplav
boosted
The number of groups with n elements goes like this, starting with n = 0:
0, 1, 1, 1, 2, 1, 2, 1, 5, ...
The number of semigroups with n elements goes like this:
1, 1, 5, 24, 188, 1915, 28634, 1627672, 3684030417, 105978177936292, ...
Here I'm counting isomorphic guys as the same.
Is there any sort of algebraic gadget where the number of them with n elements goes like this?
1, 1, 2, 1, 1, 1, 1, 1, 1, ...
No!
Not if by "algebraic gadget" we mean a thing defined to have finitely many operations which are required to obey finitely many equational laws.
(Of course one can build other operations from the finitely many given, and also derive more equations from those given.)
Apparently this follows from a result of László Lovász in 1967:
https://mathoverflow.net/q/454146/2893
The sequence I showed you has a(2²) < a(2). But he seems to have showed that if a(n) is the number of algebraic gadgets with n elements, we must have
a(n²) ≥ a(n)
because if A and B are two gadgets with A² ≅ B², then A ≅ B.
I say "apparently" and "seems" because the one paper by him on this stuff is hard for me to read. But this result sure seems nice! Does it become obvious if you look at it the right way? Like, with some category theory?
"my timelines have shortened a lot" — beginner brag
"my timelines haven't changed since mid 2020" — intermediate brag
Trying to track & reportreality — advamced brag
"Liberating what we can" - 10% Bodhisattva vow
Fondly remembering about the time when I earnestly tried to use ed for all my editing
I was an odd teenager
@genmaicha same with intralersonal happiness: "you look happier than most! You must have been tortured in the past"
Although in a panpsychist universe I could see a conservation-law style regularity pop up
@Paradox
Or ghost professors
<expression of strong dislike for university software>
Just as paramilitaries are much cooler than regular militaries, paraacademics are much cooler than normal academics
Markets=Partition-adaptive Distributed Optimization
"we live in a takeoff world"
"there are no friends at foom"
A thing @Aella_Girl's cheating research made me curious about:
Are cheaters matched together? Or is cheating asymmetric: It's usually only one partner cheats (if so, I'd wager the more attractive one, but there might be interesting game-theoretic considerations).
Pet peeve: The words "World GDP"
Technology that got stuck in in adoption: Public key crypto
Used in the background everywhere, but not as end-user product, e.g. we still sign with our hands?
Perhaps because end-users aren't smart enough to understand public key crypto
Substances for meditation enhancement are a 2×2, {low substance, high substance}×{low meditation, high meditation}.
High substance has problems: Insights don't stick/are vacuous, + dangerous
High meditation has opportunity costs: Learning rate and energy parameter are too low
Low substance and low meditation are just less effective modulo relaxation effects
But where is the pareto frontier?
I am *not* convinced by the evidence for multiplicative decomposition in judgmental forecasting[1]
https://www.lesswrong.com/posts/YjZ8sJmkGJQhNcjHj/the-evidence-for-question-decomposition-is-weak
niplav
boosted
decontaminating my brain. by september, everything will feel like a beautiful breeze
niplav
boosted
Arbitrary X aren't Y can mean:
* All X aren't Y
* Almost all X arent Y (real numbers, computable)
* Many X aren't Y, some are, and the two groups are hard to disentangle (SAT problems, sovable in polynomial time)
* Few X aren't Y, but we haven't found a way to distinguish the ones who are from the ones who aren't, and can generate arbitrary X that aren't Y (violations of strategy-freeness in voting theory)
* Almost no X are Y, but same situation as above (don't know example)
- Website
- https://niplav.site/index.html
- Pronouns
- they/them
I operate by Crocker's rules[1].
Joined Aug 2021
