2025-12-02T01:37:16.329Z

huh, looks like it maybe tried to generate a shield and was a little off?
2025-12-02T18:31:01.670Z
weird Zig feature

2025-12-02T18:32:49.510Z
If the maximum bit width allowed is 65535, does that mean i0 is allowed?
Also, is i1 just a sign bit?
2025-12-02T19:48:21.525Z
you know, when I started on CubeStat's visual design I decided to center it around black and white to make it easy, but it turns out that just means I needed ten different grays (technically two of them are the same)
2025-12-02T20:18:39.737Z
weird, thanks Michaels

wait... is their search powered by AI?

2025-12-02T20:31:44.238Z
css position is something else man. both defines how the element is positioned relative to its parent and how its children are positioned relative to it. makes sense, great job guys
2025-12-03T05:55:28.469Z
someone should make a mod which adds the Minecraft marketplace to Java Edition
2025-12-03T17:17:42.432Z
just watched an interview with a basketball player who said "my mom breeds snakes, probably over a thousand snakes"
I think we found snakes georg how do you have over a thousand snakes
or maybe that's all-time and she got rid of most of those snakes?
2025-12-03T17:19:40.486Z
this was in response to a question that was something like "do you have any pets?" btw
2025-12-04T05:29:50.931Z
okay so neat discovery that I'm sure plenty of people have found before

that's the PDF and CDF of the Student t distribution
the hypergeometric function in the CDF is the mess I've been looking at this evening
but interestingly, it turns out that it can be fairly well approximated by the PDF of the t distribution!
2025-12-04T05:33:35.131Z
specifically, _2F_1(1/2, (v+1)/2; 3/2; -x^2/v) ~= f(x/(3*sqrt(v/(v+1))); 1/2), where f(x; v) is the PDF of the t distribution
figuring out the details of that approximation was a bit of a pain, and there's probably better approximations out there, but it's interesting nonetheless
2025-12-04T05:35:36.830Z
also, that approximation gets better as v gets larger. unfortunately, approximations for large v aren't that interesting because the t approaches the normal as v gets large
also, I know that's nu (ν), not v
2025-12-04T15:02:30.515Z
btw I realized last night that I misstated that relationship
2025-12-04T15:03:37.238Z
it's actually _2F_1(1/2, (v+1)/2; 3/2; -x^2/v) ~= (sqrt(pi*v)Gamma(v/2)/Gamma((v+1)/2))*f(x/(3*sqrt(v/(v+1))); 1/2)
2025-12-04T15:05:06.220Z
or more parsimoniously, _2F_1(1/2, (v+1)/2; 3/2; -x^2/v) ~= (1+(2x^2(2a+1)/18a))^(-3/4)
basically, you just need to strip out the normalization from the PDF
oh sorry ignore that stuff with the `a`s, should be:
_2F_1(1/2, (v+1)/2; 3/2; -x^2/v) ~= (1+(2x^2(v+1)/9v))^(-3/4)
2025-12-06T15:25:22.707Z
Services that advertise themselves in their own services are wild. Really just doing advertising for the love of the game huh
2025-12-07T20:28:37.015Z
translating something like 2000 lines of FORTRAN to JavaScript
this is definitely a good idea

I love GOTOs!
2025-12-07T21:00:47.880Z
okay
this might be a bad idea
2025-12-07T21:21:23.365Z
this (sub)project, man
every time I think I've found a simplification the complexity balloons right back up

2025-12-07T21:56:40.540Z
okay, I may have found a breakthrough
I just need to approximate this function, which looks... relatively easy? that should tell you something about how it's going

2025-12-08T01:52:01.445Z
okay, I finally found a decent approach (in section 6.2 of https://numerical.recipes/book.html)
2025-12-08T17:19:25.564Z
never-ending christmas playlist should just be like those 10 hour repeat videos

2025-12-08T17:35:55.232Z
JavaScript engines aren't required to support denormaized floats? this is not a serious language

2025-12-10T04:56:47.460Z
neat, didn't realize this was a thing https://superuser.com/questions/491180/how-do-i-embed-multiple-sizes-in-an-ico-file