i bet you i could predict it with 100% accuracy if you give me another 4 months
i feel the same way but i make an exception for the live album “stop making sense” by the talking heads. specifically the songs “crosseyed and painless” and “once in a lifetime” sound so much more energetic on the live album. depending on my mood, i sometimes pick the live versions over the studio recordings. they feel like different songs to me
if they use an LLM to make the suggestions then it’s possible it ends up suggesting websites that don’t even exist. or it could accidentally suggest a malware website, or make a typo, etc.
this could be dangerous if they aren’t very careful
maybe it’s being developed in the arctic circle and there really are only four nights per year
Anyone can pay $150 to become a dues-paying member and rub elbows with the court’s nine justices at events like the dinner where Windsor spoke with Alito. (Tickets for the dinner were an extra $500.)
this is all it took for him to admit this stuff? anybody with 650$ could have walked in and asked him a couple prodding questions? these guys really arent even trying to hide it anymore
and they’re always whispering all the time too. it drives me crazy. nobody whispers that much in real life. it doesn’t make people sound more mysterious
personally i'm a fan of tearing off everything except a small corner of a napkin
applied mathematics can get very messy: it requires performing a bunch of computations, optimizing the crap out of things, and solving tons of equations. you have to deal with actual numbers (the horror), and you have to worry about rounding errors and stuff like that.
whereas in theoretical math, it's just playing. you don't need to find "exact solutions", you just need to show that one exists. or you can show a solution doesn't exist. sometimes you can even prove that it's impossible to know if a solution exists, and that's fine too. theoretical math is focused more on stuff like "what if we could formalize the concept of infinity plus one?", or "how can we sidestep Russel's paradox?", or "can we turn a sphere inside out?", or The Hairy Ball Theorem, or The Ham Sandwich Theorem, or The Snake Lemma.
if you want to read more about what pure math is like, i strongly recommend reading A Mathematician's Lament by Paul Lockhart. it is extremely readable (no math background required), and i thought it was pretty entertaining too.
you could think about it this way: one sphere and two spheres have the same “number” of points. (in the same way that there are just as many real numbers as there are real numbers in the interval (0,1).)
so, it becomes “”plausible”” that you could use one sphere to construct two spheres (because in some sense, you aren’t “adding any new points”).
but in the real world, “spheres” only have a finite number of atoms. so if we regard atoms as “points”, then it’s no longer true that one sphere and two spheres have the same number of “points”. and in some sense, this is why the sphere duplication trick doesn’t work in the real world.
it’s also worth mentioning that you have to do some pretty fucked up and unusual things in order to actually duplicate the sphere, and if you don’t allow such weird things to be done to the sphere, then it’s no longer possible to duplicate it, even with the axiom of choice.
yeah this is true. i should have clarified a bit better that a well ordering wouldn’t give you a “least gay” person in that sense of the word. it would be more correct to say there is a well ordering ⊰, and so there is a “⊰”-least gay person. but of course a “⊰”-least gay person could be in the middle of that spectrum.
but the number of people on earth is finite, so in fact the usual ordering is a well-ordering in this case. so i guess those two mistakes i made cancel each other out, and the axiom of choice isn’t even needed here.
oops. you’re completely right. i forgot there are only a finite number of people on earth. there is a gayest person