same tbh

maybe it’s being developed in the arctic circle and there really are only four nights per year

where’s the creamy filling

it was over as soon they casted kevin hart

personally i’m a fan of tearing off everything except a small corner of a napkin

go for it

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

a consequence of the axiom of choice is that every set can be given a well ordering. and well orderings always have smallest elements, but they may not have largest elements.

so there is someone who is the least gay, but there may not be a single person who is the most gay.

it is possible to rigorously say that 1/0 = ∞. this is commonly occurs in complex analysis when you look at things as being defined on the Riemann sphere instead of the complex plane. thinking of things as taking place on a sphere also helps to avoid the “positive”/“negative” problem: as |x| shrinks, 1 / |x| increases, so you eventually reach the top of the sphere, which is the point at infinity.

being a prompt engineer is so much more than typing words. you also have to sometimes delete the words and then type new ones

i think this is a fairly reasonable gut reaction to first hearing about the “unnatural” numbers, especially considering the ways they’re (typically) presented at first. it seems like kids tend to be introduced to the negative numbers by people saying things like “hey we can talk about numbers that are less 0, heres how you do arithmetic on them, be sure to remember all these rules”. and when presented like that, it just seems like a bunch of new arbitrary rules that need to be memorized, for seemingly no reason.

i think there would be a lot less resistance if it was explained in a more narrative way that explained why the new numbers are useful and worth learning about. e.g.,

• negative numbers were invented to make it possible to subtract any two whole numbers (so that it’s possible to consistently undo addition).
• rational numbers were invented to make it possible to divide any two whole numbers (so that it’s possible to consistently undo multiplication, with 0 being a weird edge-case).
• real numbers were invented to facilitate handling geometrical problems (hypotenuse of a triangle, and π for dealing with circles), and to facilitate the study of calculus (i.e. so that you can take supremums, limits, etc)
• complex numbers were invented to make it possible to consistently solve polynomial equations (fundamental theorem of algebra), and to better handle rotations in 2d space (stuff like Euler’s formula)

i think the approach above makes the addition of these new types of numbers seem a lot more reasonable, because it justifies the creation of all the various types of numbers by basically saying “there weren’t enough numbers in the last number system we were using, and that made it a lot harder to do certain things”

it’s mathematically provable that the shortest path between any two points on a sphere will be given by a so-called “great circle”. (a great circle is basically something like the equator: one of the biggest (greatest) circles that you can draw on the surface of a sphere.) i think this is pretty unintuitive, especially because this sort of non-euclidean geometry doesn’t really come up very frequently in day to day life. but one way to think about this that on the sphere, “great circles” are the analogues of straight lines, although you’d need a bit more mathematical machinery to make that more precise.

although in practice, some airlines might choose flight paths that aren’t great circles because of various real world factors, like wind patterns and temperature changes, etc.

most horrifying thing is the bathroom being at the top of a flight of (carpeted) stairs

that kind of sentence structure always trips me up. we should start using parentheses for situations like this. or invent a new symbol, or something. we give commas too many jobs.

its so tiresome to have all these services constantly made worse. these days it feels whenever a new thing comes out, it has about two or three years before it’s run into the ground in pursuit of the almighty dollar.

and this kind of thing is also happening to movies/tv shows/video game franchises. it feels like no matter how good it starts, you only get (at most) 2 or 3 sequels before the executives get their hands on it and run it into the ground. sure there are exceptions to this, but they are few and far between. and its becoming even more common for shows/video games to simply disappear if the parent company decides to remove them from online stores/streaming platforms.

all around, it just feels like things are becoming less and less permanent

this is what i do when im feeling mischievous and want to annoy my family in the morning

they’re probably assuming it will be like every skyrim update released in the past 10 years, which is a fair assumption.

and this update has also caused the widely anticipated fallout london project being indefinitely postponed. in the article linked, you can see the fallout london project lead saying:

“But with the new update dropping just 48 hours [after Fallout London’s original release date], the past four years of our work stand to just simply break.”

i don’t really see what good it does to say “nobody can know that at this time”, when people have every reason to think that it will break their mods. i mean sure, nobody knows the future, but you can say that about literally every single prediction made about anything in the future. it’s a tautology. are you trying to imply people shouldn’t make predictions about anything?

yeah it has. it’s a photoshopped picture of todd howard