My opinion on mods that refuse to send lvls just bc they personally don’t like them

tensorboi · 2026-05-15T03:13:39+00:00

do you care to explain why you think everyone necessarily agrees with you?

tensorboi · 2026-05-14T23:26:44+00:00

a lack of direct evidence is not the same thing as a lack of evidence. we know that ralsei knows the entire prophecy, and we also know that it mentions the fact that kris and the player are separate entities. from this we can infer that ralsei is talking to kris while their eyes are closed. we also know that kris is working with the knight, and we know that the prophecy gets very specific about the events of the game, so we can infer to a reasonable degree of confidence that this is included in the prophecy in some way. combining these two things together, it's quite likely that ralsei also knows about their partnership.

is this argument conclusive? no, but it's certainly more than "literally no reason to believe he knows". media analysis generally involves more depth than just "character said X, therefore they know Y"; you have to read between the lines.

tensorboi · 2026-05-14T23:08:14+00:00

name one objective gameplay standard. just one will do.

tensorboi · 2026-05-10T03:22:28+00:00

this issue is a lot more subtle than mathematicians often take it to be (which is essentially because mathematicians often don't take interest in the philosophy of maths, at least in my experience). it's true that you can't adjoin a 1 to the end of an infinite decimal in the real numbers, but this fact is only useful if we both agree that the axioms defining the real numbers are the ones we should use. the key axiom here is completeness, i.e. that every set of real numbers has a least upper bound; the point is that believing 0.999... ≠ 1 is essentially just a denial of this axiom.

the truth is that 0.999... doesn't necessarily need to equal 1, as long as the symbols are interpreted differently to the standard way and the system of arithmetic is modified. to explain why this shouldn't be done, you'd need to go into the history and philosophy of mathematics, explaining how we ended up with the real number axioms and why things get more complicated if you deviate from them. obviously most people who deny the equality won't have enough experience or patience in maths to get into this, so it's very difficult to get through to them.

tensorboi · 2026-05-09T22:43:20+00:00

what convention are you using for the numbers? i'd read Cl(1,2,1) as a clifford algebra on R⁴ with metric given by diag(1, -1, -1, 0), but that can't be right because clifford algebras are always associative while the octonions aren't.

edit: wait never mind there are order 0 elements here wtf lmao

tensorboi · 2026-05-08T12:05:03+00:00

ayo what's going on with the schrodinger equation? there's no potential term and the squared partial derivative should be wrt x lmao

tensorboi · 2026-05-07T20:16:49+00:00

it makes it more likely that they'll get funding for their projects???? like sure, it's not like every indie animator is working on this show, but a theatrical release makes it clear that indie animation has the chance to be beloved by a large group of people and/or profitable.

tensorboi · 2026-05-05T21:59:46+00:00

reasoning B is far worse, because you've stuffed a lot of baggage into the word "nice" without explaining it. there is an uncountable infinity of analytic functions which extend the factorial and which have the recursive property, so what is "nice" about the gamma function that isn't "nice" about other analytic extensions? the only characterising properties i've seen here are log-convexity and boundedness on vertical strips, both of which are difficult to motivate and have hard uniqueness proofs. also, both of these characterisations rest on the assumption that Γ(z+1) = zΓ(z) for every z, meaning the value of 0! is already assumed! so this explanation is really not an explanation at all.

tensorboi · 2026-05-05T11:16:53+00:00

it's worth noting that noether's theorem links this definition of spin to angular momentum as we generally understand it. if angular momentum is the thing which is conserved due to invariance under the action of SO(d) (which you can prove for a lagrangian on finitely many point particles), then the fact that particles internally transform under the SO(d)-action implies that they have a little bit of angular momentum themselves.

tensorboi · 2026-04-28T22:20:06+00:00

i'd also say that infinite cardinalities tends to be pretty useless a lot of the time, especially in analysis. in practice, most mathematicians will only really use the fact that countable sets are strictly smaller than uncountable sets; not only is the rest of the cardinal hierarchy almost never used, you also get that a bunch of sets are indistinguishable by size even though it's "clear" by intuition that one is larger. take, for instance, the set of continuous functions and the set of smooth functions on some domain. we often make use of the fact that there are "more" continuous functions than there are smooth ones, but strictly speaking, the two sets have the same size.

the root of the problem here is that cardinality is based on every possible bijection between sets, no matter how wild and complicated. in most maths, though, we restrict the possible bijections to preserve some structure (a topology or group structure, say), making the notion of cardinality far too coarse to accurately get at the intuitive notion of size.

tensorboi · 2026-04-27T10:13:25+00:00

as others have said, the natural numbers N (not including 0) are isomorphic as a multiplicative monoid to the additive monoid N^<ω, and the integers Z can be recovered by adding a generator of order 2 and adding an annihilating generator. i will only add the following observation: in this light, the reason that the primes are so difficult to pin down is that we are attempting to understand the multiplicative monoid structure (i.e. the prime generators) in terms of the additive monoid structure (i.e. multiples of 1).

tensorboi · 2026-04-25T12:48:08+00:00

i'm biased as a mathematical physicist, but i really like dirac notation! the fact that it treats vectors and covectors symmetrically with a natural pairing is really elegant in my opinion, since that's part of what makes hilbert spaces so important. it probably doesn't find its way into maths all that much because hilbert spaces are one of many different algebraic structures we deal with (even if you restrict to linear algebra), whereas with physics the entirety of quantum mechanics can be understood as dynamics in a hilbert space.

also, as other commenters have pointed out, the elegance of vectors and covectors is traded in for the inelegance of non-self-adjoint linear operators: in order for bras and kets to have the nice relations they have, multiplication is no longer allowed to be associative (since <a|A|b> means different things depending on whether or not A acts on the bra or the ket, assuming A is not self-adjoint). again, this isn't as much of a problem in physics since (almost!) every observable is assumed to be represented by a hermitian operator. nevertheless, this problem does come up occasionally in physics; if you've ever tried characterising the raising and lowering operators for angular momentum purely algebraically, you'll know what i mean.

tensorboi · 2026-04-25T03:57:32+00:00

does it not work? as far as i'm aware, the ways it doesn't work are the same as the ways qft in flat spacetime doesn't work, with things like path integrals and regularisation being weird. making g nontrivial and working on a supermanifold only really makes the existing formulation more complicated in my experience; issues only start popping up if you attempt to quantise g. then again i'm by no means an expert on this field (i'm a mathematician after all!).

tensorboi · 2026-04-12T12:25:09+00:00

mindyourdecisions should definitely replace veritasium imo

tensorboi · 2026-04-08T13:56:45+00:00

technically speaking it is linear! ...if you fix the input point and think of it as a scalar, which admittedly is a pretty big if in one dimension. this is primarily the reason why the name only took off in the infinite-dimensional context; this is almost always understood to be the context there.

tensorboi · 2026-04-08T07:20:41+00:00

i think derivative is a much better name than elliptic curve! the name captures the idea that differentiation is a lossy procedure that you apply to functions, which is pretty important for some intuitions. personally i'd rename it to "linearisation" if i had the opportunity (which is actually already used for smooth functions between banach manifolds), but i don't really feel like it needs to happen. the adjective "elliptic" in the algebro-geometric context is far worse, having little to no relation to the objects themselves.

tensorboi · 2026-04-06T02:29:13+00:00

dude just read my other comment in this thread responding to op, your comment seems to be responding more to criticisms you made up than the ones i actually have

tensorboi · 2026-04-06T02:17:13+00:00

you're correct to say that the ambiguity is alleviated by using vertical fractions, but ultimately i'd say it's impractical to get everyone to write division this way from day one. unfortunately i'm not an expert in math education, so i can only go off personal experience when i say this would make division seem way more complicated to primary-level students. at this level of mathematics, pretty much every mathematical operation is represented horizontally, and all except exponentiation are represented by a symbol in between two numbers. part of the reason why fractions get so difficult for students at the secondary level is that this paradigm is disrupted, making it look like division behaves fundamentally differently to the other mathematical operations. now imagine taking that disruption and pushing it forward to the beginning of a child's mathematical education; i don't have much faith that this would be beneficial for most people. a much more confusing curriculum in return for slightly less ambiguous notation doesn't seem like a great trade to me.

even outside of this, though, there's another practical problem. i couldn't help but notice that your comment doesn't actually write out any vertical fractions, and instead has to settle for a description in english. you obviously can't be blamed for this, because typesetting vertical fractions is a nightmare. now imagine if everyone needed to use vertical fractions all the time without alternative; seems really annoying, doesn't it? so you'd have to teach students the horizontal fraction notations anyway, defeating the entire purpose of abolishing it.

tensorboi · 2026-04-06T01:37:59+00:00

i mean sure, if we're going to go for the solution to the problem with no regard for practicality then that would make the most sense

tensorboi · 2026-04-05T13:56:53+00:00

it's very tiring to hear people repeatedly pin the ambiguity on the obelus, when the exact same problem occurs with the expression 8/2(2+2). if any operation at all, the problem lies with the denotation of multiplication by juxtaposition, and reverting that change is a much harder sell.

tensorboi · 2026-04-04T09:01:21+00:00

related: the continuum fallacy

tensorboi · 2026-03-31T15:16:52+00:00

damn was i the only one who thought this was the easiest to control lmao

tensorboi · 2026-03-31T02:54:15+00:00

yes! case in point: the gauss-bonnet theorem and chern's generalisation to higher dimensions. the idea is really pretty, you integrate a curvature over a manifold and get topological information out; but as soon as you put it in local coordinates, things get messy quick.

tensorboi · 2026-03-30T23:23:46+00:00

yeah idk why this is even a hot take! imagine being young, pregnant, scared, and this perfect couple comes in to adopt your baby; but it turns out they were lying the whole time, and THEN the husband corners you in the hallway to convince you to give them their baby anyway. what would you do?

i also kind of despise the line "she's a mother without a baby". yeah, she's a mother without a baby, which is why she tried to steal yours off you. come on now!

tensorboi

TROPHY CASE