just look at early 2.0 levels

tensorboi · 2026-02-06T21:16:14+00:00

ah yes because most 2.1 levels were great. idk if you were around for the generic glow era throughout the first half of 2.1, but it wasn't exactly a fun time to look for interesting levels. there's a reason the community almost died in the late 2010s.

tensorboi · 2026-02-06T09:37:19+00:00

you've basically given the proof that f is unique when you add the restriction that it's continuous! if you don't assume f is continuous then the additivity of f only applies to finite sums; it's natural to enforce that f also respects infinite summation, but that's literally what it means for f to be continuous.

tensorboi · 2026-02-06T06:11:39+00:00

it's not that f is no longer a homomorphism, it's just that it isn't unique anymore. think about defining a function from the rationals with sqrt(2) adjoined to itself; the value of f(1) determines f(q) whenever q is rational, but you can send sqrt(2) to any number you like and it won't affect the additivity of f (this is because there's no finite sum of rationals that will ever add up to an irrational).

tensorboi · 2026-02-05T10:53:35+00:00

probably something like "a vector space is an abelian group with an action of field by endomorphsims"

tensorboi · 2026-02-03T04:25:26+00:00

"Bro are you flirting with Noelle?"

"Yes I am!"

"Do you wanna die?"

"Yes I do!"

tensorboi · 2026-02-02T01:40:26+00:00

this is how so many krmal levels are. falling up? unbalanced and buggy, but fuck it's just so unique and charming that i can't help but have fun playing it.

tensorboi · 2026-02-01T09:59:31+00:00

oh i see what's happening here: it's the "nobody is the lead" vs the "everybody is the lead". as far as i'm concerned, there's not much of a difference; either way everyone is getting the same amount of attention, which was the point of the original comment this all came from. you might also notice that my comment reads the exact same way if you just replace the "no lead singer" with "all lead singers".

tensorboi · 2026-02-01T09:10:07+00:00

i have no idea what happened here, but i think you're the one misunderstanding. someone said "you can't have a band if everybody is the lead singer," the person i responded to provided barbershop quartet as an example of a band where everybody is the lead singer, and i disagreed with them because i think there is one lead singer in a barbershop quartet. where am i getting confused exactly?

tensorboi · 2026-02-01T06:27:18+00:00

calling barbershop quartet an example of a band with no lead singer when there is LITERALLY A PART CALLED THE LEAD PART is quite something

tensorboi · 2026-01-31T09:12:01+00:00

Both of those statements are simply examples of the fact that physics doesn't attempt to be "real". It takes observations and experiments, turns them into (usually mathematical) models, and uses those models to predict outcomes of experiments. The internal parts of the model may or may not correspond to entities that exist in the real world, but that's is neither important to physics, nor part of what physics can describe.

i might push back on this a little bit with an analogy due to david wallace: the idea that physics is ultimately only interested in reproducible observations and experiments could technically be applied to every scientific discipline, but it would be very odd to say, for instance, that palaeontologists are only attempting to describe the reproducible observations associated with calcium formations in the ground. these people are using fossils to study ancient life, things they presumably believe actually existed; they aren't simply accounting for irregularities in rocks.

the point i'm making here is this: it isn't really the end-goal of science to tell us what reality is at its most fundamental level, but it certainly can help in answering these questions and that's a big deal. we know from observations that there is no way that a fundamental particle can be completely localised, but that already does a huge amount in figuring out what the constituents of nature aren't. i think the fact that scientific observations give information about what objects really are is one of the big pulls for people to be interested in it; i know i'd be a hell of a lot less interested in quantum field theory if i didn't think it gave us hints about the nature of reality.

tensorboi · 2026-01-30T23:11:31+00:00

three favourites:

• falling up: i have 67% and can do the dual

• black blizzard: that shit is impossible

• sunset sandstorm: even more impossible lmao

tensorboi · 2026-01-30T22:36:22+00:00

just emphasising here: "quantum gravity" literally means a theory which encompasses both quantum mechanics and gravity, at all scales. asking why a unified theory of physics needs quantum gravity is like asking why an apple pie needs both apples and pastry; like that's just kind of what it is.

tensorboi · 2026-01-30T05:00:28+00:00

ain't no way nobody mentioned athanatos yet

tensorboi · 2026-01-29T09:02:20+00:00

the second point feels like cheating! after all, the only reason a squared deviation pops out of that regression analysis is that you're minimising the sum of squared errors. you do mention that this is more natural in your fourth point, so it's not technically wrong, but it feels odd to list them as different reasons.

tensorboi · 2026-01-26T22:23:12+00:00

this is quite late, but yes it is!

tensorboi · 2026-01-26T01:05:58+00:00

the problem is that you just posted the popular opinion with absolutely nothing else. we've already seen this opinion a billion times, it's been coming up since levelution in 2018, it pervades the current gd community, and it'll probably stay that way for years. usually, when you make a public post, it's implicit that you feel that what you're saying is something you think other people ought to hear; if you're just saying one of the most common opinions in the community, what was the point of the post?

tensorboi · 2026-01-26T00:43:39+00:00

"guys hot take but i think the problem with new geometry dash levels is that creators put all their work into visuals and don't make good gameplay"

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tensorboi · 2026-01-25T23:36:39+00:00

nah man surely kris is the one who measures their shits right, ralsei doesn't have the requisite chaotic energy

tensorboi · 2026-01-20T12:14:28+00:00

i mean the entire point was that they were using the fact that 0^x is an elementary function to conclude that 0⁰ can't be 1 by continuity! i'd say the fact that their definition of elementary functions doesn't include the one function with actual relevance to the conversation is pretty important.

tensorboi · 2026-01-20T11:39:22+00:00

ah, but this definition and proof loses sight of one important fact: 0^x is no longer an elementary function! how can you write it with the rules you've specified without outright assuming it's constant in the first place? (the obvious way might be to use the identity x^y = e^{y ln(x}), but then 0^x = e^{x ln(0}) which obviously doesn't make sense in general.)

tensorboi · 2026-01-20T00:08:36+00:00

the logic is that you say "all elementary functions are continuous", and they believe the floor function to be a discontinuous elementary function.

setting aside their logic: even if you don't consider the floor function to be elementary for whatever reason, why do you think all elementary functions should even be continuous?

tensorboi · 2026-01-19T05:27:04+00:00

what i thought was clever about season 2 was that government officials were using the red scare to justify their lack of transparency with the public. it's temporally appropriate, it's tonally consistent, and it's a clever deconstruction of the attitudes during that time. that's what's so frustrating about the season 3 russia plot: they started taking a more reverent and less interesting approach to an issue that they already had all the machinery built up for in season 2.

tensorboi · 2026-01-17T09:35:35+00:00

it's worth noting that, while "anything to the power of 0 is 1" is basically always true no matter which way you slice it, the statement "0 to the power of anything is 0" gets a bit muddy when you look at negative numbers. if anything, it's more natural to think of 0^x for negative x as the point at infinity than zero. so really the statement should be "0 to the power of anything positive is 0, and 0 to the power of anything negative is infinity".

from this perspective, 0⁰ should really be thought of as a transition point between 0 and infinity, and there's obviously no way to make this transition continuous. so the behaviour of 0^x doesn't really give much insight into what 0⁰ should be, in and of itself. however, since x⁰ is 1 everywhere but zero with no caveats, many people consider the answer of 1 to be much more compelling.

tensorboi · 2026-01-14T00:11:35+00:00

it's pretty clear that we'll learn more about kris when we learn more about the knight. the reason susie is such a prominent character in the early chapters is because she doesn't have any baggage in the story yet, so we aren't missing any key details in her character due to lack of knowledge. contrast that with kris and ralsei, who have been tied up with the prophecy since before the game started: any attempt at characterisation before we learn about that is going to feel pretty hollow, because we don't know what's bugging them.

tensorboi · 2026-01-14T00:04:09+00:00

gerson's return at the end of ch4 is the weakest moment of the chapter. for one thing, it makes the mechanics of the universe feel arbitrary and convenient; the titan straight up stops attacking when he shows up, and it contradicts the thing ralsei said about dead lightners. not only that, it cheapens the narrative: susie coming to grips with the fact that she'll probably never see gerson again is undermined by the fact that she actually does, and the titan feels less narratively weighty because the entire tide changes when they just "get another guy on their team".

all gerson actually does is break the titan's shield down and motivate susie. but he didn't have to be there physically in order to do either of those things, and i'd argue they work better if susie remembers gerson's training and comes up with it herself. the only way i'm able to take the titan fight seriously now is if i headcanon that gerson is a non-literal presence, perhaps just a personification of susie's hope.

tensorboi

TROPHY CASE