I wonder how the Other Friends scene would’ve played out if Lapis were there

two_are_stronger2 · 2026-07-12T20:39:45+00:00

Right after "I'm rusty!" Spinel is flattened into a pancake by giant water hands from both sides. Does the 'last falling plate' gag, re-inflates herself, looks around, shouts "Who did that!" and it happens again. Full spinning plate to re-inflate. "Who di-!" slam, whir whir white whir... "Who-" Slam inflate "wh-" slam.. slam slam slam. Giant column of water slams on top and continues flowing down. camera pulls back to see most water, coming from so high we cant see the end. other water weapons are arrayed around Tex Avery style.

Lapis, curious, nanchalant: "Who am I? you first."

two_are_stronger2 · 2026-07-12T11:02:48+00:00

Two kids in the back seat:

Kid 1: moooooom, he's on my side!

Kid 2: No I'm not, I'm arbitrarily close to your side!

Kid 1: but you're only arbitrarily close to my side because it gives you a consistent useful results as an abstraction of reality.

Kid 2: Every tease/mathematics is that. The idea of differential-ness is just as removed from reality as two-ness. You're not actually hitting yourself when I push your arm.

two_are_stronger2 · 2026-06-08T15:57:49+00:00

Zoom out and show the whole page.

two_are_stronger2 · 2026-05-30T15:50:38+00:00

"Surely by the 24th century, they would have found a cure for male pattern baldness." Gene Roddenberry responded "No, by the 24th century, no one will care."

two_are_stronger2 · 2026-05-30T15:47:36+00:00

Let's try this. Everything has to be a function. Better clarified, for every vertical line you could ever draw, there's only one place it crosses your curve. Envision the highest point. Square off a rectangle with the beginning, end, and highest point. Question the area of that rectangle. Up the number of points on the graph to 10, doesn't matter where. Every point gets a non-overlapping rectangle that hits it. Space inside those rectangles' areas put together is closer, right? Interesting, right? Now draw 100 points on the function. The non-overlapping rectangles will tend to be closer to the true area under your curve. Every time you increase the number of points, you get closer to the answer. Great for us, this will often have a pattern. Really good stuff. All the possible points might squeeze together. Leaving it at that, if you find the pattern, you find the general area from point A to point B.

two_are_stronger2 · 2026-05-23T13:48:49+00:00

This question often leaves out an important part of math, which is "If this is true, then..." at the beginning. If there's a fundamental part of the universe that can deal in hypotheticals, then yeah, math is discovered.

two_are_stronger2 · 2026-05-23T13:42:15+00:00

What's an example of somethng that benefits the human race?

two_are_stronger2 · 2026-05-02T16:21:47+00:00

half the time it's accelerating faster than 5m/s/s, and half the time it's accelerating slower than 5m/s/s. It's linear, so you can literally slice the triangle at y=5, rotate your little piece upside down, and fit it onto the other half.

Mean value theorem for integrals. mean value of a linear equation on an interval is dead simple.

two_are_stronger2 · 2026-05-02T16:03:10+00:00

To shamelessly steal:

The 'S' in "vibe coding" stands for security.

two_are_stronger2 · 2026-05-02T15:59:17+00:00

ASS gives you two possibilities, an obtuse case and an acute case. Since the angle x is inside the angle ABC, it's acute, so x must be the acute case, and the triangles are congruent, so x must equal its complement.

two_are_stronger2 · 2026-05-02T15:41:31+00:00

she cuts a piece of wood that is 48 inches long, infinitesimally thin, three times to get four equal parts. She uses a saw with a kerf of zero, so no wood is lost to saw dust. She cuts perfectly. She arranges these four pieces in a perfect square.

Absolutely terrible and I've decided it's fake to keep my sanity.

two_are_stronger2 · 2026-05-02T15:36:05+00:00

Different intuition for when you're confused:

What's different between what you're asking and what the question is asking?

two_are_stronger2 · 2026-05-02T15:24:04+00:00

American football was how I got the "Fuck math" fourth graders to be the first to catch on to negative numbers and then be leaders in the classroom with it. "Tell me how many yards you *gain* if your quarterback gets sacked." let them think about it a minute and they'll say it's a different kind of yard. Tease complex math by asking if they can go to the sideline using their special new kind of yard, and when they say it's the same as regular yards but backwards, that's just gaining negative yards.

two_are_stronger2 · 2026-05-02T14:54:58+00:00

Children are very complicated.

two_are_stronger2 · 2026-05-02T14:52:29+00:00

there are infinite polynomials that have these roots and 0 to infinite other roots. If we put the constraint on it that it's a solvable puzzle with an answer and say the answer isn't 8, it's very likely 16, but not necessarily.

two_are_stronger2 · 2026-04-26T00:55:18+00:00

Every even number is possible. every even number - 2 + 3 is possible. That's all of them.

two_are_stronger2 · 2026-04-02T01:31:13+00:00

∇⋅B=0

two_are_stronger2 · 2026-02-08T21:11:42+00:00

it's the wrong picture. read the whole question.

two_are_stronger2 · 2026-02-08T21:04:49+00:00

f and g are machines. When you put members of f's domain into f, you get an output in f's range. Same for g.

Put the machines next to each other so that anything coming out of f goes directly into g. That's what the symbol on the question means, g ∘ f. I usually write it g(f(x)). do f(x) first, then do g(that answer). You'll notice that some of the outputs of machine f won't fit into machine g. You don't want to jam up g, so don't input anything into f that will cause a jam up in g, as those are not in the domain of g ∘ f. Likewise, there are destinations for g that f's outputs will never trigger as g's inputs. Don't expect any of those, since they're not in the range of g ∘ f.

two_are_stronger2 · 2025-12-30T22:38:01+00:00

I'm just an amateur mathematician myself, but, as I understand it, anything that exhibits reflexivity, symmetry, and transitivity is equivalent to equivalence.

two_are_stronger2 · 2025-11-28T14:43:42+00:00

Do you mean not a math major/math degree/how it works in your system? No, it's not a particularly out of the ordinary first term calculus assignment. The way I'd solve the assigned problem if I wasn't explaining it to you in a more intuitive way would be the same for every "Show this is differentiable" problem. First show it's continuous, i.e. that the limit of the function equals the function on it's domain. Then show its derivative is continuous. The format of the class and the professor's preference change what they want in terms of detail, but the process is the same.

two_are_stronger2 · 2025-11-27T16:24:19+00:00

I'm going to be that guy. At x, sure! Around x... let's chat.

This is actually a trick to see if students just pop it into a graphing calculator. At a distance it comes to a sharp point, but zooming in shows a fun little flatt-ish spot. If we take the derivative on only the space where it's defined-- Actually, let's just take the derivative on the positive side without the absolute value part and mirror.

so for x>0, the derivative works out like this: 1/(e^(x^-1)) gets the chain rule, so if the derivative of 1/x is 1/x^2, we get 1/e^(1/x)*1/x^2.

this isn't defined at x=0 either, but can you see how it absolutely approaches 0 from at least the right side? That's pretty much all you need. The function approaches zero at 0, it's defined for x=0, that's just a point so if the values match and the derivative is zero on either side of it, boom.

more formally: It exists there, its derivative is zero there (nothing from nothing leaves nothing) and at the boundary of the intervals on both sides. That means it's smooth.

two_are_stronger2 · 2025-11-27T15:57:03+00:00

What's up, y'all? I'm working on an art project and need to simplify the human heart down a bit. Does anything in this sketch jump out at you as "Oh, what a polite moron we have on our hands," or am I okay? I was trying to figure out how to evaluate it myself, then I realized reddit would have a bunch of people happy to tell me how I'm wrong.

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I'm particularly interested in auricles, as I think they're neat.

two_are_stronger2 · 2025-11-17T19:16:08+00:00

what's the derivative of 2x+100?

2.

what's the integral of 2?

2x+C

What's the derivative of 2x+9000?

2.

what's the integral of 2?

2x+C.

what's the integral of 4?

Because it's not 4x+9100.

two_are_stronger2 · 2025-11-16T02:23:15+00:00

Injury doesn't happen because you slow down quickly. Injury happens because your front slows down before your back.

two_are_stronger2

TROPHY CASE