then-ponder

[then-ponder]

Topology Intuition Request

Let M be a closed orientable 3-manifold, S a compact surface, and f : S -> M a generic immersion. Then f(S) has self-intersections which are circles or arcs.

Let C be a circle of self-intersection in f(S), and suppose that the preimage of C is two circles. Let T be a small nbh of C in M, so that T is a solid torus. Let B1, B2 be nbhs of the preimage circles, which are either annuli or Möbius bands, such that f(B1), f(B2) are properly embedded in T. We should be able to choose T small enough that f(B1) and f(B2) are disjoint away from C. So in particular, the boundaries of f(B1) and f(B2) in the torus boundary of T are disjoint! So either both B1 and B2 are annuli or both are Möbius bands.

This seems wrong to me? Why can't a generic immersion make a non-orientable circle and an orientable circle have the same image? I think I'm convinced by the argument above, so I guess the result it true but. I have no intuition for why, from the surface's perspective.

Any clean intuition or visualisations would be appreciated!

[then-ponder]

[then-ponder]

What is the center and radius of the circle indicated by the equation?

(x−2)2+y2=36

-Cousin Throkmorton Anon

[then-ponder]

I have read about the axiom of choice paradox several times and every time I see someone talking about it I feel like I actually don’t know what it is at all. Because like, It doesn’t bother me? Like, maybe I just need to encounter it In the wild or just plainly understand it, but it doesn’t feel bad to me.

the saddest thing about finally learning algebraic geometry is the realisation that everything there is infected by the axiom of choice. in undergrad it felt confined to fringe counterintuitive results about duplicating spheres but now i find myself using facts like "every non-unit of a ring is contained in some maximal ideal" all the time to prove very general things about schemes :(

[then-ponder]

This is the older sibling the equally valid disproof by “that should’ve worked”

Proof by you'd really think so wouldn't you?

[then-ponder]

The regular couple is not infact a term for the cishets. It’s actually referring to the “+” in lgbtia+. Regular couple is actually a term that describes any two mathematicians [regular shapes], but it more broadly describes any couple of humans, n > 1, n ∈ ℝ, who are all bound together relationship wise.

In each group every subset of cardinality 2 must have a relationship vector. For a couple to be regular all vectors must be non-negative and the vector product must have a non-zero volume and have a nonzero real component.

I never got to post this here, but happy pride <33

[then-ponder]

There is a joke in calc II that goes something like. If you don’t understand the question guess pi.

[then-ponder]

After a hard day of doing math I can barely understand, I like to treat myself to a little time with a math book I understand even less

[then-ponder]

I don’t have the time to make it rigorous. But the universal set will make your explanation easier but not trivial. Basically a universal set is a set that superset of all the sets you’re working with. So for instance the universal set here would be men and it would contain two groups cis men and trans men(this is technically a special case) and the sum of them you get the universal set. The mistake that a lot of people mistake is that the set of all men’s experiences is not equal to the set of all cis men’s experiences or trans men’s experiences even though they are subsets of men’s experiences.

I want to make some sort of post about the fallacy that is "x and y are both subgroups of group z therefore x and y are the same and to say they aren't is to deny their belonging to group z" but I don't really know how to word it

people love doing this in regards to trans people

"trans men and cis men are both subgroups of the group men therefore they have the exact same struggles and rights" yeah, and cats and dogs are the same thing because they're both mammals, and if you imply they aren't you're being a bigot and saying dogs aren't real mammals

I wish people realized how this fallacy is getting them and how it is not in any way bad to admit that trans people are in fact, generally, intersectionality non withstanding, suffering much more than cis people

as with any other fallacy though, most people *do* get that it's wrong, just that online there's some very loud very wrong people who would rather not learn from their own mistakes

[then-ponder]

I have an instinctual & perhaps unfair dislike of "solarpunk" art. part of it is just a taste thing, that I can't really imagine becoming invested in a world where nothing bad happens. part of it is that it is based in stated progressive values while so often regressing back into head empty pastoralism, what if everything was a cozy farm, what if everything was automated except for the stay at home mom, etc. my knee-jerk reaction has probably led to me having a kind of narrow view of the aesthetic, though.

[then-ponder]

You’re giving them too much credit. They don’t know what any of this means. And they don’t care. They just want it to look like something that makes them look smart and that no one will investigate.

trying to figure out how they made up tariff rates

The official derivation on the gov website starts with

'"Let ε<0 ..."

which ofc triggered my calculus fight or flight instinct

but a negative elasticity would mean people import more if it gets MORE expensive, right?

that shit makes no sense to me, am I too stupid or not stupid enough?

[then-ponder]

buds, this is the wrong article to put under an email gate.

[then-ponder]

What’s the difference between a curved line and a straight line?

I love seeing a meme and being like oh, tumblrs going to love this one

[then-ponder]

in twisty puzzles, a "2x2" version of a solid is either

the normal version, but with only corner pieces

the degenerative case of having the face cuts meet in the middle of the puzzle, erasing the middle layer and leaving only the two layers on either side

With a cube, these are the same thing, but this isn't the case with other solids. The accepted version of the 2x2 megaminx (dodecahedron) is the first kind, the kilominx, and the accepted version of the 2x2 FTO is the second kind.

The type A 2x2 FTO would be like the image on the left, but without those centers. a type B 2x2 megaminx has actually been made, it's the pentultimate, shown below. 2 layers, a face cut right through the middle.

This is something that's bothered me for a bit. I feel like Type A is a more accurate generalization for a 2x2 puzzle, because 2x2 is supposed to have basically the same ideas and algorithms but just less pieces, which is why a Kilominx feels like it is to the Megaminx as a 2x2 cube is to a 3x3. the "2x2 FTO" has a completely different solve to the normal FTO, because it's type B, it has new pieces. The cube has so many perpendicular faces that cut depth doesn't change all that much, but the cuts intersect in so many more ways with the other solids, different cut depths means different sets of pieces and different overlaps. I want an actual 2x2 FTO, is what I'm saying. Corners only.

[then-ponder]

"If you don't terrify mathematics, it will terrify you."

- my papa circa 2013 AD

[then-ponder]

This is true, but it’s very concerning that your papa didn’t say what would happen if you did terrify mathematics.

"If you don't terrify mathematics, it will terrify you."

- my papa circa 2013 AD