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BigSocks

 Mathematics

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BigSocks
May 23, 2021 04:05
every open scene intersects a joke nontrivially
BigSocks
May 22, 2021 20:25
I guess by the definition of substructure it's not possible, so that would have to change in some meaningful way
BigSocks
May 22, 2021 20:25
could there be a structure (family of them) that is a quasigroup, but it has finite substructures as groups? The idea is to "lose the 1 in the limit" somehow
BigSocks
May 10, 2021 00:22
@TedShifrin are you hinting at the Euler theorem saying that you can write down rotations in 3 dimensions as rotations in 2 dimensions along a new axis?
BigSocks
May 9, 2021 20:29
yes, that's exactly how I meant it
BigSocks
May 9, 2021 20:28
pretty neat! forgot how nice calculus was
BigSocks
May 9, 2021 20:28
yeah I see it, I guess I just forgot it could happen
BigSocks
May 9, 2021 20:25
haven't done calc in a while
BigSocks
May 9, 2021 20:25
Say we are integrating something as simple as $\frac{x}{e^{x^2}}$ and for some reason you mess up and u-sub. setting $u = e^{x^2}$.
You get something like $\frac{x}{u} \frac{du}{2x e^{x^2}}$ as the integrand. It kind of looks like you could "re sub" for that $e^{x^2}$ in the second fraction to get $\frac{1}{2} \frac{du}{u^2}$ as the integrand, which still integrates to the correct answer. Just wondering if you can "double substitute" like that or if this is some coincidence.
BigSocks
Apr 28, 2021 00:55
take care
BigSocks
Apr 28, 2021 00:53
Like I remembered there were some idempotents you got in similar ways in knot theory, so maybe this happened for $S_n$
BigSocks
Apr 28, 2021 00:53
I was mostly wondering if there were obvious results I was forgetting
BigSocks
Apr 28, 2021 00:53
and I was just looking at some stuff with $S_3$, but I'll take a while
BigSocks
Apr 28, 2021 00:52
yeah in a way
BigSocks
Apr 28, 2021 00:51
but specifically those 2 so not just it being shortest will be the best I think
BigSocks
Apr 28, 2021 00:51
I guess equivalently that is what I want
BigSocks
Apr 28, 2021 00:50
nah, I want to know if you could somehow pick orderings that cancel out to a single transposition/the identity
BigSocks
Apr 28, 2021 00:48
hope and fear I guess are dual
BigSocks
Apr 28, 2021 00:48
@TedShifrin No, I hope to get something nice, but I fear I get a mess
BigSocks
Apr 28, 2021 00:46
@TedShifrin My bad, meant all of them
BigSocks
Apr 28, 2021 00:45
So are there some standard results of what you get when you take $\Pi_i^{n!} \sigma_i$ for $\sigma_i \in S_n$? I think order will matter for $n > 3$ so maybe something interesting happens when we pick some "natural" order on permutations?
BigSocks
Apr 26, 2021 23:45
why would inventing it give you a privileged position to solving it?
BigSocks
Apr 26, 2021 23:35
not in real life I don't think, but I think the correct answer might be "yes"
BigSocks
Apr 26, 2021 23:34
paint (and most real things) have thickness?
BigSocks
Apr 26, 2021 23:33
@TedShifrin but still, very weird to think of a "physical object of infinite spacial extent"
BigSocks
Apr 26, 2021 23:32
@TedShifrin makes it sound like limits, picking $\epsilon$s and $\delta$s
BigSocks
Apr 26, 2021 23:31
@copper.hat ?
BigSocks
Apr 26, 2021 23:30
exactly
BigSocks
Apr 26, 2021 23:28
Eh, I think it is kind of crap to assume such an object could exist in the same way paint could exist
BigSocks
Apr 26, 2021 23:25
@TedShifrin Hmm... I guess I never thought much more of this. I guess I could just say "paint is not well defined", but that seems unsatisfying
BigSocks
Apr 26, 2021 23:22
and how then could we address it other than how we have ?
BigSocks
Apr 26, 2021 23:21
then of what? philosophy? linguistics?
BigSocks
Apr 26, 2021 23:20
I don't understand. what's the question? "How is that possible?" or something like that
BigSocks
Apr 26, 2021 23:19
that's what I'm saying
BigSocks
Apr 26, 2021 23:18
integral for volume is finite, the one for surface area is infinite
BigSocks
Apr 26, 2021 23:17
isn't it just a couple of integrals?
BigSocks
Apr 26, 2021 22:05
I get that this may be unappealing to many, but is there a way to take a (finite) quasigroup (that is not a group, but is otherwise as nice as you like) and build a (finite or at worst countable) group that contains the original quasigroup (at least the elements and products).

I've tried a few things, but it seems that there's no reasonable way to "repair" the quasigroup. I was thinking of 2-groups and how they are basically crossed modules of groups, so you have elements and functions and they intermingle, but it is an operation that is kind of "closed" under groups. Similarly you could t…
BigSocks
Mar 26, 2021 05:55
right and that is pretty cool too. but this is definitely something I had never seen. It is called "Maquette" for what it's worth
BigSocks
Mar 26, 2021 05:54
thanks for considering it anyway :)
BigSocks
Mar 26, 2021 05:53
but on the off chance it was cool I figured I might ask
BigSocks
Mar 26, 2021 05:53
yeah, this is also my suspicion
BigSocks
Mar 26, 2021 05:52
which I think reflects the "automatically magnifies as you blow up the radius" aspect of what you said
BigSocks
Mar 26, 2021 05:52
right I imagine really moving "between annuli" is just picking different elements of the same equivalence class, but all of them "happen at once"
BigSocks
Mar 26, 2021 05:49
anyway, at least there is not obvious analogue in math for such a space
BigSocks
Mar 26, 2021 05:49
it is very strange because of this "enlarging items" property
BigSocks
Mar 26, 2021 05:48
@TedShifrin yeah, I think this is true
BigSocks
Mar 26, 2021 05:48
the thing is that if you take something from an annulus $i +1$ to an annulus $i$ the item becomes larger in the $i+1$ version, so maybe the identification is not accurate
BigSocks
Mar 26, 2021 05:47
kind of yes
BigSocks
Mar 26, 2021 05:47
there are items that you can carry "between annuli" and then you can move "back and forth" between annuli that were before coinciding
BigSocks
Mar 26, 2021 05:46
the interiors too