Mathematics

2:48 AM

Today in "Nuking a potato from orbit: proof edition" is proving that the degree of composition of functions is the product of degrees via forms

Semiclassical

I prefer "nuking with a potato from orbit"

or I would, if I knew how to do it

nuking the orbit with a potato would be very good

Orbiting a potato with a nuke?

That's just dangerous

Anyway you get the idea, probably a very high powered tool to do the job but why not?

2:52 AM

Um, I don't get why that's a nuke. It's perfectly reasonable to define degree of a map as the number the integral of the top dimensional form is multiplied by when pulled back.

Indeed, in algebraic topology, you define degree of a map $f : M \to N$ to be $f^*(1)$ where $f^*:H^n(N) \to H^n(M)$ is the map induced on top cohomology (de Rham in smooth world), and both groups are identified with $\Bbb Z$.

I mean given that we defined it via intersection number

Sure, if it's defined as the cardinality of a generic preimage that's obvious

But then it's nonobvious why that's equivalent to the version I mentioned.

I mean yeah, we did prove that

This is what I'm saying, using the degree theorem to prove this statement when it's possible to prove it outright via intersection numbers is probably not what Neves was going for

Eric Silva

i actually usually think of it in terms of forms

Lol

I mean in fairness forms just seem like a cool way to think about stuff

3:01 AM

I know you'll hate me for saying this but I can't help but thinking of them as a tool for computation

a very cool tool which saves a lot of work, sure, but i never think about them if i have a geometric alternative

I mean this is probably a personal failing

shrugs

I haven't gotten deep enough into that side of the world to say anything

Mostly I've liked that they give a nice way of looking at various things which I've appreciated

Eric Silva

i mean @Balarka maybe you just haven't done the problems that really are natural in forms :P

Degree, Cauchy integral theorem

Eric Silva

like lots of things carry the same data as forms, but sometimes things really are natural in that language

@Eric You're probably right.

Secret

3:09 AM

[Random] It is not known whether $\tau$ has special numerical properties unique to it but not $\pi$

More generally, it is not known whether given any real number $x$, whether $nx$ with integers $n$ can have new properties that are not found in the base itself

Is that so?

@Secret

Secret

3:35 AM

Actually I am not sure if what I said is correct, but I think it holds for multiples of $\pi$ I guess, but not so much for integers (e.g. 0 and 1 are very different, 3 and 2 are different because one is odd and one is even (and even numbers are part of an ideal of the integer ring

so 2, 0 has properties that 3 does not have, and 1 has properties unique to it not shared by other integers

Hmm

BAYMAX

Hi,Is there anything that does symbolic calculations?Like $a = \alpha x + \beta y$ and $b = \alpha x - \beta y$ then when i enter $a.b$ it must return me the correct result as $a.b = \alpha^{2}x^{2} - \beta^{2}y^{2}$ ?

3:58 AM

"...to my best knowledge, the book was not dedicated to erotic problems of people in outer space... As Solaris' author I shall allow myself to repeat that I only wanted to create a vision of a human encounter with something that certainly exists, in a mighty manner perhaps, but cannot be reduced to human concepts, ideas or images. This is why the book was entitled "Solaris" and not "Love in Outer Space"."

lel

Secret

4:31 AM

@BAYMAX Mathematica allows you to define symbolic operators

BAYMAX

4:50 AM

Thanks@Secret

Simple

5:05 AM

An initial condition of a pde is $u(x,0)=c$, c is a constant, after I solved the pde, then $u(x,t)=c+kt$, right? I did something completely incorrect

Fargle

5:36 AM

Hmm. ChatJax doesn't seem to be working for me.

i don't know how t =o use Chatlax at all.

Mike Miller

7:40 AM

@TedShifrin How do you feel about eigenvalues of the Laplacian?

don't know. have never studied that.

chargrin

SoumyoB

8:57 AM

soooo I got my F-1 Visa for the US confirmed today

congrats

i only know academic matters

outside schools I can't find my milieu

I did well in schools

after leaving school, I flounder in the wilderness

then return

I went to my alma mater to visit my professor in graduate school, and he blamed me for not having a paid job.

how is that your fault?

(in his opinion, of course :-)

9:11 AM

he said it's the responsiblity of an adult to have a paid job

its your choice, no?

I am a master gaduate in theoretical physics with research field in gravitation. I can't find a job requiring my expertise.

return to university and do research

there is no job opening to master graduate in theoretical physics at all

theoretical physics only has job opportunity for PhD graduates

you can be a lecturer

Alessandro Codenotti

9:18 AM

@MikeMiller I doubt I can help with the little we did in the PDE course, but on which space of functions are you considering the Laplacian?

9:35 AM

Hello

hi

Q: How must have Liu Xin calculated $\pi$?

How's everyone?

Nick

10:46 AM

Hi all

@SBM I'm good, I have an exam tomorrow though.

Hey, I've just asked a question on this question after a really long time. Check it out!

0

I know there won't be a definite answer to this question because of a lack of required historical evidence but there is so much we know of Liu Xin and of that time period. In that time, to get to an approximation 3.154 was a phenomenal feat. To this day, no one knows how Liu Xin did it but we ca...

All the best @Nick

Nick

@SBM Aww, thanks. It's math.

Maybe you guys can help me study.

OK

Benjamin

Is there a formula or algorithm for calculating the motion such that the distance from an object is changing at a constant rate, but the speed of the movement is variable.

Nick

11:03 AM

@Benjamin You can try to derive one.

Fargle

@Benjamin One could take, for example, $v(t) = (\cos (t^2), \sin (t^2))$. This always lies on the unit circle, but its speed is $|2t|$.

SoumyoB

I meant:
if in a compact space every convergent subsequence of a sequence converges to the same limit then does it imply that the sequence itself converges?

Benjamin

@Fargle Okay, that was the sort of thing I was thinking, but I wanted to see about other possible equations other than a circle.

Alessandro Codenotti

11:34 AM

Hm, I think this could go wrong in a compact but not sequentially compact space where you have a sequence without converging subsequences

Oh

SteamyRoot

Happy Towel Day everyone!

Fargle

@SteamyRoot I never could get the hang of Thursdays.

why there is no smiley here? are mathematicians usually so serious that they do use smileys?

don't

actually I don't use smileys often.

BAYMAX

12:00 PM

Happy towel day @SteamyRoot