Mathematics - 2023-06-11 (page 2 of 2)

shintuku

21:00

or why the fundamentalist interpretation of the quran would be the accurate one o.O

Sine of the Time

@shintuku that's why in my opinion we should ask experts of interpetation and not follow our logic or what we read online without verifying the source

冥王 Hades

@SineoftheTime It calls for their slaughter, so does Muhammad’s own words (Hadis) which, as he claimed, were derived from Quran

shintuku

again so does the old testament

冥王 Hades

Yeah I know. That’s why I despise religion as a whole

Sine of the Time

@冥王Hades dude that's the Quran. It's written "whoever saves a life, it will be as if they saved all of humanity". and it does not say whoever saves a muslim life, but a life in general (also disbelivers and jews)

冥王 Hades

21:03

@SineoftheTime Qur’an:9:5 “Fight and kill the disbelievers wherever you find them, take them captive, harass them, lie in wait and ambush them using every stratagem of war.”

@SineoftheTime Qur’an:9:29 “Fight those who do not believe until they all surrender, paying the protective tax in submission.”

Sine of the Time

@冥王Hades Just read the next verse and don't quote out of context :"And if anyone from the polytheists asks for your protection ˹O Prophet˺, grant it to them so they may hear the Word of Allah, then escort them to a place of safety, for they are a people who have no knowledge."

Ted Shifrin

OK, last sentences on this and then we're done.

Sine of the Time

these verses were reveled during war, so it's natural that if during war you find an enemy you've to fight it

Ted Shifrin

My apologies for opening the door.

Sine of the Time

@TedShifrin you're right, this room is for math questions :)

Ted Shifrin

21:06

and healthy math debates, too. Occasionally some of us (and I'm guilty) slip into a sentence of politics or a few sentences of health.

Balarka Sen

Yeah let us move on from here. I agree with Ted's last few opinions on religion and will say no more.

冥王 Hades

@SineoftheTime what part of “Fight and kill the disbelievers whenever you find them, take them captive, harass them…” do you not get?

It is the clearest example of violence.

Balarka Sen

@冥王Hades None of those are specific to Islam. Let's drop it.

Yai0Phah

It is the clearest example of being off-topic.

Ted Shifrin

Indeed.

Sine of the Time

21:08

@冥王Hades my last comment: you've to see when these verses were revelad and in what context. As I said, these verses were revelead during war. What part of "whoever saves a life, it will be as if they saved all of humanity" do you not get?

Balarka Sen

Lol

Ted Shifrin

STOP, @Sine.

I will have to start using time outs.

冥王 Hades

@BalarkaSen I don’t appreciate whataboutism. My debate was about Islam, so that is what I would take about.

Ted Shifrin

@Balarka Did the conormal bundle stuff work out?

shintuku

i'm pretty sure ab + cd = e implies gcd(a,c) = gcd(a,e) and like comparing two lines, one being ab + cd and the other being e makes me almost sure this is the case. does anyone have a better intuition?

Sine of the Time

21:09

@TedShifrin I made my last comment and I hopefully will not break my promise

Ted Shifrin

STOP, @Hades.

Balarka Sen

Cool, @SineoftheTime.

@TedShifrin Yup

Ted Shifrin

Pretty basic. I was confident it would.

冥王 Hades

@SineoftheTime the part where it tells you to kill the disbelievers and harass them, that part. I don’t care when they were revealed, doesn’t change the fact that it is violent. Just like every other religion

Sine of the Time

You can lead a horse to water but you can't make him drink

Yai0Phah

21:10

I guess that you could open another room to argue about these?

3

Ted Shifrin

This room was placed in timeout for 1 minute; Non-ending off-topic debate

shintuku

lads i have real math

3 mins ago, by shintuku

i'm pretty sure ab + cd = e implies gcd(a,c) = gcd(a,e) and like comparing two lines, one being ab + cd and the other being e makes me almost sure this is the case. does anyone have a better intuition?

there's a proof by contradiction to be done but, there has to be the intuitivest take somewhere

Balarka Sen

@Ted: Kashiwara-Schapira does a lot of conormal geometry for their microlocal sheaves business, and they write pages of set theory to prove very general results which are very hard to read. Thankfully, I only needed an extremely special case.

Ted Shifrin

Oh, I vaguely remember some colloquia on that kind of stuff back 40+ years ago.

Yai0Phah

@shintuku That seems to be incorrect. You could take c=1 and d=a, then gcd(a,c)=1 and gcd(a,e)=gcd(a,a(b+1))=a.

shintuku

21:16

hm..

leslie townes

shin: if you look at the argument underlying the euclidean algorithm, or other sources, you'll see tht the set {ab + cd: b, d integers} is the set of multiples of gcd(a,c). so if e is in there, e is certainly a multiple of gcd(a,c). it might be a nontrivial multiple and this could contribute to gcd(a,e).

shintuku

at yai0: thanks I will rethink this

at leslie: noted

leslie townes

.. as it appears to in yai's example.

Balarka Sen

@Ted Here is an interesting POV from their book: Suppose $\Sigma = \{\Sigma_i : i \in I\}$ is a stratification of $M$, where $M$ is real analytic and the strata $\Sigma_i \subset M$ are subanalytic. Let $X := \bigsqcup T^*_{\Sigma_i} M$ ($T^*_S M$ is my notation for conormal bundle of $S$ in $M$). Suppose for any pair of sequences $\{(x_n, \xi_n)\}, \{(y_m, \eta_m)\} \in X$ such that
(a) $\lim x_n = \lim y_m = x$
(b) $\lim \xi_n = \lim \eta_m = \xi$ and
(c) $\lim |x_n - y_n||\xi_n| = 0$,
we have $(x, \xi) \in X$.

Ted Shifrin

This reminds me of the mistake my algebra students would occasionally make: Generalizing the (correct) conclusion that if $am+bn=1$, then $\gcd(a,b)=1$, they were convinced that if $am+bn=d$, then $\gcd(a,b)=d$.

Balarka Sen

21:20

Then $\Sigma$ is a Whitney stratification of $M$.

Ted Shifrin

Well, those do look like Whitney conditions.

Balarka Sen

My intuition is (a)+(b)+(c) is saying something about converging secant and planes.

Yeah.

Ted Shifrin

I would prefer $N^*_MS$; your notation looks too much like relative cotangent bundle.

Balarka Sen

Apparently this is slightly stronger than just a subanalytic Whitney stratification.

Yeah, I should probably use that one.

Ted Shifrin

Do you know $\xi\ne 0$?

Balarka Sen

21:22

Not necessarily.

Ted Shifrin

So the case $\xi=0$ holds trivially.

Balarka Sen

Right, fair point.

Ted Shifrin

(c) is bothering me.

Balarka Sen

I think I lied.

Ted Shifrin

$|\xi_n|$ is bounded, and $|x_n-y_n|\to 0$ since $x_n\to x$ and $y_n\to x$.

Balarka Sen

21:24

$(x_n, \xi_n)$ converges to $(x, \xi)$ according to (a) + (b). But Whitney condition (a) is equivalent to $X$ being closed.

Replace (b) by the corrected:
(b') $\lim (\xi_n + \eta_n) = \xi$.

Ted Shifrin

So addition occurs in $T^*M$?

Balarka Sen

Yes

Ted Shifrin

Cuz they might live in different components.

So (c) just says that $|\xi_n|$ must be bounded, I think.

Which surely is true.

I'm still confuzled.

Balarka Sen

$|x_n - y_n|$ can be $1/n$, and $|\xi_n|$ can be $\sqrt{n}$.

I think we should observe that $\ker(\xi_n + \eta_n) = \ker(|x_n - y_n|\xi_n + |x_n - y_n|\eta_n)$. What is $\ker(\phi_n + \psi_n)$ where $\psi_n$ goes in norm to $0$? It has small angle with $\ker \phi_n$?

Ted Shifrin

Oh, so if both $\xi_n$ and $\eta_n$ go to infinity, I guess it's possible.

Balarka Sen

21:30

One can go to negative infinity.

So (b'), which is $\lim (\xi_n + \eta_n) = \xi$, is still true

Ted Shifrin

I don't know what that means. I just meant magnitudes.

Balarka Sen

Yeah, magnitude is right. I was just emphasizing that both cannot go to +infty, because of my corrected condition (b)

I think this is saying something like, if you take two different sequences $\{x_n\}$ and $\{y_n\}$ from a higher dimensional stratum to a boundary stratum, converging to the same point $x$, the angle between them (once you translate both to the same converging point $x$, in some local chart around $x$) dies like $|x_n - y_n|$.

Not necessarily from a higher dimensional stratum, one of them can be in the same stratum as $x$ -- that should imply Whitney's secant condition is true.

@Ted: See the Kuo-Verdier condition (w) here, page 9. hal.science/hal-03186972/document

Ted Shifrin

This is too much thinking for my head today.

Balarka Sen

In the paragraph after Theorem 1.3.3: "Another proof, due to Kashiwara and Schapira [63], follows from the equivalence of (w) and their microlocal condition µ [135]."

$\mu$ is what I told you.

The more I try to move on from stratified spaces, the more they come back to terrorize me

Yai0Phah

I recently heard conical smoothness of stratified spaces.

Balarka Sen

21:42

Ayala-Francis-Tanaka, yeah

It's good stuff, but I am not sure if it is too much for too little.

Fun, nonetheless.

I will have to read their work carefully eventually

The problem with trying to define a "perfect" category of stratified spaces is that they crop up in so many different contexts that it's better to use what is necessary whenever

冥王 Hades

22:03

Had to pay a fine again yesterday for driving too fast. 18,000 Yen

The Japanese police would become millionaires because of me

s.harp

22:39

My supervisor sometimes sends me weird requests, like if I can download some paper off the arxiv and send it to her

shintuku

weird

uhoh

4

Q: Can you identify this space travel related equation?

Does anyone recognize the equation carved on this object? The only hint I have is that the back side has the word "orbit" carved into it. It may be incomplete or incorrectly copied. My best interpretation in MathJax: $U_eR_o\sqrt{\frac{2g}{(R_ôh)}}$ My grandmother carved the object. She had a ...

orbital-elements

Old question, just bountied in Space Exploration SE

oneofvalts

@s.harp :D

Ted Shifrin

22:56

@s.harp My adviser told me to translate the seminal paper on combinatorial Pontryagin classes in Russian in 1977 or so.

冥王 Hades

Imagine being asked to translate a paper into Japanese

I’m leaving the program immediately

Ted Shifrin

I should say. The paper was by Russians in Russian.

冥王 Hades

You mean Soviets right? It was ‘77

Ted Shifrin

We said Russians. My grandparents were Russians.

Akiva Weinberger

Russian SSR

s.harp

23:03

@TedShifrin did you speak russian? Otherwise that would have been hell

shintuku

a lot of makoto ito's stuff hasn't been translated to english yet

Akiva Weinberger

or SFSR?

s.harp

(the hell refers to the translation)

Ted Shifrin

DogAteMy, did you resolve the reading course issue?

Ted Shifrin

23:14

@s.harp Not really. I took one year in college and had a good Russian/English math dictionary. But my Russian was better than Chern’s ;)

mick

hi

0

Q: Solutions to $f(x+1) = f(x) + f(x/2)^2 + f(x/3)^3 + f(x/4)^4+...$ ? $f(x) = O(\frac{\exp(x)}{x+1})$?

Consider the following functional equation : $$f(0) = 0$$ $$f(1)=1$$ $$f(x+1) = f(x) + f(x/2)^2 + f(x/3)^3 + f(x/4)^4+...$$ What are the solutions and what are the asymptotics ? obviously related $$g(0) = 0$$ $$g(1)=1$$ $$g'(x) = g(x/2)^2 + g(x/3)^3 + g(x/4)^4+...$$ And $$h(0) = 0$$ $$h(1)=1$$ $...

number-theory asymptotics divisibility functional-equations

crazy math again

looks like explicit form for primes with li(x) not ??

li(x) + li(x^(1/2) + ...

maybe my imagination

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$Mathematics$ Mathematics