Mathematics - 2025-01-17

Vuk Stojiljkovic

01:00

@leslietownes Hello there man

Hello there, anyone willing to check my answer to my own question 2-3 days ago? Any feedback is welcome

Ben Steffan

@Thorgott turns out the argument I thought I had for torsion might not work

Funnily enough I could make it work if I knew that $H_4(K(\mathbb{F}_p, 2)) \cong \mathbb{Z} / p^2$ for all primes $p$

this is true when $p = 2$. I don't know if it is true for odd primes

I suspect it might not be

I have a hunch that it being $\mathbb{Z} / 4$ detects something particular to $p = 2$, but I'm not quite sure what

Homesick Iguana

06:11

My paper is on arxiv yay.

one potato two potato

06:28

what is the title?

Homesick Iguana

06:53

@onepotatotwopotato "Holonomy, Zeta Functions, and Cohomological Structures
in Foliated Manifolds with Stratified Boundaries." (probably won't be processed until Sunday though).

Soumik Mukherjee

@HomesickIguana in the second line, it is written ratified. Is that correct?

Ryder Rude

hi

Soumik Mukherjee

Hi

Ryder Rude

07:09

this is a nice chat for debating creationism and materialism :)

Creationism vs. Materialism/Naturalism

A room for sharing and discussing evidences for Creationism an...

1

Homesick Iguana

@SoumikMukherjee Yes it's correct. I use it to mean that there is an injective mapping from pairs of vertices to foliations ensuring that the
"structure of the completion" is well-defined and free of redundancies. I.e. I am only considering one foliation per unique pair of vertices

Ratified can mean an agreement between two parties (or an agreement between the 2 vertices)

that is why i used that lingo

i.e. the vertices are agreeing to support only one foliation at a time (not the entire space of all possible foliations)

Soumik Mukherjee

@HomesickIguana Okay, I asked as I had never seen that term used before.

But all the best for your paper

Homesick Iguana

@SoumikMukherjee Thanks - it's my first paper

Soumik Mukherjee

Nice

Homesick Iguana

09:05

0

Q: Confused about how these two integrals can be equal?

I don't understand why this integral is one-fourth $$ \int_0^1 e^{\frac{\log^2 (2)}{\log \big(1-e^{\frac{\log^2(2)}{\log(x)}}\big)}}dx-2\int_{1/2}^1 e^{\frac{\log^2(2)}{\log\big(1-e^{\frac{\log^2(2)}{\log(x)}}\big)}}dx=1/4.$$ and this integral is also one-fourth $$ \int_0^1 e^{\frac{\log^2 (2)}{\...

Soham Saha

09:57

@XanderHenderson I was talking about this link

Ben Steffan

11:08

The $\mathbb{Z} / 4$ appearing as $H_4(K(\mathbb{Z} / 2, 2))$ is indeed special to $p = 2$: It captures the Pontryagin square.

so much for that

actually what I was trying to do here was stupid: the answer about when the hurewicz map is an isomorphism in all degrees implies that what I was doing wasn't going to work

1010011010

12:18

Hi all, I've made poor life choices and now i'm stuck with the following problem:

I have a function like so: $a(k)=\sum_{i=0}^k f_i$. I have to take the derivative with respect to $k$

Ben Steffan

the non-stupid way to figure out that $H_4(K(\mathbb{Z} / p, 2)) \neq 0$ is of course to observe that $H^4(K(\mathbb{Z} / p, 2); \mathbb{Z} / p) = [K(\mathbb{Z} / p, 2), K(\mathbb{Z} / p, 4)] \neq 0$ since the $\smile$-square lives there and to apply the UCT.

@1010011010 that makes no sense, unless you can explain what e.g. $\sum_{i = 0}^{\sqrt{2}} f_i$ should be

1010011010

@BenSteffan I think a more precise way is that I am interested in the finite difference, sorry

Thanks for pointing it out

Surely it is not $f_{k+1}$?

Ben Steffan

what exactly do you mean by finite difference? $\Delta[a](k) = a(k + 1) - a(k)$?

@Thorgott there is no UCT for cohomology with compact support, is there?

wait, there is

of course there is

I'll have to think this through later

Thorgott

13:25

the complex of compactly supported chains is not obviously the dual of anything, so I don't see a readily apparent UCT

Jakobian

14:05

@RyderRude who would want to. Creationism is basically considered to be a joke

It's up there with flat earth theory

Ryder Rude

@Jakobian i think it can lead to interesting discussions. also, there is the field of theology which is dedicated to these debates

@Jakobian lol

@Jakobian i think u also once said that you were interested in researching this stuff

Jakobian

@RyderRude I know, apologetics. That's why it's so hard to debunk those guys

@RyderRude I don't know what you mean

Ryder Rude

@Jakobian theology also involves the counter-arguments. there is a youtube channel called AlexO'Connor who is a theologian and he expertises in the counter arguments

@Jakobian i mean you researching Bible maybe. u mentioned it before

Jakobian

If you have to create a whole field to be able to stand on your head and defend your religion...

Apologetics is more like dirty tricks to use in a debate

Ryder Rude

this is the channel youtube.com/@cosmicskeptic?si=fN26kOpXj8H-WLid

i think creationism cannot be ruled out yet. but it is unlikely to be correct

as in, creationism makes claims about what's outside the universe. these are non testable

Jakobian

14:14

Depends on what type of creationism

Ryder Rude

what do you mean

Jakobian

The whole premise of "we are special" just speaks towards our ego...

Ryder Rude

i think some stories clash with science like the Adam and Eve one

Jakobian

@RyderRude there is not just one type of creationism

Ryder Rude

so if these stories are taken literally, then creation is ruled out

@Jakobian yes. There are many variations

@Jakobian some philosophies believe in free will which is supposed to be the special property of conscious beings. this is not merely religions, but also some philosophers like Kant

Jakobian

14:18

If your only source is a book and it's full of contradictions unless you bend your head backwards to come up with crazy interpretations then your religion is most likely just false

Ryder Rude

lol

Jakobian

I'm not interested in debating things I know are true

Ryder Rude

i think this is a good argument against creationism. The stories have to be not taken literally. Sean Carroll uses this argument a lot

@Jakobian i understand...

Jakobian

If you look at history of religion for example, that's interesting though. For example, Christians pretend that Satan isn't just a made up figure for their religion

Even god was described as satan at one point iirc

Ryder Rude

@Jakobian why would that be?

Jakobian

14:23

It's a word that was used to create a character because they were inspired by zoroastranism

Ryder Rude

@Jakobian pretend?

Jakobian

Yes, pretend. Look in the old testament. Satan isn't just one person, it's like a title

Ryder Rude

@Jakobian does satan make an appearance in old testament

@Jakobian is it a supernatural being?

or do humans take this title?

Jakobian

@RyderRude I think it means someone sent by god or something

Ryder Rude

a lot of religion ideas were borrowed from religions that came before, yes

Jakobian

14:26

@RyderRude I know they take the title 'lucifer'

Which was made into a synonym for satan by christians

Ryder Rude

@Jakobian interesting. it doesn't make sense for God to send satan. but i guess it has some weird story behind it

@Jakobian oh

Jakobian

@RyderRude not in christianity

Christianity is one of those religions that you can pretty confidently refute as false if you just dive into it a little

Ryder Rude

also see this en.m.wikipedia.org/wiki/Yahweh . Apparently, this is the god of the old testament. this god existed in other religions that came before

ideas gradually transition into different ideas

and stories slowly change over time

Jakobian

@RyderRude that only makes the whole idea more susceptible to criticism

As seen here

Ryder Rude

yeah... if the stories change over time, it makes them more likely to be of human origin

Jakobian

14:33

Honestly it's funny how one of the most obvious to be false religions is also the most popular one. People really stick to the whole "faith" thing without questioning it

Ryder Rude

some animals have been documented to have weird rituals. also, ancient humans had started buying the dead and had some belief in afterlife at that point. i think this is where such ideas originated

i read about it a while ago

and these ideas gradually transformed

i will try to find the article

this is the article impakter.com/ancient-humans-believe-afterlife @Jakobian

these graves are from 300000 years back. they show signs of belief in afterlife

Soumik Mukherjee

ROCKSTAR: Kun Faya Kun (Full Video Song) | Ranbir Kapoor | A.R. Rahman, Javed Ali, Mohit Chauhan

►

Ryder Rude

@SoumikMukherjee great song

We've Only Just Begun - cover - featuring Tori Holub

►

Is The Universe Conscious?

►

this video goes over the ideas of Plato, Aristotle, Descartes, Kant, Shelling, Hegel and Whiteman. i think it is thought provoking as a progression of idealism over time

Soumik Mukherjee

14:59

@RyderRude yeah, soothing

one potato two potato

what would be a geometric meaning of the integral of the mean curvature over a codimension 1 (Riemannian) submanifold?

measures how far from a hypersurface from minimal for example?

AbstractSage

It is promised that a given coin is either fair (Pr(Head) = 1/2) or biased
with Pr(Head) = 1/2 + ε where 0 < ε < 1/2. Show that 100/ε^2 coin
tosses are sufficient to correctly determine the type of coin (fair or biased)
with at least 4/5 probability

psie

15:36

A signed measure $\mu$ on a measurable space $(E,\mathcal A)$ is a map $\mu:\mathcal A\to\mathbb R$ such that $\mu(\varnothing)=0$ and for any sequence $(A_n)$ of disjoint measurable sets, the series $\sum_{n\in\mathbb N}\mu(A_n)$ converges absolutely and $\mu\left(\bigcup_{n\in\mathbb N}A_n\right)=\sum_{n\in\mathbb N}\mu(A_n)$.

Let $E$ be a topological space. The space of all signed Borel measures $\mathcal M(E)$, i.e. $\mu:\mathcal B(E)\to\mathbb R$ is claimed to be a linear space with norm $\mu\mapsto |\mu|(E)$. I think I can show that the norm is a norm, but showing it's a linear space, well, $a\mu+b\lambda\in \mathcal M(E)$ when $a,b\in\mathbb R$ since $(a\mu+b\lambda)(\varnothing)=0$ and you can add convergent series termwise and multiplying by a constant doesn't change whether it converges/diverges.

So what remains is checking the other 8 axioms of a vector space (according to my linear algebra book, at least), right?

Thorgott

15:50

it sounds like you're missing a condition, no? what forces $|\mu|(E)$ to be finite?

psie

yes, hmm. If $\mu$ is a signed measure (as defined above), then $|\mu|$ is finite. I should have probably specified that $E$ is actually a separable locally compact metric space.

the exercise is actually showing $\mathcal M(\mathbb R)$ is a Banach space with norm $\mu\mapsto |\mu|(\mathbb R)$

Jakobian

yeah it should be countable additivity that forces $|\mu|(E)$ to be finite

Hahn decomposition theorem

In mathematics, the Hahn decomposition theorem, named after the Austrian mathematician Hans Hahn, states that for any measurable space ( X , Σ ) {\displaystyle (X,\Sigma )} and any signed measure μ {\displaystyle \mu } defined on the σ {\displaystyle \sigma } -algebra Σ {\displaystyle \Sigma } , there exist two Σ {\displaystyle \Sigma } -measurable sets...

$|\mu|(E) = \mu(P)-\mu(N) < \infty$ as a sum of real numbers

@psie You are trying to show it's a vector subspace of all such functions

But trying to show $a\mu+b\lambda\in \mathcal{M}(E)$ instead of decomposing it into simpler steps... just why

but sure, we don't need to

@psie yeah no. Because all functions are already a vector space and you know that

psie

16:08

@Jakobian by all such functions, do you mean all functions with domain $\mathcal B(E)$ and codomain $\mathbb R$? I assume this is a vector space because it is of the form $F^S$ where $F$ is a field and $S$ is nonempty, which is a vector space.

Jakobian

@Jakobian I guess in this case that wouldn't make it any simpler

@psie yes, and basically yes

so all the axioms of a vector space don't need to be checked

psie

ah great, that's a relief...

Ben Steffan

16:21

@Thorgott you're thinking too low level. $H_c^*(M) \cong \tilde{H}^*(M^+)$ :)

(with any coefficients)

and for the rhs I have the usual uct

Thorgott

that isomorphism is not always true, is it

I think it should fail pretty badly if the ends of $M$ are all fucked up

Ben Steffan

it is always true for open manifolds I believe, but let me check

ah, it does require $\infty$ to have a neighborhood basis of contractible opens :/

Thorgott

16:39

yeah, something like that, acyclic should suffice too

but if the space of ends is complicated, it can get ugly

hmm, perhaps we can work with the end compactification

AbstractSage

Hi, need help with the following question. It is promised that a given coin is either fair (Pr(Head) = 1/2) or biased
with Pr(Head) = 1/2 + ε where 0 < ε < 1/2. Show that 100/ε^2 coin
tosses are sufficient to correctly determine the type of coin (fair or biased)
with at least 4/5 probability, i.e., give an algorithm that will need at most
100/ε^2 coin tosses, and should have the following guarantee: if the coin
is fair the algorithm will return ‘fair’ with probability at least 4/5, and if
the coin is biased then algorithm will return ‘biased’ with probability at

Sarvagya

16:55

hey, can someone help me with this question? we're given two polynomials $f(x)$ and $g(x)$ $\in \mathbb R[x]$ such that both aren't squares of a real polynomial (ie a polynomial in $\mathbb R[x]$). But it's given that $f(g(x))$ is the square of a real polynomial. How can I show that $g(f(x))$ isn't the square of a real polynomial?

pie

17:18

What do you guys think of " Marsden and Hoffman, Basic Complex Analysis, Freeman"? is it a good book? It is required for math 55b so I might use it for self study, but I don't know what to choose this or "Complex Analysis
Book by Lars Ahlfors" or "Complex Analysis
Elias M. Stein and Rami Shakarchi" what do you guys recommend

Soumik Mukherjee

17:28

@Sarvagya artofproblemsolving.com/community/c6h1557190p9502906

Soham Saha

18:03

@SoumikMukherjee it’s one of my favourites. Currently listening to ‘Saibo’

pie

Also how do you guys know how to use mathematica? Is there a course on how ton use such thing?

Ben Steffan

@pie if you sign up and buy a license it will come to you in the form of oh-so-many mails and promotions

just a few days ago I got one for a "course in foundations - your first steps with mathematica"

I guess that's bitterly needed since the software itself is terribly losing, as our ancestors used to say

pie

@BenSteffan in email?

Jakobian

would be easier to just pirate it first to test how it works

Ben Steffan

@pie well the course would be in person I presume, or online :^)

what I meant is that they send you email promotions, lots of them

pie

18:10

btw my email is filled with promotions and stupid notifications so it is a complete mess I spent hours once cleaning it just to return into a mess a week later I wonder how you guys deal with that

Jakobian

I just delete everything that doesn't matter to me and block/report all the spam to minimize trash amount

Thorgott

the basic numerics lecture here forces you to learn a bit of mathematica

pie

@Jakobian Somehow blocking doesn't do much...

@BenSteffan how did you learn it?

Ben Steffan

I've changed my email address a while ago, works wonders

@pie bold of you to assume I did :)

Jakobian

@pie yeah. I still get like 20 of them regularly

Ben Steffan

18:14

never did much with it

I would have tried to learn it like any other programming language

pie

I wonder should I ask on mathematica se? but since I am too ignorant to even ask I just don't want to

Ben Steffan

read some bare-bones guide for beginners and afterwards survive off of documentation and examples

the thing is, that might not work so well for mathematica

pie

@BenSteffan It is bold of you to assume that I know programming :)

Jakobian

@pie well, more like coding. Programming is much more complicated, it involves collaboration etc.

Thorgott

I never had any use for mathematica after finishing that lecture

Ben Steffan

18:16

what with pretty much every second answer or so on mathematica se seeming to boil down to "use this undocumented function that has been part of the system for half a decade"

Thorgott

other programming langauges are actually useful at times

pie

There a lot of thing that I want to learn or do like math, physics, history, philosophy, programming etc but I really don't have time for any of them, I wish I can stop time so I have time to learn all of them :(

Ben Steffan

@pie learning some python might be a better use of your time I suspect

and more pleasant at that

Jakobian

python is the only thing I ever had to use

Ben Steffan

what do you need mathematica for anyways?

Jakobian

18:18

@pie you never will, you'll waste your time trying

pie

@BenSteffan I started learning python but quit because I didn't have time for it, I wish I have time so bad

Jakobian

focus on a subject and explore that

pie

@BenSteffan a lot of numerical stuff that I work with I can't programme so I call a friend to use python or matlab to do them for me

soI figured maybe I need to learn these stuff

Ben Steffan

well if the friend uses python or matlab maybe you should too :)

rather than mathematica

pie

@Jakobian sad but true fact:( man, I reallyb wish I can stop time, I wish I sleep less than 3 hours a day..

@BenSteffan he is a very good engineer and programmer unlike me who is terrible at both

Jakobian

18:21

@pie and I wish I wouldn't be dead in the next 100 years, but I will

Ben Steffan

I don't understand the rationale. Mathematica will not magically absolve you from being good at engineering or programming.

pie

@BenSteffan I don't need it for that.

Ben Steffan

but that's what you told me you needed it for...?

Jakobian

@pie you don't need to be "good at programming". You can just try to be semi-decent to bear you through all the courses

pie

@Jakobian don't worry we will all die before 2050 because of ww3

Sine of the Time

18:24

I agree with your pessimism

Jakobian

@pie sure, I was just setting an upper bound

pie

@BenSteffan no I didn't I told u my friend who is good with these stuff is good at programming unlike me

Bml

Hi everyone. Is there any conformal mapping expert/enthusiast who can help me out on a question? I had asked some time ago, but received no reply.

pie

@Jakobian I winder what is the "sup" of that event

Jakobian

I get the appeal of "Oh my friend is good at X I want to be good at X too" but this is just a bad thought process

Ben Steffan

18:25

me: "what do you need mathematica for anyways?"
you: "a lot of numerical stuff that I work with I can't programme so I call a friend to use python or matlab to do them for me"
???

pie

@Jakobian not that, I don't want to be the "hey can you do this for me" type of person, I feel embarrassed because of I requist a lot of things

Jakobian

That your friend took time to learn those things may be admirable, but you can't judge yourself through the lens of other people achievements

pie

so I think I need to learn these things to not ask for a "favor" every now and then

.

Jakobian

@pie then learn basic python

you don't have to know what objective programming is or anything, just learn all the math tools

pie

@Jakobian how ?

I mean how to begin, videos? paid courses ? books? documents?

Jakobian

18:28

download a compiler and start writing some basic stuff to understand it

then move on to the libraries that do math stuff

pie

I don't know who to study programming or what to use

@Jakobian that part I have done most of it

@Jakobian this I don't

I even asked a related mse question aa long ago requesting a book

Soumik Mukherjee

@SohamSaha nice

Jakobian

you don't need anything advanced. Literally a youtube tutorial of some kind will do for the basics, and everything else you can just look into the documents that explain how they work

and if you still don't understand how a given function you want to use works, you can just try experimenting with it a little and so on

you don't need any kind of book, it's not that complex, for your purposes at least

Ben Steffan

Python has its own official beginner's guide wiki.python.org/moin/BeginnersGuide

and then there's probably around 5 million other tutorials and guide out there, given that it is both very popular and touted as being particularly beginner friendly

Jakobian

maybe you will like to do some exercises from projecteuler.net in python

AbstractSage

18:36

Hi, need help with the following question. It is promised that a given coin is either fair (Pr(Head) = 1/2) or biased
with Pr(Head) = 1/2 + ε where 0 < ε < 1/2. Show that 100/ε^2 coin
tosses are sufficient to correctly determine the type of coin (fair or biased)
with at least 4/5 probability, i.e., give an algorithm that will need at most
100/ε^2 coin tosses, and should have the following guarantee: if the coin
is fair the algorithm will return ‘fair’ with probability at least 4/5, and if
the coin is biased then algorithm will return ‘biased’ with probability at

Ben Steffan

@AbstractSage You've said that already, no need to repeat the whole statement.

Jakobian

a tutorial can help only in the very beginning in my opinion, after that you just need to practice

Ben Steffan

If somebody feels like helping you they will, but spamming is not welcome here.

3

Soham Saha

@pie maybe try pari/gp for numerical stuff? I used it a long time ago, and it was pretty useful to me.

Best thing is that you can try out basic stuff (at slow speed though) directly in browser

pari.math.u-bordeaux.fr/gpwasm.html

Ben Steffan

the cooler, newer version of that is sage, as far as I understand

which is python, and can also run directly in the browser

Bml

18:46

No one?

Soham Saha

@BenSteffan Yes tried Sage too at that time, but pari seemed better to me

Maybe just because of the easier to use CLI

I couldn’t even get started using the Sage CLI, but it could be that I didn’t try hard enough

Ben Steffan

tbf I've used neither much

Soham Saha

The online SageCell is pretty useful though, actually

Shareable code via links and all that

Ben Steffan

I've used SageCell for some light computer algebra but that's about it :)

Soham Saha

@BenSteffan same here, mainly some 3d plotting

Tapi

19:00

I'm reading the following theorem from the book on Brownian Motion by Mortars, Peres.

This is a part of the proof where they show that X is continuous a.s. at 0. Can someone explain this?

Bml

19:13

A long time ago I asked this question. I received a very good answer, but the result I need to arrive at is $h(u) = \dfrac{iR + u + i \sqrt{R^2 - u^2}}{2}$, with $u = x_1+i x_2$. I must somehow prove that this analytic function describes the conformal map I refer to in the question. Can anyone help me out?

Ben Steffan

21:30

did not want to read the words "addition formula for the elliptic integral $\int_0^x \frac{dt}{\sqrt{1 - t^4}}$" in a textbook on stable homotopy theory today but here we are

now I understand why J. P. May has never really done chromatic stuff

Oceans Bleed

21:57

@Shaun I mean I would love to discuss them, although I'm too busy for the next two weeks

Sine of the Time

22:10

this is interesting

hbghlyj

23:07

I am reading section "6 Proof in 3-d" of arxiv.org/pdf/1109.0595 The expected projected area of a surface element dA is obtained by integrating cos θ. Can someone explain why sin θ is there? Why is the integration dcos(θ) and not dθ?

Creationism vs. Materialism/Naturalism

Transcript for

$Mathematics$ Mathematics