HAHAHAHA rekt

a watchdog to discredit lying is a free market solution

The Pravda idea seems to be fundamentally standing upon silencing news organizations, not debunking false data.

Which is a dangerous move

but it does not matter, he is a private actor unlike the government

I don't understand your point.

meaning he has no authority

unlike the government

government = monopoly on the legitimate use of force

Musk = powerless if you have no faith in him

Elon Musk is an industrialist. Those are the people running the modern economy working under the principles of capitalism, not the government.

Sure his statements and actions influence the whole hierarchy

He doesn't have a power monopoly, sure, but that's off the point.

I agree he has power of the economy and you have every right to disagree with him

but his power is proportional to his contributions

and he really is still a small fish in the grand scheme of things

unlike the government that actually can transcend the economy

in which case, you should be afraid

I don't disagree.

am glad to hear that

Seems like we got some nerds in here

this is a math chat after all...

:O

I just think the idea of a private news-reviewing agency is good, but Musk's intention behind them trying to silence news organizations - which provide data that may or may not be systematically categorized as false by counterdata - is similar to the anti-media movement that's cropping up in the US which is dangerous. Being skeptic about data is good, silencing it isn't.

(That he's trying to silence a section of the media is evident from his tweets)

this is actually an interesting philosophical question

let me ask this

is it ok for the free market to silence news organizations, if the free market wants to?

I don't understand what "ok" means.

I think it'd lead to a destabilization of the dynamics

If drastic consequences are desirable, then it's ok, I guess :P

personally , i dont know, it seems like a tough things to figure out

I agree.

did you end up getting into the university that you wanted btw ?

@BalarkaSen

I applied to two. I think I'll get into one of them.

I hope you do

Thanks.

mathematicians are born not made, and not living like yourself, is hell

Meh, I think I'll be a-ok if I didn't study math.

really ?

Sure. I don't find life as an academician appealing, and I think I could do well if I studied, say, literature.

I think your classification of mathematicians was a dramatic cliche :P

wait a minute

i dont mean studying as being in academia , i mean just doing it, even in your free time

Oh, well, that's no way affected by my career choices :P

obviously , you like doing it, otherwise, you would not be here so often

yes, so what is the answear to my question, if i replaced studying with doing

even as hobby

What is your precise question?

how would you feel, if you were not allowed to do mathematics ever again, even as a hobby

We would go through withdrawal symptoms. Luckily math addiction doesn't have direct physiological effects.

I beg to differ

tiredness and hairloss

I saw you mike, at stony brook a month ago

Zee what do you mean by "born, not made"

@Zee I think I'd feel what Mike said. Kind of sad, a little pointless, but I'll pick up other things to do - like listening music and watching movies :P

If I had to give up math forever I'd go into physics rimshot

@GFauxPas Nice

"Mathematicians are born, not made". - Henri Poincare

@Zee Nice

Physics is cool

@BalarkaSen Nice

physics is math or totally not math

witten is a totally a mathematician in my opinion

It was a JOKE , semi don't hate me if you're here or even if you're not here

@BalarkaSen aka dead inside

Also I made myself into a mathematician, I wasn't born one. Proof by counterexample

same, but that means you were born one then made temporarily into not

@Zee Well, that's a stronk opinion :P I find listening to music and watching movies tenfold interesting than math.

Also if Poincare said that and you're not making it up, Poincare was a old hag and a cringy bat

i agree, but come on now, we both know its more than that

Okay I'm gonna describe a pigeon meme , I'm on mobile so use power of imagination

"we both know it's more than a strong position, it's an unreasonable one"

@GFauxPas I'm excited

The guy is labeled "math.se chat"

The butterfly is "pithy quotes that don't mean anything"

LOL

@MikeMiller LOL

And he's saying "is this mathematics?"

look, watching a movie is more fun than math, but i truly dont think its possible for a person born as a mathematcian to be truly happy doing anything else, movies are just a distraction

What do you guys think of my meme

@GFauxPas I think it's great and you should make it into reality

@GFauxPas agree

Maybe when I get home on my pc

@Zee Maybe you are born a mathematician and you're distracting yourself with the gibberish philosophy you're reading

Do some math brutha

haha you are the truth

Maybe I was born a movie-watcher

Who's distracting myself with mathematics

So I looked it up

i dont think your giving yourself enough credit

Poincare did in fact say it

I'm giving myself credit as a great watcher and critic of movies! I could be the next great, say, Roger Ebert

But the context is worth noting

He basically says that you sorta find two different kinds of people. Some who are principally preoccupied with logic, every step is slow but bulletproof, the other type of people who are bold and intuitive but precarious

The former are analysts and the latter geometers (even if some of the former work in geometry and vice versa)

Your not fooling me @BalarkaSen , its just a defense mechanism since you may actually be forced to abandon math by your circumstances but i truly believe, it is the most important thing in your life

And he was like yeah I don't think that's a question of just being trained one way or another, some folk just are how they are. That's the context of the quote "Mathematicians are born, not made"

www-history.mcs.st-andrews.ac.uk/Extras/Poincare_Intuition.html

the article called "the mathematician " right ?

"Intuition and Logic in Mathematics"

oh, ya, the other one is by Jon Von Nuemann :p

lol maybe i totally misunderstood

@Zee Yeah it started as a defense mechanism 'cuz I did badly at the multiple-choice section of the admission I'm hopeful about. I was sad a lot. But I asked people around and they said I'll make the cut-off just fine. So I think it's much more than simply a defense mechanism at this point, because I genuinely think broader life-goals are harmful to my sanity as a human being.

I have given a lot of thought to it over the last month

I don't value my goals of being a mathematician over my general well-being.

am in a similar situation , although , mine is more my own doing than circumstances, so i can relate to that

and your right, well being comes first, but by god

mathematics comes close

Hmm... politics and math career, hmm... (digesting...)

Maybe mathematics is essential to your well-being, that's entirely possible.

In that case you should do math.

ya ya but i think the same applied to you

Naw, I don't think so

maybe i am totally off, if thats the case , then , i have much to learn from you

I don't think you can really discern extremely how fundamental people's interests are to their lives except in really extreme cases

Yep.

Even if someone has a crapton of fun doing math, they may have other interests, stronger or weaker, that would adequately replace it

I agree but , i assume that you guys do more more math than me for various reasons, and if not for interest, and intrinsic love, than idk what for

and i think i love mathematics so , something is not clear here

It is for interest.

But you don't have to internalize that interest as an existential purpose.

That's unhealthy to the point of obsession

You can have interest and love ("intrinsic" isn't clear) but not be singularly cut out for it to the degree where you can't manage otherwise

i see

i find it very hard to relate to, but its very interesting

@Daminark The problem, here, of course, is how the socio-economic hierarchy stands as a wall against that replacement.

so you guys can really pursue something as a life career without framing it in existential terms ?

Working in a STEM field is perceived as "a greater job" by the society and economically pays off more, eg.

@Zee Overtime one has to learn to

Those who don't go through serious mental hardships over the course of their lives when faced in front of the slightest failures

Eg, equating "failing to understand a piece of math in a given amount of time" with "my life is a failure"

Those are some symptoms of the disease

well, am a bit conflicted

Evidently :)

is it that what am saying totally alien to you or

is it something you hve but got over

The latter.

@BalarkaSen I'm talking adequate strictly from a psychological standpoint, career is of course another consideration

@Daminark Ah I see.

@BalarkaSen ok, that is more familiar, was it a hard pill to swallow ?

@Zee Kind of, but it was a helpful resolution of the conflict.

I don't really buy the argument that STEM careers pay more. More than what?

And how are the comparisons being made?

lol construction workers in my neck of the woods make more than college math professor

Lawyers and MBAs typically make a lot more than I ever will.

And tradespeople typically make more early on (though they tend to top out lower? maybe?).

Say, an IT career.

@Zee scaffolders especially get paid very well

That pays off pretty well.

i know an electrician that makes 300k

IT is STEM, though.

or was that the point your were making?

That was the point, yes :P

@XanderHenderson there's probably a case that among careers that have less of an entry barrier, that STEM (really I think people look at engineers and CS folk) is generically more likely to be lucrative

The whole thing that goes on in India is a race towards the engineering and IT placements because of the whole socio-economic elitism of applied STEM fields

Perhaps, but, again, I'd like to see the statistics. Are we comparing bachelor's degrees?

look man, if you can study manifolds , you can get rich, its that simple in my mind

i.e. if you graduate from college tomorrow with major $x$, how much are you going to make over a lifetime?

Hmm, it's tricky to say what the optimal measurement standard is

math , philosophy , CS , economics, and phyics are the highest earners

over lifetime

also, what is the spread? someone with a teaching credential likely won't ever make as much as the average IT jock, but teachers typically have very stable employment, stable hours, predictable downtime, and a much narrower range of salaries.

so they might not make as much on the top end, but they are also less likely to make very little on the low end

Good point.

Stability is also very important.

who cares about money, give me 50k and am good for the rest of my life

I mean, if we want to ignore the spread, get an MFA

in film acting

Tom Cruise is nuts, and still makes more than a small army

that is where the money is

or, if you can't act, you could always hope to be Tom Brady

Jim Simons is where the money is at

he was giving a talk and i just left midway , couse, am a rebel man

actully, i like him but i got bored

"Hedge fund manager" is not a STEM career :)

The entertainment (and artistic) market is a prime example of where free market economy fails. Only an exponentially handful of actors are exponentially successful, say. Similarly, an exponentially handful of pop records get exponentially streamed.

actully, he was a mathematcians in making his money

read about him, intresting story

@XanderHenderson it's what mathematicians do when math doesn't work out :P

LOL

gets confused between communist Fourier and math Fourier

tfw they are the same persons

Weierstrass is actually Edmund Husserl adviser

who BTW weyl attended his lectures

Hilbert hated him for that

math gossip 101

This is such an awkward attempt by an underground rapper to show off as part of the Bling lmao youtube.com/watch?v=k4EX3iQ7eyw

I like it

well he does have many likes

free markey man

@Zee He made his money as a hedge fund manager, no? The fact that a math degree helped him out there does not indicate that "hedge fund manager" is a STEM career; only that it is a career in which a mathematics background can be helpful.

well Xander, you are right in the general case, but in this specific sense, this guy used fellow mathematicians, using mathematical methods to beat the market

We are talking orthogonally to each other, I think.

perhaps

@Zee Ugh

Most hedge fund managers have no more background in mathematics than the average Joe, and most people with degrees in STEM fields will have very little opportunity to make it rich as a hedge fund manager.

Yes yes

We can always cite the outliers (Mayim Bialik, anyone? clearly a neuroscience degree is the way to make it big in sitcoms).

this guy was able to cash in big using his math background now, that means you can sometimes use that background, nonetheless, i do think , there are much easier ways to make money than learning math

I'd rather listen to mumble rappers than a guy rapping about how he doesn't give a fuck at every single sentence

But, as I said before, the spread (both in terms of the range and, say, standard deviation) is much more interesting.

I need Gucci Gang to bleach my ears

yes, we arent orthogonal but identical then Xander

@BalarkaSen the best rapper ever. from NY : youtube.com/watch?v=zFVUG0nMrMU

Oakland rap $\gg$ New York rap

@Zee Ahh this sounds great

Biggie is the best rapper to ever live FACT

he should get a fields medal

just... no

listen to him, he raps iike Riemann

too bad he got shot

So, less like Riemann, more like Galois?

hahaha

I liked that song!

am glad you did

I am so far into obscure shit that I don't really know about these great mainstream rappers.

Technically I don't listen to rap, but still

i dont much too , but he is the best to ever be, in my opnion, here is a couple more

Thanks, I'll listen to them later.

am curious what you usually listen to

I listen to rap but rather uh strange ones

But otherwise I like metal, etc

am listening

here is the king of NY

ok enough for now, i gotta read about operators now

The raps which are in my "one of the top 50 songs of all time" list are this and this.

That should give an idea of how weird my taste in that genre is :P

yes, def not canonical . but i like weird!

wow that is weird :P

lol

thats great though, most people cant recommend anything different, so thanks

Glad you appreciate it. Most people don't when I link nerdy rap lol

i dont know whats going on , its like i am in the dark matter of youtube

damn you sen

ok thats enough for me, bye yall

Death Grips is extremely weird.

hmm my lecture notes say that inversion in the unit circle maps straight lines not through the origin to circles through the origin

but I'm fairly sure that's untrue

That is true.

bleh

Why do you think otherwise?

(This is not an inquisition: I think you will understand the whole situation better if we figure out the origin of the confusion)

if I take $ax + by = c$ as my straight line and map $(x,y) \mapsto \left( \frac{x}{x^2 + y^2}, \frac{y}{x^2 + y^2}\right)$ I get a circle not centred at the origin don't I?

($c \neq 0$)

You'll get a circle passing through the origin

Not centered at the origin

ohhhh

that makes more sense

lol

'Cuz infinity maps to the origin by inversion.

Right

Thanks

misunderstood the wording

I really like this little corner of geometry! I only learned it this past year. I hope you enjoy it :)

it's interesting but I've an exam in it in about 5 days and I've spent all of the time I could've spent learning it doing algebra and number theory for my dissertation

Regarding Death Grips, this is kinda sick

I'm retroactively liking it.

@BalarkaSen better give it some Tylenol

the flies may vomit them out

O no

@ÍgjøgnumMeg which corner of geometry is this?

@Daminark inversive geometry, leading into hyperbolic geometry

I see

we've basically crammed affine geometry, hyperbolic geometry, and projective geometry, into half a 1 semester long module

really dislike the way my uni does things

lol

That sounds fun but also really intense

I suppose it's interesting, but I'd rather have an in depth intro to one topic than trying to cram lots of stuff in

Was this just "generic intro to geometry"?

Yeah the module title is "Geometry and Algebra"

the algebra half is a basic intro to algebra

and the geometry half is a generic intro to geometry

lol

with barely any crossover

lamo

"series" is both plural and singular?

I want to say "two serieses"

or "one serie"

"three seres"

"four serii"

yeah "two series"

serieseseseseseses

You add another "es" for every series you're talking about

Please someone check if this is correct:

Hmm, so $xyx = y^2$, meaning $y = xy^2x = (xyx)^2 = y^4$, so yeah

Thank you very much

Would $x=(12)$ and $y=(123)$ satisfy that?

$xyx=y^2=(132)$, so yeah

In fact, I think $\langle x,y\rangle$ is necessarily isomorphic to $S_3$, with $x\mapsto(12)$ and $y\mapsto(123)$ defining the isomorphism, so the above example is essentially unique.

Odd-ball weirdness: two copies of RP^3, delete 3-balls from each. Glue them by (1) the identity homeomorphism $S^2 \to S^2$ along the boundary of the deleted balls or (2) by the antipodal homeomorphism $S^2 \to S^2$ along the boundary of the deleted balls. The results are $\Bbb{RP}^3 \# \Bbb{RP}^3$ and $\Bbb{RP}^3 \# \overline{\Bbb{RP}^3}$ respectively

The first is orientable (as RP^3 is orientable), the second isn't.

I don't believe that

Isn't $\rm\Bbb RP^3$ too symmetric for that?

I guess it's not that hard to see. Take two RP^1's in RP^3. After the second operation, they give a loop given by an arc on both copies of the connected sum so that they are flip-glued along the $S^2$ it's connected summed along

That loop reverses orientation, I think

@Akiva Not sure what that means.

Wait, I think I was visualizing it wrong

I realized this while writing down a proof that the second thing is the mapping torus of the antipodal map of $S^2$.

@BalarkaSen I'm not sure I understand

Which is a non-orientable manifold for sure

I mean, hold on

$\rm\Bbb RP^3$ is $B^3$ with the boundary identified to itself under the antipode map, right?

One of the many ways to represent it as such, yes.

It's also a spherically symmetric way to represent it

Both connect-summed manifolds just look like $S^2\times I$ (a spherical annulus) to me where each of the two components of the boundary is identified to itself by the antipode map

Wait, I'm confused. $\Bbb{RP}^3$ is homeomorphic to the unit tangent bundle of $S^2$. Fill in the circle fibers by disks, that gives a 4-manifold with boundary $M$ such that $\partial M = \Bbb{RP}^3$. Consider $M \times I$ and delete a neighborhood of $\{x_0\} \times I$ from it for some $x_0 \in M$. The boundary of that manifold is $\Bbb{RP}^3 \# \overline{\Bbb{RP}^3}$. $M$ is orientable as fuck, how can boundary of an orientable manifold be non-orientable. That would be garbage.

…Why is $\rm\Bbb RP^3$ homeomorphic to the unit tangent bundle of $S^2$

Long story

In any case I agree that it's garbage

It shouldn't be, because some other computation says it's nonorientable.

Meh, I'm sleepy. RP^3 x I, delete an nbhd of {x0} x I from it. That bounds RP^3 # overline{RP^3}, is what I meant. But that manifold is orientable as hell.

Because RP^3 is orientable.

I don't get it.

This is like a general argument. If $M$ is orientable, take $M \times [0, 1] \setminus N_{\epsilon}(p \times [0, 1])$. The boundary of that orientable manifold-with-boundary is $M \# \overline{M}$, so it has to be orientable. ???

Hey

This is a classic problem, but I am somewhat stuck. Let $f \in L^1[0,1]$, then I am to compute $\lim_{n \to \infty} \int_{0}^1 x^n f(x) dx$

I tried Dominated Convergence by setting $g_n = x^n f(x)$

But it is not clear to me how to reduce $\lim g_n$

@AkivaWeinberger Thanks for the suspicion, I suspect my other computation is incorrect, and I think I see why.

That was helpful

The correct bit of my calculation says RP^3 # overline{RP^3} is a circle bundle over RP^2. I was mis-identifying which circle bundle it is (a certain nonorientable manifold is also a nontrivial circle bundle over RP^2)

So if $M$ is orientable then so is $M\#\overline M$. Can $M\#M$ be nonorientable?

Generalization:

If $A$ and $B$ are orientable, is $A\#B$?

Of course.

So that tells you your thing is garbage immediately.

Yeah, s'pose so.

'Ncouragement

I was rather confused because it seemed plausible that if you sum a manifold and it's orientation reversed copy togather you'd get something not orientable.

@Akiva Is RP^3 # RP^3 actually homeomorphic to RP^3 # overline{RP^3}?

I think so

I know that CP^2 # CP^2 and CP^2 # overline{CP^2} aren't homeomorphic but I forget the proof.

Is there no orientation-reversing homeomorphism from $\rm\Bbb CP^2$ to itself?

Ah, bingo, indeed.

That's strange.

RP^3 clearly has one.

@AkivaWeinberger The proof exploits that $H^*(\Bbb{CP}^2) \cong \Bbb Z[x]/(x^3 = 0)$, I think. Any homeomorphism gives a ring automorphism of this ring.

If it reversed orientation it'd send $x^2$ to $-x^2$.

But that's impossible: Send $x$ to $nx$, then $x^2$ goes to $n^2x^2$, and $n^2 > 0$.

Ah, cool.

$x$ has to go to $\pm x$, as well, no?

Fair point, yeah.

$x$ is in $H^1$?

$H^2$ :)

Corresponding to the CP^1 in CP^2

$x^2$ is in $H^4$?

Yep.

Why would an orientation-reversing map send $x^2$ to $-x^2$?

Oh, 'cause it's 4D? Is it always gonna mess with the thingy of highest dimension?

That makes sense

Because orientation is choice of a generator of $H^4(\Bbb{CP}^2)$, yeah.

Thanks a lot! You just helped me remember a lot of math I'd forgotten