The h Bar

Sha Vuklia

10:00

@yuggib that's why our work load is like +50% :P

Kenshin

@yuggib na they're synergistic

Sha Vuklia

definitely ^

yuggib

@ShaVuklia but not +100%, that's the problem

Avantgarde

you can do physics without learning math on the side. Most do that. Some choose to do both as well, which can be nice. So use that opportunity to the best

yuggib

@ShaVuklia you clearly don't know them at a research level; they're miles apart ;-P

Sha Vuklia

10:01

hm yea ok, each to their own

lol ofc not, i'm a first year student:d

Slereah

well it depends what you want to do

a lot of math isn't properly defined for physics

or it's not rigorously used in almost all of physics

Avantgarde

@ShaVuklia What math courses have you done till now?

Kenshin

leave her alone dude

yuggib

@ShaVuklia I am saying that, as far as I know, focusing on one and then studying the other afterwards if needed yields better results

Kenshin

@yuggib we're scientists here, do you have any supporting evidence of reasonable sample size/

Avantgarde

10:03

Depends on the person, yuggi

Kenshin

^

for those who have the capacity, they will be served well learning both simultanously

yuggib

@Kenshin Well, I have a reasonable sample size in the community at the intersection between math and phys

Sha Vuklia

analysis 1,2a,2b,3:P linear algebra 1, and 2-ish, algebra, basic math, latex/mathamtica, intro to probability theory, and maybe some that i forgot

yuggib

and btw, what does it mean that you're a "scientist"? :-D

Sha Vuklia

oh and graph theory

Kenshin

10:04

@yuggib we like the scientific method here

Avantgarde

@ShaVuklia That's pretty nice. And what? You were TAUGHT latex and mathematica?

Sha Vuklia

lol yea it was a 4-week course

Kenshin

@yuggib a scientist is one who uses the scientific method

Sha Vuklia

like we had to program little stuff

it's a normal course, physicists have it too

not just mathematicians

Avantgarde

Damn man, that's great. I had to learn it myself

Kenshin

10:06

yeah don't tell yuggib that you learn't programming as well

yuggib

@Kenshin interesting, I would define scientist a professional working in a scientific field (with the scientific method, of course)

Sha Vuklia

yea i'm glad i was introduced to it:P otherwise i would have never used it on my own

Kenshin

@yuggib yet many scientists in our history were not professionals working in a scientific field?

Avantgarde

Yeah, the more you code, the easier you get with it. Like with all other things

yuggib

@Kenshin if you say so..

I am looking forward to see your scientific contribution then

Kenshin

10:08

I don't publish my "contributions"

I work in finance dude

why so pretentious?

yuggib

you said "we're scientist here", not me

Kenshin

yeah because to me a scientist is one who subscribes to the philosophy of the scientific method

rather than a job per se

I believe my definition is more historically accurate

yuggib

I believe not

Kenshin

and then here you are asking for my "contribution" like wtf

@yuggib perhaps thsi wll help

"A scientist is a person engaging in a systematic activity to acquire knowledge that describes and predicts the natural world. In a more restricted sense, a scientist may refer to an individual who uses the scientific method.[1]"

Scientist

A scientist is a person engaging in a systematic activity to acquire knowledge that describes and predicts the natural world. In a more restricted sense, a scientist may refer to an individual who uses the scientific method. The person may be an expert in one or more areas of science. The term scientist was coined by the theologian, philosopher and historian of science William Whewell. This article focuses on the more restricted use of the word. Scientists perform research toward a more comprehensive understanding of nature, including physical, mathematical and social realms. Philosophy is today...

The term scientist was coined by the theologian, philosopher and historian of science William Whewell.

I see nothing about "paid professional" here do you?

QED

Avantgarde

Do you use a lot of math in finance?

Slereah

10:20

Yes

Kenshin

@Avantgarde yeah but moreso alot of complex problem solving that may not necessarily involve maths

Slereah

Mostly stochastic processes

Avantgarde

so lots of probability and calculus?

Kenshin

lots of probability

stochastic calculus if you work in derivatives

Avantgarde

interesting

yuggib

10:21

@Kenshin it says systematic activity, that does not mean paid, but means that it produces some output

Kenshin

@yuggib no, activity doesn't require output, it merely requires activity

Slereah

there is actually some links between financial theory and quantum mechanics

Kenshin

activity without output is still activity @yuggib, you should know this

Avantgarde

yeah I know

Slereah

Sometimes called by the name "quantum finances"

ACuriousMind

10:22

@Kenshin Honestly, that was a fair reaction to you calling him a troll. yuggib has first hand experience in switching between mathematics and physics and I can attest to his claim that if you try to hold physics to the standard of math while learning it you will make yourself very unhappy. Most of math is utterly useless for most of physics (and vice versa), the intersection where the two are reasonably close is very narrow. (cc @ShaVuklia )

Kenshin

@yuggib and output doesn't always have to be published

ty @ACuriousMind

Avantgarde

I wonder the success rate (or probability :P) of quantum finance

what's the*

Kenshin

probably not very high

Slereah

well some people make a fair living with short term financial models

Long term predictions are harder

Kenshin

long term predictions are actually easier

long term diversified stocks rise 8-9%

Slereah

10:27

market crashes aren't too easy to predict

Kenshin

correct but they can happen in the short term too

but you can usually ride them out over the long term

like houses in the USA are already above what they were before the 2008 crash

or at least very close

John Rennie

When the site tells you one or more questions have changed, is there any way to find out which questions have changed? As it is, unless when you refresh the page you spot a new answer or score change you have no idea what to look for.

Kenshin

?

what site

Slereah

10:43

a site called "stack exchange"

Kenshin

oh interesting

John Rennie

@Kenshin If you have the PSE home page open then you get periodic notifications that a question has changed (as well as notifications that a new question has been asked).

Kenshin

oh didn't know dat

Sha Vuklia

Guys, the math chat is dead, so I'm hoping I could try here: Say we consider exponential decay $N(t)=N_0e^{-\lambda t}$. Now we can normalize this formula to convert it to a probability density function. We get $\lambda e^{-\lambda t}$, which is the probability density function of the exponential distribution.
This is all fine and well, but I don’t understand why we were converting to a probability density function in the first place, and not for instance to the distribution function? What is the ‘intuitive’ (or maybe even mathematical reasoning) for this?

Kenshin

by distribution function, do you mean cummulative distribution function?

Sha Vuklia

10:47

yes

Kenshin

I much prefer working with probability densities than distribution functions

Balarka Sen

probability density is not very physically meaningful though

Kenshin

yes it is

Sha Vuklia

well i've learned them as probabilities in my math course, but here in the case of exponential decay, i'm not sure in what way to think

i mean, i can read the answer, but i don't really see why they chose it this way

Balarka Sen

@Kenshin hm?

Sha Vuklia

10:48

maybe i could think of it as the probability times $dt$ ?

Kenshin

I can't tell you why they chose that way @ShaVuklia, it depends on what they do with the density function

Sha Vuklia

so if it's normalised, that gives us the fraction that we have

Kenshin

@ShaVuklia are you asking what is the meaning of a probability distribution function?

Slereah

"Has anything precise been written about the Fukaya category and Lagrangian skeletons?"

Lagrangian skeletons???? D:

Wrichik Basu

Very sorry to interrupt in an important discussion. I want to read and get a good hold on the topic of tensors. Can anyone refer a good book on it, perhaps one used in undergraduate level?

Kenshin

10:49

@WrichikBasu i would but not now due to your interruption

Sha Vuklia

lol

same

like, i'm out of my flow now

Kenshin

@ShaVuklia suppose f(x) is a probability density function

Sha Vuklia

(jk, i wouldn't know how to help ya sorry @Wrichick)

Kenshin

and say f(x) is the probabilyt density function of decay, and say x represents time

Balarka Sen

in my dictionary, probability distribution function <=> cumulative frequency

John Rennie

10:50

@ShaVuklia the probability density $P(x)dx$ gives us the probability that the system has a value of $x$ between $x$ and $x+dx$.

Kenshin

@ShaVuklia then this means that f(x)dx represents the probablity of decay over time dx

Sha Vuklia

yea exactly, I get it

thanks guys

Kenshin

however

John Rennie

:37320876 Oops :-)

Emilio Pisanty

Are the group theorists around?

Wrichik Basu

10:51

I don't need any more help. I've understood. I'll help myself as I've always done.

Kenshin

@ShaVuklia

@WrichikBasu iawa jokin

@ShaVuklia it is better in this case however to look at the probabilty density of survival (as opposed tod ecay)

Sha Vuklia

lol @Wrichik that's life. we're all on our own:P

Emilio Pisanty

@Slereah you do groups, right?

Slereah

>implying probabilities make sense in a non-frequentist sense

Sha Vuklia

oh really? @Kenshin

Kenshin

10:52

yeah

Slereah

Bayesians get out

Kenshin

if f(x) is probablity density of survival

Slereah

@EmilioPisanty To some degree

Kenshin

then integral of f(x)dx is probability of survival over range of integration

then if youw ant probabilty of death/decay

it is probabilty of surving * probability of dying just after

this will hopefully make sense as you progress through the topic maybe

Sha Vuklia

lol i'm only asking because of this mean time :P

Kenshin

10:53

just keep in mind, the probabilty of surviving from A to B and Bto C is the multiplicative

Emilio Pisanty

@Slereah I'm looking for some reference that classifies the subgroups of $U(1)\times U(1)$

Kenshin

but this doesn't work for dying

@ShaVuklia yeah these concepts are required to derive mean time

Emilio Pisanty

in principle shouldn't be too hard, right?

but it's turning out very hard to google

I'm obviously doing it wrong

Sha Vuklia

okay but i get it @Kenshin because for dying, you first need to have lived

Kenshin

yea

Sha Vuklia

10:54

so you multiply

Slereah

Wouldn't the subgroups of $U(1) \times U(1)$ just be the product of the subgroups of $U(1)$?

Kenshin

like probablity of dying at time between X and dX is probabilyty of surving to X then dying between X and dX

Slereah

I think the subgroups of $U(1)$ are mostly gonna be discrete rotations

Sha Vuklia

yes got it

Slereah

Although there's also the... rational rotations, I think?

And irrational rotations

Kenshin

10:55

coolz

Emilio Pisanty

@Slereah I'm mostly looking for copies of $U(1)$ which "wind" multiple times

Slereah

Those also form subgroups

Balarka Sen

@EmilioPisanty Sure, S^1 x S^1 is as a group isomorphic to R^2/Z^2.

Take a line with rational slope on R^2, and quotient down.

Emilio Pisanty

@BalarkaSen so I should just google for R^2/Z^2?

Or maybe it's just subsets of the type $\{(e^{ip\theta},e^{iq\theta}):\theta\in\mathbb R\}$ for $p,q\in \mathbb N$, and no more mystery?

oh well

Balarka Sen

@EmilioPisanty Those are the closed non-discrete subgroups. You still have to take account to the discrete ones (which are all isom to Z/m x Z/n)

There are also non-closed subgroups (which are all isom to R)

user129412

11:03

I'm looking for a graduate level solid state textbook with emphasis on mesoscopic physics, topics such as nanowires for example. Anyone here particularly fond of a specific book? I've had a look at Semiconductor Nanostructures by Thomas Ihn, which is nice and rather elaborate in that a lot of topics are covered, but quite superficial. I'd look for a little more detail perhaps.

Slereah

@BalarkaSen Is that the rotations by $\theta \in \Bbb R \setminus \Bbb Q$

Balarka Sen

@Slereah a rotation is not a subgroup... it is quotient of a line of irrational slope on R^2, yes.

It's a real line which wraps around the torus a lot. Eg in Emilio's representation, plug in $p = 1$, $q = \sqrt{2}$.

Slereah

@BalarkaSen Any clue of the name of the theorem relating sections of bundles and their retracts?

Having a hard time finding much

Balarka Sen

I think I just answered you that? The retraction info is totally irrelevant.

Slereah

OR IS IT

Because I don't think it's actually a subbundle

Balarka Sen

11:12

Well, then what you told me to prove is wrong :P

Slereah

Since I don't think $Gr(n,1)$ is a subspace of $O(n) \times Gr(n,1)$

It is just a retract of it

Hence you cannot form a subbundle of it

$Gr$ isn't a vector space, right?

Or the space of metrics, for that matter

Balarka Sen

Er, no, it isn't. What is it relevant?

Slereah

Aren't subbundles supposed to be subspaces of a vector space?

Balarka Sen

... bundles are not vector spaces. I don't understand that comment.

Slereah

I am usually confusing the bundle and the fiber :p

But you know what I mean

Balarka Sen

11:15

Fibers of a bundle is not usually a vector space. Those are vector bundles.

Slereah

Yes

Don't subbundles only apply to vector bundles?

Which I do not believe the space of metric is

Balarka Sen

@Slereah Nah.

Slereah

What is a subbundle then

is it just any bundle with a fiber that's a subset of another bundle's fiber?

Balarka Sen

Yep.

Slereah

Ah yes

Then I think it should be fine because I think you can define the subbundle with fiber $\{ I \} \times Gr(n,1)$

Balarka Sen

11:18

what is your fiber bundle?

(and what's the base space?)

Slereah

No vector bundle

The original bundle is $\pi : S(n,k) \to M$, the bundle of symmetric matrices of signature $k$

With the identity $S(n,k) \approx O(n) \times Gr(n,k)$

Balarka Sen

Ok. And you're working with $k = 1$?

Slereah

Well Steenrod's theorem is for arbitrary $k$, but $1$ is the one of interest for GR

Balarka Sen

@Slereah What is Gr(n, k)? Grassmannian of the tangent bundle of $M$?

Slereah

Yes

Xasel

11:21

Hey everybody can somebody explain me meaning of this mathematical ststement

f(x) - f(u) > -infinity

for more context

u is set of values for which f(x) is minimum/haslocal minimas

Balarka Sen

@Slereah The identity you're giving is a diffeomorphism of the total space S(n, k) with O(n) x Gr(n, k). In what sense is the latter a bundle over M?

There's some detail-thrashing I am worried about here.

Slereah

If there's a diffeomorphism between the two fibers isn't there a diffeomorphism between the two bundles?

Balarka Sen

Diffeomorphism between two total spaces, you mean?

Slereah

yes

Balarka Sen

(1) in this case, I don't even know in what sense O(n) x Gr(n, k) is a bundle over M (what is the bundle map?) (2) no :P

6

Q: Nonisomorphic vector bundles with diffeomorphic total spaces

What's an example of two non-isomorphic vector bundles $E,F$ over the same base such that the total spaces $Total(E), Total(F)$ are homeomorphic? Assume that rank of these bundles is the same as dimension of the base manifold. (EDIT: Mike Miller brought up the excellent point that I need to loo...

Slereah

11:26

Well Steenrod has more details but I'm in class right now :p

Like he spends a bit doing some witchcraft with the local trivializations

But I forget what

Balarka Sen

Alright, let me know if you end up looking at S-dawg or want to thrash detail

Slereah

I'll try

But if there's a diffeomorphism $\psi$ between the fibers, wouldn't $\pi \circ \psi : E \to M$ be a fiber bundle of fiber $O \times Gr$?

or something, I'm not sure

I slept like 4 hours

user228700

YES! Coldplay is releasing their new EP at the end of June!

Balarka Sen

You do get a diffeomorphism S(n, k) = O(n) x Gr(n, k) between the total spaces, but when you compose that to get O(n) x Gr(n, k) as a bundle over M, is it clear what the fibers are? I am not so sure.

Gr(n, k) --> M may not be a subbundle of that.

(Which brings us back to your original worry)

Slereah

I guess Steenrod probably has the details

Though I'm not gonna read steenrod tonight I think

Too tired

Sha Vuklia

11:32

Hm, I still don't understand entirely... I see that if we normalise a function, we get a density function. But I don't see why it is the density function of the distribution that belongs to the function? Like, in my eyes, it's kind of random.

Balarka Sen

fair me neither

Slereah

Assuming it is a bundle, tho

And there's a retraction to something like $\{ I \} \times Gr$

Which also forms a bundle

Does that mean that a section of $Gr$ implies a section of $S(n,k)$

Balarka Sen

If I x Gr/M is a subbundle of S(n, k)/M, you get a section. Totally, yup.

Slereah

Well, that is some progress, at least

Thanks

Sha Vuklia

(oh I think I see it. We then recognise it as the scalar of a density function)

Slereah

11:34

I guess I also need to show that $Gr$ having a section is equivalent to the Euler characteristic thing, but that's a worry for another day

the hairy balls

Balarka Sen

You're onto nonzero sections too?

Slereah

$Gr$ isn't a vector bundle, no?

I don't think it even has a zero

Balarka Sen

Yeah it isn't. So I am not sure I get what you mean by the Euler char thing

Slereah

I hear that $Gr(n,1)$ is equivalent to nowhere vanishing vector fields

Balarka Sen

Huh.

Slereah

11:37

So that this would imply the hairy ball theorem wrt the metric

Balarka Sen

I guess I haven't thought about it. fiber bundles are too hard man

literally no structure

Slereah

I'd say too much structure!

If I can just prove that theorem I will have done more work than every GR book ever written :p

Balarka Sen

you should write a new book then

Slereah

That is what I am doing

Balarka Sen

#brekthru

Slereah

11:39

Just a big block of GR theorems

Balarka Sen

gotcha

Slereah

It ain't easy

Some are hard to track down

Balarka Sen

It Ain't Easy David Bowie

►

Slereah

Also QFT stuff because I am a glutton for punishment

I just want to do semiclassical gravity :c

And yet I have to deal with functors and wavefront sets

I'm not even sure why they bother with wavefront sets since they have to renormalize anyway

the good products are all divergent

Balarka Sen

glad i dunno this stuff man

Slereah

11:46

basically you just define the QFT on open sets of the spacetime and then piece them together

So that the QFT is the same if an open set is in the chronological future of another

Balarka Sen

huh

Slereah

that kind of stuff

the net of algebra, as it is called

and that regions that can't be joined by causal curves have operators that commute

so that everything is nice and local

The hard part comes when you have to renormalize everything

Balarka Sen

isee.png

Slereah

Since there are several ways to renormalize everything

then you use the Wald big list of probably reasonable conditions for renormalization

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