The h Bar - 2016-01-14 (page 3 of 3)

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6:17 PM

@DanielSank : I think the LaTeX part is off-topic. I answered because I wanted to stress that the horizontal notation actually might contain important mathematical information. But I don't feel strongly about the question if the community wants to close it.

@Qmechanic I don't want to close it. Seems like a question I'd want a physicist to answer.

@DanielSank not sure but there is a related relation that is used a lot in optics and condensed matter physics and possibly statistics

which is the Kramer-Kronig relation

I need to somehow combine that and optical theorem to get some position space version of optical theorem

6:33 PM

@DanielSank I'm with Daniel on keeping this one. It's a question where a mathematician would go "meh! why are you worrying about that at all?".

@EmilioPisanty I made the case a while back in the meta that the answers invited by a question are more important than the question itself. whether or not that's really objectively true, I think it's an important aspect to consider when deciding on-topic-ness. In this case, as the asker is working in a physics context, they really want to know what a physicist's convention is, not an arbitrary user of the mathematical tool at hand.

So yeah, an arbitrary mathematician probably doesn't have the context and opinion the asker wants.

@FenderLesPaul Aha! Is that it? Could you educate me on how Kramers Kronig relates to diagrams?

I've seen several other places where diagramy stuff shows up in fields other than QFT. For example, when understanding how to think about signal flow in a microwave scattering system one winds up using diagrams with similar rules to Feynman diagrams...

6:50 PM

@DanielSank so in the context of QFT, kramers-kronig comes from micro causality of correlators (which is related to analyticity of correlators i.e. correlators are analytic everywhere except at branch points coming from where light cones are) and says that the real part of any loop diagram is equal to the cauchy principal value of the imaginary part of the diagram when you write the associated correlation function in the complex plane

or vice versa

Huh, I think I knew that

at least that's how I understand it

and am attempting to use it

@DanielSank I did, earlier

And now I am back again

I would still like to know why you think I'm a butterfly

0

Q: Move focus to text box when editing favourite tags

I'm not sure whether this is a problem with the new design or if it was there in the old one, but it's there. If I click on the edit button on the Favorite Tags sidebar, it brings up a text box and an Add button, as well as deletesy xs on the tags that are already there. It doesn't however, mo...

Whoa we have new profiles

How does this work now

6:55 PM

@0celo7 You have a profile page with information on it that you can read and links that you can click?

About the same as the old one, except much prettier

@EmilioPisanty "information"? "Links"?

What is this sorcery

7:11 PM

Hope I'm not intruding. Just wondered, after trickling through Chemistry Chat, if there's someone in here who'd be able to hint me a jumping-off point in terms of what to search for when I'm looking for a pigment that stays on/in skin over several days, washing or not.

@ACuriousMind o_O

Ah, yes, I think I get it.

Yes yes.

@0537 I doubt you will be doing any heavy computation, so Python should be fine. Especially I guess if you use a subset that PyPy or some more efficient implementation can compile/JIT. Pick whatever you are comfortable with.

7:36 PM

This seemed more like a physics question to me. Just in case somebody here feels like helping that guy:

in Calculus and analysis, 50 mins ago, by rcty

While going through the derivation of contact time for a hertzian contact as given in problem 3 at the following link http://s17.postimg.org/t1kq6mlxr/Capture.png , I am not able to understand how the integral form for contact time has come into picture. I understand that this is a very trivial problem but it will be a great help to understand the steps.

7:49 PM

What do you think of that? mvkonnik.info/2015/11/… Career in Science and Engineering - a road to misery, poverty, and SUICIDE

similar to "Don't become a scientist" by Katz but seems to be followed by suicide

8:16 PM

Henna (Lawsonia inermis, also known as hina, the henna tree, the mignonette tree, and the Egyptian privet) is a flowering plant and the sole species of the Lawsonia genus. The English name "henna" comes from the Arabic حِنَّاء‎ (ALA-LC: ḥinnāʾ; pronounced [ħɪnˈnæːʔ]) or, colloquially حنا‎, loosely pronounced as /ħinna/. The name henna also refers to the dye prepared from the plant and the art of temporary body art (staining) based on those dyes (see also mehndi). Henna has been used since antiquity to dye skin, hair and fingernails, as well as fabrics including silk, wool and leather. The name...

@NeuroFuzzy So simple.... Thanks

@user444214 Sad. But it's not like this is only an issue with academia. Jobs in general are difficult to come by and are immensely competitive: The brilliant professor of the article who "could [have] without too much trouble become a managing director at an investment bank or a portfolio manager at a hedge fund and make $1m/year" ended up as a bus driver.

I'd rather compare academia to the music industry: Your career largely depends on citations (album sales) and the top of the field are probably in both cases characterized by a power law, perhaps arising from the snowball effect. I'm sure many brilliant musicians never manage to make a decent living out of music. The same is true in science.

And like in music, also in science a lot of the funding goes to the popular sort of research, not the innovative and good sort of research.

I don't think that's grounds to kill oneself, but rather maybe realize that this idea of academia being an idealized meritocracy is outdated if it ever was true. Now probably only the good scientists will be remembered, but those might not be the rockstars with hot careers. I was very sad when at some point I came to the realization that the thing that I always had wanted to be, a scientist, was actually not at all what I wanted to be.

@Asmyldof np!

@alarge Scientific computing in Python isn't really Python anyway, it's usually just a easy-to-use Python wrapper around compiled C libraries.

@yuggib 3/25 people in PDE are not engineers

8:35 PM

@endolith Fail enough. But that said, you will probably end up writing quite a few loops anyway, and these are typically inefficient in Python (obviously one always tries to just use matrix operations with NumPy, but still).

8:46 PM

SchrodingersCat, India

1.7k 2 6 20

homework-and-exercises newtonian-mechanics classical-mechanics electric-circuits electromagnetism newtonian-gravity electrostatics

> I believe physics has the solution to all the global problems.

Nukes are physics, and they can certainly solve all problems.

Although that solution is like the $u\equiv 0$ solution for homogeneous equations.

9:20 PM

@NeuroFuzzy that literally looks like smeared feces on some parts of the hands...

@0537 : hi. Sorry to be slow replying, I've been tied up since Wednesday, on a course.

@ACuriousMind When I was asking about "does the mathematician's notation have advantages" I was not really talking about coordinate free...I mean is there any conceptual advantage to writing e.g. something like $H(x,y)=\langle B(x,y),\eta\rangle $ over simply $H_{ab}=\eta_cB^c{}_{ab}$

@ACuriousMind One of my profs said $R(X,Y)Z=\nabla_X\nabla_YZ\cdots$ is much nicer and conceptually clearer than $R^i{}_{jkl}=$mess of stuff

I agree with that

why is this starred?:

13 hours ago, by DanielSank

@TanMath I'm trying to figure out whether or not several of your recent comments indicate a massive lack of respect.

and is this unclear?:

-1

Q: Lindblad equation with non-Hermitian Hamiltonian

I have a Hamiltonian for 7 sites that is non-Hermitian. This is since the trapping Hamiltonian (only acting on site 3) causes the trace not to be preserved. However, I need to solve the Lindblad Equation. But the Lindblad Equation, by definition in some textbooks, is only for a non-Hermitian Hami...

computational-physics open-quantum-systems

@0celo7 ?

9:35 PM

@yuggib Most of my PDE classmates are engineers

@0celo7 ah...

probably mathematicians do the course only later

or in your university there are not many wanna be analysts ;-P

@yuggib probably

But I am an engineer.

technically, you want to be both

so what did you learn today?

@yuggib By school law he droned on about the syllabus for a bit. Then we reviewed some important things from ODE and vector calc.

He wrote some of the equations we'll study

Heat, Laplace, Wave, Schroedinger

We talked about linear operators, boundary conditions

He derived the heat equation (was pretty random)

:-D

9:44 PM

We ended by separating variables for the 1D heat equation

What really bothers me is that he wrote $$\int\int\int \mathrm{d}V$$ etc.

I am NOT writing multiple integrals

:o

I need to check that just writing $\int\mathrm{d}V$ is ok

no mathematician do that I think

They do in courses populated by engineers

usually I write $\int dx$

9:46 PM

@yuggib In geometry I write $\int\mu$

or, to be pedantic, $\int_{\mathbb{R}^d}dx$

or if I feel really smart I'll write $\int\star f$

yeah, but really do not matters so much

the triple integral, however, looks ugly

No talk about regularity or distributions or topology

@0celo7 and probably you won't I am afraid

9:48 PM

@yuggib his PhD is in applied mathematics

define applied mathematics

it's what's on his CV

beats me

> Thesis topic: Shear stabilization of morphological instability during directional solidification

does not sound so mathematical...

He's spent time at UCLA, Princeton and NYU

the univs are good

9:50 PM

PhD from Northwestern

Never heard of the undergrad school.

My analysis prof is like an 18yo Japanese math PhD

It's pretty ridiculous

@0celo7 :-D

are you sure about the age? some asians seem ageless

He's probably older...but still

Also he says "erement"

Analysis was boooooring

His research: stochastic integration, stochastic differential equations, anomalous diffusion, fractional partial differential equations

arxiv.org/pdf/1408.4377.pdf

seems mathematical

do you know at what age Terry Tao got his PhD?

@yuggib young enough to make all of us look stupid

not as I thought

21

9:55 PM

uh

that's pretty young

when did you get yours?

much later

but he passed the admission test for university at 12 or 13 I think

In analysis we pretty much did review

@0celo7 yep

but beware of japanese mathematicians

3

they can be a little bit dry, in style

speaking of dry

I have to read some sections in my algebra book for tomorrow

good reading

10:00 PM

Oh it's just review of induction, the binomial theorem and complex numbers

I'm not sure I need to read it.

usual induction or transfinite induction? :-P

@yuggib transfinite induction?

yeah...usual induction is boring :-)

Theorem 1.4 (Mathematical Induction) Given statements $S(n)$, one for each natural number, suppose that (i) $S(1)$ is true; (ii) if $S(n)$ is true, then $S(n+1)$ is true. Then $S(n)$ is true for all $n$.

I still have some books to buy!

@yuggib What's a good intro algebra book?

@0celo7 that I really don't know

10:08 PM

The prof recomments Artin to supplement our book.

But Artin is el expensivo

Theorem. (Transfinite induction) Let P be a property such that
i) $P(0)$ holds;
ii) $P(\alpha) \Rightarrow P(\alpha+1)$;
iii) if $\gamma$ is a limit ordinal, $\{P(\beta),\beta<\gamma\}\Rightarrow P(\gamma)$.
Then $P$ holds for all ordinals

Yeah I don't know what that means.

@0celo7 I have heard about it, but I don't know it

@0celo7 the same as yours

I don't know what an ordinal is.

@0celo7 natural numbers are ordinals

10:13 PM

then why not just say "natural numbers"

because there are other numbers in the ordinals that are not the naturals

also, defining the naturals to start from 1 is, in my opinion, unnatural

you're like the germans

what

in germany, they always define the naturals starting with 1 instead of 0

and that is unnatural in my opinion

I'm probably the only person in my PDE class who remembers what Dirichlet boundary conditions are using D-branes

@yuggib not as unnatural as your face

::kill confirmed::

@0celo7 well I did a course on matrices where I proved everything using operator theory :-D

10:21 PM

@yuggib well aren't you smart

@0celo7 no simply I never studied matrices, but I had studied operators

so it was easier that way

@yuggib so can you prove "every symmetric matrix is diagonalizable" using only operators

@0celo7 ahahah yes, but that would be masochism

@yuggib why

because it would be unnecessarily complicated

10:24 PM

Proof?

in the first place, you have to define compact operators

@yuggib btw something written by my PDE prof: math.utk.edu/~schulze/paper22.pdf

@yuggib why

@0celo7 seems pretty applied

@yuggib Yeah, he doesn't do multiple integral signs in his pubs

0

Q: What can we do about imperfect transitivity in marking duplicates?

Consider the following chain of questions, presented in chronological order: Redshifting of Light and the expansion of the universe Have red shifted photons lost energy and where did it go? Do photons lose energy due to gravitational redshift? If so, where does the lost energy go? Redshift due ...

discussion duplicates

10:30 PM

@0celo7 because if else you cannot prove what you wanted with operators

10:44 PM

@yuggib why

Question: what would the analog of Dirichlet boundary conditions be for a null surface, for the problem of solving for the Hamiltonian of vacuum GR? Would it just be $\delta q^{ab} = 0$ where $q_{ab}$ is the transverse 2-metric, or would it be that plus the condition that $\delta l^a = 0$ where $l^a$ is the null geodesic generator?

@0celo7 because (almost) only compact operators are diagonalizable, and the matrices can be seen as compact operators

what's a compact operator

an operator that maps bounded sets to relatively compact sets

(relatively compact means that the closure is compact)

11:10 PM

@yuggib ooh looks like the analysis reading includes a few pages on cardinality

fun fun fun

@0celo7 very well

@yuggib very...well?

so you will know what the cardinality of the continuum is

@yuggib is that a trick

is that some unsolved problem

no that's the continuum hypothesis

that is simply unprovable

but the cardinality of the continuum is known ;-)

11:13 PM

actually I don't think I will

I think you will

it seems like three pages of material and a billion exercises on countable/uncountable sets

then you will learn that reals are uncountable, and probably what their cardinality is

Theorem 1.5.6 (i) $\mathbb{Q}$ is countable. (ii) $\mathbb{R}$ is uncountable.

Well I already knew that...

I used it the other day for a geometry/topology proof. I think.

@yuggib Well what is the cardinality of $\mathbb{R}$

@0celo7 reals are cauchy sequences of rationals (and the rationals have the cardinality of the naturals)

therefore the reals have the cardinality of the power set of the naturals

11:21 PM

@yuggib yeah the book proves all of that

@yuggib hmm

@yuggib Ah, it's in the next section.

It's an exercise!

and therefore the cardinality is $2^{\aleph_0}$

@yuggib why $2$

because is the set with two elements

0 and 1

@yuggib what is the set with two elements

$\{0,1\}$

11:28 PM

@yuggib no shit, what does that have to do with anything

$2=\{0,1\}$

uh, what

it's the definition of $2$

fucking PhD set theory

@yuggib I'm asking why $2$ in $2^{\aleph_0}$

i'll answer you in ten minutes, I have something to do at home

11:46 PM

in set theory, the notation $A^B$ means the set of functions $f:B\to A$

Of course

and so $2^{\aleph_0}$ means the functions from the naturals ($\aleph_0$) to $\{0,1\}$

uhhhh

still confused

how would you express a part of the naturals?

huh?

11:48 PM

by a function that to each number assigns zero if it is not in the part, 1 if it is

ok...

therefore by a function from the naturals to $\{0,1\}$

i.e. the power set of the naturals is isomorphic to $2^{\aleph_0}$

that is also, incidentally a cardinal number

aha

and since also $\mathbb{R}$ is isomorphic to the power set, it is isomorphic to $2^{\aleph_0}$

@yuggib I'll probably try to prove that over the weekend

Oh, I remember. I needed to prove that $\mathbb{R}$ is second countable.

So I needed countability of $\mathbb{Q}$.

there's an indian called Tisquantum in this book

11:56 PM

interesting

wtf these tribes have like 3 names

gotta go now, it's gettin late here..

the name of the tribe, the English name and the name of the land

cya

bye

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