when people were used to walk to travel and ride animals, there was no varicose, no heart ineffeciency, no arthritis, no many many things, so any change in rules, is backed on a change iin data

Sir James Whyte Black discovered a revolutionary medicine (propranolol) and was awarded the Nobel Prize for Medicine in 1988. For many years the patiences with some specific diseases received as a first line therapy this drug, it was considered almost a miraculous medicine. Recently things changed. Do you wanna see some titles in papers? Beta-Blockers (propranolol also included here) Killed 800,000 in 5 Years—“Good Medicine” or Mass Murder?

@Agawa001 People also didn't tend to live as long back then. Plus, would they have had the tools to actually diagnose such things?

@Semiclassical dunno, for heart troubles, there s no miraculous tools even now

Or to add anything about Lechitine widely prescribed in the past for, say, students to support the mental efforts? Or for aged people? Read the last studies and see what they say now.

nope. but we at least have the technology to actually see the heart's electrical activity now.

and medicine is taking a stepback regarding all the failure recorded in hospitals and surgical interventions

@Semiclassical Do you think I should be expected to know that $\int dx\,\exp\left(-\frac{(x-2i(k-p'/\hbar))^2}{2d^2}\right)=\int dx\,\exp\left(-\frac{x^2}{2d^2}\right)$ without warning in a first course on QM?

One thing that does worry me is in regards to antibiotic resistance.

@0celo7 yes.

that's literally just saying that you can shift the integration variable by a constant without changing the integration limits.

by a complex constant @Semiclassical

eh, fair enough.

that does make it less apparent that it's valid.

I guess at the level of rigor of the book that reasoning is ok.

it's easy enough to verify from cauchy's theorem anyways. pick a contour that runs along the real axis, then up some imaginary distance, then backwards in the real direction, and then back down.

@Semiclassical Yeah I know how to verify it, but I was surprised Sakurai just did it without mentioning anything

True.

He actually went straight from some horrible integral to the result

Didn't even mention how to integrate Gaussians

Most QFT books explain that just in case

Most = 2 that I've read

@Semiclassical wut do u mean by the retrograding mars ? does it have a particular movement ?

I learned how to integrate Gaussians from Shankar's QM, so I kinda expected it to be in all QM books

Or at least give the formula for it

I have no clue where the $\pi$s and $2$s go!

Depends on the level of the book. If it's sufficiently advanced, they may just assume you're familiar with it.

I usually have to mentally rederive the normalization constant, since I worry about said factors of two

And if it's something like $\int x^n e^{-x^2/2}\,dx$ I have to actually work it out.

Not a big deal, but not something I remember off the top of my head.

@Semiclassical Shankar has an appendix where he derives all integrals of that form.

It's nice.

heh, I can see my copy of Shankar from here

@Agawa001 you have to joke now.

@Idomathart ?

@Agawa001 (April, 2016) Have you heard the good news? The US Government Dietary Guidelines for 2015 has removed limits on cholesterol intake (1). Now for the bad news: people are still scared to death of cholesterol and animal fat. Why? Because, for the past 50 years, they’ve been told that eating cholesterol-rich foods raises cholesterol and promotes heart disease.

Though research has failed to demonstrate this, up to 70% of physicians still recommend the old guidelines, and are trying to force us onto statin drugs.

thescienceofnutrition.me/2016/04/04/…

@Agawa001 Retrograde motion of mars

This is a story that I know for many years, and largely debated by many known doctors. It seems that things change finally.

I'm done with this. Just to know well that what I said is exactly like that: things change in medicine during the time, and what was good becomes bad in a few years, and viceversa.

Based on that, suppose you were to try to depict the motion of Mars if you assume that the earth is at rest. You'd probably come up with something very much like the diagram you linked, with all those little loops.

@Semiclassical Great book.

It was good, yeah.

It's what I used in grad school QM. For undergrad I had something else

Anyone around?

Thats a stupid question

which was fine when it came to the actual physics/math, but had certain philosophical conceptions of QM which got on my nerves

We're using Sakurai and Cohen-Tannoudgi

@Semiclassical Probably Griffiths?

No.

I'm looking for a C++ programming project, previous things ive done include Fibonacci, Quadratics, and prime numbers. Any ideas?

It wasn't a very widely-used one

What's the title? "Modern QM"?

Ah, Amit Goswami's textbook

@Idomathart never heard about someone talking good about cholesterol

Never heard of it.

googling

@Agawa001 Then there was another thing around. People on statin drugs (this is to control their cholesterol) were prescribed also Coenzime Q10 that was highly promoted as a miraculous drug. The idea was that statins deplet the Coenzime Q10 deposits in the cells. But guess what? Now the studies show that larger amounts of Coenzime Q10 may affect your memory.

amitgoswami.org/about

lol

as a text, it was by and large fine. but the philosophy...ughh

What was the philosophy about

Take a look at the book description on Amazon here, especially the few sentences at the end of the paragraph. (that's what's on the back of the book)

@Idomathart i was on a kind of memory-unfriendly drugs, yes they do damage memory

now im free of them

mostly that last "outstanding feature", lol

hah

yup

@Agawa001 Or to mention such titles Do fish oil (omega-3 fatty acid) supplements contain mercury??

@Semiclassical what fascinating philosophical bits did you retain

dunno

Mostly stuff from the last chapter, which was almost entirely philosphical

such as?

Is it obvious that the preimages of points under the Abel Jacobi map will be projective spaces?

@Agawa001 Be careful, they may be harmful indeed.

I guess the tidbit I remember the most is the suggestion that, in order to resolve Wigner's paradox regarding information in quantum mechanics, one should consider the possibility of one universal consciousness

What's the paradox?

i.e. there's no such thing as multiple conscious observers, only one universal consciousness observing itself

Wikipedia has a summary here: en.wikipedia.org/wiki/Wigner%27s_friend

Am I insane if I say the universal consciousness makes sense

@Idomathart fish ? i eat fish almost every day

aaand dont care

from my POV, yes

i gotta go, though.

@Agawa001 :D

@Alyosha what is the Abel-Jacobi map, it's one of those old concepts that should be very concrete, but everytime I look at it it's the most abstract stripped away thing ever

I'm not quite sure exactly, but I think it's the following. Fix $n$. Then it's the map from the divisors $D$ on $\Sigma$ with $|D|=n$ (equivalently, $\text{Sym}^n\Sigma$) to the line bundles of degree $n$ on $\Sigma$ (equivalently, $\text{Pic}^n\Sigma$).

Supposedly the preimages are projective spaces since each effective divisor gives a line bundle and a preferred section (which I'm OK with), or something like that, but I can't find it done properly anywhere.

@Alyosha Hmm, this sounds like something I learned about (and quickly forgot about again) when learning from Fulton's book on intersection theory.

@TobiasKildetoft Thanks, I'll have a look there.

Though note that that book is very much on the abstract side of things

@Alyosha $|D|$ means degree of the hypersurface?

Yes.

Looking at Fulton's algebraic topology p291 where he talks about the Abel-Jacobi map

This strikes odd to me, but probably because I am in the topological category.

I'm not certain that it's true in general.

Zero set of a generic line bundle should not certainly always be homeomorphic to a projective space.

In TOP, it can be any codimension 1 degree n hypersurface. Lots of such things which are not homeomorphic to projective spaces. (What is your $\Sigma$ though?)

(It's a Riemann surface)

What's the zero set of a line bundle?

Zero set of a generic section, I meant.

OK.

@Alyosha Whoa, whoa, wait a second. Preimage of a line bundle by that map then is a bunch of points, then?

Yes.

So it's feasible.

hey all

Then what do you mean by "preimages are projective spaces"?

I can't intuit the Abel Jacobi map yes, so it might just be immediate.

If $\ell$ is a line bundle and $f$ the Abel-Jacobi map, $f^{-1}(\ell)\simeq \mathbb{P}^n$.

With some conditions that I'm not familiar with.

@Agawa001 nice articles about heathy dietary you may find here health.harvard.edu

I'll go off to read Fulton now.

I mean $f^{-1}(\ell)$ is a collection of a bunch of divisors in $\Sigma$ so I can't see how it makes sense to say it's $\Bbb P^n$.

OK, so $\Sigma$ has to be a Riemann surface.

Nevermind, I guess I do see. You mean $f^{-1}(\ell)$ inside $\text{Sym}^n \Sigma$ is homeomorphic to $\Bbb P^n$?

Is that it?

Yes.

OK, gotcha.

That seems like a hard question to answer.

Need $\Bbb P^n$ always embed in $\text{Sym}^n \Sigma$, even?

I mean, take $n = 1$, in which case that symmetric space is $\Sigma$. $\Bbb P^1$ hardly ever embeds in a Riemann surface (only when it's $\Bbb P^1$, in fact).

Indeed, $f^{-1}(\ell)$ for $n = 1$ is always $\Sigma$ itself, right?

@Idomathart interesting

So if you want to pose a nontrivial question you should say $n > 1$.

@Agawa001 I wonder if @r9m is still working on my integral. :D

@Idomathart he has a rich blog btw

@Agawa001 some integrals arising around the Catalan's constant are pretty hard to do.

i ever wanted to make my own, maybe after i buy a domain name

@Agawa001 sure. Why not?

Lets see, very stupidly going off this en.wikipedia.org/wiki/Abel%E2%80%93Jacobi_map, if you envision a complex curve of genus 1 as a doughnut/torus then you can do two linearly-independent closed line integrals on the torus, since you could also do multiple integrals around the same part of the doughnut you get 'periods', generating a lattice of periods, thus quotienting out the periods gives us just the distinct line integrals.

The Abel-Jacobi map seems to just map a point on a curve to the line integral along that curve, throwing away any repetitions/periods, and living on a projective space I guess means line integrals along homotopic curves gives the same answer, or that it doesn't matter what point you start with, or something

@Agawa001 I think there could be considered a specialized area for the calculation of these integrals since they need special approaches, at least the ones more advanced.

Otherwise all end up with much headache.

It would be interesting considering the writing of a whole book only on this topic, and you would have absolutely no problem to write easily 500 pages, say.

Describing in detail the techniques to use, like more solutions for each problem.

@Idomathart cool , a new book with a new view of catalan constant, that may reflect a various coming researhes on this topic

@Agawa001 Yeah, I really think of that! I noticed that many people are in big troubles with such problems.

and maybe the not-yet solved problem about transcendance of G

@Agawa001 :D

Still I've seen no decent idea for calculating $$\int_0^1 \left(\frac{\log(1+x)}{1+x}-\frac{\log(1-x)}{1+x}\right) \arctan(x) \textrm{d}x=\frac{\pi^3}{192}+\frac{\log(2)}{2}G$$

In this chat no one has come up with one.

the main ?

@Agawa001 don't worry, no one will do it elegantly, neither Cleo nor Cleo squared, cubed or whatever.

There is a science of elegance for such problems that require much research, that means one needs years of experience.

@Agawa001 look on main, my problems slightly above average as difficulty are not finished, some are there for many months.

I don't even count the ones that could be considered hard.

The one above is just an easy-to-average difficulty problem, to be well understood.

majority have answers thu

@Agawa001 yeah, they have, but I'm mainly referring to the elegance of the solutions, and then to the integrals that are out of order.

@Agawa001 So, to come back to integrals around Catalan constant, yeah, it's a very good idea to write a book.

One can go even higher, to 700-800 pages, but you might have problems with the publisher. Some won't like that much this number of pages.

(maybe somewhere around 400-500 pages, not more)

Riemannian geometry is the worst. Why the hell does Petersen reverse $V$ and $W$ in $$R(\sum X_i\wedge Y_i,\sum V_j\wedge W_j)=\sum R(X_i,Y_i,W_j,V_j)$$

@Agawa001 I could finish it in 6 months or earlier if I were in a good shape (I'm not these days in a great shape). Maybe in 4 months if I worked like hell. Some are bad days, you know, when you're less productive, or when you simply work on other stuff, like proposed problems, articles or even another book.

@Idomathart my first puzzles in this website noone could solve them, and when they failed the blameshifting habit told em to rebound the fault on me, so i was known as a misworder for looong period

when noone can understand a problem of yours, or they make bad answers, this doesnt mean anything

@0celo7 Then why d'you do Riemannian geometry.

there is a good slicky solution somewhere

Do topology. Less indices.

@BalarkaSen Topology doesn't excite me like geometry does

@Idomathart yes im busy doing another work tis is why im away of maths

otherwise i could have given it a try

@BalarkaSen Somewhat hard problem: consider a smooth curve $\gamma:J\to M$ where $J$ is a compact interval and the image of $\gamma$ never intersects itself. Let $g$ be a smooth function on $J$. Is there a smooth function $G$ on $M$ such that $G(\gamma(t))=g(t)$?

@Agawa001 you should do more math, btw :D

@Idomathart i know it is my fuel

@Agawa001 :D

Well, maybe it's not that hard. The more I stare at it the more I think there's a really easy solution.

(Easier than the one in the literature, in any case.)

@Idomathart im eating sweets do u want some ?

@Agawa001 lolll, of course! :D

Yeah, I don't see why a constant extension in each coordinate neighborhood containing $\gamma(J)$ and then a partition of unity doesn't work.

dunno what to call that in english lemme check

Since $\gamma(J)$ is compact, hence closed, this very likely works.

It should. I was about to say that. But I haven't worked it out.

baklava!

@Agawa001 Let me prepare now green tea with mountain honey (instead of those sweets of yours) :D

I mean, locally you can assume $\gamma$ on a coordinate nbhd is a coordinate axis.

@BalarkaSen The proof in Helgason involves the implicit function theorem and is nasty.

But you need it to extend vector fields off of curves.

This is an exercise in Lee IIRC.

take, pick the one you want

google.com/…

Lee is such a good book.

I should get a hardback copy.

Carry it everywhere

Meh.

Anyway, so you're boiled down to doing it for a coordinate axis on $\Bbb R^n$.

@BalarkaSen Doesn't a constant extension work, locally?

I mean, that's how we proved that extension lemma for sections of vector bundles a month ago.

@Agawa001 haha, look at that images.google.fr/…

Then a PoU to smooth the overlaps.

@Idomathart sweets are good stimulators for the brain

@0celo7 What do you mean by a constant extension?

especially sirotonin

@Agawa001 ooo, yeah!

@BalarkaSen Good question lol.

:P

(thinking)

I might have to search the chat logs

Oh, maybe that doesn't work here.

@BalarkaSen oh, what I was thinking only works on cylinders :P

if you know the value of a function on $\Bbb R^k\times\{0\}$ you can get a smooth constant extension onto $\Bbb R^k\times(-\epsilon,\epsilon)$

Anyway for a coordinate axis on $\Bbb R^n$ this is easy. Let $g$ be a function on the x_1-axis, then set $G(x_1, \cdots, x_n) = g(x_1)$.

by just defining the extension to be independent of $t$

@0celo7 But then you can get a extension to all of $\Bbb R^k$ by a bump function trick.

@BalarkaSen Yes, that's a constant extension

Ok, so thanks for thinking for me :P

Helgason's proof is overkill. Wonder what Kobayashi-Nomizu have to say about it.

@BalarkaSen There's a subtlety in the geodesic equation. The connection is defined on vector fields on $M$, but a geodesic's tangent field is a field along the geodesic, not on $M$. You have to extend it and prove the extension does not matter.

Many books readily sweep this under the rug.

One can avoid this by pulling back the connection onto the curve.

But that's also machinery.

@Idomathart this is bread ?

@Agawa001 no, some sort of sweet

@0celo7 Funny, why does the extension not matter? I would think it does.

@BalarkaSen The proof is unsatisfying. You write it down the geodesic equation in coordinates and it only depends on derivatives and values along the curve.

Yeah, an explicit hands-on proof is not quite satisfying. The geometry is unclear.

@Idomathart i thought it a sort of waht we call in french "mie de pain"

@BalarkaSen the relevant theorem is

(from do Carmo)

part c)

@Agawa001 ah, I see.

it is also called "pudding de pain"

@Agawa001 some sort of sweetened bread?

delicesdalyss.canalblog.com/archives/2006/07/30/2376326.html

look

And what you get is $\nabla_XY=\sum_{ijk}[x_iy_j\Gamma^k{}_{ij}+X(y_k)]X_k$

I remember.

very tasty with milk

here $y_i$ are the components of $Y$

so it only depends on the values of $Y$ on $c$ and the derivatives along $c$ (through $X(y_k)$)

@Agawa001 it looks tasty, delicious ;)

And $\Gamma_{ij}^k$ being the Christoffel symbols.

yes

But I think this is the same for directional derivatives

two functions have the same directional derivative if they are equal along the curve and have the same derivatives along the curve

the values elsewhere are irrelevant

(I think I just stated a tautology)

$\nabla_X Y$ essentially means differentiating $Y$ along the integral curve of $X$, yes? I forget.

@BalarkaSen Yeah, but with a "correction term" given by the Christoffels.

omg omg i ate this sweet with its paperwrap

dont blame me it is so delicious

@Agawa001 :D

@BalarkaSen Question for you: suppose $c$ is a constant curve, i.e. $c(t)=p$ for all $t$. Then what is $DX/dt$?

I have to learn what $D/dt$ means. The zero vector at $p$?

@BalarkaSen D/dt is defined in the proposition above

@BalarkaSen No, but that's what most people think!

If you take the regular directional derivative wrt. the 0 vector, you get the 0 vector

But if you take the directional covariant derivative, you don't!

@0celo7 I haven't read it.

I guess you get a constant vector because of those correction term given by the Christoffels?

No, you just get $DX/dt=dX/dt$

It's the correction term that disappears

Huh.

The technicality is that a vector field along a constant curve can still be variable -- in the tangent space.

It traces out a curve in $T_pM$

the covariant derivative of the vector field is then the ordinary derivative of that curve

Hello.

hollow

Heyyyyyyy

Got a small mystery wonder if anyone can help me out so i put in 3log(2)+100<=150*log(2) into wolfram and got true, on my TI 84 the same thing says false. Anyone know why?

I tried parentheses...

rounding?

I mean I don't know, I mean after this I got curious and so I put 150*log(2) into my TI 84 and got 45.1544.. etc on wolfram I got 103.97... etc.

I have an 84, let me see

Oh.

log is base 10 on TI, base e on Wolfram.

That was my assumption... I was assuming different bases. Would you know anything about Big O by any chance? It's a computer science concept. i thought the base was supposed to be base 10 but wolfram gave me the right answer not the TI.

No I don't, sorry.

Hm okay, I'll figure it out. Thank you!

what about big O?

Hello!

Can smebody remind me how to use ChatJax?

$$\mathbb{Z}_{\geq 0}$$

Doesn't work.

Weird.

@TheBitByte see $\LaTeX$ in chat in the room description, upper right corner

Okay.

$\mathbb{Z}_{\geq 0}$

Doesn't work.

did you make the code a bookmark and click it while on this tab?

What?

Nope.

follow the instructions

I did. -_-

so you made it a bookmark right?

What bookmark?

>^^drag this^^ to your bookmark bar or right click on it to add it as a bookmark.

These are the instructions right there under "start ChatJax"

I asked you if you followed the instructions and you told me yes.

I don't see any.

I just have the userscript.

Did you click the tinyurl link in the upper right corner I told you to go to?

so you're looking at this right?

I'm looking at Greasemonkey, not that.

I have a userscript.

Not a bookmarklet.

okay... good luck I guess.

What?

-_-

you can get latex in chat working by following the instructions at the page I directed you to. I don't know anything about greasemonkey or whatever your talking about, so you're on your own for that. if you choose to not look into what I told you about that's up to you

@Idomathart am not :P sorry .. but I'll try later :-)

@arctictern I'm sorry for installing ChatJax just from a different link, I guess?

@r9m OK. Isn't it late there at you?

@Idomathart ya .. 5 am

@r9m Still up? Huh?

@Idomathart ya .. class test tomorrow :P (tensors)

@r9m ah, that's why! :-) Are they hard to comprehend?

@TheBitByte the reason I'm annoyed is that you never mentioned anything about having a userscript from greasemonkey or whatever until after I had already told you to go do the other webpage and you said you had followed the instructions there.

@arctictern Fine. I'm converting the bookmark into a script right now so it runs automatically.

@Idomathart I am finding it difficult to get used to the ideas .. it's new to me and the notations can get a bit tedious to follow at times ..

@r9m I see. I suppose one also needs to like an area to easily understand it.

Converted the bookmark into a script, doesn't work. I hate this.

@Idomathart yes .. and so far I ain't liking 'em :P well I suppose if I had learned a bit of geometry first I'd feel the relevance .. but as a part of Linear Algebra course I ain't getting a lot of motivation to read it :P

@TheBitByte the bookmark from the page I linked?

@r9m yeah, I know your point very well.

I mean, we just keep it a bookmark on the bookmarks bar and then click it to get latex to work in here.

@arctictern Yes.

It doesn't work again.

@r9m Indeed. It's like seeing the picture at the end. It's nice to do it having in mind the picture at the end, that you can master it, can do it, create cool problems and so on.

Strangely, the bookmarklet version does.

Guess I'll stick to manually clicking it, if I have to.

@Idomathart Indeed . . :)

@r9m It's mandatory to do it?

@Idomathart yes I think so .. well we can always go and request the prof to take it off from final exam :P .. but it all depends on how merciful he is :-)

@r9m Will you use that knowledge in other area of math you study? Maybe there is a purpose for learning that.

@r9m Gotcha.