The h Bar

A mathematician, a physicist and a engineer are asked by a student what the meaning of $$\int \frac{1}{dx}$$ is.

The mathematician says it is meaningless.

The physicist ponders it for a moment and wonders if there is some way to give it meaning.

The engineer says, "Hmmmm, I used to know how to do that."

0celo7

@NikolajK Holy crap...can you do $$\iiint \Gamma(x)\Gamma(y)\Gamma(z)\,\mathrm{d}x\mathrm{d}y\mathrm{d}z$$ where the integral is taken over the 3-D Koch snowflake?

@infinitesimalsimplicio Will show to my engineer father and brother.

I bet you're right.

YouTube commenters are the dumbest of the dumb. The upload date of the video should appear whenever one comments.

NeuroFuzzy

@infinitesimalsimplicio it's obviously $\int \frac{1}{x d( ln(x))}$

pyramids

lol @infinitesimal

0celo7

@NeuroFuzzy Naw...see in differential geometry the differential is the inverse of the derivative, so $$\int \frac{1}{\mathrm{d}x}=\int \frac{\partial}{\partial x}$$

ACuriousMind

12:47 AM

@0celo7 Obligatory xkcd. Also this one.

4

0celo7

@ACuriousMind That's scary

You're surprised I have Wald's table of contents memorized and yet you know every xkcd ever?

NeuroFuzzy

@infinitesimalsimplicio $\int\frac{1}{dx}=\int\frac{1}{1-(1-dx)}=\int 1-(1-dx)+(1-dx)^2-\cdots$. Then all the ones cancel (naturally), all the $dx^2$ and higher terms die out, and you're left with $\int(1-2+3-4+5-...)dx=\frac{x}{4}$ (by Wolframalpha regularized result).

So the answer is $\frac{x}{4}$.

(wolframalpha link wolframalpha.com/input/?i=1-2%2B3-4%2B5-6%2B... )

ACuriousMind

@0celo7 Heh. Well, memorizing useless stuff is far easier ;)

NeuroFuzzy

aww physics chat isn't copying the "..." on the url

0celo7

@NeuroFuzzy $+C$

NeuroFuzzy

12:53 AM

@0celo7 oh nooooooooo

I have sinned :(

ACuriousMind

@NeuroFuzzy Lol. That's a perfect physicist's argument :)

pyramids

hmm, reminds me of American highschool...get the $+C$ beaten into you...

0celo7

@NeuroFuzzy Also another problem... $$\frac{\mathrm{d}}{\mathrm{d}x}\frac{x}{4}\ne \frac{1}{(\mathrm{d}x)^2}$$

And another: the integrand does not make sense if you drop quadratic terms.

pyramids

quick question: can I somehow activate MathJAX for the equations?

ACuriousMind

90

A: Should chat have TeX support?

I will leave the original post for historical reference, but as mentioned in the Update below, all four bookmarks are located on this installation page. There are four bookmarks: start ChatJax installs MathJax and starts a loop that renders $\LaTeX$ as needed. This is intended for use in chat, ...

0celo7

12:56 AM

@pyramids Czech the top right corner.

pyramids

thx @ACuriousMind and @0celo7

0celo7

@NeuroFuzzy I think this is better understood in terms of a Riemann sum. $$\int\frac{1}{\mathrm{d}x}\sim\sum_i \frac{1}{\mathrm{d}x_i}$$

NeuroFuzzy

well with a riemann sum it's obviously divergent and that's no fun

0celo7

If we take each differential to be of equal width, we factor out the fraction. Then we have the sum of $1$s, which is just $\zeta(0)$.

NeuroFuzzy

oh

hmmm!

0celo7

1:00 AM

By rotating the contour, we get $\zeta(-1)$, which has the well-known value $-1/12$.

Thus $$\int\frac{1}{\mathrm{d}x}=-\frac{1}{12\epsilon}$$

Alternatively... $$\int\frac{1}{dx}=\int\frac{d}{dx}\ln dx=\int\left(\frac{1}{dx}\frac{d}{dx}\ln dx\right)dx=\frac{x}{dx}\frac{d}{dx}\ln dx+C$$

NeuroFuzzy

Where does this talk of rotating the contour come from? (just interested, I've never really done things with regularization before besides applying analytic continuation)

0celo7

@NeuroFuzzy In this case? Pure BS.

NeuroFuzzy

Would that be $\int \frac{d}{d(dx)}\ln(dx)$?

0celo7

@NeuroFuzzy Nawww ;)

NeuroFuzzy

Hah alright, was wondering what grade BS

pyramids

1:04 AM

There has got to be some other generalization, too, though:

1. We know to integrate quantities depending on $\mathrm{d}x$
2. We know how to deal with (in stochastical calculus) quantities that essentially imply inventing integrals for quantities varying with the square of $\mathrm{d}x$
3. If we form a suitable ratio....?

0celo7

See, $d$ is just a constant factor ;)

ACuriousMind

@0celo7 Right, because the operator is typeset upright.

0celo7

@NeuroFuzzy Pure. There's no spacetime here, so Wick rotation does not make very much sense I don't think.

Unless you Wick rotate $x$.

I guess you could do that.

What if the integral is to be understood in the $i\epsilon$ sense?

i.e. $$\lim_{\epsilon\rightarrow 0^+}\int\frac{1}{\mathrm{d}x+\mathrm{i}\epsilon}$$

@NeuroFuzzy Aha, then it equals $$\mathcal{P}\int\frac{1}{\mathrm{d}x}+i\pi$$

So all we have to do is find the principle value!!

NeuroFuzzy

Hahahaha welll... okay... the singularity to excise is everywhere though...

0celo7

@NeuroFuzzy Well here is where we have to get creative...

NeuroFuzzy

1:17 AM

you get the CPV by antisymmetrizing about a point... the only function which is antisymmetric about every point is the zero function

so the answer is $i\pi$ methinks!

or is that symmetrizing... I guess symmetrizing... so that just adds a constant?

0celo7

@NeuroFuzzy Hmm...please show this explicitly.

Kyle Kanos

@DanielSank: Another guitar-only VG song you might like: youtube.com/watch?v=TAlPNCTJ8Fs

NeuroFuzzy

So for $f(x)$ w/ a singularity at C, we take $\frac{f(C-x)+f(C+x)}{2}$ instead. The resulting function is symmetric about $C$. Do this for every singularity (every real number) and the resulting function is symmetric about every point. So the symmetrized function we integrate over must be constant!

Heh, not zero. That's my reasoning and I'm sticking to it.

0celo7

My next idea: $$\int\frac{1}{\mathrm{d}x}=\int \frac{ \mathrm{d}x}{(\mathrm{d}x)^2}=\mathrm{d}^{-2}\int \frac{\mathrm{d}x}{x^2}=-\mathrm{d}^{-2}\frac{1}{x}+A$$ Now the inverse of $\mathrm{d}$ is just the integral, right? So we have to integrate that twice. Thus $$\int\frac{1}{\mathrm{d}x}=-x(\log x-1)+Ax^2+Bx+C$$

NeuroFuzzy

oh god. Too far.

0celo7

1:24 AM

I think I got it.

@ACuriousMind Pls check work!?

ACuriousMind

::squints::

0celo7

Actually, those constants are fucked.

It should be $A+Bx+C=Bx+K$.

The $A$ does not get integrated.

ACuriousMind

Looks alright to me

0celo7

@ACuriousMind yay

NeuroFuzzy

Are there any further restrictions on B? We might get back $B=\frac{1}{4}$

ACuriousMind

1:27 AM

I wonder whether you used Riemann or Lebesgue integration, though

0celo7

@ACuriousMind physics integration

ACuriousMind

Perhaps a Stieltjes integral would yield a different result, too

@0celo7 Ah, the best kind of integration

NeuroFuzzy

We should have moved to the math stackexchange chat to discuss this

0celo7

I'll ask them.

Waht

Where is it?

It was just there...

in Mathematics, 18 secs ago, by 0celo7

The Phys.SE chat is wondering what $$\int\frac{1}{\mathrm{d}x}$$ is.

ACuriousMind

Do not misrepresent us! (Also, you'll get ill-defined, 100%)

0celo7

1:30 AM

@ACuriousMind "crap"

pyramids

Your $\frac{1}{\mathrm{d}^2} \int \frac{\mathrm{d}^2 x}{\mathrm{d}x}$ idea has a slight conceptual flaw, though

0celo7

@ACuriousMind Too late, they probably think we're a bunch of fools who don't even know Lebesgue integrals and interuniversal Teichmüller Mellin transforms.

ACuriousMind

@0celo7 :(

0celo7

@pyramids This whole thing is a conceptual flaw.

pyramids

$\frac{\mathrm{d}x}{\mathrm{d}}$ would(?) maybe be fine as the inverse of a differentiation...but what do we do without the $\mathrm{d}x$ bit?

NeuroFuzzy

1:33 AM

Aha!

He saw the joke

pyramids

sorry for being slow, then ^^

0celo7

@NeuroFuzzy He's pretty upset.

NeuroFuzzy

@0celo7 I took that as a joke :D

0celo7

Perhaps

Unless he thinks we're serious

In which case, it was totally the German's fault.

ACuriousMind

?

I did not advise you to take this to the mathematicians

pyramids

1:39 AM

we did get a reply, though

ACuriousMind

...I agreed with your result, though :D

0celo7

@NeuroFuzzy Well we pissed him off.

By "ignore" does he mean block?

pyramids

maybe the difference is ill-defined

(between ignoring and blocking)

ACuriousMind

How were the mathematicians supposed to tell that you were not being serious, by the way?

They get horrible questions like these every day on their SE. And they don't even close them :P

0celo7

@ACuriousMind This is the crap that high school calc teachers get asked though.

ACuriousMind

1:42 AM

@0celo7 I know. So how were they supposed to know you were not serious?

0celo7

@ACuriousMind MAGNETS

ACuriousMind

@0celo7 Someone is having a bad influence on you ;)

0celo7

I'm amazed at how little physics the average mathematician knows.

ACuriousMind

In turn, they are always amazed how much math the physicists think they know :P

0celo7

@ACuriousMind Physics math = rearranging hieroglyphs and hoping it makes sense

Anyway, I'm off.

Stan Shunpike

3:43 AM

@DanielSank So was what I wrote completely wrong?

I mean, I realized the point you mentioned when I wrote that. But no one answered the question, so I attempted at least a partial explanation. But obviously yeah there's no way bijective and involute describe the NOT operation.

I just thought those were two important properties. Did I get that wrong?

Also, can anybody explain whether $S_x, S_y, S_z$ spin operators....are these dimensions as in 3D spatial space or are these just some sort of abstract 3 dimensions?

Because I don't get why $x$ would have a different operator from $y$...wouldn't that single out a particular dimension? I know this is a somewhat trivial question, but I am asking just to clarify.

Stan Shunpike

4:22 AM

@DanielSank nvm I think I figured it out. Boy, quantum information is confusing!

Mark Mitchison

4:47 AM

@TAbraham You need to solve a first-order vectorial differential equation. There are various techniques for doing this; in this case you will almost certainly want to use a numerical solution because the analytical solution is very tedious. I recommend searching Mathematics StackExchange for help with solving such equations.

Stan Shunpike

Hey, its @MarkMitchison ! Thanks for all that help the other day

DanielSank

5:10 AM

@KyleKanos Not quite my cup of tea, but thanks!

Stan Shunpike

6:23 AM

@Danu thanks again for telling me about Griffith's. I did 5 exercises today after you told me about it. Calculating expectation values is awesome.

tpg2114

9:52 AM

Some day OSS programmers will realize that No Documentation >> Incorrect Documentation

And I would argue No Documentation > Partial/Incomplete Documentation >> Incorrect Documentation

David Z

11:19 AM

@tpg2114 I would switch those first two depending on just how the documentation is incomplete

David Z

11:37 AM

@StanShunpike those are real dimensions. But in order to write them as $S_x$, $S_y$, and $S_z$ in the first place, you have to have picked a coordinate system and thus broken the symmetry.

The three operators are components of a vector. Just like, say, momentum. If you write a momentum vector as $(0, 0, \sqrt{6})$, you've singled out a particular dimension, and if you write it as $(1, 1, 2)$, you've "singled" out a different dimension.

ACuriousMind

1:14 PM

0

Q: Where can I find a table for NIST standards on temperature and pressure?

The Wikipedia article Standard conditions for temperature and pressure notes that IUPAC and NIST are two of the most common standards for temperature and pressure in use. Even if I could have gotten my hands on the IUPAC standards, I wouldn't have wanted to use them as the standard temperature a...

fluid-dynamics

^on-topic?

Sean

1:32 PM

I think so, since it's basically a reference request

or resource recommendation

or whatever the lingo of the week is

I can tag it as such (gotta have that +2 rep for an edit!)

ACuriousMind

I'm not sure if this is resource-recommendation or specific-reference

infinitesimal simplicio

Perhaps, migrate it to Chemistry.SE?

ACuriousMind

I'm leaning towards the latter, OP seeks a specific paper, in some sense

Sean

i did specific reference

ACuriousMind

@Sean Seen and approved

infinitesimal simplicio

2:08 PM

I found negative space

ACuriousMind

@infinitesimalsimplicio ::spooky sound effects::

infinitesimal simplicio

:D

David Z

@Sean specific-reference

hm, actually... I'm not so sure. If it were asking "what is the (current) official source for the NIST standard temperature and pressure?" then it would be a slam dunk obvious specific-reference.

But if it's asking for any source that lists the NIST values... I dunno, it could definitely still be specific-reference but it's not so clear cut.

probably not worth stressing over

(one might say the question could be edited to ask for the official source and thereby put an end to this controversy :-P)

Waffle's Crazy Peanut

2:37 PM

I had a conversation with my mother regarding ear-piercing. My family believes that science supports ear-piercing.

ACuriousMind

...wat. Which science, and what does "support" mean here?

Waffle's Crazy Peanut

They simply say "science" and ask me to google on that. I don't agree with them very well, because I think of it as taking advantage of the toddler's age

ACuriousMind

toddler? Are we talking about some specific custom where children's ears are pierced here?

Waffle's Crazy Peanut

@ACuriousMind Yeah, it happens in almost all parts in India

tpg2114

@Waffle'sCrazyPeanut And all over the US. That's not uncommon

Waffle's Crazy Peanut

2:40 PM

They pierce the ears of a children (aging between 10 months and 4 years)

How could anyone even think of hurting a child and ruining such a perfectly symmetrical design (body), and call it "science"?

Once the child grows into a mature boy/girl, he/she has right to follow her own will. Then, if he/she wants to pierce his/her ears, they can...

infinitesimal simplicio

The "science" of tradition :(

ACuriousMind

Uh...that the parents want to pierce the child without their consent is rather uncommon here in Germany. It's more that the little ones want to wear "earrings like mommy".

And the league of pediatricians even advises against it, correctly calling it a form of bodily harm inflicted on children.

infinitesimal simplicio

cargo cult science

Waffle's Crazy Peanut

@ACuriousMind As far as I've seen, my cousins (I've like - 10 cousins) never told their parents that they want it. It's like a ritual, or at least tradition

@ACuriousMind Now, they're asking me for the results in the internet. A lot of parents in Parenting.SE say that it's like violating the human rights :P

ACuriousMind

Even the jewelers' union says that children should be at least over the age of 6 before they should get pierced (and then only with their consent), although there is no law on this.

@Waffle'sCrazyPeanut Those parents are wholly correct, imo

Kyle Kanos

2:44 PM

I'm not letting my daughters get their ears pierced until they're like 10 or so

ACuriousMind

The right to bodily integrity is one of the most fundamental human rights there is.

Waffle's Crazy Peanut

@ACuriousMind Yeah, I totally agree with it. But, when I show it to them, they say, "maybe those parents aren't aware of it" (sigh)

Now, I need some kinda citation to shut everyone's mouths.

They show me blog posts and crappy websites that shout that the trend is based on science, but which never point to any sort of scientific book/discussion/reference...

infinitesimal simplicio

Body piercing

Body piercing, a form of body modification, is the practice of puncturing or cutting a part of the human body, creating an opening in which jewellery may be worn. The word piercing can refer to the act or practice of body piercing, or to an opening in the body created by this act or practice. Although the history of body piercing is obscured by popular misinformation and by a lack of scholarly reference, ample evidence exists to document that it has been practiced in various forms by both sexes since ancient times throughout the world. Ear piercing and nose piercing have been particularly widespread...

ACuriousMind

@Waffle'sCrazyPeanut Well...then it is rather evident that it isn't based on science, is it? The burden of proof is on the ones who want to do the piercing, not the other way around.

infinitesimal simplicio

But they are fighting tradition...

Waffle's Crazy Peanut

2:50 PM

@ACuriousMind Yeah, I won't ever agree unless there's a satisfactory reference (having spent about two and a half years in Physics.SE) :P

ACuriousMind

But, oddly enough, not letting parents mutilate their children is one of the traditions that are hardest to fight

Kyle Kanos

@ACuriousMind Curiously, mutilate is not a word I'd use for ear piercing.

Other piercings (e.g., nose, eyebrow, tongue) I might consider using that word

ACuriousMind

@KyleKanos I'd say any change to a person's body that is non-consensual and not medicinally necessary is mutilation.

Waffle's Crazy Peanut

@KyleKanos is biased towards ear-piercing! :P

infinitesimal simplicio

body modification?

ACuriousMind

2:53 PM

@infinitesimalsimplicio I'd use "body modification" for the consensual versions.

Waffle's Crazy Peanut

The discussion popped in, because they're gonna pierce my new (an year old) cousin tomorrow, and I was curious about the need for it. I asked them,, "Why couldn't you wait for a few years?", which eventually got into a discussion of science vs. make-it-up-science

ACuriousMind

"Why couldn't you wait for a few years?" applies to almost all rituals that are carried out with small children.

Waffle's Crazy Peanut

Heh, yeah :)

ACuriousMind

It never has an answer different from "Because they might object by then"

Waffle's Crazy Peanut

Hah! :D

@ACuriousMind: Thanks to my hyper-activeness in my young age, that they never pierced my ear, because I (heard that I) was never letting anyone touch me back then... :P

Kyle Kanos

2:56 PM

@ACuriousMind Except mutilate is a rather harsh word; it literally means to inflict violent and disfiguring injury to someone.

ACuriousMind

@Waffle'sCrazyPeanut Good on you! :D

Kyle Kanos

I do not think that poking tiny holes in ones body really constitutes violent or disfiguring injury to anyone

Waffle's Crazy Peanut

@KyleKanos When it comes to parents compelling a child who's unaware of the outside world, I guess it is...

Danu

@ACuriousMind Like... vaccination? ;D

ACuriousMind

@Danu almost all.

Kyle Kanos

2:58 PM

@Waffle'sCrazyPeanut Define "unaware"

infinitesimal simplicio

they can always let the skin grow back in

Kyle Kanos

^ also that

ACuriousMind

I also already made the "medicinally necessary" exception a bit further upthread^^

Kyle Kanos

So really it's not a permanent thing

Waffle's Crazy Peanut

@infinitesimalsimplicio @KyleKanos Then, why the need for it?

infinitesimal simplicio

2:58 PM

nobody can force them to wear an ear ring

ACuriousMind

@KyleKanos I agree that mutilation is a strong word. Replace it by non-consensual body modification if you want, it's a violation of bodily integrity all the same.

Kyle Kanos

@Waffle'sCrazyPeanut I'd say that there isn't a need for it.

Waffle's Crazy Peanut

@KyleKanos The child doesn't know. It can't even oppose the giants who're constraining it to pierce a hole on its body.

Kyle Kanos

All I'm trying to point out is that ear piercing really isn't an evil or bad act

@Waffle'sCrazyPeanut Not knowing != unaware

ACuriousMind

@KyleKanos If the child cannot or does not agree, it is.

infinitesimal simplicio

3:00 PM

@Waffle'sCrazyPeanut if the parents are so stubbornly traditional, just do it. Then the child will not wear an earring and it will grow in.

Kyle Kanos

(BTW, having 4 kids, I think I can speak the most of us about what children are aware of at the earliest of ages)

Waffle's Crazy Peanut

@KyleKanos Yeah, it's not. But, that's what I meant :)

ACuriousMind

@KyleKanos The child may well be aware. But unless he or she is expressing explicit consent, one should not pierce the child's ear, right?

Kyle Kanos

@ACuriousMind I think it's the parents choice. We parents are entirely responsible for our children until they are legal adults. We make medical decisions for them, educational decisions, and so on.

Waffle's Crazy Peanut

@infinitesimalsimplicio That's why I asked, "Why force the child to wear an earring and later, allow her get rid of it?"

Danu

3:03 PM

@KyleKanos I still kinda think it's not cool to do stuff that is absolutely not necessary to a kid

Kyle Kanos

If some parents want to pierce their children's ears at an early age, it's their choice as parents to decide what is good (or bad) for their children

Danu

Just like it's not cool to send a kid to a school he hates

infinitesimal simplicio

@Waffle'sCrazyPeanut This kind of force makes rebellious teenagers.

ACuriousMind

@KyleKanos Yeah, parents make the decisions that need to be made. You cannot postpone most medical or educational decisions. You can postpone the decision of piercing without any bad effect at all.

Kyle Kanos

@ACuriousMind Actually, you can absolutely postpone medical and educational decisions.

Jiminion

3:05 PM

[spawning circumcision debate....... now!]

Kyle Kanos

There is no law to force you to take your kids to the doctor

retracted

Waffle's Crazy Peanut

@KyleKanos How can a parent even think of hurting their child, when the child hasn't done anything wrong? Because, obviously parents hurt their child only to try to stop him/her from wrongdoings... (I guess, beating a child is prohibited in the west, but I can say wholeheartedly that Indian parents are not afraid to kill their child) :P

Kyle Kanos

For most circumstances, there shouldn't be a law to force you (the parent) to take your kid to the doctor. There may be some extreme circumstances that I'm unaware of that it might be beneficial to have such a law.

ACuriousMind

@KyleKanos But not without ill effects, or rather, not taking a kid to a doctor when medicine would indicate a check-up is advised is a decision that should be consciously made.

But ear piercing...again, bodily integrity is a human right, and no one, not even parents, should be allowed to overrule another one's human right without good reason.

Waffle's Crazy Peanut

^^^ Exactly!

ACuriousMind

3:08 PM

And "I want my child's ear to be pierced"* is not a good reason at all.

Kyle Kanos

@ACuriousMind You do realize that at "check-ups," the doctors just measure the kid, check the WHO charts, and then say, How's your son/daughter been? and then you leave (after paying money

There's zero need to actually do that

ACuriousMind

In contrast, "I want my child to be healthy" is a good reason for surgery (which is also a violation of bodily integrity)

Kyle Kanos

I can do all that at home

And for free

ACuriousMind

@KyleKanos Oh, sorry, I forgot you Americans actually have to pay for basic medical care.

Kyle Kanos

@ACuriousMind Even if it were free, I'd not do that because it's a waste of time

Waffle's Crazy Peanut

3:11 PM

@KyleKanos I don't even know such a thing exists! Here, care is always taken by parents. They approach doctors only when the toddler's got any disease or something...

Danu

There is a chance, however small, that the doctor will spot something serious during a check-up that you personally missed

no matter how small, I think this chance already justifies going to check-ups at least when your child is young

(and when the care is free)

ACuriousMind

Well, at most of the check-ups I've been at, the doctors did more than measure me. They checked my coordination/reflexes looking for possible neural problems, asked me (not my parents) if there was anything wrong, tested for allergies, and occasionally took blood/urine samples

Kyle Kanos

@Waffle'sCrazyPeanut Even then, the doctor either gives you antibiotics (which often cause more harm than good) or says, Just wait it out.

@ACuriousMind Extra money to do that here.

ACuriousMind

One more reason to never settle in the US, I guess.

Waffle's Crazy Peanut

@KyleKanos But, but... That's all a doctor can do... :P

Danu

3:14 PM

@KyleKanos Antibiotics usually causing more harm than good [citation needed]

Waffle's Crazy Peanut

^^^ Yeah, that too! :P

Danu

Unless you're allergic I doubt that that happens much

(granted, quite a few people are allergic)

ACuriousMind

@Danu Well, prescribing unnecessary antibiotics undoubtedly increases the change of generating germs resistant to that antibiotic.

It doesn't really do harm to the patient, but it is not good for the larger populace if they are wastefully used.

Kyle Kanos

@Danu antibiotics cannot distinguish between the good and necessary bacteria in your body form the bad ones. See emedexpert.com/tips/antibiotics-facts.shtml

Danu

@KyleKanos But note the first sentence

Waffle's Crazy Peanut

3:17 PM

@ACuriousMind That brings the problem to an old proverb I've heard - "Too much of anything is good for nothing!"

ACuriousMind

@Waffle'sCrazyPeanut The difference between a cure and a poison is mainly the dosage ;)

(not actually true in most cases, but in some)

Waffle's Crazy Peanut

waffles agrees :)

Kyle Kanos

@Danu Yes, there are some antibiotics that are necessary for curing certain diseases. But for the generic cold that your kids get, it's not one of those necessary ones ;)

Danu

No, obviously not for a generic cold. But then again, doctors typically don't prescribe antibiotics to deal with a cold.

Kyle Kanos

@Danu You would be surprised

My former neighbor takes her kids to the doctor for antibiotics for every cold they get

And the doctors are willing to dole it out

ACuriousMind

3:21 PM

Most European doctors don't prescribe antibiotics for a generic cold.

Most people don't even go to the doctor with a cold, though.

Kyle Kanos

@ACuriousMind One of the many difference in our cultures :)

ACuriousMind

So perhaps they would if more people showed up, I don't know

Waffle's Crazy Peanut

@ACuriousMind Yep, like I said, most of the people I know of, don't go to doctors because they don't wish to spend so much money for a tiny disease...

infinitesimal simplicio

Changes are on the event horizon people.

ACuriousMind

It is actually bizarre to me that it would cost money to go to the doctor. Unless we need some very special treatment, all we pay is 10€/quarter as a general fee, and the rest is fully covered by obligatory insurance.

And even the 10€/quarter are not there for juveniles under 18 or unemployed people, I think.

Danu

3:26 PM

Well the insurance does cost something tho ;)

Kyle Kanos

@infinitesimalsimplicio What changes?

infinitesimal simplicio

15

Q: Updates to the site

My name is Stéphane and I'm a designer at Stack Exchange, you may have noticed some updates to the design lately. The updates are part of a SE network-wide update which allows us to: Have sharper / more beautiful design on retina displays Fix old layout bugs to fix any layout bugs more easily ...

discussion design

ACuriousMind

@Danu Yeah...but it's obligatory, and paid by your employer, usually. You really don't have the option to say "I don't want free healthcare".

Kyle Kanos

@infinitesimalsimplicio Oh I clicked the link. I just don't see what people are complaining about

For instance the colors (orange?) look the same as before to me

Black/grey & white

ACuriousMind

I see no change at all either

Waffle's Crazy Peanut

3:27 PM

Yeah, me either...

ACuriousMind

Except for the ugly new MathJaX font.

infinitesimal simplicio

These are people with an eye for detail :-)

Kyle Kanos

Maybe the orange links?

Jiminion

@ACuriousMind What if you are not employed?

Danu

@ACuriousMind It looks the same to me?

ACuriousMind

3:30 PM

@Jiminion Insurance for unemployed people is paid as part of the social system called "unemployment insurance" and a few other things. If you are your own boss, you are obliged by law to pay your own health insurance.

@Danu It's...thinner somehow (and I'm not talking about the pre-rendered thingy).

Waffle's Crazy Peanut

@Danu @KyleKanos: Maybe we should wait till it happens to our site. We can notice even a slight change when it comes to Physics.SE :D

ACuriousMind

@KyleKanos The "orange" seems to mean the color of the links on meta, for example of the comment author's name and the time stamp.

It doesn't look different to me, though.

Kyle Kanos

4 mins ago, by Kyle Kanos

Maybe the orange links?

ACuriousMind

Ah

Kyle Kanos

:D

Ugh...Collaborations suck sometimes: adsabs.harvard.edu/cgi-bin/…

Alfred Centauri

3:51 PM

@ACuriousMind As smart as you evidently are, you must that know it costs money to go to the doctor - (pause for effect) - independent of whether you pay the doctor directly or through some (very likely inefficient and costly) indirect system. There is a cost regardless. I presume that what you mean is that direct payment seems bizarre to you.

ACuriousMind

4:23 PM

@AlfredCentauri Yes, I know it costs money. It is just bizarre to me that that money would be actually demanded from the individual going to the doctor. As I say, obligatory insurance covers this here for everyone.

ACuriousMind

4:46 PM

And yes, the system is inefficient and costly, but it means that the division between poor and rich does not result in a division into the sickly and the healthy.

Alfred Centauri

5:03 PM

@ACuriousMind it actually doesn't mean (result in) that but this strays far from physics and so, isn't the proper forum. Maybe one day we can discuss this further in person. Chat and comment threads just aren't the proper medium.

ACuriousMind

Well, the internet in general seems to disagree ;) But I understand your point.

Awal Garg

5:31 PM

@ChrisWhite That is a good point. I now somehow feel we use Hungarian notation in physics already :/

@NikolajK nice

Physics Meta

0

Q: How can I edit my own questions and answers?

How can I edit my own questions and answers for example, give the symbols for pi, integration, and draw diagrams

feature-request

Jiminion

@ACuriousMind Where are you located (what country?)

Danu

5:51 PM

He's in Germany

David Z

6:21 PM

@AlfredCentauri well, for what it's worth... there is no (official) constraint on the topics that may be discussed in this chat room. Not sure if that's what you meant, but I don't want there to be any confusion about that.

Other than some kind of common decency constraint I guess. If something is too offensive maybe we wouldn't allow it.

Stan Shunpike

@DavidZ is there any way to avoid picking a coordinate system? We usually "pick" the z-axis, or something like that from what I understand.

David Z

Sure, you write everything in terms of dot products

or more generally, in terms of scalars. Like in relativity, it's a common problem-solving technique to write all your quantities in terms of Lorentz scalars (things with no free spacetime indices), then you can calculate different terms in different reference frames.

Stan Shunpike

Hmmm. I dunno if Griffiths discussed that. I'll have to look

David Z

6:39 PM

I don't remember it popping up in Griffiths' QM much. I know his E&M book mentions it.

But there are other references that go much deeper into coordinate-free notation. (Not that I actually know of any, but I'm assuming there must be.)

0celo7

7:21 PM

@NeuroFuzzy Know anything about induced isomorphisms on Lie algebras?

NeuroFuzzy

@0celo7 Nope. Unfortunately my group theory knowledge is deeper in the pure math end and nowhere near as deep as @ACuriousmind's

"pure math end" meaning discrete/away-from-lie-groups end

0celo7

7:51 PM

@ACuriousMind Let $L\in\mathrm{SL}(2,\mathbb{C})$. Then there is a two-fold covering homomorphism $\lambda:\mathrm{SL}(2,\mathbb{C})\rightarrow L_+^\uparrow$ such that $\underline{\lambda (L)x}=L\underline{x}L^\dagger$ where the underline denotes for each vector $x$ in Minkowski space $\underline{x}:=x^\mu\sigma_\mu$. I think I understand all of these definitions.

@ACuriousMind Then we have the induced isomorphism on the Lie algebra as $\lambda_*:\mathfrak{sl}(2,\mathbb{C})\rightarrow\mathfrak{so}(3,1)$. From the group homomorphism one can apparently obtain $\underline{\lambda_*(M)x}=M\underline{x}+\underline{x}M^\dagger$. Nakahara does not explain how to determine such an induced isomorphism. Do you know how?

Here $M\in\mathfrak{sl}(2,\mathbb{C})$.

0celo7

8:23 PM

@ACuriousMind How is $\lambda_*(M)$ to be understood? I know that $\mathfrak{so}(3,1)=\{\omega\in\mathfrak{gl}(4,\mathbb{R})|\eta\omega+\omega^T \eta=0\}$, so $\lambda_*(M)$ has to be some $\omega$, right?

FreeMind

9:55 PM

I still don't understand why we have to do $\delta S = 0$ for action minimization in the action integral !

@alarge ^

0celo7

@FreeMind That is the condition for stationary action.

What exactly don't you understand about it?

For functions we have the analogous $\mathrm{d}f/\mathrm{d}x=0$ at the stationary points.

Stan Shunpike

11:04 PM

@0celo7 but why can't we like find a nicer way to organize the indices. I mean, it reminds me of canceling units in chem, except the indices seem like a mess to work with with the tensors some how

0celo7

@StanShunpike There is no good way to organize indices on tensors (or objects) with more than three indices.

There is also no good way to write something like $g_{ij}R^{ij}$ without indices.

Stan Shunpike

I'm not saying don't use indices. I'm more complaining about where we write them. It just seems to pack a lot into a small space. It's possible i just need to get used to it, but it sure seems cumbersome.

0celo7

@StanShunpike I guess you could write $\operatorname{tr}(X,Y\mapsto \operatorname{Ric}(X,Y))$

That sure looks weird though.

Stan Shunpike

@0celo7 so the version of writing the Riemann tensor with $\nabla$ is coordinate invariant? And the version where we write it with Christoffel symbols is not? But the Christoffel symbol way permits calculation? Why? And if the invariant way doesn't let you calculate, what use is it? (Or rather remind me why the uses are)

0celo7

@StanShunpike I have a lot of work to do, let's continue this some other time.

Stan Shunpike

11:16 PM

Okay, sounds good

0celo7

11:31 PM

I went from INTJ to INTP since I learned some physics.

Also my N really went down.

Argh this project is only 15 points out of the 300 of the quarter.

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