The h Bar

Emilio Pisanty

8:18 PM

@0celo7 I'm a bit meh'd about the Cantor set at the moment

but if you do find a non-Jordan-measurable open set that'd be pretty interesting

0celo7

8:31 PM

@EmilioPisanty I got u

Emilio Pisanty

@0celo7 nice

0celo7

@EmilioPisanty I was playing around with Cantor sets and got this

@EmilioPisanty Next exercise is to show if it's sigma additive or not

It's not in the strict sense since the Jordan measurable sets are not a sigma algebra

Emilio Pisanty

@0celo7 what is?

Jordan measurable sets?

0celo7

Jordan measure

Emilio Pisanty

as in, if a disjoint union is still measurable, the measure is the sum of the components?

0celo7

8:43 PM

@EmilioPisanty no, those aren't. But assuming I have a sequence of disjoint measurable sets, is the measure of the union just the sum of the measures of the sets

Emilio Pisanty

man, that sounds so boring

Used to be I found that interesting

it appears that it's no longer the case =/

0celo7

It's true if you use Lebesgue measure. I think Jordan measurable sets have the same Lebesgue measure

Emilio Pisanty

why spend so much effort on a doomed, doomed, doomed concept of measure?

0celo7

So just use sigma additivity of that one

@EmilioPisanty fun

Emilio Pisanty

@0celo7 surely there's better places where you can have that fun?

go do some functional analysis instead

0celo7

8:45 PM

I like functional analysis too

But this is being graded

AccidentalFourierTransform

or go do drugs like normal people

Emilio Pisanty

ugh

@AccidentalFourierTransform never say things in the h bar that you're not comfortable with getting starred =P

0celo7

@EmilioPisanty if I had my way right now I'd be playing MGSV

AccidentalFourierTransform

@EmilioPisanty I regret nothing

for example

I love ISIS!!!

(the metal band, of course)

Emilio Pisanty

lolz

AccidentalFourierTransform

8:51 PM

but that is SO

Emilio Pisanty

a factor of just under two between term time and holidays

@AccidentalFourierTransform ...so what?

=P

AccidentalFourierTransform

it would be nice to have the info about PSE only

no, I mean, that graph is certainly interesting

Emilio Pisanty

don't think the analysis exists

also

AccidentalFourierTransform

but, yeah, Id like to know about PSE

Emilio Pisanty

good to see the home team topping the UK charts

AccidentalFourierTransform

8:52 PM

why only English-speaking countries though?

Emilio Pisanty

@AccidentalFourierTransform 'cause the SE analysis team are sissies

DanielSank

I am very curious what people think of this:

in Physics Meta, 47 mins ago, by Qmechanic

@DanielSank : If after all this discussion about homework in the past, the rep. king of Phys.SE still doesn't use politically correct words for homework, we can't expect to educate other users as well. Also note that the close reason already says homework-like (rather than homework).

Emilio Pisanty

can't be bothered to brave another language

DanielSank

Does a user's rep indicate that their behavior, in particular word choice in discussing site policy, should be more highly valued or more indicative of site direction than other users?

Emilio Pisanty

@DanielSank Your average rep per answer is 133?

man, I don't think I make half that number

yeah, I don't

DanielSank

8:54 PM

@EmilioPisanty Yes, and I have the highest fraction of accepted answers for people who have written at least ~50 answers.

Emilio Pisanty

@DanielSank well, fancy being you, then

DanielSank

It's my claim to fame.

Emilio Pisanty

I should get off my ass and award more rep in bounties than you currently have =P

DanielSank

...and when someone turns to JR's rep as an indicator that his behavior should somehow specially influence site policy, I am not going to be shy about sharing my claim to fame ;-)

AccidentalFourierTransform

@DanielSank let me play devil's advocate here: maybe QM meant that JR is one of the most active users (regardless of his rep), and as such, his behaviour may be a good representative of the general comunity

DanielSank

8:56 PM

@EmilioPisanty Wait what?

@AccidentalFourierTransform He's one guy though. Having a lot of use does not mean you represent the community. In fact, it's probably the opposite since most users aren't power users like JR.

Your move ;-)

...Mr. Devil.

AccidentalFourierTransform

@DanielSank E. is the user who's awarded more bounties here in PSE

by far

Emilio Pisanty

@DanielSank the total of rep I have awarded in bounties is 70% of your total rep

DanielSank

@EmilioPisanty That's amazing, but how is it related to previous discussion?

Emilio Pisanty

would take a bit, but not too much, of sustained effort to bring that up to 100%

DanielSank

@EmilioPisanty -_- jeez

Where U get all dis rep?

Emilio Pisanty

8:58 PM

@DanielSank I'm just reeling off of your awesome rep-per-answer ratio

@DanielSank no idea

DanielSank

@EmilioPisanty ohhhhh

So your claim to fame is that you've given away the most rep? That's awesome!

You're a regular Robin Hood.

Emilio Pisanty

@DanielSank pretty much, yeah

DanielSank

That's a pretty sick claim to fame.

Emilio Pisanty

@DanielSank don't think I ever stole any rep

DanielSank

@EmilioPisanty Hmmm, ok then you're just a philanthropist.

In any case, pretty awesome.

Emilio Pisanty

9:02 PM

@DanielSank philantropy is when it actually costs you

giving bounties above 30,000 costs you nothing

AccidentalFourierTransform

@EmilioPisanty so there is no word to describe you. Congratulations!

(there probably is some German word, though)

Emilio Pisanty

I just like to think of it as doing my bit to improve the site by putting the rep incentives where they will produce the most quality content

DanielSank

@EmilioPisanty It's a really nice idea.

AccidentalFourierTransform

you are such a romantic

DanielSank

Thank you again for rewarding that post about the Boltzmann constant. It was nice to see that appreciated.

Emilio Pisanty

9:04 PM

@DanielSank it was a really good answer

DanielSank

@EmilioPisanty Thanks. Pretty sure the first place I encountered the idea that temperature is a Lagrange multiplier was in Pathria's book.

Emilio Pisanty

and also, I think the site benefits from having folks who have produced that sort of high-quality content to reach the important moderation milestones faster

DanielSank

I'm surprised, in retrospect, that Reif doesn't discuss that.

@EmilioPisanty Perhaps. I feel I don't exercise my moderation powers much at all.

i.e. I never do reviews any more.

Like, ever.

Emilio Pisanty

@DanielSank maybe not, but you're able to delve into the full review queue history and suss out bad stuff if the need comes

also see & react to deleted answers, again, if there's a need to

It would be really good to have a much bigger critical mass of 10k+ users, as measured by the fraction that do occasional moderation

particularly if we as a community managed to actually use things like the recently-deleted list on the 10k tools

actually catch bad deletions if and when they happen

DanielSank

See, that sounds like work.

dmckee

9:09 PM

@DanielSank Whoa! I hadn't seen it formulated that way. Did you do a post on it? Pointer?

DanielSank

I just get so... I dunno... funky... when I do reviews.

Emilio Pisanty

@DanielSank yeah, the 10k tools could use a fair bit of improvement

DanielSank

42

A: Is the Boltzmann constant really that important?

We can understand all of this business if we visit the statistical mechanics notion of temperature, and then connect it to experimental realities. Temperature is a Lagrange multiplier (and should have dimensions of energy) First we consider the statistical mechanics way of defining temperature....

@dmckee

This is the right way to think of temperature. Statistical mechanics is a maximization problem where you're maximizing entropy.

Emilio Pisanty

also, on the bounty-to-10k front, here's a good morsel of history

3

A: Are Born-Oppenheimer energies analytic functions of nuclear positions?

Suppose that for all $z$ in some open set $Z$ of complex numbers containing $z_0$, the Hamiltonian $H(z)$ is a compact perturbation of the self-adjoint $H(z_0)$ depending analytically on $z$. Then, for every simple eigenvalue $E_0$ of $H(z_0)$ and associated normalized eigenstate $\psi_0$, there ...

DanielSank

But! You have constraints: fixed energy, fixed volume, fixed particle number...

Emilio Pisanty

9:11 PM

that bounty put Arnold Neumaier over 10k

DanielSank

Temperature, pressure, and chemical potential are the Lagrange multipliers associated to fixed energy, pressure, and particle number!

AccidentalFourierTransform

In a couple of days I'll put heather over 5k :-)

DanielSank

@EmilioPisanty You like putting people over 10k, eh?

dmckee

"Now suppose we add the constraint that the system has a certain amount of energy [...]" <== Sets off one of those "How did I miss that?!?" moments right at the top of the post.

Emilio Pisanty

@DanielSank have done ever since

DanielSank

9:12 PM

@dmckee I know, right?!

dmckee

Some days I feel like a dunce.

DanielSank

@dmckee Don't. Very few physicists seem to have ever seen this idea.

I just got lucky that I read Pathria and picked up on that little note.

Emilio Pisanty

@DanielSank I once saw a public lecture by Eric Cornell that I think you would have enjoyed immensely

Core point that nature is lazy and sloppy

so it likes to maximize the sloppiness and the unlaziness

DanielSank

@EmilioPisanty Link plz?

@EmilioPisanty I had the privilege of eating dinner with him once. Friendly guy!

Emilio Pisanty

@DanielSank this was at ICOLS 2013, and all the other talks were posted online. I emailed after a few months to ask, and they said that he's so perfectionist that he didn't want it aired until it was absolutely spotless.

dmckee

9:15 PM

They have it in our library here. I'll be back.

Emilio Pisanty

so nature likes to maximize sloppiness S and minimize unlaziness U

DanielSank

@dmckee What's "it"?

Cornell's talk?

Emilio Pisanty

but obviously that's a problem because being really sloppy also requires you to be very unlazy, and being unlazy isn't fun

so nature tries to minimize some kind of figure-of-merit

that goes like U-S

DanielSank

Free energy?

0celo7

@DanielSank He probably means Parthia.

Emilio Pisanty

9:17 PM

but obviously that's a bit too rigid

0celo7

Forgive autocorrect

Emilio Pisanty

so you need some kind of tradeoff factor

so you minimize F=U-TS

DanielSank

@0celo7 Oh right.

@EmilioPisanty Right. So here's why I like the Lagrange multiplier picture so much:

The value of a Lagrange multiplier tells you how much better you could maximize your objective function if only you would be willing to relax the constraint a bit.

A system with high temperature is one where giving it just a tiny bit more energy would let it increase the entropy by a relatively small fraction.

So, if you hook it up to a low temperature system, it will give up energy, because the low temperature guy can raise the total entropy a lot.

By the way, this helps understand why negative temperature means something is very hot.

If $T<0$, then I always want to give away energy.

Emilio Pisanty

damn

DanielSank

What?

Emilio Pisanty

9:22 PM

one of these days I'll really truly grok these things

DanielSank

@EmilioPisanty It's not complicated. I promise.

If $T<0$ that means that giving away energy raises $S$ for me.

If $T>0$ then absorbing energy raises $S$ for me.

Emilio Pisanty

oh, no, I understand everything you said

DanielSank

Therefore, if a negative temperature system touches a positive temperature one, the energy flow is from the negative guy to the positive guy.

Emilio Pisanty

I just would have been entirely unable to come up with more than 10% of it on my own, I should think

DanielSank

@EmilioPisanty Ah well, we all stands on the shoulders of our predecessors.

Emilio Pisanty

9:24 PM

On looking over your answer again, I had the same reaction as dmckee

12 mins ago, by dmckee

"Now suppose we add the constraint that the system has a certain amount of energy [...]" <== Sets off one of those "How did I miss that?!?" moments right at the top of the post.

again.

DanielSank

Interesting.

0celo7

I'm still waiting for the Eureka moment

DanielSank

When I read it in Pathria my reaction was more like "Oh! Well why didn't my undergrad course just say that?" along with "Man, Lagrange multipliers are way more interesting and important than I realized when I first learned about them".

3

heather

hello all

DanielSank

Hi!

heather

9:39 PM

oh, i noticed the homework comments made here in chat - I'd certainly be willing to help in any way I could.

dmckee

@DanielSank I had to feel very comfortable with the basic framework of Lagrangian mechanics before I could focus on the undetermined multipliers problem deeply enough to understand it and start to see the depth of it.

Sir Cumference

Howdy

dmckee

That didn't happen the first time through for me either.

DanielSank

@dmckee Ack! You can understand Lagrange multipliers without ever thinking about Lagrangian mechanics!

dmckee

That stuff is like magic.

DanielSank

9:47 PM

The basic idea is rather simple!

No no no no. There's no magic. I promise.

Suppose you have a function $f(x,y)$ that you want to maximize.

How do you do it (real question, not rhetorical).

dmckee

@DanielSank Formally. Identify generalize coordinate. Write the energies. Take derivatives. Write constraints. Take derivatives. Setup system of equations. Beat at the math until one of us surrenders.

Emilio Pisanty

@dmckee I suspect you'll enjoy this one

The Electric Slide Rule - Numberphile

►

dmckee

Is there a better way?

DanielSank

@dmckee Woah, dude. I'm just saying you have a normal, friendly function of two variables and you want to find a local maximum.

You just compute $\partial f / \partial x$ and $\partial f / \partial y$, set them to zero, and solve.

Right?

No physics here.

No magic.

dmckee

@DanielSank Oh. Yeah.

0celo7

9:50 PM

Friendly indeed

DanielSank

@dmckee Good ok. Now suppose I ask you to find the maximum constrained to the condition that some other function is equal to zero, e.g. $g(x,y)=0$.

Now we have a hard problem because setting partial derivatives of $f$ to zero will find us points that aren't on the constraint. Ok so far?

dmckee

Parameterize the solution to $g=0$ and take the derivative along that line, I guess.

DanielSank

@dmckee That would absolutely work. Unfortunately, finding a parametrization of a curve defined by a (set of) equation(s) is very hard in general.

dmckee

And cry is the solution isn't well behaved.

DanielSank

@dmckee Well let's see if we can avoid tears, eh?

Emilio Pisanty

9:52 PM

also this

The iPhone of Slide Rules - Numberphile

►

DanielSank

@dmckee The equation $g(x,y)=0$ defines a curve in the $x/y$ plane.

dmckee

@DanielSank Sure, but like you said it is probably hard to parameterize.

DanielSank

@dmckee Yes, but the curve is there.

dmckee

And it might be a more complicated set than a curve, but lets pretend that doesn't happen in physics.

DanielSank

Now here's the trick: The curve is always perpendicular to the gradient of $g$.

It has to be, because if it weren't, it wouldn't be a curve of constant $g$!

dmckee

9:55 PM

@DanielSank Hmm ... I think this is the clever part.

DanielSank

Let me know when you agree with that, or if you have a question there.

dmckee

No question, that's clear.

DanielSank

Ok cool.

Emilio Pisanty

@DanielSank objection

DanielSank

Now suppose we're walking on the curve, and as we walk on it, our value of $f$ is changing.

0celo7

9:56 PM

@dmckee unless you have a cusp, the implicit function theorem does give you a curve...

Emilio Pisanty

you never specified an inner product in $x,y$ space

DanielSank

If that's the case, we're not at a local constrained extremum.

Ok?

@EmilioPisanty Oh do shut up ;-P

This will help:

@dmckee I await your confirmation or objection.

dmckee

@DanielSank Yeah. That's why I wanted to take the deriviative along the curve.

DanielSank

@dmckee Great. But now observe: At the point where we're at a local constrained extremum, the curve of constant $g$ must be parallel to the curves of constant $f$.

Note the picture.

dmckee

Yeah. Got it.

DanielSank

9:58 PM

Ok then we're on the home stretch! We said the gradient of $g$ is perpendicular to the curve. We also know that the gradient of $f$ is perpendicular to the curves of constant $f$.

Emilio Pisanty

@DanielSank ah, yes, I remember that

DanielSank

Therefore, at our constrained extremum, we have $$\nabla f || \nabla g \, .$$

dmckee

Cute.

DanielSank

Or, in other words, $$\nabla f = \mathcal{L} \nabla g$$ where $\mathcal{L}$ is just some constant.

So, $$\nabla ( f - \mathcal{L}g ) = 0 \, .$$

In other words, we now have an unconstrained maximization problem for a new function $f - \mathcal{L}g$.

Done.

That's Lagrange multipliers.

Emilio Pisanty

@DanielSank so how does your previous comment look like in this picture?

dmckee

10:01 PM

Yeah. If they ever showed me that in a context outside of Lagrangian mechanics I forgot. Or was on the beach. Or something.

Emilio Pisanty

42 mins ago, by DanielSank

The value of a Lagrange multiplier tells you how much better you could maximize your objective function if only you would be willing to relax the constraint a bit.

DanielSank

@dmckee Beaches are good.

@EmilioPisanty I was just about to get to that.

dmckee

I'll just go order my high-durability dunce's cap, now.

Emilio Pisanty

@DanielSank ok cool I'll shut up

0celo7

@dmckee In mathy terms, if $r(t)$ parameterizes the solution set of $g=0$, then $t\mapsto f(r(t))$ must have a local max. By the chain rule, we must have $\nabla f\cdot r'=0$. Then note that $r'\bot \nabla g$, and you're done.

DanielSank

10:02 PM

Suppose the point at which we find this constrained extremum is at a point where $f$ is very flat.

In fact, suppose $f$ is perfectly flat.

In that case, moving the constraint curve a bit doesn't help us at all, i.e. there's no gain in $f$ if we wiggle the curve.

@EmilioPisanty Ok?

0celo7

@DanielSank Can you make the same thing work for maximization on spaces other than $\Bbb R^n$?

DanielSank

@0celo7 Later.

Emilio Pisanty

@DanielSank perfectly flat, yes

DanielSank

@EmilioPisanty Yeah, well if $f$ is pretty flat then $\nabla f \approx 0$.

Emilio Pisanty

for $f$ pretty flat, I'm not 100% sold

it won't change much, sure

DanielSank

10:04 PM

We have $$\nabla g = \nabla f / \mathcal{L}$$

Emilio Pisanty

this is (only) at the extremum, right?

DanielSank

Yes.

Emilio Pisanty

ok sure

DanielSank

$\nabla g$ is some fixed thing, so if $\nabla f$ is small, then we need $\mathcal{L}$ to also be small for the equation to work out.

In other words, small $\mathcal{L}$ corresponds to the case where your're in a flat area of $f$ and relaxing the constraint a bit doesn't help change the extremized value of $f$ much.

Emilio Pisanty

@DanielSank sure

DanielSank

10:06 PM

Large $\mathcal{L}$ corresponds to a case where "the constraint is holding you back a lot".

So, @dmckee, in the case of Lagrangian mechanics a large Lagrange multiplier means that the action would be much more minimized if the constraints were relaxed. In other words, the constraint forces are large.

dmckee

@DanielSank Nice.

DanielSank

@dmckee See, no magic!

Unfortunately, this entire topic is usually taught by dumping a problem on the student and telling them to follow some god-forsaken recipe to get an answer.

When I retire, I would like to write a book titled How to understand all that stuff they never explained.

heather

you should

i would definitely read it.

you explain things very well.

DanielSank

Yeah... chapters: Entropy, Lagrange multipliers, Fourier transform (already written)... what else?

Maybe I should throw in a cooking chapter. That would be awesome.

Oh, jeez, tensors.

My goodness yes there will be a chapter on tensors.

heather

YES

write about tensors

DanielSank

10:12 PM

Yes, and with pictures.

heather

i still don't really understand those buggers.

AccidentalFourierTransform

Hi there @heather

bout your comment in meta:

heather

@AccidentalFourierTransform hello =)

AccidentalFourierTransform

people didnt seem to like some (or most) of my questions, because I got many downvotes

it was probably because of the last question

which was a joke, but some people didnt realise

DanielSank

@AccidentalFourierTransform I down-voted it simply because it asked more than one question.

AccidentalFourierTransform

10:14 PM

(or they did but disliked it anyway)

DanielSank

The questions were individually fine.

AccidentalFourierTransform

@DanielSank thats what I thought

0celo7

@DanielSank sobolev spaces on manifolds

Emilio Pisanty

@heather take it easy with the tensors

AccidentalFourierTransform

therefore, I deleted all but the first question

Emilio Pisanty

10:15 PM

they look big and scary but they're honestly not that necessary for a pretty long while

DanielSank

@AccidentalFourierTransform Oh, I should un-downvote.

AccidentalFourierTransform

@DanielSank OF COURSE YOU SHOULD

DanielSank

@AccidentalFourierTransform Oh, I already did.

heather

@AccidentalFourierTransform well, anyway, maybe you could post the other questions as separate posts? I thought at the very least that #2 and #3 were good.

AccidentalFourierTransform

yeah, I will post them again

I wasnt very motivated to do so because of the several downvotes

ppl didnt like my questions :-(

but yeah, Ill post them again

heather

10:18 PM

=/ i thought they were good. and #4 was kind of fun.

DanielSank

@AccidentalFourierTransform Oh stop moping and post them separately.

I liked them all.

heather

-7

A: February 20th Ask Me Anything with heather: Question Pool

Einstein or Bohr? Harvard or MIT? Michelle or Melania? Tesla or Edison? Ubuntu or Fedora? Heisenberg or Schrödinger? Dems or Repubs? Strings or loops? Socialism or Capitalism? Frequency or time? Trump or Hitler? David Z or Ron Maimon?

^-7!? geesh.

i didn't think some of them were too bad.

DanielSank

@heather It's too many questions all together!

heather

well, yes, i suppose that is problematic.

DanielSank

...and several of them are ridiculous pop culture questions with zero context.

heather

10:20 PM

also true.

DanielSank

Michelle or Melania wat?

heather

i think that references the first ladies.

DanielSank

Yes but what's the question?

Which one you'd rather hang out with?

heather

but really that's not a fair comparison - Mrs. Obama had 8 years, Mrs. Trump had a few weeks.

DanielSank

Which one is a better first lady?

heather

10:21 PM

@DanielSank which one's better, I think.

DanielSank

Which one has better taste in polar bears?

heather

lol

definitely that.

Emilio Pisanty

which one embodies the cultural values you feel closer to

DanielSank

Well then it's Melania because she's got the ties to Russia.

::ducks::

Emilio Pisanty

like the rest of the questions

AccidentalFourierTransform

10:22 PM

wow

heather

I thought "Einstein or Bohr? [...] Heisenberg or Schrodinger? [...] Strings or Loops?" were the best ones.

DanielSank

Let's see if I get suspended for that

heather

because they asked more viewpoint/physics based questions.

hmm...

0

Q: Does Level IV Multiverse/Ultimate Multiverse contains 'impossible worlds'?

Does Level IV Multiverse/Ultimate Multiverse contains 'impossible worlds'? Does it contain universes with sets, structures, or systems that exist beyond spacetime, duality, or existence and nonexistence? Does it contains universes with different laws of logic or metaphysics than ours? Does it con...

^why was this closed as non-mainstream physics?

DanielSank

@heather Because people don't understand how to VTC properly.

heather

but John Rennie!

DanielSank

10:24 PM

It should be closed for asking too many questions because that conveys useful information to the poster.

@heather But John Rennie what? Clearly you didn't see my little rant a bit up...

AccidentalFourierTransform

^

heather

no, I didn't.

DanielSank

John has a lot of rep because he writes a lot of answers. That doesn't suggest that he is better at site policy than anyone else.

heather

@DanielSank i think they're all very closely related and basically asking the same sort of thing. I don't think it should be closed at all.

DanielSank

@heather Look here

AccidentalFourierTransform

10:25 PM

@DanielSank what? it doesn't ask too many questions! It only asks one question!

heather

@DanielSank he's more familiar with the site, he's been around for a while, and he's one of the most respected people on PSE. I count that as suggesting that he's better at site policy.

@DanielSank now that comment is preposterous.

DanielSank

@heather Which?

heather

the one you linked (QMechanics)

DanielSank

@heather He is not "more familiar with the site"!

heather

he's been around for a while!

DanielSank

10:27 PM

When the mod election happened JR showed several times that he does not understand how large parts of the site work! I'm not saying he's more ignorant than anyone else. I know little about site workings as well.

I just wish everyone would stop equating rep with "knowing about site policy" because it's wrong.

heather

@DanielSank link?

@DanielSank for the record, that's not the reason I think JR knows more about site policy.

DanielSank

@heather I'm not going on chat safari right now, sorry.

Emilio Pisanty

@DanielSank I don't think Qmechanic's comment should be read quite like that. Make a reasonable switch to "if someone who uses the site as often and for as long as JR still gets X wrong".

heather

sorry, but a claim like that i want a reference for @DanielSank.

::shrugs::

DanielSank

@EmilioPisanty But that's one person. And besides, the entire point is sunk by the fact that the policy has been called the "homework" policy and not something else.

There's no reason to expect anyone to call it anything other than the homework policy as of yet!

@heather That's reasonable. I might go hunting later, but I doubt it because I don't see the point in question as particularly important.

Emilio Pisanty

10:31 PM

@DanielSank ::shrug::

DanielSank

Why is everyone shrugging at me?

Emilio Pisanty

cf. JR's comment on the right

6 hours ago, by John Rennie

@DanielSank I gave up debating the homework policy in favour of hammering nails into my kneecaps because it was less painful and more productive.

heather

@DanielSank okay. I am interested, so if you find a comment, send it my way =)

Emilio Pisanty

it takes a good bit of energy to engage with that debate at this point

AccidentalFourierTransform

10:43 PM

Apparently, I live in Atlanta

Areas of Europe as US states of equal GDP, with corresponding cities

Secret

triangulene is created by using a afm like drive, aim voltages at two hydrogens to knock them off. The molecule may have applications in spintronics, as both electrons have the same spin

heather

ah, darn it

my answer text disappeared =(

my motivation to answer the question is now way down.

0celo7

@AccidentalFourierTransform good trap music there

heather

10:59 PM

0

Q: What happens when a cylinder collides to the point of a triangle?

In a computer simulation, what math formula do I use to predict what will happen when a cylinder hits a triangle's point if both objects were made up of pure titanium? In my mind, I picture the cylinder will have a dent in the shape of a cone assuming the cone is traveling at 100mph and the tri...