Do you know the mean value theorem yet?

not yet

Not up to that point

Well, I know it, but

Not rigorously

@Slereah Step 1: Show that a Lipschitz function is uniformly continuous.

Step 2: Show that a $C^1$ function with bounded derivative is Lipschitz.

Step 2 is hard

I recall that it is on manifolds, especially

@Slereah yes, you remember our discussion?

I do

The full proof is contained in my paper

Even Rn

But in one dimensions you can probably do it yourself

There's the intermediate value theorem

@BernardoMeurer Say :)

@anonymous Do you know how to use git and LaTeX?

@BernardoMeurer Oh no, I only know MathJax :/

Then let me give it to you in PDF

one second

Landau&Lifshitz is driving me nuts

that is all

@anonymous docdro.id/uYHTp0F

@anonymous I'm compiling a list of hard calc exercises

I need someone to curate them

@BernardoMeurer I got the problem set pdf. Which question are you having trouble with ?

@anonymous No, no, I already solved them all :P

I need someone else to go through them and tell me ones they find "too easy"

the problems are meant to be hard

Limits I can be easier

I'm the one writing that

@BernardoMeurer That'll take time. Why do you want others to go through them and tell which ones they find hard ?

@anonymous I want to pass the problem set after I'm done to the people who take the class next year

to help them study

because they're good practice problems, they're the ones we have been solving

I have more to input still though

@BernardoMeurer Oh, so I just need to tell you which ones I feel are too easy for the problem set?

@anonymous yep :)

Once I'm done, if you're interested, you can help me list answers for the simpler ones (limits, primitives, integrals). I'm not giving answers to the longer questions

@BernardoMeurer Ok, I'll check them at night when I'm free and tell you tomorrow :)

@anonymous Sounds great man, thanks for the help!

Also, can I add some problems? I've got great calculus problem sets :D

@anonymous Yes! absolutely!

Just send them to me and I'll typeset them and add them to the set

the more the merrier

@BernardoMeurer Can you give me your email id? I don't want to share my problem sets here in public :P

@anonymous You can reach me at [email protected] , or if you prefer my institutional address at [email protected]

@BernardoMeurer Thanks. How many days do you have for the work to be done? I feel we should divide it into - Limits, Continuity and Derivability , Indefinite Integration , Definite Integration.

@anonymous I have no deadline or nothing. I'm going through some stuff and needed to pick up a project to distract my mind :)

I like typesetting, and since I had a hard time with Analysis I figured I'd try and help others

Those categories sound reasonable too. I feel like after we're happy with the exercises we can reorder. I didn't think too much about the current ones, it was just to make it less of a mess

Check you gmail @BernardoMeurer Did you get the integration problem set links ? Are they working?

@anonymous Yep, just tested, both working :)

I'll start putting them in

Yay :) I'll give the other topics also soon when I am free !

And I will check your problem set at night

Bye for now

Got some work

@anonymous See you later!

@0celo7 The (essentially) unique representation of the Clifford algebra that induces the generalization of the usual Dirac spinor in all dimensions and signatures. And yes, of course the existence of the spinor depends on global properties - holonomy is not local; and indeed having reduced holonomy $G_2$ constrains the manifold to be Ricci-flat, which is a rather strong condition.

@BernardoMeurer Are you comfortable with combinatorics ? I have a good problem (which i couldn't solve) :P

@Secret You there ?

@anonymous I am, just kinda busy on some maths stuff. I am not very good at combinitorics unless it is some variation of box counting problem

@Secret Well, it is a type of box counting problem. Anyway, carry on with your work. I'll tell you when you are free :)

Morning

arxiv.org/pdf/1312.4057.pdf

this is a great paper

"To describe natural motion, on the other hand, we need a bit of cosmology. The cosmos is composed by mixtures of five elementary substances to which we can give the names Earth, Water, Air, Fire [He 312a30], and Ether. The ground on which we walk (the “Earth”) has approximate spherical shape. It is surrounded by a spherical shell, called the “natural place of Water”, then a spherical shell called “natural place of Air”, then the “natural place of the Fire” [He 287a30]."

"In a vacuum with vanishing density a heavy body would fall with infinite velocity [Ph 216a]."

@SirCumference Night :)

Sup?

@anonymous Where ya live?

@SirCumference Time here is 5pm. The city shares the same name as the country and is near to a gulf. It has an seacoast nearby. Solve the puzzle. :)

(Others don't answer. Let SirC solve it :))

@Slereah ...how did you end up there? :D

HSM stack exchange

wat

waaat?

I'm surprised by the serious tone of the question. I guess both of them had fainted :P.

thoughts on this ad to-be?

I'm out of words now XD

@anonymous lol

Maybe god is partial to us and never shows us such magic tricks. I'm starting to doubt myself now :P

@heather No idea how the math.SE folks would like that, but I think that sounds too much like a "get homework help here!" advert

yeah, okay @ACuriousMind

@heather The tagline could be something along the lines of : "Join the world's largest network of mathematics experts and amateurs "

@anonymous, good idea, I'll use that.

:)

You can modify it to make it sound better

But Im out of ideas presently

I am as well...it's morning here, I woke up not too long ago.

@anonymous, I linked to your comment on the ad post: meta.physics.stackexchange.com/questions/9554/…

@heather Nice ad. How did you make the graphics? Any software ? :)

@anonymous i used google drawings

i can't resize within google drawings (that I know of) so after making the ad, I resize it using resizeimage.net

I see. Good work! I've never used google drawings.

@heather Optically, I think the lining on the paper is a bit strong and clashes with the text; I'd have made the lines lighter

@ACuriousMind okay, I can edit to fix that.

maybe that's a little better?

What graphics app did you use in the end?

@JohnRennie, google drawings

GDraw may be a very basic program but it's surprising what you can achieve with it.

@0celo7 Nah, it's mean value inequality.

I am becoming increasingly uncertain that anyone really knows what they mean by a Majorana spinor :/

Isn't the Majorana spinor the one made with the real Clifford algebra

Rather than the fake complexified Clifford algebra

@Slereah There are at least two issues: 1. Is a "Majorana spinor" a real representation of the full Clifford algebra or only of its even piece $\mathfrak{so}(p,q)$? 2. Is the physicist's usage of "real" what a representation theorist would call "real or quaternionic"?

fuark i don't remember

People define spinors from Clifford algebras and then never use it again

It's easy to say "A Majorana spinor is a real representation of $\mathrm{Cliff}(p,q)$". But once you try to extract that from the literature in a rigorous abstract way, it all goes south rather quickly

It's never even clear what part of the algebra is the spinor and what part is the rotation group

Just look at the three references I cite at the end - they all claim different existence conditions for "Majorana spinors"!

And nobody even attempts to write out spinor solutions as members of Clifford algebras

Either at least two of them are wrong, or they're all using different definitions of what a Majorana spinor is

That's physics for you.

@Slereah A spinor is not part of the Clifford algebra. The Clifford algebra has at most two irreducible representations, both of dimenison $2^{\lfloor d/2\rfloor}$ regardless of signature. A Dirac spinor is simply something that transforms in that irreducible representation.

didn't you say that the spinor was part of it the last time we had that discussion

In even dimensions, this representation is not irreducible as the representation of the even subalgebra $\mathfrak{so}(p,q)$ of $\mathrm{Cliff}(p,q)$, it decomposes into two representations that differ by chirality, these are the Weyl spinors.

I don't even know what's real anymore

It doesn't help that the mathematicians sometimes call the Dirac spinors "pinors" and the Weyl spinors "spinors".

I thought the pinors were for $O(p,q)$

Now, a Majorana spinor should be simply something in a real subrepresentation of the Dirac spinor, if such a real representation exists.

@BalarkaSen O'Farrill is pretty close to a mathematician usually, but even he says things like "this nebulous concept is best left undisturbed" when discussing certain aspects of this...

Oh well

@Slereah It might be that we talked about that before I digged deeper into this

On what can the member of a Clifford algebra act, though, if not another member

the worrisome thing is that the existence of Majorana spinors is pretty crucial to supersymmetry in various dimensions

@Slereah On a vector space it's being represented on.

As I said, the nice result is that the Clifford algebra has essentially only one irreducible representation, so no choice there.

how do you apply a Clifford algebra thing on a vector?

I know they're forms, but they're direct sums of 'em

of various degrees

...by having a representation map $\rho : \mathrm{Cliff}(p,q) \to \mathfrak{gl}(V)$ as for every representation of an algebra?

I guess!

The physicist almost always suppresses representation maps in their notation, which is another thing that greatly annoys me :P

It's somewhat justified for the Clifford algebra since it has only that one irrep in even dimensions, but it drives me nuts for things like reps of $\mathrm{SO}(p,q)$ in general

I'm also a bit worried about the two inequivalent representations of the Clifford algebra in odd dimensions, since I've read "the spinor representation of $\mathrm{SO}(7)$" in various places

One of the worst part about the whole Steenrod affair is that the theorem in the book isn't even sufficient for what GR books claim

It only discusses the case of compact manifolds

The proof of Lorentz metrics for non-compact manifolds is in Geroch

(Spoiler they all admit one)

I'd really like to understand that theorem so I can write it down somewhere because I'm sick of just always being redirected to it

@BalarkaSen MVI follows from MVT and the book he's reading doesn't do MVI until Banach spaces, so he does indeed need MVT.

Right, MVI is a pretty easy corollary of MVT

I'm lying in bed but I think it's just replacing |f(c)| by the sup.

sup of norm of the derivative, yeah.

Forgot the prime

Arrrrgh, physicists! "We consider a cone $X$ on $Y$, i.e. $X = \mathbb{R}\times Y$"...that's not a cone, that's a cylinder...

Same as a cone, upto the cone point, so no harm done :)

@BalarkaSen Well, the point is that we want to consider a conical singularity with this local model, so omitting the cone point is...missing the point

lol oh well

Ugh, it gets worse, now he claims $\partial X = Y$...

I mean, I can decipher what all this is meant to be, but how does one get to such a sloppy usage?

A cylinder is nothing but an infinitely long cone

@Slereah I'd rather say that $[0,\infty)\times Y/(0\times Y)$ is the infinitely long cone :P

Seems legit

@ACuriousMind is that not true for a cone?

Seems true I guess

@0celo7 It's true for a finite cone, yes.

@ACuriousMind Well, boundary in which sense?

As a subspace of something

are these manifolds

ahahahahaha...don't ask

As a pseudomanifold, if $Y$ is a manifold, perhaps

I think "pseudomanifold/orbifold with boundary" is probably the best interpretation

pseudomanifold?

is that some algebraic topology thing

Not sure I want to think about whether the application of Stokes is justified here...

Nah. It's a space which is a manifold away from finitely many points.

Ah, physics

@ACuriousMind let's hope you don't need elliptic regularity for your cone :)

@BalarkaSen I think I might want the stratified version, i.e. the singular locus has at least codimension 2

Got it.

Singular locus?

We don't have any community ads for Space Exploration SE(space.stackexchange.com) and History Of Science and Mathematics SE(hsm.stackexchange.com). @heather Could you make a couple of ads for those two sites also? I feel they are great sites but with low activity.

@ACuriousMind ^^

@0celo7 The set you have to remove from the space to make it an actual manifold

@ACuriousMind Yes, sure, but what is it? A codimension 2 manifold?

No, it might itself have a singular locus, the definition is somewhat recursive

Then what does the "codimension" refer to?

Some topological dimension?

Even generic smooth dimension works, I think.

It's generically a submanifold anyway.

@0celo7 No, one can inductively define a stratified pseudomanifold of dimension $n$. There are some technical conditions on the singularities looking like generalized cones; look up "stratified pseudomanifold" if you're really interested

@anonymous, we have one for hsm (meta.physics.stackexchange.com/a/9567/121464) but sure, i can make one for space exploration =) i'm doing a few physics problems, but then i'll work on that.

I was supposed to learn stratified Morse theory but didn't

Did you learn regular morse theory?

A little.

Not much.

@ACuriousMind I've asked this a billion times, but why does the physicist approach to QM work so well

I still haven't found anything that physicists do that is actually incorrect

I.e. the result is not incorrect

At first I thought it was "compact operators are nice," but none of the operators are compact

In fact, none of the usual operators are even bounded, nor defined on the whole Hilbert space

...but why does the physicist approach to QM seems to imply there is another approach, is there?

I don't have mafia's skype, he didn't add me.

@0celo7 I largely suspect that we are seeing the results of decades of weeding out reasoning that leads to erroneous results.

@ACuriousMind unless you know of any such results, I smell a main site question

It's like canonical quantization - when one looks into formal quantization procedures, one begins to wonder why on earth canonical quantization gets so much right if it ignores so many subtleties. Then one realizes that all the other approaches neglecting subtleties simply failed, like Bohr's and Sommerfeld's approach of using action-angle variables instead of $x$ and $p$ for the CCR.

It's natural selection - if the reasoning didn't get so much right, it would have been thrown out long ago; I'm not convinced there needs to be a deeper reason than that

thoughts on this potential ad? I'm not sure I like the font.

and it might be too simple.

Why not post on SpaceEx and ask for one from them?

@ACuriousMind As a mathematician who likes physics, I constantly wonder why physics gets so much right :)

@ACuriousMind I agree with this.

But I am still curious where it fails, outside of contrived counterexamples.

@0celo7 Probably because physics is bound by experiments and math is bound by proofs/axioms/bs

bs? lol

There's loads of bs in mathematics that doesn't appear in physics texts.

@heather are you designing these in photoshop?

@KyleKanos such as?

@KyleKanos no application to the real world = bs?

@heather Thanks :)

@obe nope, google drawings

You would know how to use photoshop

@SirCumference you were right all along

He photoshopped the stars

no I didn't.

he said he used photoshop for 7 years, longer than me.

I only used it for 5.

What does that have to do with anything?

You're not an American

what does that have to do with anything?

is the real question.

@anonymous no problem - if you look at the picture I posted above, that's my first draft.

@obe because he is

@0celo7 I guess mostly notation, now that I stop and think about it. A lot of mathematics is overly rigorous for most needs

@heather I like it. Maybe you could make the color of the rocket white rather than black. It will improve the contrast. Also, if possible make the ejected gas red/orange/yellow as you wish

@0celo7 what does that imply?

@anonymous okay, lemme see what I can do.

I mean, to introduce a random variable, a mathematician would need to introduce probability space, $\sigma$ algebra, measures on the space, subsets of the space and probably a few things I'm forgetting at the moment.

@heather And the tagline could be something like "Q&A site for spacecraft operators, scientists, engineers, and enthusiasts."

okay, sounds good.

did you like the blue for the text, or should I keep it black and white (plus the color for the ejected gas)

blue.

and how's the font, as well?

@heather Blue for text looks good. But change the color of the rocket (black doesn't give the contrast)

@KyleKanos sigma algebra is the subsets

right, yes.

@0celo7 Uh, right.

Speaking of... @heather

How much naive set theory do you know

@0celo7, a bit, I suppose. I've been reading through Halmos' Naive Set Theory (though I'm not that far - I plan to read and then life gets in the way).

@heather sounds like you're ready for measure theory

Now with extra Banach spaces

@0celo7 hi/ welcome back. ps dont recall if ever asked you. we have no other volunteers/ takers at moment, think you would be acceptable/ significant guest speaker for variety of reasons if you ever find the inclination, plz consider it. :) meta.physics.stackexchange.com/questions/7783/…

Oh, HNQ, always right on the dot, you are

I would troll so hard, better not tempt me

The recent edit makes it more of a biology question: how have we evolved to be able to stand and/or jump

@0celo7 think of it as a chance to talk about physics/ math, and maybe push the boundaries some. not sure if mods will be ok with regular mtg time slot, they may object for natural/ understandable reasons, but even DS had his session outside the std time & it was well attended. am serious about this! seems you have a lot of audience already... see a lot of pluses to it. think you have some natural leadership qualities :)

@0celo7 ooh, cool! =)

@EmilioPisanty It's hot at zero votes and 57 views?

That algorithm is seriously broken

@ACuriousMind maybe there is no better candidate question right now on the site... it is a mysterious/ convoluted algorithm that gets a lot of complaints...

@ACuriousMind +2-2 votes actually.

Good question though

Wonder how much weed he smokes

@ACuriousMind How do I do a reference request question?

You check we don't already have a duplicate and then just ask it?

If you want to be helpful you can flag it right way so a mod can add the res. rec. banner

@ACuriousMind Check for dupe? Does that involve le google

@anonymous okay, how's this:

@ACuriousMind So, does the rigged Hilbert space work for all operators, or just position?

ah, right, I have to add the tagline.

The book I'm reading does not talk about it

@heather Great :-)! Can we add some stars in the background ? :P

I love Muze

wonderful person

@heather can you make me an avatar pls

@anonymous sure, that sounds like a good idea

@0celo7 what'd you like?

@heather A monkey eating a banana for him

I'm missing the joke

I wanted a Banach space actually

$W^{1,2}(\Omega)$

just to give @ACuriousMind functional analysis PTSD every time he seesme

Not much of a joke really, just something I thought of in 0.12 seconds

I didn't think it was worth any stars

Yeah, well

People like to pick on ex-cons

well, no promises on how it'll like @0celo7 but I can try to make a Banach space (wonders what she's getting into)

It has to be that specific one

$\Omega=(0,1)$ for simplicity

I was going to cancel the stars but it appears I can't do that on a tablet. Let me get to a PC ...

I was searching Google and found that

But here's a better one for your profile:

There. It's a Banach space

hi peeps

@KyleKanos That one hurts the eye!

what's yellow, normed, and complete?

a Bananach space

Needs to be square!

oh I want to do the ama thingy

to troll and shit

Let me just say that doing an ama just to troll people might be the last action you take in chat for a rather long time :P

what u gonna do? stab me?

In the heart, maybe

okay @anonymous, how's this:

@heather actually, you could draw a heat flow on a compact manifold

that works too

@0celo7 okay

:35235661 Does ignoring you count as doing something?

@heather 20 holed torus pls

@heather I personally don't like the floating "and enthusiasts" I'd rather it be somewhat even between the two lines

with some klein bottles attached

@0celo7 that sounds somewhat difficult to draw

@ACuriousMind it was at 1 when I clicked to it

@heather I can't read the text...write the text in white maybe ? And how come so many stars on the right and only 3 on the left ? :P Just keep 3-4 stars on the right.

@anonymous it's supposed to be orion on the right...

though you're right, it is a bit disproportionate

@heather that feels a ways short of the 2015 ones