The h Bar

0celo7

12:19 AM

@Slereah Where are you in Munkres?

Slereah

chapter 2

0celo7

section?

Slereah

18

continuous functions

0celo7

Those are useful.

Slereah

So I hear

0celo7

3:49 AM

chat is Dead

Yashas Samaga

4:12 AM

0

A: If hydrogen and helium are lighter than air, why won't liquid hydrogen and liquid helium defy gravity?

because gravity is science fiction and laws of density work just fine.

VLQ?

0celo7

4:29 AM

@yuggib Yosida is anti-beginner. He doesn't explain if inductive limits of LCSs are Hausdorff. Turns out they are not in general!

0celo7

4:45 AM

@yuggib Hmm. Maybe one can argue that he's saying that IF the inductive limit topology is Hausdorff (as he defines LCS to be Hausdorff), then it's an inductive limit.

It's obvious that the IL topology on $\mathscr D(\Omega)$ is Hausdorff since $\sup |f|$ is one of the seminorms.

Secret

4:56 AM

[Research ethics induction] It turns out even if you wrote about your research findings on a blog, accuracy is still important and you must correct any errors as you made aware of it

Secret

5:07 AM

O and if a student get too close to a supervisior, the supevisior can no longer be the student's supervisor to avoid perceived conflict of interest. That means once they get close, they have the switch supervisors, how will that impact the research progress?

Secret

5:22 AM

[Research ethics induction] A quantum like thinking process will explain why it is necessary to report of breach of human research code of conduct in events like you forgot to get the consent of some patient before taking their tissue samples and you then realise it and try to fix that problem by getting their consent afterwards:

Consider their possible responses to be a superposition of yes and no. Then there's some porbability that they will give yes or give no. If they give no, you are in trouble

Secret

5:45 AM

[Human ethics induction] Time travel stories taught us one thing: There is no such thing as low risk changes

Secret

6:02 AM

One aspect of human research is that humans are complicated systems. Some research need to actively deceive them of the true aim to avoid the knowledge of the true aim to distort their responses. In doing so you must demonstrate to the human ethics department in your country that you have satisfied the legal conditions, and to fully debrief the participants after the research is done so they can have the opportunity to withdrew their data

O, and sometimes, explicit consent will result in low participation. That is where the gray area is, some laws cover that

Secret

6:15 AM

[Human ethics induction] That so many research need consent of not just the participants, but alos the community, council and etc. can be summarised in one sentence:

You need to obtain consent of the community as if it is one single person

(That's the complication of systems)

That brings an interesting question: Is there any way to enlarge our influences and actions so that we can interact directly with this one 'person' without needing to go through nearly every single key components...?

It will be cool and much simpler if we can interact with the system directly

0celo7

@Secret what are you on about?

@JohnRennie morning

John Rennie

Morning. Bit busy with recalcitrant servers at the moment ...

Secret

@0celo7 Thoughts that pop up when I am doing the mandatory induction trainning modules in my uni as part of my PhD induction

0celo7

@Secret Ugh

What PhD program?

I had to be told not to rape girls and not do too many drugs...

(for my training)

Secret

Just chemistry, but WHS requirements and the research trainning department need us to do trainning on human ethics, research integrity and work and health safety

(in particular, faculty of science students need to do the human ethics module even if you are doign material chemistry)

Well, the plus side is that these modules give me more idea on what a community as a system behave and why it is so fiendishly hard to predict and manage

@0celo7 uh you raped seriously? That's a criminal offense

(Johnrennie please take appropriate action to my message if my question happened to be accidentally having dangerous consequences)

0celo7

6:25 AM

...

Where did I say I'm a rapist

I said they told me not to rape

It's implied that was an unnecessary warning

Secret

ok sorry I misunderstood

glad you clarified

0celo7

we had to take an online course about stuff like that

it was pretty stupid

Secret

yeah, I don't see how it is relevant to research training either, except maybe it is part of work heath and safety for a safe workplace environment in terms of no harassment, bullying and other psychological threats

user228700

> Recalcitrant servers

user228700

x'D

Secret

6:32 AM

[Research integrity induction] Rule of thumb for conflict of interest. The perceived conflict of interest came first

John Rennie

@Kaumudi.H The company I used to work for is doing a big server reorganisation. They have just decommissioned one of the old servers and it's caused a bit of fallout.

user228700

@JohnRennie Used to?

John Rennie

@Kaumudi.H strictly speaking I don't work for them now in the sense that I'm not an employee.

I'm a contractor. Aside from the part time nature this has legal implications to do with the amount of tax they and I pay.

user228700

@JohnRennie Ohhh, I see. So I gather that u work for multiple companies?

John Rennie

@Kaumudi.H I do work for three companies regularly and half a dozen or so on an occasional basis.

user228700

6:45 AM

Wow, OK, I see.

John Rennie

Which I enjoy - it's nice to have the variety.

But most of the work, and most of the money :-), comes from working with my old company.

user228700

Cool! :-)

John Rennie

It's a nice way to work. Basically I have enough savings that I don't have to worry too much about what work I do, so I can concentrate on stuff that is fun.

though you have to remember that to get here I spent a lot of years doing 60 hour weeks :-)

user228700

:-) That is so cool.

John Rennie

One of the (few!) advantages to being old

user228700

6:49 AM

Eh, there are several advantages of being old.

John Rennie

Hmmmm ...

@Kaumudi.H the only good thing about being old is that the alternative is worse :-)

user228700

I'd been attempting to find this quote from HIMYM:

user228700

> "Robin, life is a meal and old age is the dessert. I spend so much of my time worrying about the future. You know, where's my career going? Who am I gonna marry? But when you're old, you don't worry, 'cause that stuff's already happened. Plus, you get to wear comfy shoes and a chair takes you up and down the stairs, it's perfect."

user228700

(I'm enough of a fan to have known the name of the episode in which this is said but not enough to have remembered the dialogue :-P)

John Rennie

Looking on the bright side is good, and that's what I generally try and do. But that doesn't mean the dark side doesn't exist.

anuvaramban

6:58 AM

Suppose i have a magnetic array in a closed circular configuration over which i position and apply a small push on a diamagnetic disk, the disk keeps moving over the track - this is observed. My question is, is there work being done in this system assuming no frictions forces are in play?

user228700

Sure sure :-) However, as excited as I am about all the experiences I haven't had yet, it would be nice to know what happens in advance. Well, no, not now it won't. I'd be nice to skip forward is what I meant. And that too, not really but yeah, that's an advantage.

John Rennie

@anuvaramban it's a bit unclear what you mean, but I don't think any work will be done. What forces do you think might be doing work?

anuvaramban

@JohnRennie Gravity is acting against the levitation force right? so my intuition tells me eventually, it would stop moving on this track-orbit but mathematically, the only forces are gravity and magnetic force (given no friction forces)

@JohnRennie It seemed counterintuitive enough to warrant a visit to the hBar

John Rennie

@anuvaramban Work is force times distance or more precisely $\int F(x} dx$. If the vertical separation isn't changing then no work is being done.

anuvaramban

@JohnRennie won't the magnetic force get weakened over time?

John Rennie

7:07 AM

@anuvaramban why would the magnetic force weaken? I think this has been asked as a question on the main site. let me go look ...

anuvaramban

@JohnRennie appreciate the help!

John Rennie

8

Q: Do magnets lose their magnetism?

I recently bought some buckyballs, considered to be the world's best selling desk toy. Essentially, they are little, spherical magnets that can form interesting shapes when a bunch of them are used together. After playing around with these buckyballs for a while, I wondered: "Can these guys ever...

I'm sure there's a better Q/A than that, but I can't find it at the moment. Basically magnets are magnetic because the spins of the atoms in them are aligned. At room temperature this alignment is effectively permanent.

anuvaramban

@JohnRennie Thanks, this is a good start

Sweeper

7:41 AM

anybody home?

do anybody know what material property decides how much will that material be heated by AC magnetic field from solenoid? I am thinking about ceramics,I need ceramic that will heat as little as possible from ac magnetic field

user228700

14 songs. Ed Sheeran has released fourteen songs in the last 31 minutes ::Resists urge to binge-listen:: Must. Stretch. This. Till. Night.

alarge

8:06 AM

@DanielSank Which books are you using?

@0celo7 I guess the standard intro is Oksendal.

skill patrol

8:21 AM

Do you collect Lego sets? @alarge

If so perhaps you'll be interested in this new Lego set I just found.

:-)

John Rennie

@Kaumudi.H I'm just listening to the BBC Radio 1 MistaJam show from last night, and he was featuring the album.

Also the album by Lorde. I don't know whether you like her material.

user228700

Lorde? No, not much. To be fair though, I haven't listened to very many songs of hers--I only remember "Royals".

user129412

Quick question regarding some notation I don't fully get. On the page topocondmat.org/w1_topointro/0d.html (it's an introduction to topology in condensed matter) in the section Particle-hole symmetry they introduce $\tau_x$, the 'pauli matrix that acts on the particle and hole blocks'. How exactly is this defined? should I see it as different from a normal pauli matrix?

user228700

@JohnRennie He is gold <3

John Rennie

Gold? I would have said Ginger :-)

user228700

8:31 AM

:-) Admittedly, I'm not his biggest fan and have only listened to 10/12 songs of his. Still, he is exceptionally talented--a one-man army. Did you see his performance at the Grammys?

John Rennie

But I have to confess that I like Ed Sheeran's songs. He manages to write catchy tunes that aren't inane, which is a trick that escapes many (most?) pop stars.

user228700

Exactly. I am not a huge fan of the acoustic style but love his songs. Some of them are so touching.

John Rennie

They're a bit soppy. I can see why you girlies like them :-)

DanielSank

@alarge Van Kampen and some book about path integration...

Yashas Samaga

Flat Earth is the Truth ▶️️

►

lool

user228700

9:02 AM

@JohnRennie -_____-

John Rennie

Well, they are a bit soppy - sorry romantic :-)

user228700

Yeah, no, I do agree that they're soppy and all, but I was frowning because you said "I can see why you girlies like them".

John Rennie

:-) sorry, a bit of casual sexism there :-)

user228700

:-P Yep, it's alright.

Kenshin

yo dawgs

I never took you as the sexist type John Rennie

but the truth has been revealed

Yashas Samaga

10:37 AM

theflatearthsociety.org/home

LOL

theflatearthsociety.org/home/index.php/blog/…

^ Einstein's Relativity Proves The Earth is Flat

I am glad that Einstein is dead.

He wouldn't want to read those...

theflatearthsociety.org/home/index.php/blog/…

The Mathematics of the Infinite Flat Earth

earth is infinite plane :DDDDDD

Kenshin

The Earth is flat

Locally the Earth is flat

and "globality" is just an illusion

Yashas Samaga

All flat earthers must be travelling in space at the speed of 0.999999999999999999999c

to see the earth as flat

Kenshin

because things only ever occur locally

any event that effects you only ever does so locally

so if the Earth is locally flat, it is flat

Emilio Pisanty

@L.K. physics.stackexchange.com/questions/284143/…

that's not really the right place for that kind of question

Comments exist for clarification and improvement of the posts they're under

They're very much not for branching off into a conversation on some vaguely-related topic

If you have a new question, ask it as a separate post

L.K.

@EmilioPisanty I see

@EmilioPisanty Can I ask the same question here?

Emilio Pisanty

10:51 AM

if you have a vague question, you can ask on chat

@L.K. you can

but keep in mind that (i) you are not guaranteed anyone's time, and (ii) there's a huge range of users that can answer your questions, so just because one person gave a relevant answer doesn't mean that they're the one single user that can help you

... which is why it's best to put it in a post where everyone can see it and help

L.K.

I know that Φ(t) can be expanded in fourier series. Do you know the reason why |Φn⟩ shouldn't depend on ω?

Emilio Pisanty

@L.K. what makes you think that it doesn't?

also, what does "doesn't depend on $\omega$" even mean?

L.K.

@EmilioPisanty Please don't mind, anyway. ω using your notations

Emilio Pisanty

they're solutions of the Schrödinger equation for $H(t)=H(t+2\pi/\omega)$

changing $\omega$ means changing $H(t)$

everything changes

(also, for LaTeX on chat, see here)

user228700

@JohnR: Oh, this isn't soppy:

user228700

10:56 AM

Ed Sheeran - Eraser [Official Audio]

►

L.K.

@EmilioPisanty I am not saying to change ω but the dependence of Φn on omega

I think I am getting your point.

Emilio Pisanty

@L.K. what "dependence of $\Phi_n$ on $\omega$"?

everything depends on $\omega$

@Kaumudi.H it's pretty soppy

L.K.

@EmilioPisanty I am bit drunk, I mistook omega to be variable. But it is merely a parameter

Emilio Pisanty

@L.K. Next time, write it in a post. It forces you to actually sharpen down to a concrete question, and that's a good thing.

you don't need a go-to guy on a specific topic - just use the Ask a Question feature, it's what it's for.

Secret

One of my habits is the tendency to ask about unrealistically extreme case and how policies deal with it:

in The Ivory Tower, 1 min ago, by Secret

Here's an interesting, highly unlikely scenario and philosophical question regarding conflict of interest policies for you guys:

We all knew that when an examiner and a candidate have personal relationships, the conflict of interest policies in most institutes will require said person to withdrew from the review process.

But what if the candidate is such a famous and popular person that nearly everyone on the globe is his/her friend. Then we have a scenario where it is almost impossible to find a reviewer that will not have perceived conflict of interest with the candidate. How will confl…

L.K.

11:00 AM

@EmilioPisanty Thanks for great help. Surely

Emilio Pisanty

@YashasSamaga Flat Earth is a boring theory

user228700

@EmilioPisanty I suppose it depends on what your definition of soppy is. Some of his songs are much, much, much "soppier" than this one.

Emilio Pisanty

There is another Sun and human civilization Inside the Earth

Can you define a topology on a category, I wonder

Is there a topology for the category of all sets

Emilio Pisanty

@Slereah no

Secret

11:05 AM

Pick your poison

Emilio Pisanty

unless you assume countable AC

in which case yes

but you cannot assume full AC

in which case no

Slereah

Why not?

Emilio Pisanty

@Slereah because that would be an abomination

proof by mathematical morality

Slereah

I did not mean to offend your religion

I mean the trivial topology sounds at least easy enough to do on it

If you replace sets by categories in the definition

Secret

Topological category

In category theory, a discipline in mathematics, the notion of topological category has a number of different, inequivalent definitions. In one approach, a topological category is a category that is enriched over the category of compactly generated Hausdorff spaces. They can be used as a foundation for higher category theory, where they can play the role of (∞,1)-categories. An important example of a topological category in this sense is given by the category of CW complexes, where each set Hom(X,Y) of continuous maps from X to Y is equipped with the compact-open topology. (Lurie 2009) In another...

Emilio Pisanty

11:08 AM

@Slereah Do consider the possibility that I'm trolling.

Secret

NB, nope I don't have the requiste knowledge to fully understand this yet

Slereah

I still can't read category theory :(

"Set is the prototype of a concrete category; other categories are concrete if they "resemble" Set in some well-defined way."

It's object programming all over again

Secret

0

Q: Does infinite speed match the speed of light in reverse direction?

According to tachyon theory it is possible that a particle can travel faster than the speed of light as long as the particle was created with a higher velocity than the light speed. And the speed of light boundary, according to tachyon theory, can be approached from below or above, but not be cro...

quantum-mechanics special-relativity spacetime speed-of-light tachyon

...but there is no rest frame for light. It is unsure if this question can be answered

Balarka Sen

12:04 PM

@Slereah Well, first you have to know what that even means.

The closest answer I have for you is the Grothendieck topology.

Slereah

Well can you define topologies on the proper class of all sets

Balarka Sen

I am not sure what's the topology you're thinking of but is it natural? Is it compatible with the structure of being a category?

Slereah

I do not know

I'm guessing the trivial topology should be easy enough

just $\tau = \{ \varnothing, V\}$

Can you do the union of two proper classes?

well two classes, here

Balarka Sen

I am not very certain about a notion of topology on proper classes, but if you can you can give the trivial topology on the collection of objects in any category. But that's not compatible with the structure of being a category.

So that's not really useful

You should look at Grothendieck topologies instead; those are actually useful.

Slereah

well you don't need categories to define proper classes

you can use the whatchamacallit axiom system

Von Neumann–Bernays–Gödel set theory

Balarka Sen

12:11 PM

@Slereah Sure, I am just saying, what you said is just a notion of topology on a proper class; not a notion of topology on a category.

The information about morphisms is lost

Slereah

The discrete topology might get slightly weird

since $\mathscr P(V) = V$

4

Q: Topology in a proper class

Topological spaces are usually modelled over sets. What happens if I try to topologize a proper class? Say, the class of all maps from naturals to cardinals or similar. Suppose I specify a topology on such a class by defining convergence for a net. What usual properties or facts may I lose? I wou...

general-topology

Mostafa

12:50 PM

Level of rigor in medical researches^

Slereah

Wine seems pretty good, overall

0celo7

1:05 PM

Apparently, there is a non-Haudorff space that has unique limits

Secret

What is the name or mathematical description of that space, cause it sounds uncommon for non hausedoff spaces to converge to just one limit point for some given set of sequences?

ok nvm

2

Q: not a Hausdorff space although limits of sequences in it are unique

Prove that the co-countable topology on an uncountable set does not make it a Hausdorff space although limits of sequences in it are unique . how can I do that.I have no idea.thanks for your time.

general-topology

Slereah

@0celo7 Yeah

The uniqueness of limit thing isn't necessarily violated

But it's not guaranteed

0celo7

@Slereah how would you know??

It's pretty counterintuitive

Slereah

1:20 PM

Because I read about this very topic???

0celo7

The space is not first conntable

When?

Slereah

I dunno, few weeks back?

I was trying to find a proof of uniqueness of limits for Hausdorff spaces

To motivate manifolds being Hausdorff

"The only convergent sequences are the eventually constant sequences."

boring

0celo7

That's in discrete spaces

Slereah

So I had to make 1 kg of crepe batter

Since my eggs expired today

That's a lot of crepes

0celo7

Pic?

Slereah

1:24 PM

Emilio Pisanty

0

Q: What's the Laplace transformation of Hamiltonian?

What's the Laplace transformation of Hamiltonian? Is it partition function? Why is it that?

quantum-field-theory hamiltonian partition-function

OP could probably use some help there

0celo7

Holy crap that's a lot of crepe

Slereah

yeah

I'm gonna make a stack and eat it over the next few days

0celo7

@Slereah I don't know what the space is

I've just heard about it

Slereah

yeah, same here

I'm guessing it's not a very interesting space outside of providing a counterexample

0celo7

1:30 PM

I was wondering if limits being unique is good enough for a linear convex space to be Hausdorff

It turns out you need first countability too

@Slereah it's probably pretty nasty too

most counterexample spaces are

except for $\sin(1/x)$

that one's easy to write down

Slereah

In how many counterexample is $\sin(1/x)$

0celo7

A set of full measure

Counterexamples are funny. It's so hard to write a nowhere differentiable function, but they're actually a very large subset of the space of all functions

Slereah

I didn't know we had $\aleph_1$ math papers for that

0celo7

All continuous ones

Slereah

Nowhere differentiable function isn't too hard to write

Nowhere analytic, on the other hand

I have no idea how they cooked up that example

0celo7

1:39 PM

You think nowhere differentiable is easy??

Have you tried proving that it's actually not differentiable

Slereah

I did not!

but you know

when you hear continuous and nowhere differentiable

you have a picture of how it should be constructed in your mind

0celo7

What's this about a nowhere analytic function?

Slereah

Non-analytic smooth function

In mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions. One can easily prove that any analytic function of a real argument is smooth. The converse is not true, as demonstrated with the counterexample below. One of the most important applications of smooth functions with compact support is the construction of so-called mollifiers, which are important in theories of generalized functions, like e.g. Laurent Schwartz's theory of distributions. The existence of smooth but non-analytic functions represents one...

0celo7

Yeah, bump function?

Hmm

Slereah

bump functions aren't nowhere analytic

$f(x) = 0$ is very analytic

cf "A smooth function which is nowhere real analytic"

0celo7

1:54 PM

That does seem like a strange example.

Slereah

yeah

0celo7

It doesn't look very smooth in the picture

Slereah

IIRC there's an example that's like the solution to $f'(x) = f(2x)$

0celo7

Ew

Slereah

It's not too hard to see why it's not analytic

You get something like $x = 2x$

if you try to do a Taylor series

0celo7

2:08 PM

Yeah but how do you know that equation has a solution

And that it's smooth

I don't know if Picardy works

Slereah

It's a weird solution

Like a probability distribution or something

Fabius function

In mathematics, the Fabius function is an example of an infinitely differentiable function that is nowhere analytic, found by Jaap Fabius (1966). The Fabius function is defined on the unit interval, and is given by the probability distribution of ∑ n = 1 ∞ 2 − n ξ n , {\displaystyle \sum _{n=1}^{\infty ...

that's the one

0celo7

That looks pretty damn smooth

Slereah

it is

smooth as a baby

But nowhere analytic

Jim

2:38 PM

new favourite xkcd pic:

it's so true

ACuriousMind

@Jim How many wolves have you had to kill so far in your career?

Jim

@ACuriousMind only a few. I haven't done a post-doc yet, which in Canada means you're going out to kill a pack

0celo7

3:05 PM

Hello

I'm stuck on a PhD level geometry problem

AccidentalFourierTransform

good for you :-P

0celo7

Given $R\subset\Bbb R^n$ a closed rectangle, how would you construct a sequence of closed cubes $Q_i$, with disjoint interiors, s.t. $R=\cup Q_i$?

If the sides of $R$ are rational, it works with the obvious choice

Balarka Sen

@celo7 Why do you want to do this? I think I know but I want to clarify.

If you're trying to prove what I have in mind then you don't need to do this.

0celo7

@BalarkaSen Change of variables for Lebesgue measure

Balarka Sen

I don't know what that is. Do you need to prove that you can choose cubes instead of rectangles in the definition of Lebesgue measure?

0celo7

3:15 PM

@BalarkaSen $\int_{\phi(U)}f(y)\,dy=\int_{U}f(\phi(x))|\det d\phi(x)|\,dx$

One version of the proof requires cubes for an estimate

@BalarkaSen No.

Balarka Sen

Then where in particular do you need this?

0celo7

@BalarkaSen I need to know the outer measure of $TU$, where $U$ is open and $T$ is linear.

Balarka Sen

I think you should be able to get away by saying a rectangle is arbitrarily close to a rectangle with rational sides (which can be subdivided into cubes), hence the questions.

0celo7

It's easy to compute the outer measure of $TQ$, where $Q$ is a cube.

That's just linear algebra

Well, "easy"

Requires singular value decomposition

@BalarkaSen My prof claimed it should be exactly equal.

Not strictly contained in the union of cubes

@BalarkaSen This is also a generalization of the usual "an open set in $\Bbb R$ is a disjoint union of open intervals"

so it has independent interest, imo

Balarka Sen

That sounds much more general than you actually need. I also don't think it's actually true. If you can divide a rectangle with sides $\sqrt{2}, \sqrt{3}$ into squares of sides $x$, then $\sqrt{2} = mx$ and $\sqrt{3} = nx$ where there are $m \cdot n$ many squares in the subdivision; aka $\sqrt{2}/\sqrt{3} = m/n$. Garbage.

0celo7

3:22 PM

@BalarkaSen The squares don't have to be uniform at all.

Balarka Sen

Ah, I see.

0celo7

It could be a tiling where the smallest size goes to zero.

The claim is just that there is some covering

Maybe you pick some corner. Consider the largest inscribed (is that the right word?) cube $C_1$ that contains that vertex.

Balarka Sen

I think that's easy tho

0celo7

Is $R-C_1^\circ$ a closed rectangle?

Then just continue that process, and show you eventually pick up every point.

Balarka Sen

That's right.

Like you just blow up a cube inside the rectangle sharing one vertex so that it's as big as possible.

Then do it iteratively on what's left

0celo7

3:25 PM

yep.

How does one show that actually covers?

Balarka Sen

By construction, any given point is contained in some iteration, right?

0celo7

That's the question, no? It's not immediately obvious from a pictureless standpoint

This is so geometric it's hard to not be convinced :P

Balarka Sen

I don't really want to do the algebraic proof. I think you should be able to write out each iteration explicitly.

0celo7

@BalarkaSen I suppose you could show that if it misses some point, it misses a whole rectangle.

Balarka Sen

Mhm.

0celo7

3:28 PM

So you could just add another cube, implying the family was not maximal to begin with.

@BalarkaSen I don't suppose you understand locally convex spaces?

Balarka Sen

Nah.

0celo7

@BalarkaSen Too bad. The classic text in functional analysis is hostile towards readers not familiar with LCSs.

0celo7

3:42 PM

@BalarkaSen What's the worst induction proof you've seen?

Balarka Sen

@0celo7 Worst, or wrong? I like the horse theorem.

0celo7

Sard's theorem is bad

@BalarkaSen Horse? Googling...

Balarka Sen

here

0celo7

@BalarkaSen yes I managed to find the wiki page myself :)

Balarka Sen

enjoying the conversation in the math room

0celo7

3:47 PM

What's it about?

Horse is a strange word

Interesting. The proof breaks down in the $n=2$ case.

Slereah

Yes

Here's a counter example

A white horse and a black horse

0celo7

such a terrible font

Slereah

0celo7

@BalarkaSen I think you're being sarcastic.

Balarka Sen

nah truly was

0celo7

3:54 PM

...since when do you like drama?

@Slereah how long did it take you to find that picture?

Slereah

I dunno, a few seconds?

The time it takes to look up "white horse black horse" on google image search

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