Mathematics - 2011-11-30 (page 1 of 3)

ixtmixilix

00:07

@mixedmath i bashed my skull in and i can still laugh.

Henning Makholm

00:18

It's late; I'm off. Goodnight to whomever is out there.

mixedmath

00:52

Goodnight Henning

oh - I'm way late

ixtmixilix

c98... c97...

c7... your system had a kernel failure... c96... c87...

stream of consciousness innit

c14... d78...

hurray, i just finished finding and replacing the regex i could not be bothered to figure out how to write

whoever's listening, i have this question> has studying a particular branch of mathematics ever made your dreams more vivid?

mixedmath

01:10

I used to get algebra nightmares every now and then

but I don't think that's quite what you meant

ixtmixilix

not really, but sorta. i guess that's the opposite of the sort of dream i'm talking about

this is a 'WOW' sorta dream

could be intricate visual detail

could be you on a stage directing an entire orchestra for 8 hours with music that just comes out of your head

i guess (a la das Parfum) also some very complex smells

J. M.

02:04

@anon Henning did it for one of those deleted questions he asked about.

ziggurism

03:29

Hi. I guess stack exchange locks threads for comments after they become old, is that so?

Is it possible to unlock them?

Rajesh D

i've haven't heard about any such thing

ziggurism

Well uh

here is a question from the top of the pile:
http://math.stackexchange.com/questions/86935/homotopy-of-singular-n-simplices

Notice that each "answer" (there is only one) has a link for "add comment"

here is a question from 6 weeks ago or so:
http://math.stackexchange.com/questions/70938/coordinate-free-definition-for-the-riemannian-volume-form

the "add comment" link is not there. It seems that I can still answer the question, but if I want to engage in discussion via comments, I cannot.

or am I missing something? Is it still open for comments and I'm just not seeing it?

are you able to comment on that old thread?

Rajesh D

@ziggu : I am able to find add comment button in both of the questions you have mentioned !

ziggurism

03:45

really?

that's weird.

hmmm

you know what.

for some reason I'm not logged in on that window

I reload in a new window and everything works

mystery solved!

thank you, Rajesh!

Rajesh D

ok

i happened to me sometimes

robjohn

@ziggurism Do you see an "add/show 1 more comment" link?

below the comments.

ziggurism

@robjohn: I do, yes. Actually I see the "comment" link too now. Problem was that I wasn't logged in (in another tab)

robjohn

Ah, okay.

ziggurism

but thank you, sir!

Rajesh D

03:54

hi @rob

howz the day goin

Jacob Schlather

Rajesh

you could look at jump discontinuities with respect to a directional derivative

but I don't think it really makes sense to extend the concept

Rajesh D

04:26

Becaue you can create a function which jumps different amounts and in different directions in each of the straight lines approaching your point. I don't think the idea is as simple. – Alex Youcis

@Jacob : in this case (different amount of jumps in different directions)...for the function to be continuous in some neighborhood (except at that point) of the given point, do we need any restrictions on the amounts of jumps in different directions ?

except at that point

Jacob Schlather

04:40

So you'd say a function has a jump discontinuity

if it has a jump discontinuity

at each directional derivative?

Akram Hassan

07:29

hello there

Matt

07:49

Good morning.

Rajesh D

07:59

good afternoon Matt

Daniil

Hi guys.

Rajesh D

hi

Akram Hassan

08:46

hello there

Matt

Hi

Akram Hassan

hi matt

what are you interests ?

Matt

Mathematically or in general?

Akram Hassan

math first !

Matt

I like topology, algebraic topology, functional analysis and algebra. So far : ) You?

Asaf Karagila

08:55

Do you like Sober spaces?

Akram Hassan

i love geometry but i am an absolute beginner

Matt

@AsafKaragila Did you mean Sobolev spaces?

Asaf Karagila

No. I meant Sober spaces.

Sober space

In mathematics, a sober space is a topological space such that every irreducible closed subset of X is the closure of exactly one point of X: that is, has a unique generic point. Properties and examples Any Hausdorff (T2) space is sober (the only irreducible subsets being points), and all sober spaces are Kolmogorov (T0). Sobriety is not comparable to the T1 condition. Moreover T2 is stronger than T1 and sober, i.e., while every T2 space is at once T1 and sober, there exist spaces that are simultaneously T1 and sober, but not T2. One such example is the following: let X be the se...

Matt

Not heard of it before.

Asaf Karagila

Were you drunk?

Matt

08:57

Probably. : )

Daniil

heh

How many beginner Go players does it take to change a lightbulb? - None, they don't see ladders.

Williham Totland

Do questions about matrix-based coordinate transformations go here?

Asaf Karagila

Here in the chat? Probably not.

Williham Totland

Well, it feels a bit short for a full-fledged question.

Asaf Karagila

Then you can try.

It's the lack of LaTeX which makes matrices impossible.

Gigili

09:04

Hello, how can I show a negation of a property in LaTeX?

Williham Totland

It's really just a question of wether a torus can have its radius and thickness adjusted separately using matrix transformations.

Daniil

@Gigili \neg ?

Asaf Karagila

@Gigili Huh??

\lnot > \neg :-)

Gigili

Like B and B prim

Asaf Karagila

I am not sure what you are trying to do.

Gigili

09:06

@Daniil Um, not that one .. I don't what it's called =\

Daniil

Can you give us an example of what are you trying to do?

Gigili

$ A=(A\cap B)\cup(A\cap \primB) $

I want to prove this

First one is B, the second one is (M - B)

Asaf Karagila

LaTeX is just a typeset, you cannot "show a negation of a property" in it.

Gigili

Or (S -B)

Daniil

What do you want to typeset tho?

Gigili

09:08

(S-B)

Asaf Karagila

S\setminus B

Daniil

i.imgur.com/Qxeh3.jpg what is this D8

Uh, I really should stop browsing reddit

Gigili

@AsafKaragila Do we have in mathematics something like "van" or "wan"?

Asaf Karagila

Huh?

Gigili

=\

Van diagram

Or something like that

Asaf Karagila

09:21

Venn?

Gigili

@AsafKaragila Exactly, thank you.

According to that, I need to write B prim,

Like this , if B was the white circle

The red part

Daniil

coset of B?

Gigili

In LaTeX?

Asaf Karagila

B' ??

Gigili

Yes :D

Sorry for being extremely silly.

Jonas Teuwen

09:31

Was there someone here that wanted to do a PhD in Louvain-La-Neuve? I have a guy from there sitting in my office :-). So if there are any questions...

Matt

So if I have x_n -> x weakly implies Tx_n -> Tx weakly, where T : X -> Y is a linear map and X,Y are normed spaces, how can I show that T is continuous?

Asaf Karagila

You can force it to be.

Matt

: P

Jonas Teuwen

What does x_n -> x weakly mean?

(to you)

Matt

For all phi in X^*: phi(x_n) -> phi(x)

Asaf Karagila

09:35

It barely gets there... it takes forever!

Matt

I guess I need to do something with phi(Tx_n) -> phi(Tx)...

To show that it's continuous, do I try to show that it's bounded or use the epsilon delta definition?

Jonas Teuwen

Did you already try any of them? :-).

I would suggest that you just try and see if it works, that will help you more. If you get stuck you can ask for help (unless you're already stuck of course).

Matt

I thought I was stuck already.

It's homework so I have basically zero energy to try stuff. Must be psychological.

Jonas Teuwen

Do you know PUB?

Asaf Karagila

The place you go to drink?

Jonas Teuwen

09:48

So then you know that weakly convergent sequences are bounded.

Principle of uniform boundedness.

Matt

@JonasTeuwen I only know Pubs...

Uniform boundedness principle? I tried that already

I don't think it fits here

@JonasTeuwen: Thanks, I'll try again!

Jonas Teuwen

Assume T is unbounded, then there exists a sequence x_n converging weakly to 0 such that ||T(x_n)|| -> infty.

Asaf Karagila

@Matt: If pubs won't do the work, try pubes.

Daniil

kinky

Jonas Teuwen

(And what do you know about convergent real sequences?)

Matt

09:54

@JonasTeuwen I think your previous comment answers the question. Or am I missing something?

Jonas Teuwen

Well, those are bounded hence Tx_n cannot converge weakly.

Matt

I think I'm confused.

Asaf Karagila

Dazed and Confused?

Matt

Possibly.

robjohn

I don't know whether adding a verification as I did in this answer is useful enough to justify the extra length of the post.

Jonas Teuwen

10:03

phdcomics.com/comics/archive.php?comicid=912 great.

Matt

: )

robjohn

@JonasTeuwen sounds about right.

Jonas Teuwen

Damn :D.

Daniil

thecreationnews.com/news/science/…

robjohn

10:18

@Daniil That is hilarious!

Daniil

At first I thought this was not satirical and got really anxious

Matt

: D

Daniil

imgur.com/CqZ1z

Jonas Teuwen

I like this one: thecreationnews.com/…

Matt

That doesn't seem real.

Daniil

10:27

haha

J. M.

@Daniil The author is strangely familiar...

Daniil

8D

Matt

I wonder how the other students cope with all the homework. Maybe I'm just infinitely slow compared to others.

Jonas Teuwen

Well no.

I'm correcting FA homework. They suck mighty at making homework.

You just want to do it right, I suppose.

2

Matt

Do you have the same system as ETH? Need to show "effort" and then get score and if score is high enough be admitted to the exam?

As opposed to getting it right?

Jonas Teuwen

10:35

No. The homework counts for 50%.

No, you want to get it right too :-).

Matt

@JonasTeuwen Yes I do. Very much so. But most of the time the questions are just so many and so difficult that I have to write something to show "effort". It's very depressing.

Here they figured that they can't require people to get it right because the questions are too difficult. So instead of making the questions easier they require you to write something and you get points for it even if it's wrong.

Really, it's hard to find words to convey to you just how depressing it is.

Jonas Teuwen

I can imagine :-).

Daniil

Well, this makes sense to me. Even if you fail they can show your mistakes and might help you better.

But it does sound depressing

Martin Sleziak

@Matt So both you and t.b. are in Zurich? Is he one of your teachers?

Matt

@MartinSleziak Yes and no, unfortunately not. I think I would like him very much, he seems to have infinite patience and is very gentle.

Martin Sleziak

10:43

Well, at least we can say that he teaches you FA here at MSE.

Matt

@MartinSleziak Yes, lucky me : )

Martin Sleziak

I believe he posted answers or comments to most of your FA questions...

Matt

Yes. And he's had a huge influence on me. I'm not sure he's aware of that.

Oh, pup needs a stroll, brb

rubenvb

Hi everyone. I'm having an "applied mathematics" problem, in the form of what I can most precisely describe as bilinear regression, but a special case of that. Anyone feel like helping?

J. M.

"bilinear" - two independent variables, then?

rubenvb

10:57

I'm trying to fit a Dirac probability density j^0 (from relativistic QM) to a step function, where each basis spinor is a bunch of BesselJ functions

so I have say, 10 coefficients for 10 basis spinors, and the density I'm fitting is 1x4-vector times a 4x1 vector, resulting in a bilinear form as math describes them.

so, say, psi = a1 psi1 + a2 psi2, and j0 = psi^\dagger psi

which results in the density j^0 being of the form: sum_(i,j) a_i a_j psi_i' psi_j

so, it's not the general bilinear form, as the coefficients are a mixture of the underlying coefficients, greatly reducing the amount.

I've tried a brute-force function minimalization (Matlab's fminsearch), but the result is not good :(

I hope my explanation is somewhat clear...

I could formulate/write up a proper question?

Matt

Back.

rubenvb

I've found this, but it's too general and maybe not exactly the same: cs.duke.edu/~tomasi/papers/cohen/cohenTr97a.pdf

J. M.

11:14

"I've tried a brute-force function minimalization" - and you don't have good starting points, then?

robjohn

@Martin: you've been busy on the main site.

All but 4 of the entries are modified last by you.

Martin Sleziak

@robjohn Twice a week, approximately 10 question from algebra tag.

I've discussed it with Willie Wong, we agreed that this is a reasonable rate: meta.math.stackexchange.com/questions/1363/…

Srivatsan plans to eradicate number, see this meta post: meta.math.stackexchange.com/a/2755/8297

robjohn

Still, it is daunting to see all the questions with the same avatar underneath.

Martin Sleziak

But we discussed it on chat and we agreed not doing the algebra retagging and number retaggin on same days.

robjohn

Why would that be a problem?

Martin Sleziak

11:21

BTW do wa have meta post concerning metapost?

@robjohn Too many old questions bumped on the main site.

Originally I started retagging algebra at the rate cca 10-15 post per day. That was really too much.

robjohn

Ah, so people don't have to scroll down many pages to get to true new problems.

It's too bad that there isn't a way to adjust a post without adjusting the date (mod power).

Martin Sleziak

When we already discuss tags, relation is intended for questions about equivalence relations, partial orders and similar. Basically thing from the first course in discrete math or elementary set theory.

I would even say that it is subset of elementary-set-theory.

Does it sound right?

(At least this is what I would guess when I look at the questions tagged relations.)

robjohn

I don't know. relation seems more far reaching than simply set-theory

J. M.

Do we really need to have relation?

robjohn

that is a good question, too.

J. M.

11:26

I'd prefer it be subsumed, but maybe you guys can convince me differently?

robjohn

I'd have to look to see what kinds of problems are in it.

Martin Sleziak

Ok, I asked this because I wanted a tag wiki+tag excerpt to indicate what kind of questions should belong there.

I was under the impression that this was the intended use. (I even added this tag to some questions about equivalence relations.)

robjohn

There are many posts I can see just skimming that I would not know where to put, if not relation, and relation is the only tag they have.

or relation and reference-request...

etc

Martin Sleziak

My first draft for tag wiki was this

A *relation* $R$ on a set $A$ is any subset of $A\times A$. Often we write $xRy$ instead of $(x,y)\in R$.

This tag is intended for questions concerning partial orders, equivalence relations, properties of relations (transitive, symmetric,...), composition of relations and similar stuff. More-or-less the things about relations

For more information see e.g. [wikipedia article](http://en.wikipedia.org/wiki/Relation_%28mathematics%29).

*******

But maybe I misunderstood the intended use of the tag.

robjohn

@JM do you have a suggestion where to subsume relations?

Martin Sleziak

11:30

Sorry I mean relations.

robjohn

@MartinSleziak so did I :-)

J. M.

It looks as if most of what's in there can fold into elementary-set-theory

Martin Sleziak

J.M. wrote relation not relations above.

But that one is empty.

robjohn

@MartinSleziak I know. but there is no relation tag as far as I can see.

J. M.

oops, I forgot to pluralize. :D

Martin Sleziak

11:31

@JM I would prefer having both e-s-t and relations for such questions.

robjohn

Ah, it is empty.

Martin Sleziak

But that's just my opinion.

J. M.

Maybe post in that long thread, Martin. :)

Martin Sleziak

what about this suggestion

robjohn

e-s-t?

Martin Sleziak

11:33

e-s-t shortcut of elementary-set-theory

Matt

@AsafKaragila: Ok. I'm back to set theory now. And I have entertainment for you: if p in P is a condition and P is a poset and dot(p) denotes the canonical p-name of p and dot(p)[G] is the interpretation map of dot(p) into G then what is dot(p)[{p}]?

robjohn

I know, I was just funnin' ya

Martin Sleziak

@JM My suggestion: I will write tag wiki and tag excerpt indicating what is recommended use of that tag.

If you feel strongly about removing it, post in the long thread.

(I will probably vote agains removing it.)

Is it ok for you?

J. M.

11:45

I don't feel that strongly about it... :)

Martin Sleziak

ok, so I'll try to add tag wiki - so that at least people know how to use it.

And if somebody will come up with the suggestion to remove the tag, we can discuss it on meta.

Matt

I just fooled myself. I hate induction.

Does anyone know what the sum over i 2^{i - 1} should sum to?

Martin Sleziak

Wikipedia does: en.wikipedia.org/wiki/…

Matt

Wolfram Alpha knows: n 2^n -2^n + 1

Martin Sleziak

Wasn't that asked here before?

Matt

11:51

Possibly. I don't know.

rubenvb

@JM : no I don't have good starting points :(

J. M.

@rubenvb Your problem is then exceedingly hard. Doesn't the underlying theory allow you to estimate good starting values?

@MartinSleziak Likely, it has. Sadly searching math is tough.

Martin Sleziak

Or at least sums of similar kind like k*4^k.

I have feeling that I saw something like that.

rubenvb

@JM Damn, that's what I feared. I need to simulate a near-constant density. I tried only using the "large" component of the spinor, but the deviation at the edges is unacceptable.

That's the flattest I get is by experimenting with fitting the large component. this is j^0 vs r

notice the high peaks at the end. The center dip is supposed to be there

I'm currently attempting to extend plain linear regression for my purposes, but I hoped someone knew of an existing method. I guess mathematics is failing me here :)

Matt

phew. Fixed.

J. M.

12:00

@rubenvb As it stands, every iterative method ever made demands a starting point from its users. More often than not, the whole business is GIGO.

rubenvb

garbage indeed. I was looking for a non-iterative method...

Rajesh D

hi @JM

J. M.

hi

@rubenvb The Bessels make things quite complicated, too. Solving transcendental equations is often a pain.

Rajesh D

@JM did you see this

rubenvb

@JM but the Bessels really are only numbers. It's like fitting a linear combination of arbitrary functions to a curve defined by data points, linear regression (ie: Ax=b => x=b\A) works just fine. Now, I have a bilinear combination of arbitrary functions.

I'll write up a decent question that might make everything more clear

Matt

12:32

Off to torture class. Be seeing you!

Martin Sleziak

13:01

Hmm, torture class... They have very unconventional curriculum.

2

Skullpatrol

13:16

@MartinSleziak Wanna hear a math joke?

Martin Sleziak

ok

Skullpatrol

An engineer, a physicist and a mathematician are driving along the county side and they see a black sheep on the side of the road; the engineer says "ALL sheep are black" the physicist says "Nonsense, only some sheep are black" the mathematician ponders for awhile and finally says "All we know is at least ONE sheep is black and it is black on at least ONE side."

Martin Sleziak

Well, it's quite famous one I guess.

At least I heard this one before.

Skullpatrol

I don't really get it?

Martin Sleziak

Well it's about the level of precision.

Mathematicians are trying to express themselves very precise.

Skullpatrol

13:19

precision?

Martin Sleziak

At least they are supposed to.

rubenvb

@Skullpatrol Engineers make blatant assumptions, Physicists assume logical things (most of the time ;-)) and Mathematicians don't make any assumptions at all.

Martin Sleziak

If you hear: Let us choose any x,y \in [0,1].

Any normal person would assume that x and y are two different numbers.

Skullpatrol

@rubenvb How true is "Mathematicians don't make any assumptions at all."

Martin Sleziak

Mathematician would say "Let us choose x,y \in [0,1] such that x!=y" to stress that they are different.

@rubenvb I think adding mathjax support for chat was asked before at meta. And it was declined.

rubenvb

13:22

Well, that's the limit of the joke, really. The mathematicians I know shudder when we juggle with partial differential equations, or implicitely assume some angle is small. They would go all-in to solve it analytically.

@MartinSleziak probably performance related?

Gigili

@MartinSleziak Hey Martin, which browser do you use? FF or Chrome?

Martin Sleziak

But you might be interested in this question, if you want find some different possibilities for chat using TeX: math.stackexchange.com/questions/81365/…

@Gigili Firefox

Gigili

I installed a very useful Chrome extension about German, wanted to know if you want to use it as well ..

Skullpatrol

@rubenvb Thanks for the explanation

Martin Sleziak

Well, I'm not planing to switching from Firefox.

Gigili

13:25

I see

robjohn

@Skullpatrol I've always assumed that.

Gigili

Then :|

Martin Sleziak

@rubenvb This is basically all I know: chat.stackexchange.com/transcript/36?m=2566084#2566084

Skullpatrol

@robjohn Assumed what?

Martin Sleziak

Asaf mentioned this in chat.

But I guess you'll get some pointers in your question at meta.

robjohn

13:26

@Skullpatrol That "Mathematicians don't make any assumptions at all."

Martin Sleziak

@rubenvb This question is related to yours, but not much was said there: meta.math.stackexchange.com/questions/1088/…

Skullpatrol

@robjohn But some assumptions are needed to make any progress, isn't it?

rubenvb

@MartinSleziak thanks, strange silence. I'm surprised the math chat is as active as the SO C++ chat. It's nice to know :)

robjohn

@Skullpatrol It was a joke... I've always assumed that Mathematicians never make assumptions.

J. M.

@rubenvb This is actually a slow day. :)

robjohn

13:30

@rubenvb It might have something to do with the timezone in which the chatters live.

@JM That, too.

J. M.

@rob: I have a feeling your solution in that thread can be recast to use Chebyshev... :) but I haven't thought about it thoroughly.

robjohn

@JM Oh, I'm sure you're right, but I usually do my variational methods a bit strangely. :-)

rubenvb

@robjohn then you cannot be a mathematician?

robjohn

@rubenvb If you are to assume that I believe that mathematicians never make assumptions.

Skullpatrol

@robjohn Is that really what the joke is about?

@rubenvb Are you a mathematician?

robjohn

13:36

@Skullpatrol I assume so ;-)

rubenvb

@Skullpatrol nope, physicist (second year master student, so not quite yet)

Skullpatrol

@robjohn When you said "I assume" were you playing with words

robjohn

@Skullpatrol Yes.

Skullpatrol

implying that you're not a mathematician

because they don't like to assume

robjohn

or trying to parody the statement, because I don't think it is true...

There are many explanations. :-)

Skullpatrol

13:41

@robjohn I agree

thanks for the explanation

@rubenvb Good luck with your physics

rubenvb

@Skullpatrol Thanks, I'll need it :)

I have a f-ugly expression for a special-case bilinear regression. Ugh

Williham Totland

13:56

I'm getting some odd results here…

Please confirm: A line defined by two points can be transformed by transforming each point using a transformation matrix, correct?

robjohn

@WillihamTotland yes

At least if the transformation is affine.

Williham Totland

Good.

Ah.

That may or may not be the case.

Scaling and translation are both affine, right?

Transcript for

$Mathematics$ Mathematics