@tb there is good reason for that :-)

@JonasTeuwen good night

@robjohn which is?

@tb they were

So many things that were portrayed in movies, TV and books, were somewhat racist

That's probably what raising awareness is about...

Just consider the original title of Agatha Christie’s And Then There Were None.

But sometimes it is mind-boggling to see some things that were perfectly okay only twenty or twenty five years ago.

@Mariano: do you happen to have a slick answer for the non-linearity of the universal cover of SL_2 R ? I'd love to see one that uses a little less machinery than those given by Jim and myself.

Or uses something different.

Jim looks at the classification of representations of sl_2 and I complexify and show that every representation of the universal cover factors through SL_2

if the universal covering were linear, by complexifying you'd get a covering of the matrix group SL(2,C)

and the latter is simply connected

fffffffuuuuuuuuuuuuu this driving instructions manual is confusing me!!

@MarianoSuárezAlvarez Yes, that's putting the argument I gave a bit differently. Also nice.

(I'm not saying that the argument is from me. I don't remember where I picked it up.)

using the clasification of modules is cheating :P

I think so, too.

on the other hand, that is precisely the sort of thing what knowledge of the representations is supposed to help you do, so... :D

@tb Of course you're not. Youre angry, mad and crying.

Mad and crying, maybe, but no, I'm not angry... :p

@tb mad I can see ;-)

ouch...

@tb joking...

hey you guys saw the rant of that guy about writing proofs?

@BenjaminLim no, where?

@robjohn that was simultaneously posted :) Premonition? Fate? But it looked like it fit well...

@BenjaminLim The fellow who wants to be a high school math teacher? Oh, yes.

@tb it did to the point where I thought it was a reply.

@BrianMScott yes, he should NOT become a high school maths teacher

In fact the problem in australia now is that most mathematics teachers have this sort of attitude towards maths

@BenjaminLim what attitude is that?

@BenjaminLim As I pointed out $-$ rather bluntly, I thought, but a few later comments were even stronger.

they don't see the point of proofs

@robjohn There was a link... It happens from time to time on MO that someone a little older tells the "kids" to cool it with the abstraction.

@BenjaminLim that is not good for theoretical math, but for applied, I might be a bit more understanding. However, proofs are what make math interesting.

@tb who are the kids?

@robjohn I think high school maths teachers should get at least an undergraduate degree in mathematics

@BenjaminLim Well, duh. They don't need one?

NO NOT AT ALL.

They only need a diploma in education.

That is not good.

hahahahahahahaahhaahahah

That's more than not good.

@robjohn The real problem is that this fellow has the same confusion that a lot of my students had: having seen nothing but computation up to the point at which he finally hit a theory course, he thinks that mathematics is computation.

For me, at least till you've seen high level analysis and related topics can you motivate your students enough

@BrianMScott that is what I would probably call arithmetic.

@BenjaminLim Here in Ohio they need an undergraduate degree in mathematics that includes certain required courses (e.g., discrete math), and they need certain education courses as well.

@robjohn @BrianMScott Most people think that high school teachers should just be able to teach high school mathematics which means they don't need an undergrad degree in maths

@robjohn Well, it includes freshman calculus and most of the routine first courses in linear algebra.

@BrianMScott what?????????

@BrianMScott Well we need to write a letter to julia gillard then......

@BenjaminLim Those are courses in computational technique, not in what I think of as ‘real’ mathematics

@BenjaminLim a deeper knowledge is needed to be able to put together a course that will make sense later. But you know that.

@robjohn I think a DipED is not enough to truely be able to appreciate things like say the funddamental theorem of calculus

Here high school teachers need an M.Sc. in order to teach the last three years of High School. It was a hard fight to keep it this way when they introduced bachelor and master stuff, but I'm glad they did keep it.

I mean to prove that a continuous function is integrable don't you need to use the fact that the continuous image of a compact set is compact? I don't think they do real analysis in a DipED.

@tb The quality of mathematics education in switzerland must be very high then!!!

Well, they cut down on pedagogical courses.

Moreover, if you reach the master degree, you don't necessarily want to teach high schoolers. Thus, not really the best people end up as teachers. There's not enough incentive and that's a huge problem.

@tb Perhaps that is what they should cut out of here too. I think no matter how many pedagogical courses you have taken, if you have not see the high level stuff you cannot motivate your students enough.

@tb Tell me about it, here in australia being a high school teacher is kinda frowned upon due to low wages

That's very bad.

and people who usually want to become teachers are seen as under achievers at school.

That's what I had in mind.

@tb Here to get into university you need what's called an ATAR score

99 ATAR means you are in the top 1% of high school leavers for your year, 95 ATAR the top 5%, etc

@BenjaminLim However, I don't think it's a question of motivation. It's a question of having seen enough stuff to know what you're talking about.

But the best requirements in the world can’t completely protect us from folks like Wolfgang Mückenheim, one of the most vocal resident loons in de.sci.mathematik.

medicine: 99.5 ATAR

@robjohn huh?

@BrianMScott Oh, I love that guy :)

@BenjaminLim never mind. I wasn't reading back. I just came back from being afk. and thought that 99.5 looked like a temperature next to the word medicine.

You’re familiar with him?

@BrianMScott who is that guy?

@tb teaching? about 75 ATAR

@BrianMScott Oh, yes! We had huge fun looking at his occasional ArXiV posts.

that's why being a teacher is frowned upon

(before the endorsement system was installed)

@robjohn we use degrees celcius here in australia

@BenjaminLim Yeah, i thought of that after I posted.

@BrianMScott who is that guy?

I am off to the park with Lilly. bbl

@BenjaminLim A loon who very vocally fails to understand infinite cardinalities, Cantor, etc.

@BrianMScott there was even a question here on yet another refutation of the diagonal argument.

What is it with the reaction to the diagonal argument? It’s one of the simplest, most elegant arguments around, even if some people do insist on turning it into a proof by contradiction.

is it typed up on TEX?

What do you mean, Ben?

@tb in your comment in the question: " The use of Microsoft Word instead of LaTeX is another thing that should turn on all warning signs."

why do cranks usually not use tex? They don't know how to use it?

Yes.

man at least they should be smarter to try and make their work look more pro

That's one of the huge problems I see with TeX (or computer typesetting), actually.

huh?

@tb what kind of problem?

That it is very easy to "look pro" as you put it.

ah ok.

I remember reading an article about the crank index

was it something like 50 points for not using latex?

Baez's crackpot index

thats it

I shudder to think that most people in the world are not aware of the true power inherent in mathematics

@BenjaminLim The thing is that I grew up in a world where printed stuff was not so easy to achieve. Scripts were handwritten or written with typewriters and copied with that smelly copying machine (I don't remember its name).

hahahahaha 80s

@tb The purple peril?

Exactly. We called it Matrizenkopierer.

But I don't remember it's technical name.

I usually just called it the ditto machine.

Spirit duplicator. Ditto was a trade name.

I did exams and notes on Ditto masters for a good many years.

That's one beautiful name for that machine...

Oh, dear, poor Jordan is woefully confused again.

what is even the problem statement?

@BenjaminLim here's a nice example. If you look at newer versions, you see that he has "gone pro".

@BenjaminLim Probably he’s supposed to find a point in the interval satisfying the conclusion of the MVT.

He was learning about MVT and Rolle and the like, a few days ago.

@tb wow

@tb @BrianMScott but what is even the problem? I don't get it man this guy

@BenjaminLim Scary thing is that at that time the guy worked in a nuclear plant :/

hohoh

@BenjaminLim please go easy on him.

I know but at least copy the problem statement right????

Jordan is fighting a real problem with understanding the mathematics plus a strong feeling of inadequacy plus some resentment at having failed once and had to take the course again. He’s trying. In both senses, unfortunately, but I try to give him a break.

@BrianMScott We can do our best by not voting to close/voting down and helping him :D

sigh ‘I have forgotten what the question was asking me exactly.’

what does mathematica have to do with it?

Dunno; I just removed it.

I was hesitating because the distinction "elementary set theory" and "set theory" and "cardinals" is not quite clear to me.

I decided to add (elementary-set-theory): this is Chapter $0$ stuff, I think.

I think that's the most reasonable one, yes. But I once dared remove a set theory tag from a basic Zorn application...

... and encountered Zorn?

Exactly.

Maybe it was the equivalence of well-ordering, Zorn and whatever else people usually state in chapter 2.

Ah; I suppose that that’s a half-step up from countable/uncountable and the diagonal argument.

I’ll be out for a bit; my system is insisting that it needs to be rebooted.

Good luck!

Thanks!

I think I failed my test, I forgot how to do everything

...

good eefenink luddites and germs

anyone here?

Hey Bullmoose.

Hi

I have a question that I think is too stupid to ask on the main site

do you perchance know how the transpose operation along the South-West/North-East diagonal is called?

The usual transpose is along SE/NW diagonal

I used to remember this term, but I my linear algebra course was so long ago

and google isn't helpful (I don't know what to search for)

if you think it's a good question, I'll post it

I have never seen that called by a name

Neither have I. I would call it the "antidiagonal transpose."

hmmm thanks for your help, Mariano and anon

i like the name "antidiagonal transpose" but I don't think that was the term used by my linear algebra prof

@anon :)

google turns up the term "flip" in this paper cs.sandia.gov/~dmdunla/publications/MaMaDu03.pdf

Thank you, @David!

@MBM Generally speaking I've found that stuff pertaining to operations about the antidiagonal have the prefix per- attached to them (persymmetric, per-Hermitian, etc.), so maybe pertranspose might not be much of a stretch.

How can I write a right arrow in LaTeX with writing something on it?

Or better, how to write something on "\implies"

@Gigili $\stackrel{\text{hello!}}{\implies}$

Thanks @J.M., yeah, I'm reading the paper that @David posted, and I think that my prof used the term per-transpose

yes pertranspose, is also cited

Quick good morning to everyone before I'm off.

Hey JM : )

Hey Matt. :)

Are you back?

Not quite yet, sadly.

Ok...

for example here: perso.uclouvain.be/paul.vandooren/publications/VDoorenD83.pdf

@JM Thank you.

But good to see you.

@MattN Likewise.

@Gigili BTW, why'd you abdicate?

abdicate? she had a throne she renounced? this is news to me....

she had konigship

Do you know how to refer to an equation with a number? For further reference?

Gigili, I like your new avatar.

@JM Oh? How do you mean?

Thank you Matt.

Thank you all for your help

$$equation \tag{(1)}$$ and then within normal text just write $(1)$, I think that's what we have to do on mse

@Gigili Renounce your throne (chat room powers)

Well, Königin, seeing Gigili is a "she"...

test: $\oint f(z) dz$

I had no power!

I don't even know what language that is, let alone how it's gendered :P

@anon Thank you

@anon German. :)

@JM Is being a mod a lot of work?

have a good morning/afternoon/evening/night, everybody!

@MattN a bit.

are the thankless tasks worth the guilty pleasures?

What anon said. : )

@anon I still don't have a good answer to that question... :D

What are the native language(s) spoken in the Philippines? (in particular, what language are the signs, menus etc. written in?)

Aha.

Filipino.

@MattN That would be Filipino and English. (At least here in the capital.)

Provinces will tend to use dialects.

Yes, just saw that too.

And are they similar enough so that they can understand each other?

Or is it like in India?

@MattN Unfortunately, no. The correspondence between, say, Ilocano and Waray is rather tenuous...

@MattN Or a better example would be Germany.

But Germans understand each other more or less.

Though I struggle with some Bavarian dialects.

But then I'm not German : )

No, they do not. The Swabian dialect something totally impossible to understand.

Haha, although the other day a German asked me how come I can speak German without accent : )

That was infinitely pleasing.

Unfortunately, I think they were sucking up. (for no reason)

@Gigili Ok : )

I think the most cryptic "German" I've heard so far were two dudes from Vienna.

I could only understand the odd word. And I wasn't even sure of that.

Haha, "the worst" German.

It doesn't make sense since German is the worst by its own.

Yes, I corrected it. Because I actually like it : ) (not all sorts of German but quite a few)

@Gigili I quite like it. But I prefer "clean" spoken German.

Gotta go, see you later! : )

Me too. The most "clean" one is spoken in Hanover, AFAIK.

Have fun!

You too!

I'm not sure if the answer I just posted makes any sense!

It makes perfect sense. The notation you used was interesting though.

Thank you.

I +1ed you. I do that occasionally.

Umm, it means you don't read my answers?

How could I tell you it makes perfect sense and contained interesting notation if I hadn't read it? I always read your answers.

Yay!

I mean, apart from the ones I can't be bothered reading.

Yay/2!

still bigger than sqrt(Yay) for large values of Yay

sqrt(yay) then

How much rep did you gain in total, by asking that "3 divides 107" question then answering it yourself? Anything close to yay?

Excuse me?

I'm just teasing you. Math is such a nice place, compared to English.

So nice of you, thanks.

Much better than the "1+1" question you answered and felt extremely intelligent.

Did I answer a 1+1 question? I don't even remember doing that - oh, wait - you're teasing me now!

Ah, I think you meant math.stackexchange.com/questions/98415/… - and I ALWAYS feel extremely intelligent. Bottom of the heap, yay me!

i suppose that counts as a 1+1 question, for rather large values of the first 1

Well, I was adding one of something.

i've never quite been comfortable with limit ordinals....i can see why they're useful, but it seems to me as if their existence is a matter of "they exist because we say they do"

...and that's it for me today. See you guys... hopefully soon.

it's like with inductive proofs: i don't think they are actually proofs in a restrictive sense of the word...they're a SCHEMA for a proof.

like a proof that we could prove something, if we had the patience to do so

@JM Have fun.

morning, all

sort of like: y cld rd ths sntnc, f y prvdd th vwls

oh, no! missed J. M. :/

i don't think he died.....did you have something pressing to say?

no, nothing pressing. It's just that he's too pleasant a fellow to miss...

Morning Tee-Bee.

just my luck! now there's just you....

At least I'm still here.

maybe malcolm will come back and give me more grief

@Gigili a fact for which i am eternally grateful.

Technically, can I ever be lost if I never have a destination in mind?

well, there you're always "here" since where "here" is, is irrelelvant

of course, to me you're "there" since i'm not you, but if i was, i wouldn't be lost, would i?

@DavidWallace i believe it does. and just because we haven't read a book "completely" doesn't mean we haven't gained anything.

@Gigili 'ello, gigili

if we had "some" foundational basis for mathematics we were certain of, all of the "meta-proofs" we'd been doing up to then, could piggyback on the foundation

or at least a large enough collection of them could....i believe the current state of affairs is that NO foundation can be "broad enough"

"Here" isn't "there". To me, I'm here while you're there. So it doesn't make any sense if you ask me "are you there" since I'm not there, I am here.

I often wonder whether "real" mathematicians care about whether their work will one day be useful to someone, or whether mathematics exists truly for its own sake.

@Gigili of course, you're not me. but if you were, there would be no need to have this conversation since our thoughts would coincide.

@Gigili The flaw in your reasoning is that you're not as happy to replace "there" with "here" as you are to replace "you" with "I".

@DavidWallace i think that varies from person to person. some people work in mathematics just for pleasure. some work at it to solve some problem (developing tools to do so as needed). others mix 'n' match.

I think many mathematicians don't get too worked up about foundations. They like to indulge in them from time to time but without serious consequences. There is quite a widespread opinion that proofs are a purely sociological construct after a certain point. There also is a widespread conviction that the essential ideas will survive, no matter what. Maybe this is a bit religious, but we're human, after all.

So you mean if I could be there if I was you?

that is one point of view...that mathematics is a social endeavor. not all mathematicans hold that view.

yes, right here :P

jam tomorrow, of course, not today

How many mathematicians have the expertise to truly judge if FLT or Poincaré are completely proved?

@DavidWheeler I don't understand what you mean by "social endeavour".

that mathematics is not a description of reality or objective truth, but rather a way to communicate human views on reality

the "anthrocentric" part of this could be tested if we had more data on: the mathematics or lack of it in non-humans

Never heard of "entropy" in my whole life ...

some mathematics believe that a statement like: 1+1 = 2 reveals something essentially and eternally true, whether humans exist in the universe or not

That's an odd view, if I may say so.

I mean, the bit about communicating human views.

@Gigili entropy is tendency towards disorder or chaos. now you have. the explosion of a building is positive entropy. the baking of a cake is (local) negative entropy.

It seems more logical that the truth of 1+1=2 is independent of the existence of humans. Rather like trees falling in forests.

@DavidWallace there are even stranger views on mathematics: that it is all "made-up" and has NO validity outside of itself (fictionalism)

there's another view which espouses that we cannot even SAY what mathematics is, just what it accomplishes (structuralism)

still others that say it is just an artificial game, with rules of our own devising (formalism)

I can't speak for all mathematicians but the vast majority of those I know are all pretty sure that the most famous theorems are true/proved [fill in the appropriate adjective] and they also are (painfully?) aware that for many of those results they will never be able to judge for themselves.

various sub-categories and hybrids of these views exist as well, and there is often divergence between the mathematics one works with, and what one believes philosophically is true

That seems less strange to me than the idea that its truth depends on the existence of humans.

May we discuss your definition of entropy? It differs from my understanding.

there is a fairly high degree of consensus, for quite large areas of mathematics. more so than in other fields of knowledge.

@DavidWallace discuss away

I was under the impression that entropy was a measure of disorder, not a measure of the rate of change of disorder. So baking a cake requires a decrease of local entropy; it doesn't put anything into a state of negative entropy.

@tb i believe that the classification theorem for groups IS true...and i do not think i will ever verify it for myself. mathematicians have a surprising degree of moral truthfulness regarding how they represent their work (and here i mean "truthful" in the ordinary english sense)

That seemed to me to be different from what you were saying, but maybe I just didn't understand you.

@DavidWallace i think you're right...it's like "heat"....cold doesn't actually exist, it's just an absence of heat....but it's a common abuse of language, i believe

if you think about it, negative quantities don't exist either, but it's convenient to call a loss of 2 apples a gain of -2 apples

@DavidWheeler This reminds me of what René Thom wrote in the response to the Jaffe-Quinn controversy here: "My feeling is that it is unethical for a mathematical researcher to use a result the proof of which he does not “understand” (except for the specific case where he wants to disprove the result)."

(the debate is worthwhile reading, of course)

@tb if someone does so, it does seem to create the need for a referee, whose own ethics must then be scrutinized

@DavidWheeler That's not quite what I meant.

@DavidWheeler But this would be relying on others... We don't want to build mathematics on trust, or what else can come out of scrutiny?

I meant that your definition of entropy seemed to correspond to the rate of change of entropy as I would define it. Or, if I can draw a parallel, when asked for a definition of velocity, you gave a definition of acceleration.

But I think I probably either misread or misunderstood your answer to @Gigili, or both.

my mistake, it IS the disorder itself, and not, let's say, the gradient. i hope Gigili is not confused.

@tb so all research based on the riemann hypothesis being true should halt until a proof is discovered, or a counter-example found? it's a defensible view, but not apparently that pervasive...

@DavidWheeler No no, I got an idea of it from your answer and WP helped me to understand it better.

personally, i feel it's fine to use a result, as long as you qualify your assumptions up-front

most students use the fact that real polynomials split over the complex field far before they ever prove the fundamental theorem of algebra

By trusting other mathematicians, you may be standing on the shoulders of giants.

@DavidWheeler I don't see how that should follow.

how "what" should follow?

FWIW, David, I didn't mean to sound disparaging. I thought the explosion and the cake were excellent examples.

Why one should not assume the RH or reject it to deduce other statements.

@tb since a proof does not yet exist, obviously no one yet understands this non-existent proof, no?

therefore it appears that René Thom at any rate, would feel it is unethical to use the RH

I think it's OK to live in hope that RH will one day be proven. Mathematicians "prove" a whole lot of stuff that will become truly proven on that very day; that has to be valuable, nicht wahr?

what i think is important, is acknowledging what you start with: if you appeal to the axiom of choice...say so...this is more involved than it appears at first glance

@DavidWheeler I don't think so: the result is that people plainly state that they assume RH if they happen to do so. This doesn't normally happen when people take a theorem on faith because no-one is willing to admit that he didn't do his job properly.

@tb and that IS bad....someone needs to check the i's are dotted, and the t's are crossed

yes, but how?

with something like FLT, perhaps we're not there, yet

the examples brought up with gauss' first proof of the FTA, are to the point

obviously gauss himself wasn't happy, as he went on to write even more proofs

@Gigili You may find the WP article titled "Entropy (energy dispersal)" more useful than the one just called "Entropy".

I hated having to explain the Second Law of Thermodynamics to 100-level physics students; it was so hard to be convincing about something so abstract.

air conditioners aren't abstract

@DavidWallace I read the "Entropy (information theory)".

if you run an air conditioner in a sealed room (the whole thing, not venting it elsewhere)...it gets warmer

It is too easy and quite common to gloss over gaps in one's own knowledge. It is good to have the highest of standards. But they slow you down. Also, it is too exciting to go and see what you can squeeze out of a result by assuming all sorts of things. Once you got to a good point you're not willing and often (e.g. for economical reasons) not able to sacrifice years and years of work to put it on firm grounds.

@DavidWheeler Not necessarily.

@tb yes, there's a conflict of interest in what is "good for you" and what is "good for the community"

i think the buzz phrase is "publish or perish"

Yes. And it is too easy to get corrupted. Probably certain compromises are unavoidable.

one of those compromises is journal peer-review, and comes with its own attendant problems

But peer-reviewing is explicitly not for attaining a voucher of correctness of all the details: the reviewer looks at the results, checks if they look reasonable and checks if they are of enough interest.

@Gigili Ah, well that's something completely different!

on the whole, i am rather comforted by the thought that my own thoughts, words and deeds do not have the value i place on them, but are in the long run, judged by people with no vested interest (i'm talking very long run...the expected outcome is they all will be forgotten)

@DavidWheeler So unfair.

Woke up on the wrong side of the bed again.

@DavidWallace Oh? Peh.

@Gigili i fixed that by placing one side of my bed against the wall

Peh? Is that another Gigilism?

@tb i never claimed it was a perfect system...and the sheer volume of mathematics studied in the world precludes any comprehensive review....i'm sure some mistakes will slip in, right?

@Gigili but it does explain why zipping works better on some file types than others.

@DavidWallace Uhum.

Isn't Entropy about unpredictability?

So which side of your bed is the wrong side?

@DavidWallace so a random hex-data file won't zip as small as the same size english text, hmm?

@DavidWheeler Correct.

It heavily depends on the day, but usually the left-side.

@DavidWheeler Of course they will. A huge bulk of the results that people produce is not particularly interesting anyway. What draws the attention of sufficiently many people will be checked in many different ways.

But...only "eventually"

sometimes, i take a dilettante's interest on physicial "unified theory of everything" theories. a lot of the mathematics of that field is being done concurrently with the development of the physical theory...leaving it particularly vulnerable to the concerns we are currenly discussing

@DavidWheeler and that's what keeps you practising mathematics?

@DavidWallace no. to me mathematics is like a beautiful woman i'm wooing. perhaps if i am ardent enough, she will tell me a secret. perhaps not.

Bugger that! Give me a real woman any day.

Umm, but that's an interesting perspective, I guess. I suppose I never got to that kind of level with mathematics.

Okay, I gotta go and do some work. See you later y'all!

Good night, t.b.

good night David!

Have fun Tee-Bee.

if i had ever met a real woman who could excite me like math does, i'd be inclined to agree with you. but people have been a great disappointment to me. perhaps the fault lies within myself, but my options for self-change decrease with every passing day.