Mathematics - 2015-03-19 (page 2 of 6)

Ted Shifrin

02:00

@Semiclassical: For the applications I know of the formula I gave you, people certainly don't want to assume all the matrices commute.

Semiclassical

fair enough, though as a first example application for me I can take the case of the blocks all being circulant matrices, and therefore commuting

Ted Shifrin

It's fine for the experimental sciences, @DavidW, but it's a terrible model for mathematics (where there's almost no grant money) and the humanities. I'm not sure about the social sciences.

Semiclassical

and that's actually physically relevant

David Wheeler

Money-worship is a big problem in America.

Mike Miller

@davidw I interpreted his statement to mean that the blocks commute pairwise, in which case it does mean that they lie in a commutative subring.

Ted Shifrin

02:01

I concur, @DavidW.

Stan Shunpike

I wonder why America is prone to it.

Why here as opposed to anywhere else?

David Wheeler

People seem to have forgotten we obtain money in order to live, not live in order to obtain money.

Semiclassical

one can presumably weaken the assumptions regarding commutativity---indeed, it's evident how to do so in the 2-by-2 case

Ted Shifrin

Some of us got too rich, @Stan, and then the Republican selfish ethic took over a large portion of society.

Semiclassical

but i don't want to assume 2-by-2 if i don't have to

Ted Shifrin

02:03

@Semiclassical, what I told you is for $n\times n$, and the paper you linked did $n\times n$, too.

@Semiclassical: So, a good exercise for you (or for @Stan) is to prove the product rule for determinants using exterior algebra.

David Wheeler

@MikeMiller Are you referring to the ring generated by the matrices we posit will commute?

Stan Shunpike

Hmm....yes that would be a good one.

I did it for covariant derivatives :D

Ted Shifrin

covariant derivatives? what?

you're bad about dangling antecedents :P

Mike Miller

Yes, @DavidW.

Ted Shifrin

@Stan: So are you at U of C now?

Stan Shunpike

02:06

Yup, bout to start class in 15 days.

Ted Shifrin

Wow ... well, you'll get a tough education. Good for you.

You won't need us here :P

Stan Shunpike

Doubt it. Good teachers are hard to find :p I know. I've been a student all my life.

David Wheeler

True story-Grassmann was so discouraged by the poor reception his work received, that he quit the field of mathematics.

Ted Shifrin

BTW, I'll visit Chicago next spring, @Stan ...

I actually didn't know that, @DavidW.

Stan Shunpike

Really! That's awesome. We should have lunch or something

Ted Shifrin

02:07

For sure, @Stan ...

Stan Shunpike

Here's that product rule: math.stackexchange.com/questions/1137420/…

Semiclassical

seems like it's nothing more complicated than wedging the $n$ column vectors together and counting how many times one has to invoke antisymmetry in order to get each term $\propto e_1\wedge \cdots \wedge e_n$

David Wheeler

@TedShifrin He become a rather well-respected translator of Sanskrit. Funny how things turn out, sometimes.

Ted Shifrin

Ugh, I really can't stand the classical tensor/physics notation. It obscures so much.

Wow, @DavidW, I had absolutely no idea.

Mike Miller

Do you have a reference for that true story, @DavidW?

Semiclassical

02:09

which is nothing more than the usual $sgn(\sigma)$ sign

Ted Shifrin

Well, @Semiclassical, that shows you that $T^*(\omega_1\wedge\dots\omega_n) = (\det T) (\omega_1\wedge\dots\omega_n)$, where the $\omega_i$ are the dual basis to the standard basis. Knowing that, the product rule will follow.

@Stan: One of the great mathematicians/teachers at U of C died a few years ago, sadly.

David Wheeler

Hermann Grassmann

Hermann Günther Grassmann (German: Graßmann; April 15, 1809 – September 26, 1877) was a German polymath, renowned in his day as a linguist and now also admired as a mathematician. He was also a physicist, neohumanist, general scholar, and publisher. His mathematical work was little noted until he was in his sixties. == §Biography == Grassmann was the third of 12 children of Justus Günter Grassmann, an ordained minister who taught mathematics and physics at the Stettin Gymnasium, where Hermann was educated. Grassmann was an undistinguished student until he obtained a high mark on the examinations...

Particularly, the "Linguist" section.

Stan Shunpike

@TedShifrin Grassmann?

(lolol jk jk)

Who was it?

Ted Shifrin

Huh? No, @Stan. Paul Sally.

He was a famously great teacher.

Only had one arm, too, if I remember correctly from meeting him.

ugh, I left out wedges in my formula above. Sigh.

Stan Shunpike

"He was known to detest cell phones in class and has destroyed several over the years by inviting students to stomp on them or by throwing them out of a window."

That's original.

Ted Shifrin

02:12

If that quote is about Sally, I like him even better.

Stan Shunpike

He sounds like a unique character, something out of a book.

Ted Shifrin

And now students walk out of class because it's just so important to take a phone call in the middle of class. Makes me livid.

Semiclassical

for sake of clarity, by product rule do you mean summing over permutations of the matrix elements?

Ted Shifrin

I mean $\det(AB)=\det A\det B$, @Semiclassical.

Semiclassical

ah.

Ted Shifrin

02:14

That's really the key to the formula we're discussing.

Stan Shunpike

@TedShifrin Where in California will you live? Pasadena is nice :D

Ted Shifrin

I am not fond of LA, @Stan, although I will of course visit. I'm moving to San Diego (although I spent 18 years in Berkeley and prefer northern) because of old and dear friends there.

Semiclassical

misunderstood you, then

Ted Shifrin

I'm often misunderstood, @Semiclassical. It comes from being unclear :D

David Wheeler

That multiplicative property is beastly to prove by tracking matrix entries, and easy to prove using the alternating linear functional properties.

Semiclassical

02:15

heh, and i'm misunderstood by not actually understanding how to say what i mean :P

Ted Shifrin

Well, an undergraduate proof is pretty convincing by doing elementary matrices, which is the proof I like to give, @DavidW. But for these exterior algebra guys, yes, what you're saying is the best.

Mike Miller

@DavidW I only ask because that sounds like a canonical sort of apocryphal story. That he became a linguist is interesting.

Ted Shifrin

@Mike: Has Pedro been in evidence around here?

David Wheeler

@MikeMiller No, I understand. I've seen it on other math history sites, too, just can't summon them fast in real time.

Alex Wertheim

Are you going to do 5.18, @Kaj?

Ted Shifrin

02:18

@AlexW: Have you submitted your formal acceptance yet?

Semiclassical

leibniz's formula for the determinant gives the product rule pretty easily, if i remember right, though i suppose that's just exterior algebra in disguise

Ted Shifrin

One of our students is about to visit both San Diego and StonyBrook.

David Wheeler

I enjoy reading about the lives of mathematicians, trying to get a sense of personality. It's too bad we have so little information on earlier math greats.

Jasper Loy

@TedShifrin I visit the bathroom every day.

Stan Shunpike

Is Boole considered a math great?

Mike Miller

02:19

He left yesterday, I think.

Ted Shifrin

@Jasper: Some things are better unsaid.

not really, @Stan

Alex Wertheim

Not yet, @Ted. It's basically a done deal, but my visit to Penn isn't for another week or so, and it doesn't make sense to me to visit if I'm already committed.

Jasper Loy

@TedShifrin I thought you would say, sometimes you talk too much, lol.

Ted Shifrin

I've said that to you before, @Jasper, yes.

René clearly thinks I talk too much, too.

Alex Wertheim

Also, I was waitlisted at Michigan today, so I'll at least wait until I visit Penn to see what happens.

David Wheeler

02:20

@Semiclassical You still have to engage in some godawful subscript stuff. Not too bad if you know a little group theory.

Semiclassical

$\text{sgn}(\sigma_1)\text{sgn}(\sigma_2)=\text{sgn}(\sigma_1\sigma_2)$ and all that

Ted Shifrin

But I had someone else giving me downvotes ...

Jasper Loy

@TedShifrin What did you say to him?

Ted Shifrin

Nah, I don't want to go there, @Semiclassical.

Semiclassical

i'm a physicist, godawful script stuff is my bread and butter

Ted Shifrin

02:21

I haven't said anything to him in months, @Jasper. But he didn't like to be told he was wrong.

I want to think about composition of linear maps, @Semiclassical.

David Wheeler

@TedShifrin You can tell me I'm wrong all day long. I may cry a little, but I'll get over it.

Ted Shifrin

ah, cool, @AlexW ... Michigan is a great department, too, as is Penn.

Semiclassical

fair enough, better to avoid invoking a basis if one doesn't have to

Stan Shunpike

I got chewed out on Physics SE for assuming I was wrong about a problem when I turned out to be right.

Ted Shifrin

LOL @DavidW. I'm not the arbiter of all things math, but when someone with a Ph.D. in logic answers things in differential and algebraic geometry with absolute garbage, I'm not going to sit by idly.

Stan Shunpike

02:22

I didn't make that mistake again

Alex Wertheim

For sure, @Ted. Excellent algebraic geometry, and very good number theory too. A little closer to home as well. But I still am pretty sure about my feelings, so I don't think much will change anyway.

Ted Shifrin

@Stan: I look forward to chewing you out :)

Stan Shunpike

LOL I'm ready, bring-it-on

Ted Shifrin

@AlexW: David Speiser, who's active on MSE and MO, is an algebro-geometric guy at Michigan.

Stan Shunpike

I'm used to it. That's what happens when you argue with smart people all the time.

Jasper Loy

02:23

@TedShifrin I got 100 points for a one line answer yesterday, lol.

Ted Shifrin

I'm not that totally obnoxious, @Stan, although @Kaj might differ :P

David Wheeler

Ted Shifrin - Knight of the Round Surface.

Stan Shunpike

lolol

Semiclassical

though you can also view index notation from an abstract perspective a la penrose (though i'd be lying if i said that i ever actually bothered to understand what that means)

Alex Wertheim

@Ted: David Speyer? Yeah, he does very cool work! Algebraic geometry with a combinatorial flavor.

Ted Shifrin

02:23

LOL, @Jasper: Pretty much the most votes I've gotten on this site were for the stupidest things.

Oh yeah, I messed up his name, @AlexW. Darn.

He asked a cool differential geometry question a few months ago. He apparently liked my answer.

Stan Shunpike

Is Penrose considered a mathematician or a physicist?

Ted Shifrin

Yes, @Stan.

David Wheeler

@StanShunpike Yes.

Jasper Loy

@TedShifrin It's so sad to see that all my friends have already gotten PhDs and gotten married, and instead I am struggling with mental illness. It's very sad...

Semiclassical

i.e. this wikipedia page

Ted Shifrin

02:25

I understand, @Jasper. It has to torment you. But sitting around feeling sorry for yourself won't help you improve your plight.

Alex Wertheim

I guess I'll just have to wait a bit more @Ted. A very long process. =P

Ted Shifrin

A bit more for what, @AlexW?

Alex Wertheim

San Diego and StonyBrook are both very exciting though. :)

Mike Miller

I'm lucky in that I like most of my highly upvoted questions and answers. But I guess I don't answer a lot of stuff I wouldn't be happy about.

Jasper Loy

@TedShifrin Yes, you are right. So I try to get better, but it is hard, and the outcome is not certain. So I just keep trying and hoping for the best.

Ted Shifrin

02:26

@AlexW: I'm guessing that Bryan is going to UW. I don't think he's committed yet.

Alex Wertheim

To see things to the end and make my decision, @Ted.

Stan Shunpike

I didn't realize I could downvote questions without losing points until 2 days ago.

Alex Wertheim

Neat! That's what he seemed to indicate when we met at the visit day.

Ted Shifrin

Oh, @AlexW, duh. Of course. In the overall scheme of things, it's not a long time at all.

Oh, you can downvote questions ... but if you downvote answers, you lose points, @Stan.

Stan Shunpike

I wish I new some nice German words.

I want to use them as song titles

But everytime I google an English one, the German one just isn't as nice sounding.

David Wheeler

02:28

@JasperLoy I believe in some sort of vague "conservation-of-energy" law: so, if you work on something, you WILL get a result.

Stan Shunpike

So far I've used Italian, Spanish, English, Greek, French and Arabic

Ted Shifrin

OK, I'm out of here for tonight. You all have fun.

Semiclassical

oed und leer das Meer

Stan Shunpike

Adios

Alex Wertheim

Night, @Ted!

Semiclassical

02:29

night

Ted Shifrin

Night :)

Jasper Loy

I have a habit of sending emails without titles. Sometimes I don't know what titles to use.

@ted Yesterday the doctor said "Don't kill yourself, we can help you", lol.

Dave

I really don't understand simplification of expressions

my answer was so far from the actual answer =/

David Wheeler

@Dave It's hard to know what you mean, exactly, without a little more context

AbstractionOfMe

@JasperLoy what's your diagnosis? I have schizophrenia.

Jasper Loy

02:32

@AbstractionOfMe OCD and PTSD

AbstractionOfMe

What caused the PTSD (if you don't mind)?

David Wheeler

@Dave I suspect you are talking about "collection of like terms"

@AbstractionOfMe Jasper had an abusive father.

Dave

well i reorganised the like terms for this: 9x – 21y – 12x
so i did 9x - 12x but for some reason its actually 9x - -12x

not understanding why

David Wheeler

Are some parentheses missing?

Dave

there was brackets but i expanded them previously

David Wheeler

02:35

Perhaps at some point, you expanded incorrectly.

What was the original expression?

AbstractionOfMe

I think it's sad that antidepressant drugs aren't much further along.

Dave

let me try something first see if i can figure it out

Jasper Loy

@DavidWheeler The clonazepam helps me to calm down a lot.

AbstractionOfMe

The only thing that really worked for me was pot but it had the side effect of making me psychotic.

Committing to a challenge

@AbstractionOfMe wut

Jasper Loy

02:53

@Committingtoachallenge I hope my new email and new SE accounts will bring me good luck, lol.

Committing to a challenge

@JasperLoy They will bring you good luck if you answer heaps of questions, and also forward this message to 10 places in 24 hours or you will find an evil clown in your room tonight

Jasper Loy

@Committingtoachallenge I emailed almost 60 people last night and only a few replied. =(

Committing to a challenge

@JasperLoy I didn't reply because you are here haha

Are many from this chat?

Jasper Loy

Yes, no need to reply. But I thought they would say more things you know, lol.

@Committingtoachallenge But yes I feel much less anxious after taking a few pills since last night.

Committing to a challenge

I feel stressed :)

I'm going to blow up :)

Jasper Loy

02:58

Go take some pills.

Dave

fairly sure imma fail this assignment

xD

Jasper Loy

I got 9 badges in 1 day, lol.

Committing to a challenge

@Dave When is it due?

Dave

end of april

but im doing it early

Committing to a challenge

What is it?

Pedro Tamaroff

03:00

@JasperLoy not really wise to send my personal email publicly along with 60 other emails.

You could at least have hidden the emails.

Committing to a challenge

I did notice that @Pedro

Jasper Loy

@PedroTamaroff Is that a norm to hide the emails?

Committing to a challenge

I went through that list, but didn't recognize many: Alizter, Ted, Pedro, (myself)

Pedro Tamaroff

I'm therefore asking you to delete my email from such lists.

anon

@JasperLoy when mass emailing, yes

Pedro Tamaroff

03:01

Hi stranger.

anon

or even just emailing two people that don't know each other very well

hi

Committing to a challenge

Chris's sis was in there and it had 2001 in it

Which was confusing

Jasper Loy

OK, but would it lead to disastrous effects?

Pedro Tamaroff

How are you?

Paul Plummer

spam and harrasment

anon

03:02

pretty good. get to go on spring break finally.

Committing to a challenge

Why is Chris's sis's email a mans name with 2001?

Pedro Tamaroff

I don't know Jasper. I don't want a bunch of people I don't know to have my email.

Jasper Loy

So last night I pissed off a lot of people?

Pedro Tamaroff

Probably, Jasper. @anon Glad to hear that.

Committing to a challenge

@JasperLoy Yeah I thought probably as well haha

Pedro Tamaroff

03:03

How did classes go?

anon

they continue on after break still. doing alright.

Alec Teal

@Committingtoachallenge welcome to the internet.

Jasper Loy

@Committingtoachallenge Oh well, I am sorry. I just think it is pretty harmless. It's just an email, not a credit card number.

AbstractionOfMe

@Committingtoachallenge wut do you mean by that?

David Wheeler

@JasperLoy Bcc, there for a reason.

Committing to a challenge

03:04

By what Abstraction?

@JasperLoy I don't care personally at all

AbstractionOfMe

You said "wut".

David Wheeler

@JasperLoy I have 6,000 emails to delete. The trouble with spam is it hides the stuff you want to keep.

Committing to a challenge

You are psychotic as a result of pot?

AbstractionOfMe

Well, it brought the psychosis out, at least.

Committing to a challenge

@AlecTeal Why are you welcoming me to the internet?

ᴇʏᴇs

03:06

Welcome @Committingtoachallenge

Committing to a challenge

Welcome @Committingtoachallenge

Paul Plummer

Emails are typically attached to multiple service (like banks, facebook accounts) which could be used to social engineer or even just get info stored in the emails. so people not knowing your email is your first defence to not getting your email broken into. Also spam is just annoying

Jasper Loy

Oh dear, I pissed so many people off.

Committing to a challenge

Don't worry about it imo

People get over this stuff

Jasper Loy

imao or lmao

ᴇʏᴇs

03:09

@JasperLoy You also sent the e-mails to yourself also on the list, lol

Jasper Loy

@ᴇʏᴇs LOL

Committing to a challenge

I saw that aswell

Jasper Loy

I emailed my 4 professor separately.

Kaj Hansen

I haven't had a chance to even read them yet @AlexWertheim. Is it a good problem?

Julian Rachman

@Kaj thanks for the update

Kaj Hansen

03:13

:)

Jasper Loy

@pedro Your mask is pissing me off.

Mike Miller

I like his avatar.

ᴇʏᴇs

@JasperLoy You never watched El laberinto del fauno I guess

Jasper Loy

@ᴇʏᴇs Nope.

Committing to a challenge

If I find a course really really boring I should drop it right?

I mean, it'll just end up a crap grade probably since it is so hard to study

Kaj Hansen

03:18

@Committingtoachallenge, maybe hold out until the last day to drop? See if things improve or not?

Committing to a challenge

@KajHansen It's operations research, so the whole semester is just coding problems for optimizing stuff haha

Whereas my other 4 are pure math

ᴇʏᴇs

@Committingtoachallenge I was gonna take that class but my friend who's taking it now says it's computational and boring

Committing to a challenge

@ᴇʏᴇs It is exactly that Eyes

My girlfriend isn't in support of me dropping it

Which is my only real deterrent ahah

It's pretty much the gate to being able to do applied math out of uni(read: boring)

Alex Wertheim

@Kaj: yes, a very cool one, especially if you are interested in doing algebraic geometry in the future. :)

Kaj Hansen

That does look like a cool problem @AlexWertheim. I'll work on it tonight!

(I miss algebra dearly)

Alex Wertheim

03:32

Haha, I thought you might like it for that reason, @Kaj.

Committing to a challenge

@KajHansen I love algebra so far, so much

Alex Wertheim

It certainly is one of the harder problems on that list. Granted, I haven't read all of them, but it looks significantly more challenging than almost any of those.

But it's great stuff.

Kaj Hansen

:)

Karim Mansour

hey guys

postimg.org/image/qylgir4zz

I don't understand why it is sufficient

that if {C}_n is sequence of bla why is it suffciient to prove this theorem?

Committing to a challenge

Yes, I shall drop my 5th course so I have more time for real math

Karim Mansour

03:37

?

Pedro Tamaroff

@JasperLoy Well that is too bad.

@MikeMiller Hello there.

meer2kat

03:52

Any of my old peeps here tonight?

@JasperLoy What's up bro?

Committing to a challenge

@meer2kat Are you (possibly) the person Jasper talked about a few times?

meer2kat

@Commit Yep most likely! He recently sent me an email and it reminded me I haven't been here in a minute

Committing to a challenge

Almost a year from the transcript

meer2kat

Yeah I was on here a lot when I was doing a programming project at work. I left when I moved back to my normal dwelling

Committing to a challenge

What profession do you belong to?

Jasper Loy

03:58

@meer2kat Hi, did you go and do mission work in the end?

meer2kat

@Commit I was doing engineering. Now I'm back in school studying mathematics, english, and physics

@Jasper Not yet. Won't be for a few years yet if I get to

How are you doing?

Jasper Loy

Really bad. Might never get well, but trying to.

Transcript for

$Mathematics$ Mathematics