Mathematics - 2021-04-26 (page 2 of 3)

leslie townes

17:00

one of the best is an arbitration agreement printed on the back of a cruise ship ticket that you didn't get to see until after you bought the ticket.

enforceable.

ted shifrin is a functional analyst now.

Ted Shifrin

God only knows what immoral havoc the current Supreme Court is going to wreak.

Thorgott

banach geometry

Ted Shifrin

Maybe Leslie is going to study Alain Connes next.

leslie townes

marc rieffel was always trying to get me to read him. no thanks.

the gallic influence on mathematics is regrettable.

i did secretly sneak a read of one or two of his papers and he is clever, but maybe too clever. frenchmen.

someone once said that french politics is dumb people pretending to be smart and english politics is smart people pretending to be dumb. i don't know if that's true. in america it is dumb people not pretending to be dumb.

Ted Shifrin

These days in Britain it's not too much pretense.

leslie townes

17:09

the level of aggressive stupidity in the UK right now is something else.

it's nice to live in a part of the US where people don't feel that they need to compete to be as dumb as possible.

Flows.

what do you guys think of identity politics in universities these days?

whats it like in the US ? do you notice it?

leslie townes

i do not work in academia. my wife does, she doesn't see it but maybe that is because her school is not a school that the people who opine on such matters would have attended. it seems like a straw man to me.

Ted Shifrin

We old guys are no longer in universities. But the right-wing politicians are doing their best to make education an illiberal commodity.

leslie townes

so much of the discourse in the USA is focused on harvard, yale, and other places that people who get hired immediately out of college to report on nationwide news events attended. that's not the american experience.

robjohn

@leslietownes I remember in school, people would be proud of how little they studied. Stupid was the new orange.

leslie townes

17:16

and it's hard for me to be too distressed about someone hearing views they don't agree with. my bottom line, which is illiberal, is, if you don't want to hear bullshit, don't major in bullshit. everyone who complains about liberal bias in academia majors in bullshit.

Ted Shifrin

That certainly was not the case where I went to school, @robjohn :P

leslie townes

i've never heard a chemistry major complain about the political tendencies of the faculty.

robjohn

@TedShifrin Luckily, I hung out with the nerdier contingent, where it was cool to know things.

Ted Shifrin

@leslie We're going to disagree here. I am a big believer in the humanities (was a French major, after all).

leslie townes

i like the humanities. but, it's always some poli sci or economics major spouting off.

that's BS to me.

Ted Shifrin

17:18

Business majors don't belong in universities.

leslie townes

my wife is a sociology professor.

she can't indoctrinate anybody, you overestimate her powers.

Ted Shifrin

Well, sociology is a social science along with the two you listed.

robjohn

Yes, humanities are a linchpin of society

leslie townes

there's a lot of crap in her department, i just don't see how it harms anybody.

robjohn

. o O ( lynchpin? )

leslie townes

17:19

it's just academics doing what they do.

i was almost an english major. there's another world in which i wrote the great american novel.

robjohn

@TedShifrin they used to put the business majors in a building off-campus at UCLA. Now they have a building in the far northeast of campus.

Ted Shifrin

Somehow the history is all forgotten. There were not undergraduate business majors, and MBAs were intended for people in science/engineering. Now look at it.

Trade school.

robjohn

trade school with suits.

sort of like high school with ashtrays. That's what they called jr college when I was in college

leslie townes

i do remember a few professors saying offensive and gratuitous things in the classroom. it was not connected to the subject matter of the courses. it's always annoying when that happens, some people feel if they have a professorship they are the king or queen of some domain. regrettable but not headline national news. just people being dorks.

Ted Shifrin

Well, no, plenty of racists, homophobes, misogynists in academia, even in math.

copper.hat

17:23

that is broadly true in life

Flows.

By identity politics I meant from the left as well

leslie townes

that's mostly what i was thinking of. there were several virulent homophobes on faculty at berkeley.

Flows.

At least in the UK

leslie townes

my wife has to tolerate a lot of what would probably be regarded as leftist nonsense outside of academia. i also think it's nonsense, but it's not oppressing anybody.

Flows.

I know Edinburgh university are having to change the name of one of their buildings call Hume tower ( after David Hume)

copper.hat

17:25

maybe they can change to john instead :-) (i know, wrong place)

Flows.

because he supposedly wrote a sentence which these days would be considered racist.

Ted Shifrin

I'm fine with trying to do away with racist traditions, along with plenty of others. If that's leftist identity politics, so be it.

They are part of history, but do not deserve to be honored.

leslie townes

name changing is an interesting thing. i don't think any old dead rich person deserves their name to be perpetuated. i do question whether, if we're going to address issues, that's the first place to start. but it's easier to change names than minds.

Flows.

But if you go back far enough nearly everyone was racist

to some degree

we were idiots

Ted Shifrin

No reason to keep perpetuating and honoring it.

Flows.

17:26

we cant just stop honouring their other work

copper.hat

i see it as an extension of 'clannism'

Flows.

yeah but naming a tower after Hume is not honouring some side comment he once made

robjohn

@TedShifrin I agree, but I do not agree that taking down the monuments to the good things that people who had racist views did is good.

copper.hat

john or david?

Flows.

its about his contribution.

leslie townes

17:27

they changed the name of berkeley's law school because the guy had advocated for legislation that stigmatized and humiliated minority groups, including groups who make up a near majority of berkeley's student body today. i'm not losing any sleep over that.

copper.hat

race to blandness

Ted Shifrin

I am more concerned about the idiots who continue to fly and revere the Confederate flag in the US.

leslie townes

i don't see it as imperative. i could think of other imperatives, mainly economical ones. now i will give a lecture that radicalizes the chat into communism.

copper.hat

insecurity of some sort

Flows.

I dont agree with Bret about lots of things. But this sort of thing is awful jakubferencik.medium.com/…

leslie townes

17:29

there's something called the means of production. do you control it? what do you control? are you alienated? are you palliated by consumerism? this is a figment of your imagination.

i'm going to start a communism chat.

robjohn

If we took down all monuments to people who had some unpopular belief, we'd have no monuments

leslie townes

they'd still have the monument to me in the town square.

robjohn

I forgot about that one

copper.hat

expecting our heroes to be perfect is a recipe for failure...

leslie townes

i'm on a warhorse. i have a copy of "harmonic analysis on semigroups" in one hand and a warhammer in the other.

the inscription is in latin but basically says, as far as i understand it, that i was flawless and righteous in all things. which i am and was.

Thorgott

17:35

awe-inspiring

Ted Shifrin

awe shucks?

copper.hat

awe few?

sorry, awe some

leslie townes

we've declared a portion of long beach for the supreme soviet. all are welcome to join in this glorious revolution.

Rover

Hi guys, in This question, it's quite simple just put x=4+2-x and I am getting the integral as 1/2 , is it correct? since no option matches ...

Sorry to disturb

Ted Shifrin

You want to exploit symmetry about $x=3$. I don't ever want to read "put $x=6-x$"!!

leslie townes

17:41

yeah, what is this, a math chat? i'm uncertain as to that substitution.

i get 1, but i've been wrong before.

Rover

@TedShifrin ok right

copper.hat

i wonder if sloppy ever pays?

Rover

@leslietownes 2(Integral)=1 ?

Ted Shifrin

So, yes, add $\log(6-x)^2$ to the numerator and observe that that integral is the same. But you get $1/2$ of $2$, not $1$, so your answer is wrong.

copper.hat

because it certainly has a lot of evolutionary pressure behind it

Ted Shifrin

17:43

You should be very self-critical when you don't get any of the multiple choice options.

leslie townes

i like the contrast between "i don't want to ever read 'put x = 6 - x'' and 'i am uncertain as to that substitution.' there are tiny differences even when there are no substantive differences.

copper.hat

self doubt can be a good thing in maths

Rover

So, ans is 1/2 right!

Ted Shifrin

Well, I often get annoyed when people post that their textbook or professor has made a mistake, and almost always it's the student's mistake, not the book's or professor's. But we know counterexamples.

@Rover: Did you read anything I wrote?

throws daggers

Rover

@TedShifrin yes

Ted Shifrin

17:45

So what is the correct answer?

leslie townes

half of 2 isn't half of 1, but i was raised in a broken home by circus performers

Ted Shifrin

Even @leslie will back me to the Supreme Court on this one.

leslie townes

yes and i will even discount my normal fee to half of $0.

Ted Shifrin

Wow. I owe you half a tea.

Rover

@TedShifrin 1? But to be honest I didn't got how? see we got two integrals and I added then then I got 2(Integral)=1?

Ted Shifrin

17:49

Where did you get the 1 on the right?

Watching a viola recital from Houston — one of my talented math majors from my last years at UGA who also majored in violin/viola and is now doing a masters at Rice. Talented guy!!

Rover

I=$logx^2/(logx^2+log(6-x)^2 )and I= log(6-x)^2/(logx^2+log(6-x)^2)$

Ted Shifrin

@Rover: No, that's not how you get the right-hand side. Think.

Koro

The world is a better place with latex bookmark installed

Ted Shifrin

LOL @Koro

@Rover You've written $I$ as a function of $x$. Isn't it a number?

leslie townes

with the latex plugin installed, God's in his heaven and all is right with the world.

Ted Shifrin

17:57

Would that we could solve the world's problems with robjohn's plugin.

copper.hat

@Rover the question can be answered without doing an integral. (frankly i would struggle with the integral at the moment.)

Rover

@TedShifrin it is, I dropped limits to integral.

Ted Shifrin

Well, those are the crucial things, @Rover.

@copper He knows that.

Without the limits of integration we would not have symmetry to exploit.

Rover

Okay, so now integral is correct ?

Ted Shifrin

Huh?

Rover

18:01

Of RHS

Ted Shifrin

So what is the integral of the sum?

Rover

Ok right I should change limits of integration also

Ted Shifrin

That's how you argue that the second integral equals the first integral. You're missing the whole point.

copper.hat

the downside of multiple choice is that you can avoid doing the work or thinking that the author presumably intended.

Rover

Ok

Ted Shifrin

18:08

Well, when I wrote multiple choice competition exams (never for a real math course), I tried to include answers that corresponded to all the mistakes I could imagine being made.

copper.hat

the problem with being a good test taker is you struggle for the rest of your life (talking about my self, to avoid confusion)

Ted Shifrin

These people didn't include Rover's mistake.

copper.hat

i would just note that the integrand is in $(0,1)$ and eliminate the rest.

but i am pure lazy

leslie townes

i struggle for the rest of my life.

Ted Shifrin

@copper Then those are really crummy multiple choice answers, I agree.

copper.hat

18:13

even struggling is a struggle for me

Ted Shifrin

A well-constructed test would have several answers between $0$ and $2$.

copper.hat

well, i would have skipped computation, but if i had to evaluate in an exam (as opposed to picking a choice) i would probably have wasted time trying to solve directly first.

leslie townes

me too.

Ted Shifrin

The kids know to look for these symmetry tricks.

Symmetry tricks appear on every competition sort of exam up to and including Putnam.

copper.hat

makes sense for exam sort of stuff.

but i can easily stumble past the obvious.

leslie townes

18:16

i never heard about the putnam until the middle of my sophomore year of college. i think that's a failure of something somehow.

Ted Shifrin

One of my mantras for my multivariable course (particularly the integration half) was EXPLOIT SYMMETRY.

We all know to look for even/odd ...

copper.hat

i think that is a generally good rule in life

of course, all of the symmetric statues will be torn down in years to come precisely because symmetry was exploited.

Ted Shifrin

Well, yes, there is that.

copper.hat

i wonder if this site is the bane of modern educators?

Ted Shifrin

Because of symmetry?

leslie townes

18:28

there are no modern educators. only primitive educators

Ted Shifrin

I guess I'm going to assume Rover eventually figured out his gap.

copper.hat

often modern is primitive. my phone is just a black slate. my old phone had nice buttons to press.

robjohn

@TedShifrin I have a plugin for that, but it creates more problems than it solved.

Ted Shifrin

Gives you something to work on in retirement, @robjohn!

robjohn

something to look forward to... -_-

Ted Shifrin

18:40

It'd be a lot more worthwhile than the nothing we accomplish here :P

robjohn

I just have to figure out how to keep the sun from starting to burn helium and consuming the Earth...

Clarinetist

This is probably not appropriate for the website since I have no idea how to approach this problem, and thus can't show any appropriate work for it, but I'll try asking it here.

I have non-negative numbers $x_1, \dots, x_n$. These numbers are all percentages rounded to the nearest tenth of a percentage. Unfortunately, I don't have any of the numerators or denominators driving these percentages.

The true percentages, $t_1, \dots, t_n$, are unknown and should obviously sum up to $100$. But this is not the case for the numbers $x_1, \dots, x_n$, due to rounding error.

Since these are rounded to the nearest tenth, I propose that I should add uniform random variables $U_1, \dots, U_n$ drawn from a uniform distribution in the interval $(-0.5, 0.5)$.

This looks like it's an optimization problem in disguise, but any of you who know my views on optimization textbooks know that I don't know the subject very well.

Ted Shifrin

Isn't this really a statistics question (to do things meaningfully) rather than mathematics question?

Optimization how? What do you want to optimize?

Clarinetist

I think you might be right in both respects

Ted Shifrin

My view, knowing virtually no statistics, is that statisticians allegedly provide insight into why they use certain distributions, etc.

copper.hat

18:46

what are you trying to accomplish?

leslie townes

they do. sometimes they parrot their advisors, some of whom are parroting other people. but sometimes they know more than they let on.

Clarinetist

@copper.hat I'm just aiming to get a discrete probability distribution. That's all it is.

copper.hat

so you are trying to find some probability measure on $1,...,n$ that is 'closest' to your noisy observation?

Ted Shifrin

But you don't want to just add arbitrary things to make things add up to $1$. You could leave them all the same except fix the last one?

Clarinetist

@copper.hat Yes, that's basically it

Ted Shifrin

18:48

Closest in what sense?

$L^2$?

robjohn

@Clarinetist I don't see that adding a new random variable into the mix is any different than shifting and possibly scaling the data so that it sums to $1$

Clarinetist

Sure, it could be $L^2$. It doesn't matter as long as I get some sort of probability distribution.

copper.hat

sounds like a projection of sorts

Clarinetist

You would think that people have run into this problem before

Ted Shifrin

Presumably my suggestion is bad. Fix just the last one. It seems very not least-squares.

copper.hat

18:49

the space of distributions is a compact convex set, so you could try minimising the Euclidean distant as a first shot

that is just projection

Clarinetist

If I'm understanding what you're saying, this sounds like a Lagrange multiplier problem

copper.hat

not even, basically projecting onto a simplex.

Ted Shifrin

He's just doing normal equations projection.

copper.hat

i mean, it is Lagrange in some way.

Ted Shifrin

You want to project your given data set onto the affine linear subspace $\sum x_i = 1$.

Yes, of course, orthogonal projection is a Lagrange multipliers problem. I even work it out that way in my multivariable book as a second approach.

Clarinetist

18:54

Gosh, I wish that my linear algebra course actually taught projections. I got a crash course in some of that theory in my early grad-school stats classes.

Time to get that book out

leslie townes

malpractice. check the statute of limitations and sue.

copper.hat

what is $n$ in your problem?

Clarinetist

@copper.hat $n$ is about 800

copper.hat

just use a qp solver.

Clarinetist

... I hope I don't have to think about computational complexity

copper.hat

18:57

if you are experimenting.

Clarinetist

Great, thanks

Ted Shifrin

@Clarinet: I do least squares (projections) both with normal equations and with Lagrange multipliers. If you're interested.

copper.hat

there are reasonably efficient solvers, especially for simplices, but if you are just trying use a qp.

Clarinetist

@TedShifrin Your book is first on my list after this week is done, since I'll no longer be teaching or trying to pursue the PhD. My multivariate calculus foundation is much weaker than it should be.

copper.hat

there is an $O(n)$ solver for simplex projection

leslie townes

18:58

i used LAPACK. written in fortran 90, so you know it's good.

copper.hat

this is stuff from my past life.

Clarinetist

When I took Calc. III, we learned from Stewart and used Maple for everything. I don't remember much from that class. I didn't truly understand double integration or partial differentiation until probability.

copper.hat

i long for it, but i needed to pay the rent.

leslie townes

actually it looks like the version i would have used was written in fortran 77.

Clarinetist

To make matters worse, the analysis in $\mathbb{R}^n$ course I took was poorly taught... all I can remember from that class is spending a ton of time talking about Jordan content and rectangles

Ted Shifrin

19:00

For this look specifically in chapter 5, section 5, @Clarinet.

leslie townes

there is a lot that can be said but probably does not need to be said about higher-dimensional integration without measure theory. jordan content indeed.

copper.hat

@Clarinetist few people have perfect knowledge :-)

i think it is better to focus on your interest and backfill as needed. learning without motivation is...

leslie townes

another waste of time, extreme generalization of the fundamental theorem of calculus. when being taught that, i remember suspecting that even analysts don't care about this and the instructor was just going there because it was a theorem that could be generalized.

copper.hat

not motivating to put it politely.

Clarinetist

Yeah, I have very different motivation and a much more precise focus than I did nearly 10 years ago, that's for sure

copper.hat

19:03

there are only so many hours in the day.

and you cannot revisit yesterday.

excuse my patronising. i tell myself this everyday :-)

leslie townes

my cat is so upset that i finished my sandwich. i didn't leave her anything.

Ted Shifrin

You are always selfish, leslie.

leslie townes

i told her that it's dogs, not cats, who beg for table scraps.

Clarinetist

It is going to be different, to say the least, to adjust to learning without being enrolled in a class, but I'm looking forward to it

copper.hat

the cat is just pretending to be upset in some sort of Chomskyish experiment.

@Clarinetist it works for some, not for others. personally i need company.

Ted Shifrin

19:05

I talk about volume 0 only to prove that continuous functions on regions with volume 0 frontier (boundary) will be integrable. This isn't a huge point, but is necessary for logical completeness.

Some cats are more canine in personality. Most of mine were.

Clarinetist

The three subjects I'd like to at least have a basic foundation on before I do any further study toward my main interests are multivariate calc, optimization, and functional analysis.

Ted Shifrin

Leslie will tutor you in functional analysis.

leslie townes

olivia greets us lavishly when we come home and begs for table scraps. and meows if she's shut out of a room where people are. i've tried telling her that cats are supposed to be aloof and not play these kinds of games.

i can recommend books at a minimum.

Ted Shifrin

Yes, she probably likes snuggling, too.

leslie townes

yes, particularly with my wife. she's really a pest.

Ted Shifrin

19:07

Questions like this distress me.

leslie townes

oh for heaven's sake.

Ted Shifrin

She would snuggle your daughter if she didn't try to molest her so.

copper.hat

just the typography is enough for me.

leslie townes

this is why it's good that i don't run the world. i would jail people for asking questions like that.

copper.hat

to be fair, it can be a bit daunting unless you are used to the tricks. like cleaning a fish.

Ted Shifrin

19:09

Bold facing the $n$ is in poor taste.

copper.hat

or dispatching a chicken.

Ted Shifrin

No trick. Write down exactly what you need to show. I added a comment.

leslie townes

what psychopath writes the scalar to the right of the matrix.

Clarinetist

@leslietownes I'm planning on using Sasane's A Friendly Approach to Functional Analysis and Kreysig's Intro text as my main texts, with Conway, and Stein and Shakarchi to supplement. Thoughts?

copper.hat

hey, at least she is trying to format.

Ted Shifrin

19:09

Linear algebra is good for one-line proofs like this. But you have to read and write down definitions.

copper.hat

i'm an underdog person

leslie townes

clarinetist it is not orthodoxy to recommend it but i think peter lax's book on functional analysis, published approximately 20 years ago, is one of the best things ever written.

those books are good too.

my gripe with lax is that it is expensive.

Ted Shifrin

I used to recommend Riesz-Nagy to beginners. I no longer own any of these books.

leslie townes

riesz-nagy is my second favorite. and it's cheap.

Clarinetist

My linear algebra professor complained to me, while I was a student in her class, that students were generally not doing very well.

The only reason linear algebra made any sense to me whatsoever was because I typed up all of my notes and reworked all of the proofs on my own. That takes time.

leslie townes

19:12

a number of enterprising pirates appear to have scanned dr. lax's book. i guess it is expensive no longer.

robjohn

Arrgh!

Clarinetist

I keep forgetting to buy Riesz-Nagy. Going to put that on my Amazon list.

leslie townes

i remember when i bought it, i had some discount because of something else i'd bought. it appeared when i bought the book but had disappeared by the time it shipped. i emailed amazon asking what the hell with the two emails as attachments. the person gave me a nonanswer. i still shop on amazon. nobody learned anything from this.

Ted Shifrin

Interestingly, my multivariable math students (who were smarter bears than the typical students) found the linear algebra easy and straightforward (by comparison with the hard analysis, of course), whereas when I taught plain linear algebra, most of the students struggled.

copper.hat

One I liked was Kolmogorov & Fomin, "Introductory Real Analysis", not too formal.

Ted Shifrin

19:14

Russians are generally less formal, which is a strong point. Same with Shilov.

copper.hat

just a caveat, some older books assume Hilbert spaces are separable (so there is really just one).

but it appealed to the engineer in me.

leslie townes

there are no non separable hilbert spaces.

i mean OK there are but don't bring them up around polite company.

Ted Shifrin

There must be one somewhere. Let me look under the rug.

Clarinetist

Linear algebra was the difficult class among the actuarial science students.

For the math students, it was real analysis.

copper.hat

is aoc a politician or a religion?

i think many of these classes are difficult because one is learning stuff without a meaningful application or notion.

leslie townes

19:16

i got in a very unproductive email interchange once with someone who had 'proved' the existence of something. they were working on a decidedly non separable hilbert space with results that were known only to hold in separable hilbert spaces. he ended up publishing it but not in the journal i was reviewing for.

my thesis does contain a line, hilbert spaces are assumed to be separable unless otherwise noted, and it does not otherwise note any exceptions.

i'm happy to stay in my happy sandbox.

copper.hat

life is insufferably separable.

leslie townes

i knew him personally but was also anonymously reviewing his paper. it was confusing to wear two hats at once.

i wonder who he's bothering now.

Ted Shifrin

I had to review submissions a few times of someone I knew very well (and who, sadly, wrote very badly). Ugh.

Thanks to you guys, I'm trying to post my $\epsilon$-revised version of the diff geo notes on the AMS Open Notes website. My password no longer gets me into the site. I hate having to bother website administrators, but ...

leslie townes

it's "StopTheStealMAGA2021"

Ted Shifrin

BTW, @copper, thanks for your clear, incisive view of anakhro's question about repeatedly iterating flows.

Yeah, that would be a good password for me, leslie.

I had a website bookmarked at AMS that no longer works. So I think they messed it up in the 3 years since I posted there.

copper.hat

19:32

i've forgotten what it was about, or maybe you are pulling my leg

Ted Shifrin

No, no, not at all. Remember he was "flowing" by $f$, then by $g$, then by $f$, etc. ad nauseam.

leslie townes

i remember that. vaguely.

Ted Shifrin

Damn, I'm the oldest here and my memory is not so bad.

Wait til dementia sets in.

leslie townes

if i start popping up here and repeating myself about how bad geometry is, we'll all know it's happened.

Ted Shifrin

You already do that plenty.

copper.hat

19:36

i need a memory. i had to chase back through the transcript...

leslie townes

my short term memory is genuinely terrible. i blame the daughter. i also blame geometry.

robjohn

@leslietownes My wife and I could tell that having a small child lowered the IQ by at least 20 points.

Ted Shifrin

Well, @copper, I meant my thanks sincerely, but in the future I will skip it :P

copper.hat

@TedShifrin oh, i appreciate it very much.

robjohn

@copper.hat who needs a memory if we have a transcript?

copper.hat

19:39

:-)

robjohn

Now if I can only find the transcript from the mid 80s... my wife and I have different clear recollections about things that happened.

Ted Shifrin

Oy vey.

robjohn

Nothing all that important, so we can pretty much ignore it

but still, there may come a time.

leslie townes

i do like my daughter. she's very much me. she tells incoherent stories about animals as though they are breaking news and constantly changes the subject. last night she was on about the juncos, which are songbirds that live in a bush outside our house.

copper.hat

i used to keep a diary and found that my memory of events was quite different to what was recorded in terms of order.

verba volant, scripta manent

leslie townes

19:46

she told me the juncos had been in the house, and i said 'are you making that up?' and she said 'yes' with no shame and then kept on going about the juncos in the house.

she will be an effective litigator.

Karim Mansour

@Thorgott Do you know if integration can be defined categorically I believe that Lebesgue ntegration have categorification associated to it.

Ted Shifrin

She has your gift of garbage gab, @leslie. Your wife will kick the both of you out.

Karim Mansour

Hi Ted

Ted Shifrin

Hi Karim

leslie townes

karim i do not know if this is relevant to your interest but it is possible to develop almost all of integration, down to the measure theoretical nonsense, in terms of linear functionals on function spaces. which seems the kind of abstract stuff you might be going for.

i don't think riesz and nagy do it this way although they certainly could have and would have known about it.

Karim Mansour

19:49

oh that is cool

Do you have reference for this stuff

leslie townes

maybe it's hard to get the completion of a measure space out of it, now that i think of it. if you're tossing in sets of measure zero that don't affect integration you might actually need measure theory.

here are some notes on measure and integration in locally compact spaces. math.berkeley.edu/~arveson/Dvi/rieszMarkov.pdf

Karim Mansour

It is not related to any of my thesis but it is just out of curiosity as I am studying algebraic geometry from Ravi Vakil so redoing category theory.

leslie townes

it largely but not entirely adopts that view.

Karim Mansour

I see

copper.hat

i think rudin develops it that way for some limited context in functional analysis?

leslie townes

19:51

i've got some good notes somewhere.

rudin may have done. conway i think does.

Ted Shifrin

The Daniell integral was the approach of Segal & Kunze. Although Segal was the worst lecturer I ever had, I sort of liked that approach.

leslie townes

in my thesis i got considerable 'pushback' from writing a linear functional as $\int f(x) \, d\mu(x)$ when $\mu$ was not a measure and the functional was not integration. i explained, i need to be able to talk about the variable and change it, and the integration notation is familiar to the audience.

the member of my committee said, "OK," in the back of his mind thinking "nobody will ever read this anyway."

Karim Mansour

LOL

Thorgott

@KarimMansour arxiv.org/pdf/2011.00412.pdf

leslie townes

segal is my mathematical great-grandfather. i should check that out. i never familiarized myself with the daniell integral.

Karim Mansour

19:56

Thanks @Thorgott

Ted Shifrin

It avoids all the horrid measure theory.

leslie townes

measure theory is the junkyard of mathematics. right next door to geometry.

Ted Shifrin

Nowhere close. Good thing it's lunch time for this bonzo. Bubye.

leslie townes

enjoy your lunch.

i think i've met tom leinster.

Karim Mansour

Enjoy your lunch Ted

leslie townes

19:58

such a small world.

there's only about ten people, and you just go back and forth between them until someone files for divorce and then it's nine people.

Karim Mansour

Cool I would love to have chat with him

I watched this lecture before youtube.com/…

it is a cool one

Thorgott

Leinster has some cool stuff

one day I will find the time to read his paper on self-similarity

copper.hat

you've being saying that since inception

leslie townes

i'll read a paper about the paper about a paper on self-similarity

copper.hat

hopefully there is a contraction in there somewhere

leslie townes

20:21

i'm on an endless call. endless. could have been two emails.

copper.hat

still trying to figure out why it cost \$25 to wire $1.4k to the uk. really, in this day & age

leslie townes

well, at least 25 pigeons were involved, each of them needs $1 in birdseed.

it makes sense to me.

copper.hat

:-). maybe i can get a 10 pack or something. they used to waive these sorts of fees. what is the world coming to?

leslie townes

20:55

pigeons gotta eat, man. i dunno what to tell you.

copper.hat

the whole fbar/fatca thing really screwed up banking in ireland/uk.

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$Mathematics$ Mathematics