Mathematics - 2021-03-14 (page 2 of 3)

leslie townes

5:00 AM

not if you're a double ivy and keep your dog off your webpage.

no cats either

copper.hat

it really is a bit scary how some of these folks think.

i mean, its fun is some sort of way, but i'm thinking let me out of here.

leslie townes

you can also incorporate in a jurisdiction like nevada where it's basically impossible for directors and officers to be sued. but then the difficulty is finding investors who might later be in the position of suing you.

copper.hat

i like california because it is good for small holders.

later you should switch to delaware :-).

leslie townes

yeah, california shareholder law is about as shareholder friendly as it gets. i've discouraged friends from incorporating here for that reason. and i trust them.

copper.hat

i have learned not to trust anyone but myself. a sad & painful learning process.

leslie townes

5:02 AM

"please, if they find a page where it says you got a BA at Harvard instead of an AB at Harvard, which is what you got, you're dead in the water"

copper.hat

lol here

my mom used to describe such folks as the cream of society, rich & thick.

leslie townes

my mom said, if you want to know what god thinks of money, look at who he gives it to. i think that's a quote from somebody.

i met a lot of rich twits in law school. someday i hope to work for them.

until then i'll be doing calculus homework on math stackexchange until someone sends me my damn draft of my brief back so i can keep editing and not spend the rest of weekend in suspense.

copper.hat

i'll spend the rest of my life enabling people in large companies to efficiently use their hardware emulators.

leslie townes

i'm also selling NFTs of my daughter's finger paintings. and, of course, onlyfans.

you have to diversify your income streams.

copper.hat

:-)

i just heard about nfts for the first time a few days ago.

leslie townes

5:09 AM

i'm not sure i understand it. i mean i generally understand the concept, but it seems specific to a particular chain of blocks, or whatever they call it. like, if i started LeslieBlock tomorrow, there's no mechanism by which someone can't buy an NFT for the exact same thing on my chain, that's already in someone else's chain somewhere.

so why don't i just go down to my local tshirt shop, and print out whatever image i want on the tshirt, because the owner doesn't care. then i own a non-fungible copy of the image, from that tshirt shop's chain.

copper.hat

people over sell all the time.

leslie townes

i dunno. the NFT wikipedia page is funny. like a lot of blockchain stuff, half of it is nowhere unique to NFTs or even anything digital. it's just presented as if you need NFTs to do it.

copper.hat

it just provides some confidence that your file is really what it was in the context of that particular blockchain.

modern wax & seal.

leslie townes

here's a line from the NFT wiki page: Although an artist can sell an NFT representing a work, the artist can still retain the copyright to the work and create more NFTs of the same work.

copper.hat

=bs imo

leslie townes

5:13 AM

also true: Although an artist can sell a work, the artist can still retain the copyright to the work and create more [copies] of the same work. [indeed, this is the default in every civilized jurisdiction since the dawn of time]

does anyone think that if i buy a copy of star wars i own the copyright in star wars and can begin selling DVDs of star wars

i bought microsoft windows, now i own the copyright. sorry everybody, pay me

copper.hat

difference between picasso making a copy and my operating system making a copy.

leslie townes

i own the copyright in jimi hendrix's entire discography because he wasn't alive to do NFTs of it

copper.hat

ownership is a strange thing...

leslie townes

'theft' of IP is interesting. mostly people talk about infringement, but i mean theft of ownership rights. i've seen cases where people fake loans to other companies, pledge the IP they want to give away as collateral, then let their conspirator foreclose on the loan. conspirator obtains title to the IP. statute of limitations for fraud passes. conspirator is now the legal owner of the IP and can sue the people who used to own it.

it's insane.

copper.hat

wow. no wonder i have trust issues.

leslie townes

5:18 AM

patent rights last longer than statutes of limitations for almost anything you'd want to do with property other than real estate. it's a bad incentive.

copper.hat

i agree. in their current form they have outlived their intent.

leslie townes

never trust anybody, never help anybody

i'm just reciting parts of the attorney oath

copper.hat

hypocritic oath?

my mom did take the hippocratic oath.

here's how to do legal advertising: phoonglaw.com

leslie townes

even the original US patent term was pretty long, 14 years. not too different from now. the premise was pre-industrial. from english cases, the idea was that it took a master 7 years to teach an apprentice, and you wanted to give him time to teach two.

to, you know, invent a new way of stitching body bags or whatever it was industry amounted to in 1790

copper.hat

good idea, bad implementation

leslie townes

5:22 AM

GOT-PAIN, that's a good number.

copper.hat

eye catching in many ways

leslie townes

a lot of websites also do that. you should see my bus ad.

copper.hat

:-).

i usually see her ad on one of my weekend rides.

leslie townes

i once did some work for two clients who had an 800 number like that. they are in prison now. not because of what i did, but because of what they did. we were handling, like, advertising stuff.

copper.hat

a lot of entrepreneurs live on the topological boundary of the law.

leslie townes

5:24 AM

it's one of those cantor boundaries where if you perturb just a little, you're fine, or not.

you can deviate in either direction and still be OK or not OK.

the roof fell in when i overheard a call "what? the FBI is there? at your house?" "they're taking computers?"

...

they didn't pay our bill either. if you can imagine that

copper.hat

i did have one lawyer friend in foster city who exchanged legal favours for bottles of wine.

i like the idea of doing business after a bottle of wine.

leslie townes

one time i was in delaware for a trial, cocounsel with this guy who was renowned for bragging about his wine collection and being really tasteless about it after a big win. like passing it around and then announcing how much the bottle cost, that level of tasteless.

copper.hat

people are not so good at lying after a few drinks.

i have little time for that sort of braggadocio

leslie townes

we went to trial and we lost. at the restaurant afterward, his paralegal brought, i'm not kidding, several bottles from a wilmington liquor store that we had walked by on our way to the restaurant.

copper.hat

that's funny.

leslie townes

5:29 AM

we got a lot of it back on appeal, but not after i had two glasses of chateau de wilmington

copper.hat

i haven't had a red in a month or two.

leslie townes

it was like diluted night train, which is weird, because night train is like concentrated alcohol mixed with red food coloring.

copper.hat

thankfully i haven't had a bad wine in a few years.

leslie townes

maybe wilmington red is like the yin/yang symbol. two forces, dilution and concentrated alcohol, together in balance.

copper.hat

just the name wilmington red puts shivers in me

leslie townes

5:32 AM

if you've ever been to wilmington, it's insane. there are maybe two blocks of 'generic metro' and then it's a post-apocalyptic wasteland. you get the impression that economic development has not existed since the 1970s.

it's a lot like west oakland, if you know it.

i think they realized they could run their whole 'incorporation + courtroom' hustle with two blocks of courthouses, two hotels, and a mail boxes etc.

and they just let everything else go to waste.

i just googled and learned that mail boxes etc became "the ups store" in 2012. please update the above comment to reflect that.

they let you do mailboxes there, too.

copper.hat

yep, i cycle through the oakland docks fairly frequently

city planning is often lacking...

leslie townes

they sliced up a bunch of neighborhoods with the interstates and state highways.

copper.hat

happens everywhere.

progress

leslie townes

i used to live by the claremont avenue DMV. it was an italian neighborhood way back when, then they put highway 24 through it, separating streets, etc. my barber used to complain about it. i was like "yeah, what are you gonna do." my apartment was right under the highway.

copper.hat

just need more nuclear to complete the picture,

my kids (& wife) love fentons

leslie townes

5:38 AM

it's in at least one pixar movie. i think, up? and maybe one more.

a guy in my building used to work for pixar

copper.hat

pixar really revitalized emeryville

used to be hooker haven

leslie townes

when i first went to college i went to look for apartments, and i went to look at one in emeryville, and it was kind of rough looking, and while i was touring an apartment, a random dog, owned by nobody, wandered into the apartment and took a huge piss on the floor. and then ran away.

that's pre-pixar-gentrification emeryville.

it was a hardwood floor. easy cleanup

copper.hat

i used to rollerblade down spa when i lived in berkeley, had some entertaining convos with a number of the spa/adeline ladies.

leslie townes

i wonder if any of that exists anymore. my last trip to berkeley was about a year and two weeks ago. right before everything shut down.

i recognized very little. lots of new development near campus. even the stuff by the DMV looked upgraded. i blame computers.

copper.hat

it is completely gentrified

emeryville that is. the claremont area is post gentrified...

was up in sibley hiking (or what passes for me hiking now) a few days ago. lovely area.

i loved tech & the internet when it was in the hands of a few. selfish of me.

leslie townes

5:49 AM

i thought the first dotcom boom was stupid, but at least those people knew how to code and weren't 1000% focused on putting eyeballs on advertising

copper.hat

we are in dotcom boom 2.0 now. spacs & crypto

leslie townes

about half of the people i knew in law school had multiple friends who had relocated to the bay area after doing non-technical degrees and then being hired by facebook because it was apparently operated as a jobs program for the ivy league

and i thought, i bet one of them is living in my old apartment

nerd rage

my apartment sucked, by the way. you don't know what you'd have to do to make me jealous of someone going there and appropriating that experience

copper.hat

silicon valley 2.0 is a far cry from 'my' silicon valley.

i have managed to stay one step ahead of wealth all my life.

i didn't go to google because their early servers were held together by duct tape (to be fair, there were other reasons like my own company). didn't do facebook because they wanted a skype interview instead of an in person meeting.

leslie townes

i knew a very early google employee. he stayed there, but not for very long. in his telling, the tidal wave crashed where it stopped being about anything other than selling ads. much more quickly than the outside world would have appreciated. and the warehouses full of people cold-calling google adwords was not far behind

i am not sure that they do that anymore. but for a while ,that was a part of it

i wouldn't do facebook because the ceo looks like a turtle pried out of his shell. i'm superficial like that

copper.hat

6:47 AM

i started with cadence when joe costello was ceo. i am a cynic, but it really was a great place to work, folks like jim solomon, james spoto, etc, created a great environment, long predating the google/apple cafes, etc. money was nothing like it is nowadays, but for sheer excitement & getting stuff done, second to none. cadence is still making money from the analog simulation environment i wrote (much evolved since the early days, of course).

however i would gladly trade the satisfaction of knowing that for more $$$.

user 85795

7:48 AM

“British Double Summer Time”

There have been periods in UK history where DST was 2 hours ahead of standard time. This is known as “British Double Summer Time” (BDST), “Double Summer Time,” or “Double British Summer Time.”

During World War II the UK went on an extended DST period from February 25, 1940 to October 7, 1945, effectively adding 1 hour to the time zone (UTC+1). During the DST period in the summer, another hour was added to the time zone (UTC+2).

There was another period of BDST in 1947, which was brought on by severe fuel shortages in the country.

barista

0

Q: Exercise 11.17 on John Lee's Introduction to smooth manifolds [Proof verification]

Let $f(x,y) = x^2$ on $\Bbb R^2$ and let $X$ be the vector field $X = \text{grad}\ f = 2x\frac{\partial}{\partial x}$. Compute the coordinate expression for $X$ in polar coordinates (on some open subset on which they are defined) and show that it is not equal to $\frac{\partial f}{\partial r}\fr...

Is my proof correct? I think it's easy to check but no one is answering

copper.hat

you're kidding me. you expect someone to answer you in 40 mins?

barista

8:34 AM

sorry if that bothers you

Sarabsri mt

9:39 AM

0

Q: Find the value of the sum of only 3 digit numbers such that dividing by it leaves REM = 11?

I had asked a Q similar to this. Find the value of this 3 digit number such that dividing by it leaves REM = 11 But I want to know also if instead we take sum of all those numbers. Is there a way to solve this too in a similar way to that Q? The problem happening is how to put limits in the sum s...

linear-algebra algebra-precalculus quadratics

maths student

11:26 AM

0

Q: Differntiation in multivarIable Calculus

We say that $f$ is differentiable at $x$ if the following are satisfied: (i) The partial derivatives $D_{1} f(x), D_{2} f(x), \cdots, D_{n} f(x)$ exist. (ii) There exist $r>0,$ and a real valued function $g$ on $\{\|z\|<r\}$ such $$ \begin{array}{l} \text { that } \lim _{\|z\| \rightarrow 0} g(z)...

multivariable-calculus differential-topology partial-derivative

Jakobian

Can I get a hint?

Leaky Nun

@Jakobian the type of u is dense in the type of g

Jakobian

Yes, I know

Leaky Nun

(the type of X = the set where X belongs to)

so you can "take u = g"

Jakobian

Hmm. I don't think so

Leaky Nun

11:39 AM

or rather, -g

Jakobian

u are dense in L^1, I know that

But the issue here is that if u_n goes to u in L^1, then multiplying by g, does gu_n go to gu?

If mu(g<0)>0, I can take compact set K of positive measure on which g<0

I was thinking of, say, setting u = -g1_K

But then, I get this issue

And moreover g is bounded on K

maths student

12:25 PM

It is true that if partial derivative exist in all direction then function is differentiable?

Jakobian

Hmm. I think it's not true

user2103480

@Jakobian Do you have lebesgue's differentiation theorem for radon measures

You get that almost everywhere the integration over a ball, divided by its volume, has as limit the function's value

Sounds reasonable to get nonnegativity of integration over a ball using the assumption

But it's hard to actually find a reference for this result which sounds true
there's
https://math.stackexchange.com/questions/730242/differentiation-of-radon-measures?noredirect=1&lq=1
without an answer

and https://math.stackexchange.com/questions/137051/the-lebesgue-differentiation-theorem-for-radon-measures

with a useless answer

Jakobian

12:46 PM

I don't have that theorem

I have density of continuous functions with compact support for Radon measures

In L^p

user2103480

Okay, have you tried anything like this:

Assume there's a set of positive measure where the function is less than 0

Somehow cut this down to a set of positive measure contained in a compact set

(Should be possible)

Thorgott

approximating step functions by C_c^0 functions should yield that the integral over any measurable set is >=0, which will imply that the function is a.e. >=0

user2103480

Then find a closed subset of your measurable set with positive measure

@Thorgott also, this, yuh. I woulda just done this with extra steps but yeah ooff this is it

Thorgott

ok, glad I'm not going insane

though iirc the fact that indicator functions are approximable in C_c^0 is somewhat non-trivial

user2103480

I planned to approximate the function only on a compact set and this would probably make it easier if one doesn't have the full L^p result

Thorgott

12:57 PM

or, well, not non-trivial, but tedious

yeah, working with compacta should suffice too

there's a step via exhaustion by compacta one has to do at some point, but this just shifts the point where that step takes place

Jakobian

1:10 PM

@user2103480 like I said, I can find compact K of positive measure on which M<g<r<0 for some real M, r

So I had the same idea but I'm missing something

user2103480

The more important aspect is the approximation

So what @Thorgott uses is what we're trying to prove - that if integrating over any measurable set yields a nonnegative number, then the whole thing must be >= 0 a.e.

Thorgott

that part is obvious

integral of something <0 over a set with positive measure is <0

user2103480

Ah

And we take {f<0} and the integral over that is >= 0

so that set must have measure 0

But something's not clicking with this exercise. Something's bugging me. Maybe I'm just stupid

Thorgott

1:27 PM

Proof: take A_n={f<-1/n}, then 0\le\int_{A_n}f\le-\mu(A_n)/n, hence \mu(A_n)=0 for all n and so \mu({f<0})=\mu(\bigcup_nA_n)=0

Riya Sharma

Can someone help me to understand the lim of augmented quandles as given in Joyce thesis?

Rover

Hi All

user2103480

yeah I get that this holds that is clear, but what the crux about this exercise is is that if we want a contradiction, we should first restrict to $A = \{g < 0\} \cap K$ for some compact set $K$ since the function is only locally integrable, then $\int_A g \, \mathrm d \mu < 0$.

If we knew that the integrals of step functions approximating this must be > 0, then the contradiction directly follows, but we don't have that. So I would next want to approximate the indicator function of $A$ by functions with compact support

Then for these continuous functions with compact support s.t. $u_n \overset{L^1}{\rightarrow} 1_A$, if $\int u_n g \, \mathrm d \mu \rightarrow \int 1_A g \, \mathrm d \mu$, we're done

But I don't see this last step

Thorgott

yeah, I agree, we have to intersect with increasing balls, but that's a mere technicality

continuous with compact support is L^1-dense

so I don't think there's an issue

Using the distance function, you can create a sequence of compactly supported continuous function converging in L^1 to the indicator of a ball manually and then you can approximate an arbitrary measurable set by balls by virtue of regularity

user2103480

1:44 PM

@Thorgott yeah that makes sense, I thought about doing the distance function trick as well

But meh I'mma stop thinking about this

since it boils down to actually getting one's hands dirty with the approximating sequences

user2103480

1:58 PM

But I found a resource for the differentiation theorem: Corollary 3.30 of these lecture notes

https://www.ime.usp.br/~glaucio/mat6704/textos/GMTLecureNotes.pdf

leslie townes

2:50 PM

bookmarking that. i like the level of generality.

Leaky Nun

3:29 PM

where's the happy pi day message

Astyx

on the star board now

leslie townes

pi day was march 14, 1592. you missed it

9

you could also have celebrated it in 1593 if you endorse rounding, which i don't. truncation.

the people who endorsed rounding ("roundheads") ended up fighting against those who supported truncation ("royalists" or "cavaliers") shortly afterward. it's a shame we don't know more about european history.

love_sodam

0

Q: If $\phi:X'\to X$ is a homotopy equivalence then an induced map $C_{f\circ\phi}\to C_f$ is a homotopy equivalence

If $\phi:X'\to X$ and $f:X\to Y$ are maps, define an induced map $F:C_{f\circ\phi}\to C_f$. If $\phi$ is a homotopy equivalence then show that $F$ is a homotopy equivalence. Abusing the notation, I first tried to show $F:M_{f\circ\phi}\to M_f$ is a homotopy equivalence. My attempt is basically ...

algebraic-topology homotopy-theory

Can anybody help this? Long post but easy to read

leslie townes

i agree that it is a well phrased question. bonus points for identifying the textbook, which nobody ever does

i do not have the tools to provide an answer. but thank you for the well phrased question.

love_sodam

Thank you :)

leslie townes

3:40 PM

if you have a time machine, i may have been able to answer this question in 2006. set coordinates to uc berkeley.

Simone

4:14 PM

Hello

Shaun

Hi, I'd like some feedback on an answer of mine, please; somebody voted to delete it.

in Constructive Feedback, 1 min ago, by Shaun

0

A: Question on the order of an element in a group

No. Consider the Klein four group. It has four elements and yet no element of order four.

leslie townes

i don't understand that. your example is a good one, indeed, the smallest and arguably simplest one. i mean, generally the conjecture would imply that all groups are cyclic, as another answerer points out. but that's not any reason to downvote something that directly and simply answers the question.

people downvote for all sorts of reasons, probably due to past trauma. i prefer therapy to downvoting. mostly in the form of taking naps with my cat.

Simone

Some downvote for ego reasons, some because the question is too easy and think you're a moron for asking it.

leslie townes

i've had people downvote my answers because i addressed the question as simply as possible and did not just dump everything i knew about the subject into an answer. shame on me, i guess.

the attitude i take toward everything is that none of this exists. you're just my computer faking me out and making me think that there are other people out there. you are my CPU, with a sense of humor.

anakhro

@Shaun Might have been in error or something. I don't see any immediate issue with it. Though I would encourage people to avoid just giving away answers but to be pedagogical about it and try to lead the asker to the conclusion themselves.

Simone

4:24 PM

"this guy has only 500 points, he can't possibly have given the right answer that I couldn't give".

https://math.stackexchange.com/questions/4056341/motivation-for-proof-of-phi-to-psi-to-phi-to-phi/4056354#4056354

leslie townes

there's also that. some people are sensitive to the issue of providing answers to questions that don't show any work, and might just be paste-ins from a homework assignment. i understand that view but don't see how it mandates downvoting.

the question is almost certainly a duplicate of another question on math.SE. a sufficiently advanced AI would have closed it before any answers. this would be the theoretically correct alternative approach for people who feel they are obligated to downvote answers to homework problems.

Shaun

Thank you, @anakhro :)

Simone

One of you guys is browsing through my answers and giving me upvotes haha, thank you :D

leslie townes

i'm not doing it randomly. all of the answers i don't upvote are horrible answers that you should be ashamed of.

Simone

lmao

leslie townes

4:37 PM

maybe i should downvote them. that would make me feel big.

Simone

ok XD

leslie townes

i've also stopped doing it. the two or three is all you're getting. i have bigger fish to fry

Simone

no you must upvote this as well because I'm right:
https://math.stackexchange.com/questions/4053508/proving-that-fx-frac1x-is-not-integrable-on-0-1/4053546#4053546

leslie townes

my daughter is a little over two years old. yesterday she began talking about how she was thirsty. then she began crying. then she took an imaginary drink from a bucket. then she said "i'm crying because i'm thirsty, like this:" [very realistic crying followed by an immediate stop]. "can you cry too, daddy?"

now i know she can turn it on and off at will. this makes her dangerous.

Simone

she made a strategic error

leslie townes

4:41 PM

yes. she's the james bond villain who explains everything she just did, because she's so proud of it she doesn't realize how dumb it is to do that.

Simone

you should start worrying when she brings home The Prince from the school library

leslie townes

now i'm always going to be asking if the crying is real.

Simone

or The Art of War

leslie townes

it's weird when you first start to notice deliberate emotional manipulation. thankfully you can usually redirect to other things, at 2.4 years old. "here's your stuffed bunny!"

Simone

omg XD

leslie townes

4:44 PM

she loves animals. she can identify dozens of birds. i recommend that everybody who doesn't think it will be a hassle, and can do it, to have children.

she's also very expensive, but we won't get into that.

my wife was thinking about another one and i was like "we're barely affording this one." it's dollars and cents to me. but very funny to have a miniature version of yourself running around the house. she looks exactly like me, but with longer hair (due to corona she has never had a haircut)

are any people outside of the aged and job-vulnerable and otherwise-illness-vulnerable getting vaccines yet? my parents have had them due to age, and my wife due to job. i'm waiting.

Edward Evans

I think I'm supposed to be on some kind of priority list for vaccination but I haven't checked

Simone

Here Europe made a mess of vaccines rollout, I think I'll have to skip this next summer too

This situation made me waste 2 years of my life

anakhro

Make the best of it, don't waste it.

Thorgott

@Edward why

Edward Evans

"Personen mit einer Demenz oder mit einer geistigen Behinderung oder mit schwerer psychiatrischer Erkrankung (bipolare Störung, Schizophrenie, schwere Depression)"

Gruppe 2 - Hohe Priorität

leslie townes

4:50 PM

i can't imagine just coming out of school, or switching jobs, or retiring, any time between late 2019 and now. it seems like a nightmare situation.

i have undiagnosed depression. maybe i should get a diagnosis and jump the line, but that would require me to go to a hospital and thus expose me to the coronavirus.

anakhro

Hospitals are pretty well-controlled in my experience.

Simone

@anakhro how? I'm single and we can't date: can't go to the club, can't go to a bar, gyms are closed, parks are closed, curfew after 10

robjohn

@EdwardEvans If you are staff or faculty at a university, you are eligible. I am getting round one on Tuesday.

leslie townes

i'll continue to take my unresolved conflicts out on my immediate family, thank you.

Simone

It sounds petty but It's really messing with me

anakhro

4:52 PM

@Simone Thank goodness there is more to life than dating/clubbing/gyms.

leslie townes

anakhro, no there isn't.

Edward Evans

I'm just a bipolar master student, apparently that puts me at higher risk of getting Covid

Simone

@anakhro sorry, I'd like to have a girlfriend

Edward Evans

but I don't know what it means to be in this "high priority" list, because I haven't really read up about it

Simone

and I'm feeling lonely

anakhro

4:54 PM

@Simone getting a girlfriend doesn't solve loneliness. You should prioritize friends and family before a girlfriend if you are feeling lonely.

Astyx

Apparently local doctors here are giving vaccines to "anyone who asks" because people in priority groups are skeptical

leslie townes

our city had a sign-up thing which would supposedly alert me to available vaccines. the other day i got an email referring me to the state system, which said no vaccines. then a guy at my work told me that he got vaccinated when he went to buy beer at a drugstore because they had "leftovers" (???)

Simone

sure but I also want to find a significant other and maybe start a family, and there's no way for me to do that

Astyx

There's no way to see friends also

leslie townes

one thing that's really messing with me is that both of my parents are old and in fairly poor health. i would like my daughter to remember meeting them.

Edward Evans

4:56 PM

@anakhro I'm a very social person and I'm extremely lonely due to covid. Talking shit to random people in bars when I'm drunk is a big part of my life.

anakhro

@EdwardEvans maybe there is a lesson to be learned from that, then.

Edward Evans

What lesson? Be fine with being lonely?

Simone

@EdwardEvans I thought I was an introvert... covid shattered that self-image I had.

leslie townes

i met two of my grandparents twice, for about 5 hours. i want my daughter to have more than that.

Simone

:(

let's talk math

leslie townes

5:01 PM

i have a bunch of cool unsolved problems in operator theory but they are on my other computer. i have not managed to get it to open up to my current computer on our wireless network. i have an patch cable but windows 7 hates talking to windows 10.

anakhro

@EdwardEvans Sometimes by chance we are able to see imbalanced aspects of our lives. Social interaction is not limited to "talking shit to random people in bars when drunk", and if that was all your social life amounted to, then I think that there is definitely a lesson to be learned.

@leslietownes was your research in operator theory?

leslie townes

as mitch hedberg once said, alcoholism is the only disease that you can get yelled at for having.

yes.

Astyx

@anakhro I feel that's a very arrogant claim

Edward Evans

lol obviously my entire social life wasn't based around talking shit in bars

anakhro

@Astyx what claim?

Astyx

5:03 PM

That being lonely because of Covid means your life is imbalanced

Edward Evans

My social life was very important to me and it's something that's really missing from my life at the moment. I wouldn't call being highly sociable an "imbalanced aspect" of my life.

leslie townes

my social life was based around talking shit at work, and that was taken away from me. i have to phone individuals and talk shit.

anakhro

@Astyx Where did I claim that?

Astyx

Maybe I misunderstood what you meant

robjohn

$\Huge\text{Happy $\pi$ Day!}$

5

anakhro

5:06 PM

I elaborated,
> "Social interaction is not limited to "talking shit to random people in bars when drunk", and if that was all your social life amounted to, then I think that there is definitely a lesson to be learned."

leslie townes

whoah how did you get that cool font

Simone

I'm going through Ted Shifrin's Multivariable math and there's a problem about interpreting the Lagrange Multipliers: Suppose $\mathbf a = \mathbf {\psi} (c)$ is a local extreme of $f$ relative to the constraint $g(\mathbf x)=c$, suppose also that the function $\mathbf {\psi}$ is differentiable. I must show that $\lambda = (f \circ \mathbf {\psi})'(c)$....

That's all he tells me about psi, but I'm confused: the derivative of f in terms of psi of c is fixed, but $\mathbf {\psi}' (c)$ is not, the velocity vector could be anything... am I missing something about $\mathbf {\psi}$?

leslie townes

warning: everything i say from now on will be in that cool font

Astyx

$\text{In that font ?}$

Simone

psi should have been in boldface

leslie townes

5:07 PM

you all are cheating. you have unlocked the cheat codes.

Edward Evans

@anakhro either way, it sounds very judgmental :P

leslie townes

if talking shit to random people in bars is wrong, i don't want to be right

anakhro

No one said it was wrong.

leslie townes

i probably last went to a bar in 2010. all of this is theoretical

Edward Evans

idk what you meant then dude, just sounded judgmental and unnecessary hehe

Simone

5:12 PM

I guess I'll ask him personally when he logs on

leslie townes

simone going only on what is pasted, i guess we know that $a = \psi(c)$, but is it possible to infer any other properties of $\psi$ from context? i have generally learned that ted shifrin is unreliable and one of the usual suspects.

my dad used to work next to the police station in my hometown, and they would call him over to participate in lineups when the identity of an alleged perpetrator supposedly matched him. that's a role i see ted shifrin in.

nobody has written an article or story about that. who are the other people they call in police lineups? the answer: people who work within one or two blocks of the station and might resemble the suspect.

Simone

I might have missed something that notation would suggest, or maybe I have some prevous edition of his textbook idk

leslie townes

maybe you have defamed him and could be liable for damages. think about it.

Astyx

What is $\lambda$ ?

Simone

a Lagrange multiplier

for the local extremum

@leslietownes I have both a pistol and a sword, we could resolve this as men.

robjohn

5:17 PM

@leslietownes Right click on the MathJax to see the code used. Choose "Show Math As > TeX Commands"

Astyx

From my understanding $\psi$ is defined to be a differentiable function $\Bbb R \to \Bbb R^n$ such that 1. $\psi(c)$ is an extermum of $f$ on $\{x\mid g(x) =c\}$ 2. $g(\psi(c))=c$

Simone

right

Astyx

So what is your question?

Simone

How can $\lambda = (f \circ \mathbf {\psi})'(c)$? given that $Df(\psi(c))$ is fixed, but $\psi ' (c)$ is not, it's a velocity vector of the paramatric function psi, but psi could be any function that just so happens to have $\psi (c) = \mathbf a$

but maybe I'm missing something about psi.

Tangentially we also have that $Dg(\psi (c)) \psi '(c)=1$

I'll ask him later thx anyway

Mike Miller

5:40 PM

@leslietownes Are you comfortable talking about which little corner of operator theory? I have zero interest in trying to de-anonymize you and will make no efforts to, but I get if it's not comfortable anyway.

leslie townes

semigroups of operators on C* algebras and von neumann algebras. also some more function-theoretic stuff about limits of complex matrices.

i never solved any PDE with my research although in one or two grant applications i may have suggested that. it wasn't fraud, number one because i didn't have the intent to defraud the government, and number two, because those applications were denied, so no damages.

Mike Miller

Both of those sound pretty pleasant. One of my closest friends did his PhD on free group factor stuff. I think he tried to do some problems on group C* algebras more generally but that the work didn't go anywhere.

That's pretty standard grant applications

leslie townes

a friend of mine put some crap about algebraic curves in an NSF application and got it, i think primarily because his advisor worked in that area, and did nothing for about three years, and then graduated and went into industry. thanks, NSF.

the pleasant sideline of this is the NSF buying me beer at least a few times in the early 2000s

Mike Miller

I was never gonna be able to finish the projects I proposed in less than half a decade even if I worked real hard at it.

leslie townes

i do have a gripe generally about how the US funds academic research. it seems very much winner-take-all. which seems suboptimal. the winners, more or less by definition of the quality of their research, do not need to take all. and some people just need, like, one semester out of teaching to work on stuff, to look more like winners than whatever it is a non-winner looks like.

in my postdoc i was privy to some of the discussions of potential postdoc hires. X with 3 publications and a grant was valued over Y with three publications and no grant. why? familiarity with the grant system. no account given to the fact that Y had done the same publications as X with less research time and more teaching.

teaching didn't enter into it.

nor did anybody realize that maybe grants were awarded on the strength of the advisor and not the advisee. i dunno.

it made me even more cynical, if that was even possible.

Astyx

5:53 PM

@Simone I think you got it: we have $df + \lambda dg = 0$. Plug in $\psi'$ and simplify using what you already figured out

Akiva Weinberger

vocaroo.com/1oLKn5dquVQo

Happy pi day!

Simone

@Astyx Actually I don't think I got it, because $\psi '$ could be any vector.

Astyx

I take it the last digit of pi is 1

@Simone Yes, but you know it satifies some rule

I know you know because you wrote them out

Simone

All I know is that $Df = \lambda Dg$ at $\a$

Akiva Weinberger

No because there's only finitely many 1s in pi

(jk... unless)

mick

5:58 PM

hi all

Astyx

so plug in $\psi'$

mick

happy pi day

im still stuck here

0

Q: $\sqrt{\ \ \ } $ hypercomplex ??

Hypercomplex number is a traditional term for (an element of) a finite-dimensional unital algebra over the field of real numbers. Examples are complex numbers, quaternions, octonions etc. Complex numbers and quaternions are associative, however non-associative systems like octonions and hyperboli...

abstract-algebra radicals hypercomplex-numbers nonassociative-algebras jordan-algebras

and i do not get why it is closed

Astyx

@AkivaWeinberger 😳👉👈

leslie townes

i think this has been discussed before, where it was noted that the question is very long, when it amounts to asking for non-associative algebras over real numbers with [specified properties] in which every element is a square of another element.

for the record, i did not vote to close. but many people see posts of that length as a problem.

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$Mathematics$ Mathematics