Mathematics - 2021-04-22 (page 2 of 2)

5:00 PM

We have not yet learned about equivalence of metrics.

Quite frankly, we are getting quite tought homework for little "firepower" we learn.

instructors don't have to do much, but they ought to set up relevant context for the exercises they pose. we may have fallen into a gap here.

like that sheep in the recent viral video.

copper.hat

it is not too hard to show that $\max(|x|,|y|) \le \sqrt{x^2+y^2}\le \sqrt{2}\max(|x|,|y|)$.

So a ball in the product must contain the product of two balls and the other way around. My upbringing makes it hard to talk about balls without blushing.

leslie townes

agreed that all of this stuff is, i hate to say it, solved by drawing a picture of a ball within a ball within another ball.

robjohn

5:15 PM

Hairy ball theorem

The hairy ball theorem of algebraic topology (sometimes called the hedgehog theorem in Europe) states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in R3 to every point p on a sphere such that f(p) is always tangent to the sphere at p, then there is at least one pole, a point where the field vanishes (a p such that f(p) = 0). The theorem was first proved by Henri Poincaré for the 2-sphere in 1885, and extended to higher dimensions in 1912 by Luitzen Egbertus Jan...

@copper.hat There's one to make you blush even more

leslie townes

goodness.

i always felt that that was a somewhat bad analogy. hair is not easily analogized to tangent vectors.

Flows.

robjohn is that the saying you cant comb a sphere?

copper.hat

@leslietownes haven't you heard of brillcream?

leslie townes

a little dab'll do ya

Thorgott

my hair tends to be normal, especially after waking up

leslie townes

5:19 PM

since coronavirus limited my barber shop options, i shave my head. my hair is more analogous to normal vectors.

yeah.

my daughter's never had a haircut. she will turn 3 in october. her hair is mostly normal vectors.

my wife hates how i look with a shaved head, but she hasn't volunteered to style it. so i'll keep on looking like a gangster.

copper.hat

i stopped shaving my head, convenient though it was, because i got tired of the reactions like i some form of toxic material.

leslie townes

the problem with shaving your head is that in many places it is confused with a political position.

copper.hat

wtf, markets did some bellyup all of a sudden

yup, like mask wearing.

as is typical with local berkeley/albany hypos people are fussing if you don't wear your mask when you are 30' away.

leslie townes

someone shouted at me for having a mask off with my daughter from across the street. we're outside. it's hot. give me a break.

Manolis Lyviakis

any1 familliar with cliffords theorem on representation of groups? for the restriction to a normal subgroup?

copper.hat

5:28 PM

i would interpret the shout as intent to cause bodily harm to my daughter.

leslie townes

i told them to go to hell and some other stuff. it wasn't a pleasant experience.

copper.hat

it is beyond stupid

leslie townes

they asked me if i cared about my daughter's life. i said, she is not going to die in your lifetime. and some cuss words.

copper.hat

ask them if they care about their own

leslie townes

i'd really like all of this to be over. i've got about 2 weeks until the second vaccination.

copper.hat

5:30 PM

where were all there people in flu season.

leslie townes

i didn't get the flu this year. i always vaccinate but usually also get it. since my daughter was born i get everything.

a little over a year ago i infected my office neighbor with hand, foot, and mouth disease. i am renowned for that.

copper.hat

i think a lot of these folks are missing socialisation 101

the joys of kids

leslie townes

she was making fun of me for having 'hoof and foot syndrome' or some other name she made up. then she got it.

copper.hat

mocking is catching :-)

leslie townes

anyway i'm looking forward to a time where i can go to a barber and stop looking like a nazi.

copper.hat

5:35 PM

my local is open. i'm not particular but they are suffering so happy to give them business.

albeit if gov keeps on about taxing we may be trading places

leslie townes

i have also been following this situation with interest.

copper.hat

my yearly gains just got wiped about about 5 mins ago. corp tax i believe

leslie townes

i'm not liking the market today. it seems unnecessarily jittery. there is some very bad covid news from some countries but this shouldn't factor into the entire economy, just the companies that have supply chains impacted by that.

not to not be a patent lawyer for a minute but the vaccines should be in the public domain. there should be no property in this stuff. i don't care how expensive it was to develop, you can make that back on other medications.

copper.hat

i think the market has priced in 'its over' and reality hit. so much for the much ballyhooed group think.

plus timing of tax talk was spectacularly bad.

don't they know bad news goes out on friday

leslie townes

yeah, just wait. friday, maybe 4:30 pm. that's when you do it.

copper.hat

5:43 PM

who knows. maybe thebad news will come out tmr

dropping about $1k/min at present.

beats my hourly

robjohn

6:00 PM

@Flows. it means there will always be a sworl in the hair

@leslietownes The foreign markets seem to be doing better than the US markets.

down 1-1.5%

did something happen today?

@leslietownes I think there might not be as quick a response if that were the case.

copper.hat

gov indicated movement on corp tax rates

robjohn

ah. that would affect things.

copper.hat

im getting creamed. will be retiring in about 30 yrs

never give up your day job

my life lesson. did it 3 times. didn't learn :-)

getting admonishments on choice of language. i have capitulated. getting old.

supposedly a 7yo asked a question math.stackexchange.com/questions/4112655/a-student-says-a-b-b-a-is-this-statement-always-true-sometimes-true-or-never. i reacted badly (not realising that a 7yo could be asking questions on mse).

ok, a 12yo.

soupless

6:22 PM

@copper.hat I feel bad, too. He/she was a victim of PSQs that's why.

copper.hat

@soupless i let my emotions dictate my actions. not desirable.

soupless

@copper.hat now I feel like crying because of that

copper.hat

@soupless my life is spent in guilt anyway. this is just a top up. i do feel bad for reacting.

soupless

I tried to send a "Welcome to MSE" message but I was too late, I just adapted to the situation

the three downvotes for a first question of such a young child, though. I really feel bad to the point that I want to upvote it

copper.hat

i just squirm inside and torture myself.

leslie townes

6:28 PM

i dunno, when i was 12 i was arguing with people on the internet.

copper.hat

i was enjoying decimalisation, spitting contests and firing blobs of ink soaked blotter through biro (bic) tubes.

leslie townes

it was mostly people i personally knew. the general novelty of the internet is its ability to provide an endless supply of new people to argue with.

copper.hat

plus a few others than probably do not belong here. snuff was one, although i have no idea there was nicotine involved, one thing that i am religious about

Ted Shifrin

How did we ascertain that this person is 7 and/or 12? It's not a bad question for a young person, but still I would like to see some effort/thoughts, and not just a question posted for us to give an answer.

copper.hat

the joys of inhaling lignite burned on a cold wet day in an anthracite stove.

Ted Shifrin

6:31 PM

On the other hand, I just got an email from a student asking for hints on one of my differential geometry text problems ... saying what her teacher had told her to try (different from and harder than my hint).

copper.hat

@TedShifrin My response was inappropriate for someone of that age. Probably could generalise the last statement. Living up to the stereotype.

leslie townes

i've gotten three emails from people in brazil asking for solutions to problems in my advisor's book. a friend of mine did a postdoc there, i think he started a rumor that i like helping people.

copper.hat

I have got umpteen requests for help.

Ted Shifrin

I get dozens of requests for the solutions manual of my multivariable math book. Um, NO, those are not for the general public.

copper.hat

I ask them (mostly) to post on mse.

Ted Shifrin

6:33 PM

Although I do feel sorry for people who are "self learning" and have no way of finding out (other than posting on MSE) whether their proofs/solutions are worth a damn.

copper.hat

@TedShifrin Maybe you can offer one on one problem solving for a suitable high price?

leslie townes

one of the people, i googled him and found his band on social media. i asked him to send me recordings of his band. it was not a very good band. i ghosted him after that.

Ted Shifrin

I have told them that it's OK to find me in chat here.

copper.hat

That is sweet of you.

Ted Shifrin

LOL @ "not a very good band"

leslie townes

6:34 PM

i wanted to hear a really good guitar solo, so good that it would unlock the solutions to chapter 3 of bill arveson's book.

copper.hat

I have found (do not always adhere to my own advice) that it is best to be blunt up front.

leslie townes

i did not hear anything of the sort.

copper.hat

A close friend (who gets all my maths questions) is/was a professional classical guitarist.

He sends me renditions periodically. Rather nice.

I do his low level real analysis, he plays me music.

leslie townes

i was friends with a cellist for a while. he had spent his career with a symphony somewhere and in his retirement decided to understand calculus to the point of newton's derivations of kepler's laws. really sharp guy

copper.hat

i wish more effort was spent in making existing results more accessible. there is a big gap between research and making accessible.

Ted Shifrin

6:58 PM

Yeah, I tried to publish my thesis with a lot of the exposition in it, but was forced to cut a lot (but not all) of it out.

leslie townes

for a lot of people, making accessible is at odds with some kind of ego trip they're on. not a huge amount of people, but enough of them to make it a pain in the *ss.

copper.hat

Pity, perhaps your committee were thinking of your employment prospects which is commendable.

Ted Shifrin

Well, it's more dictated by reviewers and journals (not that I blame them), trying to keep things brief.

The thesis had it in there (by my wishes, nothing to do with the committee). I was talking about publication. In fairness, people on my committee respected my teaching skills.

leslie townes

7:23 PM

one of my daughter's day care instructors said that my daughter has begun being very contrary in the classroom. she disagrees with everything and shouts 'no' and stomps her feet if people attempt to correct her. i wonder where she got that from.

Ted Shifrin

7:48 PM

Sounds like it's time for behavior modification for you, lest she get in serious hot water before she's even in kindergarten.

leslie townes

i'll stop stomping.

robjohn

8:11 PM

@leslietownes when I was 12, there wouldn't be an internet for over a decade

maybe two

ugh

Andrew Micallef

8:42 PM

@copper.hat i propositioned a friend of a friend to provide that service for me. But my estimation of the value of his time was woofuly inadequate. And I can't bring myself to offer more, because without certification at the end, it feels like pissing away money

copper.hat

True, probably would only make economic sense for a group.

Andrew Micallef

Would it though? I dont know how much time / effort it would take to read through and provide feedback on solutions

copper.hat

Dunno. Probably not. Seems strange not to be able to capitalise.

Andrew Micallef

I did some marking once (of psychology essays) and found I couldnt do it well in the 20 mins provided for each student. I wound up spending 4x the time allotted...

@copper.hat opportunity costs, he could easily make 10x what I can offer in the extreme, by capitalising on his qualifications in a more traditional manner ie getting an engineering job

copper.hat

ahh, but the value of friendship & the intangible rewards...

Andrew Micallef

8:56 PM

I'll try price that in for future negotiations 😁

But who needs friends when you have irc anyway

copper.hat

my mum used to say "a friend in need is a friend indeed", but i still not quite sure what she meant...

Andrew Micallef

I think you need to frame it as: a friend who is there when you are in need is a true friend

Otherwise it is ambiguos, and the alternative interpretation makes me think Ben Franklins view of human psychology (which im not sure there is a whole lot of evidence for)

I make friends with everybody; its kinda my superpower ;)

copper.hat

i think she meant both interpretations, introducing me to the ambiguity of life :-)

Andrew Micallef

Actually, it makes me think "pathalogical altruists". And time for me to go

copper.hat

have a good morning!

Andrew Micallef

9:14 PM

You too, good evening (a think i should have time today to solve this circle problem at lunch...im nearly there, but got to a point where I have expressions for x and y in terms of t, but no trig formulas...so i think i made a mistake)

Ted Shifrin

@AndrewMicallef The answer (given at the end of the book) is rational functions. That's the whole point.

Andrew Micallef

@TedShifrin i didnt know there was an answer at the back (i read sequentially) but looking up the answer isnt going to help me learn ;)

And now i actually have to go

Ted Shifrin

Front page tells you what * and # mean.

copper.hat

what the *#**##

Andrew Micallef

9:59 PM

Feck, caught out. Need to be more carefull. Ok I did just skip to the excercises. But the point stands. Also, I want to apologise, Ted, I imagine your patience is running thin with me.

geocalc33

11:30 PM

If you have 6 projections $(x,y,0),(x,y,1),(x,1,z),(x,0,z),(1,y,z),(0,y,z)$ for $x,y,z \in (0,1)$ and you are given 6 congruent vector fields on the projection planes, how do you construct a vector field in $(0,1)^3?$ Would taking an average of the 6 projections to construct a vector for $(x,y,z)$ work?

Another way to phrase this, is, if on each face of a unit cube you have congruent non-vanishing vector fields, then how do you re-construct a vector field in (0,1)^3 based on the boundary information

I think one is embedding 6 copies of $\Bbb R^2$ into $\Bbb R^3$ in different configurations

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$Mathematics$ Mathematics