Mathematics - 2021-03-20 (page 2 of 2)

leslie townes

18:00

my physics teacher in high school taught both honors physics for people going to college, and the bare minimum class you needed to graduate. he used a lot of pictures in that class. english was often a barrier because the students were often new to the united states.

user586228

@leslietownes What is meant by continuous setting?

Wolgwang

leslie townes

years later i ran into one of my classmates who worked for the state in some capacity of managing water resources. he took the remedial class. he said 'i always remembered that mr. oswald told us it would be great if we could do work that isn't measured in horsepower.'

Wolgwang

How's $r-b\in S'$?

leslie townes

that is a profound message. well done, mr. oswald.

@user586228 only that when one talks about velocities, often the velocity is a function of a real variable (time). it isn't just a list of numbers, but a function on an interval. the kinds of things that appear in financial statements are snapshots in time and are, indeed, capable of being put into lists of numbers.

Leaky Nun

18:02

@Wolgwang $r-b = a-bq-b = a-b(q+1)$

Wolgwang

@LeakyNun Oh Damn! Thanks :-)

leslie townes

you can average any bag of numbers, of course, and the question is what you hope to achieve by doing that, what it tells you. "average profit" maybe doesn't tell me very much about how a business is doing. my wife works in sociology with numbers, and sometimes people just compute those things to compute them. and sometimes they assume numerical averages are representative of something, without really thinking about it.

porridgemathematics

@Thorgott thanks, also im wondering in a simplicial complex, is the $k$-skeleton equal to the union of all $k$-simplices, or all simplices of dimension less than or equal to $k$? Or are they both the same

leslie townes

on the subject of averages, here is a perspective on the AM-GM inequality i like a lot. cs.utexas.edu/users/EWD/transcriptions/EWD11xx/EWD1140.html

porridgemathematics

by simplices here i mean their images

also is the proof of the adjunction space thing pretty easy?

Thorgott

18:19

to answer the second question, yes, you can write down the obvious maps in each directions and directly check they're inverse to each other

porridgemathematics

ah okay, using the universal properties of each space, im guessing? (i.e. use both properties and combine diagrams to show we get inverses?)

Thorgott

to answer the first question, it's the latter

@porridgemathematics yeah

porridgemathematics

so it wouldn't always be correct to say that the morphism $$\coprod_{\alpha} \Delta_{\alpha}^k \rightarrow X^k$$ is surjective?

here $$X^k$$ is the $k$-skeleton of a finite dimensional simplicial complex say

or is it always true for finite dimensional simplicial complexes

whoops, I think i might be misspeaking, by simplicial complex I mean hatchers notion of $\Delta$-complex, just to be totally clear

Thorgott

take the disjoint union of a circle and a point

porridgemathematics

oh damn

that is a delta complex

for some reason I thought it had to be connected

leslie townes

18:55

my cat is just going to town on this toy where you bat a ball around a toroidal shape. the ball is sufficiently enclosed so that it can't come out. she's trying to get it out.

it's anarchy over here.

Ted Shifrin

Yes, I've seen that cat toy on YouTube videos. That'll keep her busy for a while.

Now if only you had such a toy for your kid.

leslie townes

whoever invents that toy will make a fortune.

Ted Shifrin

Maybe the same toy will work?

leslie townes

she just kicks it. torus and everything.

Ted Shifrin

Ah, no refined motor skills yet.

The cat is a superior animal.

leslie townes

18:58

she made me brew "goji tea" (= hot water with dry goji berries in suspension) for her this morning. she's on track to become the next emperor of rome.

she and the cat are about cognitively equal, but the cat definitely has her beat on fine motor skills. she is more verbal. she sometimes deploys the f-bomb. i don't mind as long as it is contextually appropriate and not gratuitous.

dc3rd

I got a new question to ask something about today @TedShifrin,

Ted Shifrin

Whew.

dc3rd

two actually one is an offshoot of the original question.

leslie townes

objection, compound

Ted Shifrin

I think you should stop deploying the f-bomb and teaching a 2-year old bad things.

porridgemathematics

19:04

im trying to solve this question, and im wondering what the catch is, suppose $X^n = U \coprod V$ is a disjoint union of open sets and $X^n$ is the $n$-skeleton of some CW complex, then show we can write $X^{n+1} = U' \coprod V'$ where $U'$ and $V'$ are open sets, and $U \subset U'$, $V \subset V'$, I don't understand why we can't just say $X^{n+1} $ is $X^n$ union a disjoint union of (open) $n+1$ cells and be done with it

dc3rd

I've been working on #17 from Sec 1.5, this was from monday when I was working on it, but anyways. You ask us to show $\mathbf{x}$ can be written uniquely in the form $\mathbf{x} = r\mathbf{u} + s\mathbf{v} + t\mathbf{w}$.

Using the hint of $v-u$ and $w-u$ (I'm not going to boldface them from here on out I think we know which is which), I can create the $2 X 2$ matrix with one column the $v-u$ and the second column $w-u$.

porridgemathematics

all the (open) $k$-cells are mutually disjoint, and are open subsets of $X$, so it seems fine to me

Leaky Nun

@porridgemathematics [0,3] is [1,2] union a disjoint union of [0,1] and [2,3]

dc3rd

I was having trouble arranging my scalars. Also we are restricted to $r + s + t = 1$

Leaky Nun

(i.e. your logic doesn't work)

or how about, [0,1] is {0} U {1} union the open interval (0,1)

Ted Shifrin

19:07

Yes, so every vector in $\Bbb R^2$ can be written as $s(v-u)+t(w-u)$ for some $s,t$, right?

dc3rd

Yes agreed.

leslie townes

the side effect of not deploying the f-bomb within earshot of the child is that i deploy it a whole lot more after she has gone to bed. or if she is in day care or after care. i'm a sailor on shore leave when she's not around.

Ted Shifrin

Subtracting $u$ is like using $u$ as the origin. So what vector should you apply this to?

Leaky Nun

@porridgemathematics lol this is a counter-example for n=0 (your question is still valid for n>0)

dc3rd

If I rewrote one of the scalars then I would have $t = 1-r-s$ for instance

porridgemathematics

19:08

@LeakyNun {1} isn't open?

Leaky Nun

{1} is open in {0,1}

Ted Shifrin

Forget that for now. Answer my question.

Leaky Nun

what's the 0-th skeleton?

porridgemathematics

yeah but the CW complex is $[0,1]$, and open sets here are open in $X$, not a skeleta

dc3rd

oh I didin't see it, it popped up after I wrote the above

Mark Giraffe

19:09

I like headers. Trying to make a proper dark mode header for Math SE.

Leaky Nun

@porridgemathematics forget whether it's a counter-example. I'm showing your why your logic doesn't work

dc3rd

WHat vector should I apply another subtraction of $u$?

Leaky Nun

because your "disjoint union of open cells" might connect U and V

Ted Shifrin

Sorry. By "this" I meant my observation about writing every vector as $s(v-u)+t(w-u)$.

Leaky Nun

showing you*

porridgemathematics

19:13

i get what you are trying to say, but they only connect $U$ and $V$ in the case you speak of because ${1}$ isn't itself open in $[0,1]$, I think they are connected

Leaky Nun

right, and our discussion shows you that one needs to be careful of what "open sets" means in "X^n = ... is a disjoint union of open sets", because obviously X^n can't be open in X

porridgemathematics

yes, that is because the problem im looking at is poorly worded though

it starts by saying 'let X be a CW complex' and then says 'open' without referring to with respect to which subspace

its likely as you are suspecting

open in $X^n$ not $X$

Leaky Nun

I would say they mean open in X^n

porridgemathematics

well, it was ambiguous, also why I asked here, and you cleared it up :)

thanks

dc3rd

well if I could write every vector in $\mathbb{R}^{2}$ as $s(v-u) + t(w-u)$, then I can subtract $u$ from it and I should still be able to get every vector in $\mathbb{R}^{2}$

Ted Shifrin

19:17

So what vector do I want to set equal to $s(v-u)+t(w-u)$?

Manjoy Das

I was reading the geometrical interpretation of Lagrange's equation and there it was written that if $z=f(x,y)$ be the solution of the Lagrange's equation $Pp+Qq=R$, then the direction cosines of the normal to the solution surface at any point are proportional to $p,q,−1$. It comes like this:
$∂f/∂x,∂f/∂y,∂f/∂z$, i.e$ (∂f/∂x)/(∂f/∂z),(∂f/∂y)/(∂f/∂z),−1$, i.e $∂z/∂x,∂z/∂y,−1$, i.e $p,q,−1$
My question is how $−1$ comes in this calculation?
There may be something silly that I am missing but I really can't figure it out.

porridgemathematics

somewhat related, if an interpretation of a question is ambiguous, and there is one interpretation that leads to a stupid question, and another one that makes more sense, it always feels grating to me to bite the bullet and interpret it in the better way, its like, i shouldn't have to untangle ambiguity that can be avoided with effort in precisely stating a question

Ted Shifrin

Because the normal vector to your graph is given by writing $f(x,y)-z=0$ @Manjoy.

porridgemathematics

its times like this that I feel like programming is more precise than maths

dc3rd

$ru = s(v-u)+t(w-u)$

leslie townes

19:19

a lot of people who ask questions in math have made two or three interpretive leaps before they ask the question. and the work of answering it is mostly backing them out of their leaps. which you don't know. they become revealed over time.

it would be simpler to say syntax error, full stop. but we don't. there are small amounts of money in it.

Ted Shifrin

@dc3rd You are not thinking clearly. Reread the problem. What are we trying to do?

porridgemathematics

@leslietownes what you said applies to human communication in general

Manjoy Das

still it should be $1$. isn't it? @TedShifrin

porridgemathematics

but programming requires more specification than that

Ted Shifrin

Why $1$, @Manjoy?

porridgemathematics

19:21

I would say holding maths to the same standard will be the way to go in the future

when automated theorem proving becomes realistic

leslie townes

@porridgemathematics this is why i try not to communicate with humans. it is fruitless.

porridgemathematics

haha

Manjoy Das

because $f(x,y)-z$=0 @TedShifrin

PM 2Ring

@leslietownes Aka the XY problem

Ted Shifrin

We have the level surface $g(x,y,z)=f(x,y)-z=0$. You're not explaining $1$, are you?

leslie townes

19:23

i'm so glad i don't work in tech support. it would drive me crazy. although in my job (attorney) it's basically the XY problem. people don't pick up the phone when they ought to. they pick it up several months later, and you get a lot of Y and not so much of X.

litigation is tech support.

Manjoy Das

got it @TedShifrin

PM 2Ring

At least with tech, there's a reasonable chance that they can explain the thought process that led them from X to Y.

Manjoy Das

@TedShifrin but look at my steps in my question. how $∂f/∂z=-1$?

@TedShifrin it should be $∂g/∂z=-1$

leslie townes

yeah, in corporate reality it's always something dumb. no thought process involved.

i submitted my taxes the other day, hrblock's automated software congratulated me on me being married to my wife for another year. i wonder what it does when you report a divorce or a death. i hope it's an audible "bwaaamp bwoooooooomp." from a trombone. you know the sound.

Ted Shifrin

If you're doing $z=f(x,y)$, it makes no sense to take derivatives of $f$ with respect to $z$, @Manjoy.

dc3rd

19:30

well since every vector can be written as above and I said subtracting $u$ from it should still give me a vector in $\mathbb{R}^{2}$. We are trying to write $x$ uniquely in the form stated above.

Ted Shifrin

So focus on $x$, @dc3rd. Basic problem solving skills. Now what?

We've already understood that we're thinking of $u$ as our tail of our vectors.

PM 2Ring

@leslietownes I saw while skimming the transcript that your daughter likes rainbows. You might like to make a water prism: a tray of water with a mirror in it, arranged so you get a wedge of water above the mirror. You can use another mirror (outside the tray) to aim sunlight into it.

Manjoy Das

that's what is done in the text books and other pdfs available on internet. they are considering $z=f(x,y)$ and then find the dcs of the normal to the surface as $\partial f/\partial x, \partial f/\partial y,\partial f/\partial z$. after that they are dividing each proportion by $\partial f/\partial z$ and so on @TedShifrin

leslie townes

@PM2Ring thanks. she does love the rainbows. it's this time of year the sunlight hits a light over our staircase, and the edges of the glass around the fixture create rainbows. we wondered at them this morning. i like the idea of manufacturing rainbows.

Ted Shifrin

You're writing garbage, @Manjoy. You cannot use the letter $f$ for both functions. (Maybe you should watch my YouTube lectures on multivariable calculus.)

Oooh, prisms!!! Great idea.

leslie townes

19:35

shifrin has lectures on multivariable calculus? youtube?

click click click

maybe i will finally understand it

dc3rd

So you mentioned subtracting......if I added the vector $u$ instead of sybtracting I get this:

Setting $x = s(v-u)+t(w-u) + u = sv - su + tw - tu + u = u(1-s-t) + sv + tw = ru + sv + tw$

Ted Shifrin

The course based on my book, @leslie. Multivariable calculus/analysis and linear algebra all integrated.

But warning: There are pictures.

Right, @dc3rd. You apply it to $x-u$. And then you're done. Good.

leslie townes

the undergrad sequence at berkeley could be taken in either order. multivar could not assume linear algebra and vice versa. this seems like a gap, somehow.

i don't know how you express the chain rule if you don't know a little bit of linear algebra. and damn leibniz to hell for all of his notation.

dc3rd

Oh...so I should originally have said $x - u = stuff$, because that will still be a vector in $\mathbb{R}^{2}$

PM 2Ring

@leslietownes Water prisms are great fun. Even a small mirror works ok, but of course they're more spectacular with a larger mirror. It helps if you have good contrast, eg do it in a room with curtains that you can adjust so that only a narrow beam of sunlight comes in.

Manjoy Das

19:39

@TedShifrin just take a look!!

dc3rd

Really shouldn't have struggled with this....oh well....learning experience in handling vectors in this approach

leslie townes

we have rooms like this. we can do quite a lot of optical experiments. we did use a CD to show her the difference between flourescent and incandescent light.

Manjoy Das

@TedShifrin tell me how comes the 2nd line in that calculation

leslie townes

i super hate how exponents are typset in that manuscript, @ManjoyDas

this isn't your fault. i'm just noting it. look at them up there. it's ridiculous.

Ted Shifrin

@leslietownes Yes, this is standard. You don't want to make engineers learn rigorous math. And I'm fine with that, actually.

dc3rd

19:42

It really is a matter of making sure to "think" and really "think"....your squeezing it out of me Ted, little by little...thanks....

As an aside to this first part you had made the claim that $v-u$ and $w-u$ are not parallel and I was trying to prove this. I went about it using contradiction.

Manjoy Das

@leslietownes nothing to do with it. this is the best available book here. everyone follows it. haha

leslie townes

i taught linear algebra for engineers at iowa as a series of algorithms. i had this amazing slide deck, every dumb theoretical problem reduced to row operations. rave reviews. i should have been paid more.

PM 2Ring

@leslietownes Nice.

Ted Shifrin

@Manjoy: They never had $z=f(x,y)$ that I can see. They defined $f(x,y,z)$ the way I defined $g(x,y,z)$. I don't see enough to see all their notation.

dc3rd

So I said "suppose $v-u$ and $w-u$ are parallel. This would mean that $w-u = c(v-u)$ for instance. Now I have a feeling that the contradiction is going to involve the noncollinearity of the vectors, but I can't seem to make the jump

Manjoy Das

19:45

yes. that was my mistake. but even this is out of my understanding how $-1$ came here @TedShifrin

Ted Shifrin

I taught standard multivariable plenty of times, @leslie, including twice for 350 students at MIT. It's not the right course for a sophisticated math major, but I have no problems with the course.

$-1$ is the partial with respect to $z$, of course.

dc3rd

Why isn't multivariable the right course for a sophisticated math major? (to be answered after you process my struggle of course)

Ted Shifrin

@dc3rd Yes, $u,v,w$ are collinear points iff $v-u,w-u$ are nonparallel vectors.

leslie townes

iowa had weirdly fragmented its calculus courses into three tracks, random folks, math-or-education majors, and engineering. berkeley followed a two-prong approach, math-physics-engineering, and everyone else.

Ted Shifrin

If $w$ is on the line through $u$ and $v$, this means precisely that $w-u=c(v-u)$ for some scalar $v$ and conversely.

Manjoy Das

19:46

@TedShifrin i was complicating things too much.. thanks for your time.

Ted Shifrin

Books are often sloppy, @Manjoy. You have to be a critical reader, which you are being, so that is good.

leslie townes

i'm not against multivar delivered in a format that isn't mathy. my own professor was very good in spite of the constraints. i find it incredibly hard to think in three dimensions, none of the engineeering/applied notation helped me bridge the gap. it was symbol pushing to me.

Manjoy Das

cheers!! @TedShifrin

Ted Shifrin

Well, @leslie, my lectures are totally rigorous (except for the proof of the change of variables theorem) and also incorporate a lot of the physical stuff, so maybe you'd like it. But you surely have better things to do.

leslie townes

we have a patent that someone is trying to kill at the patent office. but i already wrote up the argument, as a laugh. i'm just adding new notes. i will circulate it this evening.

we had a guy at iowa who was into infinitesimals, and would prove all of the multivar stuff using them. like that calculus book from, what's his name. i have it somewhere. it seemed goofy to me.

there's a calculus book from the 70s using nonstandard analysis, updated several times. he'd teach from that.

i was like, you can't bend the minds of impressionable midwesterners with this stuff. but he didn't care.

dc3rd

19:52

so are you saying $w = (1-c)u + cv$? @TedShifrin, so we are treating one of either $v$ or $u$ as the "point" and the other as the "vector"?

Ted Shifrin

I'm not a huge fan of nonstandard analysis as a pedagogical tool for freshmen.

leslie townes

it was horrific. his students were not pleased.

Manjoy Das

can anyone please tell me why the page number of a document file always appear as '{' whenever i open that file? everytime i have to double click on that symbol and select toggle field codes. after that '{' appears as a page number.

leslie townes

he also made departmental meetings unpleasant because of a strange obsession with right-wing politics and a fundamental discomfort with being employed at a public school. he was nonstandard in multiple ways.

@ManjoyDas what software is involved here?

Ted Shifrin

@dc3rd I guess I didn't do this in the text until the bottom of p. 53. Every point is a vector once we have the origin. I don't distinguish.

Manjoy Das

19:54

ms word 2010 @leslietownes

Ted Shifrin

I remember I had a big argument with Robert Bryant (who is one of the most famous superstars of my generation) when we were still grad students. He was arguing for nonstandard analysis as a tool for teaching freshman calculus; I was arguing against.

@dc3rd I'm being silly. This appeared in section 1 in the examples on p. 5 and then in exercise 9, 11, etc.

leslie townes

word is very weird with field codes. i wrestle with this every day.

i had a 20-email email exchange with somebody i work for about why i couldn't ensure that embedded hyperlinks would open on one click, instead of a control-click, in a word document. i tried to explain that this was determined by the user's word settings and not baked into the document. i failed.

keisler. that's the author of the book. i have keisler's text somewhere around here. it's a great pedagogical resource if you think of teaching as a game of chess and you've got the white pieces and you're trying to win.

dc3rd

hmmmm....I did those exercises too, but now I see they fell into the "symbol pushing" mindset when I did them.....

Manjoy Das

i copied some text from a website and pasted it in ms-word. now each time i open that file, that particular lines get encrypted by some codes. to fix this issue, i have to press shift+F9 and then that lines come back. @leslietownes

not just a single time, it happens every time i reopen that file

leslie townes

i have haunted word documents, too. i believe in ghosts now.

Manjoy Das

20:10

haha

leslie townes

my mother was a nurse and believed in ghosts. she had stories about seeing them in various hospitals. i thought, OK, it sucks to be working at 3am. i get it.

Manjoy Das

leslie townes

but then i open a ms word doc from six months ago.

it's like that spectral sequence diagram with witches and ghosts.

Manjoy Das

@TedShifrin why the $-$ signs disappear in the 3rd line from the first two fractions?

ghosts are quite interesting to me. but very much annoying in ms-word @leslietownes

PM 2Ring

@ManjoyDas That sounds like an encoding issue. One possible culprit is the infamous Latin1 (aka ISO-8859-1) / Microsoft codepage 1252 (aka Windows-1252) screw-up. en.wikipedia.org/wiki/ISO-8859-1

leslie townes

20:15

my wife has this issue right now where word lets her (meaning me) typeset equations in latex, but the minute she switches to render mode, they add in all of this spacing and sizing information, screwing up the latex and making it harder to render. it is the work of malevolent ghosts.

it's like, the whole point of latex, generally, is you don't micro manage spacing and sizing information. you toss in a \left or \right where you have to. maybe a \, every now and again. but not the whole nine yards of "let me tell the screen exactly where everything is." word wants to do that, even with latex.

Manjoy Das

@PM2Ring but how to get rid of this permanently?

leslie townes

sometimes i take the text i want, paste without formatting into notepad or something else that is unlikely to carry baggage and metadata.

then paste back.

Manjoy Das

@leslietownes that's a good one.

PM 2Ring

Microsoft software likes to modify data so that it becomes non-optimal on non-Microsoft software. A side effect of this strategy is that the data may also become sub-optimal on Microsoft software as well ..

leslie townes

i don't think it's an accident that "paste without formatting" is not the default. they want you to live in their world.

Manjoy Das

20:20

hey @TedShifrin!! are you there?

leslie townes

i think wordpad still defaults to saving in .rtf. because, yeah, that's a document format that human beings have used. said nobody ever.

PM 2Ring

@ManjoyDas 1. Find out the actual encoding of that text. 2. Convert it to UTF-8 and save it, preferably using software that can actually do UTF-8 conversion correctly. ;)

Ted Shifrin

@ManjoyDas Now I am.

leslie townes

one of my friends worked for microsoft. i asked her: why microsoft? you have other options, you're better than this. she said: money? i said: i get that.

Manjoy Das

help me please @TedShifrin

@PM2Ring ooouuufff!!!

that's why you see ghosts in ms-word @leslietownes :D :D

Ted Shifrin

20:23

They are assuming $f(x,y,z)=0$ defines $z$ implicitly as a function $z=\phi(x,y)$. Implicit differentiation will tell you that $$\frac{\partial \phi}{\partial x} = -\frac{\partial f/\partial x}{\partial f/\partial z}.$$

leslie townes

i see ghosts in a lot of places. the other day my daughter asked me if one of her imaginary friends was a ghost. i didn't have an answer to that question.

PM 2Ring

Unfortunately, there's a vast amount of software in the world that cannot handle text encoding correctly. It works ok with ASCII text, or a few accented letters & special symbols (eg the stuff that can be encoded using Latin1). But it may fail miserably on text using other characters.

Ted Shifrin

Write out the chain rule for $\frac{\partial}{\partial x}f(x,y,\phi(x,y))$, using $f(x,y,\phi(x,y))=0$ for all $x,y$.

dc3rd

Time to go make some caccio e pepe.

Ted Shifrin

That sounds promising, @dc3rd.

Use plenty of pepe.

leslie townes

20:25

cacio e pepe, the ancient roman method of coating your pots and pans (but not the pasta) with cheese.

dc3rd

Always do go hard on the pepe

leslie townes

good luck with that

dc3rd

the trick I've discovered Leslie is to do the cheese in your plate or whatver container, not the pan and let the heat of the pasta do the work

Ted Shifrin

@leslie that's the cacio part.

PM 2Ring

Embrace, extend, and extinguish

"Embrace, extend, and extinguish" (EEE), also known as "embrace, extend, and exterminate", is a phrase that the U.S. Department of Justice found that was used internally by Microsoft to describe its strategy for entering product categories involving widely used standards, extending those standards with proprietary capabilities, and then using those differences in order to strongly disadvantage its competitors. == Origin == The strategy and phrase "embrace and extend" were first described outside Microsoft in a 1996 article in The New York Times titled "Tomorrow, the World Wide Web! Microsoft, the...

leslie townes

20:26

i've got a secret roman recipe for the hardest dishes to do ever. your dishwasher won't do it. your scrubbers and scrapers won't do it.

Ted Shifrin

Right, you don't ever want heat on the cheese.

dc3rd

have to respect the heat from the meal to do the necessary work

leslie townes

that makes abstract sense. i haven't cooked pasta since my wife discovered a wheat sensitivity. we sometimes have rice noodles. wonderful but definitely not the same.

PM 2Ring

Remember, cheese is high in calcium, and so is marble. :)

leslie townes

my wife went to these high-falutin doctors in santa monica who diagnosed that she was sensitive to anything that was delicious. since then i have lived in a nightmare world.

PM 2Ring

20:29

Another option is buckwheat noodles.

Ted Shifrin

I love rice noodles, but in Asian applications, not Italian.

leslie townes

there's some other reason why soba won't work. i forget it. i hate those doctors in santa monica.

Ted Shifrin

That's what you get for going to doctors of the rich.

PM 2Ring

Potato pasta?

leslie townes

we paid them something like \$2000 to learn that my wife can't eat anything that tastes good. we eat birdseed now. and yeah, a month later they switched to a concierge medicine model where you can't pay them \$2000, you have to pay them \$20000.

Manjoy Das

20:30

if $f=x+y+xy$ where $z=xy$, then what will be $\partial f/\partial z$? @TedShifrin

leslie townes

she did see a celebrity in the waiting room, so there's that. thanks southern california.

PM 2Ring

Your wife's probably allergic to that mold in your garage, which may be sensitizing her to wheat etc

Manjoy Das

is it $1$? @TedShifrin

Ted Shifrin

No, you write $f(x,y,z)=0$ to start with. How do you make up $f$ so that $f(x,y,z)=0 \iff z=xy$? Your $f$ isn't doing it.

You can't do random stuff and expect it to make sense, @Manjoy.

leslie townes

you have a point there. my sister developed all kinds of sensitivities because of mold in the house we grew up in. my dad was too cheap to fix the roof or heat the rooms.

Ted Shifrin

20:33

I had all sorts of mold in my house in GA, thanks to living in the woods with a creek ... and plenty of GA humidity.

Sadly, most of my books show the signs of it.

PM 2Ring

Mold is a big problem in clandestine hydroponic gardens. That's why it's mostly done in rental places. There's no point growing weed in a place that's got mold.

leslie townes

if he grew up in moldy squalor, so would we. he split his adolescence between mississippi and tennessee. it damages the hell out of books.

that's the other thing, the previous owner's son had a growing op above our garage.

he left most of it. no weed though. just housings for light fixtures, reflectors, and trays where the weed would be

it seems stupid now. we live a few blocks from a state-legal dispensary. some day, all of this will seem like a past nightmare from which we have awakened.

PM 2Ring

@leslietownes I remembered you mentioning that recently, which is why I mentioned it.

leslie townes

it's connected. our daughter is super human. she doesn't seem to have either of our allergies.

Ted Shifrin

Allergies change with time. My dad ended up allergic to all sorts of stuff later in life, and other allergies went away.

leslie townes

20:36

she's also 98th percentile in height and weight. she is enormous.

i developed a sensitivity to cheese in my mid-30s. i have to ration it out.

it's not an exclusion thing, but i can't eat cheese every day of the week. there were many years when i did. then i broke out in hives and the doctor told me to stop doing that, so i did, and the hives lasted a year longer, and then stopped.

Manjoy Das

$\frac{\partial}{\partial x}f(x,y,\phi(x,y))=\dfrac{\partial f}{\partial z}.\dfrac{\partial \phi}{\partial x}$ isn't it?c@TedShifrin

leslie townes

the first time i broke out in hives i was referred to a dermatologist in south boston on what might have been the hottest day in new england in several years. i had no car. i took me 2.5 hours to get there on public transit. the first recommendation i received was to stay indoors in cool environments and not be in the heat.

thanks, doc.

Ted Shifrin

No @Manjoy. You're missing the $\dfrac{\partial f}{\partial x}$ term.

Manjoy Das

oh yes

Ted Shifrin

So that's where the formula for $\partial\phi/\partial x$ with the negative sign comes from.

Manjoy Das

20:40

$\dfrac{\partial f}{\partial x}+\dfrac{\partial f}{\partial z}.\dfrac{\partial \phi}{\partial x}$

Ted Shifrin

Right, $=0$.

leslie townes

sounds good.

Ted Shifrin

@Leslie In my 10 years in the Boston area, I did a fair amount of red line and green line.

leslie townes

the weirdest thing about law school for me is that i was within walking distance of my aunt's apartment (i could see her balcony from many places on campus) and one train stop from my other aunt's house. they knew i was there, i knew they were there. we never visited with each other although i think i saw my aunt on the street once.

Manjoy Das

thanks a lot @TedShifrin

leslie townes

20:43

when people talk about connecting to family, it's like hearing reports from a distant world where society is organized differently. we don't do that in my family

Ted Shifrin

@Manjoy In case you haven't figured it out before, the implicit differentiation you learned in first term calculus is just this formula: If $f(x,y)=0$ defines $y$ (locally) as a function of $x$, then $dy/dx = -\dfrac{\partial f/\partial x}{\partial f/\partial y}$.

Now that is a remote family, @leslie. Even my family wasn't that bad, but sadly I haven't seen some of my favorite cousins since my twenties. I've lost even the ones in my generation.

leslie townes

my stepsister apparently married her longtime companion over zoom the other day. i was like, "emoji" to that. i wonder what it's like to live in a closer family. advice columns totally perplex me. i'm like "who cares? why does anyone care?"

i met my dad's brother maybe twice before he died. i met all of my grandparents for about one or two hours and they're all dead now. i don't get the family togetherness thing. but i do wish my daughter could meet my parents.

i don't even know what my grandparents looked like

we're waiting for the vaccination to go through, and then she's going to be bombarded by grandparents. hopefully for several weeks while i can draft legal documents.

Manjoy Das

@TedShifrin i read it but was out of my memory

Ted Shifrin

Well, you learned to do it without knowing partial derivatives. I'm just saying this formula is what you were taught to do mechanically without the implicit function theorem. :)

@leslietownes BTW, don't do stuff like this. It screws up my screen on my browser every time.

leslie townes

apologies. i will work around it.

in retrospect it looks like garbage on my screen too.

you forget that the dollar sign symbol has special meaning.

Ted Shifrin

20:52

Not if you've TeXed as much as I have in 35 years.

leslie townes

i only began texing in the late 1990s.

i think you acquire the habits of whatever form of tex/latex existed at your first exposure. i worked with a guy, tom marschak, who had all of these weird tex-but-not-latex habits. it was chaotic. i told him that the world had evolved, but he wouldn't evolve with it.

he had this insane set of macros and i was like "this was worked out in 1995, at the absolute latest. you can do it with actual codes now and not your homebrew." he wasn't interested.

Ted Shifrin

I said this in here recently, but I started with AMSTeX and before the end of my first book had switched to LaTeX. Revising the book, changing problem numbers, reordering theorems, etc., was just insane. Every change meant hours of search and replaces.

leslie townes

amstex, god. someone else i worked with used that

neverending nightmare.

robjohn

@TedShifrin I fixed it. It should only mess up things if ChatJax is running. There were single $'s in the line.

monoidaltransform

0

Q: Covariant derivatives along curves proof explanation

I am curious about the following proof of uniqueness for covariant derivatives along curves. Proposition: There is precisely one operation $\frac{D}{dt}$ from $C^{\infty}$ vector fields along $c: I=(a,b)\rightarrow M$ ( a curve in $M$) such that $\frac{D(V+W)}{dt}=\frac{DV}{dt}+\frac{DW}{dt}$ $...

PM 2Ring

21:00

You could probably write code to do the search & replace. Sure, writing that code might take longer than doing the search & replace manually, but it'd be less mind-numbing. :)

Ted Shifrin

Thanks, @robjohn.

robjohn

just have to use \$ instead.

Without ChatJax running, you see lots of \$'s in that line. Oh, well.

robjohn

21:15

Oops... I killed Ted.

dc3rd

😂😂😂

geocalc33

when you exponentiate matrices that are elements of $\text{SL}(2,\Bbb R)$

robjohn

@geocalc33 Is that all it takes?

geocalc33

$\rho_T=\pmatrix{e^T&0\\ 0&e^{-T}}$. And $\det(\rho_T)=1$ $\forall T\ge0$ with $T \in \Bbb R$

@robjohn yes

therefore $\rho_T \in \text{SL}(2,\Bbb R)$

so hence we exponentiate to kill

jk lol

$\exp(\rho_T)$ is no longer an element of the special linear group over the reals, precisely because the determinant is not 1. Am I right?

robjohn

21:31

Matrices only kill on null spaces. If Ted happens to venture into one, not my problem.

Null spaces of exponentiated matrices are rather small.

geocalc33

I'm looking for a reference on the first quadrant model of the hyperbolic plane

even better, if someone knows how to map the upper half plane model to the first quadrant

Hyperbolic coordinates

In mathematics, hyperbolic coordinates are a method of locating points in quadrant I of the Cartesian plane { ( x , y ) : x > 0 , y > 0 } = Q {\displaystyle \{(x,y)\ :\ x>0,\ y>0\ \}=Q} .Hyperbolic coordinates take values in the hyperbolic plane defined as: H P = { ( u , v ) : u...

this is what I found

robjohn

22:10

@geocalc33 other than what is given in that article?

Ted Shifrin

22:41

@robjohn Did you?

Ted Shifrin

23:47

Hi, DogAteMy.

robjohn

23:59

@TedShifrin I guess it didn’t take.

Ted Shifrin

You'll be proud of my loss of cool here.

Transcript for

$Mathematics$ Mathematics