Mathematics - 2021-03-09 (page 1 of 2)

Ted Shifrin

1:12 AM

smacks Thor for his tautological answer

anakhro

:O

leslie townes

the zariski topology is perversion and self-abuse. the strong boy will 'cut it out'

or girl

or anything in between

anakhro

@TedShifrin what are your opinions on the aversion to choosing a basis unless absolutely necessary?

Same with metric, I guess.

Thorgott

i think a point is a pretty great example of a discrete space

leslie townes

when i put 'cut it out' in quotes i'm referencing a social hygiene pamphlet from the 1920s. specifically the 'outdoor life' page of thesocietypages.org/socimages/2011/10/15/sex-and-social-hygiene

a point is a wonderful example of a discrete space.

it may be prehistoric to say it out loud, but the zariski topology may hinder people's progress toward a vigorous manhood.

4

Thorgott

1:19 AM

lmao

anakhro

@leslietownes what beef do you have with the second best topology?

user2154420

Are there any algebraic geometers in this chat?

leslie townes

it's just a goofy topology. i saw a friend of mine introduced to it, and suddenly it was all he was doing. it's like heroin. not even once.

Edward Evans

why not

leslie townes

what people ought to be paying attention to are weak and weak-star toplogies on function spaces. everything else is goofing around.

Ted Shifrin

1:33 AM

@anakhro Depends on the context. As someone who likes to use moving frames in geometry, I obviously cannot be too strongly opposed to working with (moving) bases. In algebro-geometric things, we obviously don't want to use a hermitian metric to stay in the holomorphic/algebraic category. As I said, depends on context.

user2154420

Does an algebraic geometer have an opinion on this:
https://math.stackexchange.com/questions/4053116/prime-ideal-after-modding-out-by-homogenizing-variable-implies-original-ideal-pr

Ted Shifrin

I could never care about those, @leslie. You lose.

user2154420

This isn't homework, but it's been bothering me a lot recently

Thorgott

the best topology obviously being the quotient topology

leslie townes

my zen master said that sometimes it is necessary to fight a losing battle. that's what i'm doing, here and everywhere.

Ted Shifrin

1:35 AM

@user2154420 I do not think about algebraic geometry in terms of algebra, but I would say that geometrically Daniel Hast's comments are on the money. We're just lifting the projective variety to the affine cone and geometry is the same up and down.

leslie townes

he also said that the buddha taught us to joyfully participate in the sorrows of life. i do not include the zariski toplogy in that. i refuse to participate in it, joyfully or otherwise.

i do agree that it might be one of the sorrows of life.

Ted Shifrin

Why are three- and four-year old posts all of a sudden becoming active? It's nuts.

leslie townes

i'm here for it. most of my posts are about 8 years old. give me those upvotes. when i get to 10k reputation, i'll become the mayor of long beach.

Ted Shifrin

I just added a pedagogical comment to someone from 3+ years ago.

leslie townes

that's how it works, right?

Ted Shifrin

1:39 AM

Upvoting doesn't make posts active, no.

Whether Long Beach is insane enough to elect you is a totally different matter.

Why did I just get invited to a chat in Theme Decisions?

leslie townes

our mayor is actually pretty good. i think i could be elected in my hometown, but they kicked me out long ago. i do know the DA there. i could kill people and not be prosecuted. but i don't because i'm a good person.

Ted Shifrin

Oh, you're right. You do emulate Trompolini.

leslie townes

i'm having my bedroom done with gold leaf on some of the fixtures. it's great. saddam hussein would have loved it.

Ted Shifrin

Only if you put a golden toilet in it.

leslie townes

we're starting with brass. i need more money from the russians

Ted Shifrin

1:43 AM

Maybe brushed nickel is more your speed.

leslie townes

my wedding ring is something like that. it's brushed something. it was cheaper than the other metals.

it's a chromium alloy. i looked it up. it was definitely brushed.

Ted Shifrin

This is why you're so fond of brush-offs.

leslie townes

it's been massively damaged by me using metal door handles. it scratches at a moment's provocation.

Ted Shifrin

Not remotely cheap man's diamond.

leslie townes

it cost something like $120. i think anything relating to marriage is a scam so i got off easy.

my wife's ring was over my credit limit at the time, so she ended up buying it and i wrote her a check. true story.

Ted Shifrin

1:54 AM

We won't ask her if you were worth the credit risk.

leslie townes

definitely not.

mick

3:57 AM

Hi

0

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

In mathematics, 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 octonio...

Shobhit

4:38 AM

hello

leslie townes

good evening.

Shobhit

hello @TedShifrin

leslie townes

mick, re your question, division algebras and related ideas freak me out. that the dimensions of known examples were the only examples was not proved until, like, the 1950s? and only using algebraic topology of spheres? frightening.

Snapdragon-X

It's morning here!

Ted Shifrin

Hi @Shobhit

Shobhit

4:43 AM

I need help with $\lim_{n \to \infty} n.\sin(2\pi e .n!)$. Since $-1 \le \sin(x) \le 1$, I thought this would diverge, but it's given that it's a finite limit, and the proof is very ugly. Can someone help with an "easy proof" or a helpful tip? Thanks

Snapdragon-X

@Shobhit use stirling for factorial

leslie townes

math.stackexchange.com/questions/76097/… purports to solve this. the question relates to the proximity of 2pi e n! to multiples of pi.

which does implicate stirling's formula, as snapdragon notes.

i don't think you need too precise a version of the formula to evaluate the limit, or at least that solver doesn't seem to need one.

copper.hat

Good evening.

leslie townes

good evening, morning, or afternoon to all.

or brunch time. if someone's having brunch, happy brunch.

copper.hat

I'm heading straight to my glass of white.

leslie townes

4:50 AM

my favorite white varietal is gruner veltliner. the best ones are from austria. sometimes it tastes like lentils, other times it tastes like licking wet rocks. don't ask me how i know that. it's wonderful.

copper.hat

i'll add to my to taste list.

i have a preference for reds, but find they completely inhibit any mathematical thought and have the opposite effect on my vocal cords.

i like light, dry if white, pinos, etc.

Shobhit

got it, finally. thanks, @Snapdragon-X @leslietownes

leslie townes

my dad is similarly a red partisan. i grew up in napa, which is mostly known for its reds. i like wine that tastes like mineral water.

germany has so many great white wines, but they're mostly too sweet for me. and france goes all in on oaky whites. austria is the place to be.

copper.hat

to each their own. many years ago the was a wine glut in norcal and the spillover was taken and made its way into tjs two buck chuck.

leslie townes

chateau de I-5. i'm a fan of it.

value for money is what that is.

copper.hat

4:55 AM

i used to go, buy a bottle to taste, and then a few boxes if it was ok.

currently waiting on a case of 2016 Chateau Lynch-Moussas Pauillac from france.

i think they lifted the tariffs again.

leslie townes

no more of the EU strangulations? i get a commission every time i say EU strangulations on social media. i think this counts.

copper.hat

do not get the notion that i 'know' wines from the above. i find something i like and just buy it again and again

:-)

i want ireland to separate slightly from the eu.

but i don't live there so not my call...

leslie townes

i've only visited england, scotland, denmark, and sweden. all of whom i think opted out of the euro. they adopted the euro while i was in sweden and i still paid for things in kronor.

maybe it's different now. i wouldn't mind some euros in my bank account, frankly

copper.hat

yeah, i have a complicated euro setup. the whole money laundering thing really made life difficult for people who have lives in two countries.

leslie townes

ireland was a tax haven for a short while. i think they cut that off. there are still other jurisdictions.

copper.hat

5:01 AM

ireland still has some autonomy in that regard, which they should, i believe.

france & germany feel free to ignore rules when it suits.

leslie townes

i'm an attorney in real life and i've had moments where it's like, "i won't even ask why you're incorporated in the isle of man. i can guess. but anyway, if you put this money in the US the tax authority will know about it." that is usually the end of the conversation.

copper.hat

well, i am a good boy and do my fasb or whatever it is

leslie townes

that's the big somewhat legitimate knock against the EU. it's france and germany. we have the same problem in the states in our national politics, CA vs. TX and everyone else is along for the ride.

copper.hat

but i do feel that money i received from sources that have nothing whateosver to do with the usa should remain out of sight of the us authorities.

just on the lines that it is none of their business. taxes paid, etc.

leslie townes

yeah, i think the US is one of the only countries on earth that still taxes income from whatever source (perhaps subject to deductions). we want jurisdiction over everything.

copper.hat

5:04 AM

i think it hails from a more colonial perspective

irony

leslie townes

eritrea does it, or did it.

copper.hat

it is not like i have lots of money stashed away

leslie townes

the philippines gave it up a couple of years ago.

copper.hat

unfortunately

leslie townes

colonies, all of them, and we were a colony. we should give it up.

copper.hat

5:06 AM

i have an issue with an irish account at the moment, but it is hard to resolve as a non resident.

such a pain.

leslie townes

there is a section of the code where you can exclude a fixed sum of money from income. but by excluding it you also can't get credit for foreign tax you pay on that income. which is, not great.

copper.hat

taxing software is challenging.

my daughter is wondering if she gets paid as an intern in the uk if she has to pay us taxes. its stupid that a 20 yo has to even consider these things.

certainly i did not at that age.

leslie townes

it's quite dumb. we advised a band once for touring the united states. they needed to set up a US shell to get their US-sourced income or it would be taxed twice. nobody is thinking about this. nobody should be thinking about this. least of all people who can do guitar solos.

copper.hat

it takes some time to realise that the usa is really a great place

if you are wealthy

and can afford to have people take care of all the details.

leslie townes

i'm trying to get to a point where i can have people take care of everything. that's definitely the rule. otherwise, good luck

copper.hat

5:12 AM

even little things like putting assets in trusts are complicated.

been a while, i have regressed for a variety of reasons. mostly i am an expert at finding financial potholes :-).

leslie townes

trust stuff is weird. in my own experience, attorneys who are involved in that area either serve the hyper-wealthy, or grift the non-hyper-wealthy. there's no middle ground where you can just pay normal amounts of money to get normal advice for a normal person.

immigration law is the same.

i'll just say it, the USA sucks.

copper.hat

yep, i can attest to that.

i had to call in a politcal favor to get my citizenship moving.

and they still lost my paperwork the day of my citizenship.

leslie townes

criminal law is also the same, which has all sorts of social justice implications. you get the world's best service, or you get some insomniac who can't remember what your last name is.

just bring a big bag of money if you come to america. things will go well for you.

copper.hat

that is true more broadly than the usa...

i mean the criminal law...

i do think plea bargaining is insane.

then again, jury trials...

i have never made it to a jury

leslie townes

it's the cheap way of clearing a case. there's basically nothing resembling a jury trial for most stuff. i mean, juries suck and i've seen that too. the USA is also weird in following english common law as a model, yet persisting with using juries in civil trials. most countries have dispensed with that.

copper.hat

5:18 AM

partly it is because it is such a huge country with many jurisdictions...

leslie townes

we did a trial once where our jury analysis firm had found one of the members selected to be a deranged lunatic. he had a website that was very anti semitic, and we and our clients were very semitic. but we liked him for other reasons. he was like a joker card. everyone else was going to be against us.

it was so divorced from anything resembling the merits of the proceeding. that's what i remember.

copper.hat

if i have an issue in ireland there re two things (1) i can probably find someone who knows & can help and (2) even the government people are human and tend to work with you if you are reasonable.

i am still trying to figure out how to get my daughter's passport renewed without calling a favor. they replied to her today (i asked her to email them), but nothing useful.

i think i would go mad in a jury.

leslie townes

my sister has had good experiences with state job assistance in california. it was as good as therapy, which she definitely needs but cannot afford. the people in the job assistance office were unbelievably helpful. and followed up.

copper.hat

that is good to hear.

whats with the bob hope thing?

leslie townes

i like his films. i realize he was a toxic person.

copper.hat

5:22 AM

:-). everyone has good & bad.

Ted Shifrin

I'm purely good!

leslie townes

i love all of the 'road' movies, even the shitty ones. my true idol is WC Fields but he doesn't have as rich as a pseudonym.

copper.hat

i know a number of decent folks with decidedly questionable pasts.

leslie townes

when i take the DND test it says i am true neutral. neutral neutral everything.

copper.hat

@TedShifrin We know you are good :-).

Ted Shifrin

5:23 AM

Ha ha.

copper.hat

my tastes, like my wine, are simpler.

leslie townes

he's guzzling thunderbird. that's what he's trying to say.

there's no shame in it

Ted Shifrin

Even if it kills me?

dc3rd

Hellloooo @TedShifrin, so...going through some of the previously done chapters and I'm running into an issue expressing the linear transformation. So for direct reference it is example f, on pg 28.

I was trying to derive the matrix $B$. The one representing the reflection.

leslie townes

don't do it if it kills you. that's my motto.

copper.hat

5:25 AM

@TedShifrin My Artin arrived, will take a look shortly.

Ted Shifrin

Oh great!

Go on, @dc3rd

leslie townes

i also like deriving matrices. i do not have example f in front of me.

Ted Shifrin

It's geometric !

copper.hat

it is essentially a two dimensional sort of thing (not really).

dc3rd

So given that I do have the vector $(1,2)$, I was trying to get the expression for the points. Since I couldn't see what to do right away, I referred back to the basic expression used to represent a reflection in the line $y=x$, which is $(y,x)$.

Using that idea, I worked out the equation of the line for this set: $y = 2x$

leslie townes

5:28 AM

it is not quite a swap of coordinates in that case. although this is icky geometry. i feel befouled by it.

dc3rd

This being the case, I had determined that the "reflected corrdinates should be $(x,y) \to (y/2, 2x)$........

Ted Shifrin

Where do the standard basis vectors go?

copper.hat

Reflect $e_1,e_2$ and see what you get.

Bingo

dc3rd

but now writing this out again it doesn't seem right.

leslie townes

where the standard basis vectors go is absolutely the question.

the entire problem is just two problems. where do (1,0) and (0,1) go.

dc3rd

5:30 AM

I did use the standard basis vectors after I "derived" my expression. They ended up being: $(1,0) \to (0,2)$ and $(0,1) \to (1/2,0)$

Ted Shifrin

Draw pictures. What part is along the line and what part is orthogonal?

No.

You're not thinking,

copper.hat

I am screaming in agreement with Ted.

leslie townes

i limit my approval of all of this to the extent it does not implicate geometry or pictures. but a picture would probably very much help here.

Ted Shifrin

Later we learn better ways to do this, but now you have to use projection and draw pictures.

Should I muzzle leslie yet?

leslie townes

i said it would help. you win. OK? you just win on this.

Ted Shifrin

5:32 AM

scores

leslie townes

i can't believe what i'm even saying, but yes, draw a picture.

copper.hat

its the only way really...

Ted Shifrin

I have evil powers in here.

leslie townes

it might be. i think i need an appointment with my therapist.

Ted Shifrin

Two.

leslie townes

5:34 AM

and my wife's therapist. she wants to meet me for some reason. i think it's just to increase her income and not to figure stuff out.

copper.hat

my therapist is rifle range road in tilden

Ted Shifrin

Oh oh. Three, but not all my fault.

leslie townes

i saw a bobcat there once. i love wild animals.

dc3rd

So I don't know if my reflection drawing is shitty, but I drew a line and reflected it in the $(1,2)$ vector and it "appeared" perpendicular....is that the right idea?

leslie townes

you have my complete understanding if your drawing is "shitty." i have never done a non-shitty drawing.

copper.hat

5:36 AM

i was going to take a pic of my notebook where is try to find a nice geometric explanation for the det=ab-bc formula after a few glasses of wine. but its too embarrassing.

Ted Shifrin

Do some arithmetic. Use projections.

leslie townes

it's less important that it be shitty than that it be accurate. test the picture with algebra.

copper.hat

get some graph paper or whatever its called in the usa.

Ted Shifrin

Still isn't accurate.

dc3rd

projections are involved eh?, well I worked out matrix $A$ using projections so I'll work with this hint. give me 5

copper.hat

5:37 AM

forget about the matrix

Ted Shifrin

Sure.

copper.hat

find where the basis vectors go.

leslie townes

you might even just draw the point and try to see what it seems to correspond to.

this is profanity from me. it's impossible. i can't believe what i'm saying.

copper.hat

pictures are beautiful.

dc3rd

not even concerned with the matrix @copper.hat, I know how that comes about. I wanted to derive the explicit linear transformation and then verify it with the standard basis vectors

copper.hat

5:38 AM

would it be math porn to redo rudin with pictures?

leslie townes

Rudin After Dark

Rudin Nights

i'm here for it

copper.hat

then you need to think of parallel and perpendicular to the $y=x$ line.

Leonhard Euler

can (or rather, should) we learn something from the documentation?

I sometimes find the documentation hard to understand

copper.hat

@dc3rd let $v_1$ be a unit vector along the line $x=y$ and $v_2$ a unit vector perpendicular to that. Then $v = \langle v_1, x \rangle v_1 + \langle v_2, x \rangle v_2$. What will $Lv$ be, where $L$ is your reflection?

leslie townes

that was the funniest thing about the admonishment to RTFM. which i haven't seen since the 90s but i presume people still do. nobody thinks that TFM might be written by someone who is not shakespeare. putting it mildly.

copper.hat

5:47 AM

it used to be that clive molers matlab (fortran back then) would reply with RTFM if you typed help.

Ted Shifrin

Why $y=x$? We're reflecting across $(1,2)$.

copper.hat

my apologies, i thought i saw $y=x$ somewhere.

this is a problem i deal with all day at work, overlapping threads of conversations, inevitably some stuff gets lost...

leslie townes

i really like my office's IT people. once i asked them something, and it was not documented, and they said "we're asking microsoft about this." like grown ups. RTFM is edgy but doesn't get you very far. and i understand that RTFM is a proper response to 99% of requests.

Ted Shifrin

@copper The $y=x$ example is done in the text.

leslie townes

sadly math.SE seems to mostly be RTFD (definitions) these days.

copper.hat

5:51 AM

@TedShifrin i see, sry about the noise.

leslie townes

but that is what it is, i don't need to stomp on people.

copper.hat

i find, when dealing with customers, it is faster for me to read the manual and tell them.

besides, time is money :-).

echos of brendan behan.

guy was a genius.

leslie townes

behan comes back all of the time, whether you want him to or not.

copper.hat

emerson, mark twain, etc. gems.

behan was not house trained.

that would be oscar wilde.

leslie townes

we have clients who sometimes tell us, "we get that, but it needs to be this way." and it's like, OK, that's the world of make believe. that's where mr. rogers had the puppets. come back to reality, we do not lie in court for our clients.

dylan thomas had some good ones too.

copper.hat

5:54 AM

ah yes

Ted Shifrin

Tromp's lawyers lie in court all the time .

copper.hat

customers always want the impossible.

Ted Shifrin

Sorta like parents of college students.

copper.hat

alternative reality they call it, i think.

trump was just a nasty person.

leslie townes

i know a guy who was appointed to a lifetime judgeship by trump. he is, surprisingly, not an asshole. trump's friends will be repeatedly disappointed.

Ted Shifrin

5:56 AM

Still is.

copper.hat

the problem is that everything he did is tarred by his obnoxious persona.

leslie townes

he turned everything into a vote on how much you loved him. that was his toxic essence.

public health, well, how do you feel about trump?

blegh

copper.hat

education?

still, he had a few followers.

leslie townes

one time when i was teaching the parent of one of my students left a nasty message on my answering machine after a midterm grade. implying that it would not go well for me if i didn't change it. i was on the last year of a three-year postdoc. it was a weird and shitty threat.

copper.hat

wow, the parents got involved???

they left a recorded message?

leslie townes

5:59 AM

yeah it was the dumbest thing imaginable. i knew the dean, he was basically the person who hired me.

Ted Shifrin

Damn yes. The new era. Heard of helicopter parents?

leslie townes

we giggled about it a little and hit the delete button.

copper.hat

i am one, but i am certainly not getting into my kid;s college grades.

leslie townes

here's a sonnet i like as we leave winter. romantic-circles.org/editions/poets/texts/emmonsail.html

if you read it out loud, it's simply wonderful.

copper.hat

its ornithologist porn.

leslie townes

6:02 AM

yeah i'm a birder. you spotted that.

copper.hat

There was a young man
From Cork who go limericks
And Haikus confused

Ted Shifrin

Spotted wren.

copper.hat

i was attacked by an ostrich once.

leslie townes

my daughter's middle name is wren.

an ostrich kicked me once, too.

they can really kick.

Leonhard Euler

ostriches are athletic XD

copper.hat

6:04 AM

well, to be fair, i was holding on to its neck.

dc3rd

Question: Should I be projecting onto my vector$(1,2)$ like in matrix $A$ @TedShifrin?

copper.hat

two of my brothers wanted the middle name of their children to be Danger.

leslie townes

i was just trying to vibe with the ostrich. i was doing a report on ostriches for my fourth grade class. my dad knew a guy who had an ostrich farm, we went there, obtained pieces of ostrich eggshells, and met an ostrich. who was anxious and kicked me.

i still have a pic somewhere of me with the ostrich, post-kick. we made friends.

copper.hat

i got whacked in the head by its beak. it hurt.

scanning back to make amends for my earlier misleading comments

leslie townes

i got marked off a little bit because in my ostrich report i drew an ostrich in a way that suggested it had four, and not two, legs. i think my fourth grade teacher was a little persnickety about that.

i later met his brother at a math conference, and we had no idea who each other were, and then narrowed it down, "wait, is your brother the guy who teaches fourth grade?" "yes." we're all friends now.

copper.hat

6:08 AM

i can't find the original question so i can't make amends.

ostrich is tasty.

leslie townes

anyway it was weird that my fourth grade teacher turned out to have a brother who was a functional analyst that i separately met. functional analysis is not a large world.

eating an ostrich burger was part of my report. it was delicious.

copper.hat

at some point my daughter and myself (elementary school time) wanted to make a one egg omelet for her friends (but not tell them it was an ostrich egg, of course).

how did you get into mathematics from law or whichever came first?

the nearest ostrich egg was gilroy, but that was too far for a single egg.

andronicos used to carry them at some stage.

leslie townes

i started in math. some of my friends from undergrad had gone from math BA to law and seemed OK with it. i needed a way to make money. my family kind of fell apart while i was doing a postdoc and i couldn't do anything for them on postdoc wages. and it was just, how do i get some money.

it worked. it might not have been best for my mental health, but it worked.

copper.hat

$ > mental health

one you need, the other is optional

leslie townes

i basically had to quit academia because my mother might have been dying and i couldn't afford a live-in nurse. the cash grab did work. we're all happy now.

love_sodam

6:12 AM

what is an example of a ring wu

copper.hat

@dc3rd Are you reflecting in the line through $(1,2)$?

love_sodam

whose zariski topology is trivial?

leslie townes

the strong boy will "cut it out"

dc3rd

Yes @copper.hat, that's the line I'm supposed to be reflecting across

copper.hat

medical is tough here.

@dc3rd let $v_1 = {1 \over \sqrt{5}}(1,2)$ and $v_2 = {1 \over \sqrt{5}}(-2,1)$. Write $v = \langle v_1, x \rangle v_1 + \langle v_2, x \rangle v_2$. What does $Lv$ look like?

leslie townes

6:16 AM

my mom was a nurse when she was able to work. she dealt with a lot of death and maybe was too direct with me about what she was seeing. in the late 80s and early 90s a lot of people were dying of AIDS in our area and she had to deal with extremely negative family situations. it's probably some form of trauma

the important thing is she has my amazon account for groceries and we're all just waiting out this pandemic now

dc3rd

$Lv = <v_{1},x>Lv_{1} + <v_{2},x>Lv_{2}$.

copper.hat

@dc3rd Yes, but how does $L$ operate on vectors parallel & perpendicular to the line in question?

yeah, my mom passed last november. luckily i was at her bedside at the time. no mean feat given that she was in a home and the whole quarantine/covid thing going on.

leslie townes

i can't imagine not seeing people anymore, through this pandemic stuff. i want everybody to make it through to where i can see them again.

copper.hat

sorry, i made some sort of connection there and for the life of me cannot imagine what it was now!

oh, yea the amazon account.

dc3rd

@copper.hat I think that is what I'm trying to "see" either algebraically or geometrically. I know it will be similar to the regular $y=x$ case, but not completely the same.....

copper.hat

6:21 AM

my 90 year old god mother just got her vaccination today, i am very happy to say.

@dc3rd How would $L$ map the vector $v_1$?

leslie townes

that's wonderful. 90 years. i wouldn't wish that on anybody but i like hearing about it.

copper.hat

she's in great shape (for 90)

still drives.

leslie townes

it's similar to the y=x case in the sense that the picture looks the same. i hate saying this, but have you drawn the picture?

Leonhard Euler

One of my neighbors is 94 years old

copper.hat

she is unmarried. at 70, one of her exs proposed again. my sister asked her why, my aunt replied "i'm waiting for the right person".

dc3rd

6:24 AM

@leslietownes, yes. It is very similar to it. So let me work up to this scenario......In the $y=x$ case $L$ would map $v_{1}$ to $\frac{1}{\sqrt5}(2,1)$

copper.hat

And $v_2$?

leslie townes

my grandmother had a very unusual mental lapse. she had alzheimers. it affected her ability to drive. she could still sit in the driving seat and drive around and whatever. but if you put her in the passenger seat she could not attach her seatbelt. sidedness, orientation, handedness, they're nontrivial things.

Semiclassical

so here's a heck of a workaround

copper.hat

dementia is painful for everyone.

Semiclassical

my collaborator uses keynote, and i'm trying to dig through their stuff to get started on an upcoming presentation

but i have windows, not mac. luckily i have an iphone and thus access to icloud. so i can edit the presentations via keynote for icloud

that's not the workaround

dc3rd

6:26 AM

$v_{2} \to \frac{1}{\sqrt{5}}(1,-2)$

copper.hat

nope

leslie townes

i don't like keynote. a guy i work with does that too. can you just email me what you want? no, it's somewhere in keynote.

Semiclassical

the obstacle is that i can't figure out how to copy slides from one presentation to another within icloud

searched around a bunch, nada. it's trivial in keynote for mac but nada for icloud

...but, iphone does have keynote as well :)

leslie townes

my five year old cell phone crashes if i get a text massage while i'm on a phone call or vice versa.

copper.hat

sorry, not appl here. not since tim cook refused to let my company put the aapl logo on our website ;-).

leslie townes

6:28 AM

we're not having keynote.

Semiclassical

so i get on my phone, open up keynote, copy/paste the slides within keynote on my phone, and edit them on icloud

and i'll have to do that every time i want to copy/paste from one presentation to another. the shortest distance between two presentations on icloud is through my iphone

yaaaaaaaay

copper.hat

productivity tools.

@dc3rd think in terms of $v_1,v_2$ Where does $Lv_2$ end up? Visually.

dc3rd

writing out the diagram right now @copper.hat

copper.hat

Note that $v_2 \bot v_1$.

dc3rd

and I see why it was a "nope for the second one...

Semiclassical

6:30 AM

huh, didn't know $\bot$ was upsidedown $\perp$

copper.hat

a drawing is always my first step.

Semiclassical

wait

is \bot just \perp

copper.hat

i just can't get myself to type perp

leslie townes

if i'm being entirely honest, a drawing is also my first step.

Semiclassical

then what was i trying to remember as upside-down perp

right, \top

...\bot is just \top flipped. of course

copper.hat

6:32 AM

i always struggle to place stuff above & below arrows.

@dc3rd you re thinking or drawing too much.

leslie townes

tex just sucks for that stuff. or mathjax or whatever.

Leonhard Euler

Homework spelt backwards is krowemoh

which means child abuse in latin

copper.hat

i find that hard to believe.

dc3rd

defintiely the thinking......Ted's here to blast me...looking at it $v_{2} \to \frac{1}{\sqrt{5}}(-1,-2)$

leslie townes

@LeonhardEuler I verify the truth of the first of your statements. we may need to discuss about the latin.

Ted Shifrin

6:36 AM

@Semiclassical So is \top.

copper.hat

@dc3rd $v_2$ is perpendicular to the line through $(1,2)$.

Where does your reflection end up in the mirror?

Semiclassical

yeah, i got mixed up

copper.hat

@dc3rd imgur.com/a/jGsKaxT

dc3rd

@copper.hat the reflection in the mirror is really telling me $\frac{1}{\sqrt{5}}(1.-2)$....

copper.hat

nope

dc3rd

6:45 AM

let me see what your image says..

copper.hat

you don't really need specific number here.

that is why i have $v_1,v_2$.

dc3rd

actually I can't even access your image....I put up productivity blockers so I can't acces imgr at the moment

copper.hat

:-)

Ted Shifrin

@dc3rd What you need to realize is that the part of a vector parallel to $(1,2)$ stays the same, and the part orthogonal to that reflects, i.e., turns into its negative. Do you understand that?

That's what reflection in a mirror does.

dc3rd

@TedShifrin yes I understand that explanation.

copper.hat

6:49 AM

So what is $Lv_2$ in terms of $v_1,v_2$?

Ted Shifrin

So the part parallel to it is the projection. What's orthogonal is what you get by subtracting.

@Copper is asking you to rephrase what we just said.

His approach is ultimately the right approach when we get to chapter 9 (although you may have gotten there in other books).

dc3rd

using inner product coefficients to express things. I've seen it and vaguely remember its workings. But for now it is this foundation I'll work with