Mathematics - 2021-06-26 (page 1 of 3)

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12:03 AM

span, naps, pans, snap, ...

just mixing it up

PNAS.

who rejected my recommendations on a paper.

shame on them.

How dare they

12:42 AM

@Leslie Did you just utter the word "geometrically"?

@Ladiesandgentlemen Huh?

Ladies and gentlemen

1:29 AM

yeah, it's for 2-dimensional vector spaces

if you want to prove it for 2 vectors, you just need to prove it in the space spanned by those 2 vectors

i may have

It holds in infinite-dimensional inner product spaces. Why should we artificially think 2 dimensions? You do not want to use trig in the general setting.

@leslietownes May Olivia scratch you.

Ladies and gentlemen

Initially I thought it was kind of cool it worked for infinite dimensional vector spaces so seemlessly

she did

Ladies and gentlemen

but the reason it does is just that it's a statement about dim 2 spaces

1:36 AM

did it also work seamlessly?

Ladies and gentlemen

what did?

Nah, Inclaim

Ladies and gentlemen

Well my point was just that I was sort of impressed it worked for infinite dimensional vector spaces

i do love the 'trick' of specializing to the space spanned by your vectors.

Nah, I claim that’s the wrong understanding. I hate to be ungeometric for once.

Ladies and gentlemen

1:37 AM

that's very nice

You don't know that cos makes sense a priori for an arbitrary inner product.

Pedagogically for freshmen I agree, though.

Ladies and gentlemen

dang, I'm not a freshman :(

I'm a senior

well, I'm happy with my understandings even if they're wrong

Lovely comment.

Take pride in blindness.

Good for politics.

Ladies and gentlemen

I'm still struggling to see what you're saying about cos

but that's all good

That’s fine. I’m saying — why should 2D Euclidean geometry/trig make any sense in an arbitrary inner product space? I'm not quibbling about $\Bbb R^n$.

Ladies and gentlemen

1:44 AM

it needn't, but the space spanned by your two vectors is still a space with an inner product.

and the result given by the inequality is a result for that space

Not necessarily Euclidean geometry.

Why is $x \cdot y/|x||y|$ even a cosine?

Ladies and gentlemen

no, not necessarily euclidean

in any case I should just take it for granted that we won't ever agree on anything

Another lovely comment.

be careful what you wish for. i said something like that and ted and i agree all the time now.

Ladies and gentlemen

that wouldn't be bad

1:48 AM

I even took your side here, leslie.

Ladies and gentlemen

all I'm saying is that cauchy schwarz for dim <=2 implies general cauchy schwarz by taking a pair of vectors u,v and applying the result for the space spanned by them.

It's not a matter of “agreement.” I’m pointing out a mathematical subtlety. You can be a cancel culture person and deny it.

Only if you do an algebraic proof, not a geometric proof .

If it's not using 2D geometry, then of course.

Ladies and gentlemen

I'm talking about the cauchy-schwarz for inner-product spaces

The usual “correct” proof pays no attention to dimension.

Ladies and gentlemen

corre t ?

wtf that sounds like an innuendo in spanish

oh :)

yeah the proof pays no attention to dimension, and that seemed magical to me

1:52 AM

Give me a f***ing break. Typing in here on ipad sucks.

Ladies and gentlemen

I'm typing on a malfunctioning mechanical keyboard I soldered myself, it isn't much better

2:28 AM

@TedShifrin mobile browsers are icky in any case.

@TedShifrin this is a sign of the approach of the apocalypse.

Agreed.

What’s your take on the 2D suffices Cauchy-Schwarz discussion, @robjohn?

Ladies and gentlemen

clearly the correct one

the question that you had requested get reopen got reopened btw

Its a bit like saying convexity is a one dimensional thing. It is at some level but that is really a distraction, just like saying the words on a page are black and white.

Ladies and gentlemen

2:44 AM

how is it a distraction

@TedShifrin The proof I think of scales the case where $|u|=|v|=1$ and $0\le(u-v,u-v)=2-2(u,v)$

sorry for multipings

Why restrict to 2 dimensions?

@Ladiesandgentlemen Because it takes a moment of thought that adds no value.

Ladies and gentlemen

of course it adds value:

obviously you are invested in this.

Ladies and gentlemen

question: "why does it make sense for proof of cauchy schwarz to work so easy for infinite dim"

2:46 AM

Yes, I have that proof in my linear alg book, I think. The standard reason to restrict is to use trig, when e my complaint.

Ladies and gentlemen

answer: because you can just restrict to dim 2

@Ladiesandgentlemen I saw that, if you were talking to me

No, @Ladiesandgentlemen, you’re just not getting it.

You never restrict to dim 2 if you give a valid proof.

Ladies and gentlemen

whatever it doesn't matter

it's just a meta argument

No. You just don’t want to think.

Ladies and gentlemen

2:48 AM

oh ok

that must be the problem then

However, if someone has proven it in 2 dimensions, it generalizes quite easily by projecting onto the subspace spanned by the two vectors.

lots of results are of that form

Projecting? In infinite dimensions?

i would rather talk about $-{1 \over 12}$.

Ladies and gentlemen

I'll just stick to algebra and combinatorics I guess

2:50 AM

@TedShifrin two vectors will still span a two dimensional subspace

but I think I will bow out as I think I've interrupted a heated conversation.

Ladies and gentlemen

you were invited into the conversation.

But you’re not projecting. I don’t know what this 2D proof is, what I'm used to is invocation of trig.

that is my entry point usually :-)

Ladies and gentlemen

But there wasn't really a conversation.

I just said "this meta-argument is cool"

LOL @copper

Ladies and gentlemen

2:52 AM

but it wasnt apparently

tragic

don't get miffed

we have a lawyer on hand for these sorts of situations.

Ladies and gentlemen

I'm not, this is just how it works when I comment on geometry related things

maybe he's goofing off tonight.

Ladies and gentlemen

or lin alg

jeez! get miffed?! well, I never!

2:53 AM

i remember a time log ago when i got miffed

Ladies and gentlemen

What I said isn't false, it's just not kosher.

it seems

We still don’t know what your 2D proof is. If it’s dimension-independent, then this truly is a tempest in a teapot.

i'm still working through elementary group theory

Ladies and gentlemen

take two vectors u,v and suppose you want to prove the corresponding inequality

consider the space spanned by u and v. It is also an inner product space (with the same inner product).

by cauchy schwarz for low dim spaces the inequality holds in this space.

what is the proof in that low dim space?

Ladies and gentlemen

2:56 AM

cauchy schwarz for dimension 2 or 1 ?

whichever you like.

yes, let's start with 2

Ladies and gentlemen

There was one that I liked

It boils down to a polynomial having non-negative determinant I think

i think its sauvignon blanc time. wait, no, i need some wiper blades as we have some camphor trees.

Ladies and gentlemen

but what's the point?

to keep the windshield clear

Ladies and gentlemen

2:59 AM

my street name is camphor in spanish

@robjohn what's the point that you want to make when I give the proof?

ironically we live next to a street named thousand oaks with few in sight

I am just wondering if it is simply a multidimensional proof restricted to two dimensions, or if it is truly simpler by being in 2 dimensions.

Ladies and gentlemen

it is a multidimensional proof restricted to two dimensions

but the "multidimensional proof" exists within the two dimensional space

we got that part

@copper.hat Thousand Oaks (a city in Ventura County) is not far from here. However, you are probably talking about the community in the Bay Area.

or not

3:03 AM

yes, runs through albany & berkeley

all the way up to the arlington

Ladies and gentlemen

good night

It takes about 20 minutes to drive to TO

@Ladiesandgentlemen good night

i have been in to

@Ladiesandgentlemen good night, remember to sleep in 3 dimensions

i have two salvaged cars (my in laws gave them to us) but they don't have all the little details (EX vs whatever sort of thing) since there are no user manuals. And I need 3 wipers.

off to o'reilly i go

O'Reilly means books to me

It sounds as if you're going to a Pep Boys for wipers

:-)

used to be kragens here

3:11 AM

In my childhood and even later, there was BBB in Albany.

3:28 AM

we use wal-mart for wipers. i am not proud of this.

Nor should you be. I boycott Walmart. I go to Auto-Zone.

looks like there's one nearby. it's not on the way to work, but when was the last time i drove to work?

Work?

the chap in o'reilly's was very helpful, found all my blades, etc, just had to pay.

Costco has a good selection of wiper blades

3:39 AM

Some of us don’t belong.

good idea. i think my wife belongs although it is a bit of a drive.

@BalarkaSen THANK YOU! IT HELPED ALOT.

last time we went we bought a big thing of kitchen garbage bags. we're still working on it, i think we're two years in.

@leslietownes under 10 minute drive from here. I get my tires there.

Balarka is usually helpful, unlike some of us.

3:44 AM

Goose Chases R Us

3:58 AM

@copper There used to be the Thousand Oaks Theater.

4:25 AM

@TedShifrin Yeah, a bit sad the Oaks closed down.

There were plans for a fitness studio, I don't think it ever panned out.

yes, my in-laws buy ginormous costco quantities of stuff and then suffer through it forever. except when they often offload it here.

i don't need a 100gal drum of pico de gallo

i go there to get passport photos & our "christmas" card.

its amusing, i am looking at solano ave on google street view and there was a car following the camera, so it appears in most frames as you move the camera down the street.

yes, i have little to do at the moment.

Do 1-dimensional proofs of all theorems.

:-) why not zero?

Go for it.

i guess the appropriate question is what is the point :-)

zero dimensional pun

Got it.

No fun if you splain.

4:35 AM

just finished some nighttime freeway with my 17yo son, i am in an explicit mode at present

weird as that sounds

LOL

i agree, i'm winding down, it was a little tense (he's good, i'm just a little nervous).

1 hour later…

5:45 AM

my daughter will never drive a car. i've decided this. can't be trusted.

Of course these are the things to decide when she’s three.

yes. i figure it's best to plan this all out in advance.

she really likes tackling people. she tackled me maybe 30 times in a row before bed. i see a promising career in professional wrestling, maybe. also my chest hurts and i should have kids before 40.

6:01 AM

well, every path is different, but my son used to wrestle me a lot (he was/is a fairly large solid kid) but when he (& his sister) hit teens they no longer were affectionate (or wrestled). so you never know.

on the other hand, the majority of my nieces & nephews are quite affectionate.

perhaps a cultural thing

if she turns out to be genuinely affectionate it will be a first in our family

normally we say absolutely nothing and express nothing

latent irish tendency

overheard many decades ago in a working class chipper: girl: "don't you love me?", boy: "of course i do, don't i fla you and buy you chips?"

i am sure you can translate the colloquialism...

has to heard in a strong north cork (city) accent to be fully appreciated.

old irish wedding proposal: "do you want to be buried with my people?"

yes, we are an expressive group

hahaha

my mother's relatives are very funny at parties, expressive, 'gift of the gab' and every stereotype, but absolutely nothing personal ever

my son was heading out today and we were chatting at the front door. someone across the street was blasting their horn and i started gesticulating (in a maybe not so polite fashion) and the my son ran across the road and climbed into his friend's car.
later i pointed out that many could be be saved some embarrassment if he bothered to let me know that this was his friend picking him up.

when my grandmother died i don't think i saw anyone shed a tear, most of the discussion was about what to do with her car, her kitchen supplies, and clothing. this was discussed at the wake

6:09 AM

i have many such stories. guys especially cannot show grief.

we had a few (real) wakes in the family.

it's better to die of a heart attack at age 50 than show emotion ever.

a bit bewildering as a child.

its a way of dealing with stuff.

emotions are allowed to skip a generation.

or for unrelated friends

but god forbid

a parent/child relationship.

i wish i could go back and attend the wakes again :-)

seeing my parents express no emotion at a death in the family was, weirdly, a way of me appreciating how they were caring for me. the suppression of all emotions represented protecting me from, i don't know, feeling something.

haha

the way it worked growing up was that a close parent friend would tell you that your parents cared & loved you

my daughter's never met any of these toxic people and is going to be her own thing.

6:13 AM

every culture has its weirdness

we (siblings) always though irish funerals were hearthless until our parents died. we appreciated more aspects of the cultural peculiarities then.

when something awful happens i really don't want to say anything. i just want to be told where to go and what to say. it's comforting.

i suspect the whole avoiding emotions derived from famine times when there were many departures of various natures

that would be an irish funeral

so much easier than other cultures

one of the few times its good to see the priest

i was tasked with saying something at a funeral a while ago, i broke down, i said maybe 10 words and left. didn't read what i had printed out. leave it to the priest.

i can understand completely

the priest was great, too. leave it to the professionals.

my mom's priest is irish. he has a hilarious irish accent.

6:20 AM

i don't know if this is cultural or not, but i had (well, have but moved away) a Jewish friend who would share his deepest thoughts (and some details of boy girl relationships that i did not want to know). i told him i am totally uncomfortable with this sort of thing because i just block up when he goes there. he thought it was really funny and enjoyed watching me squirm :-).

haha

when friends go through a divorce i cannot help them

i mean i will help with stuff, but don't talk to me about it

my dad has six cousins, five out of six married jewish women. there's something in common between the cultures. and yes, anything involving divorce, stay out.

i knew little about Jewish culture before I came to Berkeley

i think there is a lot of commonality among older cultures

older cultures, and cultures with a history of mistreatment and persecution.

6:24 AM

we had some Jewish/Israeli friends over for dinner a few nights ago and were spectacularly envious at how close the parents & kids were.

so they are clearly doing something better :-)

fewer obvious hangups

that's one thing we very much don't have in my family. i have cousins i've never met. i met 3/4 of my grandparents exactly once in a very formal environment.

then again, i discuss cunnilingus with my daughter, so i must be making some inroads

yeah, my kids will be like that. i wish i had more kids

bit too late

and expensive

outside of my parents, i think i've spent 10x less time talking to extended relatives than i've spent on this chat.

we just don't reach out to each other.

that's very irish

if you can't be with the ones you love...

when i was in law school i lived three blocks from my aunt. i could see when she was home from my window, i could see her light was on. we had lunch exactly once.

6:27 AM

i can't even begin :-)

0

Q: Probability of choosing a central element from a set of integers

An integer is called a central element of a set of integers if at least a quarter of the elements are smaller than it and at least a quarter of the elements are larger than it. If an element is chosen randomly then what is the probability of choosing a central element? My thinking: P(Choosing a c...

probability probability-distributions integers

Can you please help me with this question ?

one of my friends had an apartment right across mass ave from her place and we went on her balcony and threw rocks at her window. just for laughs.

a neighbour had a corrugated roof. we used to throw stones on it for fun. she was known as bang bang for said reason. we (sibs) have to think to remember her proper name.

stranger i think the quesiton is underdetermined. i do not see a probability distribution on the subset of integers or any indication of what is going on there.

the comments do not seem to address this.

pinot grigio talking

6:33 AM

Actually this question is from last year of admission test of my university .

I have to solve this

actually, maybe i was ok. i think it is 0.5

We call an integer a central element of a set of integers if at least a quarter of theelements are smaller than it and at least a quarter of the elements are larger thanit. If you choose an element randomly then what is the probability of choosing acentral element?

yes, we got that first time around

Here is the full question.

does randomly mean, after having chosen the subset, uniform distribution on that subset?

6:35 AM

user image

i don't see explicit finiteness assumptions which would be needed to make sense of this.

order the elements. mark the first and last quartiles.

a central element must come from the 'middle'

the distribution is 'built in' to the question. (joe's alcohol fueled opinion.)

put it this way, if is not central it must be in the first or last quarter of elements.

What is joe's alcohol fueled opinion ?

${1 \over 2}$.

looks like $-{1 \over 12}$ from here.

ignore the last remark.

i am joe.

ok.

Can you give me an explanation of how you get the answer 0.5?

I am trying to solve this problem since last night

6:41 AM

read the last sentence in my second last comment

Yup got this

put it this way, if is not central it must be in the first or last quarter of elements.

then?

does that not answer it?

there are only four quarters...

in absence of other information we can presume some form of uniformity

There are four quartiles.

Q1, Q2,Q3,Q4

got that. the quart part is a big hint :-)

but i am a binary sort of guy.

Yup the central element must be either in Q2 or Q3

6:45 AM

that would be my reasoning

Yup. I agree with you

you & @robjohn have vaguely complimentary avatars

So actually the question wants to know that among four quartiles, what is the probability of selecting 2 quartiles ?

right ?

in an iq test sort of way

that is how i would interpret the question

nice.

Great

6:46 AM

i hated those iq tests

but why ?

why the hate?

yup why do you hate this type of iq test?

because some seemed ambiguous and you have to know the expected trick to see the 'pattern'

i could see other patterns

one examiner told me, no that is not the 'right' pattern.

got your point.

6:49 AM

i don't think they administer those sorts of tests anymore

@copper.hat I don't think there is anything nice about either avatar!

Oh, you meant complementary...

yes :-)

in a vague sort of way

i always think you (@robjohn) are angry when i look at your avatar :-)

silly of course

Joe, have you completed your PhD in CS department?

EECS. does that count?

I have read your full bio just now.

6:52 AM

i do have some cs exposure

@copper.hat I am mean, not angry.

more industry experience

I have got PhD offer from University of Maryland this year

@robjohn i think you are way above average

Will the university open its class on campus?

6:53 AM

i know a prof there in the ece dept

nice

What do you do now?

Professor in university?

great guy. very smart

no, i work in industry

i do not have the skills needed for academia

software industry?

sort of. it is known as eda

has even made it to wikipedia by now

great

That means, you are machine learning engineer

I want to complete my Ph.D. in the USA.

Then want to join in university as professor.

6:56 AM

i can with reasonable certainly assert that you own something that has been designed or verified with software that i wrote

my only claim to fame (or infame)

@copper.hat It's almost been ten years since the comment in this room that inspired my avatar.

where are you based/

Bangladesh

@robjohn what was the comment?

I have got PhD offer from UMBC.

6:57 AM

@AStranger wow, that's a fair distance away

in the maths dept?

no.

information department

cool.

@copper.hat If you look at my profile, there is a link to the comment.

I will work with computer vision in medical sector.

one hopes the two are not disjoint

@AStranger ohh, very nice, more up my alley

@robjohn got a laugh out of that

always thought tb was an unfortunate choice of username

6:59 AM

Thank you Joe.

i like the software/hardware interface.

i should have done robotics, but it was very much pre-nascent when i was a lad

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