Mathematics - 2017-06-06 (page 1 of 4)

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Akiva Weinberger

12:07 AM

> Richard Feynmann was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, though by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems, to see whether it helps. Every once in a while there will be a hit, and people will say: ``How did he do it? He must be a genius!''

(From #7 of "Ten Lessons I Wish I Had Been Taught", a presentation given in 1996 by Gian-Carlo Rota at MIT)

12:19 AM

Fine-man

12:51 AM

@AkivaWeinberger are you a fan of Feynmann?

Akiva Weinberger

@Dodsy Yeah, I like him

I've read a couple of his books.

I enjoy his stories.

Also that's an interesting concept.

1:13 AM

Useless advice

This question makes my head hurt: math.stackexchange.com/q/2311274/137524

I recognize terms in there, but I have no idea at all what they're after.

Self-consistent HF (Hartree-Fock) RPA (random phase approximation) , ok

fraction of EWSR?

isoscalar(?) monopole, dipole, quadrupole, octopole

and oh hey skyrme interaction

1 hour later…

2:40 AM

@Semiclassical lmfao, yeah that's pretty ridiculous.

The funny thing is, after looking a bit online, I mostly understand what that picture is. (The terminology is stuff I've seen before). @dodsy

(Basically, model calculations of certain calcium nuclei-nuclei interactions, and comparison with experiment)

But since they don't include a source, I have no idea what the bottom axis is or what that vertical label is supposed to mean.

As a consequence, I wouldn't be able to help even if I was willing to. (I'm not.)

How it's written is pretty bad, you must have some good knowledge if you can understand it.

I had to look up some stuff.

But I do recognize the phrase "Self-consistent Hartree-Fock Random Phase approximation".

I even know where it'd be in my condensed matter field theory book, though I don't do it myself.

lmfao, I hope I never understand that sentence, honestly.

Well, to be honest, people usually just call it RPA.

Because the name is not very helpful.

2:53 AM

do you guys think it's important to take physics in the first year of your undergrad?

Hey everyone!

Hartree-Fock, by contrast, is a more familiar thing. It comes up if you want to do density functional theory in chemistry.

And I mean, do you anticipate physics being a feature of your college experience?

Hey Dami.

And self-consistent refers to how it's being solved, namely in a way where all the constraints are required to be satisfied.

(Sometimes you have to do calculations which aren't self-consistent; it's not a great idea, but it's usually easier and can give some insight.)

2:55 AM

I am drafting my schedule, though there is a chance I may not be accepted, but if I add physics my day goes something like "Calc from 8:30 to 9:30, physics from 9:30 to 10:30, lin alg from 10:30 to 11:30" and I just feel like that'd be a tough year.

@Semiclassical that's pretty interesting, I suppose.

Tbh, if you're not planning to do a physics major (or something for which it'd be a prereq) then waiting isn't a terrible idea.

The more math you know, the easier intro physics is.

Ah, I'll have to think about it, I suppose.

But I'd ask about what courses people usually need intro physics for.

that's a good idea.

As a bit of context, I didn't take gen-chem until my junior year.

And at that point it was pretty easy. (Certain parts would be even easier now.)

2:57 AM

I took physics my first year thinking I'd be a physics major. That didn't last long

Part of it was the particular nature of that course being way over my head, but also it definitely revealed a sense in which I was not good at visualizing motion

To finish up the rest of the jargon, EWSR on the diagram = energy-weighted sum rule.

...I don't really know what that means, tbh.

Welp

I've seen the phrase 'sum rule' before, though. It usually indicates some kind of result wherein all of the possible outputs of the scattering experiment have to satisfy some consistency condition.

I mean we know it's some rule

As an example, grabbed from Scholarpedia at random: "The Adler sum rule states that the integral over energy of a difference of neutrino-nucleon and antineutrino-nucleon structure functions is a constant, independent of the four-momentum transfer squared"

3:02 AM

chuckles

The structure functions more or less tell you how the system behaves when you scatter stuff off of it.

You should imagine me waving my hands furiously here. This is physics I don't touch.

I have heard of Skyrme stuff, though. It's actually kinda neat.

Actually, scratch that last line. Skyrme is known for something else as well, but it doesn't seem to be related to what they're talking about here.

Finally, ISGMR = isoscalar giant monopole resonance.

What is this alphabet soup?

What that means...I dunno, beyond a vague notion of what 'resonance' might mean here.

heh, this: math.stackexchange.com/q/2311274/137524

I'm in pain right now

oh. And KDE apparently means kernel density estimation? I dunno man.

It's basically all nuclear physics stuff.

3:09 AM

@BalarkaSen thanks!

Yeah... I'll stick to my algebra

:P

lol

Especially now that analysis is done for the year

it's not stuff I do or would want to, if I"m honest.

Do u know why homology with coefficients in real numbers isn't considered in hatcher's?! I mean he just considered with coefficient with integers, why?

3:16 AM

universal coefficient theorem?

@arctictern what's that?

Hey @Balarka, @Akiva, and @arctictern

Integer coefficient retains more information than real coefficients, @mathvc_

Akiva Weinberger

Hi. Is stuff going on?

You totally kill the torsion in R

hi everyone

3:19 AM

@AkivaWeinberger The moon is existing, so there's that?

@Daminark How was le exam

Orthogonal to what I studied

But not fiery death and destruction

whew

There were 5 problems. Problem 1 was to show that Besicovitch in $\mathbb{R}$ worked with constant 2, and that it failed with constant 4 in $\mathbb{R}^2$. Problem 2 was to state and prove Hahn Decomposition.

Um...

right

I dunno that stuff

3:23 AM

Problem 3 gave 2 statements, that $f\in L_{\infty} \implies \lim_{p\to\infty} \|f\|_p = \|f\|_{\infty}$, and that $f\notin L_{\infty} \implies \lim_{p\to\infty} \|f\|_p = \infty$. Asked whether each was true or not. Problem 4 was to show that a function is Luzin iff the image of a measurable set is measurable

Problem 5 was to find which statement was stronger, that $\mu$ is absolutely continuous wrt Lebesgue, or that $F(x) = \mu([0,x])$ is an absolutely continuous function.

Problem 1 involved the first time in years that I used the geometry learned in 9th grade

Haha, nice.

On a different note I wonder if I should burninate some of my older, but highest voted, answers

just cuz i can

Perhaps but wai?

most of em are shit yo

I mean you put some words together that resembled an answer

Oh uh

I mean, I guess, but it's not like their existence is at all a problem

So why go through the work of clicking delete a bunch of times, you know?

fair logic

but then i have to decide how to misspend my time instead

3:43 AM

shrugs

Akiva Weinberger

user image

The squared square with the smallest known ratio of largest to smallest square size

Maybe watch more beer skits, play video games? Or study some bizarrely specific thing that isn't relevant to shit

as, it has not been decided if the square can be squarulated (???) so that that ratio is smaller?

Akiva Weinberger

Yeah

huh

3:48 AM

Interesting

This won't fall under what I said above, but consider learning about p-adics!

@Daminark Not a bad idea. I only half-like beer skits though

p-adics is good stuff

At some point in life I intend to figure those out. I know they can be good in stuff like number theory, rep theory, fourier analysis, though I haven't seen then come up naturally before

I know what p-adics are but that's it honestly

Akiva Weinberger

You can get that square on a t-shirt

P Adics in Fourier analysis??

3:56 AM

The other way around.

You can do Fourier analysis on p-adics.

or rather, adeles

I see, interesting...

Akiva Weinberger

4:08 AM

For polynomials in $\Bbb C$, why are the inverse images of bounded sets bounded?

I suppose you only need to show that the inverse image of the unit disk is bounded…

(This is clearly false for $e^z$)

Oh, wait, I think I see

$|P(z)|\to\infty$ as $|z|\to\infty$

Akiva Weinberger

Right, yeah, of course

And that just comes from the triangle inequality

$|a_nz^n+a_{n-1}z^{n-1}+\dotsb+a_0|\ge\\|a_n||z|^n-|a_{n-1}||z|^{n-1}-\dotsb-|a_0‌|$

or $P(z)/z^n\to a_n$

Akiva Weinberger

and eventually the highest order term dominates

Yeah

Proper map <=> sends infinity to infinity <=> preimage of compact set is compact

in appropriate notion of "<=>"

4:15 AM

I like the idea of a math shirt, but they all suck.

I would not wear a math shirt.

Akiva Weinberger

I like the square one

I do want a one with "Karl Marx is my homeboy" written across it.

Akiva Weinberger

I'm sure I've asked this before, but—are there functions that send connected sets to connected sets but aren't continuous?

Oh, wait, any discontinuous function with totally disconnected domain

What about connected domain?

What about like the topologists' sine curve function $f : [0, 1] \to [0, 1]$?

Akiva Weinberger

4:20 AM

Oh.

Right.

I'll take this as a sign that I should go to sleep.

All you want is for the graph to be connected, I guess.

And there's plenty of discontinuous functions with connected graph (the one I said being one)

@AkivaWeinberger your smart

Akiva Weinberger

I just missed a very obvious counterexample, but thanks

Grothendieck thought 57 was a prime...

@Zee You're* ;)

4:24 AM

@Dodsy your right

@BalarkaSen You're* ;)

Whose right?

your're

The official language of math is broken English so piss off

Your ....'re.

4:26 AM

Thank's, Dodsy

Akiva Weinberger

I need to file a complain't

Wa'o reax ownlee

Akiva Weinberger

:O

??????

We of successfully pissed dodsy

4:27 AM

Thing is, none of this is quite as broken as that one question from earlier.

actually using of instead of have pisses me off too

So I'm not impressed :P

@Semiclassical This.

@BalarkaSen I would of agreed a few years ago.

Akiva Weinberger

So a 2-distance set in $\Bbb R^n$ is one in which there are only two distances you can get between distinct points

Language is overrated, that's why philosophy always turns to nonsense

Akiva Weinberger

4:29 AM

It's not hard to get one with $\binom n2$ elements, and only slightly harder to get one with $\binom{n+1}2$ elements

Apparently there's a quadratic upper bound, but I don't see why

@Zee philosophy is logic expressed in raw ideas.

Akiva Weinberger

(Two examples in the plane would be a square and a 60-degree parallelogram)

@Dodsy that's nonsense, just like philosophy

Akiva Weinberger

(I don't know what you want to call it, the one that's two equilateral triangles stuck together)

One thing I will say for physics, we do have neat looking lattices

4:31 AM

I sat in on a philosophy class and enjoyed it.

@Zee More, just like your opinions about philosophy

I like lettuce too.

:P

@Akiva so in n = 2 you exceed (2+1, 2)

already

@Dodsy lol, I did my undergrad in it, completely

Nonsensical

4:31 AM

for instance, the Kagome lattice:

Trihexagonal tiling

In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. It consists of equilateral triangles and regular hexagons, arranged so that each hexagon is surrounded by triangles and vice versa. The name derives from the fact that it combines a regular hexagonal tiling and a regular triangular tiling. Two hexagons and two triangles alternate around each vertex, and its edges form an infinite arrangement of lines. Its dual is the rhombille tiling. This pattern, and its place in the classification of uniform tilings, was already known to Johannes Kepler...

Akiva Weinberger

@BalarkaSen I just said $\binom{n+1}2$ is attainable, but not the upper bound

@Zee did you read Plato's The Republic?

Akiva Weinberger

I don't know what the upper bound is, that's the problem

Apparently there's a quadratic upper bound and I need to show that

Also, apparently herbertsmithite is an actual name of a material that has a Kagome lattice structure.

I took three courses just on Plato, waste of time

4:33 AM

where do you get these problems from

Named for, shocker, a guy named Herbert Smith.

Akiva Weinberger

It's just this thing again. I had stopped thinking about it for a bit

I need to work on stuff like that more.

Oh.

@BalarkaSen The great big book of everything

with everything inside.

Ok, I quit because I promised myself I'd work through it carefully later

4:34 AM

That sounds awfully like the Library of Babel.

Akiva Weinberger

@BalarkaSen A little out of order, but it's 29 and 35

Yo @EricSilva

yo

What made you pick those Akiva?

@Semiclassical I like the book in The Garden of Forking Paths too

4:35 AM

We've got a third person in the chat now

Yeah.

@Daminark ?

Plus, the names of those are just great.

What is this library of babel

2000 years and nothing to show but words

4:37 AM

A short story by Borges @Dodsy

short story by Georges Luis Borges

#getsniped

hey, you had the full name

what is this :libraryofbabel.info

never seen that before

It's like they took all permutations of possible letters

4:39 AM

lol nice site

@Dodsy Araske is from the same school as Eric and I

Akiva Weinberger

The idea is that it's this infinitely large library (or the people who live in it think it's infinitely large, at least), full of books

so that it's possible to find any book possible in there.

That's pretty much what the Library of Babel is.

Akiva Weinberger

but the books are just all random

4:40 AM

Way too abstract for me.

So maybe there's one big book

The short story isn't very long and speaks for itself well enough.

Akiva Weinberger

so there might be something useful somewhere, and you can't know for sure that there isn't unless you've checked all the books

oh shit we have a third person @Daminark ???

willd

There's probably some statement re: entropy to be made here.

in that the chance of getting any book with even a somewhat intelligible portion is vanishingly small.

4:42 AM

but positive

Akiva Weinberger

Or a question along the lines of "Why is this fictional universe made entirely out of library"

"Like, this place is immense, how did this happen"

Simplest answer being "because someone got bored" :P

I find it interesting insofar as it relates to the human inclination to find pattern in seeming randomness.

and add some dark web conspiracy theory

This is assuming we can't make up new words, which we can

*attempts to make up new word*
*loses ability to speak*

4:46 AM

instructions unclear, tongue stuck in a Granny knot

Akiva Weinberger

Covf

have you never found words that don't exist?

Akiva Weinberger

Sure. Borm.

Tefalk.

Shoughlash.

or noticed the non-existence of a word to describe a concept you are thinking of

The other thing to note in that short story is that the titles of books mentioned are a bit too non-random to be liable to show up in the Library of Babel site.

4:48 AM

My favorite word that does not exist is axaxax ml\"o

for instance, it mentions one as "The Plaster Cramp"

Which means "to moonate" in English

There are plenty of words that can not be translated

I at least know sentences that don't exist

"Short Souganidis pset"

Akiva Weinberger

@Araske Oh, yeah, definitely. It's definitely a skill to be able to effectively describe a concept whose word either eludes you or doesn't exist

4:48 AM

pls

Lel

@Semiclassical So it's random but with the english language in mind?

I think that would be better

@Daminark did you see the Neves beerskit

if it took words from the english language and mixed them

Oh it was beautiful

4:49 AM

Well, keep in mind: Borges didn't write in English, if memory serves

Oh, well you know what i mean

He was a Spanish writer

legit funniest thing i've ever seen

if it took whole words instead of just letters.

Right.

The tricky thing along those lines is: Words in what language?

4:50 AM

Any, I could just translate it.

The behind the scenes thing was our TA in analysis, and seeing her get so pissed was just gloriously funny

Akiva Weinberger

@Araske In fact, isn't that how much of mathematics works? People find concepts useful, and then decide to attach words to them; that's how definitions get born. Like a "flype" in knot theory.

What if you don't know what language it is? :)

...these weights thicknesses sounds smells molecular whirlwinds chains nets and channels of analogies concurrences and synchronisms for my Futurist friends poets painters and musicians zang-tumb-tumb-zang-zang-tuuumb tatatatatatatata picpacpampacpacpicpampampac uuuuuuuuuuuuuuu

ZANG-TUMB
TUMB-TUMB
TUUUUUM

Interesting point.

@BalarkaSen acid trip.

4:50 AM

"All. you. fucking. non. analysts. don't. know. how. to. get. any. work. done!"

@akiva but you're essentially compacting a short sentence into a word

@Dodsy Nah, Battle of Adrianople.

Akiva Weinberger

I guess

like what I'm trying to get at is

snysloe

4:52 AM

Kinda reminds me of the one line of Faulkner I know.

"when she became not then half of memory became not and if I become not then all of remembering will cease to be.—Yes, he thought, between grief and nothing I will take grief."

like can you approximate any idea in a non-ambiguous way with sequences of words

@Daminark adding the puzzle pieces on the chalk board made me lose it

mostly because of how jumbled that first line is.

Akiva Weinberger

@Araske The trick is that that only needs to be done once per conversation

@Araske says you

Akiva Weinberger

4:53 AM

Or maybe a few times to remind people what you're talking about

Another tricky point in this is that: What if the text is enciphered in some way?

Akiva Weinberger

but not every time you mention the thing

true, definitions are a powerful tool

@Semiclassical Perhaps.

Akiva Weinberger

You settle on a shorthand pretty quickly if it's an important part of the conversation.

4:53 AM

oh fuck wait @Daminark i totally remember the "claudio is the fucking worst" thing was on the board literally all winter quarter

@Araske Define "cat".

Kek

featherless quadruped with...

Words are nothing but a pointing finger

Not going to lie, this is the kind of philosophy stuff that I get tired of fast.

@BalarkaSen rlv.zcache.com/… for you

@Zee Bruce Zee.

Akiva Weinberger

4:54 AM

Words are nothing. Morphemes are where it's at.

yes @Zee

@Zee I know I've seen that before but I forget who said it.

@Semiclassical This is nothing man, open up Finnegans Wake

Akiva Weinberger

(Well, morphine is where it's at. But that's another matter.)

can you point anywhere though?

4:55 AM

@Semiclassical Like a finger pointing at the moon

Do not focus on the finger

or you will miss all of it's heavenly glory.

Akiva Weinberger

Don't focus on the moon, it's a distraction

@Semiclassical the early Wittgenstein

Akiva Weinberger

DECOY MOON

I wondered if it was him, but wasn't sure.

@Araske yes, as far as the speaker and listener are concerned

4:57 AM

@AkivaWeinberger Moons, I hate the word, just as I hate all Montegues.

"The fall (bababadalgharaghtakamminarronnkonnbronntonnerronntuonnthunntrovarrhounawnskawnt‌oohoohoordenenthurnuk) of a once wallstrait oldparr is retaled early in bed and later on life down through all christian minstrelsy"

like a sequence of rationals points at a real; that there is one to point at an arbitrary real is a distinct fact

okay

Akiva Weinberger

There's a Montague Street near my house.

There's also another wrinkle to all of this: Language isn't static.

Nobody can deny that words are a powerful tool.

Akiva Weinberger

4:58 AM

Also a Love Lane.

@Zee i find it probable that all things in the world can be pointed to

@Dodsy Meh

@Araske point to your pointing finger.

Also things that exist solely as definition, like truth or justice

@Araske oh ya? Can you point to tomorrow?

4:58 AM

Hey math people

@Zee on a calender.

Give me a calendar! :P

what about structure of experience though

I tend to agree with the point, though.

@Dodsy that's just replacing the sign of "tomorrow " with a different looking symbol

4:59 AM

@Araske are you trying to claim existence of a idea or conception which cannot be broken down to words in any way in any language whatsoever

or what

re: 'tomorrow' see kant

Akiva Weinberger

Something interesting (to me): there's this notion of "common ground", which is the set of things I know, and you know, and I know you know, and you know I know, etc.

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