Mathematics - 2017-06-29 (page 3 of 9)

It's not language, it's physics, without complete knowledge of physics you can't define language logically

the way we use our language plays a way bigger role in our lives than we give it credit for man

ok @Zee

No I mean, how much do we actually disagree on stuff, versus how much we just use words differently so that's leading to disagreements in edge cases

i think we have substantive disagreements

user84215

If we have no common axioms, we can not get the truth. So the discussion is worthless.

6:09 AM

@Daminark Eric won't play with me >:(

i dont think we disagree on anything that matters though

Likely, but this language problem is actually crippling things

@Zee I challenge you to Banach-Mazur. I'm player 2 and we're playing on $\mathbb{R}$ with $\mathbb{Q}$ as the designated subset

I have no idea what you just said

@EricSilva I must yet again bring up the question that I always bring up whenever "matters" or the like come up: "to whom?"

But am serious guys, without complete knowledge of physics you can't define language

6:11 AM

idt our opinions on language (which obviously diverge a lot) should really matter to anyone

user84215

If you want to reach the truth, you should start from common axioms.

i mean idrc about them

I know I sound like a crack pot but am for real

@Zee The first part of this sentence is correct

Lol

6:12 AM

but anyway @Daminark, i think we should treat discursive language with a lot more care then we do when we have these pseudodiscourses

@Eric I tend to put a good bit of stock on such things, since they do have ripple effects on your ability to communicate

user84215

What are common axioms ?

@Daminark think about it though, am not pulling your leg, I am a filthy philosopher after all

sure? I mean my whole point earlier was that to me enjoyment has a hedonistic connotation, fulfillment does not, they're connotatively different, that's why you will choose one word over another in different circumstances

when i say two things are "true synonyms" i would hope that they have the same connotation

My "@Zee said philosophy" sense was tingling, hehe

6:15 AM

I mean, the issue is that enjoyment doesn't have that connotation in my usage

But I think that discussion will not take finite time

i mean

@Fargle hey man, did that turn you on?

you dont have to be using it to mean that

:^)

im just saying that you dont have to take pleasure in something to be fulfilled is all

6:16 AM

@Fargle ok, bare with me here

it's a very simple claim

@Fargle what do you think about this

Now you've said the word pleasure, that changes everything

Like that's something I use hedonistically

user84215

Common axioms ?

you definitely use the word enjoy hedonistically

6:16 AM

My previous usage of "enjoyment" was in no way trying to imply that

@fargle if you have complete knowledge of physics and the universe, on a physical level, only then can you define language logically

ik @Daminark im not arguing you on this

we basically agree i think

"You definitely use the word enjoy hedonistically"
"My previous usage of 'enjoyment' was in no way trying to imply that"

@Zee What do you mean "define language logically"? I want to make sure I understand what you mean so I don't make this a semantic issue.

when i say use i wasnt talkign about your previous usage

6:18 AM

Or are you saying it can be used hedonistically? Sure, that's why I put fulfillment as a subset of enjoyment

ah i see

@Fargle that words do not have a precise definition

Anyway whatever the case about those terms, I do believe that learning the truth for its own sake is a very different sort of insert applicable word here than playing paper-io

Oh, yeah, I absolutely agree on that. In fact, by the very nature of words and the fact that "definition" refers to a definition of words, I don't think any natural language can constitute a logical system.

i guess that part of what im saying is that the reason you would choose to say fulfillment over enjoyment for some things is that the words might be able to mean the same things, but sometimes they don't, and that's an important thing

6:20 AM

There are some words that you just have to leave undefined.

@Fargle do you agree with my original statement?

Not in those words.

like words are interchangeable yeah, but connotation plays a big role in the way words are chosen

Mathematics is a language that is defined logically.

i wouldnt say math is a language

maybe it's a collection of languages

6:21 AM

@fargle yes but I would not say it's a natural language

I agree that it's not a natural language in the normal sense of the phrase.

but idek about that

but is it even a language?

@Eric: more precisely, math is spoken in a language that is defined logically

I think you could get a thurstonian to agree with the idea that math can be kind of like a natural language

6:22 AM

i don't wanna force us into the corner of having to define language but I don't see how math is a language except in some poetic sense @Fargle

Anyway, so if Keerthi was meaning hedonistic pleasure, then sure, I'm behind that claim, most of the time interesting results won't be totally shiny

I take "language" to mean "a symbolic form of communication that is used to depict things and ideas"

Roughly, of course

@Daminark he definitely meant hedonistic

Okay

Does there exists irreducible polynomials over $\mathbb{Z}[x]$ and with coefficients from $\mathbb{Z}[x]$ which contains finitely many primes ?

6:23 AM

i mean, again, it's the reason the word enjoy was chosen

is because it's usually connotatively denoting hedonistic pleasure

God I wish there was some unambiguous way of communication because these definitely hold things up a bit much

@Fargle but the symbols for language came latter

Eh ?

nah dude

natural language is beautiful

@EricSilva Are you sure ?

6:24 AM

@Zee I don't mean visual symbols. I mean that the sound we make for "cat" is a (spoken) symbol for the idea of a cat.

the confusion is a small price to pay for good ass poetry

Similarly, the sound we make for "triangle" etc etc

What about my question ?

Lol I tend to view confusion as a very heavy price

@Fargle I would use the word sign for that but ok

6:25 AM

Or at least maybe that we had 2 languages, one of them was perhaps more aesthetic at the cost of clarity

i tend to view poetry as a very awesome prize

so

gg

But if necessary we can like, guarantee that the we process everything identically

I mean i know like 5 languages fairly well and 3 of them are super inconvenient but very pretty

and the other 2 are just normal languages

@Fargle again, I don't see how math is a language, it may share some aspects of what's a language but I don't think you can say math is a language, can you say hello in math?

@Zee But at any rate, it's a form of communication that uses signs or symbols to depict things or ideas. That, to me, is a language. What do you mean by a language?

6:26 AM

nah dude it would be super inconvenient to talk in some super unambiguous logic speak

I don't mean even the normal level of inconvenience, my utopia would be at least one bulletproof language

Impossible as it is :/

it's already hard to express complex ideas in english and you have a lot of heuristics

imagine trying to express everything in some perfect logic speak

it would suck

simple things would be so complicated that they wouldnt be worth saying

@Fargle by your definition the Dirac delta function is a language

and we just wouldnt have enough time to say complicated things

@Zee You're taking my words literally.

6:28 AM

Okay let's add on to that ability to talk and absorb information at a rate such that every statement can be said in a minute, supertasks or smth

I don't mean that the statements made in math are a language.

Just as this sentence isn't a language.

ok @Daminark now ur just describing some weird alternate timeline, i dont really see the point

No idea about my question ?

:'(

But the English spoken language, and the alphabet derived therefrom, constitute a language through which we can communicate.

@Fargle I want you to examine honostly and logically if math is really a language

6:29 AM

I mean basically it's an exaggeration, my real point is that communication difficulties are just really annoying

I mean it's not a point so much as it was just, ARGH

@Zee I did, dude. I gave my definition, and it fits my definition. Why do you think I'm not thinking?

@Fargle I never said you aren't thinking

@Fargle I KNOW you are thinking

Just that you were dishonestly thinking :P

Lol jk

@Fargle but I think you are fooling yourself

didnt this whole thing start bc u didnt take at face value that the keerthi quote was overtly talking about hedonistic enjoyment @Daminark

6:31 AM

Why did you ask me then, @Zee?

Felix.C

Hey I'm a bit confused as with compact spaces. Let's stick to metric spaces here to make things easier for me. Afaik if adding two elements of a vector space the result has to stay in it...A compact space is bounded as of Heine-Borel. Can't I always find elements in every compact space that the result leaves the space?

If you don't want my perspective just tell me the answer.

I mean I basically parsed out that statement as meaning, if you're happy it's trivial

@fargle I want your perspective

@Zee Then why insult my perspective?

6:32 AM

@Daminark that is like super incorrect

And I'm like, sure there's a lot of work in getting back the results and it can be merpy, but like, when you publish it's pretty happy

i mean it was a joke

sometimes publishing is too nightmarish to be happy man

ive heard horror stories

and still that's like blatantly misinterpreting the quote anyway

Well, this is exactly why the whole language problem annoys me

@Fargle because I had the same idea about math being a language, or even animals having some kind of a language, then I had a discussion with a professor once and asked me "but are those REALLY languages?" And after some thinking I saw that I was being poetic in my thinking

@Zee You decided so, sure. Not everybody thinks like you do, or has to.

6:34 AM

@fargle I'll tell you what, think about it till tomorrow, if you don't change your mind, I'll accept it and continoues our discussion

@Daminark, idk the only sketchy thing is that "interesting" in this case meant, "interesting enough to the general mathematical community to be publishable"

Please don't ask me about this tomorrow.

the enjoyment thing is on you man that's the common usage of the word

Hahaha

I'm glad you're enjoying yourself.

6:35 AM

although i have known a lot of mathematicians who use the word interesting to connote this i guess

(neves does a lot)

No that's latter tonight

but i think the thing to remember is that it was said in jest, the kernel of truth is there but it's still a joke

shrugs

@Fargle think about it

@fargle please?

@Daminark i do recommend learning a dead language though

or taking a linguistics class

6:37 AM

If I have time I definitely will

they make you think about these things a lot it's a cool subject

I was considering doing it this winter actually

learn a medieval language man

Alright guys, I got some very bad news...

But I have to go

But I dunno, I got crushed fall quarter so I decided at that time to keep it to 3 classes in the winter. In hindsight maybe 4 could've been doable, or I should've swapped out compsci tbh

6:38 AM

@Zee What bad news ?

@Zee :'(

No am going to sleep

3 classes in winter is good

winter sucks

so anything to make it manageable tbh

Compsci 152 didn't go as well as hoped anyway

Take old english

Tbh it's the coolest class I've taken here

6:41 AM

I may very well do so. I guess it's tricky though, there's all that pressure to learn languages for pragmatic purposes, and then of course, space in the schedule be lacking

I'll definitely look at auditing it tho

Tbf though it is by far the hardest class I've taken

It makes math classes look easy

(and learning languages for fun makes it easier to learn languages for practical reasons)

In terms of, the class piles on a lot or the difficulty of the subject?

Both

The subject is actually extremely technical

Good lord is Sougi's cousin teaching that class?

The teacher next year is some scholar of Norse and Saxon history

He's apparently very good

6:44 AM

Oh I likely couldn't do that next year

But if you take it you may very well have a different experience to me, I usually have a frantic approach to courses outside matj

I mean he'll teach the year after too

It'd be 4th year, next year classes/audits are gonna be near overload

Don't overload your third year m8

That's the money shot

Yeah, this is part of why I might not do analysis

I plan on only doing fun classes tbh

And sosc

6:47 AM

I really would like to, but with everything else in the mix it'll be a heavy balancing act. Enjoyable but heavy

Lol I mean, sosc can be pretty fun

Didn't u take classics

Yeah

Switch to fb

7:48 AM

Hi chat

Leaky Nun

@AlessandroCodenotti buongiorno

Is $L^2$ the only Hilbert space among the $L^p$ spaces?

Yup

($L^p$ spaces over $\Bbb R$ with the Lebesgue measure, even though $L^2$ should be Hilbert regardless of the underlying measure space)

Yeah, it doesn't depend on the underlying space.

You can do exactly the same for the $\ell^p$ spaces, even.

7:58 AM

The $\ell^p$ spaces are the $L^p$ spaces over $\Bbb N$ with the counting measure after all

I think the standard argument is that Hilbert spaces are self-dual thanks to Riesz, but the dual of an $L^p$ space is the $L^q$ space with $\frac{1}{p} + \frac{1}{q} = 1$.

Makes sense, thanks!

Hello chat

How goes ?

8:31 AM

Alright. Yourself?

I'm good

Secret

@AkivaWeinberger sorry I was busy doing my literature review thus only noticed the question today. But it seems other mathers have suggest an orthogonal (which can be made orthonormal by normalisation) basis set that cannot be produced by replacing (01) (01) with $\pm 1$. I am not sure how a choice of basis set relevant to that integral though unless it has something to do with the jacobian calculation

anyone alive?

Quite a few of us I suppose

^^

know anything about explicit solutions to odes?

8:44 AM

I know some things

Not enough probably :p

Ask your question anyway

i unsed to know somethings

used*

cant remeber how they workfor the life of me

literally cant understand the first 7 chapters of my old textbook anyway question.

$ \frac {dA}{dt}+ \frac {A}{100}=6$

any idea how to solve this?

its the easiest one i could find in my book

Do you know the solution to the homogeneous equation ?

that =0

instead of 6

?

yup

no

i dont even know how to do that

thought i do know what it means

though*

8:49 AM

It's $e^{-x\over 100}$

i always thought u could like seperate the dA and the dt and integrate somehow

That's one of the methods

how u find that?

This one I know off by heart

To prove it, you can prove it's either 0 or never cancels

lol

8:51 AM

And then divide by A and find ${d\over dt}\ln A = {-1\over 100}$

Integrate and get $\ln A = {-x\over 100}$ ie $A = e^{-x\over 100}$

Psh, $t$

ohi see thats gotta be the integral because its derivative gives you the question

$t$

also stop forgetting your constants :P

Oh yeah true

Rough morning :p

8:53 AM

Oh? More exams?

Not until next week

ic thank you

I'm doing physics at the same time