serious-discussion

[velvet dagger]

First integral converges since h is PW type

Second is straight up 0

Third is bounded by integral of h

And fourth is bounded in absolute value by |h(u)u|

And h is PW so that converges, in fact we've got a bound uniform in t

@cold needle this is your future

[cold needle]

oh my

nice ?

[astral marsh]

❌

[modest rune]

this integral is so cursed that conversation hasn't happened here since yesterday afternoon

do you feel bad @velvet dagger

[devout nacelle]

[neat lintel]

[crystal stone]

That's a pretty clever way of getting it to behave

[astral marsh]

better post that integral in #chill then

an unstoppable force meets an immovable object

[cold needle]

lmao

[solemn cargo]

So apparently people are claiming that this server is partnered with /r/math???

[cold needle]

it's not?

that is weird

[neat lintel]

it's not and i hope it never is

[solemn cargo]

Thought not.

Because if it were, I'd be missing a memo.

[devout nacelle]

Where did you see the claim?

[solemn cargo]

https://www.reddit.com/r/math/comments/ofluh6/quick_questions_july_07_2021/h4l6cox/?context=10000

[devout nacelle]

Oh, someone there clarified there is no such partnership.

[solemn cargo]

Me, yes.

[pure sun]

hi edd

[solemn cargo]

hello buncho

[pure sun]

we used to be in some other discord together

several years ago

[solemn cargo]

Yes, I remember.

[modest rune]

this is not the official r/math discord

its the official discord of Math Overflow

[toxic schooner]

[crystal stone]

is it really?

[modest rune]

no lmfao

[crystal stone]

I mean, I see research questions here all the time

Petition!

[meager sonnet]

Mod weighing in, we are actually going to annex r/math but they just don't know it yet

[leaden torrent]

MO has their own chat service

with like 80 people on it constantly

i have no clue who would want to use MO chat but

hey

seems to work for them

[limber perch]

they have their own software?

it has to be through something

like discord

[leaden torrent]

No

I mean it's probably irc-based?

But it's on the MO homepage

[dawn osprey]

I have to come up with a 5-8 digit code (example: Coffee1) to use as a moniker for my qualifying exams

Any funny suggestions? Currently i'm thinking about "residude"

[neat lintel]

your first name

[dawn osprey]

._. the point is its supposed to be anonymous

[vagrant kestrel]

smugsmug

[distant vortex]

Exactly, so they will assume it's not really your first name

[neat lintel]

TerryTao

[distant vortex]

TTerraTao

[dawn osprey]

Ok, thats funny

[distant vortex]

[dawn osprey]

HAH

[narrow rock]

ultra computer scientist arc

[neat lintel]

highschool computer science class was just a bi-daily halo tournament

[dawn osprey]

im gonna fail the real analysis exam under the moniker "TerryTao"

[neat lintel]

there were like 2-3 kids who were really good who just shit on everyone else

fun times

jesus christ the sniper rifle was busted if you knew how to use it

[modest rune]

real ones played armegetron

does anyone actually know what armegtron is beside me

[cold needle]

[modest rune]

it was very popular at my favorite summer camp

but i have no idea if anyone else knows about it

[narrow rock]

[inner finch]

🧠 🧠

equality up to nonequality

[modest rune]

$\pi_n (S^m)_{(2)}=0$

[fathom swallow]

Portugal. The Max

[pale orchid]

[languid root]

@solemn cargo heyy edd 👋

havent seen u in a long while

how u doing

[solemn cargo]

who dis lol

[languid root]

oof

u helped me out in squids server with proofs and lin alg

remember ?

[solemn cargo]

oh yeah, that server

[blazing pawn]

This question might seem extremely dumb but i dont think ive ever actually heard it for sure: if F: C -> D is an equivalence of categories does F(A) cong F(B) imply A cong B?

This should be yes I think

[scenic narwhal]

Yeah, Intuitively an equivalence of categories is essentially an isomorphism of their skeletons

[blazing pawn]

Right?

I guess this problem is just trivial then

Hurb

[scenic narwhal]

What

Formally if G is the essential inverse, A ≈ GFA ≈ GFB ≈ B

[blazing pawn]

Yeah

Huuuuuurb

[scenic narwhal]

Human use review board

[blazing pawn]

cardinality of the fibers not containing branch points

Isnt this literally just the degree of the map

Just say degree

[neat lintel]

hmm

[bronze pelican]

An analogous thing holds in number theory with splitting of primes in number fields

[blazing pawn]

[velvet dagger]

I guess in this setting yeah because holomorphic maps are always orientation preserving or something

[neat lintel]

[deep mango]

z mapsto -z moment.

[velvet dagger]

That's still real orientation preserving lmfao

[deep mango]

yes. but it shouldnt be.

[velvet dagger]

Lmao

[deep mango]

holomorphic implies jacobian determinant is equal to |f'(z)|^2 right?

so there ya go

[broken scaffold]

[ancient flame]

what should I learn after real analysis?

complex analysis?

[velvet dagger]

As an undergrad you should eventually learn real analysis, complex analysis, algebra, and some topology

[ancient flame]

algebra as in abstract?

[modest rune]

“some topology” basic AT is more important than complex analysis fight me

[deep mango]

No lies detected.

I am strongly of the opinion that the berkeley math major should replace complex analysis with alg top as a required course, and should turn complex analysis into an elective

[modest rune]

woke

fundamental groups show up everywhere and everyone loves (co)homology

[deep mango]

There isn't even a required topology course besides metric space topology in real analysis

Which isnt even always covered in depth

[modest rune]

same with uchicago

[sharp mulch]

Berkeley applied math majors can also get away with never learning differential equations

Which is the weirdest thing

[modest rune]

did anyone defend deRham when i came for it yesterday btw

[deep mango]

And you can get away with taking differential geometry which has no topology

I didnt see you come for it

But de rham is kind of stupid

[ancient flame]

what kind of jobs could you get as a math major

[modest rune]

oh

tragic

i thot ud fight me

[deep mango]

I mean like

It was the first (co)homology theory I learned

And I just didn't get differential forms well enough to get what was going on geometrically

[narrow rock]

why is de rham stupid?

[modest rune]

see #discussion

[whole copper]

They should fuse real and complex analysis into one clasa

[modest rune]

i quoted myself

[narrow rock]

hodge theory

[deep mango]

Whereas it was really clear what was going on geometrically when I learned simplicial/singular/cellular homology

And cohomology

[narrow rock]

de rham cohomology is dope

[deep mango]

Those are good reasons to dislike it max

[modest rune]

i would welcome an explanation of why my reasons for disliking it arent sufficient

[deep mango]

But it also provides access to some very nice stuff

Or at least

It occupies the same setting

[modest rune]

bc ive never really seen anything convincing

[deep mango]

As a setting which provides very nice stuff

[narrow rock]

computable characteristic classes

[deep mango]

Yeah

[narrow rock]

hodge decomposition

[deep mango]

Basically all the hodge theory people

[narrow rock]

chern weil theory

[deep mango]

Lie groups stuff. Some analysis on manifolds stuff.

Like

[modest rune]

you should explain more than just a petthecat emote lol

[deep mango]

It exists to serve a very particular audience

[modest rune]

im not familiar w any of this

I mean I know of char classes ofc

[deep mango]

And also to be a terrible way to teach undergrads cohomology

[modest rune]

but i dont work with them

[narrow rock]

you can define chern classes using curvature

[whole copper]

How else do u see cohomology classes in ur mind if not by writing down a de rham class?

Brains not big enough to imagune anyrhing else

[modest rune]

is this a real question

[whole copper]

Yes

[deep mango]

Jmask physics brain

[modest rune]

do you know what singular/cellular cohomology are?

[whole copper]

Yes, i cant see duals in my head

What do u actually see in ur head?

[modest rune]

i see the dual

and think “dual of that”

[whole copper]

I see nothing :'(

[modest rune]

no i mean

just picture the homology class

and think

“dual”

[deep mango]

WHY ARENT YOU THINKING OF FUNCTIONALS???

[whole copper]

Isnt it a lot easier just to imagine the de rham vlass lol

[modest rune]

no

[whole copper]

Rip :'(

[deep mango]

Poincare duality has poisoned your brain

[modest rune]

no poincare duality

i just pretend everything is free

[narrow rock]

here's another reason

[modest rune]

and take literal duals

[deep mango]

🤨

[narrow rock]

singular manifolds

deligne cohomology is based off de rham

[deep mango]

Complex geometers seem to like using derham

And they're close to alg geo

[modest rune]

i fully believe there are offshoots of derham that might be useful

[whole copper]

Intro phywics really makes u think in terms of de rham classes i guess because of all the examples from gauge theories and stuff

[deep mango]

Phywics.

[modest rune]

luckily i dont know any physics

so my brain is pure

[whole copper]

Im a phwysicist

[deep mango]

mommy can i have phywics pwease? 🥺

[narrow rock]

why sully @deep mango

[modest rune]

fwiw jmask i avoid working geometrically / visually most of the time

im an algebraist in a costume

well no

i like some geometric stuff too

but only when it is easy

[whole copper]

Im the opposite i guess, if i cant draw a picture ill nevwr underatand whats going on

Like homotopy of spheres, you can give me algebraic proofs of any of them with SS or whatever, but ill only ever be able to understand the low dim examples cos i can kind of see them... Lol

[deep mango]

Singular "manifolds"

[narrow rock]

okay

singular spaces

[deep mango]

Singular "spaces"

[narrow rock]

what

[whole copper]

Singular sets

Singular vaguely spatial objects

[deep mango]

Most topological spaces aren't spaces to be clear.

[narrow rock]

space = representable functor + descent

[deep mango]

:descent:

[narrow rock]

:descent:

[whole copper]

The only spaces that exist are finite topological spaces

[deep mango]

Glorified.

[narrow rock]

fied

[whole copper]

f

[narrow rock]

F

[nimble shuttle]

j.

[whole copper]

i

[narrow rock]

j.

[whole copper]

Whats that subreddit where people comment one letter at a time?

Ouija?

[narrow rock]

[pale tartan]

guys is it bad if my integral sign looks like a giant s

[narrow rock]

yes

[fathom swallow]

Brofibration

[pale tartan]

yea thats why im writing it like that, but it looks like a curved backwards z idk if i should get into the habit of doing it normally

yea i should probably work on writing it correctly

[deep mango]

Yebeta.

Yess-tset.

[modest rune]

For readability reasons try not to ever handwrite math you plan to show someone else

unless its a lecture

its wack to me that if an english major were to turn in a paper written by hand they'd get told to retype the whole thing but stem majors regularly don't use latex for their assignments

[velvet dagger]

@modest rune lol I say some topology because I'm not entirely clear on how much topology everyone should have to know

[modest rune]

all of a first graduate course

easily

[velvet dagger]

Definitely pi_1, covering spaces, and probably de Rham theory?

[modest rune]

what

no

teach them real (co)homology

[velvet dagger]

De Rham theory is literally real cohomology

:)

[modest rune]

it can't even see torsion

[velvet dagger]

Nah I mean here when I say everyone I mean like

[whole copper]

Pi_1, classification of surfaces, homology

[velvet dagger]

If you're gonna do stochastic PDE

I still will require you to see this

That's what I mean by what everyone has to know

[deep mango]

i dont write ess-tset with the horizontal strike either

Even on my keyboard theres no strike

[modest rune]

classification of surfaces is a result everyone should see vaguely sketched during a lecture with triangulation taken as given

[deep mango]

It's just the discord font

[modest rune]

thats about it

and they should know the statement of course

[whole copper]

Yeah i think rigor is not too important, but its nice to be able to manipulate like quotienting the sides of polygons and blah blah

[velvet dagger]

And I'm not entirely clear on how much that is. I'm more obviously fine with saying everyone has to know differential forms than saying everyone has to know singular theory

[modest rune]

wrong

everyone should know both

[whole copper]

Honestly my opinion is that undergrads shouldnt need to learn the rigor behind the complex analysis theorems and just know the results and how to use them to compute...

[velvet dagger]

Undergrad math majors?

[deep mango]

So if I start writing beta with a horizontal strike, your argument becomes invalid?

Or do you need a plural crowd of people doing this

[whole copper]

Well i think classification of surfaces and pi1 and stuff are more impoetant to see than rigor behind complex theorems

[modest rune]

Math majors should only have to know the rigor and shouldn't have to use them to compute

[deep mango]

Get rid of field/galois theory

[modest rune]

honest question

i have no idea how classification of surfaces works in Diff

is it nice

[whole copper]

This isnt required anyway right?

[velvet dagger]

It's basically the same

[modest rune]

nice

[deep mango]

Not at berkeley but i think it is in a lot of places

[velvet dagger]

Pretty sure a compact 2-manifold has a unique smooth structure

[deep mango]

Which is stupid

[modest rune]

its not technically required at uchicago

but like

the way they name the courses

[velvet dagger]

Chicago doesn't require it but it's pretty common

[modest rune]

makes you look lame if u dont take it

bc its just like Basic Algebra 3 so if you don't take it you look like you only did 2/3 of the algebra sequence

when really Algebra 3 should obviously be rep theory or homological algebra or both

[velvet dagger]

Yeah I agree with that

[whole copper]

Yes!!! Forgot, rep theory should definitely be core

[velvet dagger]

And then require it

[modest rune]

rep theory is dope

rep theory is probably the coolest subject in math that requires no fancy definitions to talk about imo

like you just gotta know linalg and some group theory

and you can instantly get into cool theorems

[velvet dagger]

They should do that, somehow streamline 160s to analysis

[deep mango]

What "cool theorems"

[modest rune]

I think characters fully determining reps is genuinely amazing

[deep mango]

This sounds like how elementary number theory theorems are "cool"

[whole copper]

Its already cool enough that u can decompose into irreps and classify them

[modest rune]

yeah

[velvet dagger]

Orthogonality of characters and Frobenius reciprocity

[deep mango]

[modest rune]

rep theory presents a bunch of big ideas in math that show up everywhere but does so with basic language and objects of study

its great

and ubiquitous

and fun

and has cool computations

[deep mango]

C* is all just rep theory.

What a terrible surprise.

Yes, that too.

[velvet dagger]

But yeah I'd probably say you can compress the group theory quarter of algebra a fair bit. Some stuff should be covered much faster or left to psets

[deep mango]

But my point being that the flavor of many C* arguments was rep theoretic

And everytime it came up.

It made me want to gag.

[modest rune]

yeah actually

take the finite group theory chapter

throw out like half of it

[deep mango]

Finite group theory is a waste of time

[modest rune]

include basic rep theory

[velvet dagger]

And probably I think you could speedrun the finite group theory, have a "Topics in finite groups" elective class cover fancy stuff

[modest rune]

and then make algebra 3 homological

thats my plan

[deep mango]

No

[modest rune]

or just continue ring their into like AM level stuff

either way

[deep mango]

I dont follow the operator algebras people on arxiv

[modest rune]

ring theory

[deep mango]

I should I guess

[velvet dagger]

Eh AM isn't something I'd put as required tbh

[modest rune]

I think homological algebra is something people should learn

[deep mango]

Why bother me with this nonsense. Isn't their a langlands hack that wastes their time here when they aren't making youtube videos about le epic integrals.

[velvet dagger]

Maybe? I guess it depends on how deep. Saying analysts should have to learn spectral sequences or derived categories to get a degree feels a bit excessive?

[modest rune]

no

they should

expose them to good math

[deep mango]

That was really satisfying to type, ok i'll look at it

[modest rune]

save them

[velvet dagger]

Lol

Wait I don't make YouTube videos

[modest rune]

everything i want to talk about in my talk series

requires so much background

[deep mango]

Save them from the dude who changes his profile pic more frequently than ange changes nickname.

[modest rune]

it turns out i know more math than i thought

i cycle through until i find one i like

i like this one

it should stay the same for a bit

[deep mango]

This is a pdf. Am I really gonna click a pdf from Ultra.

[velvet dagger]

I'm probably the one who has the smallest idea of what the gcd is that people should know ironically enough

[deep mango]

There isn't an arxiv link huh?

It's fine, if this is malware then I can get you banned

Worth it to brick my phone

Ok, that's a sort of nice paper

It's got holomorphic in the title

I scrolled through most of it

I want to appreciate it from a distance

[velvet dagger]

Lol, I doubt I would've been able to pull this off last year

I didn't look at it too deeply, honestly I just checked out Etienne Le Masson to get an idea of what quantum chaos on graphs is, then he cited that and I was like damn

But it seems like an interesting idea at the onset

[ancient flame]

hey y'all

what careers could I pursue if I get a major in math

(other than things involving statistics and programming)

[inner finch]

nlab editor

[ancient flame]

what's that

[inner finch]

a loser

[ancient flame]

:(

[inner finch]

😎

You can probably go into some applied or industrial math direction

maybe do something interdisciplinary

[ancient flame]

I see

thank you :)

[nimble shuttle]

Good Evening, 'IAmJon' was a 16 month intelligence operation conducted by the Central Intelligence Agency. We are now complete with our operation.

[inner finch]

good luck catching me here 😎

such a nontrivial result

[deep mango]

You know what else looks good and very deep. Deez nuts!

[modest rune]

ask ultra for papers

ban ryc

[deep mango]

The vocabulary "crossed product" is so funny

It makes me pause every time I have to say it

Which is like never

But

It is less ridiculous

[ancient flame]

there is such thing as a crossed product?

[deep mango]

Yeah but only with weird shit. Like

It's not a cross product

It's kind of like group actions / semidirect products

[ancient flame]

that doesn't help

but thanks!

LOL

[deep mango]

It's not meant to

[ancient flame]

oh

[deep mango]

There's not a lot one can do to illuminate what a crossed product is lol

[ancient flame]

o

[vivid halo]

@dull salmon any new thoughts on this automorphic factor theory thing?

Nice!

Yea I dunno how much of this will work well in general but reading this more I do get the impression most of this should be okay for quaternionic discrete series

like I would assume that trying to do this for generic discrete series (and presumably getting a totally different factor theory) would require some really new ideas, whereas the quaternionic discrete series situation should be analogous enough to the holomorphic discrete series situation that the paper might be able to be adapted

also nice because there's a LOT of explicit stuff done with modular forms for G2 by Gan-Gross-Savin (which have quaternionic discrete series representations as their Archimedean component and have a lot of behavior parallel to classical modular forms) which could be a nice source of examples

[modest rune]

broke: ignoring a headache
woke: stop using my ipad once i have a bad headache
bespoke: pop an addy (advil) and soldier on

[inner finch]

addy baddy

[deep mango]

[ancient flame]

is anyone here a math major or planning to be one? ping me if u are, I have some questions

[inner finch]

mav

[crystal stone]

Do yourself a massive favor right now. Either pick up some programming language, get some lab experience, get research experience, or get tutoring experience

ASAP

@ancient flame

I meant to ping gmod

[crystal stone]

I was a math major

[ancient flame]

I work at a tutoring company

[nimble shuttle]

Do yourself a massive favor right now. Either pick up some programming language, get some lab experience, get research experience, or get tutoring experience

[ancient flame]

here I'll dm u

[crystal stone]

Yuh

meant to being gmod norman

[inner finch]

Do yourself a massive favor right now. Either pick up some programming language, get some lab experience, get research experience, or get tutoring experience. Take cold showers, and take biohacking supplements when you wake up and before you go to sleep.

[pale orchid]

The reason doing yourself a massive favor right now produces so many gems and visionaries is because doing yourself a massive favor right now is definitively hard, and has the hardest problems known to man, so men who consistently push themselves to solve adverse problems, will attain a generalizable ability to develop creative solutions to problems with ease as oppose to only dealing with the problems of a regular joe life, people who have been through it develop street smarts and learn how to solve street problems, but you can only see so many street problems, there are thousands of doing-yourself-a-favor-right-now-related problems in physics engineering and many other disciplines it is pure beauty!

[errant rock]

are you recommending tutoring experience so they can be a better teacher somewhere down the road or is it to look more impressive on grad school apps ?

[crystal stone]

A lot of times schools will hire based on experience in math education. It can make the difference between getting a position and not at some institutions

For example, at Long Beach State there is a heavy emphasis on teaching ability

and only a slight emphasis on research ability

Also some top tier universities in Math hire positions specifically for teaching mathematics

Outside of that, making some side cash feels good

And it helps you reinforce what you need to know

[errant rock]

moonbears can i ask you a few questions via dm you mentioned something about math education a while back and i dont want to doxx myself

[nimble shuttle]

#grindset #Finance #business

[crystal stone]

sure

Office hours w/ MoonBears time

[errant rock]

okay accept my friend request from a while back

[inner finch]

😎

[crystal stone]

oh lol

[inner finch]

#grindset channel when

[crystal stone]

I don't see it @errant rock

send again?

[nimble shuttle]

need math motivation

[crystal stone]

As Do I

[atomic hornet]

Why cold showers

Cold showers r gud tho

[atomic cypress]

do yourself a massive favor right now and get published in annals. will save you a lot of work later

[inner finch]

the easiest way to cure depression and turn into a literal superhuman is take a 10C shower

[atomic hornet]

R u meming?

I feel like that is something Joe Rogan would say.

[inner finch]

i am 100% serious

literally just take a cold shower bro

man up

[torn willow]

Scrooge is as serious as Scrooge

[atomic hornet]

Cold showers, carnivore diet, TRT, nootropics

[inner finch]

Is TRT an explosive

[atomic hornet]

Explosive gains

Testosterone replacement therapy

[inner finch]

lmfao

just pump yourself full of testosterone 😎

i am very healthy

[atomic hornet]

Basically for when men turn 40-45 and T levels start going down.

[inner finch]

i will never get sick because i do mixed martial arts

healthiest body

healthy body healthy mind 💪 #grindset

[inner finch]

class warfare.....

being poor is a choice...

[lunar panther]

Please don’t

[inner finch]

?

[crystal stream]

10 c showers will literally turn you into a demigod

[inner finch]

most people can't handle 9C showers

but if you can do it

[crystal stream]

it's the one thing I can't force myself to do

[narrow rock]

90 c showers

[atomic cypress]

9c showers turn you into terence tao

[limber perch]

8c showers turn you into me

[mortal oasis]

Why are we using metric units :/

[last oxide]

only if you whistle in the dark

[static loom]

and if you say "terrence tao terrence tao terrence tao" into the bathroom mirror he appears

[deep mango]

@neat lintel

[vapid birch]

is there an acutal proof of the finite arithmetic series? for some reason, it doesn't sit right with me that its proof by induction

[deep mango]

eat it.

[limber perch]

what specifically about “the finite arithmetic series” are you confused about proving

[vapid birch]

like they say it works just bc it works for any input

but like how was it made up and how were the parts put together

there's no way somebody just put the formula together and coincidently it works

[limber perch]

which formula are you talking about…

[crystal stream]

i'm guessing little gauss?

yeah

[limber perch]

there’s a few intuitive proofs for this too

[vapid birch]

rlly?

[limber perch]

so this formula isn’t for any finite arithmetic series, it’s specific to 1 + 2 + … + n

[vagrant kestrel]

I agree induction proofs aren't satisfying

[limber perch]

(if you didn’t already realize)

[vapid birch]

oh, right

[limber perch]

but there’s this cute proof gauss supposedly did when he was 12 or something

[rose dock]

Uhhhh

[crystal stream]

there's a nice geometrical proof as well

[rose dock]

Maybe it's worth looking at discrete integration

[torn willow]

Sir,You won't like CS

[crystal stream]

discrete integrals fascinate me

[rose dock]

But there's also another way to think about it

[limber perch]

@vapid birch try pairing the first and last terms off

[torn willow]

discrete integrals are just normal sums. idk what's so special about them

[limber perch]

and see if you notice anything

[crystal stream]

mostly is that you have an analog of the ftc for discrete sums

[limber perch]

also to make things easier assume n is even

[vapid birch]

hmm, alr

[rose dock]

If you have 1, 2, ...., n - 1, n. You can put 1 + n, 2 + (n - 1), ...

If n is even you'll have n/2 of such pairs

That evaluate to n + 1.

[limber perch]

well then…

[static loom]

you have n copies of (n+1) and you double counted so n*(n+1)/2

[vapid birch]

ugh, i rlly wish i could understand this, but i just can't understand it

[static loom]

it's easier if it's just written out rather than described through discord messages lol

[crystal stream]

there's a very nice geometrical proof for the sum of odd numbers

[atomic cypress]

arithmetic is just a theory anyways

[static loom]

I'll just fix a specific n to make it clearer to type out,

1 + 2 + 3 + 4
4 + 3 + 2 + 1

5 + 5 + 5 + 5

Here I added the sum to itself, but backwards @vapid birch

there are 4 terms and each of them are 5

so it's 4*5 but we double counted so divide by 2

4*5/2 = 1+2+3+4

[crystal stream]

there's also a really nasty way of getting the result

by differentiating the finite geometric series and taking the limit as x -> 1

not particularly enlightening but it allows you to get the sum of arbitrary powers of the first n integers

[limber perch]

that was pretty enlightening

[limber perch]

this is a little more involved right

you need to multiply by x before differentiating each time

to restore the alignment

[crystal stream]

I think you can get away by just differentiating and expanding the product

[limber perch]

no I mean

you have

[vapid birch]

ohhhhhhhh, i got it now!!! thx, that display helped a lot

[limber perch]

f(x) = 1 + x + x^2 + … + x^k = (x^(k + 1) - 1) / (x - 1)

f’(x) = 1 + 2x + 3x^2 + … kx^(k - 1) = some nasty thing

then to find 1 + 2 + … + k you take the lim as x -> 1 of the expression you get for f’(x)

but to find 1^2 + 2^2 + … + k^2 you can’t differentiate f’(x) immediately. you first have to multiply by x to realign the coefficients:

g(x) = xf’(x) = x + 2x^2 + … + kx^k = some nasty thing

g’(x) = 1 + 2^2(x) + … k^2x^(k - 1) = some nasty thing

then to find 1^2 + 2^2 + … + k^2 you do the same thing and find the lim as x -> 1 of whatever expression you get for g’(x)

to keep doing this for higher powers you follow the same algorithm: multiply by x and differentiate

[crystal stream]

ye it's better that way actually

[astral marsh]

o o o o o o
x o o o o o
x x o o o o
x x x o o o
x x x x o o
x x x x x o
x x x x x x

1 o in the first column, 2 os in the 2nd, and so forth (6 in the last)

the total number of os is 1 + ... + 6

[crystal stream]

https://www.wolframalpha.com/input/?i=limit+x->+1+d%2Fdx+(x+*+(d%2Fdx+\frac{1-x^n}{1-x}))

[astral marsh]

now you can rearrange 1 + .. + 6 in the form of the xs

and you get a square

now how many os and xs do you have in total? just count the length of the sides

[limber perch]

it’s one index off from the right formula because you inputted x^k - 1 instead of x^(k + 1) - 1 in the numerator

[crystal stream]

Oopsies.

I always forget you get an n + 1 term above

[static loom]

you're welcome 👍

[vapid birch]

ahh i see, 1/2 * 6 * 7 and n = 6. thats also a very clever way

[astral marsh]

yes

you can do it for 1^2 + 2^2 + 3^2 + ... + n^2

but it's easier to just use numbers instead of shapes entirely

you do 3 triangles

-----1 n n
2 2 n n-1 n-1 n
3 3 3 n n-1 n-2 n-2 n-1 n
.. . . . . . . . .
n n ... n n n-1 ... 1 1 2 ... n

the first row of the 1st triangle is 1^2

then you get 2 + 2 = 2*2

then 3 + 3 + 3 = 3*3

so all the rows are k^2

the other triangles are the same triangle but rotated in all 3 ways

so each triangle is 1^2 + ... + n^2

but if you add up all the triangles at once

you can look at every single spot

at the very top spot it's 1 + n + n = 2n + 1. in the 1st spot of the 2nd row you get 2 + n + n-1 = 2n+1

and so forth

so you get some number of 2n+1s, and you count that number

[limber perch]

ah, that’s why the formula for squares is a multiple of n(n + 1)/2

and i bet there’s a 3 dimensional version of this with tetrahedrons which shows why the sum of cubes is (n(n + 1)/2)^2

who’s slim talking to

[cold needle]

me

[deep mango]

Do yourself a massive favor right now. Either pick up some programming language, get some lab experience, get research experience, or get tutoring experience

[limber perch]

Do yourself a massive favor right now. Answer my question in #advanced-analysis

[sharp mulch]

~r3

[quasi jetty]

From

#❓how-to-get-help

Rule 3

Stick to one channel and don't post the same question in multiple channels. Please don't ask for help in other channels if no one is responding in the one you have posted your question in.

[dawn osprey]

You know how every episodic tv show (especially the crime ones) have a "genius" episode? Where some stereotypical smart dude is involved in the case, a chance for the main characters to prove how smart they are?

I always cringe whenever they're a mathematician cause it's always variable how accurate they are

I'm pleasantly surprised that The Mentalist actually does a pretty good job!

The guy actually says stuff that makes sense about the zeta function, and some offhand remarks on 4th order differential equations

Nevermind. They just started talking about a "universal hack", something that could decrypt any encryption. So much for that

[crystal stone]

I too make off hand remarks about differential equations to my colleagues who know nothing of math

[crystal stone]

They solved the one time pad problem

[dawn osprey]

To be more explicit, the zeta function stuff was a recording of a lecture he gave

The fourth order differential equation was a textbook he had

Just to be fair :^)

[dawn osprey]

Yeah lol like to see how it works on that

[dawn osprey]

FINALLY some realism

The wife killed the mathematician because he was too busy with math for sex

Then again the device "worked" so... bleh

[sharp mulch]

[leaden torrent]

👀

[summer nest]

Gets where

[cold needle]

starlight kick

https://images-ext-2.discordapp.net/external/JbwSsqcQv8mbfIQMVJcRNyxPJS7YGc2K5iBe3T1MmDM/https/imgur.com/qq04n2C.gif

[sharp mulch]

[cold needle]

😭

[ivory mason]

https://tenor.com/view/bonk-gif-18805247

[cold needle]

i didn't even say anything horny why am i already being called out for hornyposting

😭

[ivory mason]

poggers?

[pure sun]

"already" implies that you were in fact hornyposting

[cold needle]

er

poor phrasing

fuck

[pure sun]

just that you didnt think you should have been called out for it yet

[cold needle]

time to vanish

[ocean barn]

I need some advice here, I do academic challenge (a advanced program you start in 7th grade until college if chosen) for both ELA and math, so far math has been challenging for me in terms of having the motivation to do it and understanding the new things and I really do not like doing it. Should o drop out of it and just do ELA?

[pure sun]

do what you want

if you're close to finishing it, maybe it's worth it just to stick with it to the end

just so you can say you did it, and in college you're probably going to have to take some math course

then again, i wish i had stuck with some things that i used to not like doing but now wish i was able to do

[modest rune]

thats always an interesting feeling to me bc like

part of wishing i had stuck with something

includes the idea that the labor / suffering would only affect past me

and as a result what I really want

is free skills

[neat lintel]

What’s ELA

[modest rune]

like i would love to know how to play an instrument and i never stuck with one

and i kinda wish i had

but only insofar as the hard part would already be the in the past

[neat lintel]

Ok I’ve read that ELA is English, stick to math ELA is very useless for college if u wanna study stem

[pure sun]

why are you just assuming they want to study stem lmao

[broken scaffold]

horny metal

[neat lintel]

shiver

[broken scaffold]

quake

wobble

mathematica

[neat lintel]

People who don’t give a f about math are not in a math discord

spend some more time here

you'll be surprised

[deep mango]

Definitely false, even though it is a reasonable assumption

[blazing pawn]

I wonder if there are people in the math discord here for

Help

[deep mango]

Lots of "do my homework"s here

[blazing pawn]

With math

[limber perch]

who's f

[neat lintel]

Should be restricted to people over 18 then

[deep mango]

f deez nuts

[deep mango]

Yes someone mod this person

[neat lintel]

Isn’t discord over 18 anyway?

[deep mango]

Over 13

Or 13 and over I guess

[limber perch]

if you're under 13 the fbi will come to your house

[neat lintel]

Ok

[deep mango]

We had someone joke about being under 13 and they got banned from one rando reporting them lol

Like ultrabanned

From all of discord

[neat lintel]

Lol

[deep mango]

and how precisely do you propose we stop gun violence if the cops can't raid children's homes?

Only the homes of people I don't like of course.

[pale orchid]

naryc

[deep mango]

RY Dual p.

[pale orchid]

RYpp?

[limber perch]

when you take "fuck the police" too literally

[deep mango]

[neat lintel]

Bro wtf

Is that real?

[deep mango]

What type of math do you do Len11235813

[neat lintel]

Engineering

[deep mango]

Oh, I see

[pure sun]

that explains things :/

[neat lintel]

Control theory

[deep mango]

Control theory is nice

[limber perch]

len is a narc?

[neat lintel]

Yes

Still undergrad mechanical engineering though, starting my masters next year in control and optimization. But had the opportunity to take several Systems theory and control classes and write my bachelor thesis in that field soon

[deep mango]

I don't know a ton of it, I just know a lot of the background math. Like calculus of variations.

[neat lintel]

Yeah that would get you started in optimal control really fast

The applied classes don’t really count

[pale orchid]

lol

[neat lintel]

But that’s mechanics

[odd narwhal]

Wat

[limber perch]

I saw some talk

where they said

counting the number of rational points inside the (dilated) unit circle

is equivalent to the riemann hypothesis

or something like that

yeah this makes no sense lol

https://people.math.osu.edu/aggarwal.78/iisertalk_aggarwal.pdf

lattice points, not rational

[odd narwhal]

???

How can you claim that tho

When there's like, an infinite family of counterexamples

[sharp mulch]

Counting lattice points in circles is very hard

It’s why harmonic stuff in many dimensions is hard

[vagrant kestrel]

mood

[odd narwhal]

I can imagine NJ Wildberger claiming smth like that

But for real

He'd probably have the opposite stance tbh

That there are only rational points on the unit circle

If he even believes in the unit circle since that kind of implies an infinite collection of points

[limber perch]

wow

rational points on structure x seems to form a group often

albeit the group operation being quite different in each scenario

[deep mango]

[vivid halo]

only on Abelian varieties or like affine group schemes

but e.g. rational points on curves of genus >1 you don't get the group structure

[sacred geyser]

control theory

so much fun

i got really into optimization in my first year and i do similar things still, though not remotely related to engineering

[vivid halo]

lmfao

[static loom]

he has coined this set of increasing decimal number versions of pi "Wildberger sequences"

[vast surge]

Noncommie algebra should be called capitalist algebra.

[molten oyster]

Mathematicians are masochist change my mind

Im just kidding by the way

[reef carbon]

peak humor

[torn willow]

Tell me a stem thing that doesn't involve being masochistic

[static loom]

there's some element of truth to it, but idk if I'd describe it as masochism exactly

the difficulty is part of it, everything else is just not as difficult, and so by comparison is just boring

challenge is fun

[pale orchid]

Math is indeed beautiful. The difficulty is part of it, everything else is just not as difficult, and so by comparison is just boring. It produces so many gems and visionaries because math is definitively hard, and has the hardest problems known to man, so men who consistently push themselves to solve adverse problems, will attain a generalizable ability to develop creative solutions to problems with ease as oppose to only dealing with the problems of a regular joe life, people who have been through it develop street smarts and learn how to solve street problems, but you can only see so many street problems, there are thousands of math problems in physics engineering and many other disciplines it is pure beauty!

Merosity, 12.07.2021

[static loom]

sometimes I amaze even myself with my own eloquence 😌

[pale orchid]

,pin

[cinder zephyr]

just cause it's difficult doesn't mean it's bad

many things are difficult and people find them to be worthwhile (see: art and sports as examples)

[modest rune]

to be very clear

math is like

an easy job

you cant call academia “masochistic” when like coal miners exist

or any form of stem

[torn willow]

True

[static loom]

not really what masochism means

people who do math are seeking it out, coal miners aren't necessarily

[deep mango]

I have a passion for coal mining. But I resigned myself to a fate of mathematics in a desperate attempt at self-flagellation.

[cold needle]

hextillionaire grindset

[torn willow]

Advice:Do not become a hextillionare

[neat lintel]

Advice: Don't buy an iPhone

[ancient flame]

you could be a coal mathematician

calculate the price of the coal on the spot

[crystal stone]

@sharp mulch I found a Numerical Methods book at the used bookstore

Chapra

It was pretty cheap, uses MatLab which I'm in the process of (not totally procrastinating) and learning

Do you have any opinions on this thing?

[sharp mulch]

No

[crystal stone]

Any opinions at all on numerical methods

Strong feelings one way or another for a novice

[modest rune]

masochism requires the job be hard or painful

[brave hollow]

and you to like the job?

[modest rune]

A and B necessitates A

[sharp mulch]

I usually recommend Demmel's Numerical Linear Algebra and Iserles' Numerical Methods for differential equations

[spring lodge]

I wanted to post this here since it's not a school question or anything, I'm mostly picking brains.
I noticed that sqrt(1+sqrt(1+sqrt(1+sqrt(1+sqrt(1+sqrt(1+...... = 1+1/(1+1/(1+1/(1+1/1+1/...... = the golden ratio
Why are those first two equal? Can you show mathematical proof? A link explaining it is okay.

Ping when answered, notifications are off, thanks :)

[rose dock]

Write it as a recursively defined sequence

The first number is the limit of the sequence recursively defined as 1 + 1/x where x is the previous term

And the second number is the sequence recursively defined as sqrt(1 + x) where x is the previous term.

You want to find a fixed point, so you have 1 + 1/x = x and sqrt(1 + x) = x

You can see the first and second equations have the same solution

[neat lintel]

make sure to ping em

[rose dock]

@spring lodge

[pseudo lotus]

look for geometric representations of this too.

[blazing pawn]

ok tbf academia is a thing people do specifically because they want to do academia more than anything else

I dont think there are that many people that like

dream of being a coal miner

like i dont think id call coal mining masochistic so much as it is just sadistic on the part of capitalists

[deep mango]

No, I'm an academic because my parents said I had to be one.

[blazing pawn]

Lol what a nerd doing what his parents tell him to

[modest rune]

Again you’re missing my point hahaha

Something can’t be masochistic if it isn’t painful

[deep mango]

Your point is wrong then

[modest rune]

Masochism is enjoying something painful

In particular because it is painful

So like

[deep mango]

But coal mining is just as bad of an example of masochism as academic life is

[modest rune]

Again you’re missing my point lol

I only brought up coal mining because in order to think academia is a hard job you have to be forgetting just how hard and awful some other jobs are

[deep mango]

We missed your point by staying on topic

I see

[modest rune]

Huh?

The entire topic was “stem is masochistic”

And I was explaining why that’s nonsense

[deep mango]

"stem isnt masochistic because some jobs are way more painful"

[modest rune]

Thats not what I said

Stem isnt masochistic because in order to think it is at all painful you need a stunning lack of perspective

[torn willow]

I wasn't being serious

It was more of a response to "math is masochistic"

[deep mango]

That's ok, I just want an excuse to argue semantics

[deep mango]

Now that your point is well-communicated, it is inarguable.

As in I can't argue against it

Darn.

I do think that's making a big assumption though, like surely there are plenty of people for whom stem is emotionally more painful than coal mining is physically painful (assuming best practices are taken in the mining operation)

Maybe that's not the average person

And in any case, we're comparing random coal miners with random wannabee academics, not the experience of the average person in either role

[whole copper]

Grad students suffer from great rates of depression

How is that not painful?

[leaden torrent]

i almost feel like describing that as "painful" trivializes it

or at least mischaracterizes it

in any case, one big difference between academia in general and a lot of other career paths is

if someone is picking academia, thats typically a real choice

its not like a poor rural person getting to choose "work 12 hours in a farm all day or work 10 hours in backbreaking labour in coal mines"

fair

not really

im not saying that this in any way diminishes how difficult and taxing academia can be

its just that most people who went into academia "signed up for that" so to speak

ie they went in:
(a) knowing it'd be very difficult
(b) with other real career options available

i guess that is masochism then lmao

i mean not literally

but i get what youre saying

[bronze pelican]

My career is professional masochist

[distant vortex]

I can't join this conversation in case I accidentally agree with ultra :(

Me too

[bronze pelican]

If someone enjoys really spicy food, I'll call them a masochist

[candid oak]

those guys are psychopaths for me

[leaden torrent]

but i dont think its fair to say that people in academia enjoy all the stress lmao

they enjoy the actual academics part

but not all the bells and whistles associated with it

[mortal oasis]

I think at some level they do

I know I do

[leaden torrent]

i certainly dont

[bronze pelican]

The mental pain of solving hard math problems is fun

[leaden torrent]

if i could just do research without the tenure chase and grant app process breahting down my neck 24/7

i'd be much happier

im still willing to put up with that since i like math

[distant vortex]

I mean the original person was just talking about mathematicians, so I'm pretty sure they just meant the frustration of doing math and not academia

[leaden torrent]

but its certainly not a perk

[bronze pelican]

In that sense I do math for a masochistic reason, pain is not necessarily bad

[mortal oasis]

Oh I see what u mean

[bronze pelican]

Based

[vast surge]

Yes but most of us do math for masochistic reasons

[mortal oasis]

STOP BEING HORNY FOR MATH

Got em

[bronze pelican]

I'm always horny for math

[distant vortex]

Is it still masochism if you don't like the pain but you like the relief when it ends?

[candid oak]

there's some kind of pleasure when you figure out the solution, so it's not actually doing math for pain but for something that comes after it

[crystal stone]

Academic work can still be exploitative in STEM fields, while other workers are exploited even more; I dunno if that makes it masochistic if you go into them

[bronze pelican]

No, I find the actual hard work during the problems solving fun too

I can be stuck on a problem for hours and hours and that can be both painful and enjoyable

[candid oak]

yeah it is fun indeed

[bronze pelican]

[candid oak]

but not the only fun

[candid oak]

sometimes it's frustrating

[bronze pelican]

Of course

[candid oak]

Riemann hypothesis's just a pain in the neck

[bronze pelican]

People enjoy thinking about hard problems
Not just to solve them but because it's fun to work on and make partial progress

[crystal stone]

Not finishing your PhD thesis in sub 6 months

Are you even trying Ultra?

[candid oak]

yeah well that's when you have the hope to solve the problem since the solution already exists

but what about problems that don't have soluttions yet

[bronze pelican]

That's the most exciting

You're walking uncharted territory

[candid oak]

well

true

but

what about Godel's theorem

[bronze pelican]

Ultracomedian

Of course , Godel's theorem is what causes me the most pain as an academic

[candid oak]

I personally find it unnecessary statement

it didn't advance mathematics in any way

at least for the moment

[bronze pelican]

[candid oak]

that's scary haha

[nimble shuttle]

Guys how do you cope with the fact that there are mathematical theorems that are true and can revolutionise the world but we will never be able to prove them due to Gödel incompleteness theorem

[candid oak]

ok then I'm an idiot

[brave hollow]

sigh
well i have good news
(1) literally every example of a statement independent of ZFC we have is some weird ass statement from set theory or number theory that certainly wouldnt "revolutionize" the world if it was provable - and we currently have no reason to believe we're likely to find an actually useful theorem independent of ZFC any time soon
(2) even if the above was a concern, we could simply add an axiom that asserts its truth or falsehood - thats the point of independence (and it's what we do with the axiom of choice already)
[here "ZFC" actually means ZFC + some extra topological cardinal stuff]
[blah blah semantics]
incompleteness is of far more theoretical interest than practical.
there are philosophical concerns of whether there exists a "right" framework for mathematics and whether arbitrarily adding axioms (and potentially causing our canonical model to "stray from" the "right" framework) creates philosophical challenges
but you have to be like, a hardline platonist to spend a lot of time thinking about that
and even if youre concerned by that, it hasnt really proven an issue yet besides for choice
(and we've been able to come to a pretty good consensus on choice)
that said, "math was all powerful and undefeatable" is a romanticized statement at best and certainly naive
but not really for this reason
the main practical problem posed by incompleteness isnt really incompleteness at all, but rather the halting problem
but again, the halting problem prevents a lot of stuff from being "perfect", but we can still come very very close
look at compilers; the halting problem implies no "perfect" compiler exists in that it will be able to catch any and all errors before we run the code, but modern compilers get pretty damn close for common applications.
(in the right development environment and whatnot)

i dont mean to trivialize your concerns, but i wouldn't be super shaken by incompleteness.
if there's a mathematical statement that starts with "Godel" to get shaken by, it's certainly Godel's completeness
i still dont believe it
feels too free

[neat lintel]

https://youtu.be/HeQX2HjkcNo

[candid oak]

that's convincing

[brave hollow]

credit to @ namington

[candid oak]

I appreciate you guys for sharing amazing perspectives for free

[pure sun]

who said they were for free

[candid oak]

oh crap

then I'm an idiot again

[cold needle]

Pay up.

[candid oak]

sure

but there's a little problem

I have so much money in my bank account that it has become inaccessible due to the high level of density

reminds me of information paradox

[rancid meadow]

is this real did u just write this

[brave hollow]

.

[rancid meadow]

wow

[cold needle]

lol

[brave hollow]

well I was trying to turn it into a copypasta

[vast surge]

sigh
well i have good news
(1) literally every example of a statement independent of ZFC we have is some weird ass statement from set theory or number theory that certainly wouldnt "revolutionize" the world if it was provable - and we currently have no reason to believe we're likely to find an actually useful theorem independent of ZFC any time soon
(2) even if the above was a concern, we could simply add an axiom that asserts its truth or falsehood - thats the point of independence (and it's what we do with the axiom of choice already)
[here "ZFC" actually means ZFC + some extra topological cardinal stuff]
[blah blah semantics]
incompleteness is of far more theoretical interest than practical.
there are philosophical concerns of whether there exists a "right" framework for mathematics and whether arbitrarily adding axioms (and potentially causing our canonical model to "stray from" the "right" framework) creates philosophical challenges
but you have to be like, a hardline platonist to spend a lot of time thinking about that
and even if youre concerned by that, it hasnt really proven an issue yet besides for choice
(and we've been able to come to a pretty good consensus on choice)
that said, "math was all powerful and undefeatable" is a romanticized statement at best and certainly naive
but not really for this reason
the main practical problem posed by incompleteness isnt really incompleteness at all, but rather the halting problem
but again, the halting problem prevents a lot of stuff from being "perfect", but we can still come very very close
look at compilers; the halting problem implies no "perfect" compiler exists in that it will be able to catch any and all errors before we run the code, but modern compilers get pretty damn close for common applications.
(in the right development environment and whatnot)
i dont mean to trivialize your concerns, but i wouldn't be super shaken by incompleteness.
if there's a mathematical statement that starts with "Godel" to get shaken by, it's certainly Godel's completeness
i still dont believe it
feels too free

[sharp mulch]

Real numbers don't even exist, CH has no practical implications

[narrow rock]

yup, imaginary numbers are the ones that actually exist

[sharp mulch]

Q and Q[i] might exist

[limber perch]

@ultrafinitism

[sharp mulch]

Certainly not R though

Maybe algebraic numbers exist

[short pivot]

have u ever seen one?

[limber perch]

I saw one in the wild once

it ran away before i caught a good look though

[short pivot]

oh man. may we continue our never ending search for the algebraic numbers

[sharp mulch]

I don't think I've ever seen an algebraic number before

Have you

[short pivot]

got pretty close. almost saw a wild square root after cutting some wood into triangle. measurements were off tho and it ran away

[sharp mulch]

Gosh darn measurement error

[calm vessel]

@Baratoth

@dreamy quartz

If the circle doesn't exist and is just an arrangement of points

What about the properties of a circle

Does that also not exist??

Or are properties "simples"

I. E if everything is just arrangement of partless things then what about the patterns in the arrangement

If those don't exist then what does it mean to prove something about those arrangements in math?

Can't seem to find the download

https://philpapers.org/rec/CORMNA-4

Am noob srry e.e

Like the download is paywalled :/

[neat lintel]

not for me

http://clok.uclan.ac.uk/18982/1/18982 Corrected Version.pdf

[limber perch]

scih*b exists

[neat lintel]

this wasn't stolen. i simply clicked two links from that page

[limber perch]

pro pirater

[calm vessel]

Thanks man!

[neat lintel]

CLOSED

[limber perch]

Want to improve this question?

[neat lintel]

https://mathoverflow.net/questions/187106/grothendieck-sad-news

[sleek wing]

if you write someone's name in the death thread do they die within the hour

[limber perch]

you have to think of their face while writing it

[calm vessel]

The paper outlines a reason as to why it's fine

Everything is arrangement

XD

Yeaa

[whole copper]

Atoms go brr

[calm vessel]

The paper is weird, how is him using the word collectively any different from invoking a collection of particles?

[whole copper]

More is different

[calm vessel]

So basically you make a bigger statement rather than referring to the group

That's BS

e.e

If you admit an emergent property even if via collective instantiation

Won't that entail the collection as a meaningful entity to talk about

Oh e.e

Hmmm

Okay then whats the difference between emergent properties and arrangement

I mean like

If they both arise from just simples in relation to each other

How are they different?

I mean in the sense that the "atoms" make up a chair in the same way as "atoms" making up consciousness. Like the word "emergent" looses meaning right?

[compact tartan]

hey how's MP denial going

[calm vessel]

Exactly

Like they both are identical in this framework

Oh?

I mean they both are identical kinds of properties

Both are emergent

Or both are arrangement

I mean I accept that chair and consciousness are distinct

What I'm saying is that it's meaningless to label one as emergent while the other as not

Unless there is some way to distinguish within the simples only framework

Ohh

So consciousness is a non trivial arrangement

[vivid halo]

Some people argue this yes

[calm vessel]

And chairs are pretty trivially arranged

[vivid halo]

This is what I personally lean towards in absence of actually understanding what’s going on here

[calm vessel]

This feels extra troll

XD

Simples but not when I say so

Cooool

Wha tpositiom do you take

W. R. T existence?

[median summit]

Why should you never trust an atom?

Because they make up everything

[calm vessel]

XD

[broken scaffold]

HA

[median summit]

lol

Saw it in my chemistry class

[calm vessel]

Also what does it mean for something to exist

[median summit]

What determines luck?

[calm vessel]

Dice

[median summit]

Diceee/

[calm vessel]

I meant this smwhat srsly since, if we are worried about classifying collections as existing or not. Then it means smth to say smth exists

What is that meaning??

Huh

Are you saying we can't define once and for all what it means for something to belong to another?

Can't I talk about properties

A higher thing has more properties

But also all the properties of the subset

I mean all the properties of the part

Why isn't that a formal designation of part hood once and for all

The beatles share John Lennons music

But the beatles have more music

Huhh

So John Lennons won't be considered as a part

Yeaah

But like there are stuff he did that's not beatles

Isn't that sufficient to conclude he isn't a part

[summer nest]

I feel like beatles are overrated

[calm vessel]

Doesn't it determine that he isn't a part?

Because hes done music that the beatles hasn't done

Something belongs to him that doesn't belong to the Beatles

Oh wait

You have a specific conception of part hood

Dang

Isnt that an algorithm?

Aah

So you want it to be run with Turing machines??

Yeow

What I think you're saying is that there may be no formal way to decide part hood given that part hood is when it "makes sense"

I think tho makes sense is ill-defined. But on the other hand the inability to define it is what you're claiming to be plausible.

-<

Btw this kind of piqued my interest

What does it mean for smth to exist

To a Nihilist or smth

What exactly are they denying??

[summer nest]

To a nihilist nothing probably