serious-discussion

[narrow rock]

who is Keith Elliot Peterson

[untold sapphire]

jesus don't scare me like that

[narrow rock]

[untold sapphire]

are you guys actively collaborating on this

[narrow rock]

THEY CALL ME MISTER HOMOLOGICAL ALGEBRA

[untold sapphire]

who is this

[narrow rock]

Dirac

The Rock

[untold sapphire]

oh my god

[narrow rock]

This one's pretty funny

[deep mango]

[narrow rock]

did you read this book ultra

https://www.amazon.com/Quantum-Fields-Strings-Course-Mathematicians/dp/0821820125

that author list

slim it has dynamical aspects

hermitian sex operator

she does model theory?

[deep mango]

why are you some keith character now

what happened to the days of slimvesus and brofibration

I am go to backs.

[narrow rock]

?

[deep mango]

wtf is an animated pitbull

why are you and dami pitbulls

[narrow rock]

THEY CALL ME MISTER HOMOLOGICAL ALGEBRA

[deep mango]

😵‍💫

[narrow rock]

we're pitbull

not pitbulls

I am the derived version

Jesse geometry arc

wtf there are 4 volumes

[bronze pelican]

I have no idea how to read this

[narrow rock]

it's a book cover

idk what the physics side is (the feynman diagram thing)

but the math side is the index theorem

I assume that's the point of the book

[leaden skiff]

hey what's the difference between heometric algebra and algebraic geometry

[fast ivy]

Algebraic Geometry is a big field of math that historically has its roots in the study of locus sets of polynomials.

[leaden torrent]

algebraic geometry is a field, geometric algebra is something physicists do because they dont like multivar

[leaden skiff]

algebraic geometry is abstract algebra?

[leaden torrent]

it uses abstract algebra

[fast ivy]

It uses a lot of commutative algebra

[last oxide]

geometric algebra aka exterior algebra aka geometry aka diff forms

[fast ivy]

Commutative algebra is somewhat "local algebraic geometry"

[leaden skiff]

is it differential geometry?

[leaden torrent]

commutative algebra is "collection of random facts that sound a little bit too hard for intro ring theory but a little bit too obvious for anything else"

no, differential geometry is a field of analysis

theres connections but theyre very different fields

[last oxide]

literally connections

[leaden skiff]

I really should sit down and actually study a higher math textbook someday

[last oxide]

or higher math class notes howboudah

[fast ivy]

Yeah so, algebraic geometry is really big and influenced a lot of the mathematics of the 20th century. Stuff like algebraic varieties, projective varieties, Zariski Topology, Schemes, Sheaves, Sheaf Cohomology, Cech Cohomology, Weil Cohomology...

People still do research on it up to still day

[spare osprey]

hypothetically, if i wanted to spend money, but only a little, to learn math, where should i spend it?
i wanted a kindle because epaper is nice on eyes and electronic storage is good but i heard they suck with math and i was sad
i dont like to read on my monitor. even tho its ips... oled iphone spoiled me

well rn my problem is i dont have a self study plan at all

[light needle]

get an ipad

good investment beyond math

[spare osprey]

had two ipads die on me

[light needle]

oof

get a third one

[mild nebula]

I don't see why a Kindle is a bad idea

I've never actually done that though

[spare osprey]

someone told me kindle cant handle the formatting

or something

[leaden torrent]

can kindles manage generic pdfs

or do they have to be some proprietary format

[mild nebula]

A pdf will format correctly on anything that can read a pdf

I am now realizing how little I know about Kindles

[spare osprey]

i dont rly know about kindle either so mb ur right

[leaden skiff]

idk if that's true

Ive had pdfs get mangled on my kindle

[mild nebula]

Fair, they should ideally always be the same but stuff happens

[leaden skiff]

technology is fucky

[mighty bolt]

Good news, They're considering getting me a grant for a PhD at my university!! 😮

They just need the money lol

but still

I genuinely thought I was no way near clever enough for that, so I'm really surprised about it 😮

[leaden skiff]

that's epic

but also what does that mean for you?

[mighty bolt]

It means everything. It's some sort of proof that I'm clever enough to actually achieve what I want 😮

[leaden skiff]

yeah but like what does getting a grant let you do?

[mighty bolt]

continue at my university. I love that place 😄

and also. It lets me continue on my master thesis 😄

[leaden skiff]

what would you have done if you hadn't gotten the grant?

[mighty bolt]

No idea. I haven't gotten it yet. But probably searching for a job somewhere XD

I have no idea about what I actually want besides continuing on my work from my Master's thesis

[reef carbon]

commutative algebra is one of the classes i was thinking of taking for my masters

[surreal sapphire]

do it

i wanted to do it my first master semester but the prof cancelled the class

because there is no "big theorem to work towards"

and "students will be left wondering why they even took the class"

[mighty bolt]

what 😮 that just sounds silly 😮

it sounds like the prof is only result oriented, and doesn't give a shit about the actual people attending the class :/

it's probably just an excuse, but what do I know. I'm stupid

[surreal sapphire]

well, the class should be fun for prof and people attending

a class that is just "here is a bunch of stuff that you might need later" that's not fun i guess

[mighty bolt]

True. One of the most important things are teachers who actually aspires other to continue their work

And teachers who show engagement!

[vast surge]

Commutative algebra is fun so far I think.

So far it's also pretty well-motivated, which is nice.

[neat lintel]

In the past few semesters I have never seen or heard from my teachers except for syllabus, announcements on blackboard.

I paid money for class just for weekly assignment, quiz and exams

[deep mango]

[stray kite]

is it considered appropriate to ask/email professors about things which dont have to do directly with their classes
like something in maths obv but just not to do with their classes, just something youre interested in

[deep mango]

Depends

[crystal stone]

Had an active shooter at my University this past week

Well, he wasn't active on campus, but he was active in the nbhd

Spent 3 hours locked in an office w/ no windows with like 4 faculty members

That was an experience

Nobody on campus got hurt

[neat lintel]

If it's in their research yeah, otherwise I think it's a bit rude to randomly demand their time

Maybe more acceptable if it's your supervisor/tutor

[stray kite]

i see

[crystal stone]

It was made worse when security told me that it was active on campus

[deep mango]

Wtf

That is horrible

[latent forge]

many such cases 😞

[crystal stone]

yUh. I had to yell at the math faculty to take cover

They were like what's going on

Then nobody wanted to volunteer to go lock the lab and the office (had to expose yourself to do so)

so I did it

Fkin' terrifying

[vast surge]

Depends on your relationship with them and whether it's something they know about. I'm not going to ask my analysis professor who studies ODEs that model diseases to help explain Nullstellensatz to me, and I'm not going to ask my algebra professor who studies commutative algebra and algebraic combinatorics about pandemic modelling. I'm also uncomfortable emailing professors I don't know and haven't taken courses with; there's still a few in my school's department.
There's also the fact that professors are individuals. You would know your professors better than I do; if you think they're the kind to be annoyed by a question, then don't ask them, but if they seem generally helpful and interested and go off on weird tangents about cool math in class when they're meant to be teaching other kinds of math, I'm sure they're the kind who would be more receptive to a question like that.

[mint patio]

@torn willow It's okay

Not amazing but best I can do

im not graphing v btw

[torn willow]

Good enough

[mint patio]

this is a scratch work paper

[rose dock]

Looks beautiful

[mint patio]

Thank you :)

[mint patio]

Final result https://cdn.discordapp.com/attachments/744939043955146802/881277282335993896/image0.png

b is drawn without a terminal point because it is much larger than the scale of the drawing

[mint patio]

?

[vast surge]

Why was I pinged?

[mint patio]

Good question

[vast surge]

I love evil, so we must be mortal enemies

[rose dock]

<@&268886789983436800>

[vast surge]

Please stop pinging me Al.

[blazing pawn]

[light needle]

Lol he is deleting

[blazing pawn]

he got banned

[vast surge]

Thanks

[blazing pawn]

[vast surge]

That was way too many pings

[jovial ember]

I’ve done this, like let’s say I took an algebra class w/ them and it’s over but I have an algebra class. I’ve only ever gotten good responses, in fact they’ve just told me “if I’m too busy to answer I just won’t” so they encouraged me to ask. Just my experience

[worn garnet]

There was a paper which went into detail about how people understand mathematics and give differences between the apppoarches whether it would be "symbolic", "visual", etc anyone have a link to this paper ?

Trying to find it but can't remember the title

[bronze pelican]

Thurston Proof and Progress

[worn garnet]

Yeah it was this one thx man 🙂

[analog salmon]

I asked the algebraic geometry prof at my university (who I had for a commutative algebra class) about how to construct groebner bases for a specific case since the people I were working with were topologists and less familiar with the details on the algebra side. He was happy to give a suggestion

[tall gale]

Please tell me i'm not alone. Does everyone has a subject where they become utterly dumb?

[deep mango]

Yes

In math

This is definitely algebra for me

[vivid halo]

real analysis for me

[light needle]

ditto nG

[velvet dagger]

Discipline for me 🙃

Also geometric reasoning is a bit trickier for me

[agile wedge]

anything involving computations

[neat lintel]

advanced math call is open

[weak pasture]

Anything involving computer science. Thank god I only have one more semester of it, but trying to decide even basic things like knowing how to write a "for...in... loop" just completely throws me off guard.

like... i cant even do it. Somehow I got an A in my last comp sci class, but I got lucky there. Could've been much lower if the prof wasnt nice enough to drop a second lab.

[tall gale]

Thanks god. I'm going through projective geometry and i've never go through something so slowly. Each concept and application is taking me ages to grasp. Makes complex calculus/analysis seems like a cakewalk

[untold sapphire]

what book are you reading for projective geometry

[tall gale]

Nigel Hitchin lecture notes https://people.maths.ox.ac.uk/hitchin/ as that's what my course uses as basis

I mean, it's not bad going through the notes, but then i try the exercises and i'm utterly stomped

I go from "yeah, i think i got it" to "i totally did not got it"

[velvet dagger]

Does your class have a term paper by any chance?

A "project" so to speak?

[narrow rock]

Of course. How else would the prof assign "grades"

[tall gale]

Not really, just a written test + oral examination

[velvet dagger]

Oh it was for the joke lol

[tall gale]

Its 7am and i havent slept, jokes are just going above my head. like this goddam subject

[wanton coyote]

subjective geometry

[hidden bone]

Hry

[thorn brook]

frick I have to buy my own books for school now

imma go broke

[neat lintel]

you don't have to

[thorn brook]

yeah I guess but they say that it is mandatory

[neat lintel]

just print the pdf

[thorn brook]

ez

[neat lintel]

Toki mfkin doki.....

I'm not sure what it's called in English

[thorn brook]

yo upcat

[neat lintel]

but then you can make the pdf like a book

[thorn brook]

yeah like a booklet I guess

[neat lintel]

wiring it?

dunno what those things at the end of notebooks are called, that keep all the paper together

[thorn brook]

like staples I guess

[odd narwhal]

big oof

[thorn brook]

I did that once lmao

you can like print in double pages "side ways" and then staple everything together in the middle and boom

[devout nacelle]

Printing PDFs can be very economical, there are lot of online platforms which print books and ship them

[thorn brook]

but that's a pain in the ass

[odd narwhal]

binder clips?

[neat lintel]

OOH

spiral bound it

that's the word for it

that's what I did

[odd narwhal]

adding to this, your uni might offer a cheap printing service

[neat lintel]

and still do

[odd narwhal]

with binding

[devout nacelle]

Right

[neat lintel]

it's hella cheap too

[thorn brook]

oohhh

[devout nacelle]

Like I got Munkres with the new LaTeX printed and bound for <$10

[neat lintel]

and it's pretty durable

[devout nacelle]

The paper quality is pretty nice as well

[thorn brook]

yeah I can give this a try one day

but I already bough some book lmao

too late

[devout nacelle]

[neat lintel]

noooo

[devout nacelle]

Hard to resist that temptation

[odd narwhal]

my uni offers printing for 4 cents a page

[devout nacelle]

Springer 1; Tokidoki 0

[neat lintel]

is that the college toki goes to?

[odd narwhal]

no that's the big publishing company

[devout nacelle]

No, Springer is the big publishing giant

[neat lintel]

[devout nacelle]

They have the GTM series

[thorn brook]

lmao that emote

[devout nacelle]

[neat lintel]

Small businesses rock!

[devout nacelle]

This is very economical holy shit

I'm getting 75 GSM premium paper for a little under $1/page

Oh wait no

Currency miscalculation moment

[thorn brook]

oh that's a new emote wtf

[devout nacelle]

I'm getting 1 cent/page

[thorn brook]

[neat lintel]

that's like ...

so economical

[devout nacelle]

It is!

[neat lintel]

if anyone ever plans to tackle prime numbers please get the fuck away from it

especially if you're trying to figure out the sum of all prime numbers

it brought me unluck and i haven't had this much hell in my life

[surreal sapphire]

[leaden skiff]

it's infinity

or well "it diverges" if you hate infinity

[neat lintel]

lol

well you're correct but

what i meant is

don't seek for the formula

don't work on it

[leaden skiff]

wdym formula

[neat lintel]

i have the formula because i've made it

[leaden skiff]

alright what is it

[neat lintel]

i won't tell

[leaden skiff]

why?

[neat lintel]

i already messaged my maths teacher about it and i wanna first see his reaction

he might tell me to not publish it or might tell me to do so

[leaden skiff]

why would telling us affect that?

also talking about it is not the same as publishing it

no ones gonna steal your idea

trust me

[neat lintel]

i know but you def know what i meant

that's the problem

[leaden skiff]

i don't know what you mean

[neat lintel]

nah lol you do

[leaden skiff]

not abt the primes

i have no idea what the question you're tryna solve even is

[neat lintel]

the question is none

i could make up one though

or as dumbass "scientists" wanna call it, "discover" the question

[rose dock]

[leaden skiff]

are you a troll?

[neat lintel]

no i assure you i am not a troll

[leaden skiff]

you don't even have a problem you're solving

all you've said is some weird stuff about summing all the primes lol

[neat lintel]

i still rather not say it

[leaden skiff]

not even the problem

im not asking for your solution

just what you're working on

[neat lintel]

oh

i was working on a formula that would tell me all the prime numbers

in a form of an infinite sum

[leaden skiff]

oh ok, like an infinite sum that converges to the primes?

[neat lintel]

what does converge mean ;-;

[fast ivy]

[leaden skiff]

i don't think you should be working with infinite sums if you don't know how convergence works tbh

[neat lintel]

but i literally figured out the formula because i understand the zeta function and how to multiply zeta functions

i didn't need to know what convergence is

[leaden skiff]

[leaden skiff]

what's the zeta function?

[neat lintel]

the zeta function is something like, a sum of the following thing up to a certain point

[leaden torrent]

lmao

[fast ivy]

[leaden skiff]

someone needs to pin this, please

[leaden torrent]

its #serious-discussion 😠

[leaden skiff]

would be a perfect first pin

[neat lintel]

lmao i guess it's incorrect, judging by the sarcastic tone

[leaden skiff]

it's not incorrect really

you've just described a sum

which i mean the zeta function is

[leaden torrent]

the zeta function is the analytic extension of a certain convergent infinite series to the entire complex plane (almost)

[neat lintel]

yeah

ooh

[leaden torrent]

since it obviously diverges if the real part is too small

[neat lintel]

ok

[leaden skiff]

is it the analytic countinuation specifically?

what's the original function called

[neat lintel]

do you mean ζ?

or

[leaden torrent]

"dirichlet series of coefficient 1"

[fast ivy]

From my complex analysis lecture notes

[leaden skiff]

what's the dirchlet series of coefficient n?

like in general?

[leaden torrent]

the zeta function shifted back by 1

oh wait

by n you just mean an arbitrary integer

[neat lintel]

what does shifting mean

[leaden skiff]

yes

[leaden skiff]

moving

[leaden torrent]

a scalar multiple of the zeta function then

[leaden skiff]

like on a graph

[neat lintel]

k

[leaden torrent]

the sequence a_n is your coefficients

if your coefficient is a constant, you just get a multiple of the zeta function

(factor it out)

[odd narwhal]

Is that supposed to be a zeta

That is disgusting

[leaden skiff]

how did you get to complex analysis man. i can't get through any higher math 😭

[fast ivy]

@leaden skiff the zeta function would be the analytic continuation of the series that is marked inside that green box

[neat lintel]

wait what if i shift the infinite sum of all prime numbers by -1 then? will i get interesting results?

[leaden torrent]

so yes, its specifically the analytic continuation

[fast ivy]

That would be the explicit formula for the analytic continuation

Yes

[odd narwhal]

I meant

The actual symbol

Lmao

[leaden torrent]

though of course they coincide where the series converges

[fast ivy]

OH

Yes lmao

[leaden skiff]

pin this too pls

[odd narwhal]

It's fine most people (me included) don't know hoe yo write zeta

[fast ivy]

That's the zeta my professor draws

[leaden torrent]

you get the same function but the graph is moved over.

[odd narwhal]

But that looks like a xi tbh

[neat lintel]

ok i see

[fast ivy]

I also don't know how to write zeta that well tbh

[leaden torrent]

its unclear whether youre applying the shift before or after, but in either case, its not interesting, no.

[fast ivy]

So I will give my professor points lmao

[leaden torrent]

the gamma function is left-shifted "by default" relative to the factorial

wait

[odd narwhal]

I avoid this problem altogether by typing my lecture notes

[leaden torrent]

right-shifted?

[leaden skiff]

like seriously tho man you need to like learn how infinite sums work

[leaden torrent]

whatever horizontally shifted by 1

[odd narwhal]

How old are you mate

[leaden skiff]

hey is the sum of the first n primes an interesting sequence?

[neat lintel]

i'll learn it thoroughly when i'm older lol

16

[neat lintel]

well not much tbh

[leaden torrent]

my zetas are terrible as well

i drew that with a computer mouse but its similar on paper

[neat lintel]

my zeta is l'beautiful

[leaden torrent]

(just less shaky)

[neat lintel]

1 sec

[signal oracle]

damn, I wonder how's your handwriting

[fast ivy]

I have literally taken a proper course on these basic aspects of analytic number theory this year.

So you are not so far behind

I had studied complex analysis via John Conway before

[leaden skiff]

wdym that just makes me feel even more behind

[leaden torrent]

my complex anal course covered the zeta function for like 15 minutes as an example

[fast ivy]

But I was like

[leaden torrent]

and said "classifying the zeroes of this function is moderately difficult"

[fast ivy]

Not that interested into analytic number theory

[fast ivy]

Aaa

[fast ivy]

I am sorry then:/

I mean

[neat lintel]

nvm

[fast ivy]

If you know a bit of calculus

Maybe you could work through John Conway's book

It is pretty good

And you don't need much background

[neat lintel]

i heard of conway

[fast ivy]

Just a bit of calculus/real analysis

[fast ivy]

You prolly heard of the one that worked on Knot Theory, Modular Forms, Monster Group and so on

This is a different one

I know

Crazy right?

[leaden skiff]

i remember when i thought i was hot shit cause I was watching 3b1bs calc series in 9th grade lmao

[fast ivy]

Yeah

[neat lintel]

yeah but his game of life is cool too

[fast ivy]

So this complex anal course I took was for beginning graduate students

So we went a bit further

We covered a bit of Riemann surfaces and covering spaces at the end

[neat lintel]

oh about riemann

i think i can get a number that's out of the y line

[leaden torrent]

[neat lintel]

within the -0.5;0.5 range

[fast ivy]

Oh no

[leaden skiff]

what's the y line?

[neat lintel]

where almost all numbers are

[leaden skiff]

all numbers?

all of them?

[fast ivy]

I think he's referring to Re(s) = 1/2

Lmao

[leaden torrent]

can you express zeta(3/5 + i) in a closed form for me

(i.e. as an infinite series)

if not, you really shouldnt be tackling this.

[neat lintel]

uhhh idk

[leaden skiff]

technically isn't zeta(3/5 + i) itself a closed form

[neat lintel]

i'll still tackle it tho coz i'm really interested

[fast ivy]

[leaden torrent]

sure, i mean apply the series definition

its not difficult if you know what the zeta function actually is

if you dont, you are not qualified to work on it

i'd accept an integral representation as well, you can even use Gamma()

[though its not necessary]

[odd narwhal]

$\zeta(\sfrac 3 5 + i)$

Do I win?

[fathom swallow]

ShiN

[leaden torrent]

shin cant read

[odd narwhal]

I can read

[leaden skiff]

oh i can do you one better

,ask zeta(3/5 + i)

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by OfficiallyANinja#0413

[leaden torrent]

yeah wolfram can probably do it

[leaden skiff]

it's that

[leaden torrent]

if you click "more"

[odd narwhal]

My humour is just beyond your cranial perception

[leaden torrent]

indeed

[neat lintel]

wait isn't ζ using all prime numbers?

[leaden torrent]

again this isnt a hard problem either

its just applying the definition

[fast ivy]

[leaden torrent]

literally 0 insight besides high school algebra required

[thorn brook]

oog

[leaden skiff]

wait what? huh i thought it was $\sum_{n=1}^\infty \frac{1}{n^{\frac{3}{5} + i}}$

[fathom swallow]

Ninja

[neat lintel]

1/((1-2^s)(1-3^s)(1-5^s)(1-7^s)(1-11^s)...)

[leaden torrent]

that doesnt work for real part < 1/2

neither does that

[odd narwhal]

Nami I dare you to prove $\sigma(n)=H_n+e^{H_n}\log(H_n)$

[leaden skiff]

real part is >1/2 here tho

[odd narwhal]

Bet you won't

[neat lintel]

hell no

lol

[leaden torrent]

er fuck

real part < 1

[fathom swallow]

ShiN

[leaden torrent]

brain fart

[surreal sapphire]

euler product only converges for real part > 1, same for the series

[leaden skiff]

oh ok

[thorn brook]

log of homology group

[surreal sapphire]

you need to throw some stuff at it to extend

[leaden torrent]

real part = 1 gives a fuckton of problems (you get a pole at 1, though everywhere else works fine)

[leaden skiff]

what about ramanujam summation 👀

[leaden torrent]

real part < 1 is your analytic continuation

[leaden skiff]

(idk what that is btw)

[odd narwhal]

That's what I said lmao

[surreal sapphire]

i mean in general those guys converge on right half planes

[odd narwhal]

Technically it's log of nth homology functor tho

[thorn brook]

oh crap lmao sorry

[surreal sapphire]

in this case real part > 1

[odd narwhal]

It's the harmonic number tho

It's like an equivalent theorem to RH

Supposed to be \leq tho

[thorn brook]

oog

[leaden torrent]

anyway we digress

if you dont even know that the euler product fails to converge for "half" of the complex plane

crucially, including the part the riemann hypothesis is talking about

you are not qualified to work on it.

[surreal sapphire]

i wish we had euler product everywhere

[leaden torrent]

it'd make analytic number theory a lot easier.

[surreal sapphire]

then we would understand this function pretty well lmao

[leaden torrent]

and a lot more degenerate actually

🤔

[thorn brook]

oog, out of gas

[leaden torrent]

i think you can quickly extend that to "every number is prime" in fact

i mean not just by doing monkey brain principle of explosion

but a semi-sensible path

[fast ivy]

@leaden skiff

[leaden skiff]

is it equivelant to the principle of explosion?

[fast ivy]

You would have to apply this

[leaden skiff]

wait i know that guy

who is he?

[leaden torrent]

a contradiction entails the principle of explosion

[fast ivy]

Yeah, it's Richard Borcherds

He has a series of lectures on complex analysis

[leaden skiff]

ah i tried watching one of his group theory lectures once

[fast ivy]

I've watched them for my complex analysis course

And the ICTP lectures too

[leaden torrent]

or rather

the principle of explosion is that a contradiction entails any statement

[leaden skiff]

well yes, but like is being able to prove a falsity without explosion and without secretly using it?

like this might be nonsense

but like ya know how every proof of something, no matter how different they might seem can usually be shown to "really" be the same thing? kinda?

[leaden torrent]

i just mean that by using the same "paths" analytic number theorists use to reason about number theory from the riemann hypothesis, if we had a statement like "the riemann zeta function is the euler product on the entire complex plane, which converges" and used the same "path", we'd be able to very quickly prove nonsense

yes any reasoning in a contradictive system is inherently meaningless

(ignoring paraconsistency)

[leaden skiff]

paraconsistency?

[leaden torrent]

logical wanking

a paraconsistent system is one which does not have the principle of explosion

[leaden skiff]

man every day i learn about some complete mathematical horseshit on this server

how does that work?

[leaden torrent]

idk if logicians require it to be inconsistent or not?

[leaden skiff]

(horse shit in a nice way)

[leaden torrent]

ive never looked into it

besides knowing vaguely it exists

but yeah, contradictions dont instantly lead to the system blowing up

since they lack one of the things that leads to explosion

yeah obviously, i was just wondering if it still "counts"

[leaden skiff]

maybe they can model how people deal with politcs

[leaden torrent]

makes sense

yeah i know absolutely nothing about this

i dont even know why people care about it beyond "technically you can do it"

[leaden skiff]

maybe someday someone will discover a new dimension in the multiverse because of it

[leaden torrent]

[neat lintel]

well there should be multidimensional multiverses

in theory

[leaden skiff]

in what theory

[neat lintel]

but i don't think that can happen

idk just make up a theory that this thing can fit in

[leaden skiff]

is it? idk that seems like perfectly logical to me.

[leaden torrent]

"well [statement]"
"when is that true"
"idk make something up"

[neat lintel]

no not really

[cold needle]

yeah what about the other true statements u found

[leaden skiff]

logical inconsistecies do tho

[leaden torrent]

yes it does, when i notice a plot hole my enjoyment is immediately ruined

i go on /r/movies and immediately start a thread

[cold needle]

i simply close my eyes

[leaden skiff]

like don't they for you?

[leaden torrent]

complaining at the sheer incompetency of the writers

[leaden skiff]

i don't mean like "oh the eagles in LOTR" i mean like genuine plot holes

[leaden torrent]

and demand my money back from the movie theatre staff

[cold needle]

hmm i guess its more of a problem if the one contradiction you find messes up everything else

[neat lintel]

lol im gonna make movies full of plotholes just to piss you off

[cold needle]

what if u find a contradiction that is just

[leaden skiff]

[cold needle]

by itself i guess

[odd narwhal]

I guess JoJo is paraconsistent

[leaden torrent]

i guess the argument is that its "throwing the baby out with the bathwater" when we're actually a lot more tolerant of this stuff in many common contexts

especially more informal ones

but theres no room for informality or leniancy with explosion

like, not every system of formal logic is meant to model the thoughts of Tarski himself here

[leaden skiff]

idk i wonder if that's just whether actual human beliefs are extrmely hard to describe objectively

and actual contradictions are impossible to believe in

[leaden torrent]

plenty of conspiracy theories are self-contradictory

[neat lintel]

"the erf is flat!!"
"we have all members around the glob!!"

[leaden skiff]

when?

[leaden torrent]

not really what i meant, and im not sure thats self-contradictory except for the whole ignoring evidence bit

[neat lintel]

not often at all

[leaden torrent]

isnt a lot of flat earth shit religiously motivated

a lot in common with the like

"earth is 6000 years old" thing

[neat lintel]

yeah

[leaden skiff]

is it ever truly contradictory is the thing? or does it just almost contradict? like it comes really close

idk how to explain it

[neat lintel]

the old testament has no concept of time so 6000 years could just mean billions of years

[leaden skiff]

ofc the earth is 6000 year old wdym. i read a book, how is that different from you scientists who get your info from books.

[leaden torrent]

well, the whole point of logical theories is to give us tools to explain things

if it so happens that a paraconsistent system is the most convenient model to explain things

(using "model" in a way that'll definitely give ultra an aneurysm)

then why not

[odd narwhal]

That's objectively untrue

[neat lintel]

no it's true

there is no concept of time

[odd narwhal]

It's not

I've studied the tanach

[leaden torrent]

yes

[neat lintel]

the book says adam and eve started just before the jewish calendar did but research says adam and eve lived 96k years ago or sm similar

[odd narwhal]

It's literally not and there's no interpretation that supports that statement

Adam and eve aren't real

[leaden torrent]

i choose to believe that your brain is pure unadultered formalism

[odd narwhal]

They're a myth

[neat lintel]

adam and eve are real according to my religion.

[leaden torrent]

you dont actually have brain cells, just an infinitely long tape

[leaden skiff]

legend has it ultra does arithmetic using nothing but the peano axioms

[neat lintel]

i agree tbh but that's in abstract form

[odd narwhal]

Everyone except the hardcore extremists agree that things like Job and Adam and Eve are symbolical and myths

[leaden skiff]

• ultra's consistency theorem

[odd narwhal]

Especially since the writing style is much different to the rest of the tanach

[leaden torrent]

is that why the academic job market is so bad

[neat lintel]

the fuck you mean "hardcore extremists"

[odd narwhal]

Lmao

[leaden skiff]

no that's just not true

[neat lintel]

do you believe god will not test you with torture?

[leaden skiff]

they're not the "extremists"

that's pretty mainstream

[odd narwhal]

I mean extreme sects of judaism

[neat lintel]

god has tortured me and i kept my faith in him because i know his son will save me from his tests

[odd narwhal]

I'm speaking about judaism specifically since that's where the myths originated and that's my area of knowledge

[neat lintel]

yeah

ok

[cold needle]

god is testing me rn with this convo

[neat lintel]

ic

[cold needle]

thats what

[leaden skiff]

hey @neat lintel how old are you

[neat lintel]

god is testing everyone, don't think you're alone

[leaden torrent]

87

[neat lintel]

16

[leaden torrent]

damn a bit off

[odd narwhal]

Most moderate interpretations of the tanach agree about certain tales being myths

[cold needle]

right i think this is a good place to stop

[leaden skiff]

that doesn't matter tho. like you can't claim that only extremists believe in that cause it's really mainstream. every christian I know believes in it.

[odd narwhal]

uhm

[leaden skiff]

i can't believe it'd be different for jews

[odd narwhal]

it is

trust me, I live here

[leaden skiff]

why is there a difference then?

[odd narwhal]

and was forced to study it in school

idk

[leaden skiff]

i don't wanna come across as hostile. genuinely asking

[odd narwhal]

I really don't know

[neat lintel]

wait which denomination is tanach for

[leaden skiff]

are you sure it's not just your locality?

[odd narwhal]

no

i've talked to people from a lot of sects

and people in the jewish community

tbh the more extremely religious you go in judaism the more divide there is between interpretations

[neat lintel]

yes i agree

[odd narwhal]

down to like, the next town over will have a different rabbi that has different kosher laws

[leaden torrent]

i know someone named adam and i believe someone named eve exists

am i a religious fundamentalist

[neat lintel]

no

[cold needle]

yes

[leaden torrent]

mixed signals here

[cold needle]

im blue

[leaden skiff]

depends, do you believe someone names steve exists?

[cold needle]

and older

[odd narwhal]

but generally the more moderate sects all believe some form of well-regarded interperative text

[neat lintel]

just because someone's named Adam and you know them, doesn't mean you're a religious fundamentalist

[leaden torrent]

if i was a religious fundamentalist i'd definitely think i'm doomed to burn in hell (or equivalent)

then again

[neat lintel]

well i am doomed to burn in hell near the chair of satan

[cold needle]

i would also think this

[leaden torrent]

i continue to go to #serious-discussion

[velvet dagger]

Well if you were more fundamentalist you'd probably be following the rules

[leaden torrent]

so perhaps im already in hell

[velvet dagger]

Of your religion

[cold needle]

conveniently i am already a degenerate

[velvet dagger]

So that you had an opportunity not to lol

[odd narwhal]

I think that's all I have to say on this topic

[neat lintel]

i never could follow the rules but i try to follow in Christ's path

[leaden skiff]

i would make a joke here about the catholic church but i don't want the mods to come in and ban me

[neat lintel]

patience, strength

all that

[neat lintel]

LOL

none allow eroge

[velvet dagger]

Yeah that's true Ninja we don't wanna get the mods in here

[leaden skiff]

oh wait fuck

[cold needle]

yeah i also don’t want to get the mods in here

[velvet dagger]

What's wrong?

[cold needle]

they are like cops

[leaden skiff]

damn im colorblind

[cold needle]

blue and oppressive

[velvet dagger]

Tru

[cold needle]

kind of tragic

[leaden skiff]

well you can guess the joke

and i have plausible deniability

[odd narwhal]

good thing you changed that

coos is a naughty word in hebew

[neat lintel]

what does it mean lol

[leaden skiff]

it's 0 + cos

[velvet dagger]

:0

[neat lintel]

lmfao

[velvet dagger]

Disgusting

[neat lintel]

what do you guys think about sin(x)=2

[leaden skiff]

,ask sin(x) = 2

[velvet dagger]

i'm pretty sure there's some complex number z such that sin(z) = 2

[cold needle]

ye

[velvet dagger]

Genius wolfram

BUt yeah there's this dank theorem

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by OfficiallyANinja#0413

[velvet dagger]

Which says that the image of an entire function is either all of C

Or C minus a point

[cold needle]

its a chill exercise if you learned the complex log stuff

[velvet dagger]

Hmm?

I thought there's some real work

[neat lintel]

and what if we do sin(x)=i^i

[velvet dagger]

You might be thinking that the image is dense?

[cold needle]

i always did it with complex log

to compute sin(z) = 2

[velvet dagger]

Oh

[cold needle]

er find z

[velvet dagger]

I thought you meant the theorem I'm proving

[leaden skiff]

that's really easy, i^i is like 0.2

[neat lintel]

,ask sin(x)=i^i

[cold needle]

ye no idk that one

[velvet dagger]

Was easy once you use complex log

And uh

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Mate Yzqanesim of Salevza#0045

[velvet dagger]

It's not lmao

It's called Picard's theorem

[ancient flame]

bprp has a video on sinx=2

p swag

[leaden skiff]

what does this mean btw

[neat lintel]

i love bprp and i might send him my formula

[leaden skiff]

bprp is pog

[neat lintel]

does anyone know his email?

[ancient flame]

you have a formula?

[neat lintel]

yes

[velvet dagger]

Someone else explain it to ninja

[ancient flame]

he probably has it in his about section

[velvet dagger]

I have to go change and meet a friend for food

[neat lintel]

for the infinite sum of all prime numbers

ok

[velvet dagger]

@cold needle teach the younglings

[cold needle]

what

okay ill try

[ancient flame]

ooooo thats cool

[leaden torrent]

is this not the etymology of "entire"

[velvet dagger]

Respond to this

No??????????????????

[leaden torrent]

it isnt

wtf

[cold needle]

what

[velvet dagger]

Entire = holomorphic on all of C

[leaden skiff]

u have ninja in ur username too. you must help me

[leaden torrent]

wouldnt that be

"entirely holomorphic"

[velvet dagger]

And the image might miss a point

[cold needle]

what does entire have to do with the image

[leaden torrent]

fuck that point it was irrelevant anyway

[cold needle]

anyways

[velvet dagger]

wtf is your dialect namington

[cold needle]

as for what image is

[velvet dagger]

Canadese

[leaden torrent]

im not saying your terminology was wrong

[cold needle]

um so you have functions right

[neat lintel]

do u mean canadian or canadese?

[leaden skiff]

is this dn theory

[leaden torrent]

i thought the etymology was backwards

[neat lintel]

oh no

[leaden skiff]

yeah functions. i know them

[neat lintel]

i fell for it

[cold needle]

the image of a function is the set of all points f(z) for all z in the domain or whatever set ur passing in

[leaden skiff]

mmhmm

[cold needle]

so when we say the image is C we mean that the function maps at least one point in the domain to every point in C

[ancient flame]

canadese nuts

[cold needle]

and then if its C minus a point we just miss a point in C

so that the one point we miss just doesn’t have a “preimage”

there’s no z in the domain that maps to this missed point

[leaden skiff]

mmhmm

[leaden skiff]

btw i was asking about the thoerem not the idea of the image of a function

[cold needle]

i am unfamiliar with this theorem

since i haven't taken complex analysis

[deep mango]

"entire" just means function from C to C which is differentiable everywhere

That doesnt sound like a big deal but it's a huge deal

Not many functions are entire

(because being differentiable on C is hard)

So it's really hard to prove but you can prove that nonconstant entire functions hit all but one point of C

At least

In R this is nonsense

Sin(x) is differentiable, but doesn't hit any value outside of [-1, 1]

But now think about the complex extension of sin, which is sin(z) = (e^(iz) - e^(-iz))/(2i). Now this function hits a whole lot more points.

In fact, you can prove that e^z never hits 0. (e^z is defined to be e^(Re z)(cos(Im z) + i sin(Im z)), and neither factor is ever 0).
So Picard's theorem says that e^z must hit every other point of C. Even the negative real values.

[crystal stone]

This makes me uncomfortable

Complex analysis is black magic

[leaden skiff]

what

i wanted to see that interesting definition

[frail lagoon]

oh i mean the typical way i'd define exp(z) is just via power series

and then you can just argue since exp(z)exp(-z) = 1, exp(z) can't be 0

but i deleted my comment as it detracts from the main gist of what ryc was saying

which is how cool stuff is like picard hehe

[leaden skiff]

what's the point the trig functions miss?

[leaden torrent]

all or all but one

[leaden skiff]

oh ok

that's slightly less weird then

so if you can prove a func misses at least 2 points you know it's not entire?

[leaden torrent]

sure, though usually theres easier ways than that

[leaden skiff]

that feels pretty easy to me

[deep mango]

Does sin not miss any points

Idk

[leaden skiff]

,ask range of sin(z)

,ask range of sin(z) from C

damn it

how do i ask that?

,ask range of sin(z)

[leaden torrent]

dont think wolfram will be helpful here

[leaden skiff]

😔

[grim pumice]

maybe use the def of complex sine?🤔 instead of sin(z)

[leaden skiff]

,ask range of e^iz - e^-iz / 2i

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by OfficiallyANinja#0413

[leaden skiff]

well that's not what i mean but it's bigoted against complex functions

[leaden torrent]

well thats maybe because youre saying "range"

,w image of e^(iz) - e^(-iz)/(2i)

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Namington#1983

[leaden torrent]

no it autotranslates it to range

yeah wolfarm is just useless here

[leaden skiff]

the way i was taught, elements have images, functions have ranges

[leaden torrent]

weird convention

when i hear "range" i think of high school precalc classes

i dont think ive heard it outside of that

oh, stats i guess but a kinda different meaning there

[leaden skiff]

well those are the only classes I've heard those in too

so makes sense

[neat lintel]

do you guys remember lunar arithmetics

[leaden skiff]

dang it doesn't even have a wikipedia article?

[orchid zenith]

alright it's been a bit since I looked at this but lemme do my best lol

so the basic reason you'd develop differential forms, in my humble opinion, is that you're looking for the natural object to integrate on a manifold

or submanifolds of some ambient space you're working in

(totally fine if everything is in R^n, and I encourage that for a first look)

a k-form in R^n is basically the following object:

it's defined on R^n

and if you have a k-manifold in R^n, the form tells you how to integrate on that manifold

the form takes into account what direction the manifold is facing at each point

that is, what the tangent space is at each point

and uses that to weight the integration

along these lines, we want to also have our theory build in ideas like orientation and change of variables

and at the end of the day, the fundamental theorem of calculus (stoke's theorem) needs to work as well

it's pretty clear what that should mean for like 1-variable functions, or even curves and possibly surfaces

so once you've convinced yourself of these lower dimensional analogs, when you build your theory, you want to end up with a clean stoke's theorem

so the objects you integrate (differential forms) are complicated, but they are designed to achieve these goals

be natural objects to integrate

carry orientation

work with change of variables, and the fundamental theorem of calculus

so i hope that is at least a helpful starting point for what the point is as you try to learn about this stuff

fwiw i think the stuff in chill is like, not amazingly relevant

I mean it is, but also

algebra-brained people motivate it badly by jumping right into that stuff imho

check out guillemin and pollack, I really like the coverage in that book

@supple flame after thinking about it a little more, I want to add like one other thing.

here's the concept in a nutshell

a k-manifold locally looks like R^k

so we want to integrate on it, just like we do in R^k

but it only looks like R^k up to diffeomorphism

so we need to invent a theory of integration that is invariant up to diffeomorphism

i.e., we need to build in some sort of change of variables

which then immediately brings in all the complicated exterior algebra stuff, since basically that's where the determinant comes from, and we really need that to do oriented change of variables

the actual exterior algebra is not so bad to just sit down and learn about, but that's really what's going on in a nutshell

[velvet dagger]

Bott-Tu kinda dodges exterior algebra

In that book you do things on R^n by just saying dx_i are symbols and dx_i dx_j = - dx_j dx_i

And then on manifolds you basically just pull shit back

The exterior algebra formalism is mostly nice because you can define them on manifolds "cleanly"

Operations on vector spaces can be performed "simultaneously" on all the tangent spaces (the tangent bundle)

So you can think of them as being defined in terms of bundles on the manifold rather than makeshift objects on R^n that pull through charts

But the Bott-Tu style goes from 0 to "I can do things" more quickly

[narrow rock]

Arnold's book develops forms pretty nicely

nothing particularly new

but clean

[velvet dagger]

ODEs?

[narrow rock]

he spends some time doing everything on a single vector space

[velvet dagger]

Or mechanics?

[narrow rock]

mechanics

[velvet dagger]

Lol nerd

Also apparently the classification of simple lie algebras isn't correct

@vivid halo have you heard of this?

[vivid halo]

how so?

[velvet dagger]

At least two new exceptional lie algebras were missed, E9 and E10

[vivid halo]

uhhh

these aren't finite dimensional

[narrow rock]

DN joke incoming

[velvet dagger]

Lol good one Brofibration

Parried

[narrow rock]

nG was about to get btfo'd big time

[vivid halo]

lol

[velvet dagger]

Yeah you saved him there

[blazing pawn]

it doesnt count as btfoing if its not funny

[velvet dagger]

His advisor would've just dropped him like a rock

[blazing pawn]

what im saying is that it never counts as btfoing

[velvet dagger]

O noez

Anyway yeah the joke was E10 = eaten

[vivid halo]

so you know what the story is for E_n with n>8 right?

[velvet dagger]

I googled it once you said it wasn't finite-din

Honestly I didn't know it existed

[vivid halo]

so E_9 is probably the best studied because it corresponds to an affine Lie algebra

in general E_n for n>8 still defines a Kac Moody algebra, it's just that for n>8 this is not finite dimensional

For Kac Moody algebras you can define them by abstract Cartan matrices, some of these Cartan matrices correspond to honest finite dimensional Lie algebras, a lot don't

[whole copper]

Determinant or something tells u if its finite dim?

[vivid halo]

yea so take your Cartan matrix C, decompose it as DS where D is diagonal and S is symmetric

when S is positive definite this corresponds to a finite dimensional simple Lie algebra

when S is positive semidefinite this corresponds to an infinite dimensional simple Lie algebra of affine type

otherwise S is indefinite and this gives Kac Moody algebras of "general" type

in the case of E_n the root lattice has determinant 9-n

so this explains the ranges of what's going on here

[velvet dagger]

Ah so it's -1 dimensional for E10 huh

[whole copper]

How does classification of irreps work for the infinite dimensional case?

I guess.. Maybe not that different?

[vivid halo]

yea so that's the beautiful thing, for Kac Moody algebras it's literally the same story

all the same character formulas work too

at least in the affine case

[velvet dagger]

Well that's pleasant for sure

[whole copper]

Is there any example of actually "coming across this in the wild?" like a situation in some other math problem wheres there a natural action by one of these kac moody algebras?

Cant get over the feeling that you can write down these algebras for fun and do all this tjeory, but dont really see them pop up much

Maybe need to read more super theoretical physics or something? Lol

[vivid halo]

yea so the place I've mostly seen Kac Moody algebras of infinite dimension come up is in conformal field theory, where they basically control most of the theory

[whole copper]

Oh wait actually is this like the "algebra of local conformal transformations?"

[vivid halo]

yup, one of the central examples of a Kac Moody algebra in the setting of conformal field theory is the Virasoro algebra

[whole copper]

It seemed (im a noob though) that the global transformation group should have been finite dimensional, but somehow there was a way of defining the local verskon by killing fields or something

Hmm ok

[vivid halo]

in 2dCTF local conformal transformations are made up of two copies of the Witt algebra

the Virasoro algebra is a central extension of this

it's the unique central extension of the Witt algebra

[whole copper]

Somehow also this only happens in 2D right?

[vivid halo]

yes

[whole copper]

Like in higher D u have too much consteaint to get infinite dim

[vivid halo]

anything higher dimension is just a huge headache and isn't as neatly algebraic

2dCFT is VERY close to 2dTQFT

which isn't true in higher dimensions

[whole copper]

How do you quantify it being close!

? *

[vivid halo]

how affine Lie algebras play a role in this is that the Sugawara construction embeds the Virasoro algebra into the universal enveloping algebra of any affine Lie algebra

[velvet dagger]

You put a metric on field theories ofc

[whole copper]

just to be clear; virasoro algebra shows up purely from thinking about conformal symmetries in 2D, but this algebra embeds into any any enveloping algebra of affine lie algebra; so somehow representation theory of any of the affine lie algebras tells u something about 2D cft?

[vivid halo]

yes

[whole copper]

spooky

oh I guess its like how SU(2) or SL(2,C) shows up in all the lie algebras

maybe

[vivid halo]

so the thing that happens is like

in d>2 the global transformations are just given by the conformal group

in d=2 you have additionally infinitely many local generators with relations given by the Virasoro algebra

so the constraints are a lot heavier here

which makes the representation theory interesting

as a result, the additional constraint of ensuring cobordisms in a base TQFT are conformal are quite rigid in the case d=2

whereas in the case d>2 it's not so rigid

[whole copper]

wait.. isnt it the case that TQFT is always a CFT? because everything is topologically invariant, you can act any conformal transformation and it'll still be invariant?

is this a problem between global conformal transformations and local ones?

[vivid halo]

no

yes this is the issue

[whole copper]

wow

its completely mind-boggling to me that this global<-> local issue makes so much of a difference always

[latent forge]

is all nighter good way to fix sleep schedule

[light needle]

not a good way but it gets the job done

[latent forge]

bruh

ive been awake since 7 this morning

[light needle]

probably sleep a few hrs each day

till its fixed

[neat lintel]

i prefer to go to sleep when i normally would and then force myself to wake up when i need to

although these days i go to sleep at 6 am and i have a friday schedule forcing me to get up at 7 so that's not good

[latent forge]

ik tryin to wake up at 6 or 530

lol wtf

[neat lintel]

do coke to stay up and fix your sleep

[latent forge]

you get up in an hour?

Im thinking of staying up all night until dunkin donuts opens

[neat lintel]

i should have said i will have such a schedule

[latent forge]

buying a good iced cofvefe

and then learning math ig until around 9pm

and get in bed at 930

hopefully i wake up tomorrow at 530

[neat lintel]

53 o clock

[latent forge]

yea i framed itinerary in my brain so wrll

idk how its going to be executed

since i have freetime ill dox.

Take shower at 5 watch anime or read something until 7

go to dunkin

walk to go buy groshery

but lots groshery

come back and do random shit until 330

run at 330 for 5k

come back shower

visit friend for early dinner

come back more math bs

then sleep

perfect ikr

[latent forge]

im just stuck here

idk what i can really do besides try and learn something or make something

[neat lintel]

Sleep

[latent forge]

no

im still going strong

[deep mango]

[limber perch]

sleep is a necessary component of a healthy lifestyle

[cold needle]

sleeping good

i like sleepy

[terse flax]

https://tenor.com/view/dead-chat-gif-18800792

[neat lintel]

stfu

[rose dock]

can we just yeet this troll?

[vivid halo]

vote to kick

[light needle]

I have had him blocked for months it seems

so i second

[vivid halo]

if this message gets 10 user is kicked

[light needle]

are we talking about ledog or this terry tao guy

[cold needle]

:pepeomegaworry:

in any case memes go in chill channel

[deep mango]

metalproduct is going crazy...

[clever knot]

anyone one ever heard of Hardware description language

[untold sapphire]

sure

[clever knot]

so is that what they use for making processors?

[untold sapphire]

yeah, definitelyu

[clever knot]

i was just doing some googling and i guess they use an entire language to build the chip

so i guess all the testing of the circuits and stuff is done from the code?

[untold sapphire]

well, there are a few standard languages. but yes, producing microchips is expensive so as much testing as possible is done digitially. for mass production of these microchips there is a lot of money and time in building a huge factory to produce them