serious-discussion

[split basin]

this makes sense

[foggy meadow]

What's a filtered vector space?

[split basin]

like is there a naive interpretation of what “pt/C*” should mean that makes this evident

[vivid halo]

intuitively if BC*=pt/C* is meant to be a single point with internal group of symmetries C*, then a vector bundle on this should just be a vector bundle on the single point pt which is C*-equivariant, meaning it carries an action of this internal group of symmetries C*

stuff on X/G is G-equivariant stuff on X

[foggy meadow]

the quotient of {0} over C* probably?

[split basin]

sure

[foggy meadow]

Would this be related to PSL by any chance?

[split basin]

oh

[vivid halo]

a vector space V with filtration by a bunch of subspaces

[split basin]

so you dont think of some coset space

[vivid halo]

morally this is a coset space but you are meant to remember the actual equivalence data between members in a given coset, not just collapsing them down to a single equivalence class

[split basin]

i guess that makes sense

[vivid halo]

that is the difference between these stacky quotients versus classical quotients

[split basin]

that this would be the right way to generalize classical quotients

[vivid halo]

like you want to remember why things are isomorphic not just that they are isomorphic

[split basin]

i see

[vivid halo]

remembering why things are isomorphic is a structure rather than a property

the difference between these is the difference between sets and groupoids

stacks generalize sheaves in exactly the same way

[split basin]

btw is this pt/C* example analogous to some fourier transform?

[vivid halo]

the usual gluing axiom for sheaves must accordingly be more complicated to capture this additional structure

[foggy meadow]

Man, this is wacky. Very different from like the topological view.

[vivid halo]

haha yes exactly

[foggy meadow]

Bruh.

[split basin]

idk why it just seems like it

[foggy meadow]

Yeah, I need to learn more about orbifolds I think.

[vivid halo]

this is exactly the right intuition and this is a very general phenomenon, captured by the Fourier-Mukai transform and Cartier duality

[foggy meadow]

I only get the general flow of what's happening, but not the exacts honestly.

But getting the flow down is how I start to learn things.

[vivid halo]

https://www.youtube.com/watch?v=Uz3lFI-eaGo

Gaitsgory has two very nice recorded lectures on this notion of Cartier duality and Fourier transforms, and discusses a more general version of this one category level higher

the example I described above and many others like it are explained very nicely in the first lecture

[foggy meadow]

I'm going to step back for a moment to something really simple is a mod b an orbifold of just R/Z_{n}?

[vivid halo]

idk what natural action you have in mind for Z/nZ acting on R here

but yes for example the quotient R/Z for Z acting on R by the usual translation action happens to be a classical object which is probably what you have in mind

sometimes these stack quotients are classical objects, in general they are not

whenever they are classical the intuition for stacks agrees with your usual intuition for quotients by equivalence relations

[foggy meadow]

Yeah, I get that, but I'm just curious if that's a good example of this more simply.

[vivid halo]

maybe a richer example related to this which is no longer classical would be taking the quotient of R by the slightly larger group acting both by translation and negation

some semidirect product of Z and Z/2Z or whatever

[split basin]

why does BS^1 appear here?

[vivid halo]

the scaling action by positive reals kind of does nothing here and you can contract BC* to BS^1 without any difference in the category of vector bundles

[split basin]

ok

[vivid halo]

the S^1 is maybe more evocative of why Z appears by the usual Fourier transform

[foggy meadow]

I mean is a R mod 2 then just R/Z then technically?

[split basin]

yeah

[vivid halo]

well the quotient would be some further quotient of R/Z=U(1) by this involution action of Z/2Z

[foggy meadow]

Which then is what I was understanding, okay cool.

[vivid halo]

you can keep generalizing this notion to higher notions of stacks but this is maybe a bit much to swallow for one conversation lol

anyways the point is these things are very useful and they unlock for you things which are very hard to talk about classically

[foggy meadow]

I mean, I'm still on orbifolds probably, but I was really curious about Artin Stacks. I now have a name for blah/So(3) or whatever now.
Also, thanks btw.

[vivid halo]

this example around filtered/graded vector spaces is very nice because it is often very useful to interpret various linear algebraic constructions like structures on various cohomology theories, in terms of bundles over stacks like this

there is an interesting "transmutation" one can perform which interprets all sorts of very different cohomology theories as actually the same cohomology theory but each is interpreted over some different stack like this

this is very useful because then you can just prove once and for all certain abstract properties of this single cohomology theory and then offload the actual differences in detail of different cohomology theories onto differences in detail between these different stacks

definitely takes a fair bit of stacky machinery to get this idea to work, but in the long run this is much more efficient compared to like, proving hard technical theorems a dozen times over and over in different contexts

also just very clarifying because you can start to view the actual "reasons" for deep theorems about cohomology theories and the relations between them in much more geometric terms

you can interpret all of Hodge theory and its p-adic counterpart in these terms for example

in fact this perspective is honestly the only sane way to understand p-adic Hodge theory lol

[foggy meadow]

I still need to finish reading about Geometric Algebra.

[torpid bay]

if i were to read some books about the topics for the things y'all said ot learn about it from scratch, what would be the topics?

[vivid halo]

"need" is not the right word here lol

[vivid halo]

depends on your background

[foggy meadow]

I know it's probably a must.

[vivid halo]

but here are two sets of notes which are more or less self contained and could be read by anyone who knows "basic" algebraic geometry https://www.preschema.com/papers/stacksncts.pdf
https://www.math.ias.edu/~bhatt/teaching/mat549f22/lectures.pdf

[foggy meadow]

I'm just happy lattices have helped me this far.

[torpid bay]

i got no background, other than like calc 3, some linear algebra stuff + currently doing real analysis by tao (a small bit of recognizing some specific groups and some tensors calc basics)

[vivid halo]

I mean feel free to read about it if you are very interested and find it engaging, but it's ultimately rather useless

[split basin]

maybe focus on the core undergrad math curriculum first

[foggy meadow]

What would you recommend?

[vivid halo]

with this background I would maybe suggest these notes which are just kind of a general overview of lots of very interesting topics which gives good examples related to this point of view https://adebray.github.io/lecture_notes/m390c_GL_2021_notes.pdf

but yes also this perspective I am advocating literally does not make the slightest bit of sense until you finish the usual first course in abstract algebra, and also kind of does not make sense until you finish a first graduate course in algebraic geometry at the level of Hartshorne

I'll be here if you have any questions like 2-3 years from now

[split basin]

surely it takes a lot more than just a course in algebra

[foggy meadow]

I'm still surprised my head knew what a Modular curve was.

I also realize, if I decided to do signum matrices and do something similar. I would need to define them using this type of language.

[vivid halo]

if you cover commutative algebra at the level of something like Atiyah-MacDonald then in principle you could use Adeel Khan's notes as an intro to AG, but this is only a good idea if you have bran damage of a very particular kind

[foggy meadow]

What kind of brain damage?

[vivid halo]

maybe good if you have the undergrad category theory nlab reader kind of brain damage and at least want to turn that into something useful

[split basin]

just like take core algebra topology analysis geometry classes for a few years

[vivid halo]

like this approach is ultimately the cleanest and most powerful approach to algebraic geometry when all is said and done, but it is not the approach that most people would actually benefit from learning first

[foggy meadow]

Oh dang, sounds close to what I might have, but also maybe not. Roll a d20 to find out. You have links, so I can see about it?

[split basin]

sure but less of a priority as an undergrad i think

[vivid halo]

this sort of thing makes sense to study if you are a grad student and know that you would benefit from these techniques, most people do not stand to benefit relative to the amount of machinery this approach requires

[foggy meadow]

I'll probably end up making my own sauce, and doing silly stuff again with a partial understanding. But talking like this makes that partial understand a little more full. That or I reinvent the wheel and start making chariots.

[vivid halo]

also depends on the department you are in, there are a handful of departments where this is just kind of the way that everyone learns algebraic geometry and how people talk about things, at most departments this is very much the case and not knowing more pedestrian ways of talking about geometry basically makes it impossible to talk with other people which is a big disability to voluntarily acquire

[foggy meadow]

These do go hard so far though:
https://adebray.github.io/lecture_notes/m390c_GL_2021_notes.pdf
I do see modular curves.

[vivid halo]

yeah Arun's notes on this stuff are very nice

covers a lot of interesting material in somewhat vague but still useful terms

[foggy meadow]

Why are forms everywhere and show up where and when I don't expect.

Even with my own silly math they come up.

[latent edge]

I might get cancelled if I said it

hint: it's not number theory

I find esoteric logic boring idk

[ocean robin]

theres another field of logic now??

[vivid halo]

oh it definitely is number theory, just the wrong parts of number theory

log log log log log log

[hallow plume]

read hodge correlators for intro AG

[vivid halo]

analytic number theory heads really be like "I will take the most rich and interesting subject in all of mathematics, and study it in the most dry and boring way I can possibly imagine"

[vivid halo]

unironically yes

wait no

as an intro to Hodge theory yes

[latent edge]

oh lmao yeah you are right how did I forget this

[vivid halo]

reading that paper is like eating glass

like it's such a brilliant paper but holy fuuuck

[junior turtle]

one example that comes to mind is logic

[pure hollow]

Bran damage

Logic is cool if you're autistic enough.

[hallow plume]

numerical analysis

[vivid halo]

honestly if someone solves an open problem using logical and model theoretic blackboxes, it is still an open problem

[hallow plume]

you write a program to simulate stuffs
oh compile failed have a good luck next time!

[junior turtle]

numerical analysis

[pure hollow]

just be a better programmer.

[vivid halo]

imagine you had a perfect oracle which could tell you whether a given statement is true or false but will never tell you why. You ask it whether RH is true and it says that RH is true and you're like yeah everyone knows its true you fucking dipshit I am no more informed than I was before I asked

Logicians and model theorists are this useless dumb oracle

[foggy meadow]

Hi nG!

[pure hollow]

The model theory wood chipper 9000EX method be like.

[foggy meadow]

You're looking for importance in why it's true.

[vivid halo]

understanding why is the actual important part lol

[foggy meadow]

Just change the "it's true" into the important and meaningful part some how. Then use the inverse transform to transform it back.

[vivid halo]

lol

[foggy meadow]

You got this I believe.

[latent edge]

hmm

[foggy meadow]

Make every "this is true" meaningful by inventing a new language or something so it's meaningful.

[junior turtle]

bro is bypassing nitro in a roundabout way

[hallow plume]

[foggy meadow]

@torpid bay what are you working on today?

[latent edge]

just copypasta images

[torpid bay]

i was mostly just at work

[junior turtle]

real

[torpid bay]

but

[pure hollow]

"This is clearly a job for the non model theorist and is left as an exercise to the educated reader."

[torpid bay]

ig i had 2 ideas

one was about bivectors actually

[foggy meadow]

ande hwat ist that?

[latent edge]

Geometric Algebra

[torpid bay]

im thinking, suppose there is a space S (lets say 2 dimensional), and we can ig define bivectors on it. if I can take this bivector, and move it along a closed path, and when it comes back to the starting point, but ends up with a negative orientation as what we started with, then it's a nonorientable surface thne(iff)? i dunno the official rigorous def of non orientiable surface so im just going off of intutiion

[junior turtle]

@zealous garden geometric algebra needs you asap

[zealous garden]

Yo

[junior turtle]

yoo

[zealous garden]

Damn Delty, why you doing this

[junior turtle]

i will leave the rest to you

[latent edge]

to summon you obviously

[zealous garden]

Boring? No, it was just ignored

[foggy meadow]

No it's a mobius strip.

[zealous garden]

Geometric Algebra (as in Grassman's work) underlies all of exterior algebra, clifford algebra, gibbs-heaviside vector algebra, and more

[latent edge]

just realized this is discussion 2

[zealous garden]

But props on you for realizing it was Grassman and not Clifford. Not many get this right

[pure hollow]

High school math.

[zealous garden]

Geometric Algebra with poor pedagogy

[torpid bay]

the second idea I had was about integration over closed spaces

[junior turtle]

ohhh wait, probability is a good candidate

[zealous garden]

You said what?

[foggy meadow]

*probability is probably a good candidate

[agile fiber]

also known as geometric algebra

[zealous garden]

You mean if you have a tangent m-vector of an m-dimensional manifold and you transport it smoothly on some closed loop and it flips, the surface is non orientable?

I guess?

[torpid bay]

ye

but like iff

[zealous garden]

Is that easier than showing directly that no smooth pseudoscalar field exists?

[torpid bay]

[zealous garden]

Well hold on now

[zealous garden]

If and only if?

[torpid bay]

ye

[zealous garden]

Yeah this should work out

The pseudoscalar field is basically the geometric algebraic definition of the orientation of the manifold

So if transporting your orientation around in a loop changed it, something is awfully fishy

Like the orientation not existing

[torpid bay]

does this mean you can't do GA on a klein bottle or just that orientation cant be defined?

[foggy meadow]

~~I feel like it's just that orientation couldn't be defined, but maybe I'm wrong 🤷‍♂️. ~~

[torpid bay]

^

anyway, the second idea was I saw a vid by 3b1b, and it had flux, which i had forgotten about, but that whole 0 flux if source/sink is outside of closed surface reminded me quite a lot about the 0 = closed integral curve in the complex plane if no roots or poles inside it

i feel like they're just two special cases of something more

[pure hollow]

Disagree probability is fucking insane once you deal with stochastical methods

[foggy meadow]

I thought of another way to think about the flux thing, by just taking a series of rays cast from the origin. Then summing their directions, and if it's 0 then the shape includes the origin, while if it doesn't then it doesn't contain it. But the same rules apply.

[junior turtle]

actually probability might not be that bad, but for some reason i dont really like it

i dont even know why lol

but i have been avoiding it for a long time

[pure hollow]

This is me but with graph theory

[foggy meadow]

Me working with stochastic values and graphs.

[neat lintel]

Hello

[junior turtle]

i mean i dont really care about probability, at least not for now. So imo its reasonable that i havent studied it yet

[pure hollow]

I'm eventually gonna learn graph theory but I don't see the appeal for it rn

[junior turtle]

i am prioritizing many things over it

[latent edge]

you after learning context free grammar

[junior turtle]

rn its at the bottom of an infinite list of things that i want to study

[pure hollow]

Mood

[foggy meadow]

I'm trying to learn more about GA and some other things.

[junior turtle]

real

[neat lintel]

I want to learn group theory

[latent edge]

Consider Gal(Q bar/Q)

[torpid bay]

one other thing is that I figured out what went wrong in my previous bad lower bound for primes, and it came down to counting fractions when I should've used floor after each time, which ended up overestimated the nummber of primes within a certain inverval

[pure hollow]

This reminds of a quote which basically was like "I like algebras because unlike my groceries it can be free sometimes."

[junior turtle]

sorry but it doesnt exist
-a certain someone

[neat lintel]

Tbh I can’t react because I still don’t understand what it means yet

[foggy meadow]

Floor vs Ceil transforms, I should've used floor ends up being often correct.

[vivid halo]

it's okay nobody understands this group either

[junior turtle]

nice, you can actually start rn by opening a book on abstract algebra

[foggy meadow]

What's the line over the Q mean? Just the inverse fraction?

[neat lintel]

Will do

[junior turtle]

i recommend lang's algebra for a friendly introduction

[pure hollow]

Die

[junior turtle]

(dont do this)

[neat lintel]

Thanks

[junior turtle]

noooo

[junior turtle]

check out the pinned messages in #book-recommendations

scroll down till you see a message with a list of books about abstract algebra

[neat lintel]

شكرا

[junior turtle]

people usually recommend D&F, its probably good as a start but i dont really like it so i wont recommend it myself

[latent edge]

and i took that personally

[foggy meadow]

One day may we say they're the same.

[pure hollow]

Personally I vibe with Aluffi

[junior turtle]

أهلا وسهلا

[foggy meadow]

Dwarf Fortress was a good game.

[neat lintel]

من وين؟

[vivid halo]

a group is:

[foggy meadow]

yes.

[junior turtle]

لبنان، انت من وين؟

[neat lintel]

حياك الله أنا من الأردن

[latent edge]

#arabic

[junior turtle]

حبيبي يا غالي، تشرفت بمعرفتك

[junior turtle]

Real

[neat lintel]

و أنا كمان

Ok back to English so we don’t get banned

[junior turtle]

شو اسمك؟ أني علي

[vivid halo]

mom pick me up I can't read the moon runes

[foggy meadow]

Aramaic still goes a long way in understanding and reading this

[junior turtle]

lol sotrue

[neat lintel]

My name is Anas

[pure hollow]

A group is a groupoid with a single object.

[junior turtle]

Ohh I see nice to meet you

[neat lintel]

Nice to meet you too, this is off topic but I went to Lebanon one time when I was a toddler, I went to Byblos and jeita it was scenic

[latent edge]

incoming talk about falafel:

[junior turtle]

Ohh nice, yeah the scenes there are very nice

[zealous garden]

There's so much snow

[junior turtle]

shawarma>

[neat lintel]

I mean you can’t really compare them, one is for breakfast and one is for dinner and lunch

[junior turtle]

Well both of falafel and shawarma are for lunch, I mean you could eat them whenever but that's how they are. Tho it may differ from country to country

[latent edge]

not really I once ate falafel for breakfast, lunch and dinner

[neat lintel]

Idk for us it is more of a breakfast, but I see your point

[foggy meadow]

ܝܢ ܠܐ ܡܨܐ ܡܦܫܪ ܗܐ؟ Anyway sup.

[junior turtle]

Yea I see your point, it actually differs from country to country

I mean in Iraq you see people eat like kafta and so on for breakfast

[foggy meadow]

That makes sense.

[junior turtle]

Tho it's nice to do this ngl

[foggy meadow]

I feel like if you live where it's arid then yes.

[neat lintel]

Honestly this is unpopular opinion but I like hummus with mashawi more than with falafel

[junior turtle]

I mean that's the right way

[neat lintel]

I’m glad to see someone agree

[junior turtle]

I don't remember ever eating hummus with falafel, but actually I don't even remember the last time when I ate falafel so my memory might be failing me

But I am almost sure that I have never done that tbh

[neat lintel]

Interesting

[junior turtle]

But yeah hummus is peak if it's done in the right way

It's tasty on its own

like you can make a sandwich of hummus, tomato and olive oil or something like that for example

It will have a very good taste if the hummus is done in the right way trust

Ah I miss manakish 🥀

[neat lintel]

Olive oil the pinnacle of the levant

[junior turtle]

Real

[neat lintel]

Where do you live like which country?

[junior turtle]

Currently in brazil

[neat lintel]

Interesting, I heard there is a big Syrian and Lebanese community in Brazil.

[latent edge]

https://klipy.com/gifs/brazil-soccer

[junior turtle]

Yeah, the size of the Lebanese community in Brazil is like double of that in Lebanon

[junior turtle]

What about you?

[neat lintel]

US

[junior turtle]

Ohhhh nice

[neat lintel]

But Brazil is kind of niche tbh, most Arabs when they leave the Middle East they usually go to Europe or the US, but it is interesting to see Latin American countries as destinations for some

[junior turtle]

Hmmm I would say it depends on the Arabic countries themselves. Like in Lebanon for example, people go to Brazil more than say Europe or the US. At least this applies to people from south Lebanon

[hallow plume]

a group is an object whose delooping BG is a 1-truncated ∞-groupoid whose higher homotopies are contractible? sotrue

https://klipy.com/gifs/galaxy-brain-meme

[upbeat kraken]

Hello

What kind of proofs should I be able to do before I go to learning calculus proofs

I am learning basic proofs and want to know when it is ok to learn calculus proofs

[vivid halo]

honestly it really does not matter

if you have covered some portion of basic intro to proofs material then that's more than enough to get started

you can also get started with absolutely none of that material as long as you have basic reading comprehension skills and a brain

the only function that intro to proofs serves as a course is to sort prospective mathematics students into two camps, the first camp is "students who understand what words like "and" and "or" and "if/then" mean intuitively and without much conscious effort" versus "students who can mimic this understanding only with a great deal of concentration and conscious effort"

all the students in this latter group get removed from the pipeline and end up doing something else more worth their time, all the students in this former group probably didn't need this course in the first place

[acoustic zealot]

doing proofs is not only about understanding some rudimentary logic notation…

[timid cypress]

yo

[severe steppe]

They're right, but they're being elitist about it.

The "intro to proofs" course is basically a filter for logical intuition. Most of what you learn there is just formalizing things you already do when you solve a puzzle.

[vivid halo]

I wouldn’t say I’m going out of my way to be elitist here just being a bit brutally honest about the overall role of these courses

That said these courses are not entirely useless and their main merit is that they give you a bit of time to just start working on basic mathematical writing skills which takes time for anyone to develop and is slightly orthogonal to the skill of coming up with logically valid proofs

sometimes it feels like these skills can be quite poorly correlated, loads of incredibly technically skilled mathematicians are also absurdly bad at writing clearly

most good intro to proofs courses end up feeling like courses on technical writing and most bad intro to proofs courses end up being courses on mathematical logic in a way that really misses the overall point

[severe steppe]

I think that's a much stronger point now. I agree that there is a difference between solving a problem and communicating the solution. In fact, a lot of smart guys fail because they think getting the right answer is enough.

[vivid halo]

Most mathematicians are really bad at this it’s a really huge cultural issue which I could absolutely continue to bitch about

Like it’s a hard skill to write or deliver lectures with clarity but the bar is so absurdly low here and so many people constantly make such easily avoidable mistakes about this

Shit like “oops I forgot to think for a single minute about the intended audience”

[vast wraith]

a group is a joke to him

[vast wraith]

which group would you say aspiring logicians fall into

[vivid halo]

Idk what do you think

[vast wraith]

idk all the aspiring logicians i know are currently hospitalized

[vivid halo]

[severe steppe]

I don't blame them that much, because once most people understand something complex, they will forget what it's like to be confused by it.You see this in CS all the time too, the documentation that is written by engineers for engineers are usually unreadable garbage because they skip the obvious steps.

One of the easiest ways to get ahead currently is to explain a concept without confusing the hell out of the reader, because by that point you will be already ahead of most PhDs.

[vast wraith]

admittedly i know just two

[vivid halo]

Well I would imagine that the feeling of struggling with logical connectives and their manipulation would be like, kind of a bad sign for anyone trying to become an expert in the topic which deals most heavily with precisely this

It’s like trying to become a low dimensional topologist while also having incredibly poor spatial reasoning skills or being blind

Like you can overcome those things with a lot of work but more often than not it is a bad omen of sorts

likewise just because someone stuggles quite a lot earlier in mathematics with something like this doesn't mean it is impossible for them to become a good mathematician, there are fields medalists for whom this sort of thing is true, but generally speaking it just shifts the odds against you

[acoustic zealot]

You did sound elitist

[vivid halo]

most people do not become marathon runners if they find it hard to enjoy running

[vast wraith]

yeah i was thinking less about struggling with them and more about conscious effort, i dont think the latter is necessarily bad, it just lends itself better to different pursuits

Weil has an interesting discussion on this in the introduction to hos foundations of algebraic geometry, he talks about two kinds of mathematicians, which he calls “creative” and “critical,” having in mind someone like Segre versus Peano

[vivid halo]

ah that's an interesting dichotomy I haven't heard before

people often talk about the dichotomy between "theory builders" versus "problem solvers" which is not unrelated in some ways

[vast wraith]

i love math astrology

[vast wraith]

it’s a fun and short read i think https://archive.org/details/foundationsofalg0029weil

[vivid halo]

one thing I have noticed about people who are like, really really good at mathematics usually at the PhD level is like, they tend to be able to read mathematics texts rather quickly without getting stopped constantly by the voice of skepticism

obviously one has to be a little careful about just instantly accepting things as true this often leads to bad mistakes, it's not quite like that

usually once you are closer to finishing a PhD thesis you can read papers in that area at some incredible speed and everything feels very natural and obvious, while papers outside that area will still often be a slow stuggle to understand

but like some people develop this sense of intuition much more quickly than others

[vast wraith]

i dont think i have ever managed to read any math of some complexity quickly

[acoustic zealot]

How is almost 400 pages short?

[vast wraith]

i meant just the introduction

[acoustic zealot]

Ah

[onyx reef]

Right now I spend on average like 45-50 mins per page when doing folland... hope I can speed that up at some point

[vivid halo]

[vivid halo]

do you have a sense of why it is taking this long?

[vast wraith]

my psych claims this is likely at least partly due to my being somewhat dramatically underweight but idk

[vivid halo]

yeah sometimes that can be a factor

[onyx reef]

I try to often prove theorems on my own first, though the major reason I think is that folland skips over a lot of "trivial" steps and I sometimes have a tough time filling in the gaps

[vivid halo]

right okay, yeah sometimes this can take a fair bit of time

what is your cutoff on time spent being stuck on those sorts of proofs before looking up any hints which might help with them?

[onyx reef]

I somehow never tried to actually analyze why though.. I'll try to pay more attention to it next time and see if I can find rooms of improvement where the solution isn't just "do more math and git gud"

[vivid halo]

I mean I can tell you why right now and how to fix this pretty quickly

[onyx reef]

That's the thing, I'm not really sure... I'll pay more attention next time ig

[onyx reef]

Sure

[vast wraith]

this is a good reason to take time i think, it only recently dawned on me that i should be looking at my own examples meanwhile reading through a text, ehehe

[vivid halo]

people are often given the advice that you should try to prove a bunch of things completely on your own and that you shouldn't "cheat" with any hints or whatever but this is generally quite poor advice, it is usually very counterproductive and leads to massive slowdowns which aren't worth the benefit this advice is trying to get at

[onyx reef]

Yeah it's definitely worth taking time to think about and truly absorb the concepts that way

[onyx reef]

(pretty sure I'm one of those people )

Ig yeah if I want to cut down on the time I should stop doing that

[vivid halo]

you probably don't want to have such a low tolerance for frustration that you immediately google everything that takes more than 10 seconds to think through carefully, and ideally you should not be looking up the same things over and over and over again without internalizing them

in most cases it is most productive to not waste too much time on these things, look up hints if things feel like they are taking too long, or just move on and skip some things and return to them later if you want

[onyx reef]

Yeah makes sense, I'll try to apply that advice next time

[vivid halo]

people seem to have this idea that you should work through a textbook completely linearly and work all the details to completion and you will somehow emerge from the other end having completely internalized all the content, but this literally never actually happens in practice

[onyx reef]

Ig I need to find a middle ground

[vivid halo]

like another thing to keep in mind is that often it is impossible to actually have the proper context for completely understanding the mathematics in textbooks like this, like loads of exercises do not have obvious importance until you encounter some version of the same problems in actual research and then you see why people actually care about them

[onyx reef]

yeah makes sense... there's a sense of achievement when you complete something without external guidance but ig I need to weigh that against wasting too much time

[vast wraith]

as a sort of opposite extreme to this idea of having a complete understanding of a theory, is conway’s idea that math is not about theorems, but rather about examples having a deep understanding of particulars

[vivid halo]

yeah it is nice when this happens but there are much bigger victories to be had which are only possible if you let go of these kinds of expectations

[onyx reef]

True.. I just went through an example of that recently when I did a question whose significance I couldn't understand till someone told me it's something complex analysis related (which I haven't done yet)

[vivid halo]

right yeah this happens a lot

[onyx reef]

True true

[vivid halo]

at some point everyone is forced into this sort of strategy of being fast and loose with it as soon as actual research is happening

if we had unlimited cognitive ability it would be nice in principle to like, understand literally every definition and every theorem you are citing as input to something you are doing in research, but realistically no human can actually do this

[onyx reef]

Yeah makes sense since that stuff is a bit time bound

[onyx reef]

ok sorry but I need to go study rn

[vivid halo]

good luck

[onyx reef]

Thanks for the advice

[vivid halo]

try to get in the habbit of skimming and see how it feels for a bit

[onyx reef]

Yeah, I'll let you know how it goes

[vivid halo]

very good exercise at some point is to try and read some math books at the same speed you would read a novel and just see what happens

very very useful skill to develop

[hollow ivy]

Hello to everybody, I'm still thinking about what career I can choose to study, I was investigating a little bit about maths and I really like the option, however, when I get into a "Jornada a puertas abiertas", that is like a meeting where professors explain you about the different professions, I saw a obscure and boring path to deal with maths. Besides, my current tearcher of maths is heavily into maths, and talk just about maths. What is the real deal for studying maths an why it can be so interesting, in addition to the bare prejudice about that graduating from maths is to be professor or to study for the rest of your life like a investigator about abstracts things that maybe will never come out of anything. I don't mean to bother, just asking if the career is worth.

[limber thunder]

for some the act of studying mathematics in itself is the interesting bit, it can be very rewarding to see your own progress in understanding things or sharing ideas with people at e.g. a conference if you're a career mathematician

for others math becomes especially interesting when it's applied or applicable, that's also valid and you can seek an applied math major or specialize in a master's or PhD after graduating in math, these days I know of a bunch of people that majored in math or physics and then did data science, or software development or statistics

[junior turtle]

how does one skim a math book tho? do you like go over the statements of theorems without proofs or something like that?

[slate beacon]

why just skim? what about almond or whole?

no soy though

[vivid halo]

I mean yeah kinda

Skim proofs for some idea of how detailed or involved certain proofs will turn out to be, get some sense of which parts are long tedious computation which you can skip later and which parts are genuine insights

[junior turtle]

ohhh i see, this will likely not work perfectly from the first time. But it will probably save plenty of time

[vivid halo]

yes it's absolutely not supposed to work perfectly on first pass that's the point

[junior turtle]

usually i avoid skipping a proof/a section/a theorem etc... but i think that i should start changing that

tho i still dont feel too much comfortable about doing that ngl

lol

[scarlet crane]

hiii

[vivid halo]

lol you need to learn to get over that discomfort

[junior turtle]

yea ig

yesterday i tried leaving complex analysis and studying modular forms and then returning to complex analysis along the way when i face things that idk in it

[novel void]

hey guys im thinkin bout getting into finance would getting a maths deg for bachelors be good?

[vivid halo]

like the point is on first pass you are trying to figure out what is even worth revisiting in much greater detail on second pass in the first place, and figuring roughly how things are laid out and what the overall ideas you should expect to revisit

[junior turtle]

i think that i will try this strategy for a while and see where i get with it. I am not sure if this is the right thing to do but i wont know unless i try ig

[vivid halo]

this is absolutely the right thing to do and there is a huge cognitive science literature which consistently points towards this being way more efficient than the alternative

[junior turtle]

yea that makes sense

what made me do this step was because there are many things that look interesting to me which i want to study, specifically stuff around number theory. But then i should have quite a bit of background so eventually i couldnt wait anymore and i was like ok its time to study what i am interested in and pick up necessary tools along the way

I had these thoughts very recently and only really started with it yesterday

but now i might start doing it with everything and not just complex analysis

[vivid halo]

yeah this strategy applies to most other academic fields this is hardly specific to math

nothing that is genuinely difficult ever takes a single pass

but yeah also when you start to read fewer textbooks and start to read mostly research papers this is literally the only possible way you can have any chance at reading a useful quantity of things and getting to know the rough impression of what things people have already done and what things are interesting

even if you are very skilled as a speedreader trying to just move your eyes over a sizeable portion of decent papers in most active subjects in mathematics takes quite a long time

obviously skimming this aggressively often means you retain very few actual details from any single paper but this does leave you with the incredibly valuable knowledge of where to look if you should ever need some detail later

[junior turtle]

Yea that makes sense, otherwise no one could have read tons of papers

[junior turtle]

I can imagine that, I mean even reading novels quickly would take a long time

[vivid halo]

yeah for a lot of research the obstruction to finding loads of very easy fruit to pick is just like, most people don't read enough papers to be able to do this

[vivid halo]

there are tricks that can speed this up to a spooky degree

one which unfortunately doesn't work with latex documents but works very easily with any plain text document is like

[junior turtle]

Hmmm I see, so at that level the goal isn't to understand all the details of each and every paper because you can look things up whenever you want?

[vivid halo]

there is some software which lets you read plain text at maybe 2x or 3x the speed you would otherwise be able to with surprisingly little loss of retention

it's not magic either it's such a stupid trick

[vivid halo]

yeah

[vivid halo]

the trick is "what if I didn't have to waste any time moving my eyes"

[latent edge]

The art of pulling out different sources and jumping back and forth

[junior turtle]

ohhh, it wouldnt help as much for math tho right? I mean ig some papers mostly consist of plain texts rather than latex no?

[vivid halo]

yeah unfortunately it doesn't work for math, or at least it could work in principle but you would have to write custom software for this

[latent edge]

Sounds like a project I could work on (eventually give up on it)

[vivid halo]

at best you could maybe get this to work for inline stuff but any display math is fucked so unfortunately that trick isn't such a good trick anymore

but like for reading novels it's really hilarious

I guess the other downside to that trick is you have to be like

[junior turtle]

I prefer to read the whole paper in details rather than doing this

[vivid halo]

REALLY LOCKED IN and can't stop locking in

[latent edge]

Tfw last midnight I was so stubborn locking in and now I feel horrible

[vivid halo]

I mean there are better speed reading tricks out there anyways but they require some training, this one is just really funny because it just instantly works out of the box

[junior turtle]

you shouldve locked in on the bed

[latent edge]

Can't be bothered to use noggin in the morning it's slow as fuck

[vivid halo]

a mildly terrifying rabbit hole to go down is like, what kinds of speeds and retention people who are REALLY GOOD at speed reading can pull off

[latent edge]

Maybe I should take amph

[vivid halo]

you act like a crackhead half the time when you are sober, you don't need meth

some of the best speedreaders have unlocked incredible cheats like "what if i just stopped reading the words or the lines and just took a picture of the entire page all at once with my eyeball"

[pure hollow]

I should either be insane or cracked for this

[junior turtle]

lmao what

[junior turtle]

what if you are both

[vivid halo]

the people who are best in the world at this are genetic freaks and it's not really a skill that most people can actually replicate, but there are freaks out there with weird brain quirks that makes this possible lol

but like short of being fastest at this a lot of people can train this skill with a fair bit of effort and still get quite good at it

[pure hollow]

Right but at one point of time I used to average like 120 pages a day I don't this is possible with math

[vivid halo]

but yeah the people who are fastest at this the speed really just does not make sense and it sounds fake until you put them through cognitive tests for information retention and it still kind of makes no sense

[junior turtle]

you were really locked in huh

[pure hollow]

Definitely

I can't do 1/10th of this in a month for math

[junior turtle]

real

I am reading it like a novel but surprisingly i dont understand a thing

[vivid halo]

for some numbers: average reading speed is maybe around 250 WPM, most people can hit around 750 WPM comfortable with this kind of software that just flashes text in front of your eyes as quickly as you can process that stream visually

[latent edge]

Gotta have the insane picture memory for these things

[dim plank]

trust me bro amphetamine is a very poor substitute for discipline

[vivid halo]

the people that can photoread entire pages at a time tend to be in the ballpark of 10k WPM to 25k WPM with varying degrees of retention

[vivid halo]

yeah that's the trick that most people cannot pull off

[latent edge]

WHAT

[junior turtle]

what is this hack

[pure hollow]

This reminds of how fucking cracked scholze and stix were to absolutely dunk on mochizukis proof

[vivid halo]

the hack is called savant syndrome and it also usually means that you are so autistic that you are functionally disabled in many other areas of life

but it's kind of insane that this is actually possible at all even in freak cases

there is one very insane case of photomemory in a savant who can do fun things like

you take him up in a Helicopter above the NYC skyline for a few minutes

[pure hollow]

I remember watching this absolutely insane

[vivid halo]

then proceeds to paint a perfect photorealistic recreation of the skyline

every window, every building, everything

[latent edge]

Yeah insane skills

[vivid halo]

I mean my iphone camera can do that but still cool I guess

[junior turtle]

you: my iphone camera
him: my brain camera

[vivid halo]

lots of other fun cases around standard tasks like "memorize deck of cards"

and of course people have turned this into an autistic sport

you have to memorize the sequence of cards and then regurgitate that sequence without any errors

current world record is 12.74 seconds for memorization

[pure hollow]

We need this but "memorize nlab"

[vivid halo]

of course some of this is incredibly silly and doesn't actually translate to other cognitive tasks lol

reminds of the whole thing about chess players being able to photomemorize chess board configurations very very easily

if you move a couple pieces into an illegal configuration that cannot be reached by the normal chess rules, instantly they cannot memorize it anymore

[pure hollow]

Just have extreme cognitive abilities of all kinds.

[junior turtle]

sotrue

[vivid halo]

insta reels photomemory champion

[pure hollow]

It's too easy, that's why I severely disable my frontal lobe to have a challenge.

[pure hollow]

This sounds like a bane.

[vivid halo]

I have crazy photomemory that lets me recall all the traumatic things that have happened to me in the last 27 years

[pure hollow]

Many such cases unfortunately

[vivid halo]

the amazing cognitive ability to forget information faster than anyone else can

[junior turtle]

i have an even crazier photomemory that lets me forget everything that happened to me in the last 19 years

[pure hollow]

MEEEEEEEEEEE

[junior turtle]

an accurate description of me

[vivid halo]

very fun cognitive science fact is that if you are unable to forget things then you suddenly become massively less efficient at remembering things also

[pure hollow]

I don't think the inverse is true 😔

[vivid halo]

it is somewhat true, this is largely the cognitive role of forgetting things and pruning irrelevant information from memory

[pure hollow]

Right I wonder what's actually classified as relevant information

[vivid halo]

this tends to be a measurable issue with people who have perfect recall of their day to day activities and things like this

like there are people who can remember in perfect chronological order every single meal they have ever eaten

this isn't some skill it's a memory disability

here is a helpful picture that explains what is going on there

[pure hollow]

Makes sense I do wonder how much efficient memory recall affects daily life, like it surely has a impact but how much or is this even a valid question?

[junior turtle]

this also gave extra information about whats happening in the outside world, not just inside the brain

[split basin]

this is pretty silly though imo

[pure hollow]

This is how I imagine windows file search engine tries to find files

[pure hollow]

Is this outside world even real if so what's the interpretation?

[vivid halo]

it realy depends, you tend to see pretty variable outcomes with cases like these but the point is that those cases provide really interesting insight about how memory actually works

[split basin]

i mean there is a lot of variation across fields of math in terms of problem solving vs theory building being more central

[vivid halo]

weirdly enough Chimpanzees have much better photomemory than we do

[split basin]

but idk if it’s productive for individual people to pigeonhole themselves in this way

[pure hollow]

how do we categorize the outside world
What if the outside world is extended to non commutative cases
Thoughts of the utterly deranged (me)

[vivid halo]

basic cognitive test for this is like, take a 10x10 grid of LED squares, flash some random configuration of n squares on this board for a fraction of a second, then have the person or chimp touch all the squares which were lit

most people can do this very easily up to some cutoff n beyond which the skill rapidly deteriorates

[latent edge]

Chimpanzees should do Langlands then I give up

[vivid halo]

chimps can do this for larger n than we can

[pure hollow]

If I'm not remembering it wrong wasn't it more of short term but really good memory retention?

[latent edge]

hmm

[vivid halo]

this is a pretty specific cognitive task which is largely dependent on photomemory but it very heavily loads short term memory

[split basin]

is that actually a good example of this

i thought it was more like a testament to their patience

[vivid halo]

for most short term memory tests like this there is a fundamental cutoff on the number of bits of information that you can instantly memorize and retain for short durations

[pure hollow]

I don't know maybe? I just have a lot of thoughts floating around and if there's a match I'm reminded of it

[vivid halo]

that cutoff tends to be pretty uniform in people

[split basin]

i actually dont know though

[vivid halo]

like you will see a pretty clear correlation between outcomes on this test and general short term memory metrics which scale in a predictive way with things like eye queue and so on

[pure hollow]

Makes sense

[vivid halo]

but then you hit a cutoff beyond which people really cannot do this reliably even as eye queue scales

[pure hollow]

I think it could definitely be both

[turbid ocean]

Mathcord neuroscientists and psychometricians in discussion

[pure hollow]

and one crank(me)

[turbid sedge]

dont forget the drug addict

[brazen mulch]

🔥

[foggy meadow]

You're 27?

[upbeat kraken]

Thank you for your response

[upbeat kraken]

I actually had a question about this as well

I am in grade 12 I have completed pre calculus 12 which was all computational and I am now learning proofs to fix my mathematical gaps

I do not plan becoming a mathematician or publishing papers or doing anything to do with mathematics

I wanted to learn proofs so I can understand mathematics specifically calculus at a deeper level than just mechanical problem solving

Given my goal of understanding calculus deeply and not publishing math papers or being a mathematician at all

Should my goal be to write proofs as cleanly and as high quality as possible

Of course I won’t be writing gibberish, but do I have to put extra emphasis on communication my proofs because I am just doing this for myself and not trying to become a mathematician or pursue mathematics at any form after high school

[torpid bay]

There's quite a bit of math after calculus, and also quite a bit of calculus as well, you may end up going much further than it as your understanding grows

gl

[placid flume]

Hello, does anyone have any recommendations for (not wildly expensive) ereader which is good for reading textbook PDFs or ebooks?

I have no room to store any more books, but the ipad screen tires my eyes when I try to read

[steady grotto]

Did you tried red screen mode?

I know some e-ink devices, but I didn't have them before

[placid flume]

Hmm maybe I will look into this red-screen mode thank you

[thorny wraith]

I am currently a math major student interested in homotopy theory and higher categories but i am having a lot of problems finding professors who work in that area in europe to get some kind of a project , is there a way i can find such ppl ?

[junior turtle]

you might get some answers if you ask in #advanced-lounge

[thorny wraith]

Thank you very much

[main star]

Fourier>>>laplace

[willow juniper]

On g fr you w it on gang

[rocky shuttle]

why?

[vast wraith]

https://tenor.com/view/frieren-sip-frieren-sipping-tea-book-gif-1603575268151458399

[vast wraith]

i believe some ppl at ntnu in trondheim work on this, in particular rune haugseng

[vivid halo]

only correct take

[foggy meadow]

Circles are better than non circles, who knew.

[shadow palm]

hello nerds²

Ofc whenever I come, everyone leaves

[worldly horizon]

as in nerdss or nerds nerds.

[foggy meadow]

Hi mike

[shadow palm]

This is discussy 2, so you folk get called nerds²

[noble tinsel]

i thought the nerdsquared were in #foundations

[shadow palm]

False, those are f(nerds)

[thorny wraith]

Thank you very much

[south orchid]

TIMEEEEEEEE

[olive fjord]

A jewish man goes to his rabbi and says “Oh rabbi! You will not believe what happened to me! My son left the house and became a Christian!”

The Rabbi responds in frustration “Hush, Hush, YOU would not believe what happened to ME! My child left the house and they too became a christian!”

Man says “What do we do?” To which the Rabbi says “We Pray to God and ask for his guidance”

The two men started Praying, and God responds! He tells them:

“You would not believe what happened to me…”

[peak tide]

literally a dad joke!

[rich quail]

Lol

[upper vine]

guys i have mathematics test tomorrow
and i dont know anything
Maayyy GOD Save my AZZ

[peak orchid]

@wicked cypress

Bhai

What happened

Tell me

[solid yarrow]

Frieren :3

[vast bloom]

https://tenor.com/view/frieren-frieren-dance-cat-dance-frieren-break-dance-cat-break-dance-gif-10384889003607498994

[old oak]

sub-par embed

[fresh comet]

[limber thunder]

https://tenor.com/view/frieren-frieren-dance-cat-dance-frieren-break-dance-cat-break-dance-gif-10384889003607498994

[drifting lark]

It's crazy that, if you pick a random positive integer, the probability of it being greater than TREE(3) is 1.

[latent edge]

hmm

[chrome cairn]

[shell slate]

Gl my bro

[muted marlin]

guys can you help me with my homeworks pls😭

[stiff turtle]

?

#1021175428326633542 maybe is the better option

[urban vigil]

It's 0

[errant bone]

can i ask for help with physics here or do i need to go to another server or what

[urban vigil]

You can

[muted marlin]

I did 😭😭😭😭

[stiff turtle]

Physics is mostly math at the peak level

Ig

[urban vigil]

Indeed, i can confirm

[stiff turtle]

Where? Lemme see it

[stiff turtle]

Yea like I just checked out the multivariable calculus and they were discussing smth abt fluid mechanics ig

[urban vigil]

That's indeed very high level

It has pre requisites of canabi yau structures

And QCD landau pole

[stiff turtle]

Eh what is that?sounds disturbing

[urban vigil]

Calabi–Yau manifold - Wikipedia https://share.google/ySnrZXFFnxTjKKcDM

[urban vigil]

6 dimensional manifold used in string theory and algebraic geometry

[stiff turtle]

Can I get that space by applying transformations to a six by six matrix?

[stiff turtle]

Algebra getting too complex lol

[urban vigil]

There is lie algebra waiting for ya

It is a vector space applied to a complex manifold

[stiff turtle]

Ahh i see

[stiff turtle]

And the lie is?

[stiff turtle]

I assume that this wasn't the lie..

[thorn wren]

Calabi Yau*

[foggy meadow]

Hello

[foggy meadow]

@blazing pawn I found you're ancient language twin.

[rich quail]

Me vibing around

[glossy wind]

me when politics

anyway

[crimson nebula]

Lmao

Welcome to mathcord!

[glossy wind]

indeed!

what you up to? aside from arguing online lol

[crimson nebula]

Studying mostly

[glossy wind]

oh are you in school?

[crimson nebula]

Undergrad

[glossy wind]

what's your major?

[crimson nebula]

Math and EE

[glossy wind]

okay wait whats EE

[crimson nebula]

Electrical engineering

[glossy wind]

ohhh

wait thats cool

have you made anything cool?

[crimson nebula]

Ive built some computer architectures, and ive built a transceiver

[glossy wind]

was it for something specific?

[crimson nebula]

Hobby projects

[glossy wind]

thats fun

[crimson nebula]

Transceiver was an excuse to use maxwells

[glossy wind]

the...

equation?

me googling

[crimson nebula]

Yeah

Very rich math there

If youre into geometry and PDEs

[glossy wind]

Ah like I said before, I'm really bad at math

I wanna do psychology so I need calc and vectors

[crimson nebula]

I am too lol

Just gotta grind at the math mines if you wanna get better

[glossy wind]

not like me, i havent done math since grade 7 (my life has been a ride)

joined this server cuz i was looking for direction on how to get good

lol

hello lurkers

👀

[crimson nebula]

Sad! You should study more math now that you have an excuse

Once you get to proof-based math, it actually gets really interesting

[glossy wind]

its hard on your own and idk where to start

i mean im not opposed to math as a concept

i think its cool

i just have a hard time with it

[crimson nebula]

I suppose if i had to give advice, you have to read textbooks and repeatedly practice problems

Almost everyone is much more capable of math than they think, its just that math is hard

It takes a long time and discipline

[glossy wind]

what year are you?

did i ask that

[crimson nebula]

Senior, rising super-senior

[glossy wind]

4th year then?

[crimson nebula]

Yeah

[glossy wind]

are u american lol?

[crimson nebula]

Ill meed another year to finish both majors

Mhm

[glossy wind]

figured cuz you said senior

well good luck on your studies, what job do you want?

[crimson nebula]

Idek yet

Tbh

Ive been wanting to get into academia

Teach and research

But im constantly debating between just going to industry and making money

[glossy wind]

you could do both, one now and the other later

[crimson nebula]

Thats what im aiming for right now, but its a bit scary

[glossy wind]

why? the industry not good or... just general fear?

[crimson nebula]

Academia scares me

Quite a lot of downsides that come with it

[glossy wind]

really?

[crimson nebula]

The pay isnt great, its insecure, incredibly difficult, and failing a single test can throw you into debt at the worst

[glossy wind]

oh

[crimson nebula]

Among a lot of other issues

[glossy wind]

yeah thats scary

[crimson nebula]

But its a major passion

I love teaching and learning

[glossy wind]

im sure you can do it, just have money saved up in case of emergencies

i also love teaching, i wanna work in schools either has a teacher or a school psychologist

[crimson nebula]

Id like to teach college if anything, maybe AP highschool classes

Having gone through hs, i really dont want to put up with their immaturity

[glossy wind]

aw really? i wanna work in high schools to help kids out

[crimson nebula]

Maybe

[glossy wind]

i didnt really attend high school though

and when i did it was awful

[crimson nebula]

What do you wanna teach?

[glossy wind]

probably english lol. or special ed

special ed is such a blessing when its facilitated properly

[crimson nebula]

It takes serious patience

Thats good to see tho

[drifting lark]

What do you mean?

[lucid obsidian]

.

[glossy wind]

@green idol What time is it for you?

[green idol]

11:10 AM

[glossy wind]

Oh wow

Are you in Europe?

[green idol]

Switzerland

[glossy wind]

Oh cool, do you like it there?

Or are you neutral

Heh

[green idol]

Idk man, if I were to ask you that you would say “neutral” . I lived here of course its just normal 50 50 ( boring )

[glossy wind]

I’ve never been to Switzerland but yeah

I mean if you asked me if I like where I live I’d say no

[green idol]

So you are from Egypt ye?

[glossy wind]

Yep! But I currently live in Canada

[green idol]

Ah nice

[glossy wind]

I hear Switzerland is nice, maybe not for a Muslim idk how the tolerance is there

But nice nonetheless

[green idol]

🤷

[glossy wind]

Do you not have class today?

[green idol]

nah I just got home

my class today was 7:30 - 10:30 am

[glossy wind]

Ah so early

What’s your major?

[frail anvil]

Why do u have class during night

[glossy wind]

He means in the morning

[frail anvil]

Oh

[green idol]

EE😂

[frail anvil]

My condolences

[glossy wind]

Once again, lots of engineers here

Made anything cool?

[green idol]

Nah, only focus on studies

[glossy wind]

That’s respectable

What sort of job do you want?

[green idol]

I like transmission

[glossy wind]

Like cars and stuff?

Sorry if that’s a stupid question

Ping me if you come back I guess

[quaint sky]

I made a radio!

[glossy wind]

Oh cool

Can it broadcast?

[quaint sky]

If I had made an antenna for it yeah

[ancient hemlock]

hello

[glossy wind]

Do you use it to listen to the radio?

[quaint sky]

Had to make a transmitter and receiver

[glossy wind]

Hi

[quaint sky]

Nah it was just a conceptual thing, it was tuned into one frequency

But I want to modify it to listen to aviation band so I can hear local air traffic

[glossy wind]

Oh that’s fun

[ancient hemlock]

Sometimes, yeah

I like some fm stations

[glossy wind]

Is it complicated to be able to tune it to other frequencies?

[glossy wind]

Do you have a favourite?

[ancient hemlock]

out of what tho

[ancient hemlock]

Its a local one, u won't know it

[quaint sky]

The way I set it up yes, everything is hard coded to one frequency because I used resistors and capacitors, but if I used potentiometers it would be super easy, as long as the power rating didn’t go too high and burn out a resistor

[quaint sky]

Breadboard, capacitors, resistors, and op-amps

[glossy wind]

Is there a reason you didn’t use potentiometers ?

[quaint sky]

Didn’t have them at the time, plus our professor wanted it to be set to an exact frequency, I could’ve used a potentiometer (or several) but I would’ve had to fine tune each one for the testing purposes

[glossy wind]

Ah I see. Yeah sounds like a hassle

[quaint sky]

Yeah, but if you’re just making a receiver it’s really easy

[glossy wind]

I’ll have to take your word for it

Anyway I think I’m heading to bed now

I’m super sleepy

[quaint sky]

Real I should be too

Rest well!

[glossy wind]

You too!

[ancient hemlock]

gn

[long matrix]

,av 358704260839374868

[fathom swallow]

desdemonaii's Avatar

Click here to view the image.

[long matrix]

kawaii

[turbid sedge]

https://klipy.com/gifs/bugs-life-a-bugs-life

[pastel blade]

i eat ur kind

[urban vigil]

wut

[fallow token]

someone help me make a money printer

[limber thunder]

wtf win98 emoji W

[reef carbon]

@neat lintel so what exactly was that joke

i kinda don't get it

[neat lintel]

psychic -> telepathy type

uh forget it

bad framing

[reef carbon]

i... still do not understand the joke

what's telepathy gotta do with anything

[long matrix]

reading minds allows you to understand languages probably ?!

[reef carbon]

...

confused as ever

[proud copper]

peeks into mind
hears unga bunga noises
?????

[fallen quiver]

I too was jokin, ma’am

Lots of languages. Spies. Mission impossible

[reef carbon]

yeah idk it feels like you kinda hit a sore spot with calling me a spy

[pastel blade]

Yoooo I'm aro(too) ace
Glad to see ones here

[reef carbon]

oh yeah hi

[fresh comet]

I have been summoned

[radiant sparrow]

Hiiiiiiiiiiiiiii

[radiant sparrow]

Also hiiiiiiiiiiiiiii

[fresh comet]

https://tenor.com/view/bunny-bunnies-rabbit-kiss-bunny-kiss-gif-21363678

[old oak]

Now that's the kind of content I want to see in this server

[radiant sparrow]

https://tenor.com/view/cat-rabbit-purr-friends-relax-gif-5184653

[fresh comet]

https://tenor.com/view/cat-rabbit-cat-rabbit-cat-and-rabbit-cat-sleep-gif-5780726925060253864

[restive mirage]

When mathematicians ran out of real problems, they literally invented numbers.
(i=\sqrt{-1})
If I told my bank my account balance was "the square root of negative one," I’d be arrested for fraud. In math, they give you a PhD for it.😂

[old oak]

Revolutionary observations, I don't think anyone came up with that point of view before

[sharp mulch]

Stunning and innovative

[old oak]

Here's something to ponder: all numbers are invented.

None of the supposed "natural" numbers exist anywhere in nature

[mellow wedge]

You got the whole class laughing fr

[agile fiber]

not true, i met a wild 2 while hiking!

[old oak]

Wild

[sharp mulch]

wild

[magic python]

Must've been the wind...

[tawdry musk]

Has FUSRP 2026 sent out offer letters?

[solid yarrow]

Wait you 2?

[old oak]

They do occur in pairs

[rich quail]

Lol

[drifting lark]

I thought of an interesting way to generate huge numbers. Idk how it measures up to, say the Goodstein meta-sequence or the TREE function, but basically...

The first number is 1.

To get the next number, you take the first number (1), and you concatenate to it all of the nonnegative integers less than it, descending to 0. In this case, the only nonnegative integer less than it is 0, so the second number in this series is 10.

To get the third number, you take the second number (10) and repeat the process. You concatenate to 10 all of the nonnegative integers less than 10, descending to 0. So the third number in this series is 109,876,543,210.

To get the fourth number you take the third number, and you concatenate to it all the nonnegative integers less than it, down to 0. This number is so large that I would need some time to compute how many digits it has.

The study of unfathomably gigantic numbers is really interesting to me.

[solar spire]

its like more than 109876543210

idk how much more tho

[drifting lark]

Yeah

The upper bound would be 109876543210 × 12

[sterile bobcat]

can you explain it for a layman or undertanding this as a a layman is very difficult

ohh i got it

[torpid bay]

10^k -> ~10^(10^k)

ig

wait hm

k -> ~ k^k

a little bit less

but good enough

roughyl equal to $^{k}x$ for k iterations when starting at number x

[fathom swallow]

Yeatte

[foggy meadow]

hi

[rough needle]

pop quiz: what is the binomial coefficient

[mystic hill]

Coefficient of a term of the expansion of a binomial to the power of a natural number

Also known as the number of ways to choose k things out of n things where it's the kth terms coefficient and the power of the binomial is n

[rough needle]

yipee u got right

[foggy meadow]

Wait until they find out trinomials exists.

[mystic hill]

Multinomial coefficient

Justice for trinomials

[gleaming abyss]

I just wanna say I've been reading this series called Dungeon Crawler Carl and it is so good. Not math related really but yeah. It made me enjoy reading again.

[carmine cosmos]

hi chat

[carmine cosmos]

It's okay

i think

you can talk something off-topic

also

i enjoy reading too

i like Philosophical Books

[analog silo]

Hi everyone,
I’m looking for help with a mathematical manuscript focused on dynamical systems. The core of the work involves delay differential equations, Lyapunov stability and bifurcation analysis, asymptotic methods, and center manifold reductions.

I should mention that I’m not a math student by training, which is exactly why I’m seeking help—especially from someone very strong with rigorous calculations and analytical details (Hopf bifurcation, normal forms, Lyapunov exponents, etc.).

I’m specifically looking for someone who can commit to the project and has enough available time to help build and check the proof in a sustained way, not just give quick comments.

The project is interdisciplinary, at the interface of mathematics, nonlinear dynamics, and neuroscience (EEG–fMRI (observer/operator) modeling).

If this aligns with your expertise and availability, or you know someone who might be interested, I’d really appreciate connecting. Thanks!

[ionic tree]

Just a reality check btw (as a math professor) I'm totally with your concept but the problem with your request is that solving complex equations requires time and energy that most math graduates unfortunately lack of

[dull socket]

my intuition says this server is 80% indians

[analog silo]

Right, to make sure I understand … are you saying I have very low chances of getting help from a grad student because they might not have Time and energy?

[ionic tree]

Not very low im saying you need time to find someone like that

[gritty heath]

Its also much easier if you ask in person than online

Its hard to get people to commit to anything to strangers online

[analog silo]

I am not a math student, I m more in the computational neuroscience field… this step of solving the paradox is fundamental for the développement of other measures for precision psychoatry diagnosis (that I have in mind)
This is a long lasting project that I wish to start, and whoever I will choose to work with me will probably stick along for a few years and maybe partner with me… I m looking for a student who has been doing math but isn’t able to find what to do with it explicitly. Someone who doesn’t have solid future plans and is looking for one… I want to create a team … but like you said this will take me a while but I have to start somewhere.

I could do this in many other ways formally through labs or universities but for the moment i am a medical student so I don’t have many options, I would have to wait till I graduate

I have a big Chunk of the proof ready I just need a calculations guy

[analog silo]

I mean I m not asking for ppl to commit right away, it could be like a few sessions of interviews and we ll figure things out

And we re students not just strangers, give yourself and us some crédits, I for sur don’t seem to be trying to scam anyone

[mortal marsh]

Not enough people talk about the importance of nutrients to the human body

[torpid bay]

hai

[fresh comet]

[ionic tree]

I understand what you mean I just feel it will take time time to find a person to help you

[urban vigil]

@analog silo you should try in specialised channels depending on the topic of yours, since grads mostly don't check this discussion channels

I didn't read it yet(will do)

[analog silo]

Thank you, I will do that

[urban vigil]

#dynamical-systems

I am not an expert of dynamical systems tho

So I don't think I can help much

[analog silo]

Thank you for your guidance 🙏

[foggy meadow]

How goes the maths

[torpid bay]

i got through a real analysis problem that i procrastinated on

nothing new other than that

[languid patrol]

I'm interested in working through a math book but I don't have any list of homework problems from a course. Is there any kind of service in the math community where people can help a student chose a set of appropriate problems from each section of a book for learning?

[torpid bay]

I haven't heard of one, but depending on what subject in math you're reading through, there should be some other books or materials online for it. The earlier the math the more likely it is you'll find it

there will be tons of stuff calc 2 and below, a long with linear algebra

what book you reading through?

[languid patrol]

Hey thanks for responding!

[languid patrol]

It's called Functional Analysis by Jain and Ahuja

[torpid bay]

i found some functional analysis problems, quite a lot, 152 pages of it. https://thichchaytron.wordpress.com/wp-content/uploads/2013/10/functional-problems-anhle-full-www-mathvn-com.pdf

[languid patrol]

Aw thank you for looking for me. I'll bookmark this.
What I think I should find is someone who knows the subject who's like a tutor who I could consult with for an hour or something and come up with a good list of problems from the book.

[torpid bay]

i just looked up 'func analysis problems' hopefully it would cover the same topics, but yeah always a good chance that your book covered stuff they found to be important enough but the link i gave didnt

[languid patrol]

Do you know if there are like, paid math consultants/tutors who can do this sort of thing? How would I find those people?

[torpid bay]

in this server, tutoring and giving money for tutoring is against the rules, the best you'll find is recs

[languid patrol]

I wonder if I could find someone who would do it out of the goodness of their heart 😄

[torpid bay]

school maybe

[languid patrol]

Or I could just find another book, maybe.

[torpid bay]

[boreal fulcrum]

Helloo

[fresh comet]

[old oak]

<@&268886789983436800> I have no idea what this is, but it seems shady

[frail lagoon]

This sounds very dodgy, deleting

[glass peak]

But I wanted to be crypto scammed

[astral bay]

has anyone here heard of netmath at UIUC, or taken any of their courses? i am interested in their MATH 444 course. wondering if anyone has taken it or heard about it.

[cinder zephyr]

I took a netmath calc 3 course at UIUC while I was in high school

it was fine but I think I benefitted alot from there still being a teacher at the high school I could ask questions to

doing Math 444 completely online, idk it depends on your strengths and how good you feel you are at studying on your own (I went to UIUC so I know what 444 is, intro real analysis)

I mean using mathematica for calc 3 stuff was nice

idk how useful it is for proof based courses though

[astral bay]

nice, it's good to hear from someone with firsthand experience

so i am kind of going back and "filling in the gaps"... i was an engineering student, so i only had up to calc 3. since returning to school i've taken foundations, vector spaces, group theory, rings and fields, all kinds of stuff, never an analysis course.

or actually i had linear algebra and diffeq too

[astral bay]

so i guess they assign an online mentor/instructor? how was that process?

[foggy meadow]

Are you going through it ?

[torpid bay]

oh, this is for someone else

im going through tao's analysis

ive procrastinated far too long with it

[foggy meadow]

Me with half my world.

[torpid bay]

I'm kinda liking geometric algebra less and less

half the notation i've seen that GA loves is just bad notation

[zealous garden]

like what

[zealous garden]

heard you were talking shit

[torpid bay]

well

[zealous garden]

https://tenor.com/view/yotsuba-to-gif-23424183

[foggy meadow]

I mean in what sense?

[torpid bay]

I was looking at geometric algebra notation for calculus, with nabla, but then 3 different obejcts end up having the same exact notation as each other, (some seem to change this slightly), and i haven't seen much complaint in various geometric algebra videos about it.

[zealous garden]

I'm also curious, I can't think of too many standard notations with ass wads

[torpid bay]

specifically maxwells equations

[zealous garden]

AHAHAHA

[foggy meadow]

So, actually applying GA.

[zealous garden]

That specifically is a good one, but I'll say part of the reason you won't see a complaint is that most actual sources will actually have a single consistent convention, but there isn't a standard I would say

[torpid bay]

[zealous garden]

to which 3 objects do you refer

I assume you mean the gradient, vector/geometric derivative, and spacetime gradient?

[torpid bay]

take the gradient of a vector field, taking the nabla geometric product vector field, and whatever he last one is called where they write the same thing being nalba F = J

[zealous garden]

gradient of a vector field is the geometric derivative of the vector field

and the last example is literally just the geometric derivative, but acknowledging the underlying manifold as spacetime and not just space

and the geometric derivative of a scalar field corresponds exactly to the gradient of a scalar field as well

it's actually well justified

and the geometric derivative squares to the laplacian as well

[torpid bay]

[zealous garden]

the only real confusion I see there is from the fact that people often intermix classical and relativistic ideas when discussing maxwell

So you have a spacelike gradient and laplacian, and then separate time derivatives, or you have spacetime derivatives.

Have you seen how GA unifies the lorentz force law?

[torpid bay]

hm

[zealous garden]

This is the fun thing, GA can, regardless of whether you chose to use a relativistic, or more classical, formulation, unify the lorentz force laws into a single form, just as they reduce maxwell to a single equation.

[torpid bay]

i think ill do that part, dont spoil it

annoying how none of the actual geometric algebra sources atually explained that stuff above

[zealous garden]

Where have you been learning GA

[torpid bay]

1: youtube, 2: wiki

flawless combinatoin i know

[foggy meadow]

Get LAGA?

[zealous garden]

There is a textbook of decent utility that I've skimmed and stolen/modified some notation from, not on my usual list of recommendations but the author has the PDF freely available on his website

[torpid bay]

i do have a question about the last nabla F = J thing

[zealous garden]

Maybe, how much do you already know @torpid bay

[zealous garden]

Yes

[zealous garden]

this book btw

[foggy meadow]

AG is fun.

[zealous garden]

https://peeterjoot.com/archives/math2018/GAelectrodynamics.V0.1.6.pdf

[torpid bay]

using $\Psi = E + B\gamma$ and $p_\Psi = p_e + p_m\gamma$ and $j_e+j_m\gamma = j_\Psi$ I have $(\partial_T+\nabla \gprod)\Psi = p_\Psi-j_\Psi$

[fathom swallow]

Yeatte

[zealous garden]

they are not the same no

Their intersection might not be trivial though

[torpid bay]

hm

[zealous garden]

is gamma your imaginary unit?

[torpid bay]

yeah

i let gamma = w

originally i had them be seperate, but they always showed up together and kinda made them equal as a "what if"

[zealous garden]

[zealous garden]

if gamma is the imaginary unit, then F= E+B\gamma works.
If gamma is a timelike basis vector, then F= E+B\gamma is absolutely wrong

[torpid bay]

hold on, im thinking through the question

[foggy meadow]

wick rotation?

[torpid bay]

ah yeah gamma^2 = -1

[zealous garden]

That's fine, you can do spacetime algebra in +++-

the square of gamma is not the issue, desu

[torpid bay]

but ye it imaginary thing

[zealous garden]

E+B\gamma cannot possibly be the correct type of quantity when gamma is a vector

[torpid bay]

for me, gamma was the way to translate magnetic vector thingy into electric vector thingy and back

and the two 3 vectors end up as seperate spaces

[zealous garden]

If we have moved to a 4D relativistic representation, F is a bivector. E and B have to be bivectors. Furthermore, E is actually the one that picks up a factor of the timelike vector, while the magnetic bivector field B remains a product of only spacelike vectors

[torpid bay]

i just multiply by gamma to go between the 2

E and B are the 6 bivectors in 1,4,6,4,1 then ig?

[zealous garden]

if gamma is acting as the imaginary unit in a 3D representation, it is best thought of as a trivector, where it then encodes a duality between vectors and bivectors within its subalgebra.

[torpid bay]

yep

[zealous garden]

acceleration is rotation in spacetime, so the vector forces become bivectors in 4D

[torpid bay]

another naggin reason i wasnt liking GA for maxwells, was because it felt like magnetic and electric fields were arbitrarily treated differently, (tho one could always turn their vector-bivector status into bivector-vector via a dual)

so 4D spacetiem fixes that then

[zealous garden]

It's not arbitary at all actually

yeah so you start from a 4D perspective

then project!

realize that you can't actually see along the timelike direction

therefore, these Electric bivectors with a timelike direction, get cut down into lines

[torpid bay]

I wanted stuff to represent magnetic and electric fields as symmetrical (to the maximum extent i could)

[zealous garden]

There's a more rigorous formulation of this, the spacetime split, that allows us to see how the rotations of this 4D space project down into a particular observer's 3D reference world

[torpid bay]

also, that rotaiton is just the lorentz boost, right?

[zealous garden]

Yes

accelerations are lorentz boosts

[torpid bay]

if i really wanted to

I could modify maxwells equations and make the magnetric field the vector and the electric field the bivector instead right? or vice versa?

[zealous garden]

Well, vectors and bivectors in 3D are related through duality. Duality also relates the exterior and interior products, and therefore the curl and divergence. So yes, you should be able to convert all of the statements in whichever direction you want through intelligent application of the dual

[torpid bay]

oh yeah

i never got a nice version for the lorentz

force

i rememer now

or is it lorenz

[gray glade]

aren't lorentz boosts just changing velocity in that direction

as in, non-physically

[torpid bay]

the best I could do was making a certain kinda of new dot product that in back then's words would be "real part of q vector multiply be real part of psi vector plus imaginary part of q vector multply by imaginary part of psi vector"

[gray glade]

just changing coordinates to some constant velocity

[torpid bay]

$F_\Psi = k_\Psi q_\psi\cdot(1+\vec{v}\wedge)\Psi$

[fathom swallow]

Yeatte

[zealous garden]

tf

[torpid bay]

k is just a constant

[zealous garden]

what is that

[torpid bay]

[zealous garden]

what is F_psi

[foggy meadow]

What is all of it?

[torpid bay]

force due to the electromagnetic field, Psi

[zealous garden]

.

[torpid bay]

k is a constant, i would have to look up later exactly what it is, just say its 1 for now

as for the pseudo dot product

[zealous garden]

Just the Force?

[torpid bay]

$(q_e + q_m\gamma) \cdot(E+B\gamma) = q_eE +q_mM = q_\Psi\cdot\Psi$

yes

prob some other notation for this

[gray glade]

it's amazing how many different ways you can phrase CED

[zealous garden]

I have Joot's answer in my clipboard for you

[gray glade]

and how compactly you can do it

almost intimidating

[zealous garden]

Lorentz force and power

[fathom swallow]

Yeatte

[torpid bay]

a scalar cdot a vector, a little cursed but

matrices i just didnt want to bother with

[foggy meadow]

Programmers ^

[zealous garden]

what do you mean by that

[zealous garden]

https://tenor.com/view/huh-dog-hug-dog-question-mark-dog-question-mark-gif-14144426802562365039