serious-discussion

[zealous garden]

This is just a 1-vector in CGA

Thanks, that bugged me

It also bugged me when Richard Behiel, in his newest video, cancels Psi on the right side of the equation; excuse me is this an integral domain? How do I know that manipulation was valid, it feels illegal

[vast wraith]

this is wrong, the complex plane and the extended complex plane are different, only the latter is a topological sphere

[hazy bough]

i have theorem i will get it in a sec

[old oak]

If you can find a homeomorphism between a compact space (sphere) and the Euclidean plane, I will be deeply impressed.

[hazy bough]

im not trying to find homeomorphism im trying to find the theorem(i hope it will work) not 100 percent sure tbh

[hazy bough]

https://drchristianphsalas.com/2020/04/25/topological-equivalence-of-the-2-sphere-and-the-extended-complex-plane-the-riemann-sphere/

[old oak]

extended complex plane.

[hazy bough]

no

remember

homeomorphism transitive

[old oak]

What do you mean by that?

[hazy bough]

one sec let me type it out

complex plane homemorphic to riemann sphere(stereo projection) and riemann sphere homeomorphic to sphere

thus complex plane homeomorphic to sphere

its the transitive property

[old oak]

complex plane homemorphic to riemann sphere(stereo projection)
What do you mean by that?

[hazy bough]

homeomorphisms are an equivalence relation

[old oak]

I know this; how do you understand "the complex plane" here? And how do you understand "riemann sphere"?

[hazy bough]

the complex plane with its usual topology

[old oak]

And the Riemann sphere?

[hazy bough]

both with their usual topologies

[old oak]

What is the Riemann sphere?

[hazy bough]

does the argument make sense?

i couldnt find the theorem i wanted to

so i just did the transitivity thing (easy way out)

[old oak]

It doesn't, because the complex plane is not compact, and the Riemann sphere (which is homeomorphic to the extended complex plane) is compact.

A compact space cannot be homeomorphic to a noncompact space

[hazy bough]

oh wait yeah your right mb

[icy heron]

This is the stereographic projection I think you're talking about. It maps P on the sphere to s(P) on the complex plane by drawing a line from the north pole N through P. Notice that you can't map N itself to any point on the plane; you either need to remove N, or add a point to the complex plane, which we call the point at infinity

[hazy bough]

oh i get it now, they are only homeomorphic with the extended complex plane right?

rieman sphere homeomorphic with extended complex plane

not complex plane?

[icy heron]

Yep, the extended complex plane is homeomorphic to the sphere

[hazy bough]

oh ok that explains it

[fresh comet]

I prefer to think of it as R^2 is homeo to the sphere minus a point

[hazy bough]

i havent done math in a real long time lol

[hazy bough]

extended r2

not r2

right?

[fresh comet]

no

normal R^2

[hazy bough]

but the sphere minus the point is the rieman sphere then right?

[fresh comet]

the Riemann sphere is the sphere

not the sphere minus a point

[hazy bough]

ohhhh

sweet

that clears it up lol

i have not done math in a while

[zealous garden]

The better way to think about it is that R^2 has S^2 as the one point compactification, so when you add on the structure of C to R^2, it turns S^2 into the Riemann Sphere

[empty topaz]

@zealous garden ur bio says I should ping u

[lavish vale]

hi guys i need help

write random number n

print all the purmutation of n

like n =3

[zealous garden]

Based, thank you

[zealous garden]

!help

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[hazy bough]

whatever question you have its probably an unsolved problem in number theory tbh lol

[empty topaz]

Np I'm tryna be nice today

[hazy bough]

actually prob not

all permutations easy

[empty topaz]

After all my problems got t solved and I almaot failed math and my friends betraying me but ok

[hazy bough]

just exponential time

factorial time to be precise

[neat lintel]

Wordle 1,498 4/6

🟨⬛⬛⬛🟨
⬛🟩🟩⬛⬛
⬛🟩🟩🟩🟩
🟩🟩🟩🟩🟩

[stuck tendon]

Yo

[worldly gorge]

gng I want to learn the secrets of hte universe, what should I self study?

[stuck tendon]

Astrophysics

And pure math

[worldly gorge]

yeah thats what I thought. Ive mastered single variable calculs and got a B in differential equations. I havent done much physics since high school. An I ready or should I do the book fundamentals of physics first?

[stuck tendon]

Astro study the very small and the very big and all in between and math allows representation of disparing concepts

[stuck tendon]

Fundamental physics

[worldly gorge]

ok ill probably do that

[stuck tendon]

Then go reading on math as the tools pop up

[worldly gorge]

and I did calculus 3 but im not proud of that experience, but I know hte basics tahts for sure

[stuck tendon]

Start with kinrmatics and go climbing up

[stuck tendon]

Physics allow physical corolation

Is better to learn

[worldly gorge]

alr im thinking do the book called fundamentals of physics, then an introduction to modern astrophysics

[stuck tendon]

Halliday one?

Who is the autor?

[worldly gorge]

let me check

[stuck tendon]

Fymann are also good

[worldly gorge]

yes

[stuck tendon]

Ima go lunch

Bye bye

[worldly gorge]

and inroduction to modern astrophysics by Bradley Caroll

bye, thx

[true zinc]

I mean, why not just do a classical mech book, a electrodynamics book, a quantum book, and then anything after that

[stuck tendon]

Good also, but fundamental physics is good to show how basis is set

More how we define physics, good start to show what is fundamentals and the machanics of how physics experimental and theoretical is done

[empty topaz]

What is 0 decided by 1

[worldly gorge]

could work

[true zinc]

0/1 = 0; 0 choose 1 = 0

[empty topaz]

K tbx

[sharp olive]

Hey guys, I built something for y'all and I would love your feedback...

I guess I cant attach a pic, we built a fully navigable database of math. Currently, we have linear algebra and we're working on adding calculus by the end of Septemeber

It's a full graph of theorems, definitions, axioms, etc

[limber thunder]

seems like a for-profit app and that you joined solely to post this link, I'll let you know unsolicited advertising is against our #rules

[sharp olive]

Oh, I was looking for that in the rules... :/

It's free to use

[limber thunder]

with eventual paid tiers, from what I gathered

honestly it would be fine if you had a link in your bio or if you actually had a demo you wanted feedback on

[sharp olive]

We do have a demo, that's what I'm trying to share

Yes, the paid tiers are geared towards professors/researchers

It's in my bio now if anyone is interested

[limber thunder]

okay, sorry if my reaction seems a bit harsh we just tend to enforce a strict policy on this given that we're a big server that gets a lot of spam

fwiw the concept seems interesting

[sharp olive]

Thank you! No worries, I understand how annoying spam and promos are. We've been trying to filter out spam from our signups as well

[latent edge]

@jagged forge I used markov chains to figure out something in my life

tfw it helped

[zealous garden]

Wtf

[limber thunder]

yeah I'm kind of curious how was it useful

does your life include a M/M/1 queue or something

[old oak]

I once used markov chains to estimate DPS in World of Warcraft

[latent edge]

What is this

[limber thunder]

fancy way to say you have a queue, clients arrive according to a Poisson process and they also leave in exponentially distributed intervals https://en.wikipedia.org/wiki/M/M/1_queue

continuous time Markov chain

[latent edge]

Oh lmao no my markov chain was not this complicated

Granted if you want to use it for something big it will be more complicated

[old oak]

Arguably with continuous time this isn't really a Markov Chain? At least when I hear "Markov Chain", I think a finite number of states with transition probabilities between them.

[latent edge]

tfw dynamical systems

I should study dynamical systems it has been intriguing me recently

[limber thunder]

countably many states is a common thing to assume as well

[old oak]

Although the Wikipedia article seems to refer to the MM1 queue as a "continuous time Markov Chain", so I will not fight over terminology

[limber thunder]

like in this case

e.g. a discrete time chain could be some random walk in Z

[zealous garden]

Random walk in Z? That's my wife!

[rocky shuttle]

#math-discussion

[haughty panther]

a continuous time markov chain can still have finite number of states, though it's defined in a more complicated way than the discrete "depends only on the latest state"

and you can still represent it by a matrix in the finite-state case

[vivid halo]

read Deninger's papers

[latent edge]

meme or serious?

[vivid halo]

if you want to learn some spooky arithmetic geometry and also learn all these analogies with dynamical systems yeah it's worth reading

there is plenty of stuff from Deninger's papers which is less schizo and is actually useful in practice at least

[latent edge]

https://www.math.u-bordeaux.fr/~bmorin/Deninger-WA5.pdf

lmao

[vivid halo]

there is a lot of related work by Connes and his coauthors on this sort of thing too

[latent edge]

At first glance I don't see any reason not to read more about these stuff

[vivid halo]

a nice perspective is like, if you have a variety over a finite field F_q then the Frobenius gives you a discrete dynamical system and the closed points are periodic orbits

something like this should be true over Spec(Z) or over Arakelov compactifications but it's more schizo

https://arxiv.org/abs/2501.06560

this is the closest I've seen to actually talking about these things rigorously

[latent edge]

peak

[vivid halo]

the adele class space A_Q/Q* that Connes talks about is the same one which Connes uses to give some very natural spectral interpretations of L-functions

there is a scaling action by positive reals on this space, the periodic orbits have length log(p) for each prime p, which is part of what Deninger's conjectures demand of Spec(Z) seen from a dynamical point of view

lmao

[latent edge]

gives pi_1 vibes

[vivid halo]

yeah the paper I linked really nicely explains how this sort of thing makes the knots and primes analogy very explicit

like it's the closest thing you can get to actually viewing primes in Spec(Z) as "knots in a 3-manifold"

the main catch is this has to be some sort of non-commutative space

[latent edge]

this seems like a nice thing to give a talk about

[vivid halo]

take one copy of this picture on the left for each prime p and then glue all the generic orbits together, so you're left with one periodic orbit of length log(p) for each prime p, and a single generic orbit

you can't do this sort of gluing in a reasonable way without working with noncommutative spaces

[latent edge]

scary

but

interesting

[vivid halo]

also quite nice because the paper spells out how you can recover class field theory and view the monodromy of periodic orbits in this space in terms of linking numbers

[latent edge]

[vivid halo]

it is quite robust especially when considered in the context of Connes' other work using these same spaces to do spectral theory around L-functions

it's a little frustrating that this sort of NCG approach is sort of orthogonal to algebraic/analytic geometry but it's clearly useful in a lot of ways

maybe when you're handed a construction like this which seems to have all the right properties you shouldn't complain just because it's not what you expected

ultra knows way more about NCG than I do in case you do want to dig into this stuff and ask questions

[vast wraith]

this is nice 😌

[foggy meadow]

What does this even mean.

[vivid halo]

I feel like it's kind of impossible to draw a reasonable picture for the second thing

the first thing is very classical though

I guess the closest thing that comes to mind for the second thing are various pictures of chaotic attractors

those are also very classical examples in dynamics

[iron delta]

#chill pls help

[foggy meadow]

They do look like that, but are they really that in some sense?
I mean the graph looks similar.

[vivid halo]

should be taken with a large grain of salt not least because we have no clue how to write down these required arithmetic dynamical systems

[foggy meadow]

So, they are / maybe "arithmetic dynamical systems?"

[vivid halo]

in the finite field case yes these things exist with all the right properties, in the number field case sort of yes sort of no

there are extremely strong analogies that constrain what should be true about these things and there are some constructions which realize some aspects of these naturally and realize some other aspects in a very unsatisfactory ad-hoc way, with no good way of addressing certain analytic difficulties

like along with these sorts of dynamical realizations of arithmetic schemes there should be some corresponding cohomology theories which are in close analogy with previously studied leafwise cohomology for foliated spaces

[latent edge]

this diagram is so satisfying to look at

[vivid halo]

you should have a dynamical Lefschetz trace formula for these which recovers zeta functions of arithmetic schemes just as the usual Grothendieck-Lefschetz trace formula recovers zeta functions for schemes over finite fields

it's just that the kinds of dynamical systems that necessarily show up in the number field setting are much more complicated than the discrete dynamical systems that play the analogous role over finite fields

[foggy meadow]

The three classes of being.

I wish I understood more of these terms, but this is interesting.

[vivid halo]

part of what is appealing about this sort of idea is that it gives a completely uniform cohomological description of the local factors of L-functions

over non-Archimedean places typically you can write down the corresponding local factors by taking the inverse characteristic polynomial of the Frobenius acting on suitable cohomology theories for varieties defined over finite fields or their algebraic closures

over Archimedean places it would seem like there is nothing like an "Archimedean Frobenius" which plays an analogous role and which recovers the usual Gamma-factors in completed L-functions

[bronze pelican]

[vivid halo]

something like this does exist, at least through some slightly ad-hoc constructions, but it's not the sort of discrete dynamical thing you would get by iterating Frobenius over finite fields, instead you genuinely have a continuous flow with infinitesimal generator and you can look at regularized determinants of this

[bronze pelican]

Where's the cohomology

[vivid halo]

yeah good question, nobody knows any good constructions of this

like we know what it should be locally at all places but you can't just glue together the expected answers over each place and expect to be able to extract global arithmetic information like this

similar to how we know what the Fargues-Fontaine curves look like locally at all places but nobody knows how to define a "global Fargues-Fontaine curve" which specializes to all of these upon localization

but like here's a fun example to contemplate, consider the following R-vector spaces, for each place v of Q:

for v=p a finite place take R_p to be the R-vector space of R-valued finite Fourier series (in y) on R/log(p)Z
for v=\infty the infinite place take R_\infty to be the R-vector space R[exp(-2y)]

[foggy meadow]

(Side note it's crazy to go from writing in Hebrew and Gandhari today now trying to understand this.)

[vivid halo]

all of these carry a natural R-action s^t by translation (s^t f)(y)=f(y+t) with infinitesimal generator \theta=d/dy, whose eigenvalues are the poles of the corresponding local L-factor \zeta_v(s), and one has the following regularized determinant formula:

$\zeta_v(s)=\mathrm{det}_\infty(\tfrac{1}{2\pi}(s-\theta)|R_v)^{-1}\text{ for every }v$

[fathom swallow]

nGroupoid

[vivid halo]

here det_\infty is the zeta regularized determinant exp(-\zeta'_\theta(0)) where \zeta_\theta(s)=\sum_\alpha \alpha^{-s} is the spectral zeta function of \theta

you can similarly rig up such formulas which recover the local L-factors for basically any variety over a number field, the R_v's should be some shadow of some globally defined (and almost always infinite dimensional) cohomology theory which nobody knows how to define in an especially natural way

assuming such a theory exists it seems like it should involve a lot of really hard analysis to say anything interesting about on top of any already difficult arithmetic geometry

[foggy meadow]

Thanks for the explaination.

[vivid halo]

compare this to the Ruelle zeta function: if you take the primitive orbits of the flow to be the periodic orbits of length log(p) for each prime p then Ruelle zeta = Riemann zeta, this is where a lot of the analogies come from

[foggy meadow]

https://ncatlab.org/nlab/show/Ruelle+zeta+function
I recognize the form here is an SSP (sum sum product), but the extact motivation is still unclear.

hyperbolic manifolds section, it does seem useful, I feel like I have seen holonomy and length products elsewhere.

[vivid halo]

these Ruelle/Selberg zeta functions tend to show up a lot in quantum field theory around various partition function computations among other things

they show up naturally when working with various sorts of dynamical systems that's the main context in which these things are defined

the way that Selberg originally encountered these things was in parallel with the Selberg trace formula on hyperbolic surfaces where you can produce nice formulas and asymptotics for counting geodesics

this is the same sort of question as asking about the spectrum of the Laplacian for various hyperbolic surfaces

the Selberg zeta function of a Riemann surface encodes the length spectrum and this is an isospectral invariant, that's one good reason to care about such things

you can get explicit formulas relating the zeros of the Selberg zeta corresponding to Laplace eigenvalues and counting prime geodesics up to a given length bound, just as you get explicit formulas relating the zeros of the Riemann zeta function and counting primes up to a given bound

pretty much all the things you can do with one are in complete parallel with the other, including various conjectures in both settings really looking like the same statements in different contexts

[foggy meadow]

Strange, I wonder where else they show up.

[vivid halo]

these things are very closely connected to analytic torsion/Reidemeister torsion and eta invariants, those also show up a lot in physics around QFT and encode a lot of subtle information coming from index theory among other things

[foggy meadow]

Honestly I wish I knew QFT more from the math side.
Although, this is really really neat, and a lot of things flying around at once.

It's really cool you know this, and it's really cool that you're like explaining it out.

[vivid halo]

[foggy meadow]

The main reason I know about QFT is LQFT and trying to program that. Along with regge calculus, etc. I know mostly about Zeta stuff from the p-adics and Lattice theta functions being used in string theory. And me trying to understand why lattices show up there. I recognize a lot of the formulas/equation types(?) from this conversation. As I said I did see the SSP which I know from LQFT actions. (LSS being a programer sucks.) But over all a lot of terms, equations, and mathematical notation sort of flies over my head.

Also, Modular stuff sort of goes with trees, and just generally modular forms / theta functions, etc.
Lastly I guess know a lot of this stuff does blend together at different points.

[verbal mountain]

hello um anybody familiar with the Diophantine equations? I have a simple question: the satisfactibility problem (SAT) is turing computable so is computably enumerable (simple proof), then by Matiyasevich's theorem it is diophantine correct?

[thin gazelle]

Do you ever feel like you arent good enough for math? My uni entrance exam results came in couple days ago and i can only enter unis (specifically the good/top ones in my country) for a science major and i am not even good enough for engineering stuff unless i apply for a more average university , maybe this is just an asian system sorta thing where they do exams super duper hard just to eliminate people and it doesnt show ur true worth but there were still people who did better than me and who were good enough despite the fact that i also studied very hard too (i feel like i would have felt this way less if i didnt study very hard)

maybe i am indeed not good enough for math/physics stuff even though i genuinely enjoy studying them a lot idk

[fresh comet]

Do you ever feel like you arent good enough for math?

all the time. you might be surprised how many people feel this way

[thin gazelle]

is it really good enough though if u are really passionate about something but not necessarily talented at it? as much as i dislike beiliving in talent

the whole uni exam thing made me realize no matter how hard i try or how much i love the thing i am not good enough

[fresh comet]

a single exam is not representative of your capacity to do mathematics

[thin gazelle]

ye thats true but it really feels like it when u worked for it a lot

[thin gazelle]

like whats the difference

Between me and the people who did better than me?

[bleak hatch]

Where did your marks get cut?

If you work on the areas where your marks got cut, then you should be scoring very well in the next exam

[thin gazelle]

…

this is embarrassing to admit but there was a reading compherension part

on the exam

and uh

that didnt go very well-

but people who are better than me did both good on that and also math/science part stuffy

so therefore

I am still not good enough

because surely there are people who can do good on everything

[bleak hatch]

It will take time to progress, don't give up and keep practicing in areas you are weak at

[serene vault]

that's my thoughts too. and i still do think so. but people here have started to convince me that perhaps there is a reason no mathematicisn knows everything

[latent edge]

Math is girlboss

[latent edge]

do you ever feel like you arent good enough for math?
Yeah but I don't really care. If you have the passion for it then you wouldn't mind getting stuck on problems (because you will do all the time). You need to be stubborn enough and things will click eventually

[foggy meadow]

Do you ever feel like you arent good enough for math?
It seems like for an eternity, then again I program mostly.
My uni entrance exam results came in couple days ago and i can only enter unis (specifically the good/top ones in my country)
Apprently I did above average on my entrance stuff, and I never studied.
But I'm not sure America counts in this way.

I also don't know if Uni here would be the same thing.

[junior veldt]

i used to think that I wasn’t good enough a lot more

now im ok

[foggy meadow]

Everybody here in chat* rn knows more than me.

[junior veldt]

probably false

[thin gazelle]

ye but i would like to be atleast enough for it

like i am pretty ok with not knowing everything

[junior veldt]

to be honest im not even sure if it has a truth value

[thin gazelle]

Honestly knowing everything would be very boring or like being very smart

[latent edge]

Okay then you just put in work

[thin gazelle]

but i still wanna be enough for the thing i like D:

[regal gulch]

Wowi

[thin gazelle]

I did and it wasnt enough

[latent edge]

For what?

[foggy meadow]

I mean passing literally means you're okay for it.

It's more a "must be this tall to ride" rather than "noooo you will suck."

[latent edge]

I don't think this is true. Given enough time and dedication you'll get the hang of some topic

[thin gazelle]

Idk by top universities’s standards?D:

[latent edge]

It doesn't work for this case

[foggy meadow]

Then study?

[latent edge]

There are other factors you need to consider

[thin gazelle]

I did though

like from the exam’s standards i get into 2-3% but the good unis dont really care for anything below 1-1,5% it seems like;_;

[foggy meadow]

Did you pass?

[thin gazelle]

wdym pass?

[foggy meadow]

The exam?

[thin gazelle]

doesnt everyone who get into the exam automatically pass it though

By pass u mean get into the place i want

n o

[foggy meadow]

Can you retake?

[thin gazelle]

ye but after one year

I genuinely have no idea what the people who did better than me did differently

And i really dislike the idea of

t a l e n t

like i dont wanna beilive that they are just naturally better than me

[foggy meadow]

mannn

[regal gulch]

Well u have to ....I had to and it sucks

[thin gazelle]

D:

[regal gulch]

Yea );

[foggy meadow]

Everything can be learned, or at least gotten to.

[latent edge]

If you want to get into the "top" go into a "mediocre" one and transfer afterwards idk

[thin gazelle]

that was my plan too

[thin gazelle]

or well like go into a science field in the top ones

but i feel like

I am being too delusional again

Like having too much hopes on that

if i work hard enough

i can get there

[regal gulch]

If u aim for the highest u will get higher so

It's worth trying

[thin gazelle]

Even though i already tried the working hard thing

[thin gazelle]

But if i cant do it i will probably crash down very badly D:

[latent edge]

Idk I really can't give good advice on these stuff. They tend to involve nepotism and P2W methods so if you have these ig you can get in

But the advices I gave should work for math

[regal gulch]

Working hard and study never goes in vain u will always have some result

[latent edge]

or any field of study really

[foggy meadow]

This I have heard of a lot in the US.

[latent edge]

[foggy meadow]

You will do well, and I hope you get where you're going.

[foggy meadow]

Okay, explain something here, is the a_{i1} ... a_{il} like adding them together separately, adding over them, or multiplying?

[thin gazelle]

Thank u-

[vivid halo]

slop

[latent edge]

Ask Aluffi, Chen or Marcolli

[latent edge]

It's a mistake

The amount of times I see slop... It's not "weird" anymore

[jade owl]

Its ryoever

[barren parrot]

I'm 16. I love math. But I somewhat suck at it. I started studying graph theory and fell in love with it. Now it's getting harder and harder to understand certain ideas cause I have zero background in pure math. Do I continue this or do I start over from the basics?

[regal gulch]

Start with basics I'd say honestly u need some kind of guidance for maths not teacher but a guide who'd show u the right path to study

[barren parrot]

Ok then. Thanks!

[rocky shuttle]

the optimal path to mathematical mastery

[haughty panther]

you should probably know the basics, but learning math is not really "linear" in the sense that you learn all math up to certain level before moving up to more advanced stuff
after some point there's too much to learn to cover every branch of math so you have to backtrack whenever you see something new

[barren parrot]

That point of yours actually makes so much sense. Thankyou!

[north topaz]

@rain patio go to #❓how-to-get-help

as you said yourself, you need to make a private channel

[ember bay]

everybody lies

[mint canopy]

Hi @neat lintel, welcome to the mathcord! I noticed you posted your question in several other peoples' help channels and people quite politely asked you not to do that. That's spam! Please don't do that!

I know it can be very frustrating when people don't immediately come and help, but everyone here is a volunteer, not on payroll.

[hazy bough]

but what if he is hungry and he needs to eat spam for hunger purposes

[tender pike]

Hey everyone, I'm a French student and I was wondering if there's an official mathematics curriculum for grades 9 to 12 in US. I'd really appreciate book references or any resources that could help me understand in depth what is taught during those years.

I tried looking it up online, but every website seems to say something different.

[thorn jay]

@cobalt escarp ???

Were you saying something

[bright walrus]

t'es en quelle classe frérot ?

en vrai il y a pas mal de trucs ici, tu dois pouvoir trouver de quoi te satisfaire même si tu es au lycée

[wild lantern]

I don't think there's a definitive list but the kind of common list of courses (optimistically) would be alg 1, alg 2, geometry, trig, precalc, maybe calc 1, but very often not. It depends heavily on the individual school though.

When I went through the US public education system a very long time ago the requirement to finish high school (12th grade) was just geometry with a C or better I think. I remember taking alg 2 and dropping it to work part time.

Later when I went back to school at the community college level it seemed most students finishing high school aiming towards stem degrees finished as far into calc as they could.

So probably the mandatory amount is lower than that.

[verbal quest]

there are different state standards and varying textbooks, unlike France
it looks like US Integrated Math is more like what's taught in France
the sequence Dooter said (except Trig and Precalc are usually the same course) is common

[abstract cairn]

Hi Im planning on posting an answer book for exercises in curtis abstract linear algebra on a blog or something, mostly for fun, but also I was wondering if colleges would care much about that.

I know thats pretty basic but if I can show at least some profficiency in proof writing I feel like that would at least make me stand out a little.

If it makes a difference Im coming out of highschool not cc going for a physics degree.

[sharp cedar]

I have an encryption method/program i've been working on and i want to ask if people can help determine if it's secure. could that just be discussed here or would a help channel be better?

[unborn meteor]

can you show it?

i'm probably bad at this but i wanna see it

[sharp cedar]

yeah, here is the most recent version: https://github.com/Ernesti04/general_projects/blob/main/necklace_data_encoding_v3.py
you can either run the program and it'll ask you for stuff or this version has command line arguments as an option. you do -d to decode and -e to encode, -o followed by the output type if you only want one, then do -t followed by either the text to encode in quotes or the encrypted text to decode

it's still a work in progress so the code is a bit messy but i tried to label a lot of it, please let me know if there's any bugs

[unborn meteor]

also, https://discord.com/channels/268882317391429632/1160361906536710265 exists

[icy heron]

Wait, does it do encryption or encoding? There doesn't seem to be any keys/passcodes involved

[sharp cedar]

i don't have a method of exchanging keys so they're all at the top of the program with a b c and d

[icy heron]

Oh, I see

Just to be clear: encoding is very different from encryption: encryption involves keys: you need a key to encrypt the plaintext, and you need the same key to be able to decrypt it again. Encoding on the other hand is just a reversible transformation of the data, like base64 encoding or HTML encoding

[unborn meteor]

ok, i can run statistical tests on it tommorow

[unborn meteor]

.remindme 17h do this

[quasi jetty]

Created reminder do this (#serious-discussion message) for <t:1753706330:f>

[icy heron]

You seem to use the words encoding and encryption interchangeably, so I thought I'd point this out

[sharp cedar]

okay, i say encoding because if the program is left unchanged then it is. if you change the keys then it is encrypted because someone else has to have the same set to decrypt

it's very confusing though so thank you for pointing that out. I'll try to get better with it

[sharp cedar]

okay, thank you!

[unborn meteor]

@sharp cedar sorry, i'm on my phone so its hard to read the code, can you explain how it works?

block cipher or stream cipher?

[sharp cedar]

it's weird is what it is lol
i think stream cypher fits better(?) it converts each character but it can also treat each word differently if you split it (poorly named standard mode in the program)

but it converts each character into a binary necklace based on a b and c with the alphabet being shuffled with d. the higher the values for a b and c the harder it is to brute force

[unborn meteor]

necklace?

[sharp cedar]

i'm pretty sure that just one or the other would basically be a cypher, but both of them together (at least as far as i can tell) makes it pretty secure

[unborn meteor]

can it encrypt arbitrary binary data?

is the substitution the same for all letters?

[sharp cedar]

i think it's a combinatorics thing? basically a set of characters with an alphabet and a given length where none of them can be cyclically rotated to match another

[unborn meteor]

so you permute and then substitute?

how long are the keys?

[sharp cedar]

it can encrypt binary, it treats it as individual characters when doing it however. each letter is substituted on its own but will match, so they are randomly rotated. this makes it so you can't get the original value without knowing a
technically a is the key length, it't the length of the necklaces

you could theoretically factor the length to get it so non-prime values are used and a random set of junk bits is added to the end to detur that

[unborn meteor]

what's the maximum d?

and b and c

[sharp cedar]

d is used to seed the random function so whatever that accepts is the bounds

b needs to be low enough that there are enough possible necklaces in a set of length a to fit all alphabet and spacer characters
c needs to be small enough to accomplish the same thing

so b and c are bound by a, a higher a gives b and c a higher bound

[icy heron]

I think in practice d is the actual key; a, b and c seem too restricted

[sharp cedar]

a b and c together is basically a key while d is its own key

abc determines the necklaces that will be generated

[icy heron]

It's not a good idea to have two keys, one of which is only "basically" a key. Should you keep a, b, c secret? If b and c is almost always between 1 and 10, how much extra security does it provide to keep them secret?

Almost all cryptosystems have only one key, it's more practical, and usually more secure, because it's easier to protect one key than two

[unborn meteor]

i mean

if a, b, and c are all between 1 and 10 that's slightly less than 10 bits of information

you could do say, 8 rounds of this

with round key a, b, c, d generated from a 128-bit key

and also the 1-round version is breakable

for every possible a, b, c, do frequency analysis to recover d

[sharp cedar]

my thought is that abc is for configuration and d is what's used as an actual key

plus the values aren't that limited. with a, b, c = 24, 31, 3 i get

xcb210674h884j7f04h28h29h8d11h8ff0406g8fk121iec3g233gc31h1

[unborn meteor]

this actually works for an n-round version as well, so this is insecure if i understand it correctly

you need to add data-dependant stuff

[icy heron]

You could think of a, b, c as parameters, like the exponent e in RSA. It's not secret, it's just something you can adjust

[sharp cedar]

yeah, that's a much better way to look at it i think

[icy heron]

Btw, I think this line makes the encryption non-deterministic: https://github.com/Ernesti04/general_projects/blob/fff7a91dd673ae00fb7bb1cb8abfc7300b676290/necklace_data_encoding_v3.py#L349
Since you're using random.randint after this point

[unborn meteor]

you could make d operate on 2-byte sections

and iterate it like 32 times with key-dependant a, b, c, d for each round

that would be much harder to break

[sharp cedar]

that's done so the necklaces can be rotated randomly and not be determined by any seed. if a b and c are known then it makes no difference but it makes it harder to determine otherwise

[sharp cedar]

what do you mean by that?

[unborn meteor]

you have some big key

and you generate a, b, c, d by taking various bits from it

for each round

or, you could set a = 128, do 1 round, but do it in CBC mode, and then do like 32 outer rounds of that

[icy heron]

Hmm, so encrypting the same text multiple times results in different ciphertexts, but it can be decrypted to the same plaintext?

[sharp cedar]

yes, exactly that. and so multiples of the same character are harder to identify

[unborn meteor]

oh, interesting

[sharp cedar]

okay, i'll look into it!

[unborn meteor]

frequency analysis is still possible with this kind of cipher however

so d only operates on individual characters and not groups of them?

[sharp cedar]

right now d just shuffles the alphabet once

[unborn meteor]

actually, you need to do it in reverse CBC every other round for security

[icy heron]

That's pretty weird, not sure how much effect it has on the security 🤔

[unborn meteor]

actually, this still isn't secure, you need to do some kind of data-dependant stuff

[icy heron]

Actually maybe not so weird, I think it's basically the same idea as using a random IV for a block cipher

[unborn meteor]

true

[icy heron]

Btw, I hope this is more like a fun project and not something you're planning to use for important stuff. Creating a secure cryptosystem is really hard, and nobody here really has the expertise to say for sure whether a cryptosystem is secure or not

[sharp cedar]

oh yeah, i'm a cyber operations student and thought it'd be fun to try and make something like this. i'm just wanting to see if i did a good job of making something new that's secure enough, not something to replace anything lol

[icy heron]

I see, that's cool I have one last suggestion: maybe put some of the code in the main if-statement into separate functions encrypt() and decrypt(), so it's easier to read, plus it makes it possible to use the encryption directly from python

[sharp cedar]

yeah! this isn't a final version yet (i want to add encrypting/decrypting files as well) and i planned on doing things like that to make the code neater!

to people who want to try and break it, here is a sentence with abcd all modified

x5a1661k529w4e71C2121scf81l4261D757oa421r2121y4622s81a2w529r345z4f12m8v5b82u85m529o345vd78B69dp307F4942k8563za611z8224k1

[sharp cedar]

do you have any suggestions?

also here's another program i've made on the same concept if anyone wants a visualization or cool looking graphics
https://github.com/Ernesti04/general_projects/blob/main/improved_circle_plotting.py

[short lagoon]

Dih

[unborn meteor]

try using letters to index others

e.g. for each letter, set it to the ((previous letter's index + this letter's index) mod length of alphabet)th letter

[sharp cedar]

so like each letter in the text to encrypt becomes a different one based on the one before it? how would that be reversed? get the first letter and store its index, get the next letter and reverse it by the index of the previous letter? would it be better if they cascaded or only the original index of the previous letter matters?

[sharp cedar]

?

[latent edge]

@solid yarrow

[unborn meteor]

cascading is better

you do it backwards + subtraction for reversing it

[sharp cedar]

okay, thank you!
that sounds like a really good addition so I'll work on adding something like that next time I'm working on it!

[ocean robin]

what book is this? :o

[latent edge]

My first complex analysis book

[ocean robin]

wowie! i miss complex analysis and i need a book to continue my knowledge and review :(( (wont ask here bc theres a channel for that)

[cobalt barn]

<@&286206848099549185>

[solar nebula]

you gonna say something or just ping helpers?

[cobalt barn]

No

I need help

I alrdy made a forum

[solar nebula]

for future reference you should ping helpers in there and not here

[cobalt barn]

They said ping helpers after posting for 15 min

Ok

[ocean robin]

hi everyone :]

[vivid quest]

discussy is going too fast for my tired brain

i think i'll sleep

bye

[ocean robin]

have a good sleep!!!!

[livid night]

helooo

[ocean robin]

hello!!!

[livid night]

hru??

[ocean robin]

i'm alright :] about to head to bed, hby?

[ebon lodge]

Its morning here

[livid night]

same

goodmoring

[ebon lodge]

Good night

[livid night]

[ocean robin]

xDDDDD

[foggy meadow]

@vivid halo
Hey so, I was wonder about that equation you were talking about the other day. I have been looking The Ruelle Zeta Function over more, and read a bit about the motivation for his Selberg trace formulas. It has me thinking what exactly do they mean by f: M → M. I see the Selberg trace formulas looks at "sums of eigenvalues of the Laplace operator" could f be the laplace operator then too? What exactly could f be?

[vivid halo]

This is rather different geometrically speaking to what is considered for Selberg zeta functions

f is certainly not the Laplace operator

[short lagoon]

Dih

[vivid halo]

The second section on that nlab page for compact hyperbolic manifolds is a bit closer to what would show up in Selberg’s trace formula

[foggy meadow]

That only feels a little better in terms of understanding it more.

[vivid halo]

These Selberg trace formulas are an identity between information involving the eigenvalues of the Laplacian on the spectral side, and information involving orbital integrals and geodesics on the geometric side

A lot of what Selberg was originally up to was extracting interesting spectral information from geometric information like this

This becomes hard outside the case of compact quotient because both sides of the trace formula will diverge and require regularization

[foggy meadow]

Man physics people do wild things, honestly.

[vivid halo]

This is what number theory people do too

[foggy meadow]

Honestly wild enough, I like the thought in it.

[vivid halo]

https://people.maths.bris.ac.uk/~majm/bib/selberg.pdf

This is a great set of notes on the classical stuff around the Selberg trace formula

[foggy meadow]

I found that the otherday.

[vivid halo]

And then this massive survey by Arthur summarizing various aspects of his generalizations of this https://www.claymath.org/library/cw/arthur/pdf/62.pdf

Arthur’s trace formula is probably the biggest cornerstone to most of the Langlands program in the classical arithmetic setting

A lot of modern number theory (e.g. the proof of FLT) would not exist without some form of these kinds of trace formulas

[foggy meadow]

Tr go burr.

[vivid halo]

Trace but everything is infinite dimensional

[foggy meadow]

Honestly I need to learn more things.

All of this thought doesn't seem too bad, just more of a time sink.

[foggy meadow]

Besides recursive functions (I love them, but can't understand them at that level).
What else have you been up to?

[vivid halo]

Trying to finish some papers now that I am back from vacation

[foggy meadow]

One's you're reading or writing, and like on what exactly?

[vivid halo]

Writing

[foggy meadow]

Writing what?

[vivid halo]

Three or so papers (had to split them up because it got way too long for a single paper that tries to do everything)

Surveying and organizing various examples around Beilinson’s conjectures on special values of L-functions, mainly around those aspects which do not fit into the usual conjectural framework but where there is clearly room for generalizations

Upshot is there are more L-functions which show up in nature but which lack clear explanation

[foggy meadow]

in nature
Mean's what exactly in this context?

[vivid halo]

Also lots of parallels with partition functions in physics which have guided the thinking around this

By nature I mean they show up even in pretty low hanging examples that one inevitably runs into when playing around with mixed motives

But also like half the people I talk to about this stuff locally (a few collaborators) are string theorists and a lot of the examples I have were things which showed up in their work

[foggy meadow]

Okay, so for an example the Ising Model, does it show up there somewhere?

[vivid halo]

No they mostly work around computations of string amplitudes particularly in higher genus

You encounter things like modular graph forms and iterated integrals of Eisenstein series or other kinds of automorphic Greens functions for example

[foggy meadow]

Well, that might be why I haven't used them before.

[vivid halo]

There are quite a few examples around genus 1 amplitudes which involve iterated integrals of modular forms which are very much beyond what the usual conjectures about L-functions can tell you about

Those are what got me interested at the start of the year

Or like here is a more accessible example related to Chern Simons

If you have an arithmetic hyperbolic 3-manifold (e.g. a knot complement) then its volume can be computed in terms of special values of dilogarithms and the value at s=2 of the zeta function of its trace field

[foggy meadow]

I know about modular forms because of lattices, and messing with them.

[vivid halo]

But there is a natural complexification of the volume which recovers both the usual volume and also the Chern-Simons invariant

[foggy meadow]

Why would integrating them be interesting?

[vivid halo]

Well this is how you produce period integrals which are known to relate to special values of L-functions

Like the L-function of a modular form is literally just integrating from 0 to i\infty as a Mellin transform

[foggy meadow]

Huh.

[vivid halo]

There are much more general L-functions relating to various generalizations of modular forms but the relation to period integrals is nowhere close to this simple

[foggy meadow]

So then \int_{0}^{\infty} \theta(\tau)x^{n} dx?

[foggy meadow]

Well I'm looking for simple, so I can like grab and work up a bit.

[vivid halo]

Vaguely like this yes

[foggy meadow]

Like how would you write it out?

[vivid halo]

here \theta_f(t)=f(it)

(this is when f has constant term 0, if you have something like an Eisenstein series you have to remove the constant term otherwise things diverge)

in general you are usually given something that behaves like a theta function \theta(s) and you can write this as a sum \theta^0(s)+\theta^\infty(s) where \theta^\infty(s) has exponential decay at infinity, then take the Mellin transform to get an L-function

but you can also iterate these Mellin transforms and this is where you start to get some really new things going on

a favorite example involves the double L-values of Eisenstein series \Lambda(G_4,G_10;s_1,s_2)

if you let f=\Delta be the cusp form of weight 12 for SL_2(Z) (this is the simplest modular form which is not an Eisenstein series) then you can write the first really interesting L-value L(\Delta,12) as a very particular linear combination of \Lambda(G_4,G_10;2,5) and \Lambda(G_4,G_10;3,4) for example

but there is also an accompanying period integral "c(\Delta,12)" related to \Lambda(\Delta,12) which does not fit into the usual conjectures about special values of L-functions, nevertheless you can again write it in terms of \Lambda(G_4,G_10;3,5)

so in this case you get a very interesting transfer of information between these double integrals of Eisenstein series and single-integrals of cusp forms, as well as a "new L-value"

these "new L-values" are confusing for the same reason that the "complexified volume" of 3-manifolds is confusing and subtle

it is a little tricky to formulate the right kinds of conjectures because these these types of "new L-values" will live in something like R/Z rather than R, there is some extra indeterminacy that you need to account for compared to the usual conjectures about special values of L-functions

a good analogy is that the special values of L-functions tend to have conjectures of the form "|Period|^2 ~ L-value" whereas now you want to say something about the argument of the period rather than its norm, which has additional ambiguities or anomalies associated with it

in physics you typically cannot observe phase angles like this but there are still some things you can say about them especially when keeping good track of anomalies and so on

[foggy meadow]

Are these functions related to the gamma function?

I know that might seem out of pocket, but they look similar to me.

[vivid halo]

you typically see terms involving the gamma function as coming from the Archimedean place sure

[foggy meadow]

Also, again off topic a bit, is there like an inverse real gamma function? And not an approximation?

[vivid halo]

what do you mean

[foggy meadow]

Well I have been dealing with functions of logs.
And I found that it would be nice if there was an inverse gamma for x >= 1.

[vivid halo]

what do you mean by inverse gamma?

just an inverse function?

[foggy meadow]

Yep, it would help me get exact numbers for a problem I have.

[vivid halo]

certainly this exists yes although it cannot be single-valued and I don't know of any good integral expressions for this

[foggy meadow]

And I could also solve another problem because of it.

[foggy meadow]

Well I know of an approximation, which gets better with bigger numbers.
I also know I can make the approximation better, just by adding some terms.

So, I feel like it should be possible, but it might look weird.

[vivid halo]

https://en.wikipedia.org/wiki/Inverse_gamma_function

yeah this is certainly not so nice

the asymptotic is not horrible I guess

[foggy meadow]

I don't want all of it though.

Like a sqrt(x) isn't the whole parabola if that makes sense.

[vivid halo]

even just a single branch isn't going to have such nice formulas

[foggy meadow]

I know, I have seen the aproximation ones.

[vivid halo]

if approximations are enough for what you need then yes this can be improved

[foggy meadow]

Well, I just need what I posted in chill.

[vivid halo]

but yeah I've never encountered this function before

[foggy meadow]

Yeah, it feels like it should be more used, it would solve a few things.

[foggy meadow]

I did say I found an inverse for the log integrated Kepler's equation, but it involves the inverse gamma like the one I have in chill.

But if I want an exact inverse, it needs this function to be exact. Not just approximated.

[vivid halo]

this is probably the best sort of exact formula you can hope for I would imagine

reciprocal gamma has a much cleaner expansion and then you can extract some kinda awful expression in terms of polygammas from this if you like

works for any choice of branch you want

there's probably other formulas which might be more or less appropriate for what you need idk

[foggy meadow]

Again I stumbled across it, and sort of was like huh and kept going.

[vivid halo]

yeah lmao I feel that

I ran into some strange stuff with elliptic q-gamma the other day

it's always funny to me when you run into the inevitable section on these special functions pages like "here it is as a Meijer G-function" like wow thanks that's useless

[solid yarrow]

Are all your books in physical format? Or just your favourites? o.O

[latent edge]

Most of my books are non physical

The physical ones are either really old (I got them when I started getting interested in serious math) or my favorites

[solid yarrow]

so ca is special :3

[junior veldt]

complex analysis is very cool

[hasty shoal]

smooth manifolds by lee

what do yall think of it

[fresh comet]

love it

I’ve been working through a lot of it in #1368757937954099342

Lee is really good at exposition and quite a careful writer, imo

he does talk a lot, but I don’t mind that

[latent edge]

Yes :3

[latent edge]

Indeed

[solid yarrow]

very gud

[solid yarrow]

[latent edge]

How's your day foxy

[solid yarrow]

Woke up, showered, ate chilli. Then I failed at solving my exam assignment and prepared some questions for the upcoming "extra class". Wbu?

So short answrr: oki?

[latent edge]

I'm reading over NT

I kinda lost interest in my research project this summer

[solid yarrow]

Way to go lmao

[latent edge]

only one month left

[solid yarrow]

[latent edge]

but it was a good experience

[solid yarrow]

Do you heave a deadline?

[latent edge]

yeah it's basically a job

[solid yarrow]

This... sounds... not gud

[latent edge]

why

[solid yarrow]

Well don't you like... have to work?

I mean

[latent edge]

yeah

[solid yarrow]

You get

Money

[latent edge]

but math

[solid yarrow]

Hm

Mathing

[latent edge]

[solid yarrow]

Btw ehy did you mute discussy 1

[latent edge]

also it seems like my advisor won't really write a recommendation letter

[solid yarrow]

:(

[latent edge]

[solid yarrow]

Why not

[latent edge]

idk

[solid yarrow]

You're not lazy right?

[latent edge]

no?

[solid yarrow]

Good

Then I don't like your advisor

[latent edge]

yeah idk

well if they don't want to write one it's not the end of the world

I will choose a different prof

[solid yarrow]

Hm?

I.e. switch advisor?

[latent edge]

yes

[solid yarrow]

New field?

[latent edge]

the one im doing currently is combo rep theory

[solid yarrow]

Mhm

[latent edge]

yeah idk

I know a prof I'm really familiar with

but they don't take undergrads for research

[solid yarrow]

Wait

I thought you were in masters

Now I am really confused

Or was that vero?

[latent edge]

Vero is doing masters yeah

did she get banned?

i don't see her around

[solid yarrow]

Idk tbh

[restive salmon]

@neon garnet cleooo I’ve made up my mind
I think I’ll start jogging / walking everyday
It has sooo many benefits it’s crazy
Edit: I did some research ima go with running even ehheheheheheh

[solid yarrow]

Idk @ her but I am not sure of the name

[latent edge]

@jaunty ibex

[solid yarrow]

Reminds me again of CA

[latent edge]

what does remind you of CA

[solid yarrow]

Automorphisms

Riemann Mapping Theorem and the like

[latent edge]

oh lmao

[solid yarrow]

[foggy meadow]

$$\frac{d}{dx}\left(\ln\left(x!\right)\right)=\gamma - \sum_{n=1}^{\infty}\zeta\left(n+1\right)\left(-x\right)^{n}$$

[fathom swallow]

Cyberist

[foggy meadow]

Why, did I have to bump into zeta, ughh.

[foggy meadow]

@thorn wren You were talking about weird publishing methods. If and when I will totally randomly post some dumb desmos charts in here of some cool stuff I found recently.

[eager reef]

Don’t start running every day if you’re not used to it

Walking every day is fine of course

Going from not running to every day running is asking for injuries

Unless I’m reading this wrong and you’re experienced

[errant zenith]

+1

[solid yarrow]

This might sound really stupid, but it is meant more curious. Injuries from running? I mean yes you can get sore legs and/ or fall on the ground. Can you really get "injured" from running? I mean you're muscle won't magically rip apart, no?

[dim forge]

yo chat

[eager reef]

Overuse injuries in knee/shins are very common in running

[dim forge]

I'm feeling kinda low rn

🥀

tired

[solid yarrow]

In the shin?

How does that work out

[eager reef]

Shin Splints

[solid yarrow]

it does what

[eager reef]

That’s the name

[solid yarrow]

oh

[eager reef]

…

[solid yarrow]

misread

i read split

[dim forge]

lmao

[solid yarrow]

oh lmao

i have that

when i play basketball

._.

though i haven't really thought about the bones etc.

that's good to know

[eager reef]

Inflamed tendons in the foot are common as well

Even small fractures

[solid yarrow]

so going jogging once a week should be fine though?

no?

[eager reef]

Yeah

[solid yarrow]

to start off

and then slowly increase

[eager reef]

Yeah that’s how you wanna do it

[solid yarrow]

at what point do you "go up" in training time?

like what's a good rule of thumb

for jogging/ running ofc

[eager reef]

Don’t really know I already did it from a pretty young age

[solid yarrow]

hm

[eager reef]

It depends on how well your body is adapted already

[solid yarrow]

not gud

[eager reef]

You’ll find information on this if you search for it actively

[solid yarrow]

I was thinking of starting to go jogging. Since my stamina in basketball is ass

hm

[eager reef]

Im just a random dude on discord

[solid yarrow]

yeah probably

was just wondering

[eager reef]

You can find professionals talking about this

[solid yarrow]

still thanks for the info for injury though

that was pretty helpful

[eager reef]

Yw

You can try lower impact forms of cardio

[solid yarrow]

?

[eager reef]

Biking for example

[solid yarrow]

ah ic

yeah might help for starting out too

or just an alt for jogging

[eager reef]

They combine nicely as well

[dreamy ore]

we making some cubics today people

[ocean robin]

oooh

[vivid quest]

Im on light mide, i didn't see there was a matrice, i was like

Lmao

Im so dumb

[dreamy ore]

yea sorry

wolfram gave me transparent bg images

[restive salmon]

Yea I’m gonna start like 3-2 times a week and I won’t RUN run more like jog
Yea so I won’t start sprinting everyday without proper training

[vivid quest]

Oh you like running?

Running feels so good to me for some reason

[restive salmon]

Well I haven’t started yet…

But yea generally I do enjoy running

When I do run

But I haven’t taken it as a habit or anything

I’m trying to do so tho

[vivid quest]

👍

[restive salmon]

[dreamy ore]

altho the graph im tryna interpolate kinda looks like this

which idk if thats gonna be well approximated with a cubic

but we'll see

[neon garnet]

yayyyy that's such a great decision nona!!

[neon garnet]

i love running. i love how i feel when doing it. i learned recently that your diaphram is a muscle that's important to train too for running a lot.

i'm super curious to hear your journey!! running is def a topic that interests me. i feel excited for working up to a long, pain free running experience, for me c:

[serene vault]

i hear running 👀

[neon garnet]

@jaunty ibex verooooo we miss you girl 💖

hope you're welll

[vivid quest]

Running feels so good for some reason

[steel vessel]

she'll be back when deltoid remembers the password

[neon garnet]

pff

[restive salmon]

Yayyyy so Pilates and running sounds like a nice calming combo
I wanna like acc be able to run without running out of breath loll

[neon garnet]

@latent edge so disorganized tsk tsk /j

[steel vessel]

omg pilates is so peak

[neon garnet]

omg yessss i love pilates

[restive salmon]

Sameee

Even tho I still shake

Through almost the whole thing

As if I was electrified bahhhahha

[neon garnet]

it's so funny. like, my knee hurts too much to run more than a few minutes, so i feel limited by my musculoskeletal system more than my cardiovascular system for running right now. i hadnt expected to experience that before

[steel vessel]

thats fine, tbh the most important thing is having good form and really activating that mind body connection so u activate the right muscles

[restive salmon]

Oh well ig ima experience both lollll

I’m starting tmrw

[neon garnet]

super truee

[neon garnet]

also i learned about the TVA??

lower back on the floor!! (if mat pilates )

[restive salmon]

Yea quality over quantity

https://media.discordapp.net/attachments/565706425616171008/1181058816180232243/20201112_162314-1.gif

[neon garnet]

you go girll!!

[steel vessel]

dont forget ur pelvic tilts

[restive salmon]

Yayy

[steel vessel]

its js so much better, also slow movements burn more LMAOO

[neon garnet]

yep yepp
deep core deep core

[restive salmon]

Although I can’t start running right away bc my body isn’t used to it and it’s also dangerous

So I’ll start with walking and then maybe switch to running

Idk I need to read more about this matter

[restive salmon]

For realll

[neon garnet]

you can explore this too! [1]

they value preventing injury a lot

i could do that lowk.

[restive salmon]

Ooh tysmmm

[neon garnet]

mhm!!

[serene vault]

always start slow and low

[restive salmon]

Mhm I will

[serene vault]

i know some ppl start and immediately go "i wanna run 10kms"

[restive salmon]

Nah

Maybe in 2years

[steel vessel]

nah thats way too much

[restive salmon]

[restive salmon]

Fr

[steel vessel]

u have to build up to it

[serene vault]

yeah exactly

but it's possible

[neon garnet]

it'd be so cool to run a marathon

in like 2 or 3 years maybe

[serene vault]

i nearly C4'd my heart and after four years of recovery i was able to slowly complete a 10km recently

[vivid quest]

Oh that cool be a cool goal

[neon garnet]

yayyy congrats ^^

[steel vessel]

im not into running but i do cheer u on fr

[serene vault]

i believe in you folks!

[neon garnet]

mhm fr. my friend ran one recently. so inspirational

[vivid quest]

I'd have to buy better shoes tho

Mine are kinda starting to hurt

[serene vault]

if you intend to jog, try shoes with curved soles

and cushioning

[vivid quest]

That's impressive ngl

[serene vault]

ngl, thankfully i'm still young. if i was older probably would have been harder

[vivid quest]

Let's rename discussion 2 into running

[serene vault]

kek

[errant zenith]

Running is very healthy for your heart!

[serene vault]

you are correct!.... but not for my condition

i have to always be mindful of high blood pressures

[quasi jetty]

@unborn meteor asked to be reminded <t:1753645130:R>, do this

[restive salmon]

Woww impressive

[serene vault]

took a lot of physical training under medical guidance tbh

[unborn meteor]

uhh do you mean literally C4'ed

cause that's kinda hard to do

[serene vault]

it's a euphemism ofc

[unborn meteor]

ah

[serene vault]

but close to it

in a sense, what ended up happening could be described as a kind of c4-ing

[twin flicker]

i think its a recommendation to get 150 mins of steady state cardio a week

im tryna figure out how to get it in

[livid night]

I can barely get out of bed

[solid yarrow]

Maybe try to split it up?

[south kelp]

Start off by doing like a 30 min walk 5x/week while browsing something on ur phone, better than nothing . Eventually you get the urge to try jogging a little in between and then it just gets more and more addicting and faster from there. That's what I did but with 1 hour walks.

[twin flicker]

i try to do 10k steps a day but its kinda hard

just in terms of time

[south kelp]

hmmm 10k steps a day probably takes longer than 150mins of steady state cardio a week? Idk.

Maybe you could get a walking workstation? Admittedly I've never tried to do math on one, seems kind of hard.

[flat dome]

you can have a walk by the park for 20mins at night so you can cross the 10k steps mark i used to do this, about 6k steps before walking the park

[silver basalt]

yall

i both really like this server and despise it

[old oak]

Same, except for the "like" part

[silver basalt]

its a gigantic public server
and i know the US government joins those in mass
so im both being spied on and am available to be seen by an audience of hundreds of thousands

whenever i do anything ever

[meager goblet]

What yall know about the pretty lines and colors in lambda

[silver basalt]

oh hi kirbs

[silver basalt]

lmfao

[meager goblet]

Hoii

[old oak]

This really wasn't the direction I was expecting this to go.

[silver basalt]

explain

[old oak]

Of all the reasons I could come up with to despise this server (and there are many), "being spied on by the government" would honestly be quite low on the list.

[meager goblet]

That’s fair

[silver basalt]

dude the colors mean nothing
it just helps keep track of wth is going on

[meager goblet]

But they pretty :(

[silver basalt]

ok

[silver basalt]

glam up your factorial function 💅

[meager goblet]

Slay💅💅💅

We slaying with the lambda calculus on a daily basis💅💅✨✨✨

[livid night]

Your name is funny

[meager goblet]

Thank you

It supposed to be like the guy in my pfp

[livid night]

Oh yeah

[haughty lion]

@junior turtle corporate needs you to find the difference between these two pictures

one is "with deliberate mistakes" and the other "clean and correct"

[slender tinsel]

I dont understand lol

[haughty lion]

continuation of a discussion from #advanced-lounge

I asked chatgpt to generate a diagram like the one here https://math.stackexchange.com/questions/2245314/complex-keyhole-contour-integral

[vast wraith]

both are wrong

[silver basalt]

im going to fucking explode

[old oak]

Not the wisest thing to say if you think the US government might be listening

[cyan goblet]

nuh uh

[silver basalt]

lmao

[silver basalt]

is that a raven with rolly chair legs

[cyan goblet]

pukeko

[last trellis]

hello guys. I wanna study master degree major applaid mathamatics but which bacholovr subject important for this specialty/

[latent edge]

What's up?

[jaunty ibex]

[rocky shuttle]

[jaunty ibex]

Hi zan

[rocky shuttle]

Hi vero

What's up?

[jaunty ibex]

I'm doing fine

hbu

[rocky shuttle]

also fine, can't wait for my vacation in august

[jaunty ibex]

oooo

Where?

And why?

[rocky shuttle]

I'll be at an anime convention this weekend

Afterwards, I'll visit my home country for 1 month since I haven't been there for almost 3 years

[jaunty ibex]

[rocky shuttle]

bnuuy indeed

[jaunty ibex]

This implies you finished something

And now you are taking a break

[rocky shuttle]

oh yeah, I finished my phd if you didn't know already

[jaunty ibex]

Oh

Congrats!

[rocky shuttle]

Thanks!

[jaunty ibex]

Prof. Zan

[rocky shuttle]

uhh

still a long way to go to become a prof

[jaunty ibex]

Not yet

I just use professor for phd holders

[rocky shuttle]

[jaunty ibex]

Dr. Prof. is for actual professors

[rocky shuttle]

ok sure ig

[jaunty ibex]

I quit masters btw

I went back to my job

[rocky shuttle]

[jaunty ibex]

[rocky shuttle]

Are you happy with your current job?

[jaunty ibex]

Yes

I was having a bad time in my masters and I thought it was really not worth all this mental health problems

[rocky shuttle]

I see

I think what really matters is that you found a satisfying job that you can live with

[jaunty ibex]

Yeah I'm happy with my current job. I just thought of doing masters as a break from my job but it was not worth it apparently

[rocky shuttle]

[jaunty ibex]

[solid yarrow]

Gn peeps

[solid snow]

Pinging you in here since I don't think advanced needs any more LLM convo @old oak

But, I recently saw some video on social media talking about how LLM ads present the weirdest, most alien use cases for 'AI'

"Hey meta, pick up [friend] from airport"

(how does the friend know what car to look for, which airport, etc. - just silly as presented)

Granted, there are some approaches using multiple "agents" to try to be able to do this work flow, but I think it rings true that these tech company try to manufacture these nonsensical uses

I don't know at what point we decided as a collective that we wanted to delegate our actual human lives to AI instead of just the boring stuff

Oh, another goofy one was some AI glasses commercial where the scenario was being in a museum and being interested in a display, but the display mysteriously has no info placard, so you use your AI vision to learn some definitely accurate facts about whatever's in front of you

Who is the target audience??

[old oak]

To be honest I don't need any more LLM convo, but I agree with all your points.

[solid snow]

Fair lmao

[old oak]

And I'm not just saying this to get out of the conversation, it's almost all dystopia, bullshit, or dystopian bullshit, and I'm just so tired

For all my genuine interest in machine learning and AI, if it was possible to ban it all tomorrow, erase all the models and make it impossible to train more, I'd consider it a net positive.

[latent edge]

based

[solid snow]

Yeah I think we just need a full stop as well

At least its presence lets me easily filter out the companies that use it in their ads, etc.

[latent edge]

AI stopped being funny when they started using it for technical interviews

[neon garnet]

yep

[unborn meteor]

@haughty loom hi!!!!

[haughty loom]

hi!!!!

crank time incoming i think

[unborn meteor]

oh no

[haughty loom]

@neat lintel conversation moved to here to not make mods mad

[unborn meteor]

wait what

boytjie shut down the entire convo lol

[haughty loom]

nevermind they're leaving

[unborn meteor]

lets not continue it somewhere else

[haughty loom]

alright

[haughty lion]

The experience of going to a museum when you dont speak the local language

[solid snow]

I honestly hadn't thought of that tbf

[unborn meteor]

anyone here

[steel vessel]

hi

[fresh comet]

hi

[unborn meteor]

hi

[rocky shuttle]

hi

[latent edge]

bye

[ocean robin]

hi

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[iron nimbus]

welcome to the mathcord! see #❓how-to-get-help to open a help channel

Yes? I'm fine with pings, but other helpers may not; just a notice.

Also, I don't see your help channel yet

are you asking for study tips then?

#study-discussion

or book recommendations #book-recommendations

yeah, #book-recommendations might be the best place to go

if you don't have a specific math question, then don't open one

happy to help!

[fresh comet]

@limber haven welcome to the mathcord!

[ocean robin]

welcome!!

[topaz mantle]

welcome! :)

[livid night]

[ocean robin]

[fresh comet]

[ocean robin]

[livid night]

Do u like snorlax

[ocean robin]

i do like snorlax!!

[livid night]

snorlax is my favorite

[fresh comet]

https://tenor.com/view/snorlax-pokemon-sleep-gif-5673328

[ocean robin]

that's a great favorite!!! my fav is chandelure :]]]

[livid night]

woah

[neon gyro]

hi, I'm new to this channel. I'm starting A-level maths and additional maths after the summer and I have a somewhat descent knowledge of maths after taking additional maths last year. I would be happy to help with anything I am able to but my knowledge is currently limited so there may be some things I need help with or don't understand

[ocean harbor]

if u need help with math feel free to open a help channel in #❓how-to-get-help

and if u want to help ppl, there is a "Math Help" category where it says "Occupied" u could help people there

welcome to mathcord btw

[neon gyro]

thank you

[livid night]

I LOVE ADO

im listening to her colab with imagine dragons

[ocean harbor]

based

[livid night]

its so good dude

[ocean harbor]

indeed

[neat lintel]

yall

[neat lintel]

hello

[ocean harbor]

hi

whats good

[neat lintel]

nothing much

just learning abt making money using crypto

I just joined this group 😄

[ocean harbor]

oh I see

welcome to mathcord

[neat lintel]

thank you

[neat lintel]

https://tenor.com/view/krunkergang-krunker-gang-fien-travis-scott-tweak-gif-5276987523118708093

[outer crag]

Welcome to the server @neon gyro

[neat lintel]

SEE

SEE

[outer crag]

unc why are u here rn

[neat lintel]

YSST KNOWS WHICH PERSON IS WHICH

[outer crag]

[neon gyro]

hi

[neat lintel]

yep airstrikign me

over one simple math equation

[outer crag]

It's over for you vro.

[neat lintel]

ysst are you actually ai?

ima take that as a yes

[outer crag]

No.