serious-discussion

[neat lintel]

I can’t

The best i rendered was Mandelbrot using Java

No clue about 3D fractals

[zealous garden]

I should figure out how to do that

[neat lintel]

Quaternion fractals

[rocky shuttle]

some Menger sponge I did

[sonic sentinel]

sick

[zealous garden]

Why would I limit myself like that

[sonic sentinel]

i wonder if fractal architecture is a thing

[zealous garden]

I have the full power of a geometric algebra

[neat lintel]

I did this when I was 16.
It’s coded in Java and multithreaded

[zealous garden]

But yeah quaternions are the obvious answer

[rocky shuttle]

Nice!

[deep mango]

@bright hill tell slurp goodnight

and also

WTF are you asking??

[brazen patrol]

Hahah, nah, there are loads of talented fractal artists out there. 🙂

[bright hill]

he told me you said yes???

[neat frost]

Cuz he did

[bright hill]

@neat frost good night, bitch

[neat frost]

THATS NOT SINCERE YOU ASSHAT

[bright hill]

cry about it

[deep mango]

I literally didnt

[neat frost]

I bet yohan would give me a sincere goodnight

[rocky shuttle]

Good night Xlurp

Sincerely, zan

[neat frost]

Thanks Xannie!

[zealous garden]

GOOD NIGHT SLURP

[neat frost]

Image evidence says otherwise

[zealous garden]

HEART

[neat frost]

Goodnight wraithy!

[deep mango]

i didn't call you a punk either

[neat frost]

Lmfao

[deep mango]

clever using 2 fonts in your edit!

very tricky

[neat frost]

I wish

Apple only has three fonts to choose from

Helvetica, Georgia, and noteworthy

[deep mango]

lol

[neat frost]

None of them match this remotely

Which is unfortunate

[long matrix]

immature children

[violet wraith]

fuck you ryc

[deep mango]

what

[violet wraith]

❤️

[cold needle]

#chill

[cinder zephyr]

dumb question

what is a "Lagrangian Filling"

an REU I'm looking at has this as a project title but no abstract

All I'm seeing is stuff mentioning knots and manifolds but tbh all I'm finding are papers that I don't have anywhere near the background to understand

[frigid matrix]

🥵

i have an jdea though

[cinder zephyr]

I have been googling and found nothing besides papers 🙃

[frigid matrix]

just read them lol

https://en.m.wikipedia.org/wiki/Symplectic_filling @cinder zephyr

[cinder zephyr]

this is greek lmfao

[frigid matrix]

no no

think of a manifold

call it X

we call a filling of X a manifold W such that boundary of W is X

w/o using word manifold i can give example

like u have a triangle like this 🔼

the white part ye

a filling is this 🔺

sorta like what the word is

[cinder zephyr]

hmmmm

ok fair enough

[void tundra]

a manifold is just a topological space where for every point you can find a neighborhood homeomorphic to euclidean n-space

cant wait to do topology and cry

[cold needle]

i need to check out reus i still havent peeked at any of them

Also surely the process is much easier after having done it once right

[cinder zephyr]

surely

rn I'm just trying to get my letter writers to submit stuff in places

some places are using NSFETAP, some places are using mathprograms, some people are annoying and have their own special system

also this one REU

for one half of the projects, they have one application system

and for the other half, they have a separate system

why? god knows

[brittle socket]

[cold needle]

[cinder zephyr]

and yes, I need to have my letter writers send their letters separately to these

[brittle socket]

Hi metal

[cold needle]

very odd

[cinder zephyr]

I hate this

[cold needle]

hello grass

[cinder zephyr]

I emailed them and they said it's cause of some NSF funding guidelines or whatever idk

[cold needle]

lmoa

[cinder zephyr]

it's the DIMACS REU btw

New Jersey moment tbh

[cold needle]

o oki

ill keep an eye out for it oogissimo

[brittle socket]

What does oog mean

[cold needle]

Oog is a typo for oof that stuck with me

its like

oog…

[cinder zephyr]

bro has an inside joke with himself

[cold needle]

it seems to have stuck with others in the server

[cinder zephyr]

oog

[cold needle]

oogissimo

This list of reus looks pretty cool

[cinder zephyr]

link?

[cold needle]

its the google docs one u probably saw it

let me get it

[cinder zephyr]

ah

wait google doc or sheet?

[cold needle]

https://sites.google.com/view/mathreu

sheet

oop

yes

[cinder zephyr]

oh wtf there's a webpage for this?

[cold needle]

i was curious at what was going on in the summer

[cinder zephyr]

I've only had a link to the sheet itself

[cold needle]

lmao

[cinder zephyr]

oh there's an email

I can finally have them use a proper date format

to make sorting easier

[cold needle]

so far i found like 5 or 6 i might be interested in but the notes for each program are very vague ill have to pore thru each program carefully

but thats a problem for next week

[cinder zephyr]

that's what I've been doing except it's more like 30

[cold needle]

thats a good problem i feel

last year i applied to ten begrudgingly

i only really had a strong inclination for about half but i did have some interest in the others

its not good i need to loosen up

[cinder zephyr]

I have 0 self confidence in getting into an REU (and more importantly I'd like to have options)

thus, shotgun approach

Also once you have a personal statement and a research statement

making edits is exceedingly easy

at least that's how it's been so far

[brittle socket]

Oh lmao

[frigid matrix]

Are you an undergrad?

[shut aurora]

@echo tundra was looking through the server and saw your name, can I take it to mean you're good with NumPy?

sorry for the ping, I won't do it again if you mind

[echo tundra]

Well, it depends on the work. It's been some time I have used it. Do you need some help with numpy?

[shut aurora]

my internet drops right after I @ someone

[shut aurora]

specifically scipy.stats

think you could help?

please

[bright hill]

that's not a part of numpy tho, right?

[shut aurora]

it's built on numpy, is it not?

and by the same person

[bright hill]

oh?

[shut aurora]

it's just more useful for scientists like the name implies

[rocky shuttle]

ask scibpy

[shut aurora]

lol

[echo tundra]

This is most likely true but I haven't used scipy except for few very particular stat modules it has

[shut aurora]

I specifically need help with scipy.stats.nbinom and .poisson

it's a very specific coursework and I can't find any help in forums and stuff

so I thought I'd try my luck at asking someone 1 to 1

[echo tundra]

If forums didn't work I don't think I would be of much help. Tell me the issue

I'll see what I can do, just don't have high expectations

[shut aurora]

thanks

btw is this the right channel? don't wanna clutter it

[echo tundra]

You can dm me instead of talking here

[shut aurora]

alright

[echo tundra]

I don't have much idea about what this channel is for

[neat frost]

Haha nub get rekt

Good morning DarQ!

[brittle socket]

Hi Slurp

[neat frost]

Good morning grass!

[void tundra]

evening for them (?)

[neat frost]

No.

[void tundra]

Ah

good morning to you too

[bright hill]

good morning!

[neat frost]

Kawaii

[bright hill]

[long matrix]

meow

[rocky shuttle]

mrow

[wooden shore]

ayo does anyone can help me with chemistry?

the short formulas totally suck

[tough trellis]

No

[neat lintel]

Is this factorial symbol? (L thing)

[woven whale]

🤷

[neat lintel]

Well it was in my practice test of binomial theorem; I assumed it to be factorial according to the given data

I was curious if this was another weird notation of factorial

[woven whale]

I usually use that notation for the natural logarithm lmao

[swift sinew]

It is indeed a weird notation for factorial

[long matrix]

,,\Gamma

[long matrix]

not even

[rich glen]

..

why bot deleted my message?

[rich glen]

it

can be

i_q question

send the full photo

[woven whale]

looks like a drop shadow lmao

[rich glen]

bruh

[rich glen]

yeh lol

[cinder zephyr]

I've never seen that notation for factorial

I hate it

[neat frost]

Lmfaooooo

[neat lintel]

Lol

[hollow kettle]

That’s Ukrainian letter

I meam

I mean

Not Ukrainian

But we have it

In our Alphabet

[wild ravine]

guh

[cinder zephyr]

It's a Greek letter originally so I'm not surprised that it's appeared in other languages

[hollow kettle]

Our Alphabet

Derived from Greek

[cinder zephyr]

Tho tbh I can't think of another alphabet other than Greek and Ukrainian that has it

Yea

[hollow kettle]

While Western countries

Derived from Latin

Letters

Btw

Pi or Tau

[wild ravine]

pi

[hollow kettle]

pi

Even tau is natural constant for circles and convenient

pi is already used

That’s a convention

To use pi

Same as Kelvins are used over Celsius in physics

Even Celsius are most convenient

Because of 0 as freezing point of water

But Kelvins still used

Because of Absolute zero

[woven whale]

no it's not?

also tau = 2pi lol

[limber coral]

hey guys I need help with my homework xd

its till the new year

[cinder zephyr]

#❓how-to-get-help

[limber coral]

oh sorry

[storm sage]

Ґ

[hollow kettle]

Yes?

Why mathematical books use pi then

I’ve never seen any book of my life for my 12 years of education in 2 countries

To have tau in formulas instead of pi

Well maybe USA uses tau

I don’t know anything about USA

[hollow kettle]

Also why are you asking me

[small dust]

i’m in the us and have never seen tau used in schools

[hollow kettle]

I can say for Ukraine and United Kingdom

We don’t use tau

In any educational book

I can say for those 2 countries

[cinder zephyr]

lmao I've never thought about it this way but it makes sense why someone would say considering the US's love for not using the standard units

but no, the US uses pi also

[hollow kettle]

Oh

I thought

[cinder zephyr]

No one uses tau really

[hollow kettle]

Well you use Farengheit

[cinder zephyr]

yea

[hollow kettle]

As temperature

[cinder zephyr]

and inches and feet rather than __meters

[hollow kettle]

What does 0 in Fahrenheit represents?

[cinder zephyr]

it's cold

[small dust]

honestly never really heard of tau before this discord lmaoo

[hollow kettle]

0 in degrees of Celsius is freezing point of water

And 100 is boiling point

[small dust]

i think it’s something to do with salt water HAHA

[hollow kettle]

Yeah and horse’s blood

Mixture of Horse’s Blood and Salt water

Something like that

[small dust]

[cinder zephyr]

0 in Fahrenheit is "goddamn it's getting dangerous to be outside" because cold and 100 in Fahrenheit is "goddamn it's getting dangerous to be outside" because heat

[hollow kettle]

Well every physics gigachad

Uses Kelvins

Because 0 is fucking coldest

Temperature

When matter decays

[surreal sapphire]

0 in fahrenheit was the coldest winter on record in some town

[hollow kettle]

0 in Kelvin is -272 in Celsius

[surreal sapphire]

because the inventor didnt want negative values to appear in everyday life

[hollow kettle]

Yeah those old times

People were scared

Of negative numbers

[surreal sapphire]

no

[hollow kettle]

Now we even have square roots

Of negative numbers

And we use them in quantum physics lolllll

The only thing that is strange for me

Is p-adic numbers

Still don’t get how can be something “outside” of Complex Numbers

[small dust]

only????

[hollow kettle]

I thought Complex Numbers are all existing numbers

And now they tell me, man how about p-adic numbers

I’m like wtf is p-adic number

[hollow kettle]

Yes

Imaginary numbers are much more “normal” for me

Than p-adic numbers

Because imaginary numbers just exist perpendicularly to real numbers

But p-adic numbers

Is parallel universe

They never meet

Imaginary and real numbers have 1 point of intersection

Is 0

I would say it’s nor real nor imaginary number

Because 0 is the same as 0i right?

[small dust]

[hollow kettle]

Anyway

Gtg

[small dust]

loll ok cya ^^

[hollow kettle]

sure

[cinder zephyr]

I think people in here would find this gift I got pretty cool

[long matrix]

only if original copy

[cinder zephyr]

now that would be a gift

[bronze pelican]

Thsts a pretty cool gift

[cinder zephyr]

I'm looking forward to occasionally glancing at it

as with all the texts I have

[wooden flax]

dang nice!

costco?

[cinder zephyr]

Idk where it's from lol

[wooden flax]

ah i see

lots of interesting results in there

have fun

[wet notch]

Hey uh
How would one calculate the force of gravity on an N-body simulation with a periodic boundary?

Gravity simulations are fun, but due to the nature of the thing, a large number of particles are liable to be flung off, never to return. A periodic boundary would fix this, if not for the fact that the whole situation with wrapping around makes a fun infinite sum that I have no idea how to resolve

[swift sinew]

There shouldn’t be any worry about infinite sums. There exist distance formulae for the closed manifolds (which is what you’re thinking about when you say “wrap around”) such as the sphere, torus, their higher-dimensional analogous, and more. You can either look these up online or perhaps calculate them by using representations like the one in this picture (that’s for a torus)

This is how one would use that drawing to calculate distance

[bronze pelican]

ive thought about electric charges on the torus

if you want to calculate a potential function in the naive way, you end up needing to form an infinite sum

[swift sinew]

I think there’s some active research being done on evenly spacing points on the torus (possibly check out Dmitriy Bilyk)

(Which is essentially the question that you’re asking)

Oh sad, he hasn’t published anything yet - Im pretty certain he’s working on it though

[bronze pelican]

the way you define your potential function changes what the minimal energy congifuration of point charges can be

[bronze pelican]

i think the point Dorkly was getting at is that even though there is a minimal distance geodesic on the torus between any two given points, those two points will experience attraction/repulsion through other geodesics/directions in the torus

[static loom]

same, except on a sphere, kind of interesting how it wraps around

[bronze pelican]

because your universe is wrapping around

[static loom]

If two points are exactly on opposite sides of the torus or sphere, they end up being in some kind of equilibrium there

If a point is slightly moved away from opposite "poles" then you might be able to get away with approximating with a taylor series expansion

maybe this idea can be used to approximate to arbitrary accuracy anywhere

[bronze pelican]

yes i agree, that should be the case no matter how you define electric potential

[static loom]

well, actually a closed form might not be so hard to be honest, I think it ends up being like a geometric series

since we're on a flat torus

feel like a weierstrass p function is gonna pop up

since we have a bunch of lattice points

interesting

I wish I thought about periodic boundary like a torus before, kind of cool that the force of a particle on itself should be 0 since every force from itself at v will be cancelled by itself at -v (when thinking from the lattice picture)

[bronze pelican]

https://diegolopez.me/McGill-Physics-Hackathon-2020/

[static loom]

I suppose for a potential $v$ we can write the potential at a point due to to the lattice as $$V(\vec r) = \sum_{\vec z \in \bZ^2} v(\vec r-\vec z)$$

[fathom swallow]

mOwOsity

[static loom]

so now it's a matter of plugging in your favorite v here

if v(x) dies off as |x|-> infty then you can approximate to arbitrary accuracy (if no closed form is easy to find)

what happens if we imagine the weierstrass p function is a potential, what do the dynamics of particles look like?

looks like a Primon gas 🤓 (joking)

[neat lintel]

Any thoughts on Duolingo math ?

[static loom]

that's a thing?

[neat lintel]

They just recently launched and announced it

[bronze pelican]

i had a very simple question I wanted to prove about 5 point charges in the square torus

[neat lintel]

https://www.duolingo.com/math @static loom this

[neat lintel]

Square torus ?

What's that ?

[bronze pelican]

A square torus is when you quotient the plane by a square lattice

[static loom]

sounds fun

[bronze pelican]

Consider the square torus given by quotienting the complex plane by the lattice which is the ideal (1+2i) inside the Gaussian integers Z[i]

[static loom]

cool, considering

[bronze pelican]

I wanted to know if the five points given by the representatives of Z[i]/(1+2i) are a global minimum for electric potential energy of 5 point charges in this torus

turns out the answer is sensitive to how you define potential energy. But numerically at least this looks like a local minimum for potential defined by certain elliptic functions

i wasnt able to prove anything tho :

[storm sage]

I think it's really funny that they're doing this

[static loom]

hmm sounds cool, I think we could do it

yeah, how are you defining electric potential

or what form(s) do you want

like V(z)=A/|z|^n or something

[neat lintel]

Yss

[static loom]

I think it wouldn't be unless you place the 5 point charges very carefully now that I'm thinking about it

[bronze pelican]

what do you mean?

[static loom]

maybe I misunderstand, you are placing 5 points randomly and want to see if their minimum of potential energy is at the 5 representatives in the torus?

or if you place 5 points at the 5 representatives then they will all be "stuck" there?

I think that can be proved by symmetry

I think any sublattice will work in the same way

like go to the universal cover -> your representatives looks like a lattice, for any point on the lattice, suppose it's at the origin without loss of generality, then there's some point at u and -u with their forces cancelling out at the origin

it's kind of weird because the 5 distinct points become indistinguishable from 1 point

in the universal covering

hopefully that's clear and I understood correctly

[bronze pelican]

hm

but somehow I want to say these 5 points are 'better' than Z/(1/5)Z

[static loom]

better?

[hollow ginkgo]

Fun fact: the quotient of Z[i] by (3+3i) is F_9.

[static loom]

than Z/(1/5)Z? maybe we could but I'm not sure what it means yet

you sure it's not Z/9Z, I don't think (3+3i) is a maximal ideal since (1+i) and (3) are prime ideals

[hollow ginkgo]

Yes

[static loom]

where's my mistake then

only way you can get a field is by quotienting out by a maximal ideal right

[bronze pelican]

if the quotient were a field then the ideal would be maximal which its not

[bronze pelican]

its hard for me to explain because i dont have a good understanding of electrostatics

but let me just try to say what I observed

[hollow ginkgo]

Hmm

[bronze pelican]

imagine a single point charge at the origin

what is the potential energy at any other point in the torus?

[static loom]

I'd describe it with $$V(\vec r) = \sum_{\vec z \in \bZ^2} v(\vec r-\vec z)$$

[fathom swallow]

mOwOsity

[bronze pelican]

okay

[static loom]

since each point on the lattice is describing looking at the same point but wrapped around multiple times, which gets weaker each time it wraps

[bronze pelican]

so that potential energy is minimized at 1/2 + i/2 right?

[static loom]

yeah

and at 0 too

(maybe?)

let's ignore the origin since there's a particle there and it might explode with a singularity or something

[bronze pelican]

yeah it should blow up at the origin

[static loom]

well in a sense it shouldn't

like from a physical perspective

[rocky gate]

Which question are we solving today?

[static loom]

I guess it's just undefined to consider the force of a particle acting directly on itself

[bronze pelican]

it should. the fact that it blows up means you cant bring two point charges too close together

[static loom]

but if you remove that one contribution, the force on itself from where it sees itself periodically will all cancel out by symmetry

[bronze pelican]

oh you mean in the sum, sure

[static loom]

yeah I am talking about the potential on the particle due to itself, not other particles yeah

[bronze pelican]

yeah

[static loom]

ok cool we're on the same page now

but we're ignoring that anyways so haha

[bronze pelican]

yeah

okay anyway we have this function V

in particular the potential energy of two point charges in the torus, which one of them at the origin and the other at p should be V(p), right?

[bronze pelican]

i mean that's just how we defined it

[static loom]

the contribution at the origin from p? yeah

[bronze pelican]

oh so do you also need to add the contribution at p from the origin?

[static loom]

well at any point of space it's a linear combination of the potential from the other points dependent on their distance

so like let's say you have the three position vectors x, y, z then the potential at the position r is going to be v(|x-r|) + v(|y-r|) + v(|z-r|)

I put the magnitude of the vectors in for emphasis

since potential is usually just a function of the distance, it doesn't depend on the direction

x,y,z are fixed in space, r can move around to probe the potential at other points of space

[bronze pelican]

right but what is the total potential energy of 3 point charges in the torus?

[static loom]

it would be computed the same way, except now every point gives a contribution based on all its copies in the lattice

since this is sort of more clear to think of than wrapping around multiple times

to be a bit more explicit $$\sum_{a=-\infty}^\infty \sum_{b=-\infty}^\infty v(|x+(a,b)-r|) + v(|y+(a,b)-r|) + v(|z+(a,b)-r|)$$

[fathom swallow]

mOwOsity

[static loom]

as far as computing this goes, v(d) -> 0 as d-> infinity should be the case

which shouldn't be too hard to confirm with like p-series test for a typical example I think

[bronze pelican]

I want to define the potential energy of 3 point charges x, y, z in the torus (with position also called x, y and z respectively) to be V(x,y,z) = V(x-y) + V(x-z) + V(y-z)

so then I can talk about minimizing V(x,y,z) as x,y,z range over all 3 point configurations in the torus

[static loom]

I don't know if I'd call that a potential energy

[bronze pelican]

yeah i am not too sure of the correct terminology in electrostatics

[static loom]

well ok wait, I feel like the analogy doesn't matter if what you want to do is not really related

like you want to really just minimize this function f(x,y,z)=g(x-y)+g(y-z)+g(z-x) on a torus I guess really, right?

[bronze pelican]

yeah but 5 points

[static loom]

I assume U is an even function right

or what's the domain/codomain

U(x)=U(-x) is really what I'm checking holds true

[bronze pelican]

yeah

U is Z[i] periodic

[static loom]

could we say U(x) as U: Z[i] -> C could be redefined as V(|x|) as V: R>=0 -> C

I mean the domain there of V is nonnegative reals

or actually we can probably just say the codomain of both is R and not C

just trying to make sure I'm thinking a same conceptual idea as you here

[bronze pelican]

yeah U is real valued

U: C -> R and is Z[i]-periodic

[static loom]

I guess what I said must be wrong if it's Z[i] periodic

since |.| is not Z[i] periodic

[bronze pelican]

plot of U

it achieves a minimum at 1/2 + i/2 as expected

[static loom]

wait I don't understand what I'm looking at

this function has an input of 5 points in Z[i]

but the domain looks like 1 point in Z[i]

this looks like a function f: Z[i] -> R

but U: Z[i]^5 -> R

[bronze pelican]

how is it a funciton on Z[i]

its a function on C

[static loom]

sorry replace Z[i] with C

[bronze pelican]

my U is what basically playing the role of your V

i think

[static loom]

wait, the picture you showed looks like U: C to R since it's 3 dimensional

[bronze pelican]

yes

[static loom]

but the way you defined U earlier was U: C^5 -> R

[static loom]

here

[bronze pelican]

U only takes in 1 argument in the screen shot

[static loom]

sorry Potential: C^5 -> R, since U is used to define that

[bronze pelican]

yes

[static loom]

I thought this was a graph of the potential but it's a graph of U I see

[bronze pelican]

yeah

[static loom]

but your comment was you predicted that the potential is minimized at (1+i)/2, not U

or maybe I'm mixing up U and the potential

[bronze pelican]

im not being carful with my words sorry

i dont know what is the right thing to be calling potential

[static loom]

I suppose you could say U is like the potential from a single point

but your formula for "Potential" is not what I'd call a potential in physics

so it's confusing to use that word here

[bronze pelican]

okay

what would you call my formula

[static loom]

and I think it'll cause you headaches in trying to think intuitively about it by conflating them

I don't know what I'd call it

a wave function lol

with bosonic symmetry 🤓

don't actually do that though, I say just don't give it a name for now unless there's some specific reason to

I think that's what got me confused in the first place was thinking it had a bunch of properties and things that it didn't actually have cause the name made it sound like it had them

[bronze pelican]

ok

can I call it total energy of a configuration of 5 point charges?

[static loom]

I guess since your U already has the periodicity of Z[i] baked in, you could minimize your P(x_1,...,x_5) function with lagrange multipliers on the unit square

I guess it's kind of like an internal energy of how all the particles are squished together or something, yeah that might work idk

what is your form for U(z)=A/|z|^n or something else

[bronze pelican]

https://en.wikipedia.org/wiki/Electric_potential_energy#Electrostatic_potential_energy_stored_in_a_system_of_point_charges

"Electrostatic potential energy stored in a system of point charges"

this is what I'm trying to minimize

[bronze pelican]

no that's not periodic

[static loom]

oh yeah good point, sorry I should have said something like U(z)=sum_k u(z-k) with u(z)=A/|z|^n

[bronze pelican]

So that's not the U I used

so I used the U function given by this paper, it has a complicated defintion in terms of Jacobi theta function

[static loom]

ok, I guess it's not too serious then

[bronze pelican]

the reason they use this is because its a 'greens function for the laplacian on the torus'

[static loom]

we could start here, $$E(x_1,y_1,\dots,x_5,y_5)=\sum_{i\ne j} U((x_i,y_i)-(x_j,y_j))$$
then the gradient being 0 minimizes it, so we can differentiate wrt $x_k$,
$$\pdv{x_k}E = \sum_{\substack{i=1\i \ne k}}^5 \pdv{x_k} U((x_k,y_k)-(x_i,y_i))$$
$$0 = \sum_{\substack{i=1\i \ne k}}^5 U'((x_k,y_k)-(x_i,y_i)) \vec x_k$$

[fathom swallow]

mOwOsity

[bronze pelican]

okay anyway, using this defintion you can numerically compute that the 'total energy' of the five points Z[i]/(1+2i) is less than the 'total energy' of Z/(1/5)Z

I'm wondering if its a global minimum

[static loom]

so really we can then try to solve this, which might not be so hard $$0 = \sum_{\substack{i=1\i \ne k}}^5 U'((x_k,y_k)-(x_i,y_i)) $$

[fathom swallow]

mOwOsity

[static loom]

Maybe a bit cleaner to put back in terms of complex numbers, fix an $z_j$ then find the $z_i$ for $i=1$ to $i=5$ with $i \ne j$ such that $$0 = \sum_{\substack{i=1\i \ne k}}^5 U'(z_j-z_i) $$

[fathom swallow]

mOwOsity

[bronze pelican]

Ok, that's all I wanted to say, i'm going to eat now

[static loom]

if you can give me the output of U' from U (since it's complicated) then maybe I could do a bit more on it

alright later

[bronze pelican]

well

[static loom]

I just mean in your calculator, output the derivative of this wrt z

it might end up simplifying pretty substantially since this sum is =0, and the logarithm might turn it to a product a bit, etc etc

[bronze pelican]

We should have that U'(1/2 + I/2) = 0 since its a minimum/maximum right?

[static loom]

not necessarily, but that would be sufficient

actually not sure

I think U'(0)=0 is what we'd need

since inside U' is z_j-z_i, and when they're both equal to (1+i)/2 then it becomes 0

really all I'm doing is looking at your function of the 5 complex variables as a function of 10 real variables, looking at the gradient, and setting it to 0

then it's sufficient to focus on each of the coordinates being 0 for it to be at an extrema

since it's on the unit square, by symmetry we just need to worry about solving only the 5 x-coordinates, and all the equations are essentially the same by symmetry of the x_i

so you should have it boil down pretty nicely

and if you're brave you can even check the hessian to see if it's really a minimum

[bronze pelican]

i dont understand

Numerically, U'(1/2 + I/2) = 0

(ND = numerical derivative)

[bronze pelican]

is j supposed to be k here

and is it fixed?

Ok good

[bronze pelican]

oh if you want the symbolic derivative, this is what mathematica tells me it is, though I dont fully trust it because it has Abs' and Im' which I dont know how to interpret

[static loom]

well think about it this way, U(z) is minimized at (1+i)/2 so for U(x-y) to be minimized we would expect x-y=(1+i)/2

[bronze pelican]

sure

[static loom]

I guess we can't do that across all 5 points though of spacing them that way, so we'd have to arrange them differently

[bronze pelican]

yeah

[static loom]

well like I said, this all just boils down to rolling up your sleeves and computing the partial derivative and setting it to 0 and solving I think

[bronze pelican]

in fact people have proved that this configuration of points gives the centers of the optimal packings of up to five equal circles on a square flat torus

[static loom]

oh interesting

[bronze pelican]

https://link.springer.com/content/pdf/10.1007/s13366-011-0029-7.pdf

their proof uses topological graph theory

i believe this same answer should give the global minimum for "total energy" of 5 point charges in a square torus

but I havnt been able to prove that. I like your idea with checking derivative = 0. It checks out numerically

But how do you prove something is a global minimum

You have to find all places where derivative = 0 and then check this is really the one with the smallest value

[static loom]

yeah, basically

since it's continuous on a compact domain you'll know it'll be global

you have to check the hessian to prove it's a minimum

[bronze pelican]

huh

[static loom]

hessian is basically the second derivative test, checking the concavity

[uneven lantern]

didnt understand anything

[static loom]

that way you know your points aren't maximums or inflection points that kind of thing

[bronze pelican]

you want all partial derivatives to vanish at the minimum right?

[static loom]

yeah

[bronze pelican]

ok i really should just eat and then go sleep

[static loom]

yeah I have to work on finding a mistake in some proof I came up with yesterday

I think I proved that there are infinitely many regular primes, assuming the generalized riemann hypothesis

[bronze pelican]

Here's the mathematica file ive been working in

[static loom]

oh nice

[uneven lantern]

cool

[bronze pelican]

if its true that's a big deal

anyway, if you get any more progress proving this is a global minimum, let me know

[static loom]

yeah, I found an alternative representation of Bernoulli numbers with 2-adic generating functions. Then assuming there are infinitely many primes such that 2 generates (Z/pZ)^x, then I use this to prove that these primes are regular because they don't divide the denominator.

[bronze pelican]

huh interesting

[static loom]

Yeah, I will

[bronze pelican]

i guess you have to make sure your representation is correct

[static loom]

The thing is, the proof is simple, it just depends on this weird formula for the Bernoulli numbers I found earlier this year which I proved is correct

in fact I have sage code to check it and it is valid up to several thousand, just checked back then

[bronze pelican]

ok thats good

[static loom]

Not sure what I'm going to do if it is correct and I can publish it

never published before and not in an institution and trying to avoid crankery, so I probably will just write up something, post it on my own website, and put out some videos explaining it on youtube.

well, probably the proof is wrong

[bronze pelican]

if its correct then thats at least a phd thesis bro, this is an open problem since 1850 💀

[static loom]

yeah, it would be nice

[static loom]

Yeah the proof is wrong lol

[brittle socket]

[static loom]

Thought about it a little more, N(3+3i)=18, since the norm on Z[i] always coincides with the number of elements in our ring, it's a ring with 18 elements. A little playing around with it, the integers {0,...,5} in here behave exactly the same as if it were mod 6 arithmetic. For instance 2*3=6 and since 6=(3+3i)(2-2i), we have found some zero divisors. (in case it was in question that there were any fields that didn't have a power of a prime number of elements)

[rocky falcon]

Oof

[long matrix]

That's why u plan to settle at 26 so that with those downside ups and upside downs, u will be ready by 30

[neat lintel]

Yes ^°^

[long matrix]

idk, im not comfortable with fixed things

ig our lifespans are <100, say in general

but still

[neat lintel]

U don't have to be, this is what I have set as standard for myself
I wanna be able to do things quickly and live a long life in quick time

[long matrix]

You seem to like planning far ahead, but that's the opposite of me ig

[neat lintel]

Study the things I want and have hobbies that I love and a stable family or person to care for ^°^

[long matrix]

I take things as they come in small steps

[neat lintel]

I plan our large steps in a non specific way, but as their approach close, I begin to make them more and more specific

[long matrix]

I feel like I don't want to think about 'getting settled', until I 'feel' the time is right

Only at that time do I feel I can make the best decisions

And planning

idk

Even with a non-specific plan, I feel it's a waste of time if there's a high chance it won't be executed

[neat lintel]

I have actually heard that a lot from people
But I never understood what it meant ?

[long matrix]

Well idk let's say you're in high school

and u think

I want to do XXX at XXX uni

then get XXX job

[neat lintel]

"feel the time is right" stuff thing

[long matrix]

and then do XXX

[long matrix]

Like how many times out of 100 is this really going to happen as you say it?

Your plan as you set it

Idk - I feel like for most people its more of a 'dream' than a plan

haha

[neat lintel]

I want to 🛎️🛎️🪄🧼🎊🗝️

[long matrix]

Well you gain experience. Wisdom. As you grow older

And your thought process 10 years later will almost certainly be very different to that of 10 years ago

And then that plan you came up with 10 years ago will not be the one you want

ik rn i think fairly differently to how I did 5 yrs ago

And what I might've thought back then would not be the same as now

So I wouldn't make plans the future me probably won't follow.

[neat lintel]

But I plan them generally tho, so rn I next day I wanna do XXX
In uni I wanna study YYY and develop AAA or atleast AA amount of habits to guide myself through life better
Then I wanna do BBB or CCC or DDD or EEE things depending on the scenario
I don't plan things specific, it's a very general plan filled with lot of "or"s to account for that time scenario

[long matrix]

Everyone is different and I don't think your way of thinking is wrong at all

I can see how it is better than my way of going about things in several aspects

but it just wouldn't suit me

[neat lintel]

That's okay ^°^

Ur way sounds nice too

Unlike mine, it is filled with surprises and fun at every corner of ur life

[long matrix]

haha

Yes, I considered around a month ago maybe I want to leave the country

[neat lintel]

Mine is much more stricter without allowing me to diverge much and achieve specific things

[brittle socket]

Yeah personally I don't plan too far ahead either.

[long matrix]

That, I would not have considered (at all) 2+ months before

[neat lintel]

YEAH MAN THE FUTURE IS CRASY

12 months ago I wanted to be an engineer, now im Designer

[long matrix]

like if u had asked me 2 months ago 'would u consider leaving the uk for elsewhere' i wouldve gone 'probably no'

But now im really considering it within the next few yrs

as a possibility

Oh yeah and during uni if you asked me 'do you want to go into finance' i wouldve gone 'hell nah', but here I am.

[neat lintel]

I never specified my goals either
Even my current life situation is like that but even more complex
I am interested in maths, video game design, physics, chemistry, medical science, neuropsychology computational & neuropsychology, and a lottttttttt of other things like even photography, political science, economist
And for now I just gave myself time to decide with the main idea
"If I can't decide everything by the time of my board exams (the exams in next 2 months) I will do everything and I will give my best to do everything on that list, I will take a drop and develop myself some very good and productive habits for them"

[neat lintel]

U r doing finance rn ? That's fun ^°^

[long matrix]

im not sure where i am

i feel like im going up a slope, but idk which one

[neat lintel]

Nah, u r smart enough dw ^=^

Maybe u r developing more and more sustainability cus u can't really be perfect in any subject, u can just get better and better and u r getting better and better dw

[woven whale]

idk if I'm at the valley of despair or x = 0

[neat lintel]

Bruh u ? U r already enlightened man ???
Wdym ??? U r already so smart tho

If u r at x = 0

I am just living in negative numbers

[woven whale]

I doubt I'm already competent

[neat lintel]

U r clearly definitely smart which is very good tho
You are certainly smart in maths

[woven whale]

I think you're overestimating me lmao

[neat lintel]

Mathematics is often misused as a way to measure intelligence

"woah you do math you must be so smart!!!"
I feel like I hear this kinda stuff sm but it's so weird when I know deep down like whatever I do isn't smarter than anyone else.

like doing math is cool but it's as cool as anything else

[bronze pelican]

When every people say that to me I stay absolutely silent

[long matrix]

you watch anime, you must be so smart!!!

[neat lintel]

people rly do say that anime a comment a lot

[bronze pelican]

Why thank you

[neat lintel]

I think I normally just say like "nah I'm dumbo"
it's such an awkward position because I don't wanna agree with it and sound full of myself but I also don't like rly disagreeing with people

people rly need to stop complimenting people

lol idk, im probably just akward

[bronze pelican]

Yeah its awkward so I make them know its awkward by not responding

[neat lintel]

I think I would die

but alright I'll try that next time

[grave torrent]

Im pretty much just arriving at the valley of despair

[proud olive]

I'm at some peak but idk which one

[neat lintel]

Im not on that graph

the valley of despair is such a mood

[grave torrent]

its inspiring tho

theres so much to learn

[neat lintel]

We can never learn enough

We don't know anything about the universe

The matter we know, the one we observe and study, makes up only 5% of the observable universe. The rest is Dark Matter and Dark Energy.

I find this fact crazy the fact we don't even know anything about the 95% of universe matter

[grave torrent]

not yet

[neat lintel]

well DM me when you confirm String Theory

I have spent so many hours reading about string theory this last year

I finished up two books by Michio Kaku and another one by Brian Greene, but they just made me realise we're so damn far from even proving any of them

[grave torrent]

String theory is correct i just confirmed it

[eager reef]

I mean

[grave torrent]

You're welcome evryone

[eager reef]

Nowadays string theory is mainly done by mathematicians who find the structures interesting afaik

[neat lintel]

axions

[arctic grove]

based

[arctic grove]

theres a lot of math phys people and theo phys people too

i think

[woven whale]

@eager reef every mirror you buy is in used condition

[long matrix]

not necessarily

[deep mango]

How do you not use a mirror

Also it's crazy that mirrors just like

Keep on reflecting like that

It's kind of like magnets I guess

[violet wraith]

[deep mango]

Things shouldnt be able to just keep doing stuff

That doesn't make sense

[long matrix]

this ego

[deep mango]

Shuri!

My mom got me two shirts and two pajama shorts for Christmas

[long matrix]

no i dont care

[deep mango]

So yes I did try all of them on this morning

[long matrix]

christmas is stupid

[deep mango]

And yes

[long matrix]

if i got delivered catgirl stuff it might be less stupid but alas

[deep mango]

I did check myself out in the mirror in my new clothes 🧡

[long matrix]

[deep mango]

I almost want to never stop being ryc cube

But I will

Soon

[violet wraith]

fuck you ryc

[long matrix]

ikr

[frigid matrix]

how do i turn 1 band into 10 mathematically speaking

[neat lintel]

Aliens exist: YES \ NO

I proudly say YES

[mint canopy]

discussion and discussion-2 are good and nice channels

[fair mural]

so true

[neat frost]

Peepee poopoo

[long matrix]

meow

[tough trellis]

Meow

[bronze pelican]

Why all this ryc hate bro

Its so sad

Bird can't catch a break

[long matrix]

deserves it for being too merry

for anyone whos bored try integrating sqrt tan x

absolute nightmare

[mint canopy]

Facts

[fair mural]

that would just make me more bored smh

[jovial ember]

,w int sqrt(tan(x))

Owned

[fathom swallow]

Results provided by WolframAlpha

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

Requested by Chmonkey#9767

[long matrix]

not chmowned, dont care

[fair mural]

fake

[violet wraith]

it's a joke ❤️

[fair mural]

no it’s not

[long matrix]

ryc is

[fair mural]

so true shuwu

i’m so bored

[jovial ember]

<@&268886789983436800>

serveur con vie vie à le

[dapper torrent]

@neat frost

[violet wraith]

@violet wraith

[grave torrent]

@violet wraith

[leaden torrent]

please dont pingspam.

[storm sage]

Probably

[long matrix]

specimen S: slurp

[violet wraith]

LOL

aliens very likely exist but they're unlikely to be in the form that we think of

[hollow sundial]

,w int sqrt(tan(x))

[fathom swallow]

Results provided by WolframAlpha

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

Requested by riemann#2529

[void tundra]

reminded me of this: https://www.smbc-comics.com/comic/derivative

[storm sage]

https://www.smbc-comics.com/comic/noooooooo

[void tundra]

my life goal is to make the most useless mathematics possible

[fair mural]

no u uwu

[brittle socket]

Im making a hardcover (that the softcover slots into) for my copy of Jacobson :D

[limber stirrup]

Hi, I want to say "h[n] is non-zero only when the value of n is one of the following". Is this correct notation? $h[n] \ne 0 \iff n \in {-2, 0, 1, 3}$

[fathom swallow]

jet

[limber stirrup]

in my head i read it as:

[surreal sapphire]

well, "only when" and "if and only if" mean different things, the latter is a stronger statement

if you only want "only when" it should be $... \implies ...$

[fathom swallow]

Lochverstärker

[surreal sapphire]

i.e. every time h[n] is nonzero, n is in this set

[bright hill]

I wonder what similarities we share

That'd be really interesting

Especially if they're intelligent

Wouldn't it be interesting if there are stuff that all intelligent life forms share?

[limber stirrup]

in this case they both seem to be equivalent? if h[n] ≠ 0 implies that n is a member of the set ("only when"), there is no situation where h[n] ≠ 0 and yet not be a member of the set, meaning that, if n is in the set, h[n] ≠ 0

[surreal sapphire]

i don't know, but if this is the case you can make this (stronger) statement

[limber stirrup]

what information is missing here for you to decide? (will help me provide more context next time)

[surreal sapphire]

no idea what h[n] is

[uneven lantern]

tan(a+b)=?

[uneven lantern]

what is it?

[neat lintel]

,w tan(a+b)

[fathom swallow]

Results provided by WolframAlpha

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

Requested by 北京#2768

[neat lintel]

fail

[uneven lantern]

cos(a+b)= cosacosb-sinasinb

so tan(a+b)=?

[neat lintel]

You know that google exists right?

What do u all think about artists ?

I was able to find it in 10 seconds, how come you aren't

[neat lintel]

That I love them, and I also am one.

[uneven lantern]

yeah

[neat lintel]

Like painters and stuff ?

Yeah! My best friend is someone who is studying Fine Arts, and I myself spent years drawing and I'm enrolled into Design Uni

[uneven lantern]

thx

[neat lintel]

I have self learnt how to draw realism, and I can't say I'm bad either

I just love drawing because it relaxes me and produces wonderful results.

I don't like artists

[brittle socket]

Yayy Im almost done with making my hardcover for Jacobson's Basic Algebra I!

Just need to squash it under some stuff and wait for it to dry

[odd brook]

classic book !! looks lovely btw

[neat lintel]

I feel like they are just really really pretensious with all their "deepness" stuff
Most of them didn't develop brain after 14, they are just people stuck in their I am 14 and this is deep stuff
So I wanted to know what others think about artists lol
Thanks for your opinion ^°^

[neat lintel]

That's wonderful 💝💝

[brittle socket]

Thank you!!! :D

[brittle socket]

Thanks!!

[neat lintel]

wdym didn't develop brain lol.

[odd brook]

i should get a hard copy at some point or another of both I and II because the only ones i've been able to reference are abysmally-printed pdf versions

[neat lintel]

They are still stuck in their I am 14 and this is deep phase

Am I not an artist

You are

But I am saying like "professional painters"

Who I have to study in school for some annoying reason

You probably met the wrong ones. My friend is studying in Fine Arts college and she learnt some good stuff there

It's also hard to be there

I mean I'm a very rare case to be fair

It's rare an artist like me also does stuff like Calculus and all the other scientific subjects.

Well u might have seen people who are stuck in their 14 year old phase ig ?

Well only thing I despise is many contemporary artists

[neat lintel]

Leonardo Da Vinci was an artist whose work lies more in biology than art probably
Also he had a great mathematician still well known as his math teacher
Tbh, Leonardo Da Vinci was like that one aesthetic girl in biology class who can actually draw better diagrams than teacher

He studied anatomy to draw Monalisa

And also provided work which hadn't been done before

[neat lintel]

What is contemporary art?

I can't properly describe it, but it's the late XX century and XXI century art that no longer focuses on figurative approaches to convey feelings and ideas to the viewer through direct and clear representations. This type of art lets the observer create a feeling out of something that possibly doesn't have any. Most of this art focuses on materials, structural approaches and techniques, rather than a strong tradition of skills, painting or drawing, basically it tries to break all the previous boundaries from traditional art to achieve something beyond all the previous eras.

Ah!! The banana on the wall people!!!

That's the contemporary art

I have so much unfinished art in my closet, do you want to see lol

[neat lintel]

Sure, did u tie banana in ur closet ?

Lol

Nah I just practice portraits or also copying old masters. I'm not exceptional, but I do it out of fun

I self learnt at 16

I generally just don't like things which are "emotional" and are suppose to give me sense of some deep abstract emotions
I want patterns, rules, algorithms, things that don't have any emotions and just purpose and objective
Like I have a lot of interest even in other scientific fields apart from maths like physics, neuroscience, chemistry and stuff but then I am extremely terrible at "expressing myself" and emotions and stuff like that in general
When I express emotions, I cringe at myself

I want analytical things

[odd brook]

these are gorgeous

[neat lintel]

They are unfinished tho. I have way better.

More and more, I always try to treat my life like algorithm where I must perform steps one after another with no care for emotions

[neat lintel]

Those are actually good potraits!!! They look very nice

helo

Ik, but at the same time I can't change much

That's one of the most recent things I have been doing actually, trying to work on algorithms and understanding them in computer science and then think of my life as one and turn all my habits routines and everything to an algorithm with clear set of instructions that I must execute

You know I studied anatomy as well, like Da Vinci did? Many people enrolled in good Fine Arts school do it as well

Anatomy is cool tbh

[neat lintel]

That's wonderful!!!

[ocean pivot]

now thats a vibe

[neat lintel]

Now, my favorite thing is figure drawing probably.

[neat lintel]

That's just my entire personality at this point

ima 3d artist

i make human sculpts

Very nice!

old people only ahah?

i love wrinkles

i hate making girl models

or i cnt make girl sculpts lol

god of war

Sadly I can't post most of my art, because figure drawing involves partial nudity most of the times 🤣

[neat lintel]

https://tenor.com/view/oh-my-star-trek-gif-19129737

[neat lintel]

jake draw me like one of ur french girls xd

This is a training copy exercise from an artist I like

[neat lintel]

wat do u use

or like wats the best tool for u

acrylic charcoal oil

etc

A2 paper (42 x 59cm). Charcoal, Graphite, White coal

oh wow

I'm still learning colours drawing, I'll learn it this year

charcoal is hard

also pretty expensive pencils

Charcoal pencil isn't expensive realy

the coloured ones are tho.

it kinda is compared to regular pencil

but ye

[neat lintel]

i joined this server bcuz i hate maths

If you want some good affordable brands I can make some reccomendations

was thinking if i cn chnge my mind

[neat lintel]

its fine i am sticking to 3d now

I am enrolled into Ind. Design, so I take several mathematics.

that's why I'm here.

idk wats ind

Industrial Design makes concepts and sketches for products, while also dealing with concerns of materials, production and sometimes even economics or patents.

Pretty much every product you see in life, a designer made it anyway.

i use to make products

for 3d printing

[neat lintel]

wat color is ur bugatti xd

I doubt I'll ever work at Bugatti.

[neat lintel]

i love ur pfp

It's a painting.

is that a ghost

ye i kinda figured

Ill do 3D modeling as well

cool

wat software\

I have not started it yet. They get taught in 2nd\3rd year of Uni.
I think they teach SOLIDWORKS

or RHINO

It's necessary to learn it, because after one does a freehand\CAD project of the product, it's also essential to do the rendering and 3d model of it with textures, materials, etc...

[neat lintel]

ye fosure

There's some insanely talented people out there

[neat lintel]

if they r making u learn houdini gud luck

[neat lintel]

i open artstation n want to quit sometimes

[static loom]

houdini is awesome

[neat lintel]

https://www.pluralsight.com/content/pluralsight/en/blog/manufacturing-design/the/the-industrial-design-process-part-4-taking-2d-concept-designs-into-the-3d-world/_jcr_content/main/hero_blog_block/image-res.img.jpg/1527709388860.jpg

if i see nodes im not doing it

or rigging

but it is indeed a powerful software

[neat lintel]

thats pretty easy

hard surface

Well not easy for me. I've got to learn all of that next years. Never done it in my life.

[neat lintel]

oh ok u will find it easy

Nice

idk if unis will use blender

since its not industry standard

might use maya

or cinema 4d

I also need to make that stuff IRL tho lmao

lol

we have laboratory activity, with laser cutter, wood workshop, etc.

[neat lintel]

wat is ur degree call

Industrial Design?

is it in bachelor arts?

oh i mean wat field is it in

maybe fine arts

My country is cursed

it's in the Architecture Department formally

Only here ☠️

Doesn't have shit to do with Architecture tho

[neat lintel]

china?

Gosh I gotta remove my chinese username.

I'm Italian. Just studying Chinese as 3rd language.

oh cool

+100 social credit

[rocky gate]

Loved your work but honestly that beard looks ugly

[neat lintel]

我不是中国人 😦

[neat lintel]

ye blender crashed bcuz i dont retopo n added hair

my potato pc cnt take it

[rocky gate]

I mean this beard

[neat lintel]

yes thats wat i mean

[rocky gate]

lmaoo okii

[neat lintel]

cnt shape it

lagging so much

[rocky gate]

Best of luck tho

[neat lintel]

lol

danke

venge, do you know that I was about to join Fine Arts degree (Digital Media)

[neat lintel]

so i hate maths how do i like it

[neat lintel]

fine arts is cool

the issue is I can't afford to study away from my city, because the nearest city that has that teaching is 150km away from home

[rocky gate]

It requires math to build all those??

[neat lintel]

but u hv to be able to starve xd

[neat lintel]

make the bread xd

[neat lintel]

nah

thats just sculpting

Nah. I just decided to give up on it, I don't want to graduate in fine arts and have a 25000€ debt on myself.
I rather study in my local university something a little different.

[neat lintel]

but in physics like smoke somulation or liquid simulation i need maths

[sonic sentinel]

how common is 3 first languages?

[neat lintel]

like viscocity temp density

[neat lintel]

in W. Europe, pretty common. Can't guarantee everyone is good at them tho.

[rocky gate]

Um... I see interesting stuff

[neat lintel]

i know 3 langauge

its pretty common if ur not a english speaker

[neat lintel]

so r u a mather

I'm native italian speaker, fluent in English, took 3 years of Spanish, and I'm taking Mandarin Chinese for 9 months.

[rocky gate]

nah just a curious high-school dude

Alright continue the great work, goodbye

[sonic sentinel]

wdym? id honestly be surprised if there was a negative correlation between speaking english and being trilingual (also my question was about three first languages)

[neat lintel]

i failed french in college

but i know some words just to troll

un petit peu

livre

[neat lintel]

https://tenor.com/view/cow-wig-gif-19175049

[neat lintel]

25k

[sonic sentinel]

cows <3

[neat lintel]

Renting is expensive girl

It's not even the tuition being expensive here

You can get tuition for 1000-2000€ a year in most cases

But renting can be up to 500-1000€ a month in big cities

do u take a loan

for uni?

Me? No.

[neat lintel]

ye pretty much

I decided to study in my own city, I don't need to rent anything; hence no loans.

when i was in college my rent was 100 usd for a 1 bedroom apartment

was cool living there

My parents pay for me, I am in highschool

[neat lintel]

smart

😎😎

highschool is free here

highschool was a nice time

smoking weed n drinking

dont do that tho

well I did the drinking part sometimes. Weed is illegal, I'd never do it.

gud

also dont smoke

@neat lintel can we be art friends

[neat lintel]

sure

I don't do drugs at all

No smoking

No alcohol

No weed

[neat lintel]

do u hv cool concept art

im out of ref images

what concept art

hv ?

Venge

have you heard about Generative Design techniques?

To me it looks like alien stuff so much

From what I understand of it, you basically let an AI\Algorithm use some constraints, requests and conditions for building an object.

[neat lintel]

i hope ur not talking about ai

The algorithm finds the most stable and well performing shape using mathematics

https://resources.altair.com/corp/images/Applications_IndustrialDesign_generativedesign_3-Column-Card_Image.jpg

They look heckin' weird

I love AI art 💞💞💞💞

ai is taking jobs of 2d artist

sad