More generally it converts the problem into a PDE and therefore take advantage of all the tools from that

@BalarkaSen so yeah, it's pretty neat

One would like to do a similar path in magnetoststics, and in the context of magnetic materials a similar trick is possible

@Semiclassical Right.

Yep, it's a nice perspective.

@Semiclassical I'll ask you more when I learn electromagnetism :)

But in general the potential for magnetic fields is a vector function so things become more involved

Mmkay

Where things really get miserable is when you have EM radiation

That is a real pain to do analytically

heh I see

(not surprising when you realize that connects to both wave and geometric optics)

It's in that realm where the full terror of classical electromagnetism hits

Tayor expansion of $f(x_1,x_2,x_3,x_4)$ can be expressed in terms of the operators $^nL_k^{n_1,n_2,n_3,n_4} = -i x_1^{n_1} x_2^{n_2} x_3^{n_3} x_4^{n_4}$, $n = n_1+n_2+n_3+n_4$ apparently, anybody see it?

@Semiclassical happy birthday by the way

Oh, yeah, happy birthday

I ate so much food :/

whenever I go to all you can eat sushi with my girlfriend

she orders too much

and I end up having to eat all of her food...

lol rekt

i don't believe in foods to be honest

oh interesting

You sound like me.

lol

Hi @Daminark

"I don't believe in wearing socks"

is something I often say.

or

"I don't believe in taking advil"

i use paracetamol

@BalarkaSen imgur.com/a/pero9

...

lol

w/e man

Yeah...

Would anyone know why Mathematica doesn't simplify FullSimplify[x == 0 || x \[Element] Integers]?

@Dodsy thanks!

this must be why people have been downvoting my things lately.

@user76284 No idea. Did you try asking at MathematicaSE?

Hey, how's it going?

Hey Daminark

Nice to see you again

I haven't made a question for it yet, just wondering if anyone here knew already.

@user76284 Here's another odd one: Refine[x \[Element] Integers, x == 0] returns True, but Refine[x == 0, x \[Element] Integers] returns x==0

You can also ask in the chatroom for MathematicaSE before asking a question.

@Semiclassical That looks like a bug.

I suppose I get that, though. Knowing that $x$ is a particular integer doesn't tell you any more than $x=0$ does, but knowing $x=0$ tells you that it's definitely true that it's an integer.

@Daminark Report? :P

@Daminark lame drama and no hope.

i.e. $x=0\implies x\in \mathbb{Z}$ is true but not the converse

Wait nevermind, it makes sense.

Not sure about FullSimplify though.

Yeah I was thinking x == 0 && x \[Element] Integers.

Yeah. That one should simplify to x==0.

You mean x \[Element] Integers?

Since it's an or.

hrm, yes

Interestingly FullSimplify[x \[Element] Integers && x == 0] works

But the disjunction doesn't.

That's weird.

okay

what the fuck

imgur.com/a/ThNOX

I am really getting upset here.

So we proved the general theorem that there are infinitely many primes that are 1 mod n for any n

Literally being backstabbed.

@Dodsy I suggest stop interacting with Duck.

FullSimplify[x \[Element] Integers || x === 0] works

I thought he and I cleared everything up.

The plot thickens

But now he's trying to get me into trouble with moderators.

I already reported the flag business to DanielF so he knows.

I just don't understand.

I am at my wits end.

@Semiclassical did you figure out the puzzle yet

nah, haven't thought a lot about it today

me either.

i did some neat numerics with it though

ya?

Yeah.

Basically, I finished my Mathematica code to randomly generate such configurations and test them for conductivity

hm, interesting.

Oh, Astyx's grid puzzle?

And the way I did that made it easy to generalize the problem to having edge probabilities other than 1/2

He showed me the solution.

Astyx is not a liar.

So I can produce instances with any edge probability.

Which leads to...

I probably should have waited, at least until the weekend, though…

I forget what size that was---maybe 5x(5+1)?

Ooh. Whoa, that's not increasing??

One of the dots is lower than its two neighbors!

Sure, but note the vertical axis

Each data point represents how many out of 300 randomly generated circuits came out as conducting

So it's statistical.

Oh, OK, so this was a Monte Carlo thing.

Got it

pretty much.

Looks vaguely symmetric

Yeah.

Kind of like the gambler's ruin curve? Whatever that's called?

What's really fun is the width of the transition goes down as n increases.

Like gambler's ruin.

So the bigger of a lattice you pick, the sharper the transition from "almost nothing conducts" to "almost everything conducts"

Sounds right.

Makes sense

Akiva of course he isn't a liar.

@bolbteppa I don't know what that is but congratulations

Good done.

That is confusion abated

I'm glad.

So easy yet so confusing

What even were you trying to do

Where did it come from in i.stack.imgur.com/vcVYH.png

Only with even more confusing notation

So that you thought you were expanding $f$ in terms of the $L$'s for some reason

...sheesh, the cure is worse than the disease there

Basically you have to replace normal equality (which may be approximate) with syntactic equality.

It kind of makes sense.

Sure, but

yeah.

So x === 0 || x \[Element] Integers works as expected, for instance.

It reduces to x \[Element] Integers

Daminark

how have you been?

Here's a math problem

Wait a minute, I was wrong. x === 0 is evaluating to False, that's why the disjunction is simplified. Hmm.

@Dodsy just read that whole mess. That's not at all how it went. Amwhy kind of asked me if I had any ideas, and since people were upset with stuff in general lately I just gave a general of anyone who might've been upset.

I read the transcript.

honestly, i thought you did say something about a closure, but I was probably mistaken. I mean, I kind of just answered whatever came to mind. Also, I wasn't "trying to feel integral to it". I was already involved when twice new users bit my head off and then changed their nick to amwhy.

so it's not like I butted my way in. I was just as much getting issues about it as well

whatever

@Dodsy funny thing is, is that amwhy was completely fine with me until I happened to mention that I was surprised all her downvotes went away when I remembered downvoting one. Then, she actually went to a post of mine, and basically said a bunch of mean stuff almost 24 hours later. We hadn't even spoken in between. It's like she just flipped out at me for no reason.

I mean, I could understand if she was upset right then and got mad for downvoting, but all she did was say something like "well all of them were reverted".

and then to top it all off when I confronted the rude post, she acted like she never posted it and deleted it. It's like someone was using her account or something.

either that or she was lying

@Dodsy How were you planning to start that?