Primes and Squares

I've been thinking about the name of this room, and it doesn't feel quite right to me. It makes me feel as if this room and its users are somewhat "better/higher" than those on TNB

Nathan Merrill

I was worried about that. I'm open to suggestions

PhiNotPi

Can confirm: current name is a poor choice

Nathan Merrill

room topic changed to No name: For discussion about programming, math, and science, or whatever we feel like. Not about PPCG or golfing. (no tags)

Nathan Merrill

7:09 PM

room topic changed to Nonsquare rectangles on an n X n board.: For discussion about programming, math, and science, or whatever we feel like. Not about PPCG or golfing. (no tags)

Kritixi Lithos

I like this new name, it is both related to programming and mathematics

PhiNotPi

Would this be a good room for talking about the quantum-particle-in-a-box simulator I've been working on?

Nathan Merrill

for sure

Kritixi Lithos

ooh, what is that?

PhiNotPi

So I'm writing something that simulated a discrete wavefunction.

0

A: Sandbox for Proposed Challenges

Simulate a vibrating string code-golf Vibrations are an integral part of physics. In this challenge, you will be implementing a simulation of a vibrating string. This is actually rather easy to do as a result of the Huygens–Fresnel principle, which allows us to use a simulation process simila...

^ I wrote a classical version of the program

although I haven't actually written the spec, it's pretty simple. Now I need to figure out how to update it to use Schrodinger's equation instead of the classical wave equation.

Kritixi Lithos

7:21 PM

@PhiNotPi By wave function, do you mean something like this?

PhiNotPi

yes

for right now I'm attempting the 1D case

Quantum Waves visualized in 3D

►

Nathan Merrill

room topic changed to Nonsquare rectangles on an n X n board.: For discussion about programming, math, and science, and related topics. Not about PPCG (the site itself) or golfing. (no tags)

@PhiNotPi I feel entirely unknowledgeable about the wave function. Like, I know that strings vibrated, but nothing more :P

PhiNotPi

7:44 PM

so here's the problem I'm currently facing, and it has to do with energy conservation

So I have a complex number Y at a particular time step, and know the value of dY/dT at that time step, how to best approximate Y at the next time step.

Nathan Merrill

isn't that well defined?

like, as long as you know the length of time between the two time steps

you simply multiply that by dY/dT

PhiNotPi

the problem I'm having is that the complex number typically rotates over the time step.

If Y and dY/dT are at right angles, then Y should be rotating around the origin.

Nathan Merrill

so, use polar coordinates?

actually, I think the problem is that you need both dY/dT and dX/dT

PhiNotPi

Y is the complex number, I should clarify, and dY/dT is also a complex number.

Nathan Merrill

hmm...I'm pretty lost then. Like, I know what polar coordinates are, but I've never actually plotted them

hmmm, interesting (looking it up)

can you always reduce a complex number to the form x + yi?

PhiNotPi

7:55 PM

yes

Nathan Merrill

I mean, so this is fundamentally a 3D graph

PhiNotPi

Perhaps my choice of variable letters in confusing, let W be the complex number.

Nathan Merrill

you have T going in one direction

and the two parts of the number the other two axis

Kritixi Lithos

Does W move along T, or does it rotate around T? (sorry if this is a stupid question)

Nathan Merrill

so, you can either make it a 3D graph, or plot the two parts of the number for each time step (and don't plot T at all)

PhiNotPi

8:01 PM

Let me clarify some variable names going forward. T = time, S = space, W(s,t) = complex number wave function value, dW/dT change in wave function value over time.

let x and y be the components of the complex number, neither of which are real space/time

Nathan Merrill

how does space change?

or is space literally a spot in space (like a 3D coordinate)?

PhiNotPi

Time and Space are two independent variables.

Nathan Merrill

right, I get that

but is "change in space" mean movement?

PhiNotPi

yes

^^ Schrodinger's equation

let me simplify it some...

Nathan Merrill

so, what are you trying to plot, exactly?

how the wave function changes over time at a particular spot in space?

PhiNotPi

8:04 PM

yes

Nathan Merrill

then, I go back to my original statement: you need 3 axis.

you have 3 things to plot: x, y, and T

PhiNotPi

Yes, but I don't need to actually graph it. just calculate the points.

Nathan Merrill

which variables do you need to calculate? w1 from w0?

PhiNotPi

yes

Nathan Merrill

then why doesn't w0 + dW/dT*T work?

I guess the word "rotates" throws me off

PhiNotPi

8:07 PM

because it doesn't conserve energy

Let's say we have a simple standing wave. The complex number should rotate perfectly around the origin.

Multiplying by a complex number with an absolute value of 1 is a rotation.

if W0 is a real number, then dW/dT is a pure imaginary number (no real component)

when you add them, you get a complex number with an absolute value greater than what you started with

Kritixi Lithos

Can't you normalise it if the value is too big?

El'endia Starman

I think you could do norm(W1)*mag(W0).

PhiNotPi

the problem is that sometimes the amplitude is supposed to change

right now I'm reading this thing to see how they handled it: pnas.org/content/83/15/5360.full.pdf

Nathan Merrill

8:26 PM

hey, I think I got a good KoTH idea, but I want to play it with somebody to see how it pans out

anybody want to play?

PhiNotPi

what is it?

Nathan Merrill

(this one)

El'endia Starman

@NathanMerrill Huh, that's surprisingly relevant to the title of this room... ;)

PhiNotPi

> Your goal is to ensure your opponent zones as few squares as possible.

Nathan Merrill

oh, it gave me the idea

PhiNotPi

8:30 PM

not to zone as much as possible?

Nathan Merrill

right

PhiNotPi

is score = your zone - opponent's zone?

Nathan Merrill

nope, just opponent's zone, lower is better

El'endia Starman

Hmm. Curious.

Nathan Merrill

that said, they are often closely correlated, but I indicated that to emphasize that strategies other than "Fill an entire half of the square" work

because p1 could do that, and then its an exact tie

El'endia Starman

8:32 PM

Yeah, you deny zones to your opponent by disrupting 2x2 blocks.

PhiNotPi

let's say that p1 played a 2x2, then p2 filled an entire half

Nathan Merrill

still a tie

because p1 would be able to fill in the remaining squares

PhiNotPi

all remaining squares?

Nathan Merrill

yep

PhiNotPi

So you can zone rectangles which overlap previously zoned rectangles?

Nathan Merrill

8:34 PM

because you have a hard limit on the total number of squares you can fill

no, but there's no configuration of a 2x2 and a 20x10 that block me from filling in the remaining squares

El'endia Starman

Neither player can occupy more than half the board, so the game becomes one of making areas unzonable.

Nathan Merrill

only for 1 player. The other player can play until he's filled in the remaining area

P1: 2x2 square in bottom right.
P2: 10x20 square on left
P1: 2x8 square on right
P1: 8x10 square in middle-right

both players end up with 1/2 exactly

El'endia Starman

Hmm, wait, couldn't you zone a 10x20 rectangle, but leave a one-square-wide strip on one side?

Nathan Merrill

yep

but rectangles need to be at least 4 squares big

I didn't say anything about a 2x2

El'endia Starman

Oh, so 1x4 is possible?

Nathan Merrill

8:41 PM

yep

I'm actually considering raising that.

El'endia Starman

Very interesting. That does make this challenging.

Nathan Merrill

to 5, I think

it forces you to have at least 3 squares in a direction

but I'd like to play test it, if anybody wants to play a game with me

El'endia Starman

Where?

Nathan Merrill

Zoning game

Let's play a game of zoning

El'endia Starman

(Though I probably shouldn't play now, being at work and all...)

PhiNotPi

8:54 PM

lol

Zoning game

Transcript for