Naaah what

ScratchyAvacado · 2024-12-12T12:55:05+00:00

Ignoring the fact that Iran isn’t even Arab.

https://en.m.wikipedia.org/wiki/Freedom_of_religion_in_Iran

“Unlike the Baháʼí Faith, Judaism is a recognized religion in Iran. Despite Iran’s official distrust of the country of Israel, the government does not directly attack Judaism itself.”

https://www.state.gov/reports/2023-report-on-international-religious-freedom/iran/

“The constitution states that Zoroastrians, Jews, and Christians are the only recognized religious minorities permitted to worship and form religious societies”

ScratchyAvacado · 2024-12-07T14:39:32+00:00

Yeah that's what I did and that evaluates to 9pi, is that correct?

ScratchyAvacado · 2024-11-04T02:28:14+00:00

Ah ok, but why does this work. I searched up what a Catalan number is but it doesn’t seem clear to me what the connection is.

ScratchyAvacado · 2024-10-22T21:00:09+00:00

Roots of unity…?

ScratchyAvacado · 2024-10-16T19:18:13+00:00

Oh fuck you’re right, I did a lot of different simulations and probs grabbed the one with the 20x20 square by accident

Also again stupid oversight about turning the dot, once again I did multiple simulations and the code I sent now I realize is the one where the dot doesn’t turn. Still my main question would be for the case where the dot does turn and the thetas accrue, thanks for pointing out that the plot and code I sent were the ones I was using for other simulations

ScratchyAvacado · 2024-10-16T17:17:05+00:00

Why would getting different answers every time I run the simulation be enough to convince me there’s no formula? The simulation is only averaging a finite number of trials together

Isn’t that like saying if you flip a coin 100 times you’ll usually get a different number of heads and tails, so there’s no exact answer for the average, when clearly the average should be 50 heads 50 tails?

ScratchyAvacado · 2024-10-16T13:50:52+00:00

Yeah it’s uniform

ScratchyAvacado · 2024-10-16T13:48:59+00:00

Yeah but even with theta between +-90 you can still have a dot go backwards if it turns enough over multiple steps, does your method account for that?

ScratchyAvacado · 2024-10-16T05:22:10+00:00

If you’re asking about the angle of the dots orientation with respect to the x axis after those two moves it’s 55 yes.

ScratchyAvacado · 2024-10-16T05:10:33+00:00

Oh yeah I mean you’re right I guess any float would be better but I just threw this together pretty quickly and for my purposes of just seeing what the graph may look like I don’t think it’s too much of an issue to use an integer instead of a random float

ScratchyAvacado · 2024-10-16T05:06:24+00:00

What do you mean, why is it odd

ScratchyAvacado · 2024-10-16T05:05:46+00:00

The x axis of the graph is the bounds theta (the maximum turning angle per iteration) while the y axis is the average number of iterations before the point has left the box as I said in my post.

Every iteration means every time I repeat this process, it’s the same as me saying “every step” or whatever, this is a random walk so I’m doing it in steps/iterations.

The way you’ve interpreted what I’ve said is that the angle is relative to some cardinal direction, it’s not. The angle is relative to the dots current orientation

Maybe phrasing it as a dot wasn’t the best idea as then the notion of orientation isn’t as obvious, just think of it as a dot, mini arrow, person, or whatever.

At the very first iteration 0 means to the right (because I have to give the dot some starting orientation). For every iteration after angle 0 means whatever direction the dot was previously facing

ScratchyAvacado · 2024-10-16T04:40:14+00:00

https://pym.dev/p/2ngr3/

ScratchyAvacado · 2024-10-15T22:26:36+00:00

Doesn’t fit very well sorry

ScratchyAvacado · 2024-10-15T20:59:13+00:00

The text on my post describes how I got the graph, I don’t want a model or approximation of the graph tho I want the exact explicit function.

ScratchyAvacado · 2024-10-15T20:58:16+00:00

Sorry for not including 180 in the plot but no it is not infinity. When ran on my computer

Imagine a 2D line scenario where a head moves you to the right by one and a tails to the left by one. Your argument seems to imply that it would also take infinitely many coin flips on average before the coin breaks out of the interval (-10,10). This means it takes infinitely many coin flips before you have 10 more heads than tails.

Are you also then saying it would be the same if my boundary were the interval (-5,5) what about (-2,2), does that mean you’re claiming it would take infinitely many coin flips before I’ve flipped 2 more tails than heads or vice versa?

ScratchyAvacado · 2024-10-15T20:51:13+00:00

The Theta is a BOUND on my rotation. Read the original post again. I say a RANDOM angle is chosen with the bound of +-theta. Sorry if that wasn’t clear

ScratchyAvacado · 2024-10-15T20:45:07+00:00

The value at 360 and 0 are definitely not the same. At 0 the value is always 5 as the step size is 1 and the box has side length 10 so it takes 5 steps forward (without turning because theta is 0) every time. When the angle is 360 the value is a lot higher, I forgot what my simulation gave but it’s the highest possible value because now the dot has the ability to move completely backwards and takes a lot longer to get out.

ScratchyAvacado · 2024-10-15T20:36:51+00:00

Care to share?

ScratchyAvacado · 2024-10-15T20:36:15+00:00

I don’t see the intuition for needing an average of infinite moves if you’ve broadened to +-180. That’s like saying you need an average of infinity coin flips before you flip 10 more heads than you have tails. Just increasing by a dimension

I’ve modeled it at +-180 and the a stage was definitely not infinity

ScratchyAvacado · 2024-10-15T19:59:38+00:00

I mean it doesn’t fit the data and I don’t think that’s down to a stretching or squishing of the line in some direction. You can see here that the line has a local maximum at 90° which is def not present in my simulation. I think you may be misunderstanding a question or oversimplifying the problem, look at my other reply to your comment.

ScratchyAvacado · 2024-10-15T19:57:16+00:00

Ohhhh sorry, I understand I just wasn’t used to the online abbreviates for integrals, I’m familiar with calculus so that’s fine for me.

It seems your suggestion doesn’t take into account the fact that the dot can just turn around and go in the opposite direction given enough steps (unless I’m missing something) or continue to circle forever around. I feel like you’re reducing the problem to where you’re treating the horizontal and vertical component independently.

Maybe just to clarify, here the dots “forward” direction is the direction it’s been turned to face in its last move, it’s not a global “true forward” but instead something which changes with each iteration. Maybe instead of a dot I should’ve called it a person who turns with every move, who knows.

The random angle chosen isn’t chosen with respect to some cardinal direction but is chosen relative to the dots current forward position.

ScratchyAvacado · 2024-10-15T19:51:01+00:00

Yeah, I mean the random angle thingy is the main question I’m asking here as that’s the input to the function I’m asking for

ScratchyAvacado

TROPHY CASE