The Dumbest Way To Solve A Maze - Numberphile 

Make pressure, so they go the right way slightly more often than the wrong way each loop

Who imports numpy as numpy. Everyone I know imports numpy as np. He might want to use numba to speed up his code.

It would still work with only one particle... if you want an even dumber way!

L

What programming languages are Matt Henderson using to produce those beatiful animations? Can anyone tell me?

This is the first thing which came to my mind

What mught be the sorting equivalent of lightning maze solver??🤔

Since you were first to say it then you get likes

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now throw a NEAT instead of pure randomness and now its NEATboggosolver!

That sounds intriguing. I'd love to see the results.

2. that

@@wolfmoz2232 3. that.

4. that

" A-star, but it only knew about walls it had "seen" "so kinda like D-star?

Now, that's a fun fact !

Is that the same principle used in a Tesla valve?

@@NickACrowley That's the first thing I thought of! Is there a telsa valve such that particles escaping through it at a specific initial preassure is statistically impossible?

@@NickACrowley It's similar. In a Tesla valve, the side path ways reverse the momentum of some fluid and then send it back into the main stream, so it's like you're subtracting the velocities from each other (that's not strictly true in a physics sense, but it's the right idea). The end result is fluid flow with an average velocity much closer to 0. Labyrinth seals rely much more on random chance instead of intentionally 'subtracting' velocity.

@@Kwauhn. no, Labyrinth seals mostly used for high viscosity fluids like grease. All they do is make the path much longer and higher friction than a straight path

As they did in this video? Very easy. Though it looks like he over-complicated things quite a bit...

"that depends, do you want the big effects or the really tiny ones?"

??

Similar, in your cube there is air. If you blow through it, the air in the 'wrong' path can't escape, you're pushing it into a dead end. Your breath will take the path of least resistance. Since this model doesn't simulate air pressure, or any interaction between the molecules, there is the same resistance going into a dead end as there is following the correct path (none at all), where in the real world there is a difference in resistance. That makes your real world example more efficient than this model.

So basically if I'm ever trapped in a huge cube, follow the breeze, or perhaps the condensation...

@@oddlyspecificmath light some incense

A local engineering competition had a remote controlled robot challenge. You got points for completing various tasks. Then some points for time. The year before I participated, the team from my school just made basically a RC car and went straight for the finish without doing any of the tasks. They got first place. Needless to say they changed the scoring grid for the following year.

??

This is basically the Bellman-Ford algorithm for finding shortest paths.

A different kind of -philia?

numberphallic

One of our professor at the university made us code exactly this, while of course also explaining the mathematics. It was 10 years ago and still one of my favorite algorithm, I was kind of blown away by it. As far as I remember, it also gives a very beautiful visual representation of the answer as a gradient (?), with as you said, the walls with value infinite. So yes, you are not the first to think about it, but it is indeed an awesome idea!

@@leodarkk sounds about right. I would sincerely hope I'm not the first person to come up with this idea. like i said there is 500 years of research behind these subjects.

Like letting an electric current flow through the maze. Pour carbon power onto the floor, same conductance everywhere, except walls which are modelled as conductors with zero conductance. Solve poisson equation of the electric field with boundary condition entry maze=1V, exit maze=0V, constant conductance everywhere except where wall present.

Semantics to the rescue ! In the best way possible ! :)

turn around and exit at the entrance! 4d chess solution to a maze

@@TheJunky228 that's a big brain move

It depends on what "way" means. Not all ways to solve a problem work.

It's like the Jack Sparrow meme: "This is, without a doubt, the worst way to solve a maze!" "Ah, but it does solve the maze."

So long as you don't run into a loop, which shouldn't be possible if the exits are on the outside of the maze, it will always get you through the maze.

@@Aaron-cs3xl And the maze is purely 2-D without "wormholes".

That is called the Left-Hand Rule, and it actually works very well. If the maze is simply-connected, meaning all the walls touch one another, then you are guaranteed to eventually reach the exit.

@@kindoflame And, of course, the Right-Hand-Rule works equally well in such mazes.

@@George4943 only for British mazes ;)

A Tesla valve wouldn't be anything interesting since the particles don't interact with each other.

Heuristically longer path means longer exit time, hence you want your maze tree to be a path, which results in zig-zag path maze (the zig-zag pattern can be altered aswell).

I'm thinking zig zag with as few straight-aways as possible. Though maybe a succession of ever smaller chambers with a single entry and exit for each. Would be interesting I agree.

@@glenneric1 Maybe as many straight-aways as possible, since on a diagonal you can reach the next box with an average step size of sqrt(1/2), whereas on a straight path the required distance is 1. Atoms don't have memory regarding their direction, and straight alleys doesn't allow you to cut corners, so to say.

A particle could never reach the exit... so forever

i love the internet

Sorry to burst your bubble, but that solution is not forthcoming. Sperm are attracted to progesterone, which is secreted from the egg's companion cells. Sperm are not randomly swimming in every direction.

+ as a function of the length of the shortest exiting path.

Since he has the molecules just doing a random walk, doubling the number of molecules would cut the average time in half. If he were using pressure, I would expect the average time to drop more than that. [Edit: not true. See responses]

@@charleslivingston2256 Can't be just the inverse of the number of molecules. There is a non-zero minimum to cross the maze. Rather, I'd expect it to exponentially decay towards the minimum.

@@jursamaj yes

@@charleslivingston2256 It doesn't work like that, I fear. That would mean you could find an arbitrarily quick/short path by having an arbitrarily large number of atoms, but the shortest path doesn't have length zero. It even doesn't qualitatively scale like that when you have few atoms. Unimpeded brownian motion spreads according to a gaussian bell curve; twice as many samples doesn't get you twice as far then.

If the simulation is deterministic you can recover all the data from the initial conditions.

If you were an actual CS, you would know how entirely bogus the arguments are.

@@johndododoe1411 if you were an actual human, you would have kept this to yourself

Yeah i guess unless there's a place they can get stuck and keep going in cycles

Do not forget, some infinities can be bigger than other infinities.

You will end up with infinity amount of success particles and also with infinity amount of failed particles. The failed infinity amount will be bigger.

Yes, as all paths will be taken.

If there exists a path through the maze, every random walk will eventually exit

Je serais intéressé par les détails de ton algorithme!

@@valovanonym My algo is very basic. Hereafter is its pseudo-code. Unfortunately YT prevents me from giving a link in the comment so that I cannot share the Excel file. // First assign a random number to the walls of each cell For each cell in the grid assign a random value to the right and bottom walls // and taking care of grid borders Do some init While all cells have not been inflated // Loop until all cells are inflated, and each time, explode the less resistant wall on the border of the already inflated cells Do some init For each inflated cell in the grid // Find the cell whose wall (left, top, right or bottom) is the less resistant if its left/top/right/bottom cell is not inflated yet // and taking care of grid borders if the left/top/right/bottom wall is the less resistant already seen // the cell is a candidate to explode one of its walls if none of the walls already seen had the same strength remember the current cell else // Bring a little randomness randomly choose between the current cell and the other already remembered cell and remember it end end end end //for // all inflated cells have been visited : explode the less resistant wall delete the left/top/right/bottom wall of the remembered cell mark the new left/top/right/bottom cell as inflated continue end //while Bon amusement

If you can represent the problem as a quadratic unconstrained binary optimization

It isn't going to be faster, since you nonetheless have to obtain information of the whole map, the complexity can't be lower than linear to the size of the map, which classical computers can already do.

Quantum computers should not be allowed to exist. No honest person should forward the research into their creation and use.

@@johndododoe1411 Why?

@@mrosskne Currently, quantum computer algorithms exist that will break even encryption and signature tech widely deployed. We need to hold back quantum computer creation until everyone has non-NSA post-quantum encryption protecting everything they've done since birth. Which won't be this century.

That’s hilarious to me fsr

@@MaryamMaqdisi :)

But what if _3D_

(as long as the maze doesn't have loops)

@@Hermaniac8 No. You can only be stuck in the loop If you follow the inner wall of the loop. If you stick to one wall in the beginning you will never touch the inner wall off the loop. The outer wall must have an opening to the end.

Actually, I don't think that matters, as any wall loop would have to be free floating in the maze matrix, and thus defined by the outer housing which will have to be a left or right wall. But if you have a link to a maze that beats the "choose a wall" method, I'd totally dig that.

@@andvil01 - exactly, that's what I thought as well.

Yeah I felt that one.

nah... there are dumber ways. humanity: hold my beer.

Walk on top of the wall.

Mathematically? Not much, until the step size gets comparable to the maze box size.

@@jursamaj you pulled that out of your ah without doing the math. didn't you?

If the step size becomes too big, it may never be solvable (if you always hit a wall). But as long as the step size is much smaller than the boxes, you would expect the number of required steps to increase quadratically with the reduction in step size: i.e. 10x smaller steps require 100x more steps, so the total length of the path becomes 10x longer too.

​@@landsgevaer isn't quadratically first order approx? my guess is larger step sizes would also increase the time spent on a deadend

doesn't work in every maze (it depends on what/where the goal is)

That fails if there is a loop though, right?

@@Math.Bandit if the maze is from outside to outside then it works even with loops. it can fail if the goal or start is somewhere isnide the maze and all starting walls aren't connected to the outside wall.

@@dovos8572 Even if it's from outside to outside, wouldn't it fail to a very simple "around a block" type of loop, where you're making the same four left (or right) turns around a single area over and over again?

if you have max 1 particle in cell pressure, you expand in new cells always, through known path

ironically most of your science is done this way you just demonstrated, rip

you claim to be smart but you are not, complex is not always better than simple, monte carlo random walk simulations is what you just demonstrated

ok so first construct a tree of all possible connections, then find the shortest path to the exit

cause of law is trash ways of doing things

i wanna know this too i imagined more like a circle, with its circumference made of infinite points, and all of them bouncing around the walls until it reaches the end i wonder what the pattern of the circle would look like if every point that went to the exit was colored differently

Didn't they do a similar video on that already? The illumination problem is the one I was thinking of. Box where it is impossible for light to reach all of it from a single source.

only if you program in the collisions between each of the molecules which would have the same effect of creating higher pressure where there are more molecules. He mentioned the he has it programmed now each molecule just ignores all the others like they aren't there. so there is no pressure in the system. all adding more molecules might do is find the solution faster purely as a result of it being more likely you have a lucky molecule. the point of having a fan is just to create high and low pressure, which is the same effect you would get with the collisions.

No, the way he has it implemented, the molecules have no effect on each other, so more molecules doesn't actually matter. The wind would change the distribution of the random steps, making each molecule more likely to step towards the exit.

@@longleaf1217 That sounds like a much more lengthy running and complicated program. It would be much simpler if each particle, for each move, just picked a random adjacent cell to the one it's in that it hadn't been in before and doesn't have a wall along the side then to get the result just select the particle that exists the maze first.

@@jursamaj What would the 'wind' be and how would it interact with the molecules? What would makes the wind different to the path finding molecules? Surely the whole idea of a wind is just having the molecules interact and flood the maze with more of them?

@@ChrisLee-yr7tz The wind would literally just be a net force in the direction of the exit that gets weaker as a particle gets further from the start.

???

Depends a bit, only if the maze is planar and the start & finish are both on the "outside". Doesn't work to reach the exit if you get lost in a cave system.