Explanation: Random walk in 2D has a unity probability of making it back to the starting point as the number of steps approach infinity but random walk in 3D only has ~0.34.

  • zkfcfbzr@lemmy.worldEnglish
    232·
    1 year ago

    Expanding on what OP is talking about:

    In this context, a random walk happens on a 2D coordinate plane. Your drunk person starts at the origin, (0, 0), and for a “random walk” they move either left, right, up, or down by exactly 1 unit each step. It’s a mathematical fact that this process, taken to its limit where infinitely many random steps are taken, will always have the drunk return to the origin - in fact, for any given integer coordinate on the plane there’s a 100% chance the drunk will eventually visit that coordinate following a random walk.

    This doesn’t work in 3D though, where there’s an x, y, and z axis. A random walk there won’t always return to the origin - it only will about 34% of the time. If the drunk gets too far away the probability of ever finding their way back at random quickly drops to 0.

    • o_oli@lemmy.worldEnglish
      131·
      1 year ago

      So if we ignore that birds can’t fly infinitely high, and also that they don’t live in the air they live on a surface, in essentially a 2D area the same as humans, maybe this is interesting? But not really lol.

      • zkfcfbzr@lemmy.worldEnglish
        5·
        1 year ago

        If you limit the extent of the third dimension to any finite value then my intuition says the probability is probably back to 100% but I don’t know for certain.

    • M1st3rM@discuss.tchncs.de
      4·
      1 year ago

      That doesn’t make sense to me. Sure, the probability in 3D is gonna get really low. Never 0 though since there is a chance the previously taken steps will be done in reverse. And since we talk about infinity here … the drunk bird should also find home.

      • zkfcfbzr@lemmy.worldEnglish
        8·
        1 year ago

        I was maybe a bit sloppy when I said it “quickly drops to 0” instead of it “quickly tends to 0”. It’ll of course always be positive - in fact if N is the sum of the absolute value of the three coordinates of its current position, the probability of returning to the origin is strictly greater than 1/6ᴺ.

        But it does tend to 0 in such a way that the probability of its random walk ever returning to the starting position is not 100%. It has a 34% chance of ever getting back at the very start of its journey - but if it gets too far off track that probability is going to tend to 0 fast enough that it’s not likely to ever make it back, even with infinitely many steps. Here’s a youtube video (that I did not watch myself) that seems to go over the topic.

  • neptune@dmv.socialEnglish
    13·
    1 year ago

    Gravity gives up and down a lack of symmetry that left and right maintain. A drunk bird is more likely to fall than fly to the moon.

    Also, in materials science, randomly walking atoms (Brownian motion) in a crystal structure displace roughly at, if I recall, the square root of their velocity, on average.

  • Maharashtra@lemmy.world
    10·
    1 year ago

    Everyone is always equally drunk, and the road is always the same

    Guys, an unpopular opinion, but perhaps you shouldn’t take too long showers, eh?

    • t_jpeg@lemmy.world
      5·
      1 year ago

      We’re fine at finding our way home because we only have to navivate an effectively 2d space (as we are on the ground). Imagine if we had to fly and so had to navigate 3 directions (height as well) whilst being intoxicated. We’d be fucked… is what I think OP is trying to say.

  • SaintWacko@midwest.socialEnglish
    5·
    1 year ago

    But a drunk bird will start from the ground, and probably end on the ground, which collapses its random walk back to a 2d plane

    • sparky_gnome@lemmy.world
      1·
      1 year ago

      I don’t think that changes it actually. Even if the drunk guy lives on a floor that’s high up, he didn’t fly to get there, so there is some combo of random walking and moving that gets him back there. Like walking into an elevator that happens to be on the ground floor, and also happens to be going up to the right floor at that time. Or walking to the base of a staircase, and (50/50) randomly going up it. It definitely isn’t technically a 2d plane anymore, but there are still a finite number of 2d planes that he could be trying to get to ( the highest floor on the building with the most floors).

    • Sethayy@sh.itjust.works
      12·
      1 year ago

      Youre telling me people aren’t actually entirely 2 dimensional?? No way captain obvious, next thing youre gonna say is that knock knock doors are factually incorrect because no one is actually knocking on a door

      Tbh your lack of understanding the inperfection of mathematical models is the only stupid as fuck thing here

    • Gogo Sempai@programming.devOP
      12·
      1 year ago

      It’s a “shower thought” lol, not a research paper. Take it as a meme on random walk, which is always explained in universities using the example of a drunk guy so much so that it’s also known as “drunkard’s walk”. Should’ve posted this in a science/physics meme community, my bad.