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.
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.
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.