A collection of random walks creates a normal distribution. The fact that we start at zero is key.
The Radiation of Probabilities
[Louis Bachelier] Was the first one to attempt to price options and essentially use mathematics to model financial markets. He submitted his PhD thesis to some guy named [Henri Poincaré].
Think of a galton board, every ball essentially follows a random walk, as every time it hits a triangle, it has a 50/50 change of going left or right. We can map the triangles to time (indexed by ) and the motions of individual balls to random walks. Since all walks come from a hole at the center (0), and the triangles are positioned so that a ball can either go left by one unit or right by one unit when it hits it, we got ourselves a simultion of a lot of sample random walks!
What we find is that the balls follow a normal distribution that broadens with time!!!!!, and this is physics, empirical observation saying it!
So while one path is impossible to predict, all the paths form a predictable pattern.
Robert Brown noticed that if you look close enough at particles making up something, they will be moving by tiny amounts in random directions.