I mentioned chaos and the butterfly effect earlier on in the book. We saw how uncertainty about the system’s initial conditions, or very slight changes to them, could mushroom to produce huge effects later on. The eminent physicist Michael Berry gave a beautiful example of this. He pointed out that all the objects in the universe are linked by gravity, so that, in principle, a perturbation of one will impact all the others, albeit in an absolutely tiny way for distant objects. Berry imagined removing just one electron at the edge of the universe (that is, about 1010 light-years away), and looked at the gravitational effect of this change on the angle at which two oxygen molecules on earth are deflected when they collide. He showed that after about 56 collisions between molecules, the angle of deflection could be completely different from what in fact occurred when the electron was present. Now imagine following the paths of oxygen molecules as they bounce around in the air, bumping off each other and off walls and other objects. If we follow one such molecule, then its path will be completely different, after less than 60 collisions, according to whether that one electron is or is not present at the edge of the universe. For air, each gas molecule goes from one collision to another in about two ten-billionths of a second on average, and each molecule is involved in about 5 billion collisions each second. This means that removing the electron at the edge of the universe would have completely changed the paths of oxygen molecules in the air you breathe after just a 100 millionth of a second. Michael Berry also showed that the mass of the two human players is enough to completely alter the angle of deflection of two balls on a pool table after just nine collisions. The movement of the players around the table leads to dramatic shifts in the probabilities that the balls will follow particular paths: the law of the probability lever.
A great example to illustrate the initial concept of chaos theory, where how seemingly minute changes in the initial conditions can cause super large changes in the later stages. Just a slight change of the mass of 2 human players can completely change the outcome of a game of pool.
That’s why it becomes so hard to make exact, accurate predictions of complex systems such as our financial markets. One small change in the initial conditions can have a massive impact in our models.
