Physics of Risk

Physicists love mathematics. Especially and most usually differential calculus. Mathematical description of any system using differential calculus is usually referenced as dynamical description. Thus in this case equations themselves are called dynamical equations. Purely theoretically it appears that if we know precise form dynamical equations we know everything about the system, we can make precise predictions of it’s evolution.

The problem is that this impression is only theoretical. In practice one must take measurements of reality. As we all know it measurements are just approximation – every measurement has some error related to it, no matter how small or apparently insignificant it appears. Measurement bias in the linear systems may play no role at all – system evolves as predicted with small or no corrections at all. But most of the interesting systems are not linear! In fact most of them are strongly non-linear. Non-linearities in dynamical equations may cause accumulating differences between solutions with apparently insignificant variation in initial conditions. Thus over the time in non-linear system prediction of evolution and observed evolution may start to disagree by far more than just by primary measurement bias. This behavior is known as dynamical chaos.

Most widely known example of dynamical chaos is the Butterfly effect – butterfly flapping it’s wings may cause hurricane on next week, but thousand kilometers away. In this section of Physics of Risk website we will attempt to show that even smallest bias of initial conditions, of reality itself, might be the reason for unexpected results and chaos.

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