Invariance principles and laws of nature

The world is complicated and physics has made it appear relatively simple. Everything that we study in physics is reduced to a mathematical law of nature. At very small distances nature is governed by relativistic quantum field theory. At very large distances, for phenomena where both light speed and gravity matter, we have general relativity. In between, where neither atomic scale phenomena nor light speed matter, we have Newtonian mechanics. We have a law to understand and explain everything, at least qualitatively, except phenomena involving decisions made by minds. Our success in discovering that nature behaves mathematically has led to what a famous economist has described as “the Tarzan complex,” meaning that physicists are bold enough to break into fields beyond the natural sciences, beyond the safe realm of mathematical laws of nature. Where did our interest in economics and finance come from?

From my own perspective, it started with the explosion of interest in nonlinear dynamics and chaos in the 1980s. Many years of work in that field formed the perspective put forth in this book. It even colors the way that I look at stochastic dynamics. From our experience in nonlinear dynamics we know that our simple looking local equations of motion can generate chaotic and even computationally complex solutions. In the latter case the digitized dynamical system is the computer and the digitized initial condition is the program. With the corresponding explosion of interest in “complexity,” both in dynamical systems theory and statistical physics, physicists are attempting to compete with economists in understanding and explaining economic phenomena, both theoretically and computationally.