Excerpt

Stuart Kauffman’s work extends a hallowed tradition in statistical physics to a new domain: the system that governs the switching on and off of an organism’s genes. The fundamental postulate of statistical mechanics, originating in the work of Ludwig Boltzmann and Josiah Willard Gibbs, is an acknowledgement and celebration of ignorance. It asserts that for an isolated thermodynamic system at equilibrium all microstates of the system that are compatible with the macroscopic constraints of isolation (e.g., having the same fixed total energy E, volume V, and number of particles N) are equally probable. The statement of “equal probability” is an acknowledgment of complete ignorance or the maximization of entropy. However, this assertion of ignorance, circumscribed by what we do know about the system, is a source of great power. It defines a statistical ensemble, or a probability distribution over microstates, parameterized by E, V, and N, from which one can compute the average of any desired function of the microstates. Amazingly, averages computed from the theory agree with observations.

In the 1950s, Eugene Wigner introduced a statistical ensemble of matrices of a high-dimension N to describe the spacing of energy levels observed in individual atomic nuclei. Wigner’s hypothesis was tantamount to saying that certain properties of a complex-enough quantum mechanical system (like an atomic nucleus) are identical to the averages of a suitably chosen random ensemble of systems. These properties, too difficult to derive theoretically for any particular system, could be easily calculated from the ensemble and agreed with experiments. Random matrices have since been applied as a powerful tool in many different areas, including condensed matter physics, biology, and finance.

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