Closer To The Ideal

Anyone alive today grew up in the era of Heisenberg’s uncertainty principle, Max Plank and quantum mechanics. As such, it seems natural to us to think of probability when we think of physics. Einstein may have said “I can not believe that God is dicing with the Universe” but dicing is the view dominates physics today. We are taught these ideas in school. Because of this, we have a hard time remembering what a surprise probability was to scientists working at the end of the 1800s. By that point, Western science had spent 200 years working with Newton’s view of a mechanical universe, and physics was seen as the most pure of the sciences, and therefore the most mechanical, the most free of randomness. Who would have guessed, in 1880, that physics was about to transform from the science most free of probability to the one that depended on it in its most fundamental theories?

Consider this bit of history from “The Human Use Of Human Beings: Cybernetics And Society” written by by Norbert Wiener in 1950.

The beginning of the 20th century marked more than the end of a 100 year period and the start of another. There was a real change in point of view even before we made the political transition from the century on the whole dominated by peace, to the half century of war through which we have just been living. This was perhaps first apparent in science, although it is quite possible that whatever has affected science lead independently to the marked break which we find between the arts and literature of the 19th and those of the 20th centuries.

Newtonian physics, which had ruled from the end of the 17th century to the end of the 19th with scarcely an opposing voice, described a universe in which everything happened precisely according to law, a compact, tightly organized universe in which the whole future depends strictly upon the whole past. Such a picture can never be either fully justified or fully rejected experimentally and belongs in large measure to a conception of the world which is supplementary to experiment but in some ways more universal than anything that can be experimentally verified. We can never test by our imperfect experiments whether one set of physical laws or another can be verified down to the last decimal. The Newtonian view, however, was compelled to state and formulate physics as if it were, in fact, subject to such laws. This is now no longer the dominated attitude of physics, and the men who contributed most to its downfall were Bolzmann in Germany and Gibbs in the United States.

These two physicists undertook a radical application of an exciting, new idea. Perhaps the use of statistics in physics which, in large measure, they introduced was not completely new, for Maxwell and others had considered worlds of a very large number of particles which necessarily had to be treated statistically. But what Bolzmann and Gibbs did was to introduce statistics into physics in a much more thoroughgoing way, so that the statistical approach was valid not merely for systems of enormous complexity, but even for systems as simple as the single particle in a field of force.

Statistics is the science of distribution, and the distribution contemplated by these modern scientists was not concerned with large numbers of similar particles, but with the various positions and velocities from which a physical system might start. In other words, under the Newtonian system the same physical laws apply to a variety of systems starting from a variety of positions and with a variety of momenta. The new statisticians put this point of view in a fresh light. They retained indeed the principle according to which certain systems may be distinguished from other by their total energy, but they rejected the supposition according to which systems with the same total energy maybe clearly distinguished indefinitely and described forever by fixed causal laws.

There was, actually, an important statistical reservation implicit in Newton’s work, though the 18th century, which lived by Newton, ignored it. No physical measurements are ever precise; and what we have to say about a machine or other dynamic system really concerns not what we must expect when the initial positions and momenta are given with perfect accuracy (which never occurs), but what we are to expect when they are given with attainable accuracy. This merely means that we know, not the complete initial conditions, but something about their distribution. The functional part of physics, in other words, cannot escape considering uncertainty and the contingency of events. It was the merit of Gibbs to show for the first time a clean-cut scientific method for taking this contingency into consideration.