The beginning of the twentieth century marked much more than the end of one century and the beginning of another.Long before we had completed the political transition from the last century, which was ruled by peace on the whole, to the war-filled half-century we have just lived through, people's views had real Variety.This change may have first manifested itself in science, but it is quite possible that what influenced science alone caused the marked rift that we see today between nineteenth- and twentieth-century literature and art. . Newtonian physics, which ruled with little opposition from the end of the seventeenth century to the end of the nineteenth century, described a universe in which everything happened precisely according to laws. A universe organized in which all future events strictly depend on all past events.Such a picture is by no means a picture that can be fully proved or refuted by experiments. It is to a large extent a concept of the world, which people supplement experiments with, but in some respects it is better than anything that can be verified by experiments. Everything is more general.

There is absolutely no way we can use some of our incomplete experiments to check whether this or that set of physical laws can be verified to the last decimal place.But Newton's view compels one to state and formulate physics as if it were really governed by such laws.Now, this view is no longer dominant in physics, and the people who contributed the most to overturning this view are Bolzmann in Germany and Gibbs in the United States. Both physicists have radically applied an exciting new idea.The statistics which they have largely introduced in physics is perhaps nothing new, since Maxwell and others had long assumed that the world of extremely large numbers of particles must be dealt with statistically.But what Boltzmann and Gibbs did was to introduce statistics into physics in a more radical way, making statistical methods effective not only for systems with a high degree of complexity, but also for Simple systems work just as well.

Statistics is a science of distributions, and the distributions these modern scientists have in mind are not those of vast numbers of identical particles, but of the wide variety of positions and velocities from which a physical system starts. In other words, in the Newtonian system, the same laws of physics apply to different physical systems starting from different locations and having different momentums; the new statisticians approached the problem with new eyes.They did retain the principle that some systems could be distinguished from others by their total energy, but they dropped the assumption that all systems with the same total energy could be distinguished more or less unambiguously, And it can always be described by the established law of cause and effect.

In fact, an important statistical reservation was already implied in Newton's work, although it was completely ignored in the eighteenth century when Newton lived.Physical measurements are never exact; what we have to say about a machine or other dynamical system really has nothing to do with what we must expect when the initial position and momentum are given perfectly exactly (which never happens), but rather All that is really involved is what we would expect if they were given roughly exactly.This means that what we know is not all the initial conditions, but a certain distribution about them.In other words, no practical part of physics can fail to take into account the uncertainty and contingency of events.It is to Gibbs' credit that he presented for the first time a definitive scientific method of examining this contingency.

It is in vain for the historian of science to seek a single thread of historical development.Gibbs's work, though well cut, was badly sewn, and what he started was left to be done by others.The intuition he used as a basis for his work is, generally speaking, that in a class of physical systems which continue to maintain the identity of their class, any one physical system will in almost all cases eventually reproduce what all systems of the class were at any given moment. The distribution shown.In other words, under certain circumstances, if a system is kept running long enough, it will traverse all distributions of position and momentum compatible with its energy.

But this latter proposition is neither true nor possible except for simple systems.But even so, there is another way to achieve the kinds of results that Gibbs needed to support his hypothesis.It is a coincidence in history that at the same time that Gibbs was working in New Haven, the road was being very thoroughly investigated in Paris; It was not productively combined before 1920.I thought I had the honor of midwifery to the firstborn born of this union. Gibbs had to use scale theory and probability theory as research tools, both of which were at least twenty-five years old and clearly not suitable for his needs.At the same time, however, Sorel and Lebesgue in Paris were devising a theory of integrals which proved to fit Gibbs's ideas.Borel was a mathematician who had already made a name for himself in probability theory and had excellent insights into physics.He did work leading to this measure theory, but he didn't get to the stage where he could formulate a complete theory.This was done by his student Lebesgue.Le Besgue was a different kind of person altogether, he had neither knowledge nor interest in physics.But even so, Lebesgue solved the problem left by Borel, but he regarded the answer to this problem only as a tool for studying Fourier series and other branches of pure mathematics.Later, when they both became candidates for membership of the French Academy of Sciences at the same time, they had a dispute among themselves, and it was only after many mutual reproaches that they were jointly awarded the honor of being a member.However, Borel continued to insist on the importance of Lebesgue's and his own work as a tool in physics; however, I think I was the one who applied the Lebesgue integral in 1920 to a particular physical problem, Brownian motion Be the first person on the issue.

This happened long after Gibbs' death, and for two decades Gibbs' work remained one of the mysteries of science, the sort of question that is being studied, though it seems that it should not be.Many people have intuitive abilities far ahead of their time; this is especially true in mathematical physics.Gibbs introduced probability to physics long before the theory of probability he needed.But despite these deficiencies, I believe we must attribute the first great revolution in twentieth-century physics to Gibbs, not to Einstein, Heisenberg, or Planck. The effect of this revolution is that today's physics is no longer required to discuss what will always happen, but to discuss what will happen with overwhelming odds.At first, in Gibbs's own work, this contingency view was superimposed on Newton's basis, in which the primitives for which we are going to discuss the probabilistic problem are all systems that obey all Newton's laws.Gibbs' theory was essentially a new one, but it was compatible with the same permutations as those considered by Newton.What has happened in physics since then is that the Newtonian rigid foundation has been thrown out or changed; by now Gibbs' contingency has become perfectly clear as the whole foundation of physics.It is true that the discussion in this area is not quite over yet, and Einstein and, to some extent, de Broolie still think that a world of strict determinism is more desirable than a world of chance; However, these great scientists fought on the defensive against the overwhelming power of the younger generation.

An interesting change has taken place in that, in the world of probabilities, we no longer discuss quantities and statements related to this particular real universe as a whole, but instead propose Answers to all kinds of questions can only be found in this book.Thus, chance, not only as a mathematical tool of physics, but also as a part of physics, has been accepted by people. The acknowledgment of a less than fully deterministic, almost irrational element in the world; this is in one respect compatible with Freud's acknowledgment of a deeply ingrained irrational element in human behavior and thought of.In a world now in which political chaos is as much intellectual chaos, there is a natural tendency to lump together Gibbs, Freud, and the founders of modern probability theory, as representatives of a single trend of thought; However, I don't want strongmen to accept this view.Too great a distance exists between Gibbs-Lebesgue's method of thought and Freud's intuitive but somewhat inferential one.Yet they are close to each other, and to the St. Augustine tradition, insofar as they both recognize the fundamental element of chance in the very fabric of the universe itself.For this random element, this organic incompleteness, need not be exaggerated, we can see it as evil, as the negative evil which St. active and hostile evil.

The purpose of this book is to show the influence of Gibbs' views on modern life, to show the essential changes we have brought about in developing science through it, and the changes it has brought about indirectly in our general attitudes to life. The subsequent chapters, therefore, have both a technical narrative and a philosophical content concerning what we do with the new world we face and how we should approach it. To repeat: Gibbs' innovation was that he considered not one world but the whole of the world that could answer a limited set of questions about our surroundings.His central idea is how visible the answers to questions we can give about one set of worlds are in a larger set of worlds.In addition, Gibbs also has a theory. He believes that this probability increases naturally as the universe progresses.The measure of this probability is called entropy, and the characteristic trend of entropy must increase.

With the increase of entropy, the universe and all closed systems in the universe will naturally tend to deteriorate and lose their specificity, moving from the smallest visible state to the largest visible state, from which there are various characteristics and forms. Organized and differentiated states move into chaotic and monotonous states.In Gibbs' universe, order is the least visible, and chaos is the most visible.But when the universe as a whole (if there is a universe at all) tends to decay, there are local regions within it which seem to develop in the opposite direction to that of the universe as a whole, and which are temporarily and finitely organized within them. increasing trend.In just a few places in these localized areas, life found its home.The emerging science of cybernetics started its development from this point of view as the core.