Ilya Prigogine

"We believe that it is precisely this transition to a new description that makes this moment in the history of science so exciting. Perhaps it is not an exaggeration to say that it is a period like the time of the Greek atomists or the Renaissance, periods in which a new view of nature was being born." p. 2

""Primary" laws control the behavior of single particles, while "secondary" laws are applicable to collections of atoms or molecules. To insist on secondary laws is to emphasize that the description of elementary behavior is not sufficient for understanding a system as a whole." p.8

"As we shall see, the second law corresponds to a selection rule, to a restriction of initial conditions that is then propagated by the laws of dynamics." p. 16

"One of the strongest motives that lead men to art and science is a flight from everyday life with its painful harshness and wretched dreariness, and from the fetters of one's own shifting desires. A person with a finer sensibility is driven to escape from personal existence and to the world of objective observing and understanding." p. 20

"One widely-studied example was the three-body problem, perhaps the most important problem in the history of dynamics. The moon's motion, influenced by both the earth and the sun, is one instance of this problem. Countless attempts were made to express it in the form of an integrable system until, at the end of the nineteenth century, Bruns and Poincare showed that this was impossible....Although this discovery was not clearly understood at the time, it implied the demise of the conviction that the dynamic world is homogeneous, reducible to the concept of integrable systems. Nature as an evolving, interactive multiplicity thus resists reduction to a timeless and universal scheme." p. 72

"What is remarkable that, despite their exceptional character, integrable systems dominated science until the 1950's, and they still constitute the main subject of most mechanics textbooks. Their great historical role and their undoubted pedagogical value are certainly a partial explanation of this paradoxical situation." p. 93

"In dynamics, a system changes according to a trajectory that is given once and for all, whose starting point is never forgotten (since initial conditions determine the trajectory for all time). However, in an isolated system all non-equilibrium situations produce evolution toward the same kind of equilibrium state. By the time equilibrium has been reached, the system has forgotten its initial conditions -- that is, the way it had been prepared." p. 121

"Irreversible processes have an immense constructive importance: life would not be possible without them" p. 125

"How, for example, could Darwinism -- the statistical selection of rare events -- be reconciled with the statistical disappearance of all peculiarities, of all configurations, described by Boltzman. As Roger Callois asks, "Can Carnot and Darwin both be right?"" p. 128

"The processes that define chemistry -- chemical reactions characterized by reaction rates -- are irreversible through and through." p. 131

""Order through fluctuations" models introduce an unstable world where small causes can have large effects, but this world is not arbitrary." p. 206

Indeed, history began by concentrating mainly on human societies, after which attention was given to the temporal dimensions of life and geology. The incorporation of time into physics thus appears as the last stage of a progressive reinsertion of history into the natural and human sciences." p. 208

"For many years physicists remained reluctant to accept such a "historical" description of cosmic evolution.... The whole story appears as another irony of history. In a sense, against his will, Einstein has become the Darwin of physics. Darwin taught us that man is embedded in biological evolution; Einbstein has taught us that we are embedded in an evolving universe. Einstein's ideas led him to a new continent, as unexpected to him as America was to Columbus." p. 215

"Demonstrations of "impossibility" have a fundamental importance. They imply the discovery of an unexpected intrinsic structure of reality that dooms an intellectual enterprise to failure.... Thermodynamics, relativity, and quantum mechanics are all rooted in the discovery of impossibilities, limits to the ambitions of classical physics. Thus they marked the end of an exploration that had reached its limits. But we can now see these scientific innovations in a new light, not as an end but a beginning, as the opening up of new opportunities." p. 216

"All description thus implies a choice of the measurement device, a choice of the question asked." p. 224

"No single theoretical language articulating the variables to which a well-defined value can be attributed can exhaust the physical content of a system. Various possible languages and points of view about the system may be complementary. They all deal with the same reality, but it is impossible to reduce them all to one single description. The irreducible plurality of perspectives on the same reality expresses the impossibility of a divine point of view from which the whole of reality is visible.... the real lesson to be learned from the principle of complementarity, a lesson which can perhaps be transferred to other fields of knowledge, consists in emphasizing the wealth of reality, which overflows any single language, any single logical structure." p. 225

"Thus the paradox: the reversible Schroedinger equation can be tested only by irreversable measurements that the equation is by definition unable to describe.... Schroedinger's equation does not describe a separate level of reality; rather it presupposes the macroscopic world to which we belong." pp. 228-9

"[Einstein speaking]: Michele has left this strange world just before me. This is of no importance. For us convinced physicists the distinction between past, present, and future is an illusion, albeit a persistent one." p. 294

"It is only the unification of dynamics and thermodynamics through the introduction of a new selection principle that gives the second law its fundamental importance as the evolutionary paradigm of the sciences.... The world of dynamics, be it classical or quantum, is a reversible world. As we have emphasized in Chapter VIII, no evolution can be ascribed to that world; the "information" expressed in terms of dynamical units remains constant. It is therefore of great importance that the existence of an evolutionary paradigm can now be established in physics -- not only on the level of macroscopic description, but also at all levels." p. 297

"As long as the second law is considered to express only improbability, it has little theoretical interest. You could always hope to overcome it with sufficient technical skill. But we have seen that this is not so, At its root is a selection of possible initial states.... it is only after the symmetry-breaking that any propabalistic interpretation becomes possible." p. 297

"Today we believe that the epoch of certainties and absolute oppositions is over. Physicists have no privilege whatever to any kind of extra-territoriality.... In his Themes Merleau-Ponty also asserted that the "philosophic" discoveries of science, its basic conceptual transformations, are the result of negative discoveries, which provide the occasion and starting point for a reversal of point of view. Demonstrations of impossibility, whether in relativity, quantum mechanics, or thermodynamics, have shown us that nature cannot be described "from the outside" as if by a spectator. Description is dialogue, communication, and this communication is subject to constraints that demonstrate that we are macroscopic beings embedded in the physical world." p. 299

"Classical science denied becoming, natural diversity, both considered by Aristotle as attributes of the sublunar, inferior world. In this sense, classical science brought heaven to earth. However, this apparently was not the intention of the fathers of modern science. In challenging Aristotle's claim that mathematics ends where nature begins, they did not seek to discover the ummutable concealed beneath the changing, but rather to extend changing, corruptible nature to the boundaries of the universe. In his "Dialogue Concerning the Two World Systems", Galileo is amazed at the notion that the world would be a nobler place if the great flood had left only a sea of ice behind, or if the world had the incorruptible hardness of jasper...." p. 305

"The questions we have investigated have led us to emphasize aspects that differ considerably from those to which Kuhn's description applies.... The past one hundred years have been marked by several crises that correspond closely to the description given by Kuhn -- none of which were sought by scientists. Examples are the discovery of the evolving universe. However, the recent history of science is also characterized by a series of problems that that are the consequences of deliberate and lucid questions asked by scientists who knew that the questions asked had both scientific and philosophic aspects." pp. 308-9

Prigogine, Ilya, Exploring Complexity, Freeman, 1989

"Suppose now that because of some perturbation, the pattern of oscillation -- the normal heartbeat rhythm -- is upset. Since the human system is subject to a great many perturbations every day, if the heart functioned as a pendulum does, fibrillation [failure of the heart to beat regularly] could well have occured in the embryo, before birth. But the heart is not like a pendulum, [i.e., the heart is not a conservative, reversible system] it does not "remember" the effect of a perturbation by permanently changing its pattern of oscillation; if no permanent damage has occured and the cause of perturbation is removed, the heart resumes its normal rhythm." p. 20

"But in a nonlinear system adding a small cause to one that is already present can induce dramatic effects that have no common measure with the amplitude of the cause." p. 59

"Beyond a critical value, denoted by gamma, we find that the state on this branch has become unstable: the effect of fluctuations or small external perturbations is no longer damped. The system acts like an amplifier, moves away from the reference state, and evolves to a new regime... this is the phenomenon of bifurcation...." p. 71

"[A]ll conservative [reversible, timeless] systems are structurally unstable, since the presence of small dissipative terms (like a small friction in a pendulum) qualitatively alters the phase portrait by conferring the property of asymptotic instability to certain preferred solutions, the attractors." p. 98**?

"The most clear-cut case of selection arises when the symmetry-breaking bifurcation is a unique, non-repeatable event. One example is the selection of matter over anti-matter which, once performed, leads the universe to a point of no return beyond which it is impossible to imagine a different realization -- at least at a time scale of 20 billion years." p 145

"Beyond its specific applications to combustion-related problems, the phenomenon of bifurcations in time provides a new model of differentiation and evolution that have a purely internal origin in non-equilibrium systems. Indeed, the system need not be continuously disturbed for this purpose by the external world. ... Rather, the deviations of the dynamics from equilibrium that are created temporarily are sufficient to induce, during some time interval, an interval differentiation: during the slow periods of the evolution, fluctuations endow the system with a variety of states visited with some probability, but the initial state remains dominant; the occurence of the fast stage then entrains some of these states at such a high rate that they soon lose track of the common ancestor, thereby producing a new clone of their own." p. 178

"Indeed, the instability of motion associated with chaos allows the system to explore its state space continuously, thereby creating information and complexity." p. 192

"The property of asymptotic stability which permits a system to forget accidental perterbations does not apply to conservative dynamical systems." p. 195

"In the world of unstable dynamical systems we can only look through a "window" in the outside world. We witness here the breakdown of the ideal of complete knowledge that has haunted Western science for three centuries." p. 197

"As noted by Norbert Weiner: in any world within which we can communicate, the direction of time is bound to be uniform and irreversible." p. 197

"Randomness presents an adaptive value in the organization of the society." p. 233

"What is the best balance between fluctuations, which allow discoveries, and accurate determinism, which allows immediate exploitation?" p. 235

"Contrary to the molecules, the actors in a physico-chemical system, or even the ants or the members of other animal societies, human beings develop individual projects and desires. Some of these stem from anticipations about how the future might reasonably look and from guesses concerning the desires of other actors.... In other words, is past experience sufficient for predicting the future, or is a high degree of unpredictability of the future the essence of the human adventure, be it at the individual level of learning or at the collective level of history making? The developments outlined in the preceding chapters suggest that the answer to this question should lean toward the second alternative." p. 238