Monday, November 22, 2004

What we do not know ?


Ilya Prigogine, Nobel Prize in Chemistry, Belgium


Born in Moscow in 1917, the Viscount Ilya Prigogine emigrated to Belgium with his parents in 1921 and has lived there since. In 1977, Prigogine won the Nobel Prize in chemistry for his discovery of dissipative structures. He has held the Ashbel Smith Chair at the University of Texas, Austin since 1984 and is the director of the Solway International Institutes of Chemistry and Physics in Brussels. He is also the author of close to thirty works all of which have been widely translated.


What do I not know? This question makes me think of another question, which might be seen as complementary : "what do I know?" My answer to this question is clear : very little. I say this not out of some excessive modesty, but from a profound conviction : we are at the end of that era in the history of science which opened with Galileo and Copernicus. A glorious period indeed, but one which has left us with an over-simple picture of the world. Classical science emphasized the factors of equilibrium, order, stability. Today, we see fluctuation and instability everywhere. We are becoming aware of the inherent complexity of the universe. This realisation is, I am certain, the first step towards a new rationality. But it is only the first step.

For the founding fathers of Western science, such as Leibniz and Descartes, the goal they set themselves was certainty. And it is still the ambition of the great contemporary physicists, Einstein or Hawking, to achieve certainty through a unified theory, a geometrical description of the universe. Once this goal has been reached, we would be able to deduce from our model all the various aspects of nature.

However, the more we explore the universe, the more we are struck by the narrative element which is to be met with at every level. One thinks inevitably of Sheherazade who only interrupted one story in order to begin another which was yet more beautiful. Nature, too, presents us with a series of narratives inscribed each within the other: cosmological history, history at the molecular level, and the history of life and of human kind, right down to our own personal history. On every level we see the emergence of the new, the unexpected.

Science, on the other hand, from Newton to Schrödinger and Einstein has been based upon deterministic laws in which past and future act out symmetrical roles. How then can we fit the narrative element I have just described into a context governed by such laws? Many researchers have tried to avoid this problem, by invoking the approximations which are introduced into the laws of nature whenever they are applied to complex systems. But this solution has always seemed odd to me. For if that were the case, we would be the "father" of time, rather than its "child".

It is true that the scientific inheritance of the twentieth century has two different aspects. One is the laws of nature, and the other is the thermodynamic description of phenomena associated with the growth of entropy. This conception is certainly that of a world in evolution. But how then does it fit into the fundamentally atemporal description given by "the laws of nature"? In addition, there is a second difficulty, for the growth of entropy is normally associated with a growing disorder. How then could such a process produce complex structures such as life, in particular human life?

These are the questions to which we are only just beginning to imagine answers. Two recently-developed domaines of science play an essential role here : the physics of disequilibrium, and the theory of "chaos" associated with unstable dynamical systems.

Consider first the physics of disequilibrium. The great surprise here is what happens if one pushes a system far out of equilibrium (and the conditions of our own planetary system and even of our cosmological situation are such that practically all the systems around us are far from being in equilibrium; a good example of this is the ecosphere) : new structures appear at the points of "bifurcation". Thus we often speak of self-organisation leading to the formation of "dissipative" structures.

As an example, we may take chemistry. In this domain we can see self-organization at work in the emergence of spatio-temporal structures related to ruptures of symmetry. One example which has been well studied is that of oscillating reactions. The conditions for the emergence of such unstable structures are given by the non-linear character of the equations which govern the chemical processes. As is well known, non-linear equations have more than one solution. The solution which corresponds to these "dissipative structures" occurs in a state far fom the equilibrium position. Moreover, these processes are necessarily self-catalyzing. It's the old story of the chicken and the egg. The chicken lays eggs, which in turn hatch into chickens. Self-catalyzation is typical of those biological phenomena in which nucleic acids encode the protein synthesis process which in turn catalyzes the replication of nucleic acids. The emergence of such structures shows the constructive role played by temporal irreversibility. Far from the equilibrium position, matter acquiress new properties which remain hidden to us as long as our attention is restricted to stable states.

In a recent report, C.K. Biebricher, G. Nicolis and P. Schuster write : "The maintenance of the organization of nature is not - and can not be - achieved by central management; order can only be maintained by self-organization. Self-organizing systems allow to adapt to (...) the outer conditions. We want to point out the superiority of self-organizing systems over conventional human technology (...). The superiority of self-organizing systems is illustrated by biological systems where complex products can be formed with unsurpassed accuracy, efficiency and speed".

But much progress still needs to be made, as much in non-linear mathematics as in experimental research, before we can describe the evolution of complex systems outside certain simple situations. The stakes here are considerable. In particular, it is necessary to bridge the gap in our understanding which presently separates complex physico-chemical structures from even the simplest of living organisms.

Whatever advances may be made in this direction, one conclusion is already clear : the direction of time, the "narrative" element has an essential role to play in the description of nature. If that is so, then narrative time must be included in our formulation of the laws of nature. These laws as Newton formulated them were intended to express certainties. Now we must make them express "possibilities" which may or may not be realised in the future. This is where we have to turn to the theory of chaos associated with unstable dynamical structures.

A typical example is the case of "deterministic chaos". In such systems, two trajectories which are as close to each other as one may imagine diverge exponentially with time: this is called "sensitivity to initial conditions". As we only ever have a limited knowledge of initial conditions, the predictability that defined classical mechanics cannot be sustained.

There exist even more pronounced forms of instability which are related to the appearance of "resonances" (a phenomenon discovered by Henri Poincaré). Every one has an intuitive idea of what resonance is. When you hit a note on a piano, you can hear the harmonics, such as the octave or the fifth. In classical and quantum mechanics, resonances provide the coupling between dynamic phenomena. This is a highly technical subject, but we can summarize its principal results. Traditionally there are two formulations of the laws of nature : one in terms of trajectories (classical mechanics) or wave functions (quantum mechanics), and the other in terms of set theory. This second formulation is statistical in nature. For stable systems, these two formulations are equivalent. For unstable systems, which are the majority of the systems we observe, this is no longer the case. Instability can only be incorporated on the statistical level. It is this approach which can then allow us to express the laws of nature in a form which includes the arrow of time, and describes possibilities rather than certainties.

At first sight this conclusion may appear revolutionary, but it corresponds in fact to a historical necessity. When great scientists like Gibbs and Einstein first introduced set theory into physics, it was so as to be able to formulate thermodynamic laws at the microscopic dynamic level for cases both of equilibrium and disequilibrium. For them, this resort to set theory was merely the sign of a lack of information about the initial conditions. But was there not a deeper reason for this move? If that were so, then the phenomena described by thermodynamics such as phase transition would be due ultimately only to our lack of information, our approximations. Once more, this is an anthropomorphic vision which it is difficult to accept. For if that is so, why sets rather than trajectories or wave functions? This is the question which the dynamics of unstable systems is beginning to answer.

It is impossible in such a brief article to describe the reformulation of the laws of nature which is necessary when they are extended to cover unstable dynamical systems. I will point out only that they apply for instance to situations such as a liquid or a gas which is the scene of persistent interactions. If we could observe the atoms or molecules involved, we would see a perpetual motion according to no particular order. It is this "chaotic" motion which gives such systems both their limited predictability and their capacity for self-organization.

For the classical world view, science went hand in hand with certainty. The supreme glory of the human mind seemed to depend on the possibility of achieving certainty. However it is my belief that on the contrary the idea of certainty leads to contradictions, to an irreconcilable split in our vision of the world. I share the opinion of Karl Popper who wrote in his book "The open universe - an argument for indeterminism" : "I regard such Laplacian determinism - confirmed as it may seem to be by the prima facie deterministic theories of physics, and by their marvellous success - as the most solid and serious of difficulties in the way of an account of, and a defence of, human freedom, creativity, and responsibility".

From its earliest days the thought of the Greeks contained two major projects : the intelligibility of nature, and the construction of a democracy based precisely on the ideas of freedom and responsibility. For a long time it was held that these two projects could only coexist within a dualist conception of nature, whether this were Cartesian dualism, the noumenal and phenomenal worlds of Kant, or more recently the introduction of the "anthropic principle" in cosmology.

The elements of progress which I have summarized here allow us to go beyond this duality and the contradictions which it contains.

Collingwood was right when he wrote in his work "The Concept of Nature" : "(A new) view of nature, which first begins to find expression toward the end of the eighteenth century and ever since then has been gathering weight and establishing itself more securely down to the present day, is based on the analogy between processes in the natural world as studied by scientists and the vicissitudes of human affairs as studied by historians".

Seen from this angle, we are now moving into a new phase in our description of the concept of nature, a phase which will transform the very foundations of our scientific project. My friend Leon Rosenfeld, Nils Bohr's closest collaborator, always liked to say that one understood a physical theory by grasping its limits. It has taken nearly three centuries to reach the limits of the classical concepts through the discovery of instability. As I emphasized at the opening of this article, we are only just beginning to explore the complex world we have discovered. But we can already be certain that the temporal, evolutionary character of this world will henceforth have a central place in its physical description, as it has had in the biological sciences since the time of Darwin. We are rediscovering time, but it is a time which instead of opposing man and nature, may explain man's place in an inventive, creative universe.

UNESCO Philosophy Forum
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