August 24, 2011 4 Comments
I. Prigogine, From Being to Becoming: Time and Complexity in the Physical Sciences, WH Freeman, 1980
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“This book is about time.” But it has much to say about complexity, uncertainty, probability, dynamics and entropy. It builds on his Nobel lecture, re-using many of the models and arguments, but taking them further.
Being is classically modelled by a state within a landscape, subject to a fixed ‘master equation’ describing changes with time. The state may be an attribute of an object (classical dynamics) or a probability ‘wave’ (quantum mechanics). [This unification seems most fruitful.] Such change is ‘reversible’ in the sense that if one reverses the ‘arrow of time’ one still has a dynamical system.
Becoming refers to more fundamental, irreversible, change, typical of ‘complex systems’ in chemistry, biology and sociology, for example.
The book reviews the state of the art in theories of Being and Becoming, providing the hooks for its later reconciliation. Both sets of theories are phenomenological – about behaviours. Prigogine shows that not only is there no known link between the two theories, but that they are incompatible.
Prigogine’s approach is to replace the notion of Being as being represented by a state, analogous to a point in a vector space, by that of an ‘operator’ within something like a Hilbert Space. Stable operators can be thought of as conventional states, but operators can become unstable, which leads to non-statelike behaviours. Prigogine shows how in some cases this can give rise to ‘becoming’.
This would, in itself, seem a great and much needed subject for a book, but Prigogine goes on to consider the consequences for time. He shows how time arises from the operators. If everything is simple and stable then one has classical time. But if the operators are complex then one can have a multitude of times at different rates, which may be erratic or unstable. I haven’t got my head around this bit yet.
… the main thesis …can be formulated as:
- Irreversible processes are as real as reversible ones …
- Irreversible processes play a fundamental constructive role in the physical world …
- Irreversibility … corresponds … to an embedding of dynamics within a vaster formalism. [Processes instead of points.] (xiii)
The classical, often called “Galilean,” view of science was to regard the world as an “object,” to try to describe the physical world as if it were being seen from the outside as an object of analysis to which we do not belong. (xv)
… in physics, as in sociology, only various possible “scenarios” can be predicted. [One cannot predict actual outcomes, only identify possibilities.] (xvii)
… dynamics … seemed to form a closed universal system, capable of yielding the answer to any question asked. (3)
… Newtonian dynamics is replaced by quantum mechanics and by relativistic mechanics. However, these new forms of dynamics … have inherited the idea of Newtonian physics: a static universe, a universe of being without becoming. (4)
The Physics of Becoming
The interplay between function, structure and fluctuations leads to the most unexpected phenomena, including order through fluctuations … . (101)
… chemical instabilities involve long-range order through which the system acts as a whole. (104)
… the system obeys deterministic laws [as in classical dynamics] between two bifurcation points, but in the neighbourhood of the bifurcation points fluctuations play an essential role and determine the “branch” that the system will follow. (106) [This is termed ‘structurally unstable”]
.. a cyclic network of reactions [is] called a hypercycle. When such networks compete with one another, they display the ability the ability to evolve through mutation and replication into greater complexity. …
The concept of structural stability seems to express in the most compact way the idea of innovation, the appearance of a new mechanism and a new species, … . (109)
… the origin of life may be related to successive instabilities somewhat analogous to the successive bifurcations that have led to a state of matter of increasing coherence. (123)
As an example, … consider the problem of urban evolution … (124) … such a model offers a new basis for the understanding of “structure” resulting from the actions (choices) of the many agents in a system, having in part at least mutually dependent criteria of action. (126)
… there are no limits to structural instability. Every system may present instabilities when suitable perturbations are introduced. Therefore, there can be no end to history. [DJM emphasis.] … we have … the constant generation of “new types” and “new ideas” that may be incorporated into the structure of the system, causing its continual evolution. (128)
… near bifurcations the law of large numbers essentially breaks down.
In general, fluctuations play a minor role … . However, near bifurcations they play a critical role because there the fluctuation drives the average. This is the very meaning of the concept of order through fluctuations .. . (132)
… near a bifurcation point, nature always finds some clever way to avoid the consequences of the law of large numbers through an appropriate nucleation process. (134)
… For small-scale fluctuations, boundary effects will dominate and fluctuations will regress. … for large-scale fluctuations, boundary effects become negligible. Between these limiting cases lies the actual size of nucleation. (146)
… We may expect that in systems that are very complex, in the sense that there are many interacting species or components, [the degree of coupling between the system and its surroundings] will be very large, as will be the size of the fluctuation which could start the instability. Therefore … a sufficiently complex system is generally in a metastable state. (147) [But see Comments below.]
… Near instabilities, there are large fluctuations that lead to a breakdown of the usual laws of probability theory. (150)
The Bridge from Being to Becoming
[As foreshadowed by Bohr] we have a new form of complimentarity – one between the dynamical and thermodynamic descriptions. (174)
… Irreversibility is the manifestation on a macroscopic scale of “randomness” on a microscopic scale. (178)
Contrary to what Boltzmann attempted to show there is no “deduction” of irreversibility from randomness – they are only cousins! (177)
The Microscopic Theory of Irreversible Processes
The step made … is quite crucial. We go from the dynamical system in terms of trajectories or wave packets to a description in terms of processes. (186)
… Various mechanisms may be involved, the important element being that they lead to a complexity on the microscopic level such that the basic concepts involved in the trajectory or wave function must be superseded by a statistical ensemble. (194)
The classical order was: particles first, the second law later – being before becoming! It is possible that this is no longer so when we come to the level of elementary particles and that here we must first introduce the second law before being able to define the entities. (199)
The Laws of Change
… Of special interest is the close relation between fluctuations and bifurcations which leads to deep alterations in the classical results of probability theory. The law of large numbers is no longer valid near bifurcations and the unicity of the solution of … equations for the probability distribution is lost. (204)
This mathematization leads us to a new concept of time and irreversibility … . (206)
… the classical description in terms of trajectories has to be given up either because of instability and randomness on the microscopic level or because of quantum “correlations”. (207)
… the new concept implies that age depends on the distribution itself and is therefore no longer an external parameter, a simple label as in the conventional formula.
We see how deeply the new approach modifies our traditional view of time, which now emerges as a kind of average over “individual times” of the ensemble. (210)
For a long time, the absolute predictability of classical mechanics, or the physics of being, was considered to be an essential element of the scientific picture of the physical world. … the scientific picture has shifted toward a new, more subtle conception in which both deterministic features and stochastic features play an essential role. (210)
The basis of classical physics was the conviction that the future is determined by the present, and therefore a careful study of the present permits the unveiling of the future. At no time, however, was this more than a theoretical possibility. Yet in some sense this unlimited predictability was an essential element of the scientific picture of the physical world. We may perhaps even call this the founding myth of classical science.
The situation is greatly changed today. … The incorporation of the limitation of our ways of acting on nature has been an essential element of progress. (214)
Have we lost essential elements of classical science in this recent evolution [of thought]? The increased limitation of deterministic laws means that we go from a universe that is closed to one that is open to fluctuations. to innovations.
… perhaps there is a more subtle form of reality that involves both laws and games, time and eternity. (215)
Relationship to previous work
This book can be seen as a development of the work of Kant, Whitehead and Smuts on emergence, although – curiously – it makes little reference to them [pg xvii]. In their terms, reality cannot logically be described in terms of point-like states within spaces with fixed ‘master equations’ that govern their dynamics. Instead, it needs to be described in terms of ‘processes’. Prigogine goes beyond this by developing explicit mathematical models as examples of emergence (from being to becoming) within physics and chemistry.
According to the quote above, sufficiently complex systems are inherently metastable. Some have supposed that globalisation inevitably leads to an inter-connected and hence complex and hence stable world. But globalisation could lead to homogenization or fungibility, a reduction in complexity and hence an increased vulnerability to fluctuations. As ever, details matter.
I. Prigogine and I. Strengers Order out of Chaos Heinemann 1984.
This is an update of a popular work on Prigogine’s theory of dissipative systems. He provides an unsympathetic account of Kant’s Critique of Pure Reason, supposing Kant to hold that there are “a unique set of principles on which science is based” without making reference to Kants’ concept of emergence, or of the role of communities. But he does set his work within the framework of Whitehead’s Process and Reality. Smuts’ Holism and Evolution, which draws on Kant and mirrors Whitehead is also relevant, as a popular and influential account of the 1920s, helping to define the then ‘modern science’.