Until
next week,The Matter of Mind (2)
Dateline: December 7, 1997
IAN Stewart and Jack Cohen’s Figments of Reality (see last week's feature) presents a joint biological/mathematical view of mind as an emergent, complex phenomenon fundamentally off-limits to standard reductionist methods of inquiry. Nobel Laureate Ilya Prigogine (The End of Certainty, 1996) in a sense takes up where Stewart and Cohen leave off, and proposes a way into the complex phase spaces representing the growth and behavior of mind and other emergent phenomena, using leading-edge mathematical tools from Complexity Theory.
Prigogine has come up with a mathematical theory to extend—and perhaps begin to replace or unify—classical, quantum, and relativistic theories. His theory, he claims, establishes that there is, after all, an arrow of time. The theory was built using new mathematical tools of functional analysis involving fractals to study non-equilibrium physics/chemistry and unstable systems.
In Newtonian physics (which is good for describing the approximate behavior of fairly big things, from molecules to stars), quantum physics (good for describing the behavior of very small things, from atoms to quarks), and relativity (good for describing the behavior of huge things, like space and time), both the future and the past can be predicted, given sufficient baseline information. For Newton's classical mechanics, the baseline information needed is the position and momentum of an object over time—its trajectory. For quantum mechanics, the baseline information is the wave function, which describes the quantum state of a particle. Relativity deals in mass, energy, and gravity, which describe the geometry and dynamics of space and time.
Since trajectory, wave function, and space–time equations can be run forward or backwards, time is "reversible" and predicted events are certain to occur or to have occurred (depending on which way you run the equations). But this turns out to be true only for simple, stable phenomena and not for the complex, unstable phenomena we observe at the macroscopic levels of physics, chemistry, and biology. For the latter—which turns out to be the way the universe we observe is predominantly organized—time flows only in one direction, from the past to the future, and neither can be predicted (or retrodicted) with certainty. They can, however, be predicted (retrodicted) with probability.
Life is possible only in a non-time-reversible, non-equilibrium universe because non-equilibrium—instability, chaos—is pre-requisite for the self-organization which is the hallmark of the beginning of evolution and life. One way to define stability is to say that small changes to the conditions that created a stable system do not have much effect on it. And it is not difficult to track the changes to a stable system—the trajectories of all the bits contributing to the change—through reductionist methods of traditional science.
Chaos is the opposite. Small changes in the initial conditions can have enormous effect on the trajectories of elements in an unstable system, and it is impossible to track the trajectories. Impossible, say folks like Stewart and Cohen, because there are just too many trajectories to track. For example, to track the well-known "butterfly effect" of chaos theory, which says that a butterfly flapping its wings in Beijing can precipitate a thunderstorm in Paris, it would be necessary to map the trajectory of every molecule jostled along the path between the butterfly's wings and Paris, while also computing the jostling effects caused by all the other butterflies, airplanes, people, cars, smoking chimneys, pressure differentials, etc., etc., etc. in the global atmosphere.
Einstein's contemporary J. W. Gibbs noted that:
The laws of thermodynamics, as empirically determined, express the approximate and probable behavior of systems of a great number of particles, or, more precisely, they express the laws of mechanics for such systems as they appear to beings who have not the fineness of perception to appreciate quantities of the order of magnitude of those which relate to single particles, and who cannot repeat their experiments often enough to obtain any but the most probable results.
This is redolent of Stewart and Cohen's idea of rules leading to emergent properties through a complex middle layer in multidimensional phase space. The middle layer is statistical—probabilistic—in its very nature. We observe the result (the statistic, the emergent property), but we cannot reduce a statistic to its individual components and even if you could, you could not use the information to predict anything. If you are told that the average income of individual Americans is $50,000 per year, you cannot tell what Bill Gates' income is. And knowing Bill Gates' income gives you no clue to the average American income (don't you wish it did?!).
The great mathematician Henri Poincaré predicted that physical laws would one day take on a completely new, statistical, character and form, and it looks like he was right.
In a simple stable system, it is easy enough to describe what happens to the trajectories or wave functions of individual bits of the system (depending on whether you are using Newtonian or quantum mechanics) individually or statistically. But in a complex unstable system, you have only one choice: statistics—probability. It is important to stress that this is a reflection not of computational difficulty but of the fundamentally probabilistic nature of unstable systems.
Says Prigogine, it's not a matter of being computationally extreme to track and analyze the trajectories of gadzillions of molecules. That's not how it happens. What happens, in fact, is probability, and one of the nice things about probability is that it is computable, particularly given new mathematical understanding and tools that let us into phase space.
Both Prigogine and Stewart/Cohen hone in on phase space as the container for the complex dynamics of unstable systems. Where Stewart and Cohen wring their hands over the computational nightmare that lies therein, Prigogine says not to worry: just treat it as a probability distribution, and he provides the math showing just how to do that. This treatment does mean that you cannot reduce the system to its individual components (as Stewart and Cohen recognize), and that the reductionist approach is therefore useless for analysing the non-equilibrium emergent properties of the universe, but that's just the way it is as a physical fact: probability itself is a fundamental property of nature. Einstein must be turning over in his grave.
So if tracking all the individual microscopic trajectories in a complex unstable system is both impossible and misguided, how can we figure out what's going on in the black box of phase space? We watch for macroscopic phase transitions, that's what. An example of a phase transition is when a liquid turns into a gas. Gaseousness is an emergent property of liquid under certain conditions (being heated, for example). So to examine, describe, and predict emergent properties, we need to examine, describe, and predict phase transitions. Emergent properties are by definition novel and seemingly, therefore, unpredictable. Philosophers Henri Bergson and Martin Heidegger, mathematician Alfred North Whitehead, and physicist Arthur Stanley Eddngton all thought so, although both classical and quantum science were saying: "Wrong!"
Enter complexity theory, and particularly the study of dissipative structures. Dissipative structures break the symmetries of time and space, branching off in multiple spatial directions but in only one time direction—forward, toward the future. They create a radically new structure, and with it the opportunity for the new structure to self-organize. Complexity theory has proven so successful in bringing order out of chaos in climatology, biology, sociology, and economics that institutes devoted to it have, appropriately enough, emerged all over the world.
Complexity theory is also pointing the way to a new approach to technology. Human technology to date is the result of reductionist science leading to simple, stable technologies. But such technology, lacking the dissipated structure of complex systems, cannot self-organize in response to changes in its environment; it requires an outside, central controller to make the changes. It required chaos to create that extraordinary machine, Homo sapiens, and it will take chaos to create Machina sapiens.
Prigogine reminds us of Epicurus’ lament: "It would have been better to remain attached to the belief in gods rather than being slaves to the fate of the physicists." The greatest western thinkers, says Prigogine, face "a tragic choice between an alienating science or an antiscientific philosophy," and Western philosophy itself has been characterized by "perpetual oscillations between the world as an automaton and a theology in which God governs the universe." Both, he notes, are forms of determinism. Time and determinism are what separate science from philosophy. If Prigogine's theory is correct, in solving the riddles of time and determinism, he has achieved his boyhood dream of unifying science and philosophy.
Until
next week,
NEXT WEEK: The Matter of Mind (3): Roger Penrose's The Large, the Small and the Human Mind clarifies (somewhat) his argument that we are missing some physical principles, probably having to do with quantum gravity, in seeking to explain mind.