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| The End of Certainty by Ilya Prigogine |
When waves are superposed atop one another, they may cancel each other out, or they may reinforce one another. When waves of closely related wavelengths reinforce one another in just the right way, they create resonances. Prigogine shows how resonances in nature make for instability, first, and then new order.
When a violinist bows a string, the body of the violin resonates in sympathy with the frequencies at which the string vibrates in air — the fundamental frequency of the note being played along with all its harmonic overtones — to make music. When resonances occur in natural systems, they provide opportunities for new and more complex order to arise. I discussed these ideas about resonances in more detail in Chance ... or God? and in The World as Music.
Resonances in nature's dynamical systems — systems made of moving objects and thus undergoing change over time — are associated with instabilities. In the "phase space" representing all the possible states a system may visit during the course of its journey in time, at those points where resonances occur there is chaotic unpredictability. Certain of the systems which interest Prigogine most are "dissipative" ones; imbibing energy and exporting waste, they hold themselves far from thermodynamic equilibrium. These dissipative systems include all living organisms. When these far-from-equilibrium systems experience the instabilities associated with resonances, they "choose" between two or more new arcs through their phase space. These new paths represent a higher and more complex order than the order which existed before the instability. Accordingly, new order emerges spontaneously out of chaos.
What Prigogine's mathematical descriptions do not tell us is why the system chooses one new path instead of another. In the simplest case, that of a "pitchfork bifurcation," the system has two equally likely choices and picks one of them. Why that one? Why not the other? How is the choice made?
The choice is probabilistic. Descriptively, the same laws of chance apply to a pitchfork bifurcation as to the flip of a coin. Statistically, over a long enough series of trials, half the time the coin will come up heads and half the time tails. Likewise, at a pitchfork bifurcation the dissipative system seemingly has a 50% chance of picking path A and a 50% chance of picking path B.
In Chance ... or God? I suggested that the supposedly random decision made by a dissipative system is somehow influenced by a God who "stills the seas" of chaos to allow new order to emerge. This is an idea which does not appear in Prigogine's discussion, since it lies beyond science.
It may be that at any given branching point, God is equally happy with path A or path B. But it seems likely — since God is thought by many believers to prefer the specific evolutionary pathways that allowed intelligent creatures such as ourselves to arise on earth — that in at least some bifurcations God has a definite preference. What happens then?
Setting aside the question of how God does whatever he does, what does he do? Does he, for example, somehow coerce a dissipative system at a crossroads of instability to take path A rather than path B?
My own inclination is to believe that God never forces such divinely favored choices on nature. If we think about what such a policy of coercion would imply, we have little choice but to imagine God as canceling whatever freedom nature-per-se was originally granted to make its own choices. But why would God create nature in such a way as to have nominal freedom of choice but no real freedom, in that God himself preempts nature's freedom at the drop of a hat?
My feeling is also that the imaginable divine methodology that lies at the opposite conceptual extreme is not the case either: the one in which God takes no purposive action whatever. True, it is not unthinkable that God somehow designed the world in such a way that, left entirely to its own devices, it might (albeit gradually) evolve creatures like us. But that would imply that God is blithely unconcerned about the possibility of "wrong" choices made by nature along the way, not really caring whether a free Mother Nature errs and evolves a soulless world by accident.
We are taught by our religions, however, that God rues our choices when they don't correspond to his own desires. Why wouldn't that apply to nature writ large?
If God neither coerces nature nor is content with whatever probabilistic choices nature happens to make, "right" or "wrong," is there some middle conceptual ground which allows God to call forth from nature the evolutionary pathways he prefers? I would like to believe that there is.
Specifically, I would like to imagine that God in effect "beckons" to the physical world. The world can then freely "choose" whether or not to follow.
If the world does not respond to God's beckoning, then the "godless" picture drawn by Prigogine says it all. When an evolving dissipative system arrives at a pitchfork bifurcation — to take the simplest case — it chooses blindly which of two possible paths to follow. The two paths, in the case of the pitchfork bifurcation, are equiprobable. One is as likely to be taken as the other, and the question of how the actual choice is made is unanswerable.
But if the world indeed responds positively to God's beckoning, then the system in question "defies the odds" and follows the path God intends it to follow.
It is for several reasons that I like this image of God beckoning and the world freely responding by defying the odds and following the evolutionary pathways God favors.
One reason is that, as far as I can see, it comports perfectly with Prigogine's mathematics and physics. According to his model, various types of physical systems, including those which he terms dissipative, have certain characteristics in common: they are best described by probability distributions; they can be modeled abstract waves stacked atop one another; they have irreversible arrows of time; they are prone to points of instability that mimic chaos; from these chaotic instabilities new order arises probabilistically. Nothing in my image of a God "beckoning" to a natural world, which then freely responds by "defying the odds" and picking from supposedly equiprobable options in accordance with God's preferences, contradicts that.
Rather, when the metaphorical coin of a probabilistic choice made by nature happens to come up "heads" — as presumably desired by God, inasmuch as it furthers his plans for an evolving world — then for all we know it happened by blind luck.
Every metaphorical or actual coin flip represents what students of probability and statistics call a "trial." There is no way to learn whether or not an ordinary, non-metaphorical coin-flip, seen as an individual trial, has a truly random result ... as opposed to being a response to some unseen factor that has influenced the coin to come up heads.
True, when one makes a long series of trial flips, one expects half the flips to come up heads and half tails. But if it just so happens that there are a lot more heads than tails in any series of trials, then, well, so be it. It is not totally impossible for a truly fair coin to come up heads 100 times in a row, or 1,000, or even 1,000,000. So if the results of 10,000 flips are 7,500 heads and 2,500 tails, the coin could still be fair.
Likewise, if the results of 10,000 choices made by evolving dissipative systems in the natural world go in favor of what we assume God would prefer fully 7,500 times out of 10,000 — or 9,000, or 9,999, or 10,000 — we still have no proof that there really is a God. Prigogine's "godless" picture of chance alone making choices in the natural world could still be all that's going on.
Prigogine's systems cannot help but evolve. This is one meaning of the arrow of time which his equations demonstrate. Just as Darwin showed, as biological systems evolve, new species originate. Presumably, evolutionary novelty enters the picture at bifurcation points where dissipative systems' behavior patterns grow unstable. At these points, resonances make for chaotic behavior ... and then new order unfailingly arises.
My suggestion is that Darwinian evolution is real, but that God "beckons" to systems at crossroads of instability. Then they may (or may not) freely choose to follow one particularly "blessed" arc through phase space instead of any of the other possibilities. For all science can detect, this choice is a matter of blind chance.
The late Harvard paleontologist Stephen Jay Gould, one of the best known popular writers on evolution science, had it that our species appeared on earth by blind luck. If we were to rewind the tape of evolutionary history and play it again, he famously said, Homo sapiens would surely never appear. The odds against our ever having evolved are astronomical. That we did evolve is a matter of, again, blind luck.
Gould may have been right about the astronomical odds against our appearance, if evolutionary changes happen at random. Other theorists offer better odds, ones that hinge on the tendency of the systems which Prigogine calls dissipative to "self-organize." Self-organizing systems are biased in favor of ever-increasing complexity, which makes it easier to imagine ourselves as (in the words of theoretical biologist Stuart Kauffman) "we the expected."
Yet the views of Gould, Kauffman, and Prigogine are all basically "godless" — as they should be, since science has no way to detect the influence of God on evolutionary processes. But it should be kept in mind that there still may be a God who beckons to nature and elicits behavior which science is powerless to disentangle from the workings of chance.
Beckoning-and-following is one useful metaphor for what happens when a superintending God modifies the workings of chance. Another might involve an image of calling-and-responding: God calls to nature and nature answers back by doing his bidding. Yet another analogy is my favorite: annunciation-and-assent.
Chapter 1 of the Gospel of Luke tells the story of the angel Gabriel coming unexpectedly to a not-yet-married Mary and announcing God's intent to give her a son, to be named Jesus, without benefit of having had the usual marital relations. "And Mary said, 'Behold, I am the handmaid of the Lord; be it to me according to your word.' "
When God beckons to a dynamical system undergoing a crisis of instability, I take what happens to be a sort of mini-annunciation. If the system responds by, in effect, saying "be it to me according to your word," a mini-miracle occurs. It is by a series of such mini-miracles that evolution defies the odds and produces creatures like us that find favor with God.
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