The Critical Rationalist Vol. 02 No. 03 ISSN: 1393-3809 15-Sep-1997
(4) There is another aspect of this last problem, which exhibits as "conservation of complexity" assumptions. We like to believe that the results of an experiment, or the aggregate of a set of processes, are at the same level of complexity as we started with (Cohen & Stewart 1991a, Cohen & Stewart 1991b). We find it difficult to handle, in general, the fact that one growing feather is, by any measure of complexity, more complex than the group of cells on the yolk which produced the whole chicken. Stewart and I have reformed the emergence/conservation-of-complexity problem as "Ant Country", the unresolvable complexity which is located between top-down and bottom-up explanations in nearly all cases (Stewart & Cohen 1994, Stewart & Cohen 1997). We think that Dawkins' hierarchical reductionism (Dawkins 1989), which uses only two "levels" of emergence to explain scientific problems, addresses this same problem in a more usable, but less theoretically satisfying, way.
(5) There are many theoretical assumptions made by those physicists who are committed to Theory-of-Everything models of the universe. They are committed, firstly, to that reductionist rhetoric which claims that explanations converge, so that "deep" cosmology and "deep" atomic-structure-chemistry are both explained by quantum physics equations. The ultimate convergence they dream of is one final equation which lies at the root of the Universe, the Thought in the Creator's Mind. So these theoretical physicists always have more fundamental levels to test their theories against.
(6) Stewart and I have allegiance to the opposite view, which is that explanations diverge (Cohen & Stewart 1994, Stewart & Cohen 1994, Stewart & Cohen 1997); real reductionist explanations of each property of the cell must require many chemical experts, then many physicists to explain each chemical property. We called this the Reductionist Nightmare. We agree that, working upwards from quantum theory, it is (just) possible to predict/explain/justify a few of the many chemical properties, but we believe that the properties to be explained multiply upwards too. Because of the emergence of many properties at the chemical "level", and because of the fungibility of much of the substructure, the Theory of Everything cannot actually explain anything. It is as useless as an explanatory device at the bottom as is the concept of God at the top (often used by the same physicists...). It certainly cannot serve, in our view, as the ultimate touchstone (for Popperian disproofs).
(7) Biology, unlike physics (and much chemistry) cannot be tested by appeal to either Higher or More Fundamental laws. We cannot test theories about the behaviour of ants (especially Langton's Ant, see below) by appealing to predictions from Theory of Everything, or by appealing to general Laws of Behaviour. Predictions must be restricted to our experimental or observational level, and it is at this level that they must be disproved. Contrast a theory that dried fruits have more calories per fruit than fresh fruits, which can be disproved--theoretically--by appeal to the Law of Conservation of Energy--whether or not they provide more calories when eaten, this is the wrong touchstone theory. As a biologist, I am unhappy about this technique of disproof by appeal to what is known. But very many of the physicists' theories seem to be disproved by incongruence with another theory or accepted argument (or, more usually, accepted because of congruence with such theories). Popper clearly approved of this--indeed, in some senses it is obviously necessary to have some touchstone theories for any disproof strategy to be applied. It seems to me that this can only be satisfactory in a tiny subclass of well-understood, essentially Laplacian, universes. Yet most, of even such simple universes will have an Ant Country, just as our much messier system does, and simple theory-touchstones won't exist.
(8) Langton's Ant is a beautiful examplar here (Gale 1993, Cohen & Stewart 1994). Its universe is a simple cellular automaton, a square grid of black or white cells with simple rules. In this case there are just two rules:
We do know the Theory-of-Everything in this case, so it looks like a great candidate for the Laplacian universe appealed to above.
(9) Now it turns out that there is a simple repetitive behaviour that the Ant consistently "finds" after tens of thousands of seemingly chaotic moves. This behaviour consists of a sequence of 102 moves which brings the Ant back almost to where it started, but one square up and one square to the right (or one square down and to the left). This then creates a characteristic diagonal "highway".
(10) All moves of the Ant are deterministically specified by the rules above. This includes the initial "disorganised" phase before the "highway" behaviour is discovered. In this sense, all behaviour in the system is "microscopically" predictable (given the details of the initial arrangement of black and white squares on the playground, and the initial position and orientation of the Ant). But despite this "perfect" knowledge, there is, to date, no mathematical proof that the Ant will always find a highway. It just always has.
(11) In this Universe we know the initial conditions, and the rules (its Theory-of-Everything, indeed), yet we are unable to predict even very simple things. So even for Langton's Ant, unknowable-in-generality Ant Country intervenes between our top-down and our bottom-up arguments. How much more this must be true for real ants! But I think that it is true for electrons, too.
(12) In our new book (Stewart & Cohen 1997), we replace the argument about phase spaces with which we attempted to handle some of these problems in Collapse, by the similar concept "game trees". These are the whole sets of possible moves in any game (for example chess or snakes-and-ladders or, in principle, football). Any actual game marks out a path within this space, a tiny fraction of all possible moves. The developing chicken is, in a sense, playing its own life game, and it can be thought of as interacting with many other players in its environment. Some of these are "rules" about viscosity, about fats being hydrophobic, about necessary properties of dividing cells, others are contributions like yolk, or the egg-shell, with which it must overtly interact. Embryology navigates much the same path--a similar chess game--in the development of each chicken (just as flames reproduce without heredity, by accessing rules about hot air rising, about radiation and about oxidative chemistry), producing a similar morphology in each generation of chickens (or flames). And the complex feather is the result of many interactive "moves" in the game of development. The chicken is genuinely much more complicated than the egg, and is a new complex entity in the world, not simply an unfolded, previously cryptic code. It is certainly not the fowl DNA code made flesh, which is the model purveyed by those who espouse "conservation of complexity" philosophies, and whose science does not contain emergence. So theories of feather development--on which I did my Ph.D.--cannot be checked according to the Popperian doctrine of disproof (Cohen & 'Espinasse 1961). My thesis had the right form, with complex unlikely predictions confirmed, never disconfirmed by technically-difficult experimental results. But the result was bogus Popper, as it so often is in written-up biology. Popper himself was very taken with emergence, but did not, so far as I recall, feel that it posed problems for theory-testing. I believe that it does, and that the Popper-concerned scientist must play a different game of her own.
The Critical Rationalist Vol. 02 No. 03 ISSN: 1393-3809 15-Sep-1997
Copyright © 1997 All Rights Reserved.
TCR Issue Timestamp: Mon Sep 15 19:14:01 GMT 1997