How the Leopard Changed Its Spots:
The Evolution of Complexity

by Brian Goodwin,
272 pages,
ISBN: 0025447106

At Home in the Universe:
The Search for the Laws of Self-Organization & Complexity

by Stuart A. Kauffman,
321 pages,
ISBN: 0195095995

Vital Dust:
Life As a Cosmic Imperative

by Christian De Duve,
384 pages,
ISBN: 0465090451

Post Your Opinion
Peaks, Dust, & Dappled Spots
by Richard Lubbock

Darwinism is often said to show that biological species originate in descent from earlier types, with variations that arise by accident. In Darwin's theory, novel improvements are selected from the current crop of accidents by the hand of an incorporeal but immanent breeder, the occult but wise force of natural selection, which greatly resembles Adam Smith's equally mystical Invisible Hand of the marketplace. This is the nub of the modern neo-Darwinist doctrine, whose most perfervid spokesman is Richard Dawkins, inventor of the metaphor of the selfish gene.
Dissent raises its fists from all sides. Three recent books, whose themes interlink, tread the borderline of orthodoxy without actually denouncing the core. Their writers, all bona fide scientists, suggest, albeit mildly, that genes are not the only players in the formative biological game. Thus they hope to evade the wrath of the Darwinist elders.
The title of Stuart Kauffman's book, At Home in the Universe, tells us he's a man of cosmic appetites. Kauffman, a member of the renowned Santa Fé Institute, which studies complexity, uses computers to model biological processes. He has woven a web of chemical speculation and computer experiment that leads him to assert that nature offers organisms "order for free". He believes that biology grows out of chemical systems, living or non-living, that are able to organize their own agenda despite their environment. "Life," he says, "is a natural property of complex chemical systems," and is therefore far from improbable.
Drawing on the work of the geneticists Jacques Monod and François Jacob, Kauffman disputes the standard Darwinian view that selection offers the one and only source of order in living organisms. Instead he focuses on the way genes, which are chemical substances, interact. They are self-organizing chemical entities, he says. To model this chemical process in his computers he sets up simple interactive systems he calls "random Boolean networks". These resemble networks of electrical switches that can turn each other on and off according to random logical instructions. However, such a setup, with or without selection, would seem to lead to ferociously complex combinations that would mask any possible orderliness.
Nonetheless, if you know how to look for it, self-organized order can be observed. To extract some order out of the huge combinatorial mess of the Boolean networks, Kauffman restricts the number of connections in a reasonable and natural way. He has run thousands of experiments on his computers in which he encourages his mathematical models to grope their way around abstract versions of what he calls "fitness landscapes", in search of peaks of fitness.
He is able to show that a sparsely coupled network of 100,000 switches-not coincidentally, close to the number of structural genes in the human body-will spontaneously gather itself into a stable cycle, or attractor, of only 317 recurring states, or fitness peaks. And it also turns out that this number 317 is not much larger than the number of different cell types we actually find in the human body, about 256. If this sounds a bit like Pythagorean number magic, well, so be it.
While Kauffman's experiments do not involve living organisms, or even actual chemicals, he feels entitled to claim that order will elbow its way up to the top of some hill or another, even before life begins and natural selection starts to take its cut. Order emerges of its own accord, fast and free in non-equilibrium chemical systems, he says, no matter what the hand of selection may choose or reject. It would seem that mathematical logic itself exerts the power to sculpt behaviour. What's more, Kauffman runs on to apply his insights to complex ecosystems and "an emerging global civilization".

In How the Leopard Changed its Spots, Brian Goodwin, of Britain's Open University, treats another aspect of the same self-formative power of mathematical objects. Not surprisingly a friend and admirer of Kauffman, Goodwin argues that, emerging in biology, there is "a qualitatively new set of ideas and theories relevant to understanding living processes." One of these ideas derives from the biological work of Alan Turing, the British mathematician best known for his contributions to the logical definition of computation. Turing also founded biological field theory (which we mustn't confuse with the dubious "morphogenetic field" idea floated by the New-Age writer Rupert Sheldrake).
Turing set out to explain the dappled beauty of living things celebrated in poetry by Gerard Manley Hopkins. He investigated the mathematical properties of "excitable media". An excitable medium is any physical or chemical system that displays certain properties exemplified in a nerve fibre.
In its resting state, a nerve fibre is kept pumped up to a distinct level of chemical energy, which is ready to discharge at any time, like a trail of gunpowder. A stimulus applied to a point along the fibre causes that section to discharge, and sets off a discharge in the next section and so on to the end. Once a length of fibre has discharged, it will not respond to another stimulus until the nerve cell's activity has pumped it up again. This is called the refractory period of the fibre. So a fibre continuously stimulated will transmit a pulse, rest for a fraction of a second, and then transmit another pulse and so on.
These cyclical properties are exemplified in many biological processes, and in some non-living chemical and physical structures, too. You find excitable media in many places: in the strange organisms called slime moulds, in the hearts of all creatures, in brains, and in the intestines.
Turing's paper The Chemical Basis of Morpho-genesis showed that biochemical reactions in excitable media could produce spatial patterns like the spots on the leopard and the arrangements of leaves on plants. The markings of dappled things, it seems, result from the workings of universal differential equations as much as they result from the directions of local genes, selfishly selected or otherwise.
Goodwin builds on the ideas of Turing and others to design computer models that imitate the properties of his favourite organism, the green alga acetabularia. He uses the language of non-linearity and of mathematical attractors to denounce Richard Dawkins's picture of organisms as clocks assembled in sets of selfish genetic lego blocks. "Organisms," he says, "are not molecular machines. They are functional and structural unities resulting from a self-organizing, self-generating dynamic."
Goodwin believes that his notion of self-generating fields in living organisms can be generalized further, to clarify the larger problems of human societies. Like Kauffman, he offers a serious and passionate alternative to the Darwinists' ill-defined concept of natural selection, an alternative that seems to demand some sort of eternal platonic realm of interwoven forms of process: a ruling mathematical structure outside of, or transcending, the actual universe.

The colleagues of Kauffman and Goodwin have been heard to complain that neither of them is a "real" biologist, a scientist who handles real living systems in the field or in the lab. But the same complaint can't apply to Christian de Duve, who shared the Nobel Prize for biology in 1974. De Duve's expertise lies in the field of the structural and functional organization of the cell, and his book Vital Dust: Life as a Cosmic Imperative surveys the origins of life in terms of biochemistry and cell structure. "Vital Dust seeks to retrace the four-billion-year history of life of Earth," he says, "from the first biomolecules to the human mind and beyond."
He dismisses the arguments for design that depend on improbability, such as Sir Fred Hoyle's analogy of a Boeing 747 arising ready to fly from a tornado-swept junkyard. Instead he tells in convincing detail how it is that "most of the steps involved must have had a very high likelihood of taking place under the prevailing conditions" [his italics]. "In other words," he says, "contrary to Jacques Monod's affirmation, the universe was-and presumably still is-pregnant with life."
But de Duve rejects the idea that life owes its existence to any special vital principle. He stoutly abjures all arguments in terms of pre-planning and final causes. "Design has given place to natural selection," and natural selection selects for the ability to innovate. Life can be explained strictly in terms of the laws of physics and chemistry. And he proceeds to review all the biochemistry the educated layman needs to know in order to understand how life rolled, inevitably it would seem, out of the fairly simple chemistry of the early Earth, from simple hydrocarbons to nucleic acids, to proteins, cells, tissues, plants and animals, and ultimately to human minds and civilizations.
Along the way he pays tribute to Stuart Kauffman's computer models of artificial life. But he takes care to turn part of Kauffman's imagery on its head. Where Kauffman likes to speak of a "rugged fitness landscape" with "adaptive peaks" separated by "valleys", de Duve finds "the image of falling into a basin more representative of reality than that of climbing to a peak." Life is more likely than not. He praises the mathematical modelling approach, but he insists that life is a chemical process, whose synthesis, if done at all, will require a chemist, not a computer.
In his final chapter de Duve turns to the meaning of life, and considers the ideas of two contrasting Frenchmen: a priest, Teilhard de Chardin, and an existentialist and atheist, Jacques Monod. Teilhard, a palaeontologist of high repute, proposed an extreme expression of Aristotle's doctrine of final causation. He suggested that the whole world was evolving toward a final conscious Omega Point, which would, in effect, play the role of God, somehow guiding evolution from the future. Monod, on the other hand, believed that life had emerged from a concatenation of accidents and was not moving in any preferred direction at all. De Duve neatly balances Teilhard against Monod, and manages to cite Pascal and Voltaire into the bargain.
De Duve's majestic survey of the marvels of life ends with the conclusion that we are not alone in the cosmos, and that the intricately interlocked facts strongly suggest life is meaningful in some sense, although he delicately declines to explain exactly what that sense might be.

None of these authors directly dares to challenge the strict Darwinist party line. But untutored peasants such as this reviewer continue to nourish a strong suspicion of Darwinist selectionism and its many squalid brain children. While de Duve, Kauffman, and Goodwin fiddle furtively under the fringes of the monolith, bolder spirits, and not only religious ones, are starting to say openly that the term "natural selection" explains nothing by itself, because, despite frantic denials, it cannot work without a knowing selector who discriminates, like a horse breeder.
If the complexities we observe arise more from the arithmetic of reproduction than from our genes, then how does it come about that plain arithmetic can lead to such elaborate order in the face of the second law of thermodynamics? Perhaps arithmetic can lead us into differential equations and these can lead us into chaos theory and mathematical attractors. But surely the mathematical attractors must be eternal and independent objects, not themselves subject to evolution. So this reviewer ends by suspecting that the Victorians' notion of fixed species may be correct, and the platonic ideal object Wolf exists as a discrete attractor in some obscure, if not actually occult, mathematical space, such as that of a Grassman algebra, for example.
It begins to look as though the work of our genes may mostly be done by the Boolean networks of Stuart Kauffman, the chemical field equations of Brian Goodwin, and the irresistible chemistry of Christian de Duve, all of which originate in a form of order that transcends space, time, mind, and matter. But it is still too early to kiss Darwin goodbye.

Richard Lubbock has written for many years on scientific subjects. He has also worked in radio and television, photography, and advertising.


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