Complex Food for Thought and Imagination

	Book review on Chaos and Life: Complexity and Order in Evolution and Thought by Bird, Richard J (2004) Reviewed by Jane Lorimer
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This order did none of gods or men make, but it always was and shall be: an ever living fire, kindling in measures and going out in measures.
Heraclitus

This interesting book by Northumbria University senior lecturer Richard Bird provides food for thought on perennial questions about order and design in nature, and their resonance with the mathematical mind. The first six chapters are very readable introductory accounts of the more familiar tenets of complexity, fractals and "the mathematics of chaos" (Stewart, 1990). True to the book's title these mathematically-based paradigms are related to the life sciences, highlighting the increasingly familiar cry of a "Crisis in Biology" which is "hamstrung but two approaches that … will not advance it." The first is the "chemical thinking" of molecular biology and genetics, and the second is the neo-Darwinian theory.

SMN readers familiar with the biophysical models of Mae-Wan Ho and the electromagnetic body model of Zhang (Network 81) will likely agree. But, Bird's approach resonates even more directly with Brian Goodwin's work on "the evolution of complexity." However, unlike Goodwin (1996) who focuses on detailed empirical examples, and never mentions fractals, Bird is broadly theoretical, keen on fractals and ultimately deeply interested in models of iteration and recursion, explored in the latter half of the book.

The book is successful in conveying, to non-mathematicians like myself, something of the potential of complexity theory in helping advance us to the next, as yet elusive, evolutionary paradigm. Bird reveals his philosophical, almost mystical, inclinations in his apt quotes from Heraclitus: "The real constitution of things is accustomed to hide itself" and his asides on homeopathy, coincidences and other topics.

Although mostly substantial and even enjoyably provocative, I objected to certain conclusions in chapters 7 and 8. Bird's scenario of the emergence of the first humans, as brainy mathematically-minded outcasts, suggests a mathematician's wishful thinking and clashes with anthropological paradigms of the evolution of Homo sapiens consciousness through archaic, magical and mythical structures long before the manifestation of true maths orientation. Likewise, a macabre linking of "amputation wannabes" with psychological fixation on asymmetry, seems marginal to the many excellent examples of contrasting symmetry-asymmetry patterns that pervade almost every biological group. Ironically, these departures from otherwise interesting themes are conflated with molecular biology minutiae ostensibly criticised in earlier chapters.

The remaining chapters show Bird's complex thinking on inherently paradoxical problems and their significance for life, ontology and consciousness. He reviews common definitions of entropy, order and complexity which suggest that life overcomes entropy, building energy, order and complexity (negative entropy and information) against a background of energy dissipation towards randomness and universal heat death. This confuses order and complexity, and he suggests a different view: that the entropy of organisms (and hence complexity and information) increases with time, in a sense defining time's arrow. (Thus, organic life flows with, not against, the grain of inorganic entropy). Entropy is in fact the Greek translation of Evolution.

Mathematically, entropy corresponds to increased information, so, we may view "Life as entropy" and even believe that "order and entropy are psychological variables, not physical ones." Thus, following Schrodinger, food intake is not merely an organism's energy gain, but its way of lowering entropy (increasing order). Order consumed by organisms and removed from the environment, supposedly makes it less orderly. But this assumes a limit on available order. The supply could be inexhaustible. "The image to come out … is of a dynamic process [attractor] on a grand scale, unfolding through time to produce information pockets." Some may appear simultaneously in different locations creating apparent coincidences of thought (e.g., Newton and Leibniz, Darwin and Wallace).

Maths is "true," Bird claims, because it echoes the world and our brains recognise the resonance, particularly, with iteration and recursion. The former performs the same operation over and over in time (like counting) carrying the result forward to the next cycle, while the later generates an infinite set of values (theoretically outside time, like remembering) by making a function one of its own arguments. These processes may help mathematicians resolve problems of paradox and indecision that frustrated Whitehead, Russell, Gödel and Turing: namely that properties of a system can not be decided within a system (because the assumption of truth or falsehood leads to contradiction). But iteration allows something to be true and false at different times. Thus, those who believe "math objects have timeless existence" like Penrose and Barrrow, are mistaken. The world is not timeless. Truth values may change. Indeed iteration of paradoxical contradictory statements, with truth values varied from 0-1 (rather than simply 0 or 1) produce beautiful fractal-like patterns with organic forms. Life "embodies" iterations or recursions of rationally un-decidable formulae including that most familiar of phenomena - language. And why not? Life is based on antagonistic, contradictory, opposing, but necessary, forces (e.g., anabolism-catabolism, waking-sleep, truth-falsehood etc., ).

In general agreement I borrow this closing statement: Nothing repeats itself without some measure of novelty entering in (Johnson 1957, 126) as a compelling philosophical parallel to Bird's recursive thesis. Johnson believes "the little-known philosophical works of Mr. Douglas Fawcett… by a stroke of genius [find] a clue to the great Mystery." The essence of this philosophy is that creation is a process of divine (and human) imagination or imagining characterised by both conservative and additive (novel) elements that maintain familiar structure and habit (morphic resonance?) while introducing creative innovations. This faculty of imagination "is the psychical spring within the mind from which all other faculties derive" it is "more original, and more essential a factor in the mental life than sensation or understanding or reason." Thus, "the mathematician … fancies imaginary numbers, infinite numbers, and queer kinds of space" and, citing Whitehead, mathematics consists "in the organisation of a series of aids to the imagination in the process of reasoning." (op cit., p. 37-38) Thus, Bird's book is a product of this creative imagination that grapples with the very process itself.

References

Johnson R. C. 1957Nurslings of Immortality. Harper and Brothers, New York. 279p.
Stewart, I. 1990. Does God Play Dice? Blackwell, 348p

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