The recent thinkers included here, and the titles of their books, are as follows: John H. Holland, “Emergence”; Stuart Kauffman “At Home in the Universe”; Ilya Prigogine, “The End of Certainty”; Roger Penrose “Shadows of the Mind” and “The Large, the Small and the Human Mind”; John Conway (cellular automata; the game of Life); Douglas Hofstadter “Goedel, Escher, Bach” and “Fluid Concepts and Creative Analogies”; Gregory Bateson “Mind and Nature”; Stephen Jay Gould “Wonderful Life”. Others are mentioned in passing.

Prigogine shows WHY the emergence of novelty is possible, namely because of frequently repeated interactions in multiple particle systems with N of the order of Avogadro’s number. This marks a transition from thinking in terms of mechanics, which is time-reversible, to thermodynamics, in which the arrow of time appears. Yet even this is still time-reversible in principle, although highly improbable. However, in open systems far from equilibrium, true time irreversibility appears: rewinding and rerunning the tape of evolution would produce divergent results, as Stephen Jay Gould also shows.

John Holland shows HOW novelty is created. Even in seemingly simple systems governed by only a few rules, such as the game of checkers, neural nets in the brain, and cellular automata (e.g. “the game of Life”), give rise to combinatorial explosions of possibilities in subsequent states of these systems, leading to unexpected surprises, and thus the phenomenon of emergence. These are complex systems, in spite of the paucity of rules. Even language consists of only 26 letters (in English), music of only 8 notes of the octave, and the genetic code of only 4 codons. Yet all literature, all music, all life can emerge from this as a novelty, a surprise.

Stuart Kauffman supplements this by showing how the combinatorial explosions are controlled to create some stability, i.e. to proceed from chaos to order. We get this order for free, because of the properties of his network models. Life exists at the edge of chaos, but in the region of order. There is mainly homeostasis (a frozen core of order), but also islands of chaos to provide flexibility and adaptability in face of changing conditions. Organisms are in the subcritical region of order, ecosystems are right on the edge of the phase transition or near it, while the biosphere as a whole is supracritical, i.e. still evolving.

Kauffman’s models are still only models, not the real world. (“The map is not the territory”, said Korzybski, the founder of general semantics.) Holland stresses that, to . construct successful models, the scientist must distinguish between the features of the observed world that are important (salient) and those which are irrevelant, mere details. The same applies to making maps.

How do we do this? It seems that humans are particularly good at this, i.e. at perception of patterns, while computers can hardly do it at all. (This adds to Penrose’s conception that computers can only do algorithms, while humans can also grasp non-theorem truths, i.e. beyond Goedel.) The question is: by making such seemingly arbitrary distinctions, do we actually create a meaningful reality, as Maturana would say, while Popper’s World I reality (things in themselves) is only 2 jumble of details?

Do ordinary sane minds have a built-in filter to pick out only the significant parts from the immense stream of sense data? (Holland maintains that, in the visual field, we do it by our eyes jumping from point to point in saccades. He calls for all models to be “saccade-based”.) And does schizophrenia arise when that filter is lost? when the doors of perception (Aldous Huxley) open wider? Do we actually receive more information about World I in the schizophrenic condition? But if so, the richness gained is a negative benefit to us, in terms of navigating in our environment and of functioning in practical life. We must build models to think effectively. Only a reasonable reduction of overabundant data leads to practical knowledge.

Thus, from the Brusselator to the Santa Fe Institute, we delve into complexity theory. But the search is only just beginning. The key seems to be the role of time. In developing game trees, in doing computer simulations of models, in the generation of deterministic chaos from simple equations, we use time steps in the mathematical method of iteration. This is the mathematics appropriate to complexity theory, just as the calculus and differential equations are appropriate to mechanics, and combinatorics and factorials are appropriate to thermodynamics. Computers must have clocks, and both ontology and evolution (Bateson’s two main stochastic systems) proceed stepwise. This is why we living beings perceive time as flowing past QS, while an electron, if it were conscious, would not.

Mathematics intrudes into physics, as Penrose sees it, as only a partial stream from the larger Platonic sphere of thought and knowledge. Why do particular forms of mathematics fit the physical world so well? (Particularly if it is only a jumble of details?) But then, Penrose would have a small stream from the Physical sphere pass into the Mental sphere by emergence (the very mechanism that Holland and Kauffman try to elucidate). And then he would see a small stream from the Mental sphere pass into the Platonic sphere, in terms of the human understanding of mathematics, or abstract symbols in general. (See Terrence Deacon, “The Symbolic Species”.)

Penrose’s Three-Spheres model of what I call the World Process has one peculiar feature: it is intransitive. This seeming irrationality is made possible by the difference in the verbs connecting the three spheres. Just as in the intransitive children’s game “scissors, paper, stone”, scissors cut paper, paper wraps stone, stone breaks scissors, we are left wondering which is the strongest, so in the intransitive cycle: Platonic intrudes into Physical, Physical emerges into Mental, Mental understands Platonic, the verbs are different, but we a~} left wondering which sphere is the primary one.

There is no answer to this question; it is an indissoluble (non-decomposable) Trinity in Unity. It is an expression of the concept that Mind and Matter are coeval in eternity, although Mind is emergent from Matter in the temporal world. Since we necessarily live (because we live) in the temporal order, the concept of Mind as emergent from Matter is more congenial to us.

The cellular automaton of the game of Life (a computer model) can be abbreviated to “cellular life” to transfer its meaning from the model to the thing modelled. (The territory rather the map.) This becomes relevant to the World Process in the emergence of mind from matter, the understanding of symbolic systems by mind, and the discovery of the relevance of mathematics to physics. This connecting inter-sphere matrix of life (the ultimate concept in complexity theory) is itself part of the World Process cycle, and thus not an accident in the Universe. Yet God may have other designs as well, such as macro-coherence.

The Bible Code predictions of future imminent catastrophes are hedged by questions “can you change it?” This hints that the world is an agent-based simulation model (as in Holland’s book), and that humans are independent free-willed agents. However, we operate in a state of very incomplete knowledge of the consequences of our actions, which may well be counter-intuitive and unintended. Preventing the end of the world is not as simple as in the film “The Seven Seals”, where all Abbie had to do is “die for him”. We might want to “change it”, but we don’t know how. Of course, there are also people who myopically look out only for short-term personal benefits, or even have total ill-will; these are the elements of sin, either by omission or by commission (Augustinian or Manichean devil).

Hofstadter made another advance in models: in his Copycat model, not only do the states of the system change, the. connections can change too. This is a development of his previous ideas in GEB that a number string can function either as data or as program, interchangeably. Now he adds a third function of such strings: as an id (identification) tag, in an address. This is the idea of “fluid concepts”, that an entity can change its function (its connection to the system) in mid-stream. It reminds us of Kauffman’s self-catalytic (or mutually catalytic) networks, and of the fact that a ribozyme can function either as a template or a catalyst at different times.

Coming back to the human facility in picking out the significant features from a welter of details (needed in the creation of models and maps, but also very much a part of normal mental functioning), Holland turns to the function of a metaphor in creative thought, either by an artist or a scientist. This faculty can be called intuition, except that it also functions unconsciously in visual perception, which is already an elaborated interpretation of the virus field, not a passive photograph.*

Intuition is the basis of creativity, which is a mental faculty different from, and perhaps beyond, intelligence. In the concept of ever-subtler (less material) bodies in esoteric religions (e.g. Alice Bailey), we have the physical body, the etheric body (physiologic process, health), the astral body (sphere of emotion and reason), and only after that the intuitive body. (Three or four other “bodies” follow, up to the direct connection with God.)

Intuition (some would call it adduction) complements induction and deduction in the structure of the scientific method. It is the formulation of hypotheses for empirical testing, the recognition of significant patterns, the Eureka moment – so much like the artist’s inspiration -and both dependent on metaphor, the main trope in poetry. This is why mathematicians and physicists insist that their proofs and theories should be “elegant”, Le. have elements of beauty as well as truth. (Why did physicists initially call the Bottom and Top quark Beauty and Truth, respectively?) Intuition works by pattern recognition; metaphor finds pattern similarities in two or more otherwise unrelated objects.

Intuition seeks meaning, insight, understanding. All these are beyond knowledge (while remembering that knowledge lies beyonf data or facts). However, knowledge of facts and practice of skills (as in piano playing or bicycle riding or swimming) are prerequisites for mastery or understanding. The higher must always build on a solid foundation of the lower, just as a house is stabilized by its foundation. (Note: the above is a metaphor.)

The objective is improvement, not optimality. (I called my book on U.N. reform “Design for a Better World”, not the best.) Kauffman makes the same point: in evolution within an eco-system, species climb the nearby peaks in a mutually changeable landscape. Distant peaks may be even higher, but are invisible and thus inaccessible. “You can’t get there from here.” We seek a niche, not Nirvana.

*See also George Lakoff and Mark Johnson, “Philosophy in the Flesh” Bas1c Books, 1999, who say that we cannot help using unconscious metaphors.