More?

Sometimes the title of a work can imply more than the text delivers. So it is with Edward Wilson’s Consilience: The Unity of Knowledge. When I first read this title, a kind of excitement stirred within me. What could the good biology professor have to say about his own science, physics, art, music, literature...? What kinds of connections were to be made? However, as I began processing the text, I was brought down a bit once I realized that at its foundation, Wilson’s thesis was ultimately reductionist. Let scientists do their work, and ultimately they will explain all of the arts, indeed all of human creativity.

Not that there is anything wrong with reductionism – the attempt to find fundamental laws of the Universe has been amazingly successful, even though they still remain incomplete. Metaphorically speaking, the pilgrimage from Copernicus to Kepler to Galileo to Newton, with the leap to Einstein, has been remarkably successful in its description of the mutual relationships of mass, space, and time. Similarly, the progressive reduction of atomic theory to successively more “fundamental” particles/wave-fields in the context of quantum mechanics is another triumph of theory and experiment.


However, the same disciplines that produced Relativity and Quantum Mechanics also produced recognition of inherent ambiguity: Heisenberg’s Uncertainty Principle, Clausius, Boltzmann, and Gibbs thermodynamics, (with help from the logical, mathematical, and computer science fraternity) Gödel’s Incompleteness and Chaos. That is, for example, an understanding of an individual human being – his/her life, thoughts, and actions – is beyond the capacity of science to fathom.


In the decades preceding Consilience, and in the few years since, other analogous ideas have been percolating, especially in the more general area of “popular” science, though they are manifest in varying degrees in the “hard” science they are attempting to describe or motivate. The most reductionist of such ideas is GUT: the Grand Unified Theory.


GUT is the “holy grail” of physics and cosmology. In it, Einstein’s Relativity and Quantum Mechanics and the principal forces will find unification. GUT is a presupposition of Consilience, but is it achievable? Some physicists are enamored of “string theory” in which the familiar four dimensions (x-y-z and time) are augmented by as many as twelve more, tightly twisted in micro-micro “space”, thus far, they are beyond the reach of observation or experiment (both by reason of scale and seemingly intractable mathematics).


Another example: It has been said that one difference between dogs and cats is that one can never reliably predict what a cat will do, while a dog, especially one who has been with the same master since a puppy, can be expected to behave in specific ways. Yet, even a dog’s behavior is never fully anticipated. Statistical expectations can accumulate through experience and experiment, whether dealing with feline, canine, or human, but precise, individual outcomes are forever beyond the capacity of any scientific program to develop; to be more specific, as Chaitin as noted (discussed more completely below), a scientific theory, to be of any value, must be significantly more compact than the phenomena it is attempting to characterize or predict.


Reductionism is, virtually by definition, compressive. The properties of an electron within a particular state are applicable to any electron in the same state. Explain one, explain all. Explain an individual proton or neutron. Explain an atom, comprised of a finite number of neutrons, protons, and electrons, in a particular state. Explain a molecule of atoms. Explain a crystal of molecules. The complexity may or may not increase, depending on the state and on the presence of defects or impurities. Complicate the state, moving from solid to liquid to gas to plasma, and the compressional explanation of each particle’s behavior is gradually lost. Characterization becomes statistical: thermodynamic, depending on whether equilibrium is attained, and, in any case, subjective (that is, from the perspective and knowledge of the observer). Some might argue that thermodynamics is reductionist, but the combination of temperature, volume, and pressure characterize an ensemble of particles, not individual particles. The reductionist task is to characterize each particle and from their interactions infer the outcome. To the extent that multiple particle interactions cancel one another out, such predictions can be made. However, when small perturbations in a particular system can produces large changes (the butterfly effect), beyond the capacity of any conceivable computer to calculate, it is difficult to anticipate a reductionist unity of knowledge.


What might I have expected from Consilience that it does not deliver? How about recognition of common structures in human creativity: art, technology, and scientific discovery? Could “consilience” contain “coherence”? Can reason apply at non-reductionist levels? Must we derive grand theories of everything in order to define morality? Herein is an alternative approach to a “unified” theory of knowledge – science, humanities, invention, and even software development. This idea of unification is not intrinsically predictive; so, maybe it’s not even a hypothesis, much less a theory); rather it might be considered a heuristic for recognizing and utilizing coherence, with some speculative theoretical underpinnings.


Two other ideas that have germinated and flourished in recent decades incorporate aspects of coherence. Both emerged in the Seventies, although progenitors can be recognized decades earlier. The first, “Chaos theory” has several components: (1) even “simple” similar physical systems can evolve in vastly different directions with only minor changes in initial assumptions (the “butterfly effect”); (2) despite unpredictability, constraints on a chaotic system can produce repetitive patterns (parameterized, in some cases, by a “strange attractor”); (3) such repetitive patterns may manifest a nested predictability: Mandelbrodt’s “fractals”, documented both mathematically and supported by observation.


The other idea builds upon the philosophical implications of Gödel’s Incompleteness theorem. His demonstration that a seemingly comprehensive system of logic, the Principia Mathematica of Russell and Whitehead is either incomplete or inconsistent, undermined a major thread of mathematical investigation, and, at the same time, provided a basis for a new computational theory that became foundational to digital computing. The methodology utilized by Gödel involved two key elements that computing uses: (1) substitution of whole numbers for mathematical or logical symbols and expressions and (2) substitution of the numeric transforms for expressions back into the same transformed expressions, thereby introducing recursion. Hofstadter has recently called this recursion a “strange loop” (in I am a Strange Loop), rather like the “strange attractors” of Chaos theory. Initially, this idea of cross-dimensional recursion to which Hofstadter has attached the new name was introduced in his idiosyncratic Gödel, Escher, and Bach in 1979. In GEB, he suggested that the recursive loop is critical to understanding the nature of human consciousness. As apparently no one picked up this idea in the intervening years, Hofstadter produced “I am…” In both GEB and I am… Hofstadter noted the similarity of Gödelian recursion to Mandelbrodt’s fractals, although not by name; where the recursion apparently differs from fractals is that fractal structures are progressively nested, larger to smaller, at finer and finer spacing, while (the key difference) the smallest of the structures is not reinserted and rescaled into the largest (as implied by the algorithm of Gödel).


Hofstadter proposes that that experience of recursion in the brain is the source of the sense of consciousness that we experience as humans. He extends the idea further by suggesting that our experience of one another incorporates additional “loops” into our brains. Thus our memory of another is that of the other’s consciousness, to the extent that we have come to “know” them.


What’s Missing?


Grand unified theories, reductionism, consilience, fractals, recursion, and strange loops: I have a sense that each of these ideas is more tightly linked to the others than presently understood.


What’s missing? First, I suggest entropy, that fuzzy concept that entrances and mystifies so many. It should be noted that the definition of the term, “entropy”, is not universally agreed upon. I building upon an understanding first advanced by Jaynes, which has (to me at least) intriguing characteristics and possibilities.


Next, the fractal concept finds plausible application not only to observations of the physical universe, but to aspects of human creativity. Science itself, while it seeks to understand the laws of the Universe, is still very much a human endeavor. Can we add the very nature of scientific research “progress” to the mix?


And, can human creativity in other, non-scientific fields of endeavor be incorporated, beyond the reductionist, consilient approach? The arts and humanities might well be illuminated in any successful grand “theory”, not to mention the social sciences.
 
(4/9/2007)


Next: Connections