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COMMENTARIES Readers' comments offering substantial theoretical and practical contributions to issues that have been raised in texts published in Leonardo are welcomed. The editors reserve the right to edit and shorten letters. Letters should be written in English and sent to the Main Editorial Office. COMMENTARY ON "SYMMETRY AS A SUPERPRINCIPLE OF SCIENCE AND ART" In spite of the mathematical and scientific material to which he refers, Alexander Voloshinov's approach ("Symmetry as a Superprinciple of Science and Art," Leonardo 29, No.2, p. 109, 1996) to what he calls the "superprinciple of symmetry" in nature and aesthetics has an esoteric, metaphysical drift to it. I want first to expand on this idea and then to suggest possible redirections closer to the logic of everyday cause and effect. Most of us are familiar with the intellectual process of taking a real object or system apart through a series of reductive "unpackings." One might, for example, reduce a mechanical clock or gearbox to its component cogs, the cogs to the metal of which they are composed, the metal to crystals, crystals to a molecular lattice, lattice to atoms , and so on-each step in the cascade explicating the anatomy of the one before. I would like to introduce the expression "reductive cascade" to refer to this progression toward the atomic and beyond. Let us take a human example: nations may be reduced to their component groups and institutions; these may be reduced to people in interaction ; the people themselves may be reexamined as assemblages of organs, limbs, etc.; these assemblages may be reduced to cells, fluids and so on down into biochemistry, atoms and particles. It is a truism to say that at each step in the process-at each level of analysiswe find the local structure and function manifesting differently. I am not out to challenge the conventional scientific insight that ultimately we are all clouds of particles. Rather, I believe that things that are relevant in the analysis at one point in the chain frequently become irrelevant at another. This means that we should take care not to transport systems of explanation from one level to another where they may be inappropriate, nor should we substitute generalized global concepts for concrete understanding. Sometimes it happens that features described at one level have equivalents at others, but the one is not essential to the other. Recently, physicist Steven Weinberg had this to say about the monotonous recourse of radical social scientists to the work of Heisenberg (famous for his principle of indeterminacy in quantum physics) as legitimizing uncertain verdicts, if not subversion, in the social sciences: I suggest the following thought experiment : suppose that physicists were to announce the discovery that, beneath the apparently quantum mechanical appearance of atoms, there lies a more fundamental substructure of fields and particles that behave according to the rules of plain old classical mechanics. Would Professor Levine [a correspondent from the area of critical analysis of culture who quoted Heisenberg] find it necessary to rethink his views about culture or philosophy? If so, why? If not, then in what sense can these views be said to be implied by quantum mechanics [l]? This point about the uncertainty of carrying principles across levels of analysis applies not only to the reductive cascade but also to sequential causal systems. Our sensory experiences can be traced back to physics in the sense that under ordinary conditions we experience color, form, movement , depth, aesthetic effects and so on as a result of the behavior of light. Light, as we know, is ambiguously or complexly thought of as having particle properties (photons of different energy levels) or wave properties (wavelength). But once the effects of these photons or waves have changed the configuration of photochemicals in the eye, and that in turn has translated itself into nerve impulses, release of nerve transmitters, and so on, it does not matter whether light is a particle or a wave, the pressure of a finger on the side of the eyeball, a shock to the brain or a migraine attack that set things going. When we consider Voloshinov's superprinciple of symmetry in the context of the reductive cascade, this caution about...


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