Macrons

The evolution of form and information from chaos has been termed "morphogenesis" and related to philosophical literature from many cultures. Mathematician Ralph Abraham (1976) has compared mathematical descriptions of the dynamic evolution of biological form to the Rigveda, I-Ching, Kabala, and Heraclitus. Using the catastrophe theory of Rene Thom (1973) and an observational device, the macroscope of Hans Jenny, Abraham has studied collective vibrational patterns which occur widely in nature and which he calls "macrons." Abraham describes physical, chemical, and electrical categories of macrons which may be further subdivided according to the material state of the macron medium. For example, physical macrons may occur within a solid, isotropic liquid, liquid crystal, or gas. Abraham cites one example of a solid macron: if a flat metal plate is vibrated transversely by an external force such as coupled electromechanical transducers, a vibrational pattern may be observed as a

"spider-web" of motionless curves (the "Chladni" nodal lines). Originally observed by sprinkling sand on a vibrating plate, these patterns more recently have been observed by laser interferometry. The pattern is the "macron" and depends upon intrinsic dimensions and elasticity of the medium, and extrinsic frequency and amplitude of the driving force. The plate is a two dimensional example, however a simple rubber ball may be visualized with stable vibrational modes characterized by symmetric distortions of shape separated by motionless nodal surfaces. Another macron example is a round dish filled with a thin layer of isotropic liquid. If the bottom of the dish is heated, the liquid will soon begin to simmer; careful observation reveals nodal lines and packed hexagons called Benard cells within which the liquid convects toroidally. This Benard phenomenon, also seen as wind induced patterns in the sands of the Sahara and other deserts, is also considered by Abraham as a macron. These macrons or stable modes also depend on intrinsic controls such as shape, compressibility and viscosity, and external controls such as frequency and amplitude of the driving force.

Other forms of macrons described by Abraham include smoke rings, opalescences like abalone shell, and the aurora borealis or Northern Lights. Turning to the brain, Abraham conjectures: "a thought is a macron of the brain bioplasma." He proposes that spatial patterns of EEG are electrical macrons at dendritic surfaces or that macrons occur within nerve cells. He suggests that repetitive reinforcement of specific macrons "hardens" them into a structural form in a learning mechanism. Abraham's macrons may be compared to standing waves, reaction diffusion systems, and holograms which can all manifest 3 dimensional analog patterns of interactive information suitable to the cytoskeleton. Another "digital" system of interactive patterns in dynamic lattices is the "cellular automaton."

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