On Symmetries and the Structure of Our Own Nature

Leonardo, Vol. 7, pp. 147--148. Pergamon Press 1974. Printed in Great Britain ON SYMMETRIES AND THE STRUCTURE OF OUR OWN NATURE Roland Fischer* There is a remarkable passage in a discussion given by the late Aharon Katzir-Katchalsky at the Art and Science Symposium in Tel Aviv, 19 April, 1971 [l]. He emphasizes that beyond all relative points of view there are absolutes and these absolutes are principles of symmetry. ‘The symmetries of modern science are very abstract symmetries like balance in modern art’, he concludes. Are not these symmetries and balances very much reminiscent of Pythagorean harmonia? The meaning of that harmony was not-as it is todaya concord of several sounds but the orderly adjustment of parts in a complex fabric. Georgio de Santillana [2] views the cosmogony of the Egyptian Book of the Dead of comparable subtlety: ‘I am Atum when I was alone in Nun. ...’ Atum, like the Monad, stands for ‘that is all’. B u t 4 am paraphrasing Santillana-the built-in guiding and corrective power provided by number and geometry carries the Greek system on to developments that were beyond the reach of archaic theory. I submit that the number principles-the ratios and symmetries-constitute the order and balance in a strange mirror that is our own brain. The Pythagorean harmonies or the symmetries of Katzir-Katchalsky are re-presentations of the nature of our thoughts and images. Numerical ratios seem to reflect the structure of our analytical, rational, sequential and verbal mode of cognition rooted in the ‘major’ or dominant (cortical) hemisphere , while symmetries and harmonies reflect the mode of cogniton associated with the synchronous spaces, the non-verbal hallucinatory and dreamy gestalts and geometrized fields of the intuitive ‘minor’ brain hemisphere. How did Socrates explicate Protagoras who’s ‘man is the measure of all things’? ‘...if anything else is beautiful besides beauty itself’, concluded Socrates, ‘what makes it beautiful is simply that it partakes of that beauty’ (italics mine) [3]. * Dept. of Psychiatry and Behavioral Sciences, John Hopkins University, School of Medicine, Baltimore, MD 21205, U S A . (Received 11 September 1973.) Address correspondence to: Maryland Psychiatric Researchcenter , P.O.Box 3235, Baltimore, MD 21228, U.S.A. Order, symmetry and beauty are thus in the eye of the beholder [4]. A system appears to an observer to be in harmony and balance in proportion to the amount of self-awareness (that is, information about itserf) that the system exhibits. These conclusions , says Stafford Beer [5], may be tested in the cases of bees that have to be programmed to build a hexagonal honeycomb and a cloud of hot gas that has to be programmed to maintain a high temperature. They do not have to be programmed, in fact; only recognized for what they really are. In an unpublished study by John Baird, Professor of Psychology at Dartmouth College, submitted to Psychologische Forschung, subjects generated numbers within selected regions of a scale (say, 1-1OOO) nad then the frequencies with which different num bers wereproduced by a large group were computed. Not unexpectedly it was found that certain categories were clearly ‘preferred’ over others. These preferred numbers were multiples of 10, 5 and the lower boundary number used to delimit the range of responses. More careful analysis indicated that subjects responded as though they were preferring those numbers that contained a single significant digit (nonzero) and that could be obtained from at least one of the numerical systems based on 10, 5 and the lower boundary. A preferred state, s, can be described mathematically by a power function: where b is the base system, n is the place integer and k the category integer (including zero). A similar pattern of preferred states emerged upon examination of the numerical responses used in judging physical stimuli with the method of magnitude estimation. Therefore, for the case of numbers it appears that the physical continuum is transformed by the subject into a new set of ordered, preferred states according to the specifications of selected base systems. Baird’s theory assumes that all stimulus continua are transformed in the manner just described for numbers but that different base systems are in operation. s...