On Symmetries and the Structure of Our Own Nature

Abstract

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 [1]. 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'. But-I 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].