Mathematics, physics and biology
Abstract
The methodology of present day science relies, apparently, on physics being the model science that is nearest perfection. The claim is put forward that the successful application of mathematics in physics derives from the empirical basis of truth in the game of mathematics. However, physics will never suffice to provide complete descriptions of biological phenomena. When the author studies matter on a higher level or organisation, additional principles of activity are realised by processes like spontaneous symmetry breaking. Moreover, explanations of the mathematico-mechanistic type may have limitations not only in biological sciences but also in physics. The atomistic approach to the ultimate 'nature' of matter may soon give way to the view that only the manifest and the partially broken gauge symmetries are fundamental, whereas the breakings, which are spontaneous rather than dynamical, are historical accidents during the evolution of the universe as a whole. Such a historical approach is analogous to that of biologists who explain speciation in an integral fashion and parallel evolution by parallel adaptation, and who discern species turnover by the study of fossils.
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