Abstract
The twentieth century has witnessed a geometrization of physics, that is, a reduction of the basic concepts of physics to geometric concepts. The topological approach to biology, recently proposed and to some extent developed by the author, is a small step in the direction of geometrization of biology, but is unable to achieve the main purpose of such a geometrization of biology, namely, the reduction to geometric concepts of such purely biological concepts as ingestion, digestion, assimilation, etc. To achieve this purpose we must find geometric structures or spaces, in which different geometric properties stand to each other in the same formal logical relation, as the different concepts of biology stand to each other. If this were possible, then a set of geometric theorems could be “translated” by an appropriate “glossary” into a set of biological laws.
While not offering a solution to this problem, the present paper illustrates the possibility of such an approach on several examples. Certain new types of topological spaces are introduced, which are used for illustration purposes only. It is shown, however, how from a theorem about such spaces a verifiable biological prediction could be made, if these spaces were to be taken seriously.
A possible application to biology of E. Artin's theory of braids is outlined.
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Rashevsky, N. The geometrization of biology. Bulletin of Mathematical Biophysics 18, 31–56 (1956). https://doi.org/10.1007/BF02477842
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DOI: https://doi.org/10.1007/BF02477842