Hi, Dvaid Spivak of MIT defines a functor as a mathematical equation that connects one category to another:
Different branches of mathematics can be formalized (111114-1) into categories. These categories can then be connected together by functors. And the sense in which these functors provide powerful communication of ideas is that facts and theorems proven in one category can be transferred through a connecting functor to yield proofs of analogous theorems in another category. A functor is like a conductor of mathematical truth. The planckian distribution (PD) that I have been discussing on these lists is to me a mathematical (or quantitative) functor satisfying the definition of a functor given by Spivak, since it connects at least 6 categories in natural and human sciences as summarized in the attached table. Spivak's definition of functor motivates me to suggest that there may exist "qualitative fucntors" in addition to the "quantitative functors" that he and other mathematicians are mainly concerned about. One concrete evidence to support the concept of qualitative functors (defined as verbal regularities commonly found among two or more disciplines, fields or categories) is the isomorphism found between human and cell languages (please refer to the references given in the legend to the table attached.) I think even a more general and deeper example of qualitative functor is the Peircean theory of signs or semiotics (see the last row of the table attached.) If these conjectures turn out to be valid, it may be natural for us to conclude that the quantitative and qualitative functors reflect the complementary aspects of the ultimate reality and hence that the principle of complementarity advocated by N. Bohr and Taoist philosophers throughout the ages constitutes the Natural Transformation of the category theory in mathematics. With all the best. Sung __________________________________________________ Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net
Functors_11112104.pdf
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