”The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it. It is not at all natural that ‘laws of nature’ exist, much less that man is able to discover them. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” – Eugene Wigner
“The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.”– Bertrand RussellReading E.O. Wilson’s “Consilience,” in which he explores the possibility of the unity of all knowledge. Wilson seems eager to rekindle the Enlightenment optimism in unlimited progress, in the steady advance of reason toward a better, more just society. I’m skeptical of that, but I’m interested to see how he attempts to unite the hard sciences with the humanities, or as Russell implies, mathematics with poetry. Wilson seems, at this stage of the book, to want to impose the methodologies of the natural sciences upon the social sciences and humanities, which has been tried unsuccessfully many times before.aaron
There will not likely ever be any unification of knowledge. Godel’s theorem prevents a unification of mathematical knowledge within a single axiomatic system. It is then not likely there can be a complete unity of mathematics and science, even though science employs mathematics as a language or mode of description. Further unifications between mathematics and science with topics like psychology, sociology or humanities such as literature or history is even less likely.
At best a sort of descriptive relationship is possible. It probably is best that a complete unification is not possible, for that might permit a continuing discussion on these matters.
IMHO this unification has already arrived under the cover of AI and new contemporary knowledge. Complex systems have many dimensions with seemingly incompatible and contradictory visions, e.g., particles & waves in QM, brains & consciousness in humans, individuals and group survival in societies. A broader view will help. I.V.