on the mathematical representation of spacetime: a case study in historical–Phenomenological desedimentation

This essay is a contribution to the historical phenomenology of science, taking as its point of departure husserl’s later philosophy of science and Jacob klein’s seminal work on the emergence of the symbolic conception of number in european mathematics during the late sixteenth and seventeenth centuries. since neither husserl nor klein applied their ideas to actual theories of modern mathematical physics, this essay attempts to do so through a case study of the concept of “spacetime.” in §1, i sketch klein’s account of the emergence of the symbolic conception of number, beginning with Vieta in the late sixteenth century. in §2, through a series of historical illustrations, i show how the principal impediment to assimilating the new symbolic algebra to mathematical physics, namely, the dimensionless character of symbolic number, is overcome via the translation of the traditional language of ratio and proportion into the symbolic language of equations. in §§3–4, i critically examine the concept of “minkowski spacetime,” specifically, the purported analogy between the Pythagorean distance formula and the minkowski “spacetime interval.” finally, in §5, i address the question of whether the concept of minkowski spacetime is, as generally assumed, indispensable to einstein’s general theory of relativity.