Circularity and Quantification

Aristotle asserts that an infinite circular movement has no magnitude, because magnitudes are always finite. Bergson shows that the representation of Continuity as an extensive magnitude involves the introduction of divisibility. Together, these theses suggest that the determination of the length of a Circumference entails a double falsification--it treats a circumference as a finite line, a line which is furthermore construed as the sum of rectilinear segments. Even Calculus exhibits the inadequacy of the latter phase of the procedure--while purporting to equalize Curve and Tangent via Integration, it can still only formulate the units of curvilinearity in awkward terms of those of rectilinearity, e. g. as 'distance per time squared'. In other words, Circularity is essentially unquantifiable, regardless of the undeniably useful superimpositions upon it by Geometry and Calculus. But, if so, then not only is ╥ not a constant, it is not even a number, which three futile millennia of attempting to calculate it tends to confirm.