Bergson and the Geometry of Duration

One of Bergson's original central arguments is that the geometricization of Duration as a straight line is inadequate to Durational continuity. However, he himself later represents Elan Vital as a curve. Perhaps in the interim he comes to recognize that a straight line is per se itself continuous, and that it is not actually fractured by the superimposition over it of a perpendicular line. Perhaps he further realizes that the inadequacy of a straight line to Duration consists not insofar as it is internally divisible, but insofar as even an infinite aggregate of discrete straight lines, e. g. tangents, can only approximately reconstruct a curve. Now, the curve-tangent relation is a geometrical representation of the Acceleration-Velocity contrast. Furthermore, Force is defined in terms of Acceleration, and Elan Vital is conceivable as a Force. In other words, the inadequacy of a straight line as a representation of Duration consists not in its divisibility, nor in its geometrical nature, but because it is simply the wrong geometrical representation of it, i. e. while a straight line represents Velocity, Duration is an accelerating motion.