It is just intellectualism's attempt to substitute static cuts for units of experienced duration that makes real motion so unintelligible. The conception of the first half of the interval between Achilles and the tortoise excludes that of the last half, and the mathematical necessity of traversing it separately before the last half is traversed stands permanently in the way of the last half ever being traversed. Meanwhile the living Achilles (who, for the purposes of this discussion, is only the abstract name of one phenomenon of impetus, just as the tortoise is of another) asks no leave of logic. The velocity of his acts is an indivisible nature in them like the expansive tension in a spring compressed. We define it conceptually as [_s/t_], but the _s_ and _t_ are only artificial cuts made after the fact, and indeed most artificial when we treat them in both runners as the same tracts of 'objective' space and time, for the experienced spaces and times in which the tortoise inwardly lives are probably as different as his velocity from the same things in Achilles. The impetus of Achilles is one concrete fact, and carries space, time, and conquest over the inferior creature's motion indivisibly in it. He perceives nothing, while running, of the mathematician's homogeneous time and space, of the infinitely numerous succession of cuts in both, or of their order. End and beginning come for him in the one onrush, and all that he actually experiences is that, in the midst of a certain intense effort of his own, the rival is in point of fact outstripped. We are so inveterately wedded to the conceptual decomposition of life that I know that this will seem to you like putting muddiest confusion in place of clearest thought, and relapsing into a molluscoid state of mind. Yet I ask you whether the absolute superiority of our higher thought is so very clear, if all that it can find is impossibility in tasks which sense-experience so easily performs.