The first of these artifices is that from which results the possibility of decomposition or recomposition according to arbitrary laws. For that we need a previous substitution of symbols for things. Nothing demonstrates this better than the celebrated arguments which we owe to Zeno of Elea. Mr Bergson returns to the discussion of them over and over again. ("Essay on the Immediate Data", pages 85-86; "Matter and Memory", pages 211-213, "Creative Evolution", pages 333-337.) The nerve of the reasoning there consists in the evident absurdity there would be in conceiving an inexhaustible exhausted, an unachievable achieved; in short, a total actually completed, and yet obtained by the successive addition of an infinite number of terms. But the question is to know whether a movement can be considered as a numerical multiplicity. Virtual divisibility there is, no doubt, but not actual division; divisibility is indefinite, whereas an actual division, if it respects the inner articulations of reality, is bound to halt at a limited number of phases. What we divide and measure is the track of the movement once accomplished, not the movement itself: it is the trajectory, not the traject. In the trajectory we can count endless positions; that is to say, possible halts. Let us not suppose that the moving body meets these elements all ready-marked. Hence what the Eleatic dialectic illustrates is a case of incommensurability; the radical inability of analysis to end a certain task; our powerlessness to explain the fact of the transit, if we apply to it such and such modes of numerical decomposition or recomposition, which are valid only for space; the impossibility of conceiving becoming as susceptible of being cut up into arbitrary segments, and afterwards reconstructed by summing of terms according to some law or other; in short, it is the nature of movement, which is without division, number, or concept. But thought delights in analyses regulated by the sole consideration of easy language; hence its tendency to an arithmetic and geometry of concepts, in spite of the disastrous consequences; and thus the Eleatic paradox is no less instructive in its specious character than in the solution which it embodies. At bottom, natural thought, I mean thought which abandons itself to its double inclination of synthetic idleness and useful industry, is a thought haunted by anxieties of the operating manual, anxieties of fabrication. What does it care about the fluxes of reality and dynamic depths? It is only interested in the outcrops scattered here and there over the firm soil of the practical, and it solidifies "terms" like stakes plunged in a moving ground. Hence comes the configuration of its spontaneous logic to a geometry of solids, and hence come concepts, the instantaneous moments taken in transitions.