With the appearance of the Arabs on the scene of history, human thought turned to the additive concept of number, and the original distributive concept receded gradually into oblivion. The acceptance of the new concept made it possible for the first time to conceive the zero. It is clear that by a continuous division of unity one is carried to a constantly growing number of constantly diminishing parts, but without ever reaching the nothing represented by the number zero. To-day we should say that in this way we can reach zero only by an infinite series of steps. Yet the idea of the infinite did not exist in this form for ancient man. On the other hand, in the arabic conception of number the steps necessary to reach zero are finite. For just as by the external addition of unities we can step forward from one number to the next, so we can also step back on the same path by repeated subtractions of unities. Having thus reached One, nothing can stop us from going beyond it by one more such step. The arabic numeral system, therefore, is the only one to possess its own symbol for zero. It has been correctly noted that the penetration into European thought of this additive concept of number was responsible for developing the idea of the machine; for it accustomed human beings to think calmly of zero as a quantity existing side by side with the others. In ancient man the idea of nothingness, the absolute void, created fear; he judged nature's relation to the void accordingly, as the phrase 'natura abhorret vacuum' indicates. His capacity to think fearlessly of this vacuum and to handle it thus had to be developed in order to bring about the Machine Age, and particularly the development of efficient steam engines. Consider also the decisive part played by the vacuum in Crookes's researches, through which the path to the sub-physical realm of nature was laid open. Yet nature makes use of number as a regulating factor in quite a different way from its appearance in the purely electrical and gravitational connexions of inorganic matter, namely where sound-ether from the upper boundary of nature so regulates nature's dynamic that the manifold sense-qualities appear in their time-and-space order. When we interpret the arrangement of numbers found there on a nominalistic basis, as is done when the axis- and angle-relationships of crystals are reduced to a mere propinquity of the atoms distributed like a grid in space, or when the difference in angle of the position of the various colours in the spectrum is reduced to mere differences in frequency of the electromagnetic oscillations in a hypothetical ether - then we bar the way to the comprehension not only of number itself, as a quality among qualities, but also of all other qualities in nature. * (e) LIFE