for the germ-plasm may be a physical continuum throughout innumerable generations. Somatic death is only a destructive metabolism: it is a catastrophic metabolism, if we like. We may legitimately discuss such problems as the origin of the protoplasm of the prototrophic organism, or that of the chlorophyll-containing cell, or that of the nerve-cell. On the mechanistic view each of these conditions is a phase of a transforming physico-chemical system, and it is within the scope of the methods of physical science to investigate the nature of these transformations. But if the argument of this book is sound, then the problem of the origin of life, as it is usually stated, is only a pseudo-problem; we may as usefully discuss the origin of the second law of thermo-dynamics! If life is not only energy but also the direction and co-ordination of energies; if it is a tendency of the same order, but of a different direction, from the tendency of inorganic processes, all that biology can usefully do is to inquire into the manner in which this tendency is manifested in material things and energy-transformations. But the tendency itself is something elemental. APPENDIX MATHEMATICAL AND PHYSICAL NOTIONS[35] [35] It must be understood that some of the things dealt with in these appendices are very hard to understand by the reader acquainted only with the results of biological science. We urge, however, that they are all relevant if biological results are to be employed speculatively. INFINITY What is really meant when the mathematician uses the concept of infinity in his operations? Suppose that we take a line of finite length and divide it into halves, and then divide each half into halves, and so on _ad infinitum_. We make cuts in the line, and these cuts have no magnitude, so that the sum of the lengths into which we divide the line is equal to the length of the undivided line. We can divide the line into as many parts as we choose, that is, into an “infinite” number of parts. Suppose that we are making a thing which is to match another thing, and suppose that we can make the thing as great as we choose. If, then, no matter how great we make the thing, it is still too small, the thing that we are trying to match is infinitely great. Substitute “small” for “great,” and this is also a definition of the infinitely small. Clearly the idea of infinity does not reside in the _results_ of an operation, but in its tendency. It inheres in our intuition of _striving_ towards something, but not in the results of our striving. FUNCTIONALITY