Let us look back over the history of mathematics. The primitive human individual did not need to count. He dealt with things as he met them, and he disposed of them singly and individually. A squirrel does not count the nuts it gathers; it simply accumulates a store, and it perishes or survives according to its instinctive ability to do this. Just so was primitive man. The savage, when he organized the first formed tribes, learned to count the days of a journey and the numbers engaged on opposite sides in battle. He employed the "score" of his fingers and toes, and our use of this very word is a survival of such a primitive method of counting.
The abacus of the Roman and Chinese extended the scope of simple mathematical operations as it employed more symbolic elements. With the development of Arabic notation capable of indefinite expansion, the science progressed rapidly, and in the course of long time it has become the higher calculus of to-day. The conceptions of geometry have likewise evolved until to-day mathematicians speak of configurated bodies in fourth and higher dimensions of space, which are beyond the powers of perception, even though in a sense they exist conceptually. The behavior of geometrical examples in one dimension leads to the characteristics of bodies in two dimensions. Upon these facts are constructed the laws of three-dimensional space which serve to carry mathematical thought to the remoter conceptual spaces of which we have spoken. It may seem that we are recording only one phase of mental evolution, but in fact we are dealing with a larger matter, namely, with the progressive evolution of knowledge in the Kantian category of number.
Natural science began with the savage's rough classification of the things with which he dealt in everyday life. As facts accumulated, lifeless objects were grouped apart from living organisms, and in time two great divisions of natural science took form. Physics, chemistry, astronomy, geology, and the like describe the concrete world of matter and energy, while the biological sciences deal with the structure, development, interrelationships, and vital activities of animals and plants. Surely knowledge has evolved with the advance in all of these subjects from decade to decade and from year to year. And just as surely must evolution continue, for the world has not stopped developing, and therefore the great principles of science must undergo further changes, even though they are the best summaries that can be formulated at the present time.
Philosophy deals with general conceptions of the universe. When we look back through the ages we find men picturing the world as an aggregate of diverse and uncorrelated elements--earth, air, fire, and water. The synthesis of facts and the construction of general principles down through Bacon, Newton, and Schopenhauer to modern world conceptions results in the unification of all--"the choir of heaven and furniture of earth." The lineal descendant of the long line of ancestral philosophies is the monism which sees no difference between the living and lifeless worlds save that of varying combinations of ultimate elements which are conceived as uniform "mind-stuff" everywhere. Whether or not this universal conception of totality is true, remains for the future to show. For us the important truth is that here, as in all other departments of knowledge, evolution proves to be real.
In closing the present description of the basis, nature, and scope of the doctrine of evolution, I find great difficulty in choosing the right words for a concise statement of the larger values and results of this department of science. So much might be said, and yet it is not fitting for the investigator to preach unduly. The lessons of the doctrine must be brought home to each individual through personal conviction. But because I firmly believe in the truth of the statement made in the opening pages, namely, that science and its results are of practical human value, it is in a sense my duty as an advocate of evolution to make this plain.
The method of science is justified of its fruits. At the very beginning we learned how, and how only, sure knowledge can be obtained and how it differs from a belief which may or may not correspond with the truth. Based upon facts of smaller or larger groups, scientific laws are so many summaries of past experience, and they describe in concise conceptual shorthand the manifold happenings of nature. Their difference from belief inheres in their ability to serve as guides for everyday and future experience. This entire volume is a plea for the employment of common-sense as we look upon and interpret the world in which we have our places and in which we must play our rôles. Our search for truth will be rewarded in so far as we organize our common-sense observations into clear conceptions of the laws of nature's order.
The doctrine of evolution enjoins us to learn the rules of the great game of life which we must play, as science reveals them to us. It is well to remember that a little knowledge is a dangerous thing, but because evolution is true always and everywhere, an understanding of its workings in any department of thought and life clears the vision of other realms of knowledge and action. Perhaps the greatest lesson is at the same time the most practical one.
It is that, however much we may concern ourselves with ultimate matters, our immediate duties are here and now, and we cannot escape them without giving up our right to a place in nature. We are taught by science that we live under the control of certain fundamental biological, social, and ethical laws; we might well wish that they were otherwise, but having recognized them we have no recourse save to obey them. Evolution as a complete doctrine commands every one to live a life of service as full as hereditary endowments and surrounding circumstances will permit. Thus we are taught that the immediate problems of life ought to concern us more than questions as to the ultimate nature of the universe and of existence.
Every one can find something worth while in the lessons of evolution, summarized in the foregoing statements. The atheist, who declines to personify the ultimate powers of the universe, may, nevertheless, find direction for his life in the principles brought to light by science. The agnostic, who doubts the validity of many conventional dicta that may not seem well grounded, can also find something to believe and to obey. Finally, the orthodox theist of whatever creed may discover cogent reasons for many of his beliefs like the Golden Rule previously accepted through convention; and he must surely welcome the fuller knowledge of their sound basis in the materials and results of comparative analytical study. To every one, then, science and evolution offer valuable principles of life, but great as their service has been, their tasks are not yet completed, and cannot be completed until the end of all knowledge and of time.