Page:Popular Science Monthly Volume 9.djvu/227

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207
MATHEMATICS IN EVOLUTION.

sideration of the laws which have been stated, and which are closely borne out by observation, would lead us to expect just what we find, namely, in the processes of development intermediate links would drop out after comparatively brief existence between planes of life increasingly separated, so that the last difference of power and intelligence would be the greatest of all.

And, furthermore, the same laws make intelligible the vast gulfs we find fixed between our intellectual giants and the rest of mankind, so that they form a small solitary band above us all, leaving a mere understanding of their mighty works the test of our highest powers. A single English dramatist and a single English mathematician have probably equaled in scope and excellence of original work, in their several fields, all the like labors of their countrymen put together.

Two other mathematical laws, abstractedly of great power and generality, may be noticed in the many phases of evolution, namely, those treating of the relations between areas and solids of the same form, varying in size. In like plane figures, boundaries increase directly as like dimensions and areas, as the square; in similar solids, surfaces increase as the square and contents, as the cube of like dimensions. These laws state in an abstract way the economy of aggregation, whether domestic, industrial, social, or political. The farmer profits by them when he takes down costly fences in enlarging his domain; the ship-builder avails himself of them when he models his monster craft which shall carry the cargo of half a dozen small vessels at half the expense; the Broadway architect embodies them in his lofty designs, rivaling in a business structure the height of a common church-steeple, putting two ordinary buildings on one lot of ground.

From the time when animals first noticed that two together were stronger than two singly, the gregarious instinct has been assisted in taking a firm hold on many species from its usefulness in attack and defense; where it is not exhibited, exceptional circumstances prevent: for instance, a spider would have nothing to gain by going into partnership, for it preys on flies much weaker than itself, and no company of spiders, however large, could do battle with a swallow, or a housemaid armed with a broom.

Speaking in a general way, such savage tribes of men as have had the strongest social feeling, and the largest mutual confidence, have, other things equal, had an advantage over less coherent neighbors, and so on, until now modern history deals with national groups fewer than ever before, and becoming fewer still.

In commerce, also, the largest banks, mercantile firms, and factories, grow continually larger by virtue of the less expense attending the management of extensive groups. The costly competition of many small manufactories and merchants is passing away before the more economical methods of a few strong concerns. Coöperation in