A LAW OF ACCELERATION (1904)
IMAGES are not arguments, rarely even lead to proof, but the mind craves them, and, of late more than ever, the keenest experimenters find twenty images better than one, especially if contradictory; since the human mind has already learned to deal in contradictions.
The image needed here is that of a new centre, or preponderating mass, artificially introduced on earth in the midst of a system of attractive forces that previously made their own equilibrium, and constantly induced to accelerate its motion till it shall establish a new equilibrium. A dynamic theory would begin by assuming that all history, terrestrial or cosmic, mechanical or intellectual, would be reducible to this formula if we knew the facts.
For convenience, the most familiar image should come first; and this is probably that of the comet, or meteoric streams, like the Leonids and Perseids; a complex of minute mechanical agencies, reacting within and without, and guided by the sum of forces attracting or deflecting it. Nothing forbids one to assume that the man-meteorite might grow, as an acorn does, absorbing light, heat, electricity — or thought; for, in recent times, such transference of energy has become a familiar idea; but the simplest figure, at first, is that of a perfect comet — say that of 1843 — which drops from space, in a straight line, at the regular acceleration of speed, directly into the sun, and after wheeling sharply about it, in heat that ought to dissipate any known substance, turns back unharmed, in defiance of law, by the path on which it came. The mind, by analogy, may figure as such a comet, the better because it also defies law.
Motion is the ultimate object of science, and measures of motion are many; but with thought as with matter, the true measure is mass in its astronomic sense — the sum or difference of attractive forces. Science has quite enough trouble in measuring its material motions without volunteering help to the historian, but the historian needs not much help to measure some kinds of social movement; and especially in the nineteenth century, society by common accord agreed in measuring its progress by the coal-output. The ratio of increase in the volume of coal-power may serve as dynamometer.
The coal-output of the world, speaking roughly, doubled every ten years between 1840 and 1900, in the form of utilized power, for the ton of coal yielded three or four times as much power in 1900 as in 1840. Rapid as this rate of acceleration in volume seems, it may be tested in a thousand ways without greatly reducing it. Perhaps the ocean steamer is nearest unity and easiest to measure, for any one might hire, in 1905, for a small sum of money, the use of 30,000 steam-horse-power to cross the ocean, and by halving this figure every ten years, he got back to 234 horse-power for 1835, which was accuracy enough for his purposes. In truth, his chief trouble came not from the ratio in volume of heat, but from the intensity, since he could get no basis for a ratio there. All ages of history have known high intensities, like the iron-furnace, the burning-glass, the blow-pipe; but no society has ever used high intensities on any large scale till now, nor can a mere bystander decide what range of temperature is now in common use. Loosely guessing that science controls habitually the whole range from absolute zero to 3000 degrees Centigrade, one might assume, for convenience, that the ten-year ratio for volume could be used temporarily for intensity; and still there remained a ratio to be guessed for other forces than heat. Since 1800 scores of new forces had been discovered; old forces had been raised to higher powers, as could be measured in the navy-gun; great regions of chemistry had been opened up, and connected with other regions of physics. Within ten years a new universe of force had been revealed in radiation. Complexity had extended itself on immense horizons, and arithmetical ratios were useless for any attempt at accuracy. The force evolved seemed more like explosion than gravitation, and followed closely the curve of steam; but, at all events, the ten-year ratio seemed carefully conservative. Unless the calculator was prepared to be instantly overwhelmed by physical force and mental complexity, he must stop there.
Thus, taking the year 1900 as the starting point for carrying back the series, nothing was easier than to assume a ten-year period of retardation as far back as 1820, but beyond that point the statistician failed, and only the mathematician could help. Laplace would have found it child's-play to fix a ratio of progression in mathematical science between Descartes, Leibnitz, Newton, and himself. Watt could have given in pounds the increase of power between Newcomen's engines and his own. Volta and Benjamin Franklin would have stated their progress as absolute creation of power. Dalton could have measured minutely his advance on Boerhaave. Napoleon I must have had a distinct notion of his own numerical relation to Louis XIV. No one in 1789 doubted the progress of force, least of all those who were to lose their heads by it.
Pending agreement between these authorities, theory may assume what it likes — say a fifty, or even a five-and-twenty-year period of reduplication for the eighteenth century, for the period matters little until the acceleration itself is admitted. The subject is even more amusing in the seventeenth than in the eighteenth century, because Galileo and Kepler, Descartes, Huygens, and Isaac Newton took vast pains to fix the laws of acceleration for moving bodies, while Lord Bacon and William Harvey were content with showing experimentally the fact of acceleration in knowledge; but from their combined results a historian might be tempted to maintain a similar rate of movement back to 1600, subject to correction from the historians of mathematics.
The mathematicians might carry their calculations back as far as the fourteenth century when algebra seems to have become for the first time the standard measure of mechanical progress in western Europe; for not only Copernicus and Tycho Brahe, but even artists like Leonardo, Michael Angelo, and Albert Durer worked by mathematical processes, and their testimony would probably give results more exact than that of Montaigne or Shakespeare; but, to save trouble, one might tentatively carry back the same ratio of acceleration, or retardation, to the year 1400, with the help of Columbus and Gutenberg, so taking a uniform rate during the whole four centuries (1400-1800), and leaving to statisticians the task of correcting it.
Or better, one might, for convenience, use the formula of squares to serve for a law of mind. Any other formula would do as well, either of chemical explosion, or electrolysis, or vegetable growth, or of expansion or contraction in innumerable forms; but this happens to be simple and convenient. Its force increases in the direct ratio of its squares. As the human meteoroid approached the sun or centre of attractive force, the attraction of one century squared itself to give the measure of attraction in the next.
Behind the year 1400, the process certainly went on, but the progress became so slight as to be hardly measurable. What was gained in the east or elsewhere, cannot be known; but forces, called loosely Greek fire and gunpowder, came into use in the west in the thirteenth century, as well as instruments like the compass, the blow-pipe, clocks and spectacles, and materials like paper; Arabic notation and algebra were introduced, while metaphysics and theology acted as violent stimulants to mind. An architect might detect a sequence between the Church of St. Peter's at Rome, the Amiens Cathedral, the Duomo at Pisa, San Marco at Venice, Sancta Sofia at Constantinople and the churches at Ravenna. All the historian dares affirm is that a sequence is manifestly there, and he has a right to carry back his ratio, to represent the fact, without assuming its numerical correctness. On the human mind as a moving body, the break in acceleration in the Middle Ages is only apparent; the attraction worked through shifting forms of force, as the sun works by light or heat, electricity, gravitation, or what not, on different organs with different sensibilities, but with invariable law.
The science of prehistoric man has no value except to prove that the law went back into indefinite antiquity. A stone arrowhead is as convincing as a steam-engine. The values were as clear a hundred thousand years ago as now, and extended equally over the whole world. The motion at last became infinitely slight, but cannot be proved to have stopped. The motion of Newton's comet at aphelion may be equally slight. To evolutionists may be left the processes of evolution; to historians the single interest is the law of reaction between force and force — between mind and nature — the law of progress.
The great division of history into phases by Turgot and Comte first affirmed this law in its outlines by asserting the unity of progress, for a mere phase interrupts no growth, and nature shows innumerable such phases. The development of coal-power in the nineteenth century furnished the first means of assigning closer values to the elements; and the appearance of supersensual forces towards 1900 made this calculation a pressing necessity; since the next step became infinitely serious.