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.
A law of acceleration, definite and constant as any law of
mechanics, cannot be supposed to relax its energy to suit the
convenience of man. No one is likely to suggest a theory that man's
convenience had been consulted by Nature at any time, or that Nature
has consulted the convenience of any of her creations, except perhaps
the Terebratula. In every age man has bitterly and justly complained
that Nature hurried and hustled him, for inertia almost invariably has
ended in tragedy. Resistance is its law, and resistance to superior
mass is futile and fatal.
Fifty years ago, science took for granted that the rate of
acceleration could not last. The world forgets quickly, but even today
the habit remains of founding statistics on the faith that consumption
will continue nearly stationary. Two generations, with John Stuart
Mill, talked of this stationary period, which was to follow the
explosion of new power. All the men who were elderly in the forties
died in this faith, and other men grew old nursing the same conviction,
and happy in it; while science, for fifty years, permitted, or
encouraged, society to think that force would prove to be limited in
supply. This mental inertia of science lasted through the eighties
before showing signs of breaking up; and nothing short of radium fairly
wakened men to the fact, long since evident, that force was
inexhaustible. Even then the scientific authorities vehemently resisted.
Nothing so revolutionary had happened since the year 300.
Thought had more than once been upset, but never caught and whirled
about in the vortex of infinite forces. Power leaped from every atom,
and enough of it to supply the stellar universe showed itself running
to waste at every pore of matter. Man could no longer hold it off.
Forces grasped his wrists and flung him about as though he had hold of
a live wire or a runaway automobile; which was very nearly the exact
truth for the purposes of an elderly and timid single gentleman in
Paris, who never drove down the Champs Elysees without expecting an
accident, and commonly witnessing one; or found himself in the
neighborhood of an official without calculating the chances of a bomb.
So long as the rates of progress held good, these bombs would double in
force and number every ten years.
Impossibilities no longer stood in the way. One's life had
fattened on impossibilities. Before the boy was six years old, he had
seen four impossibilities made actual--the ocean-steamer, the railway,
the electric telegraph, and the Daguerreotype; nor could he ever learn
which of the four had most hurried others to come. He had seen the
coal-output of the United States grow from nothing to three hundred
million tons or more. What was far more serious, he had seen the number
of minds, engaged in pursuing force--the truest measure of its
attraction--increase from a few scores or hundreds, in 1838, to many
thousands in 1905, trained to sharpness never before reached, and armed
with instruments amounting to new senses of indefinite power and
accuracy, while they chased force into hiding-places where Nature
herself had never known it to be, making analyses that contradicted
being, and syntheses that endangered the elements. No one could say
that the social mind now failed to respond to new force, even when the
new force annoyed it horribly. Every day Nature violently revolted,
causing so-called accidents with enormous destruction of property and
life, while plainly laughing at man, who helplessly groaned and
shrieked and shuddered, but never for a single instant could stop. The
railways alone approached the carnage of war; automobiles and fire-arms
ravaged society, until an earthquake became almost a nervous
relaxation. An immense volume of force had detached itself from the
unknown universe of energy, while still vaster reservoirs, supposed to
be infinite, steadily revealed themselves, attracting mankind with more
compulsive course than all the Pontic Seas or Gods or Gold that ever
existed, and feeling still less of retiring ebb.
In 1850, science would have smiled at such a romance as this,
but, in 1900, as far as history could learn, few men of science thought
it a laughing matter. If a perplexed but laborious follower could
venture to guess their drift, it seemed in their minds a toss-up
between anarchy and order. Unless they should be more honest with
themselves in the future than ever they were in the past, they would be
more astonished than their followers when they reached the end. If Karl
Pearson's notions of the universe were sound, men like Galileo,
Descartes, Leibnitz, and Newton should have stopped the progress of
science before 1700, supposing them to have been honest in the
religious convictions they expressed. In 1900 they were plainly forced
back; on faith in a unity unproved and an order they had themselves
disproved. They had reduced their universe to a series of relations to
themselves. They had reduced themselves to motion in a universe of
motions, with an acceleration, in their own case of vertiginous
violence. With the correctness of their science, history had no right
to meddle, since their science now lay in a plane where scarcely one or
two hundred minds in the world could follow its mathematical processes;
but bombs educate vigorously, and even wireless telegraphy or airships
might require the reconstruction of society. If any analogy whatever
existed between the human mind, on one side, and the laws of motion, on
the other, the mind had already entered a field of attraction so
violent that it must immediately pass beyond, into new equilibrium,
like the Comet of Newton, to suffer dissipation altogether, like
meteoroids in the earth's atmosphere. If it behaved like an explosive,
it must rapidly recover equilibrium; if it behaved like a vegetable, it
must reach its limits of growth; and even if it acted like the earlier
creations of energy--the saurians and sharks--it must have nearly
reached the limits of its expansion. If science were to go on doubling
or quadrupling its complexities every ten years, even mathematics would
soon succumb. An average mind had succumbed already in 1850; it could
no longer understand the problem in 1900.
Fortunately, a student of history had no responsibility for the
problem; he took it as science gave it, and waited only to be taught.
With science or with society, he had no quarrel and claimed no share of
authority. He had never been able to acquire knowledge, still less to
impart it; and if he had, at times, felt serious differences with the
American of the nineteenth century, he felt none with the American of
the twentieth. For this new creation, born since 1900, a historian
asked no longer to be teacher or even friend; he asked only to be a
pupil, and promised to be docile, for once, even though trodden under
foot; for he could see that the new American--the child of incalculable
coal-power, chemical power, electric power, and radiating energy, as
well as of new forces yet undetermined--must be a sort of God compared
with any former creation of nature. At the rate of progress since 1800,
every American who lived into the year 2000 would know how to control
unlimited power. He would think in complexities unimaginable to an
earlier mind. He would deal with problems altogether beyond the range
of earlier society. To him the nineteenth century would stand on the
same plane with the fourth--equally childlike--and he would only wonder
how both of them, knowing so little, and so weak in force, should have
done so much. Perhaps even he might go back, in 1964, to sit with
Gibbon on the steps of Ara Coeli.
Meanwhile he was getting education. With that, a teacher who
had failed to educate even the generation of 1870, dared not interfere.
The new forces would educate. History saw few lessons in the past that
would be useful in the future; but one, at least, it did see. The
attempt of the American of 1800 to educate the American of 1900 had not
often been surpassed for folly; and since 1800 the forces and their
complications had increased a thousand times or more. The attempt of
the American of 1900 to educate the American of 2000, must be even
blinder than that of the Congressman of 1800, except so far as he had
learned his ignorance. During a million or two of years, every
generation in turn had toiled with endless agony to attain and apply
power, all the while betraying the deepest alarm and horror at the
power they created. The teacher of 1900, if foolhardy, might stimulate;
if foolish, might resist; if intelligent, might balance, as wise and
foolish have often tried to do from the beginning; but the forces would
continue to educate, and the mind would continue to react. All the
teacher could hope was to teach it reaction.
Even there his difficulty was extreme. The most elementary
books of science betrayed the inadequacy of old implements of thought.
Chapter after chapter closed with phrases such as one never met in
older literature: "The cause of this phenomenon is not understood";
"science no longer ventures to explain causes"; "the first step towards
a causal explanation still remains to be taken"; "opinions are very
much divided"; "in spite of the contradictions involved"; "science gets
on only by adopting different theories, sometimes contradictory."
Evidently the new American would need to think in contradictions, and
instead of Kant's famous four antinomies, the new universe would know
no law that could not be proved by its anti-law.
To educate--one's self to begin with--had been the effort
of one's life for sixty years; and the difficulties of education had
gone on doubling with the coal-output, until the prospect of waiting
another ten years, in order to face a seventh doubling of complexities,
allured one's imagination but slightly. The law of acceleration was
definite, and did not require ten years more study except to show
whether it held good. No scheme could be suggested to the new American,
and no fault needed to be found, or complaint made; but the next great
influx of new forces seemed near at hand, and its style of education
promised to be violently coercive. The movement from unity into
multiplicity, between 1200 and 1900, was unbroken in sequence, and
rapid in acceleration. Prolonged one generation longer, it would
require a new social mind. As though thought were common salt in
indefinite solution it must enter a new phase subject to new laws. Thus
far, since five or ten thousand years, the mind had successfully
reacted, and nothing yet proved that it would fail to react--but it
would need to jump.