| CHAPTER XXXIV
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| A LAW OF ACCELERATION (1904)
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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