A Budget of Paradoxes, Volume IDe Morgan, Augustus
Philosophy
A Budget of Paradoxes, Volume I
De Morgan, Augustus
Circle-squaring; Perpetual motion; Science -- Miscellanea; Trisection of angle
Modern discoveries have not been made by large collections of facts, with
subsequent discussion, separation, and {86} resulting deduction of a truth
thus rendered perceptible. A few facts have suggested an _hypothesis_,
which means a _supposition_, proper to explain them. The necessary results
of this supposition are worked out, and then, and not till then, other
facts are examined to see if these ulterior results are found in nature.
The trial of the hypothesis is the _special object_: prior to which,
hypothesis must have been started, not by rule, but by that sagacity of
which no description can be given, precisely because the very owners of it
do not act under laws perceptible to themselves.[130] The inventor of
hypothesis, if pressed to explain his method, must answer as did Zerah
Colburn,[131] when asked for his mode of instantaneous calculation. When
the poor boy had been bothered for some time in this manner, he cried out
in a huff, "God put it into my head, and I can't put it into yours."[132]
{87} Wrong hypotheses, rightly worked from, have produced more useful
results than unguided observation. But this is not the Baconian plan.
Charles the Second, when informed of the state of navigation, founded a
Baconian observatory at Greenwich, to observe, observe, observe away at the
moon, until her motions were known sufficiently well to render her useful
in guiding the seaman. And no doubt Flamsteed's[133] observations, twenty
or thirty of them at least, were of signal use. But how? A somewhat
fanciful thinker, one Kepler, had hit upon the approximate orbits of the
planets by trying one hypothesis after another: he found the _ellipse_,
which the Platonists, well despised of Bacon, and who would have despised
him as heartily if they had known him, had investigated and put ready to
hand nearly 2000 years before.[134] The sun in the focus, the motions of
the planet more and more rapid as they approach the sun, led Kepler--and
Bacon would have reproved him for his rashness--to imagine that a force
residing in the sun might move the planets, a force inversely as the
distance. Bouillaud,[135] upon a fanciful analogy, rejected the inverse
distance, {88} and, rejecting the force altogether, declared that if such a
thing there were, it would be as the inverse _square_ of the distance.
Newton, ready prepared with the mathematics of the subject, tried the fall
of the moon towards the earth, away from her tangent, and found that, as
compared with the fall of a stone, the law of the inverse square did hold
for the moon. He deduced the ellipse, he proceeded to deduce the effect of
the disturbance of the sun upon the moon, upon the assumed theory of
_universal_ gravitation. He found result after result of his theory in
conformity with observed fact: and, by aid of Flamsteed's observations,
which amended what mathematicians call his _constants_, he constructed his
lunar theory. Had it not been for Newton, the whole dynasty of Greenwich
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