Three Scientific Revolutions: How They Transformed Our Conceptions of Reality (10 page)

Westfall adds that “few periods have held greater consequences for the history of Western Science than the three to six months in the autumn and winter of 1684-5, when Newton created the modern science of dynamics” in
De Motu
(p. 420). When Halley read the treatise he too recognized that Newton's “celestial mechanics embodied a step forward so immense as to constitute a revolution” (p. 404).

After a series of revisions Newton gradually expanded the original nine page essay into the two volumes of the
Principia Mathematica
retaining the title
On the Motion of Bodies in Orbit
shortened to “
The Motion of Bodies
” as the subtitle of the two Books of Vol. I and “
The System of the World
” as the subtitle of Book III of Vol. II. In the spring of 1686, he gave the completed manuscript to Dr. Nathaniel Vincent, a member of the Royal Society, who brought it to the Society; and largely due to the tenacity of Dr. Halley, who oversaw the drafting of the book along with its preparation for publication, it was finally published on July 5, 1687. In the first volume Newton graciously acknowledged Halley's assistance in its final publication while Halley reciprocated with an “Ode Dedicated to Newton” that concluded with the following marvelous verse introducing volume one of the
Principia.

Then ye who now on heavenly nectar fare,

Come celebrate with me in song the name

Of Newton, to the Muses dear; for he

Unlocked the hidden treasures of Truth:

So richly through his mind had Phoebus cast

The radiance of his own divinity.

Nearer the gods no mortal may approach.
³³

In the
Preface to the First Edition
he presents a precise statement of his intent:

I offer this work as the mathematical principles of philosophy, for the whole burden of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena; and to this end the general propositions in the first and second Books are directed. In the third Book I give an example of this in the explication of the System of the World; for by the propositions mathematically demonstrated in the former Books, in the third I derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets. Then from these forces, by other propositions which are also mathematical, I deduce the motions of the planets, the comets, the moon, and the sea. (pp. xvii–xviii)

As he acknowledged, his “System of the World,” although in a more concise way, recapitulates Kepler's astronomical contributions and Galileo's general program of scientific inquiry: mathematics as the language of nature, the centrality of motions, the mutual forces of gravity causing the motions of the planets, the comets, and the moon into a celestial mechanics, but he brought it to a much higher level of unification and computation. Galileo had tried to determine the velocity of light by measuring the time it took to pass from two men with lanterns some distance from each other signaling when it arrived, but its velocity was too great to be detected. Newton also rejected the instantaneous velocity of light, stating in the
Opticks
that “Light moves from the Sun to us in about seven to eight Minutes of Time, which distance is about 70000000
English
Miles, supposing the horizontal Parallax of the Sun to be about 12".”
³⁴
This indicates that he, like Olaf Roemer, who also measured the speed of light in 1675, were concerned to determine light's exact velocity.

Furthermore, Newton even repeats Galileo's assumption that the final answers to the mechanistic problems will depend upon understanding the causes of the motion of the insensible particles of nature, as he states in his Preface to the
Principia
:

I wish we could derive the rest of the phenomena of Nature by the same kind of reasoning from mechanical principles, for I am induced by many reasons to suspect that they may all depend upon certain forces by which the
particles of bodies
, by some causes hither to unknown, are either mutually impelled towards one another, and cohere in regular figures, or are repelled and recede from one another. These forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to this or some truer method philosophy. (p. xviii; italics added)

As he will later add in the
Opticks
: “There are therefore Agents in Nature able to make the Particles of Bodies stick together by very strong Attractions. And it is the Business of experimental philosophy to find them out” (p. 394). What a prescient statement! Perhaps influenced by Boyle's experiments to determine the constituents of water, he even suggests that by probing bodies with rays of light one might determine the size of the inherent particles. Indeed, it was due to following a similar method in the following centuries that led to the discovery of the negatively charged electron, positively charged proton, and neutrally charged neutron that would explain these attractions and repulsions, along with the atomic structure of molecules.

He begins Book I with precise definitions of concepts we now understand as ‘mass,' ‘inertia,' ‘acceleration,' and ‘centripetal force,' followed by a S
CHOLIUM
defining his conceptions of time, space, and motion: “Absolute, true, and mathematical time,” “Absolute space,” “Place as a part of space which a body takes up . . . either absolute or relative,” “Absolute motion” as the “translation of a body from one absolute place into another; and relative motion, the translation from the relative place into another” (pp. 6–7). Interestingly, his motivation in adopting these absolutes was to support belief in God. As he wrote to the Reverend Richard Bentley: “When I wrote my treatise about our Systeme . . . I had an eye upon such Principles as might work w
^th
considering men for the beleife of a Deity . . .” (Westfall, p. 441).

The evidence and arguments for these absolute conceptions seem reasonable enough at first glance, but even Newton's justification of absolute motion in relation to absolute space appears somewhat contrived. As proof of absolute motion Newton depicts a bucket half filed with water attached to a strong, lengthy rope, the surface of the water remaining flat when the rope is unwound. But when twisted and then allowed to untwist causing the bucket to rotate, the water begins to rise at the inner sides of the vessel forming a concave shape. Newton inferred from this that the “ascent of the water shows its endeavor to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, becomes known, and may be measured by this endeavor” (
Principia
, Vol. I, p. 10).

Thus, owing to Newton, space and time were considered absolute until the Michelson-Morely experiments in 1887 and Einstein's special theory of relativity in 1905 proved that all temporal and spatial measurements, such as the simultaneity of events, were relative depending on the respective positions, velocities, and strength of the gravitational forces of the measurer and what is measured. The one exception was the constant velocity of light also regarded as the ultimate limiting velocity.

Continuing our discussion of the
Principia,
the definitions in the S
CHOLIUM
are followed by his presentation of the A
XIOMS
, or L
AWS OF
M
OTION
some of which continue to be valid to this day (within certain limits) followed by six C
OROLLARIES
and another S
CHOLIUM
discussing Galileo's law of free fall. This takes us to
Book One,
T
HE
M
OTION OF
B
ODIES
, consisting of several hundred pages of complex geometrical diagrams and discussions of the mathematical relations pertaining to the various kinds of celestial and terrestrial motions. Though his supporting diagrams are usually geometrical, he occasionally uses his theory of fluxions or differential calculus when discussing magnitudes approaching “vanishing limits” or zero: for example, when explaining Aristotle's problem as to how there can be instantaneous velocities that imply motion in durationless intervals.

Newton explained this with his fluxions by showing how the rate of a dependent variables, such velocity or distance, can vanish as the independent variable, such as time becomes zero as in the differential equation ds/dt, where s stands for speed, d for distance and t for time. He also used his fluxions when he demonstrates how the attractive gravitating force of the nearest massive object deflects planetary bodies from circular to elliptical orbits permitting the deduction of the exact ratios of the distances, forces, and velocities to produce Kepler's three laws.

The second book of Volume I consists of nine sections analyzing the effects of different media on the motions of bodies along with their ratios, such as the properties of the particles in fluids affecting their fluidity as had been investigated by Boyle; the effect of air on the motion of pendulums; and how oscillating bodies in general are affected by the compression of air and the density of fluids. Though only a brief account of the scope, originality, and complexity of his investigations, it should be sufficient to convey the extraordinary range and depth of his thinking.

Turning to Volume II containing Book III of the
Principia
, including the subtitled T
HE
S
YSTEM OF THE
W
ORLD
(the title that was the basis of Hooke's charge of plagiarism because it duplicated the title he had used for one of his early works and that brought on a lasting contention), Newton originally intended it to be a nonmathematical popularization of his scientific achievements, but finally presented it in his usual mathematical rigor to avoid controversy by those unable to comprehend the mathematics. As he wrote in the introductory paragraph:

In the preceding books I have laid down the principles of philosophy; principles not philosophical but mathematical: such, namely, as we may build our reasoning upon in philosophical inquiries. . . . It remains that, from the same principles, I now demonstrate the frame of the System of the World. Upon this subject I had, indeed, composed the third Book in a popular method, that it might be read by many; but afterwards, considering that such as had not sufficiently entered into the principles could not easily discern the strength of the consequences, nor lay aside the prejudices to which they had been many years accustomed, therefore, to prevent the disputes which might be raised upon such accounts, I chose to reduce the substance of this Book into the form of Propositions (in the mathematical way), which should be read by those only who had first made themselves masters of the principles in the preceding Books. . . .
³⁵

In insisting that his principles of philosophy be mathematical and not merely philosophical he was distinguishing himself from Aristotle and Descartes, but following Kepler, Galileo, Huygens, Hooke, and the future tradition of science. This is followed by his list of the four R
ULES OF
R
EASONING IN
P
HILOSOPHY
which again are nearly identical to those stated previously by Galileo.

Rule I: “
We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearance.
”
. . .
Rule II: “
Therefore to the same natural effect we must, as far as possible, assign the same causes.
”
. . .
Rule III: “
The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.
”
. . .
Rule IV: “
In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.
” (pp. 398–440)

However, he was not always consistent in following his own strict rules of reasoning. At the end of the G
ENERAL
S
CHOLIUM
in Book III, he states that

hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. (p. 547)

Yet in the following paragraph he introduces the hypothesis of a “subtle spirit” pervading all bodies to explain gravity, motion, and all kinds of interactions in contradiction to his previous objections.

And now we might add something concerning a certain most subtle spirit which pervades and lies hid in all gross bodies; by the force and action of which spirit the particles of bodies attract one another at near distances, and cohere, if contiguous; and electric bodies operate to greater distances, as well repelling as attracting the neighboring corpuscles; and light is emitted, reflected, refracted, inflected, and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain to the muscles. But these are things that cannot be explained in a few words, nor are we furnished with the sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit operates. (p. 547)