Isaac Newton (28 page)

20
. Even seventy years later, one of the first post-Newtonian calculus texts, John Colson’s 1737
Method of Fluxions and Infinite Series
, broached the dangerous and unfamiliar topic this way: “… that quantity is
infinitely divisible
, or that it may (
mentally
at least)
so far
continually diminish, as at last, before it is
totally
extinguished, to arrive at quantities which may be called
vanishing
quantities, or which are
infinitely little
, and less than any
assignable
quantity.…” In Cohen and Westfall,
Newton: Texts
, p. 400.

21
. “Of Quantity,”
Questiones
, p. 5;
Math
I: 89.

22
.
Questiones
; cf.
Math
I: 90, n. 8.

23
. Galileo,
Discorsi
.

24
.
Math
I: 280.

25
. Ibid., 282.

26
. Ibid., 302 and 305.

27
.
Questiones
, p. 10.

28
.
Questiones
, p. 68.

29
. Cf.
Math
I: 377; Michael Mahoney, “The Mathematical Realm of Nature,” in Garber and Ayers,
Cambridge History of Seventeenth-Century Philosophy
, p. 725.

30
.
Math
I: 29.

31
. “To find the velocitys of bodys by the lines they describe.”
Math
I: 382.

32
.
Math
I: 273.

33
. Much later he recalled: “When I am investigating a truth or the solution to a Probleme I use all sorts of approximations and neglect to write down the letter o, but when I am demonstrating a Proposition I always write down the letter o & proceed exactly by the rules of Geometry.” Add MS 3968.41.

34
.
Math
I: 377ff., I: 392ff, and I: 400ff. The tract of October 1666 (Add MS 3958) was published for the first time 296 years later in Hall and Hall,
Unpublished Scientific Papers
, pp. 15–65.

35
.
Math
I: 402.

36
. As Koyré puts it, “To have achieved this transformation is the undying merit of Newton.… Mathematical entities have to be, in some sense, brought nearer to physics, subjected to motion, and viewed not in their ‘being’ but in their ‘becoming’ or in their ‘flux.’ ”
Newtonian Studies
, p. 8.

4: TWO GREAT ORBS

1
. The last authoritative twentieth-century account of the Scientific Revolution, Steven Shapin’s
Scientific Revolution
, began, “There was no such thing as the Scientific Revolution, and this is a book about it.”

2
. Goodstein and Goodstein,
Lost Lecture
, p. 39.

3
. “The appearance of Newton’s
Principia
in 1687 changed all this.… [It] made continued support for Aristotle’s geocentric cosmology untenable. After 1687, medieval cosmology became irrelevant, because it no longer represented even a minimally plausible alternative to Newtonian cosmology. Unlamented, it simply faded away.” Grant,
Planets, Stars, and Orbs
, p. 10.

4
. Yet I. Bernard Cohen sees the Copernican revolution as “a fanciful invention of eighteenth-century historians.” The revolution, Cohen asserts, “was not at all Copernican, but was at best Galilean and Keplerian.”
Revolution in Science
, p.
x
. Meanwhile, Cohen and other scholars suggest that Newton’s reading, wide-sweeping though it became, may have never included Galileo’s
Discorsi
or anything of Kepler. Nor, at his death, did his considerable library contain any work by Ptolemy, Copernicus, or Tycho. Cf. Whiteside in
Math
, VI: 3 n. and 6 n.

5
. Now we say these were the first two of Kepler’s three “laws.” We conventionally date these to 1609, when he published his great work,
Astronomia Nova
. He put forth a notion of gravity, too: “Gravity is the mutual tendency of cognate bodies to join each other (of which kind the magnetic force is).” Nevertheless, by the time of the
Principia, at
the far end of the century, few astronomers accepted Kepler’s ideas as firm truths; nor did Newton, in the
Principia
, see Kepler as a significant precursor. “It seems clear,” I. B. Cohen remarked, “that there was no Keplerian revolution in science before 1687.”
Revolution in Science
, p. 132; Whiteside, “Newton’s Early Thoughts on Planetary Motion,” p. 121; Gjertsen, “Newton’s Success,” in Fauvel et al.,
Let Newton Be!
, p. 25.

6
. Galileo,
The Starry Messenger
, in
Discoveries and Opinions
, pp. 27f.

7
. The only mathematics, except that Galileo declared the moon’s distance to be sixty diameters of the earth—off by a factor of two—and made a brief computation of the height of lunar mountains, declaring (correctly) that they were as high as four miles and (incorrectly) that the earth’s mountains never reached as high as one mile. For a moment, it was easier to see the moon than the earth.

8
. Two years later:
Discourse concerning a New Planet; tending to prove, that it is probable our Earth is one of the Planets
. Wilkins also wrote another book cherished by the young Newton,
Mathematical Magick
.

9
. Wilkins,
Mathematical and Philosophical Works
, pp. 34 and 11.

10
. Bacon, “Of Tribute: Praise of Knowledge,”
Works
VIII: 125.

11
. Bacon,
Novum Organum
, pp. 217 and 260.

12
. Wilkins,
Mathematical and Philosophical Works
, pp. 47, 49, 97, 100, 110–13. For flying to the moon, Wilkins did wonder about the cargo problem: “Nor can we well conceive how a man should be able to carry so much luggage with him, as might serve for his
viaticum
in so tedious a journey.”

13
. Ibid., pp. 4 and 13: “For it is probable that the earth of that other world would fall down to this centre, and so mutually the air and fire here ascend to those regions in the other; which must needs … cause a great disorder.…”

14
. Ibid., pp. 61 and 14.

15
. Ibid., p. 114.

16
. He copied bits of Wilkins into his Grantham notebook (cf. Manuel,
Portrait
, p. 11, and Gjertsen,
Newton Handbook
, p. 612). Wilkins also expounded systems of “secret writing”—how to hide one’s meaning through obscure or invented or encoded characters (
Mercury; or, the Secret Messenger
, 1641). He became a doctor of divinity and a prominent Parliamentarian, married Oliver Cromwell’s sister, and soon after was made Master of Trinity College, a preferment he held only briefly before being ousted upon the restoration of Charles II. He moved to London and became a council member of the new Royal Society.

17
. Herivel,
Background to Newton’s Principia
, p. 67; Add MS 3968.41; Westfall,
Never at Rest
, p. 143.

18
. The river flows from four memoirists in particular: his niece, Catherine Barton; Marton Folkes, vice-president of the Royal Society; Barton’s husband, John Conduitt; and Newton’s first would-be biographer, William Stukeley. “The notion of gravitation came into his mind,” Stukeley wrote (
Memoirs
, p. 20), “… occasion’d by the fall of an apple, as he sat in a contemplative mood.”
   Voltaire related the story first in
An Essay on Epick Poetry
and then in
Letters on England
(p. 75): “Having retired to the country near Cambridge in 1666, he was walking in his garden, saw some fruit falling from a tree, and let himself drift into a profound meditation on this weight, the cause of which all the scientists have vainly sought for so long and about which ordinary people never even suspect there is any mystery.”
   And Conduitt: “Whilst he was musing in a garden it came into his thought that the power of gravity (which brought an apple from the tree to the ground) was not limited to a certain distance from the earth but that this power must extend much farther than was usually thought. Why not as high as the moon said he to himself.…” Keynes MS 130.4.
   The apple story took on an independent life and evolved over centuries. Perhaps its most wonderful feature is how often, by the twentieth century, the apple was supposed to have struck Newton on the head. This may not have been necessary.
   Westfall argues, appealingly (
Never at Rest
, p. 155): “The story vulgarizes universal gravitation by treating it as a bright idea.” Of course! Yet it was a bright idea. We feel this deeply. Surely that’s why the story has so rooted itself in our collective consciousness. The bright idea was a crystallization of a preexisting unconscious knowledge—shared by animals and children—that objects fall to the ground. The bright idea was that this behavior implied a force—to be named and then studied and measured. “A bright idea cannot shape a scientific tradition,” Westfall adds, and this, too, seems self-evident. But it did.

19
. Galileo,
Two New Sciences
, p. 166, quoted in Cohen,
Franklin and Newton
, p. 103.

20
. One detailed set of calculations fills the so-called Vellum Manuscript—the reverse side of a lease. Add MS 3958.45; Herivel,
Background to Newton’s Principia
, pp. 183–191.

21
. Where the “cubit” is the distance from elbow to fingertip. Herivel,
Background to Newton’s Principia
, p. 184.

22
. Thomas Salusbury, 1665.

23
. Herivel,
Background to Newton’s Principia
, p. 186.

24
. “The cubes of their distances from the Sun are reciprocally as the squares of the numbers of revolutions in a given time: the endeavours of receding from the Sun will be reciprocally as the squares of the distances from the Sun.” Add MS 3958, in Herivel,
Background to Newton’s Principia
, p. 197; Westfall,
Never at Rest
, p.152. In the same spirit:
Principia
, Book III, Proposition 10, Corollary 3 and Corollary 5 (first edition), where Newton explicitly considers the sun’s heating of the planets as a function of distance.

25
. This was eventually known as Kepler’s third law, the law of periods.

26
. Herivel,
Background to Newton’s Principia
, p. 141. Descartes had proposed such a principle for bodies both in motion and at rest, though not for circular motion. It still defied people’s intuition about moving objects. “That when a thing lies still, unless somewhat else stir it, it will lie still for ever, is a truth that no man doubts of,” Hobbes wrote in 1651. “But that when a thing is in motion, it will eternally be in motion, unless somewhat else stay it, though the reason be the same (namely, that nothing can change itself), is not so easily assented to.” People get tired and stop moving, so they imagine inanimate objects do, too. “From hence it is that the schools say, heavy bodies fall downwards out of an appetite to rest, and to conserve their nature in that place which is most proper for them.”
Leviathan
, II.

27
. Herivel,
Background to Newton’s Principia
, p. 158.

28
. Ibid., p. 153.

29
. Nor was Latin any better. In trying systematically to define concepts in terms of simpler or more basic concepts, he always reached a wall—a problem of infinite regress. Yet he kept trying. In an undated notebook (Add MS 4003): “The terms
quantity, duration
and
space
are too well known to be susceptible of definition by other words.