Letter, Physics Today: Hooke, Newton, and the Trials of Historical Examination
From: Sam Wormley (swormley1_at_mchsi.com)
Date: 08/18/04
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Date: Wed, 18 Aug 2004 22:12:03 GMT
Ref: http://www.physicstoday.org/vol-57/iss-8/p19.html
Hooke, Newton, and the Trials of Historical Examination
The February 2004 issue of Physics Today included a letter (page 13)
in which Michael Nauenberg criticized my book Meanest Foundations and
Nobler Superstructures: Hooke, Newton and the Compounding of the
Celestiall Motions of the Planetts (Kluwer, 2002). The book is a study
of a most consequential episode in the history of celestial mechanics:
Robert Hooke's proposal to "compoun[d] the celestial motions of the
planets of a direct motion by the tangent & an attractive motion
towards a central body," which he submitted to Isaac Newton in a
short, intense correspondence during the winter of 1679−80 to be
realized in Newton's Principia.
The historiography of science has recently escaped somewhat the
boundaries of academic esoterics to gain a new amateur readership;
Nauenberg's letter represents an approach prevalent among that welcome
new audience. Therefore, I thought it appropriate to point out some
examples in which he misunderstands my arguments and the primary
texts. A more detailed reply to his letter is forthcoming in the
journal Early Science and Medicine.
My book analyzes Hooke's construction of his very original concept of
bending heavenly rectilinear motion into a curved trajectory and
demonstrates that Hooke developed his notion of "inflection" within
the framework of practical optics. Nauenberg argues that "Hooke
explicitly rejected the optical analogy [for] the '[b]ending' of the
motion of planets." This is exactly the reason why I use terms like
"construct" and "develop": There was no optical analogy for Hooke to
discover and follow. Rather, "inflection" is a concept Hooke produced
by purposeful manipulation of existing resources, utilizing aspects he
found useful, such as the continuous change of direction, and
discarding other aspects, like the reference to medium.
Nauenberg claims that I aver "without justification that the 'novelty
of De Motu thus encapsulated [Newton's] willingness to represent
forced motions by closed curves.' " On the contrary, my statement is a
conclusion of a straightforward historical narrative (much of my
chapter 3) in which I attempted to answer the following question: Why
did Newton—and René Descartes, Christiaan Huygens, and
others—not develop a scheme of planetary motions similar to
Hooke's, in which central attraction "inflects" the inertial
rectilinear motion of the planet into a closed orbit?
When Hooke finally introduced his "Programme" in 1666, it was a
complete novelty, and he struggled another 15 years before Newton or
anyone else appreciated its significance. I discovered, to my
surprise, that a closed curve orbit created by force had simply been
inconceivable for even the most innovative of his peers. Prior to
Hooke's program, all models of planetary orbits (circulating slings,
rolling balls, conical pendulums, and so forth) either assumed a
circular cause—a rotating sun (Kepler for the planets) or
turning hand (Descartes for the sling)—or simply posited a
circular and force-free motion (Newton and Huygens).
It is here that my work distinguishes itself from Nauenberg's: The
difference between what Newton should have realized and what he
actually did, between what is formally trivial in hindsight and what
was self evident in his day, is the historian's starting point.
Nauenberg is completely right in that Newton did develop "a
sophisticated mathematical theory of orbital motion," but only in his
1684 De Motu. Time, for the historian, is of the essence. The cause
must precede its effect, and the "sophisticated mathematical theory"
and the description of orbital curves could have accounted for
Newton's 1679−80 words to Hooke only if they were extant
beforehand.
Nauenberg concludes by claiming that "both Hooke and Newton had a very
similar and quite modern approach." "Modern approach," however, is
hopelessly vague. If Nauenberg wishes to express empathy with the work
of two 17th-century natural philosophers, that is
commendable—provided one keeps in mind that Hooke and Newton
were not attempting to meet our standards, but it is rather we who
emulate theirs. If he means that Hooke and Newton were closer to us in
their treatment of natural phenomena than most of their contemporaries
were, he is right—that is what places them in the canon of the
history of science. If he means that they were closer to us than to
their contemporaries, he is wrong: Hooke and Newton were 17th-century
natural philosophers, and their interests, skills, motivations,
approaches, and audience were of that era.
However, if Nauenberg simply means that Hooke's and Newton's ways of
creating knowledge are more similar than different, he is gloriously
right. Indeed, I am rather baffled by Nauenberg's mentioning "Gal's
argument that Hooke's scientific style was 'radically different from
Newton's.' " My book definitely contained no such argument and no such
phrase. Here, precisely, is the main message of my book: that the
works of the "genius mathematician" and the "ingenious technician" are
similar in ways far more interesting than their differences. If that
is all Nauenberg or any reader learns from Meanest Foundations and
Nobler Superstructures, then, to quote Hooke one last time, "I am
abundantly satisfied."
Ofer Gal
(ofer@science.usyd.edu.au)
University of Sydney
Sydney, Australia
Nauenberg replies: Ofer Gal writes that he discovered, to his
surprise, that "a closed curve orbit created by force had simply been
inconceivable" to Isaac Newton before Newton finally learned about the
idea from Robert Hooke. But ample historical evidence indicates that
Gal's opinion is incorrect. For example, in a cryptic remark written
in his notebook 15 years before his 1679 correspondence with Hooke,
Newton stated that "if the body moved in an Ellipsis, then the force
in each point . . . may be found."1
In another manuscript, composed before his appointment as the Lucasian
chair in mathematics in 1669 at Cambridge University, Newton found
that "the force of gravity [at Earth's surface] is 4000 times and more
greater than the endeavor of the Moon to recede from the Earth."2 The
discrepancy between Newton's figure and the correct value of
approximately 3600 (according to the inverse square law) resulted from
the erroneous estimate that he used for Earth's radius.
Apparently, Newton did not discover his error until shortly before
starting to write the Principia. By applying Kepler's third
law—that for the "primary planets the cubes of their distances
from the Sun are reciprocally as the square of the number of
revolutions in a given time"—Newton had found that his
apparently failed assumption that Earth's gravitational force
satisfies the inverse square law did apply to the gravitational force
of the Sun. He wrote that "the endeavours [of the planets] of receding
from the Sun will be reciprocally as the squares of the distances from
the Sun."3
By insisting that Newton did not develop a "sophisticated mathematical
theory of orbital motion" before 1684, Gal indicates that he cannot
understand the subtle mathematical results about orbital dynamics that
Newton had exposed in his 13 December 1679 letter to Hooke.
Acknowledging those results, however, would invalidate Gal's arguments
of what Newton learned about orbital dynamics from his correspondence
with Hooke.
References
1. J. Herivel, The Background to Newton's Principia, Clarendon Press, Oxford,
England (1965), p. 130.
2. Ref. 1, p. 196.
3. Ref. 1, p. 197.
Michael Nauenberg
University of California, Santa Cruz
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