December 14, 2009
This is a pretty worthless collection of unoriginal essays committing several basic staple errors of poor historical scholarship. I shall give a few illustrations of the author's blatant prejudice and lack of understanding.
Newton's proof of the law of ellipses "catches the eye of the present-day reader" since "there are no differential equations at all." "Rather he proceeds in the opposite direction and solves the inverse problem: given ... an ellipse, he shows that if the center of attraction is at the focus, the centripetal force must decrease with the square of the distance" (p. 59), and then he deduces the direct problem as a corollary.
A more modern-looking, analytic solution to the direct problem was supplied by Bernoulli. "Newton ... had always started from the geometry of the problem---a curve, a surface or a streamline, etc. In contrast, here [in Bernoulli] the starting point is provided by the dynamic concepts---the energy, the force, the angular momentum." (p. 130)
Bernoulli's step is hailed by Speiser as "great progress" (p. 130), "a turning point" (p. 130), a "major step ... that cannot be overestimated" (p. 108), etc. This is a textbook example of the ignorant nonsense produced by second-rate historians who are looking for precursors of modern ideas.
The supposed "progress" made by Bernoulli consists in that "this starting point leads to much more powerful and general methods" (p. 130). But as Speiser himself admits, "Bernoulli does not pursue these possibilities. It cannot even be said that he had clearly grasped the potential." (p. 130). Well then wasn't the "great progress" that "cannot be overestimated" actually made by those who did in fact pursue these possibilities and did in fact grasp their potential?
A contemporary source gives a more intelligent evaluation of Bernoulli's alleged "progress": "I am amused by his impudence ... He has with a great deal of labour showed that the curve described must be a Conick-Section ... But after all, Newton ... has given us a demonstration ... in three lines, where Bernoulli employs 7 or 8 pages." (Keill, quoted from Guicciardini, Reading the Principia, p. 230)
But let us pretend for the sake of argument that the differential equations approach to dynamics was somehow profoundly important (even though Bernoulli did not achieve anything new by its use). Even so, there is no reason to single out Bernoulli as supplying the "insight" on which "all further progress in mechanics is based" (p. 108). For the so-called "insight" was a pretty trivial idea at the time. In particular, this "insight" was of course clear to Newton, who used it in private (see Guicciardini, Reading the Principia, §4.5) but chose not to publish since there was nothing this method could do that could not be done more elegantly by other means.
Another example of mistaken hero-worship occurs in the case of Galileo. Here again we find very ignorant precursor-nonsense:
"The parabola was already known to Apollonius, who many centuries earlier had interpreted it as a section of a cone. But the novelty introduced by Galileo was to lay it out in a grid, thus opening ante litteram the use of Cartesian coordinates." (p. 35)
This alleged "novelty" is in fact nothing but one of the most elementary propositions of Apollonius's Conics.
This is not the only mistake caused by Speiser's failure to realise that Galileo was a mathematical dilettante. For example, after noting one of Galileo's many errors of elementary mathematics, Speiser claims that it "simply reflects the lack of mathematical competence of his times" (p. 27). There was nothing wrong with "his times": there were probably hundreds of competent mathematicians who could have handled this type of problem. The incompetence resides with Galileo, and Galileo alone.
Here is another example of the extravagant measures people must resort to in order to protect the myth of Galileo the mathematician:
"Should we perhaps agree with Panofsky that Galileo's most serious error, that is, his tenacious refusal of Keplerian ellipses, was due to his Renaissance admiration for the perfection of the circle, while the ellipse, the child of Mannerism, was despised?" (p. 23)
No, we should not agree. A much more plausible theory (amply supported by evidence, unlike this whimsy speculation) is that Galileo rejected ellipses because he could not handle the mathematics involved.
Yet more ignorant precursor-nonsense is provided in the case of Descartes:
"Descartes is not among the founders of the theory of gravitation ... but he does have an important place indeed ... in the prehistory of the solar system [because,] as we know today, a vortical motion is, in addition to gravitation, somehow responsible for the formation of the solar system as well. ... It was Descartes, and not Newton, who sensed the importance of the alignment of the planetary orbits and took the first step in what proved to be ... the right direction, even if he was not aware of the true significance of this step." (p. 121)
Again this is so stupid on so many levels. Even putting aside the childish nonsense that some fluky, far-fetched pseudo-affinity with modern theories confers on a scientist "an important place indeed," this passage is still incompetent since Kepler placed very great emphasis on this very idea many years before Descartes.