Re: more squiggly lines

["J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>]

Gunnar,
      I don't think that I want to get into the philosophy/
epistemology debate here.  But, all you have shown
here is that Newton was aware of the "three body
problem," a deep problem in Newtonian mechanics
that he failed to solve and understood that he had
failed to solve.  Its "solution" ("description," "explanation"?)
came with Poincare in 1890, and involved the discovery/
invention of qualitative differential equations, as well as
of chaos theory, although that name would not be applied
to it until the 1970s.
Barkley Rosser
----- Original Message -----
From: "Gunnar Tomasson" <gunnar.tomasson@xxxxxxxxxxx>
To: <pkt@xxxxxxxxxxxxxxxx>
Sent: Tuesday, July 30, 2002 11:15 AM
Subject: Re: more squiggly lines


> Alan:
>
> Re. the following:
>
> > On Mon, 29 Jul 2002 18:07:31 -0400 Gunnar Tomasson
> <gunnar.tomasson@xxxxxxxxxxx> wrote:
> > > My offer stands:
> >
> > >>> I shall be pleased to respond to any substantive comment you may
have
> on
> > > my
> > >>> proposition that Newton's Equations were, are, and will ever remain
> > >>> DESCRIPTIVE - that is, NON-EXPLANATORY - of observed orbital
> mechanics.
> >
> >
> > But you are not pleased to do so. I said:
> >     So perhaps you are claiming merely that some
> >     descriptions are not explanatory and that while Newton felt himself
to
> >     be both explaining and describing planetary motion, you know better:
> >     he was really giving *only* a description.
>
> Newton "felt himself to be" doing no such thing - for, as detailed by one
of
> his modern biographers, Gale Christianson, the record "tend[s] to prove
that
> Newton never believed his natural philosophy had been brought to a
> satisfactory end, a painful thought, which he carried with him to the
> grave."  ('In the Presence of the Creator', The Free Press, New York,
1984,
> p. 570)
>
> Indeed, Newton kept working on the Moon's orbital mechanics until his
final
> days.  Alas, we don't know why Newton was concerned that his Principia
work
> was unsatisfactory - apparently, Newton's working papers on the subject
> matter did not survive along with his voluminous working papers on
biblical
> prophecy etc. which Keynes would later acquire and study.
>
> Considering Newton's towering ego and contempt for "second inventors", I
> have long suspected that these working papers were committed to the flames
> when, on one of his "progressively rarer visits" to the Mint in London,
> Newton "burned several boxes of papers, the unknown contents of which have
> troubled the sleep of Newton scholars ever since." (Op. cit., p. 574)
>
> Why Newton's concern?
>
> We will never know - but as one who claimed to abide by that "rule of
> reasoning in philosophy" which demands that "We are certainly not to
> relinquish the evidence of experiments for the sake of dreams and vain
> fictions of our own devising; nor are we to recede from the analogy of
> Nature, which is wont to be simple, and always consonant to itself,"
Newton
> could not have been oblivious to his own blatant violation thereof in his
> work on the Moon's orbital mechanics, as reflected, inter alia, in the
> following commentary at the outset of Book Three of Principia:
>
> After elaborating the mathematical fine points of his 'Proposition 4.
> Theorem 4', which holds "That the moon gravitates towards the earth, and
by
> the force of gravity is continually drawn off from a rectilinear motion,
and
> retained in its orbit," Newton effectively acknowledged that, in this
case,
> he had NOT abided by "the analogy of Nature" aspect -
>
> "This calculus is founded on the hypothesis of the EARTH'S STANDING
STILL,"
> Newton wrote and proceeded directly to a mathematical argument which he
> prefaced as follows: "for if both EARTH and moon MOVE about the sun, and
at
> the same time ABOUT THEIR COMMON CENTRE OF GRAVITY...."
>
> Hence my conclusion:
>
> Equations predicated on the COUNTER-FACTUAL pre-supposition of "the
Earth's
> standing still" - rather than moving about the Earth-Moon System's center
of
> gravity - cannot in principle be EXPLANATORY of the true physical FACTS
> involved.
>
> Gunnar
>
>
> ----- Original Message -----
> From: "Alan G Isaac" <aisaac@xxxxxxxxxxxx>
> To: <pkt@xxxxxxxxxxxxxxxx>
> Sent: Monday, July 29, 2002 10:15 PM
> Subject: Re: more squiggly lines
>
>
>
>