Re: [gang8] General [?] Theory [Was: Re: Quo Vadis 2003? -

[Ben Day <day@xxxxxxxxxxxxxx>]

At 11:16 PM 1/1/2003 -0500, Gunnar Tomasson wrote:
> I don't understand the proposition that "restrictive axioms" - whatever they
> may be - have a bearing on the distinction between the Newtonian and
> Einsteinian theories of gravity.
>
> Nor do I understand how Keynes might have squared this notion with
> Einstein's own statement in 1919:
>
> "Let no one suppose, however, that the mighty work of Newton can really be
> superseded by this [General Relativity] or any other theory.  His great and
> lucid ideas will retain their unique significance for all time as the
> foundation of our whole modern conceptual structure in the sphere of natural
> philosophy."
>
> Please explain.
>
> Gunnar

Gunnar - I think the point is that Keynes's intention in titling the
"General Theory" was not to claim that it was somehow an ahistorical, or
transhistorical document, suitable for all times and places.  He was
arguing rather that classical theory, by abstracting away money through the
assumption of neutrality, would have to generate additional ad hoc
explanations for "aberrant" phenomena like non-clearing markets and the
underemployment of resources.  When we abandon monetary neutrality, though,
many of these phenomena cease to appear as aberrations.  The General Theory
is more general than classical theory because we can encompass a broader
range of real world events without resorting to additional ad hoc models -
an operation which at the same time requires tacking on limiting clauses
("restrictive axioms") to the central edifice (for example, markets clear
/except/ when such-and-such conditions pertain, in which case we must
resort to a different model). It's entirely possible, though, for Keynes's
model to be more general than classical theory without being "ultimately"
general in the sense that it can explain /all/ real world phenomena without
need for limiting clauses.  Only in this latter case, I think, would Keynes
deserve James's lacerations (that Keynes was being "presumptuous" in his
choice of title, since it doesn't apply to all times and places). I think
James would have a difficult time supporting this attribution to Keynes,
though.

The parallel with General Relativity is not perfect, but clear
enough.  When we interact with objects moving at relatively slow speeds -
and "slow'" here encompasses almost everything until we approach the speed
of light - the world will behave /very/ much like the Newtonian model tells
us it would.  Only when objects approach the speed of light relative to us,
do they begin behaving significantly differently.  And it was precisely the
experience of misbehaving fast-moving objects - in labs, not everyday life
- that prompted Einstein to develop the theory of general relativity (e.g.
fast-moving molecules travelling further distances than they should be able
to, given their life span). So, although the world never actually behaves
like the Newtonian world says it will, the more we abstract from relative
motion, the closer the world resembles that of Newton's model.  One can at
least see a family resemblance to the classical abstraction from monetary
effects. Under the theory of general relativity, one doesn't have to
generate ad hoc explanations for things "misbehaving" by Newtonian standards.

-----Ben