Re: Occam's Razor

["Gunnar Tomasson" <gunnar.tomasson@xxxxxxxxxxx>]

Paul:

Just a brief comment re. the following:

I wrote:

> >I also submit that my following suggestion accords with Hilbert's point
B:
> >
> > > >Indeed, as indicated by Einstein's comments on the General Theory's
> >"logical
> >> >completeness," remove one axiom and the whole axiomatic structure
> >("theory")
> >> >reduces to incoherence.

You responded:

> Because Einstein's General Theory contains fewer axioms -- if it is the
most
> general theory conceivable then it is true that removing one axiom from
its
> foundation reduces it to incoherence!!

Comment:

As indicated by the following remarks by Leopold Infeld (Einstein's
long-time collaborator and co-author), it is flat out wrong to suggest that
the General Theory "contains fewer axioms" than Newton's (classical) theory:

"The classical physicists thought about our physical space as a
three-dimensional Euclidean continuum, our physical time as a
one-dimensional continuum common to all observers, whether in relative
motion or not.  These concepts were changed completely when Einstein, in
1905, formulated the special theory of relativity.  The physicist learned
that, in ordering physical events, it is much more convenient and simple to
consider a four-dimensional pseudo-Euclidean time-space continuum as the
background for these events.  Then, in 1914, he had to learn again that, in
order to understand the phenomenon of gravitation, he must generalize his
concepts once more.  In the general theory of relativity, the universe is
represented by a four-dimensional manifold, its metric shaped by masses,
their motion and radiation; far from masses and sources of energy, this
Riemannian space-time continuum more and more closely approaches the
pseudo-Euclidean space-time continuum of the special theory of relativity."
('On the Structure of our Universe', in 'Albert Einstein,
Philosopher-Scientist', The Library of Living Philosophers, Open Court,
Cambridge University Press, Third Edition, 1988,  pp. 477-478)

Where the classical theory had the twin axioms of Space as three-dimensional
Euclidean continuum, and Time as one-dimensional continuum, Einstein's
General Theory is predicated on the Four-dimensional pseudo-Euclidean
time-space of Special Relativity become four-dimensional manifold whose
metric, being a function of  masses, their motion, and radiation, spans the
spectrum from Black-Hole singularity to the pseudo-Euclidean space-time
continuum of Special Relativity.

Apply Occam's Razor, and General Relativity must yield to
Classical/Newtonian Theory!

Gunnar

----- Original Message -----
From: "pdavidso" <pdavidso@xxxxxxx>
To: "Gunnar Tomasson" <gunnar.tomasson@xxxxxxxxxxx>
Cc: <pkt@xxxxxxxxxxxxxxxx>
Sent: Wednesday, January 29, 2003 1:57 PM
Subject: RE: Occam's Razor


> >===== Original Message From Gunnar Tomasson <gunnar.tomasson@xxxxxxxxxxx>
> =====
> >
> >I submit that my following proposition accords with Hilbert's point A:
> >
> >> >If, as I suggest, axiomatic structures become Theorems X, Y, and Z are
> >> >"non-overlapping" in the sense that the rules/games of (a) Chess, (b)
> >> >Contract Bridge, and (c) Gin Rummy may be said to be so, then the
number
> >of
> >> >axioms is immaterial.
>
> There are no rules (axioms that are common to Chess and to Bridge -- so I
do
> not see the relevance of your comments.
> >
> >You comment on my proposition as follows:
> >
> >> I am sorry to say but these comments below are irrelevant. If Theories
X,
> >Y,
> >> and Z do not share any common axioms then your point is correct --BUT
> >> our discussion requires the recognition that all economic theories
share
> >some
> >> common axiooms. It is not that on the first Monday economics is a game
of
> >> bridge, on Tuesdays it is a game of gin rummy; on wednesday --
blackjack,
> >etc,
> >> Or ar you arguing that the rules of the economicgame change every day?
> >
> >I disagree - Hilbert's point A applies to (X) Newton's Gravitational
Model;
> >(Y) Einstein's Gravitational Model/General Relativity; and (Z) any
would-be
> >Quantum Mechanical Model of Gravity all of which "share" or have in
"common"
> >the "field" axiom.
> >
>
> Notice you have three models all oabout gravity.  Einstein's called his
theory
> the GENERAL theory of relativity because it required less axioms than
> Newton's.
>
> Moreover, bioth Lord Robert Skidelsky (Keynes's biograpgher) and Jamie
> Galbraith a have written that it is not accidental that the first three
words
> in the title of Keynes's 1936 book mimics Einstein's first three words in
his
> monumental work -- for both of them were able to explain more things in
there
> theory by invoking fewer restrictive axioms.  If you do not belikeve this
you
> should read Keynes's preface to the German language edition of the General
> Theory -- where Keynes specifically says that he calls his theory general
as
> compared to the classical thoery because it requires "fewer restrictive
> axioms". [ Please note that you must read the German langauge edition to
see
> his quote -- not the english translation of the German edition's preface
in
> CWK.
>
>
>
> >I also submit that my following suggestion accords with Hilbert's point
B:
> >
> > > >Indeed, as indicated by Einstein's comments on the General Theory's
> >"logical
> >> >completeness," remove one axiom and the whole axiomatic structure
> >("theory")
> >> >reduces to incoherence.
>
> Because Einstein's General Theory contains fewer axioms -- if it is the
most
> general theory conceivable then it is true that removing one axiom from
its
> foundation reduces it to incoherence!!
>
>
> >
> >You comment as follows:
> >
> >> Not necessarily as my example of he classical fixity of money wages
> >implies--
> >> IF one removes the fixity assumption, the ergodic axiom [so that
> >uncertainty
> >> is the motivating force behind a demand for liquidity] and the lack of
> >gross
> >> substituion (only) between liquid assets and illiquid products of
> >industry --
> >> while stil permitting gross sunstition among the products of
industry --
> >and
> >> one has a comlete system (with fewer restrictive axioms) showing the
truth
> >of
> >> the possibility of involuntary unemployent. The resulting complete
logical
> >> system known as THE GENERAL THEORY OF EMPLOYMENT INTEREST AND MONEY
> >
> >In response, I submit that Keynes' modus operandi represented "a practice
> >which in the rigorously logical building up of a theory is not
admissible."
>
> Clearly here we differ and communication breaks down between us.  Bu8t I
note
> you do not deny that Keynes's analysis requires fewer restrictive axioms
than
> the classical [neoclassical] theory -- so casting stones of "not
admissible"
> is not relevant IMHO.
>
> Paul
>
> Paul Davidson
> Editor, Journal of Post Keynesian Economics
> University of Tennessee
> SMC 503
> Knoxville, Tennessee 37996-0550
> phone # (561)369-1951; fax #(561)369-1951;
> email pdavidson@xxxxxxx
> http://econ.bus.utk.edu/davidsonextra/Davidson.html
>