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Here is a brief follow-up to
"Einstein's Unfinished Revolution" which I posted today to the NKS
Forum.
Gunnar
*****
The
concepts of ?Scientific Theory? and ?The Realm of Science? outlined in my note
of 11/22/03 on ?Einstein?s Unfinished Revolution? and identification of the
latter as the domain of Hermann Weyl?s ?Realistic Mathematics? imply that, just
as Gödel?s Incompleteness Theorem does not apply within that domain, so Stephen
Wolfram?s concept of ?Computational Irreducibility? is inapplicable to ?The
Realm of Science?.
For Wolfram?s concept is predicated on ? and relates
to - what Ludwig Wittgenstein termed ?the illusion that the so-called laws of
nature are the explanations of natural phenomena,? translated into the modern
notion that a ?scientific theory? is to be judged by its PREDICTIVE power alone
rather than by its LOGICAL coherence AND adequacy of its representation of what
Einstein termed its ?empirical contents and their mutual relations? as indicated
by its PREDICTIVE power with respect thereto.
The difference between the
two sets of criteria is reflected in Einstein?s comments on the General Theory
of Relativity cited in the earlier note: ?The chief attraction of the theory
lies in its LOGICAL completeness. If a single one of the conclusions drawn from
it proves wrong, it must be given up; to modify it without destroying the whole
structure seems to be impossible.?
That is to say, the theory?s
representation of empirical phenomena must be judged inadequate on discovery of
a single phenomenon which is not consistent therewith.
Also, as detailed
in my note of 11/8/03 on ?Einstein?s ?Scientific
Testament??, Einstein recognized that the theory?s axiomatic premises themselves
might prove untenable ? this would affect neither its predictive power nor
logical coherence but the adequacy of its axiomatic representation of ?The Realm
of Science?.
The following extract from a draft version of my note of
11/22/03 addresses related issues in less
formal fashion.
THEORY AND PREDICTION
The detailed observations of
Tycho Brahe and Kepler of solar system orbital patterns represented ?the
evidence of experiments? which ?[found] their representation in the conclusions
of [Newton?s] theory.? This fact was
reaffirmed through the discovery in 1846 of Neptune, whose existence had been
signaled by observed perturbations of the orbit of Uranus (discovered in 1781)
which could not be explained on Newtonian principles. Yet, these principles were
later ?falsified? when non-Newtonian aspects of Mercury?s orbit, which had been
construed to signal the existence of an inner planet (Vulcan), were instead
judged to reflect ?relativistic? effects.
By the same token, the fact
that ?the evidence of experiments? on Mercury?s orbital pattern accords with the
General Theory of Relativity is no warrant in logic for using ?the conclusions
of [Einstein?s] theory? as presumptive evidence of the existence of
never-observed aspects of the Cosmos such as Black Holes and Big Bang
Creation.
It is ?vain fiction? to suggest otherwise; for, as Einstein
once observed, ?as far as the propositions of mathematics refer to reality, they
are not certain; and as far as they are certain, they do not refer to reality.?
(?Geometry and Experience?, lecture 1921, reprinted in ?Ideas and Opinions?,
Dell/Laurel Paperback, 1976, p. 228)
In the field of particle physics,
Pauli?s ?prediction? in 1931 of the yet-to-be-discovered neutrino within the
conceptual framework of the Standard Model mirrored that of the planet Neptune
within the Newtonian Model of solar system orbital mechanics ? yet, the Standard
Model breaks down with respect to whatever ?Vulcan? phenomena may be encountered
at scales smaller than that of the Planck Length.
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