Re: definition of science

From: D. F. Siemens, Jr. <dfsiemensjr@juno.com>
Date: Tue Apr 26 2005 - 14:51:23 EDT

That mathematical calculi should apply to empirical matters is surprising
only if one does not recognize their nature, which is the same in this
regard as that of logical calculi. Both are empirically empty but present
necessary connections. If the logical or mathematical variables (terms)
match the empirical ones closely enough, then the formal connections will
represent the empirical ones reasonably. There is not an exact match, for
the gapless continuum cannot exist in a "granular" universe of atoms,
quarks, electrons and photons. But the numerical applies down to the
physical limit.

There is a restriction in the application of any formal calculus to
"reality." There has to be a match. Aristotelian logic cannot be used for
items that exhibit degrees, for example. Statistics can deal with matters
where a simple true-false doesn't work. Still, correlation measures are
often misapplied, usually measures appropriate to ratios are used for
ranked data. The formulas are as easily calculated to produce nonsense as
to retain relevance. I recall hearing, some 3 decades ago, that a stat
prof required his students to present six misuses of statistical measures
in peer-reviewed publications. Some universities require that
experimental designs be checked by a statistician before being
implemented.

Obviously, not all calculi can be applied. Einstein required a Riemannian
metric. Current measurements indicate that the universe is flat, i.e.,
Euclidean. I do not recall encountering an application of Lobachevskian
geometry. Also, applications differ. I recall ignoring imaginary roots
that emerged from word problems in high school algebra, but physicists
find them relevant in electromagnetic theory. "Imaginary" popularly
equates to "nonexistent," but not always. One may need to change outlooks
radically to discern the "obvious."
Dave

On Tue, 26 Apr 2005 06:51:45 -0700 "Don Winterstein"
<dfwinterstein@msn.com> writes:
Dave Siemens wrote:

"...Many mathematicians are persuaded that they
discover rather than construct such relationships...."

Many mathematicians indeed believe their results somehow exist
independently of human minds and are discovered rather than invented, but
they continue to recognize that these results involve symbols exclusively
and not objects of the physical world. Some of the mathematicians I've
talked with have been horrified to think that their beautiful
relationships might be considered for application to real world problems!
 There is a lot of math that as yet has no application to the physical
world.

The surprising thing to many physicists, formerly also A. Einstein, is
how well certain physical relationships are described by certain math
relationships. So there seems to be some deep connection between the
world of pure symbol (math) and the physical world. ("God is a
mathematician.") This connection underlies our ability to understand our
world, especially as we expand the math meaning of symbol to include
word, concept or idea. That some physical relations are accurately
described by abstract math relations tantalizingly supports the idea that
human understanding is sometimes close to absolute understanding and
hence more than just metaphor.

Don
Received on Tue Apr 26 15:05:33 2005

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