From: D. F. Siemens, Jr. <dfsiemensjr@juno.com>

Date: Tue Apr 26 2005 - 14:51:23 EDT

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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