sci.physics.electromag

On Mar 21, 6:53=A0pm, "Robert J. Kolker" wrote:
> maxwell wrote:
>
> > Sorry, Fred, not even 'real' numbers are real.
>
> True. But without Platonic Real numbers we would not have physics, would
> we? =A0Physics cannot be done without mathematics. Mathematics is
> necwssary (but not sufficient).
>
> Bob Kolker
Robert, you are falling into the trap that desCartes unwittingly set
when he defined 'real' numbers to link geometry (the perfect
abstraction) with the CONCEPT of numbers. Prior to this (pre-1600) it
was recognized that geometry was only about relationships, including
greater-than or equal. Positive integers were associated with the
RESULTS of the COUNTING operation. In general, mathematics remains
linked to reality when its operations are mapped to real verbs, i.e.
verbs describing ACTIVITY in the real world. The danger is when this
activity is viewed as real nouns (that is, gerunds, like Count =3D
Counting). Nouns can reference real existents, in which case they can
be said to be referring to real THINGS, the rest are abstractions (our
higher level of language). It is still possible to construct finite
mathematics in terms of integers (see Kronecker). Repeating decimal
numbers can be useful when the series of terms is finite but this
would remove the magical allure of the infinite that has mesmerized
mathematicians since Pythagoras.