Thus spake "
Oh No wrote:

We don't say the Ptolemaic model of
the Solar System is still valid within its "domain of applicability",
do we?

Funnily enough, it is perfectly possible to construct an ellipse from an
infinite sequence of wheels within wheels. This is a generalisation of
the theory of Fourier transforms, so if we so desire, and wish to be
amusing, we are quite entitled to say exactly that.


Brilliant!

I think you have gone quite a ways in proving my contention that, as
with statistics, with mathematics one can "prove" whatever one wants to
prove, or "disprove" whatever one wants to disprove.

This is not true. One can prove that an ellipse can be approximated by a
Ptolomeic system. This does not prove that a Ptolomeic system is
valuable in understanding the motions of the planets.

Not dissimilar mathematics is extremely valuable in other circumstances.
For example, a knowledge of spherical harmonics is essential for
analysing cosmic background radiation.

The thing that
keeps science honest is that nature exists, that we can observe its
properties, that we can predict the results of future observations and
learn whether we are right or wrong. Our understanding of nature can
improve, so long as we are willing to accept nature's verdicts and
learn from them.

By dispensing with mathematics and statistics in the way in which you
have, you also dispense with the methodology by which we do learn
whether we are right or wrong, and actually make it appear as though you
present these fine sentiments as a charade to try and make yourself look
good, while not actually being in the least bit concerned to accept
natures verdicts or learn yourself.



Regards

--
Charles Francis
substitute charles for NotI to email