exerpt on Ptolemy

[thejohnlreed]

Where Wigner noted the "uncanny" usefulness of mathematics, I noted
that the usefulness remains, regardless of the veracity of our a
priori assumptions. As an example, first consider the Ptolemaic, earth
centered model of the solar system. The sole quantitative connection
to the real universe, in this "still useful" model, is the efficient,
least action, time-space property, attendant to each of the otherwise
contrived, circular, cyclic and epi-cyclic orbits. A circle is an
efficient enclosure of area. Equal arc lengths will radially enclose
equal areas of the circle. This is an efficient area enclosing
property of the circle itself. It is consistent with Kepler's law of
areas which law would be redundant in the case of perfectly circular
orbits. With the circle it is the circumference arc and its radially
enclosed area. In the orbit it is the time interval of the orbit and
its radially enclosed area. The law of areas is a function involving
time and space. It is a least action function. So Ptolemy constructed
several imaginary mathematical circles upon circles to match the time
space function of the real orbits. The least action aspect of the
mathematics in describing the least action aspects of stable universe
systems, assured his success. Imagine it otherwise.

The Ptolemaic model shows that accurate mathematical predictions serve
us to a limited operational extent, but provide no absolute basis for
an accurate conceptual view. Viewed through the clearer lens of
hindsight, here, we can see that our conceptual questions must be
framed correctly, prior to selecting the mathematical model. Must we
frame our conceptual questions any less correctly today?

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