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such aI think this began with Boyle, et al, in the 1600's. Prior to this,
then it hasmode of understanding was not even a part of human thinking. Since
Middlebecome the essential feature of every human invention which goes by the
name of quantitative science (and quantitative recreation, etc.).
Bob,
Although I agree with your approach, I would push quantitative
thinking as a test of "validity" back to at least Hipparchus. In the
Ages and before, the Ptolemaic system with it demand of mathematicalsimplicity
precision and the Aristotelian system with its thoroughness and
coexisted. It is Keplier's demand that the paths of the planets fit theaccepted.
theory that establishes the quantitative approach as the one to be
If there is one thing that sets physics apart from the other sciences,it is
the ease with which Nature seems to fit the numbers (i.e. the quantitiesor
things that we measure). If only there was such a singular measure oflearning.
A Mathematician friend of mine would argue that mathematics isnot a
human construct since say a prime number is a prime number no matterwhich
system of mathematics it is found in. I have always like his proposal toof
communicate with other civilizations (al. a. SETI) by sending a sequence
primes like, two, three, five, eleven, thirteen, seventeen, andnineteen,
over and over again, with the obvious answer "seven stupid."explain
One of the constant tensions in physics has been between the
Newtonian approach that if the laws describe nature that is all that is
necessary, and the Cartesian approach that looked for mechanisms to
physical laws. I think constructionist approach is the latter approachto
physics and may as well be fundamental as to how we learn things. Itaught
optics last term and was struck by how many different approaches areused to
describe light - from rays, through Huygen's wave, E-M waves to quantumdifferent
electrodynamics. We still uses them all to describe light under
conditions.
Gary
Gary Karshner
St. Mary's University
San Antonio, Texas
KARSHNER@STMARYTX.EDU