Re: The Thumbprint Of God - Fractals...The Colors Of Infinity

In article <101120092025193127%john@xxxxxxxxxxxxx>,
John Wilkins <john@xxxxxxxxxxxxx> wrote:

Not all math works. As Bacon wrote, men mark it when they hit, but they
do not mark it when they miss. The math that has no empirical impact is
quietly shelved. So we might think with Wigner that the working math is
what we use again.

And taken off the shelf when its found useful. Matricies were developed
a lot, but apparently not used much in physics until the rise of quantum
mechanics.

<http://en.wikipedia.org/wiki/Matrix_mechanics>
The quantities in Heisenberg's formulation were the classical position
and momentum, but now they were no longer sharply defined. Each quantity
was represented by a collection of Fourier coefficients with two
indices, corresponding to the initial and final states.[5] When Born
read the paper, he recognized the formulation as one which could be
transcribed and extended to the systematic language of matrices,[6]
which he had learned from his study under Jakob Rosanes[7] at Breslau
University. Born, with the help of his assistant and former student
Pascual Jordan, began immediately to make the transcription and
extension, and they submitted their results for publication; the paper
was received for publication just 60 days after Heisenberg¹s paper.[8] A
follow-on paper was submitted for publication before the end of the year
by all three authors.[9] (A brief review of Born¹s role in the
development of the matrix mechanics formulation of quantum mechanics
along with a discussion of the key formula involving the non-commutivity
of the probability amplitudes can be found in an article by Jeremy
Bernstein.[10] A detailed historical and technical account can be found
in Mehra and Rechenberg¹s book The Historical Development of Quantum
Theory. Volume 3. The Formulation of Matrix Mechanics and Its
Modifications 1925­1926.[11])
Up until this time, matrices were seldom used by physicists, they were
considered to belong to the realm of pure mathematics. Gustav Mie had
used them in a paper on electrodynamics in 1912 and Born had used them
in his work on the lattices theory of crystals in 1921. While matrices
were used in these cases, the algebra of matrices with their
multiplication did not enter the picture as they did in the matrix
formulation of quantum mechanics.[12] Born, however, had learned matrix
algebra from Rosanes, as already noted, but Born had also learned
Hilbert¹s theory of integral equations and quadratic forms for an
infinite number of variables as was apparent from a citation by Born of
Hilbert¹s work Grundzüge einer allgemeinen Theorie der Linearen
Integralgleichungen published in 1912.[13][14] Jordan, too was well
equipped for the task. For a number of years, he had been an assistant
to Richard Courant at Göttingen in the preparation of Courant and David
Hilbert¹s book Methoden der mathematischen Physik I, which was published
in 1924.[15] This book, fortuitously, contained a great many of the
mathematical tools necessary for the continued development of quantum
mechanics. In 1926, John von Neumann became assistant to David Hilbert,
and he would coin the term Hilbert space to describe the algebra and
analysis which were used in the development of quantum mechanics.[16][17]

</end quote>

I suppose that non Euclidian geometry and tensor calculus were also
mathematical curiosities before General Relativity.

Of course, from a pantheistic or panentheistic point of view or even a
theistic point of view) there is nothing at all surprising about the
role of mathematics.

--
A computer without Microsoft is like a chocolate cake without mustard.

.

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