### Mathematics as Carrier

Applied mathematics as a reliable carrier of information, is modulated
by interpretations which are subject to noise, dispersions, &c.
Theory is complementary to empiricism in the sense that synthesis
is complementary to deconstruction.
A theorist generally employs synthesis and modelling in anticipation
of finding a new signal, or looking for a match with some known signal:
F'(w) -> f'(t)
f'(t) = ?
f'(t) = f(t) ?
An empiricist generally employs deconstruction of a given signal:
F(w) <- f(t)
F(w) = ?
In a general sense, the application of synthesis-deconstruction are
complementary functions which seem subject to an uncertaity relation.
\delta {theory} \delta {empirical results} >= k
in the same manner that we extend the Fourier uncertainty (bandwidth theorem)
to the Heisenberg uncertainty.

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