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Topic: Dualisms across fields
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Posts: 220
Registered: 12/8/04
Dualisms across fields
Posted: Sep 28, 1998 7:05 AM
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The following dualisms are suggestive that an underlying "wave-particle"
duality can be extended to non-physical applications particularly in the
sense of "particle" being some entity or sample, which may be classified as
being instantiated with a "state", or indeterminate in its state and the dual
spaces in which it is observed:

Quantum Mechanics:
Bohr vs. Einstein
(empirical vs. theoretical)

space (length) vs. time (duration)

Probability Theory
Frequentists vs. Bayesians
(an infinite number of dice thrown all at once vs.
a die thrown an infinite number of times)

Statistics (stock options pricing)
Technicians vs. Fundementalists

Information Theory
Table based vs. Adaptive prediction

Digital signal processing
frequency (spatial) vs. time based

numeric calculus vs. analytic geometry

The pairings are respective in the sense of that the dualism on
the right sides are all similar; as with those on the left.

The last pairing is more difficult to perceive and I have not
adequately explored it yet.

It suggests that certain fundemental concepts of mathematics
are dualisms and at first thought the associated constant
that in Relativity is c, and in QM is h, and in DSP is 1/2,
and is in mathematics e ? (Since it binds the time-based
waves of trigonometric origin to the frequency (spatial) based
complex-plane of Guassian coordinates)

In QM, interference results when a particle is not classified into
one or more states, and is called "entanglement".
In statistics the indecision as to state is similarly displayed
in terms of "correlated" states.
In probability theory the determination of fuzzy set membership seems
to be the underlying representation of the dualism with the
time based Bayesian approach conjugate to the sample (particle/spatial)
based Frequentist approach.
In mathematics, time based periodic waves vs. spatial analytical/algebraic

The additional dualism of phase (in the time domain) vs.
particle (sample) number or "population" in the (spatial)
frequency domain seems to be inadequately explored ?


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