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Dualisms across fields
Posted:
Sep 28, 1998 7:05 AM


The following dualisms are suggestive that an underlying "waveparticle" duality can be extended to nonphysical 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)
Relativity 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
Mathematics 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 timebased waves of trigonometric origin to the frequency (spatial) based complexplane 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 geometry.
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 ?
 http://www.bestweb.net/~ca314159/
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