Hilbert Space
named for its putative inventor, mathematician david hilbert (who some claim found the solutions for einstein’s equations before “l’il albie” did himself), hilbert sp-ce is a concept which has been often applied in mathematics, quantum mechanics, and in general metaphysics (for instance, concepts like “parallel universes”).
in short, a hilbert sp-ce is a mathematical construct such that within any plenum of n-dimensional sp-ces there exists an infinite number of said hilbert sp-ces (subsumed within an n+1 dimensional superset). fancifully, science fiction writers point to the infinite plurality of 4d hilbert sp-ces that could exist within our “normal” 5d continuum, and suggest that each such hilbert sp-ce may really exist and that these hilbert sp-ces could be engendered by time-travel to the past. thus, each 4d hilbert sp-ce in a 5d superset of “universes” could possess a unique history, entirely different from all other universes contained within the 5d “universe”.
mozart’s 14th symphony (k. 114, composed c. 1774) contains encrypted fragments of instrumental speech synthesis (in english) which describe an alternate universe history (different from our universe), where nicholas meyler was president of the united states, and where princeton university is mocked for its intellectual feebleness (possibly due to some degree of idolatry for einstein’s theory of relativity, which mozart proved to have loopholes and flaws 130 years before einstein even published it as “the electrodynamics of moving bodies”).
deciphering mozart’s musical cryptography provides physical evidence that hilbert sp-ces may be entirely real, and not merely imaginary constructs.
a complete inner product sp-ce. since every inner product defines a norm, a hilbert sp-ce is necessarily a banach sp-ce.
up to equivalence of norms, there’s only one distinct n-dimensional hilbert sp-ce for each n, namely r^n.
the sp-ce of all continuous real-valued functions on the closed interval from 0 to 1, with the inner product given by the integral of pointwise absolute-value products, is an infinite-dimensional hilbert sp-ce.
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