Soaring in Hilbert Space.mpg

Eagles are soaring in 3-dimensional space but mathematicians were soaring beyond 3-dimensional space to end up with infinite dimensionality.

Since the area of greek mathematics (the time of the famous mathematician Pythagoras, about 2500 years ago) infinity has been figured out to be a wild animal which does not allow to be tamed. Thus it took about 2500 years until Georg Cantor came up with his foundation of set theory, which gave modern mathematics a complete new basis and allowed finally the taming of infinity.

Based on Georg Cantor's work another famous mathematician, David Hilbert, developed his powerful theory of function space, where one of his most powerful creations is now known as Hilbert space.

No wonder that Hilbert space is the mathematical basis of quantum mechanics since David Hilbert was permanently in direct touch with quantum physicsists during the evolution of quantum mechanics.

In a metaphorical language we could conclude that eagles might feel infinity by soaring in their three dimensional space but Hilbert space is a tremendously richer environment which allows mathematicians and physicsists to soar in infinite dimensional space.

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[quantanalounge]

Thanx, cheezman111, your appreciation is really motivating. Interestlingly you got the point right away. It took me lots of efforts to realize by myself which core aspects of Hilbert space theory are actually required by quantum theory, I made a trial to express these topics by art and not by description. Most fascinating is that infinity could not be taimed over 2500 years by the best mathematicians, until Georg Cantor digged out the raw diamonds, which David Hilbert brought to brilliance.

[emknightauthor]

Wonderful.

[cheezman111]

You have such a great way of making poetic statements out of the math while still keeping its accuracy!