From: Amara Graps (amara@amara.com)
Date: Mon Dec 11 2000 - 09:57:16 MST
From: scerir <scerir@libero.it>
>So, how can we know the dancer from the dance?
>Israil M. Gelfand (now at Rutgers University)
>studying commutative C*-algebras found (1943)
>an amazing representation theorem:
>every commutative C*-algebra is *-isomorphic
>to an algebra of continuous functions
>vanishing at infinity on some topological
>space with the sup-norm.
>Dancers are points, dances are functions.
>Points presuppose functions.
>Dancers presuppose the existence of dances,
>the existence of all possible dances.
>There is, of course, a correlation between
>dancers and dances, singers and songs.
>In which consciousness "resides".
You like those synthesis-thingies, I see. (me too)
Here is something I conjured up a couple of years ago while riding
the train home, triggered by a chapter I was reading: "Myth and Music" in
Levi-Strauss' book: _Myth and Meaning_.
Synthesis: Wavelets/Myths/Language/Music
Expanding from Strauss' initial lists and connections
Comparison of Structures
Myth Language Music Wavelets
------ --------- ------ ----------
-- phonemes notes vectors
mythemes words --- wavelets
myths sentences melody wavelet family
"Continuous Reconstruction"
Understanding as a totality
Myth - You have to understand it as a totality because the meaning
is conveyed by bundles of events (mythemes) that appear at different
moments in the story.
Orchestral Music- Each page is a totality with a musical theme
apearing at different moments in the piece.
Fugue Music - Manipulates a melodic subject, those subjects
appearing simultaneously with itself.
Wavelets - The wavelets (basis functions) associated with the
segmentation of a signal or function are scaled and translates of
the same general shape, and a wavelet transform provides a total
glimpse of the data at the different scales.
Evolution of Music and Myth both start with language
Myths <== From Language ==> Music
emphasizes emphasizes
meaning sound
Amara
********************************************************************
Amara Graps email: amara@amara.com
Computational Physics vita: finger agraps@shell5.ba.best.com
Multiplex Answers URL: http://www.amara.com/
********************************************************************
"Sometimes I think I understand everything. Then I regain
consciousness." --Ashleigh Brilliant
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