Conference rusure::math

1814.0. "relating a non-linear to a linear code" by FRASER::FRASER (Jim Fraser) Wed Nov 10 1993 13:01

    From:   US2RMC::"aboulanger@BBN.COM" "MAIL-11 Daemon"
    To:     snac-ext@Think.COM
    Subj:   Fundamental result alert!
    
    Science, Vol 262, 29 Oct, page 658-659 reports on a result in coding
    theory which I think is much more fundamental. The result relates a
    nonlinear code (Nordstrom-Robinson) code with a linear code
    (octacode).
    
    They are related via a projection of the linear code. I believe this
    result is more fundamental:
    
    1) It relates higher dimensional linear systems to lower dimensional
    nonlinear ones. This may lead to ultimate reason why low-dimensional
    chaos seems so ubiquitous.
    
    2) It is interesting in the light of projection pursuit statistical
    methods.
    
    3) Bruce B., left the question during one of our forays into quantum
    chaos on the relationship of the infinite-dimensional Hilbert space
    (linear) quantum mechanics works in and the low-dimensional chaos we
    see in systems at scales above quantum mechanics. Here is a sketch of
    how this all might work:
    
      No quantum system is normally isolated. Recent empirical results on
      the "Watch Pot" problem verifies that a system will have collapsed
      eigenstates as long as it is watched and furthermore other coupled
      systems can be the "watchers". If this collapsing is the right kind of
      projection, we can have our "emergent" nonlinearity in the
      macrosystem. The fact that quantum systems are interacting in an open
      system fashion, may lead to the macroscopic nonlinearity we observe.
      (I believe the quantum  measurement theorists have been saying all
      along that the perceived randomness in QM come from the measurement
      process.)
    
    
      I am not an expert here, comments?
    
    *END Fundamental result alert*
    
    Albert