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CERTAINTY

                                                      January 16, 2019

Richard Feynman, in his series of lectures
collected as "The Character of Physical Law"
compares mathematics and physics, making the
point that the mathematician typically goes       Elsewhere-- I think in
after a very general, very abstract               conversation with Freeman
understanding, but the physicist is typically     Dyson-- Feynman argued
interested in a very specific case that's         for working with physical
more grounded in reality.  He argues that for     intuition rather than just
the physicist, the words they use have very       taking a purely mathematical
definite meanings and that's sometimes missed     approach, suggesting that
by people who come to physics from                the elder Einstein had
mathematics.                                      wasted a lot of time on
                                                  this without much result.



    In some places in these lectures he
    emphasizes that physicists have learned
    not to trust their intuition about what
    seems reasonable but rather to settle         He makes the point that
    issues through experiment-- in other          science can't possibly
    places he seems to be placing emphasis        achieve absolute
    on the need to develop physical               certainty, if only
    intuition, to make guesses--                  because of these issues
                                                  with range of application.

                                                          Theories are tested
                                                          in very specific
  Newton's understanding of gravity had a                 ways-- general
  wide range of application, explaining                   confirmation under
  both the behavior of falling bodies, and                every possible
  the movements of celestial objects-- it                 circumstance is an
  worked so well that an apparent                         impossibility.
  discrepancy with astronomical data was      
  resolved by assuming that Newton was                    The scientist
  right, and light did not travel                         must make guesses
  instantaneously, but rather moved at a                  about what
  certain speed which could now be                        experimental
  measured.  Other discrepancies led to the               conditions are
  discovery of new planets as we inferred                 important.
  that there must be other gravitational      
  sources in play.                                           Mathematicians
                                                             are more reluctant
  It was a surprise that there are                           to give up on
  extreme cases where the behavior of the                    that dream of
  real world differs from classical                          absolute truths.
  physics-- discrepancies in the orbit of  
  Mercury requires something like General  
  Relativity to understand.                        Science: uncertain but real,
                                                   Math: certain but ideal.
  So: should the experimentalists have     
  qualified their understanding,                         MATHISM
  specifying the range of energy and       
  velocity the results were known to be    
  good for?  But how would you know that   
  energy or velocity was the key?  What    
  about, say the material of the objects        "If you thought that science
  involved, or the time of day or the           was certain-- well, that is
  time of the year, or the feelings of          just an error on your part."
  the experimenter, or any number of       
  other circumstantial features that                Richard P. Feynman
  *might've* turned out to be important?   
                                                "The Quotable Feynman", p.349,
                                                Princeton University Press
      In the beginning was the guess.                          [link]
                                               
                                           
















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