basic non-commutative geometry
  think of x, y alt. as -coordinates- on R^2 (position)
    and as -operators- (multiplication)
  think of d/dx and d/dy as coordinates on the -tangent- space
    (velocity, or rather momentum)
    and as -operators- (naturally)
  ...and then everything commutes -except- [d/dx,x] and
  [d/dy,y] -- and this is -exactly- the statement of
  Heisenberg uncertainty!
  [I don't know the connection with the Fourier theory POV]

