Mathematics as Carrier

    
  Applied mathematics as a reliable carrier of information, is modulated 
  by interpretations which are subject to noise, dispersions, &c.

  Theory is complementary to empiricism in the sense that synthesis 
  is complementary to deconstruction.

  A theorist generally employs synthesis and modelling in anticipation
  of finding a new signal, or looking for a match with some known signal:
     F'(w) -> f'(t)
     f'(t) = ?
     f'(t) = f(t) ?

  An empiricist generally employs deconstruction of a given signal:
     F(w) <- f(t)
     F(w) = ?
   
  In a general sense, the application of synthesis-deconstruction are
  complementary functions which seem subject to an uncertaity relation.

   \delta {theory} \delta {empirical results} >= k
  
  in the same manner that we extend the Fourier uncertainty (bandwidth theorem)
  to the Heisenberg uncertainty.