Conservation of Difficulty



 Hi everybody,
 a couple of years ago, one of my theoretical physics
 professors cited the "Law of Conservation of Difficulty".
 I thought I should share this law with the computational
 chemistry community on the net.
 As the name suggests, the law states that the difficulty
 of a problem is conserved, no matter how you reformulate it.
 I will demonstrate this by a few examples.
 Take Density functional theory (DFT). We start off with the
 terribly complicated Schroedinger equation -- for the electrons
 in a molecule, say. We reformulate it in a very clever
 way to obtain DFT. Now what have we got? Indeed, we have a
 beautiful formulation of the same problem: the basic variable
 is the density, an observable that depends on three coordinates,
 rather than 3*N as is the case with the wave function.
 Thus, the problem has been simplified considerably.
 However, all the difficulty comes back in the exchange-correlation
 functional. (Remember that its functional form is unknown).
 Another example is given by Molecular Mechanics. Again, the
 very difficult problem of the time-dependent Schroedinger equation
 is reformulated as simple classical equations of motion.
 However, the difficulty is conserved. In this case, it pops up
 in the necessity to obtain reliable force fields.
 I suppose I have to modify the law somewhat since it is certainly
 possible to make life MORE complicated (by doing lots of stupid
 things). Maybe the "difficulty" is an entropy-like property?
 Does anybody want to comment on the above?
 If so, then I shall summarize to the net.  In particular, I
 would like to get a reference ...
 Yours, Georg
 P.S.   Don't take me too serious on this one ...
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 Georg Schreckenbach                      Tel: (Canada)-403-220 8204
 Department of Chemistry                  FAX: (Canada)-403-289 9488
 University of Calgary                    Email: schrecke' at
 \`zinc.chem.ucalgary.ca
 2500 University Drive N.W.,  Calgary,  Alberta,  Canada,  T2N 1N4
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