# 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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