From schrecke@zinc.chem.ucalgary.ca Tue Mar 5 15:34:37 1996 Received: from zinc.chem.ucalgary.ca for schrecke@zinc.chem.ucalgary.ca by www.ccl.net (8.7.1/950822.1) id OAA06956; Tue, 5 Mar 1996 14:58:58 -0500 (EST) From: Received: by zinc.chem.ucalgary.ca (AIX 3.2/UCB 5.64/4.03) id AA16492; Tue, 5 Mar 1996 12:48:31 -0700 Message-Id: <9603051948.AA16492@zinc.chem.ucalgary.ca> Subject: Conservation of Difficulty To: chemistry@www.ccl.net Date: Tue, 5 Mar 1996 12:48:29 -0700 (MST) Reply-To: schrecke@zinc.chem.ucalgary.ca (Georg Schreckenbach) X-Mailer: ELM [version 2.4 PL23] Content-Type: text 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 ... ============================================================================== Georg Schreckenbach Tel: (Canada)-403-220 8204 Department of Chemistry FAX: (Canada)-403-289 9488 University of Calgary Email: schrecke@zinc.chem.ucalgary.ca 2500 University Drive N.W., Calgary, Alberta, Canada, T2N 1N4 ==============================================================================