Is science sometimes in danger of getting tunnel vision? Recently published ebook author, Ian Miller, looks at other possible theories arising from data that we think we understand. Can looking problems in a different light give scientists a different perspective?

How Do We Know Computations Are Right?

One concern I have as a scientist, and one I have alluded to previously, lies in the question of computations. The problem is, we have now entered an age where computers permit modeling of a complexity unknown to previous generations. Accordingly, we can tackle problems that were never possible before, and that should be good. The problem for me is, the reports of the computations tell almost nothing about how they were done, and they are so opaque that one might even question whether the people making them fully understand the underlying code. The reason is, of course, that the code is never written by one person, but by rather a team. The code is then validated by using the computations for a sequence of known examples, and during this time, certain constants of integration that are required by the process are fixed. My problem with this follows a comment that I understand was attributed to Fermi: give me five constants and I will fit any data to an elephant. Since there is a constant associated with every integration, it is only too easy to get agreement with observation.
An example that particularly irritated me was a paper that tried "evolved" programs on molecules from which they evolved (Moran et al. 2006. J. Am Chem Soc. 128: 9342-9343). What they did was to apply a number of readily available and popular molecular orbital programs to compounds that had been the strong point of molecular orbital theory, such as benzene and other arenes. What they found was that these programs  "predicted" benzene to be non-planar with quite erroneous spectral signals. That such problems occur is, I suppose, inevitable, but what I found of concern is that nowhere that I know was the reason for the deviations identified, and how such propensity to error can be corrected, and once such corrections are made, what do they do to the subsequent computations that allegedly gave outputs that agreed well with observation. If the values of various constants are changed, presumably the previous agreement would disappear.
There are several reasons why I get a little grumpy over this. One example is this question of planetary formation. Computations up to about 1995 indicated that Earth would take about 100 My to accrete from planetary embryos, however, because of the problem of Moon formation, subsequent computations have reduced this to about 30 My, and assertions are made that computations reduce the formation of gas giants to a few My. My question is, what changed? There is no question that someone can make a mistake, and subsequently correct it, but surely it should be announced what the correction was. An even worse problem, from my point of view, was what followed from my PhD project, which involved, do cyclopropane electrons delocalize into adjacent unsaturation? Computations said yes, which is hardly surprising because molecular orbital theory starts by assuming it, and subsequently tries to show why bonds should be localized. If it is going to make a mistake, it will favour delocalization. The trouble was, my results, which involved varying substituents at another ring carbon and looking at Hammett relationships, said it does not.
Subsequent computational theory said that cyclopropane conjugates with adjacent unsaturation, BUT it does not transmit it, while giving no clues as to how it came to this conclusion, apart from the desire to be in agreement with the growing list of observations. Now, if theory says that conjugation involves a common wave function over the region, then the energy at all parts of that wave must be equal. (The electrons can redistribute themselves to accommodate this, but a stationary solution to the Schrödinger equation can have only one frequency.) Now, if A has a common energy with B, and B has a common energy with C, why does A not have a common energy with C? Nobody has ever answered that satisfactorily. What further irritates me is that the statement that persists in current textbooks employed the same computational programs that "proved" the existence of polywater. That was hardly a highlight, so why are we so convinced the other results are valid? So, what would I like to see? In computations, the underpinning physics, the assumptions made, and how the constants of integration were set should be clearly stated. I am quite happy to concede that computers will not make mistakes in addition, etc, but that does not mean that the instructions for the computer cannot be questioned.
Posted by Ian Miller on Sep 9, 2013 4:31 AM Europe/London

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