“Less is more” and the art of modeling complex phenomena: Simplification may but need not be the key to handle large networks

I n the October 21, 2005 issue of the magazine Science a perspectives article by Stefan Bornholdt addresses the problem of the proper level of details in the description of complex systems [1]. “Less is more” is used in this article to encourage the usage of highly simplified dynamical elements for modeling large and complex nonlinear systems. The special case considered is modeling of large genetic networks, but the problem is much more general, arises often in science and beyond and, perhaps, deserves broader attention. Some older examples of “less is more” that have already reached a certain degree of maturity and common acceptance may be useful with respect to the recent revival of this paradigm. I shall present here two different problems from the interface of physics and chemistry, which were heavily debated in the past and for which consensus has been achieved by now, before returning to the burning biological questions. The first example starts with Paul Dirac’s famous comment [2], “... The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. ...” The reactions of the scientific public were extremely ambiguous: Quantum chemists used Dirac’s statement as the figure-head for their many decades long search for better and better approximations to the Schrodinger equations, whereas the majority of experimental chemists were truly upset. The reason for the uneasiness also shared by other nonphysicists was certainly not only the overstatement of a then 27-year-old and somewhat arrogant physicist but also an intuitive feeling that quantum mechanics provides the tool to reduce and integrate chemistry into physics, thereby sacrificing chemistry’s autonomy [3, 4]. Putting aside the philosophical questions, we are left with a pragmatic problem: Is quantum mechanics appropriate to describe molecules and chemical bonds for the chemist at the workbench? There are two reasons, among others, that suggest the application of a different, preferentially less sophisticated level of description: (i) Some older examples of “less is more” that have already reached a certain degree of maturity and common acceptance may be useful with respect to the recent revival of this paradigm. PETER SCHUSTER