Biomedical Engineering Reference
In-Depth Information
nomena, but that it not entail badly distorted or nonexistent phenomena in other
respects.
6.3.2.
Two Stories and Some Morals
Let me give two examples from very early in the study of complex systems,
which nicely illustrate some fundamental points.
The first has to do with pattern formation in chemical oscillators (147). Cer-
tain mixtures of chemicals in aqueous solution, most famously the Belusov-
Zhabotinsky reagent, can not only undergo cyclic chemical reactions, but will
form rotating spiral waves, starting from an initial featureless state. This is a
visually compelling example of self-organization, and much effort has been de-
voted to understanding it. One of the more popular early models was the "Brus-
selator" advanced by Prigogine and his colleagues at the Free University of
Brussels; many similarly named variants developed. Brusselator-type models
correctly predicted that these media would support spiral waves. They all, fur-
ther, predicted that the spirals would form only when the homogeneous configu-
ration was unstable, and that then they would form spontaneously. It proved
very easy, however, to prepare the Belusov-Zhabotisnky reagent in such a way
that it was "perfectly stable in its uniform quiescence," yet still able to produce
spiral waves if excited (e.g., by being touched with a hot wire) (148). The Brus-
selator and its variants were simply unable to accommodate these phenomena,
and had to be discarded in favor of other models. The fact that these were quali-
tative results, rather than quantitative ones, if anything made it more imperative
to get rid of the Brusselator.
The second story concerns the work of Varela and Maturana on "autopoe-
sis." In a famous paper (149), they claimed to exhibit a computational model of
a simple artificial chemistry where membranes not only formed spontaneously,
but a kind of metabolism self-organized to sustain the membranes. This work
influenced not just complex systems science but theoretical biology, psychol-
ogy, and even sociology (150). When, in the 1990s, McMullin made the first
serious effort to reproduce the results, based on the description of the model in
the paper, that description proved
not
to match the published simulation results.
The discrepancy was only resolved by the fortuitous rediscovery of a mass of
papers, including Fortran code, that Varela had left behind in Chile when forced
into exile by the fascist regime. These revealed a crucial change in one particular
reaction made all the difference between successful autopoesis and its absence.
(For the full story, see (151,152).) Many similar stories could be told of other
models in complex systems (153); this one is distinguished by McMullin's un-
usual tenacity in trying to replicate the results, Varela's admirable willingness to
assist him, and the happy ending.
