Notes

Chapter 5: Two Dimensions and Beyond

Section 7: Systems Based on Constraints


Explanations based on constraints

In some areas of science it is common to give explanations in terms of constraints rather than mechanisms. Thus, for example, in physics there are so-called variational principles which state that physical systems will behave in ways that minimize or maximize certain quantities. One such principle implies that atoms in molecules will tend to arrange themselves so as to minimize their energy. For simple molecules, this is a useful principle. But for complicated molecules of the kind that are common in living systems, this principle becomes much less useful. In fact, in finding out what configuration such molecules actually adopt, it is usually much more relevant to know how the molecule evolves in time as it is created than which of its configurations formally has minimum energy. (See pages 342 and 1185.)


From Stephen Wolfram: A New Kind of Science [citation]