Sync

The Emerging Science of Spontaneous Order

In his book, Steven Strogatz advocates a different approach to the study of emergence. Suggesting the real question is one of "emerging order," Strogatz argues we should include certain forms of synchronization (as when two clocks are touching and their pendula gradually be synchronized) as prototypical examples of emergence.

While most of us consider the emergence of life and mind as things which are categorically different from such simple "emergence of order," Strogatz suggests the fact that we understand these emergences to a very complete degree (mathematically) means we should try to use them as our paradigms for understanding emergence. Clearly, if we can model higher-order emergences as the emergence of synchronization, then this may be a profitable approach. But it is not yet clear that it is possible to do so.

A potential weakness in Strogatz's argument is that forced harmonic oscillators are traditionally thought of as linear systems. While Strogatz has demonstrated that they can be viewed as nonlinear systems (by the introduction of time as a third dimension) and that there may be advantages to doing so, it is not true that most nonlinear systems (including most examples of emergence) can be thought of as linear systems. Thus, if our mathematical insights into the emergence of synchronization are dependent on the convenient fact that it is possible to view it as a linear system, those insights will not be applicable to many of the most common examples of emergence.

Interestingly, Strogatz's other work (specifically <i>Nonlinear Dyanamics and Chaos</i>) has been used by Gottman et al. in <i>The Mathematics of Marriage</i> to suggest another alternative explanation for the ubiquity of emergence: That linear systems can never produce a stable set point while nonlinear systems can. If nonlinear systems with stable set points can be shown to produce emergence, this may be another way of approaching the problem.

See also Math and Investigations.

— Scotus - 12 Jun 2003