Page:Lawhead columbia 0054D 12326.pdf/187

From Wikisource
Jump to navigation Jump to search
This page has been proofread, but needs to be validated.


in other important dynamical respects.

Generalizing from this case, we can conclude that knowing λ, ε, and t is enough to let us put a meaningful cap on the resolution of future predictions (i.e. that they can be only as fine-grained as the size of the neighborhood given by ε(eλt) ) only if we stay agnostic about the presence (and location) of interesting macroconditions when we make our predictions. That is, while the inequality in 5(j) does indeed hold, we have no way of knowing whether or not the size and distribution of interesting, well-behaved regions of the state-space will correspond neatly with size of the neighborhoods defined by that inequality.

To put the point another way, restricting our attention to the behavior of some system considered as a collection of states can distract us from relevant factors in predicting the future of the system. In cases where the dynamical form of a system can shift as a function of time, we need to attend to patterns in the formation of well-behaved regions (like those of thermodynamic macroconditions)—including critical points and bifurcations—with just as much acumen as we attend to patterns in the transition from one state to another. Features like those are obscured when we take a static view of systems, and only become obvious when we adopt the tools of DyST.

5.1.5 Feedback Loops

In Section 5.1.2, we considered the relationship between non-linearities in the models of dynamical systems and the presence of feedback generally. Our discussion there, however, focused on an example drawn from economics. Moreover, we didn’t discuss feedback mechanisms themselves in much detail. Let us now fill in both those gaps. While CGCMs are

177