In Search of Certainty

Chapter 2. Feedback Patterns and Thresholds: How the relative sizes of things govern their behaviours

Astronomy is 1derful,
And interesting 2,
The Ear3volves around the sun,
That makes a year 4 you.
The Moon affects the sur5 heard,
By law of phy6 great,
It7 when the stars, so bright,
Do nightly scintill8.
If watchful providence be9,
With good intentions fraught,
Would not been up her watch divine,
We soon should come to 0 (nought).

—Unknown²¹

Before we can argue how stable systems ought to be, we have to be able to measure how stable they actually are²². That is a surprisingly difficult thing to do. To understand better, we need to cover some more of the basic science of scales, and explore how these affect stability.

There are two essential reasons for wanting to measure stability: the first is to be able to put a practical figure on the result for the sake of comparison. The other is to know how it arises so that one might diagnose failures of stability. By understanding how to measure a thing, we also hope to learn something about it in the process. From the previous chapter, it should come as no surprise that stability is closely related to scales in the system²³.

Consider some examples. A computer program crashes, or undergoes a failure, when the amount of memory it needs approaches the scale of total amount of memory available in the computer. It reaches a limit for its container. The size of the container influences the functioning of the software. Even though the container is ...