Decision Tools

Notes on software and processes for collecting, analyzing and acting on data

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Working Notes : Regularity and Large Numbers

Highly regular, predictable events are likely to be reducible to laws. Whether we consider an abstract mathematical relationship or a complex physical system with reproducible behavior, the lack of surprises allows the law to represent the system.

The behavior of less predictable systems can't be so easily captured by rules. And the mathematics of chaos and complexity have proven that the rules that govern a system can't be used to predict the system's behavior. Simple sets of rules can generate unpredictable behavior.

With a large enough set of observations any system becomes predictable in the aggregate. Its average behavior and the limits of its behavior are known. Over long periods of time, with many many events, predictability becomes better. The large numbers smooth over the unpredictable granularity of individual events.

WIthout those large numbers, there are no laws, only instances. Each new event provides important information about what might happen in the future. Anecdotal evidence, observations of single unusual cases, represents new and surprising information about the system. In a new system, every new experience is an anecdote. Once large numbers of observations have been made, predictability is good and the system becomes boring, reducible to simple models like mathematical laws.