Concept
Fractal dimension
A coastline has no length: shorten the ruler and the measurement grows without converging, because structure is present at every resolution. The dimension is the non-integer number saying how thoroughly a pattern fills the space it sits in — a line is 1, a plane is 2, Britain's west coast about 1.25. Turned on a situation it gives the exact form of why enumeration cannot finish: looking closer reveals more rule, not the last few rules.
Where it appears
Treated in
- Part Four — The Ground UnderneathThe Limits of Running It ForwardFinding the rule is not predicting the form. Two things make a Global Form unpredictable, a named rule is only a hypothesis, and fatalism turns out to be unavailable rather than false.