paradox · counting
Coastline paradox
A toy shore and a ruler.
Yellow pins and the yellow line are end to end. That length stays. Green is the shore, and it stays still. Red is the ruler. Why does a shorter stick measure more?
72 end to end
74.5 this ruler
16 stick length
End to end is 72. This ruler measures 74.5. The long sticks cut across the bends.
The green shore stays still. Only the red ruler changes.
End to end is the yellow line, 72. That length stays.
A long stick cuts across a bend. A shorter stick goes into that bend, so the red total changes.
The same shore measures 74.5, then 78.9, then 97.4, then 105.3, then 115.9, then 129.2.
A table edge would stop once the stick was shorter than its bumps. A real coast keeps a smaller bend, so the length has no final value.