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4.7 Scaling Effects

In biology, the square-cube law explains why we’ll never see elephant-sized spiders. The bug’s weight scales with volume, so it goes as O(n^3). The strength of the leg scales with the area of the cross section, so it goes as O(n^2).

If you make the critter ten times as large, that makes the strength-to-weight ratio one-tenth of the small version, and the legs just won’t hold it up.

We run into scaling effects all the time. Anytime you have a “many-to-one” or “many-to-few” relationship, you can be hit by scaling effects when one side increases. For instance, a database server that holds up just fine when two ...