Increments of tiny things can add up to something large

Small sections of a curve is being analyzed, yielding insight about the whole. Create WikiCommons

Small sections of a curve is being analyzed, yielding insight about the whole. Create WikiCommons

Calculus

  • Infinitesimals add up to something. When I took calculus, the first thing that surprised me was that many very small pieces could add up to a palpable amount. So when someone says “that only costs a dollar”, it’s not totally unreasonable to be concerned that spending many of those “only” dollars can wreck your budget.
  • In high school, when we discussed the distance a bouncing ball traveled, I learned that no matter how long somethings go on, sometimes a limit is reached. Calculus broadened that insight to include other types of infinite series which were bounded by a number. That underlies the economic insight expressed in the law of diminishing marginal utility.

Geology

How could a continent be in a vastly different location relative to other lands in the times of the dinosaurs? A continent only moves between 0 and 10 centimeters each year. Wait, the dinosaurs died out 65 million years ago. A move of 10 cm per year results to a move of 60 miles each million years. That’s more than 4,000 miles since the dinosaurs last tread this Earth.

Biology

Evolutionary changes are small. Each mutation is but a single step. How to account for the huge difference between humans and other creatures?

We diverged away from chimpanzees 10 million years ago

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