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 — Very small sections of almost nothing add up to the whole

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. 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 some things 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.

Chalk cliffs provide another example. The maximum rate of deposition is estimated as one-eighth of an inch per century. Beachy Head in Sussex at 532 feet required at least 5 million years to achieve their height. (A useful rule of thumb: 1 inch change in 100 years implies that 1 mile change requires 6 1/3 million years.)