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LESSON 3 · Think Like a Mathematician

Watch the Scaling

When you estimate anything in three dimensions, scaling can fool you. A box 3 feet on each side holds 27 cubic feet. Double the side to 6 feet and the volume jumps to 216 cubic feet — eight times larger, not twice. A good estimator expects this and catches the trap before ordering eight times too little material.

Estimation is a muscle. Try one Fermi problem each morning this week: How many flights take off globally each day? How many words have you spoken in your lifetime? How many liters of water does your city use daily? You will be wrong on the details and right on the scale — which is exactly the point.