Today, let's cut the earth down to size. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

Columbus sailed off, with one part courage and two parts madness, to sail around a spherical world. Actually, his trip was based on a terrible miscalculation. He underestimated earth's diameter, and he overestimated the width of Asia. He thought Japan lay only 2700 miles west of the Canary Islands. A correct calculation would've put it 10,000 miles away -- far beyond the reach of any 15th-century ship. And yet Columbus had access to a much better estimate of earth's size -- one that was 1700 years old.

The ancients thought the earth was flat, but then so did you and I when we were too young to know about spheres. Understanding a round earth came in stages. First the Pythagoreans argued by induction, 2500 years ago: The moon is round, they said. So is the sun. Surely the earth must also be round.

Two centuries later, Aristotle argued from observation. When a boat sails off in any direction, he noted, its hull always disappears before its sails do. The hull is obviously being obscured by curvature, so the earth must be round.

Science writer John Noble Wilford notes that going from flat to round meant carving earth down from indefinitely large to a much more confined place. The longest journey on a round earth will sooner or later take you back where you began. The round earth had somehow been made into something less than the flat earth was, but how much less? Educated people knew the earth was round in the 3rd century BC, but they still didn't know how to measure its size.

Then the Egyptian Eratosthenes, director of the Library in Alexandria, wedded observation to calculation. His idea was as simple as it was brilliant. When the sun was directly above Aswan, 500 miles away, he measured the shadow cast by a vertical tower in Alexandria. The rest was simple trigonometry. He calculated earth's diameter with only 16 percent error, and his method was used right down to modern times.

Mystery had been removed. Earth was now within our grasp. Understanding earth meant we would ultimately control it. Of course, Columbus wanted the earth to be smaller, so he deceived himself. He was no scientist. In a sense, he wanted to conquer the earth, and so he carved it down to fit himself. The crowning irony is that he actually succeeded.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

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Wilford, J.N., The Mapmakers. New York: Random House, Vintage Books, 1982, Chapter 2.