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[The Navy] gave [Lawrence Waterhouse] an intelligence test. The first question on the math part had to do with boats on a river: Port Smith is 100 miles upstream of Port Jones. The river flows at 5 miles per hour. The boat goes through water at 10 miles per hour. How long does it take to go from Port Smith to Port Jones? How long to come back? Lawrence immediately saw that it was a trick question. You would have to be some kind of idiot to make the facile assumption that the current would add or subtract 5 miles per hour to or from the speed of the boat. Clearly, 5 miles per hour was nothing more than the average speed. The current would be faster in the middle of the river and slower at the banks. More complicated variations could be expected at bends in the river. Basically it was a question of hydrodynamics, which could be tackled using certain well-known systems of differential equations. Lawrence dove into the problem, rapidly (or so he thought) covering both sides of ten sheets of paper with calculations. Along the way, he realized that one of his assumptions, in combination with the simplified Navier-Stokes equations, had led him into an exploration of a particularly interesting family of partial differential equations. Before he knew it, he had proved a new theorem. If that didn’t prove his intelligence, what would? Then the time bell rang and the papers were collected. Lawrence managed to hang onto his scratch paper. He took it back to his dorm, typed it up, and mailed it to one of the more approachable math professors at Princeton, who promptly arranged for it to be published in a Parisian mathematics journal. Lawrence received two free, freshly printed copies of the journal a few months later, in San Diego, California, during mail call on board a large ship called the U.S.S. Nevada. The ship had a band, and the Navy had given Lawrence the job of playing the glockenspiel in it, because their testing procedures had proven that he was not intelligent enough to do anything else. |
It was meant to be an easy question to see if students understood Newton's third law, but one student filled in the entire test with momentum calculations showing that the boat would actually move forward at X velocity because the sail would essentially redirect some % of the air backwards like a reverse thruster (conservation of momentum). He left the rest of the test blank because he blew the whole time limit on the first question.
The professor was perplexed when grading this student's exam and built a "sailboat" out of a pinewood derby car with a dowel rod mast and aluminum foil sail. He taped a handheld fan to the car, pointed into the sail, and indeed, the car moved forward (this part he demoed to the class as he was telling the story and just before he did it, he took a poll to see how many people thought it would move forward, backward, or stay still - "stay still" won the poll)
The student reportedly got 100% on the test and the professor threw out that question on future exams.