My friend John is a long distance swimmer and a member of the Dolphin Club. They are the people who frequently debunk the notion that no inmate could have escaped from Alcatraz by swimming.
As practice for his upcoming swim of the English Channel, John asked me to be his kayak escort on the 6 mile ocean swim from Capitola to Santa Cruz, CA. As escort, it was part of my job to stop every thirty minutes and make sure John drank his nasty energy drink. It was a hellishly windy day, and what should have taken two hours dragged on for nearly four. Throughout, I kept wondering what could possibly be going through the mind of someone battling these endless freezing waves while physically in the water. (It was bad enough in the bloody boat.)
Anyway, at one of the stops, I found out. While slurping Goo, John started ranting about this mathematical vision he was having. "I can see squares!," he yelled, "Squares!". I was tempted to yank him into the kayak and signal for the rescue boat, but he seemed otherwise coherent. Because of huge wax plugs in his ears he couldn't hear a thing I said, so just nodded and let him start back on the swimming. I was kept in the dark about those squares.
Finally at the end of the race, he explained. It turns out that during the endless swim, his mind started to wander, and stumbled onto visualizing numbers. More specifically, his mind's eye started drawing out the quadratic equation in a way he had never thought of before -- and neither had I. Based on what he saw, for the first time I could understand what the heck that equation means. Check this out:
If you forget the equation and just see shapes plotted on a flat grid, the whole thing becomes clear... even that crazy +1 at the end.
During the channel swim, John plans to try the same with the cubic equation.
I'm not going along on that one.
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