My mind wanders as I'm heading down Interstate 87 to New York. I'm staring at something I've been staring at for decades of driving, namely the little signs that very precisely measure the distance from the road's terminus. A green rectangle with white type marks each mile. Every tenth of a mile is marked with a smaller white sign indicating the mile, decimal fraction, and a reminder of the name of the highway. Between those are even smaller white rectangles on posts with nothing written on them that appear every quarter of a tenth of a mile. I know there's some good reason for making the highway into a gigantic yardstick, but when I see the numbers going by I sometimes imagine myself performing an experiment that would in practice be a stupendously bad idea. Here it is: What if the mile markers were my personal speed limit? What if for some perverse reason I had to exactly match my speed to the number on the signs at every point?
Up around Plattekill where the numbers are pretty close to the actual speed limit, no one would notice anything odd. By the time I was approaching Woodbury the other cars would start to tap their horns and whiz around me. By the time I reached the Tappan Zee Bridge there'd by angry, drawn-out honking behind me and barely averted smashups. In the Bronx I would be driving so slowly that to the casual observer I would appear to have stopped. How long would it take to get to mile zero, assuming I'm not rear-ended and killed in a pointless and avoidable fiery wreck? If I'm really going the number of miles per hour that equals my distance from the Triboro Bridge,* I guess I'd never get there at all. But this apparently simple set of conditions produces results that I can't wrap my head around. I don't know the way to work out, for example, how long it takes to get from Plattekill to Woodbury even if I know the exact distance (I think it might require calculus, which I never learned). I suppose if I knew all the answers I wouldn't be wondering about any of this.
Many years ago I had a little plastic alarm clock that I accidentally swept off the bed stand while reaching for the snooze button. The fall smashed the protective cover and slightly bent the second hand. I was too stingy to get a new one, but the clock still seemed to function okay. A week passed, and one afternoon when I was lying in bed, staring at the ceiling and wondering what to do with my life, I slowly became aware that in addition to its usual electronic humming, the clock was making a new sound. Periodically the humming would get slightly louder and more pissed off sounding and then there would be a tiny scratching sound. What was happening was that every minute the bent second hand would run into the minute hand and push into it until the force of the motor overcame the resistance and the two hands disengaged. The second hand flicked forward in compensation and still maintained accurate time, I guess because the clock was regulated precisely by quartz (how the hell does that work, anyway?). Once per minute: buzz, scrape, normal hum. Buzz, scrape, normal hum. But then it occurred to me that each time they reunited the minute hand had moved forward a tiny bit while the second hand had been making it's circuit. So it was really a minute and one second between scrapes. But, no, that wasn't right either, because EVEN DURING THE EXTRA SECOND THE MINUTE HAND WAS STILL MOVING. So how long was the interval between scrapes? Questions like this one seemed to justify the aimless afternoons of staring at the ceiling.
Here's another problem: Why do I feel so defensive about these idle thought games? There are whole university departments dedicated to subjects that are commonly perceived as impractical intellectual exercises. Yet somehow the puffed up status conferred by academia doesn't make the useless discipline more compelling to me. The most appealingly pointless ideas live away from the comfort of institutions, shivering in the cold.
*I refuse to call it the RFK bridge. This has nothing to do with my feelings for the former senator from New York. I just think some things are fine the way they are.