A logical approach to going long
There are better ways to pass the time on a long run than listening to re-runs of Serial, says James Leakos.
“We’ve got two more miles until we turn around, and before we get there, you need to prove to me that there are infinitely many prime numbers.”
In college, we had two kinds of long runs. The first sort, often the hardest day of the week, was the “up-tempo 17” — really closer to 21 because we’d hit 5:20s before even flipping to come home. Those runs were the ones I’d think about when warming up for the big meets, but wouldn’t tell coach about for fear of not being allowed to run Tuesday’s workout. I still remember most of these runs, and very fondly; they are not, however, today’s topic.
Today’s topic is the second sort of long run, often referred to as “time on your feet”. This sort of run, though probably as important, ranked far down on our list of things we’d like to do. If someone managed to force through our thick skulls that we shouldn’t destroy ourselves for no good reason on a dirt trail in Lincoln, MA, because we had something important the next weekend, we’d face some two hours of trudging along in abject and utter unhappiness.
This is when I got good at logic problems.
At some point during my sophomore year, it became clear that our various girl-related woes were no longer able to occupy the entirety of a slow long run: indeed, barring a major romantic catastrophe or some serious embellishment of an unfortunate encounter, they could last barely six miles. The rest of the run was spent in silence, or half-heartedly playing “I spy”.
On the brink of abandoning the sport, we were saved in the early spring by none other than the major financial institutions of Wall Street, New York. As our teammates turned their aspirations away from medicine and law, they began to interview at places that would appreciate them more: part of this process involved lovely little riddles, which they began to bring back to us. One of these early ones I remember clearly:
Three persons wearing hats face each other, blindfolded. When the blindfolds are removed, each person will see the hats of the other two, but not their own hat. Each hat is independently randomly white or black. Before the blindfolds are removed, the people are told that they are allowed to devise a strategy such that they will maximize their chances of defeating the following game. The game is as follows: after the blindfolds are removed, and they see the hats of the other people, each player will either say “black”, “white”, or not speak at all. If more than one person speaks, it will be at the exact same time (therefore, the colour they say will not communicate information to anyone else. Incidentally, this is a logic problem, not a riddle. There are no tricks… they don’t wink at each other or anything like that. Don’t think outside the box. Remember, this is corporate America). If anyone says the correct colour of their own hat, and no one says the wrong colour, they all win. If anyone says the wrong colour, despite any correct statements, they all lose. If no one says anything, they all lose. What should their strategy be to maximize their chances of winning?
This problem apparently had implications for investment strategy for some hedge fund — but for us, it was something that got us through a mile of a terrible run. As time went on, and we got better, we started to think about what would happen with blue eyed people on islands, prison wardens, and other such situations.
Here’s the point. If there’s a time, as a runner, that you need a bit of help, it’s the month of February. If you want to listen to Serial for the third time, you do you. But if you’re going slowly enough to think straight, and your iPhone is frozen over, there are a bunch of people figuring out if they get to leave an island or not — you’re welcome to join us.
*think about it on your long run this week. We’ll update this story with the answer on Monday February 22.
