Marilynne Robinson writes that “I remember once, as a child, walking into a library, looking around at the books, and thinking, I could do that.” My “I could do that” moment happened when I was in my early thirties.
“Hey, Doc!” Ben said as he poked his head through my office door.
“I’m not a doctor yet—I’m just a graduate student,” I replied.
“Okay . . . but you’re teaching my class and I’m very confused.”
I was very aware that Ben was in one of my classes. There weren’t a whole lot of 6’10” black guys on Marquette’s campus, and he was the only one in either of my classes. I would have known who he was, though, even if he wasn’t one of my students. I have been a college basketball fan since my youth, and Ben was one of the best players on the Marquette Warriors, the university’s very fine division one basketball team. His eligibility to play depended on a number of things, including not failing any of his classes.
I was in the first semester of my second year of doctoral studies at Marquette. The research assistantship that had paid my tuition and a monthly stipend pittance during my first year had shifted to a teaching assistantship. I had been a teaching assistant during my years earning a master’s degree at the University of Wyoming, but at UW that simply meant leading a couple of Friday discussion groups trying to explain to confused students what the professor had been talking about in the two lectures earlier in the week. At Marquette, a teaching assistantship meant that I had my own classes—two sections of Logic—for the first time in my life. And I had never done this before.
Most graduate students in the Marquette philosophy department had a cubicle with a desk in a large room with at least a dozen such cubicles where they held “office hours.” Since I was six or seven years older than my fellow PhD wannabes, I was special enough to have my own office. Actually, it was the office of a professor who was on sabbatical for the year; the authorities were good enough to allow me to squat there until he returned.
I invited Ben to sit down and asked “So what can I help you with? What are you confused by?”
“Pretty much everything,” he said. We were only three weeks into the semester, so there hadn’t been a whole lot of graded material yet. But his average on the first two quizzes was a 40. “But I guess I’m most confused by the ‘necessary and sufficient’ thing.”
“That’s pretty basic,” I thought. We had worked on the important difference between necessary and sufficient conditions the previous week. I had illustrated the distinction with what I thought were clear and creative examples in class, and no one—including Ben—had raised a hand when I asked, “are there any questions?” It would take a good deal more experience in the classroom before I realized that very few students ever respond in class to that question even if they are completely confused.
After a few seconds, I decided to try bringing logic into Ben’s world by inventing a hypothetical end-of-game scenario on the fly. “Okay, here’s the situation. You’re playing the University of Wisconsin (Marquette’s hated in state rival), The Warriors are behind 75-74 with five seconds left and have the ball. You are underneath the basket calling for the ball, but before the pass comes the guy guarding you pushes you from behind and the ref calls a foul. There’s one second left on the clock. Now what happens?
“I get to shoot free throws!” Ben said with a smile.
“That depends on whether we’re in the bonus or not. I get two shots if we are, but it’s a one-and-one if we aren’t.”
Sidebar for non-basketball fans: First, what’s wrong with you? Second, after a team collects seven fouls in a half, the opposing team gets a one-and-one opportunity for every foul afterwards, which means that if they make the first foul shot, they get a second one, but don’t get a second shot if they miss the first. After 10 fouls, every future foul means two shots for the opponent, whether they make the first one or not.
“That was Wisconsin’s eighth foul of the half, so you’re in the one-and-one,” I said. Ben stopped smiling, since he was not a particularly good free throw shooter. “So what do you have to do in order not to lose the game?”
“I have to make the first free throw.”
“Right, because if you miss it the game’s over and you guys lose. What happens if you make the foul shot?”
“The game is tied, and I get another foul shot,” Ben replied.
“Okay, in other words in order for you guys to not lose the game, it is necessary for you to make the first free throw. What happens if you miss the second free throw?”
“The game goes to overtime!”
“Where you could either win or lose. What happens if you make the second free throw?”
“We win! I’m the hero! The crowd goes wild!”
And now it was time for me to bring the lesson home.
“So you just showed the difference between necessary and sufficient conditions! In order for the Warriors not to lose the game, it is necessary for you to make the first free throw. The team doesn’t have a chance to win unless you make that shot. But making that first shot isn’t sufficient for the win. You could still lose if you make the first shot but lose automatically if you miss it. Making the first shot is a necessary condition for victory, while making the second shot is sufficient for victory. Get it?
“Yeah! That’s really cool! I need to practice my free throws!” Ben picked up his backpack and left, with a “Thanks, Doc!” as he walked out the door.
“I’m not a doctor yet . . .” I started to say, but he was already well down the hall. “But I will be one before long,” I thought. “That was fun! I can do this.”