The Piano Teacher’s Parable

The analyst’s dinners with his Aunt Sarah had gotten less frequent in recent years as he spent more time on his job and with his now-growing family, but he still treasured these opportunities. She had been his first piano teacher, and from her patient but insistent coaching back then, he had come to rely heavily on her advice in general. Now they were dawdling over dessert, savoring the last of the wine and enjoying the cozy ambience of the restaurant. “So,” Aunt Sarah prompted, “tell me more about how work is going.”

“Well, it’s pretty good, as I said, but I am a bit frustrated,” the analyst admitted. “I seem to spend more and more time on problems where management wants a quick answer and isn’t willing to wait for a thorough analysis. I keep wanting to take more time to make sure my answer is right, and I’m not getting it.”

“Ah,” Aunt Sarah smiled. “So you haven’t applied what you know about music to how you’re doing your job.”

The analyst looked puzzled.

“Remember,” Aunt Sarah continued, “how I made you practice not only to play certain pieces as well as you could, but also to be able to sight-read and improvise well enough to play other pieces fairly well without much practice on those pieces? Those are two different skills. Sometimes you want excellence. At other times, though, what matters is facility. I think I told you the story of how Arthur Rubinstein got a big break early in his career when another pianist got sick. Rubinstein was offered the chance to fill in – but it meant he had to learn the Grieg A-minor concerto in less than a week … and he did. It wasn’t the best he ever played it, but being able to get fairly good quickly was more important. This sounds like your situation, doesn’t it?”

“It certainly does!” the analyst exclaimed. “I hadn’t really thought of it this way, but we do have the same problem in my field, all the time. For big, complicated optimization problems, we often choose a solution method that doesn’t necessarily get to the optimum, but gives us a high probability of getting close in much less time. I suppose we have to do the same thing, less formally, in how we handle projects and clients, too, but it’s still uncomfortable never getting to do something thoroughly.”

“I’ve gathered from some of our past conversations that you don’t care much for Condoleezza Rice, but you and she have something important in common,” Aunt Sarah told him with a sly grin. “You know that she started out wanting to be a concert pianist, right? Well, I saw an interview with her a few years ago, when she was national security advisor. The interviewer asked, ‘When did you decide you weren’t going to be a concert pianist?’ And she replied, ‘When I got to college and saw 12-year-old kids sight-reading pieces I’d been working on for a year.’ She had the talent and dedication to get to excellence, but not whatever she thought it would take to get to facility. Or maybe she just decided the difference wouldn’t be as large in another field.”

“Actually,” the analyst demurred, “she seems to have gotten a reputation for making decisions too quickly, without digging into them as deeply as she should have. If you’re right that she chose a field where she could get facile, maybe she ended up neglecting the hard, slow work you have to keep doing to make sure your answers are still good. That’s not what you’re recommending, is it?”

“It’s a balance, and you need to keep doing both,” Aunt Sarah explained. “If you never take a piece all the way to perfection, or as near as you can get, and play it in public, you lose some of the understanding and technical skill that makes your improvisation better. If you never improvise, you get stuck in a narrow set of ideas about how to play the pieces you know, and you can end up losing your feel for the music as you concentrate on perfecting every last detail.”

“That gives me another idea,” the analyst said excitedly. “One of the big unsolved problems in my field is how to decide when ‘good enough’ really is good enough. For a decision analysis, you’re supposed to obtain the preferences of everyone whose opinion matters, but you can’t always do that, or even identify them all. So how do you decide that you’ve interviewed enough people to make a sound decision? For an optimization, how do you decide when you’ve searched enough possible solutions to be confident, though not certain, that the best solution you’ve found so far is close to the true optimum? How do you decide that you’ve run a simulation enough times to be confident that there isn’t some high-consequence rare event you don’t suspect is there, waiting to wreck your conclusions? I think we need to study the problem of how much analysis is optimal, taking the cost of analysis into account. I’d bet some of my colleagues would love to do some research on this!”

“Maybe,” Aunt Sarah agreed, “but don’t count on it. From what you’ve told me, most of them, at least the more research-oriented ones, are still focusing exclusively on ‘the best’ no matter how long it takes or how much it costs. And they won’t see the problem with that any more readily than you did!”