Musings: On Being Wrong

Physics professor Benjamin W. Schumacher celebrates an underrated condition

My friend Mike is a mathematician at another college and a collaborator of mine on quantum physics research. A college administrator once asked him why scientists were so much easier to deal with than other faculty. Mike replied, "Because we're more used to being wrong." In science, you see, ideas can be rigorously disproved. If that happens to one of your own pet ideas, there is nothing to do but change your mind. This frequent experience, Mike argued, makes a scientist more reasonable and less obstinate.

I don't necessarily endorse this theory of faculty politics. We scientists seem to be endowed with at least our fair share of folly and mulishness. But I laughed when Mike told me the story. I knew that he was really talking about our Game.

Mike and I spend months or years struggling with really hard problems in mathematical physics, and the Game helps us keep going. It works like skeet shooting. One of us tosses out a "clay pigeon," an idea or mathematical relation that might get us nearer to our goal. Once the clay pigeon is launched, both of us do our best to shoot it down using examples, calculations, and logical arguments.

Almost all of our ideas, in fact, turn out to be wrong. The fun and the profit lie in demolishing them as quickly as possible. By now we are pretty good at shooting clay pigeons. Some are easy and take us only a few minutes. On a good day, we might kill a dozen or more. Other ideas take hours or days to reveal their fatal flaws. Once in a while, though, even our best efforts are not enough. When that happens, the idea just might be correct.

Or it might not. We might be fooled for a long while. One time we invented a way of describing the correlations among quantum systems with simple diagrams of dots and lines. Hard mathematics was reduced to counting which lines went where. It was elegant! Since we could not actually prove that the method was right, we never published it. Yet we could never quite prove it wrong, either. Eventually we began to use the dot-and-line diagrams as our own private tool for thinking about quantum correlations. We drew hundreds of them, using the diagrams to formulate conjectures and understand other mathematical calculations we did. A couple of years later, however, some clever colleagues showed us a situation that no dot-and-line diagram could possibly describe. Our graphical "technique" shattered like the clay pigeon it always was.

Were we disappointed? We did hate to see those pretty diagrams go away. But our main reaction was elation. We grinned at the news. We had been wrong because the quantum world turned out to be stranger and more marvelous than we had first supposed. Only the most pinched imagination could possibly be disappointed by that.

On occasion, some idea of ours turns out to be right, and then we've made a discovery. These occasions are wonderful and gratifying, of course. They are also rare, because most new ideas are wrong. The trick is to be verifiably wrong most of the time. If our ideas are verifiably wrong, then we can eventually get rid of them, like those pretty pictures of dots and lines. And if our ideas are wrong only most of the time, then every so often one of them is right. That's enough.

When I was in grad school, my research advisor used to tell his students, "Make as many mistakes as possible, as quickly as possible." At the time this seemed like cockeyed advice. Who wants to make mistakes? Now I understand that he was on to something. Launching and shooting clay pigeons keeps the imagination alive and the wits sharp. Every error, once discovered, is a step closer to the goal. Being wrong a lot is just the price that must be paid for occasionally, improbably, astonishingly being right.

Professor of Physics Benjamin W. Schumacher is a recipient of the Quantum Communication Award, the premier honor in the field of quantum information theory.

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