The Sting (directed by Roy Hill, 1973), besides its many other endearing qualities, is a two hour documentary of what happens in the mind, in a fraction of a second, when we are trying to solve a mathematical or logical puzzle. I had an opportunity to convince myself of this recently while watching it again 25 years after I first saw it.
The overall effect of the movie on the viewer is like the moment when the solution presents itself to you after you’ve been staring at an equation or a proof. It is neat and elegant, and seemingly effortless, but between the moment you think you don’t know and the moment you do the brain will have performed dozens of operations. Just how? Well, I can only know retrospectively by writing each step out on paper, and even then I can’t be sure my account is really a reflection of what has happened in my head, or only some kind of simplification.
Those steps, which I write on the right hand side of a proof, are like the title cards in the movie. And, uncannily, the title cards actually correspond to the sort of operations required in a logical proof. The Players (step 1) is a set of premises which I must list, together with the conclusion. The Set-Up (step 2) is the planning: the laying out of a strategy which I will follow. This involves thinking many steps ahead, predicting what will happen, say, on line 17 while I’m still on line 7. It’s a process which requires that many items of information be held in the head simultaneously, without letting go of any of them, while the brain is mapping out the route.
The Hook (step 3) is very much like the assumption that I must make to break up an intractable string of symbols. Like in the movie, what I do at this stage will pay off much later, more handsomely than anything I would have achieved without the assumption. But also like in the movie, I have to discharge the assumption, that is, I can’t have a sentence starting with ‘then’, ‘therefore’, ‘thus’ or ‘so’, without being bound by the ‘if’ of the assumption in the same sentence. In the movie, once Gondorff pulls the first stunt on Lonnegan at the poker table, there is no turning back. He and the boys are now committed to working towards closing the scam.
The Tale (step 4) is basically working restlessly through the material now at hand applying the various rules of inference until a workable formula crystallizes. In the movie, it is the putting together of various parts of the elaborate off-track betting den hoax.
The Wire (step 5) and The Shut-Out (step 6) are unconventional or counterintuitive moves, which may surprise the problem solver himself – something such as bringing an entirely new expression into the proof by means of a disjunction (known as addition) or considering two alternatives (proof by cases) whereby you can assure yourself of the correctness of your reasoning by getting the same result from both alternatives.
Finally, there is The Sting (step 7) – the last title card in the movie – when all the strands come together and all the loose ends are tied up. Beats me.
The overall effect of the movie on the viewer is like the moment when the solution presents itself to you after you’ve been staring at an equation or a proof. It is neat and elegant, and seemingly effortless, but between the moment you think you don’t know and the moment you do the brain will have performed dozens of operations. Just how? Well, I can only know retrospectively by writing each step out on paper, and even then I can’t be sure my account is really a reflection of what has happened in my head, or only some kind of simplification.
Those steps, which I write on the right hand side of a proof, are like the title cards in the movie. And, uncannily, the title cards actually correspond to the sort of operations required in a logical proof. The Players (step 1) is a set of premises which I must list, together with the conclusion. The Set-Up (step 2) is the planning: the laying out of a strategy which I will follow. This involves thinking many steps ahead, predicting what will happen, say, on line 17 while I’m still on line 7. It’s a process which requires that many items of information be held in the head simultaneously, without letting go of any of them, while the brain is mapping out the route.
The Hook (step 3) is very much like the assumption that I must make to break up an intractable string of symbols. Like in the movie, what I do at this stage will pay off much later, more handsomely than anything I would have achieved without the assumption. But also like in the movie, I have to discharge the assumption, that is, I can’t have a sentence starting with ‘then’, ‘therefore’, ‘thus’ or ‘so’, without being bound by the ‘if’ of the assumption in the same sentence. In the movie, once Gondorff pulls the first stunt on Lonnegan at the poker table, there is no turning back. He and the boys are now committed to working towards closing the scam.
The Tale (step 4) is basically working restlessly through the material now at hand applying the various rules of inference until a workable formula crystallizes. In the movie, it is the putting together of various parts of the elaborate off-track betting den hoax.
The Wire (step 5) and The Shut-Out (step 6) are unconventional or counterintuitive moves, which may surprise the problem solver himself – something such as bringing an entirely new expression into the proof by means of a disjunction (known as addition) or considering two alternatives (proof by cases) whereby you can assure yourself of the correctness of your reasoning by getting the same result from both alternatives.
Finally, there is The Sting (step 7) – the last title card in the movie – when all the strands come together and all the loose ends are tied up. Beats me.
Let me recommend A Serious Man by the Coen Brothers. Gematria, numerology, the uncertainty principle, the Mentaculus (by Arthur Gopnik), Schroedinger's Cat as well as the Meaning of Life in the Goy's Teeth (or not) - a wealth of intellectual pleasures.
ReplyDeleteWonderful. One to watch and rewatch over the years.
I will be heading for the DVD shops then. Thanks Michael.
ReplyDelete