The surprise exam
It’s never going to happen.
Today’s problem could be a description of my own classes – slow and lazy. The teacher tells the class that they’re going to have a test, focusing on Aristotle in particular, some time between now and the end of the term. And it’s going to be a surprise.
Later Bob and Pat are talking about the announcement. Bob, being a shining example of slowness and laziness, is worried, but Pat’s not so sure that there’s even going to be a test. She reasons that the closer to the end of term it gets, the less of a surprise the test will be. But this chain of logic can be used to work backwards, thus making it seem that there’s never going to be a test at all.
About a week later, though, the teacher announces the test much to Bob’s dismay.
Was Pat’s reasoning flawed or what?
Pat’s reasoning doesn’t seem wrong. The longer the teacher leaves the test, the less surprising it’s going to be. It wouldn’t be a surprise if it was left until the last day of term, and since that date can be eliminated, so can the previous day and so on. In reality, on the other hand, the teacher is free to set the test at any time. To set it a week after it was first announced is as good a time as any.
Later Bob and Pat are talking about the announcement. Bob, being a shining example of slowness and laziness, is worried, but Pat’s not so sure that there’s even going to be a test. She reasons that the closer to the end of term it gets, the less of a surprise the test will be. But this chain of logic can be used to work backwards, thus making it seem that there’s never going to be a test at all.
About a week later, though, the teacher announces the test much to Bob’s dismay.
Was Pat’s reasoning flawed or what?
Pat’s reasoning doesn’t seem wrong. The longer the teacher leaves the test, the less surprising it’s going to be. It wouldn’t be a surprise if it was left until the last day of term, and since that date can be eliminated, so can the previous day and so on. In reality, on the other hand, the teacher is free to set the test at any time. To set it a week after it was first announced is as good a time as any.
Another gradient problem tomorrow and an old friend – the Sorites Paradox.
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