Monday, August 1, 2011

The Final Question -- and Cupcakes

Once upon a time, there was a math professor that gave an exam. When the students entered the testing room, they were given a mathematical framework and a list of problems to solve, each of which built on the solution to the previous one. The professor told them that they must solve all the problems in the time allotted, and that whoever did so, would pass; whoever did not, would fail.

The professor also told them that they should take each proposed problem solution to a machine in the corner. If the solution was correct, the machine would give them a cupcake.

Well, on the first problem some of the students who found the solution first got a bit rowdy and started waving their cupcakes in the faces of those who were slower and teasing them. The professor told them to settle down and stop it, or the professor would kick them out and they would fail.

At that that point, one of the students said to several others: “Look, this test is hard, and I think it’s so hard that none of us is going to pass unless the professor lets us. So the best way to do that is to show the professor that we appreciate all that he has done to teach us, and that we’re trying hard to please him, and we’re good people – not like those rowdy ones. So let’s all work together on each problem, and when we get our cupcakes we’ll keep giving some of them to the professor. And if we give him enough cupcakes, even though we will never answer all the questions, we’ll still pass.”

Many of the students, looking at the nasty problems coming up, were convinced that this was the only way they were going to pass, and so they agreed. But the student did not convince everybody. Some students rejected the idea that the test was impossible, and that passing the exam depended in any way on the professor.

Then there ensued a strange scene. On each problem, the students working together in a group solved the problem faster, and so should have given the machine the solution ahead of the few who were working solo. But many of them were concerned that they didn’t have enough cupcakes to give, and so they were over trying to convince the ones who were doing it alone that they should try to join the group. And sometimes they would succeed, as one of the loners felt that the test was becoming too hard; and sometimes they would lose a member, as some members of the group felt their point of view wasn’t being listened to. And then sometimes one of the group would get hungry and eat a cupcake instead of contributing it; so they had to kick that member out of the group until the member said he or she was sorry. And then they had to spend some time gathering the cupcakes and giving them to the professor. So as it worked out, the loners were solving the problems just about as fast as the group.

And then they got to the problem right before the last one. And it was a really nasty problem. Moreover, because they had been working in a group, the members of the group hadn’t been paying close attention to all the details of the previous solution, so none of them could put it all together and come up with the last step in this solution. And they were really worried that they hadn’t gotten enough cupcakes yet.

So finally one of the loners came up with the solution. And this caused an even bigger argument among the group, but finally one part of the group went over and looked at the loner’s answer, and got the solution – although they didn’t really understand that last step. And now there were two groups. The first group said, we haven’t got enough cupcakes, but if everyone comes back and helps us solve the next-to-last problem, and gives us their cupcakes, we’ll have enough. And the second group said, yes, we solved the next-to-last problem, but if we don’t get the cupcakes for the next-to-last problem from everybody, the first group and the loners, and give them to the professor, the professor will decide that we can’t work together and just aren’t nice enough. And the loners just kept being stubbornly convinced that it was all about solving the final problem.

And now there was frantic activity all over the room. The first group was still trying to solve the next-to-last problem, and badgering the second group and the loners for cupcakes. The second group had given up on the final problem (partly because they still thought it was impossible, and partly because they couldn’t solve it anyway, since they didn’t understand the solution to the next-to-last problem) and was badgering the first group and the loners for cupcakes. And the loners were trying to work on the final problem, and telling both groups that if they weren’t going to help solve the final problem, at least they should go away and stop bothering them. And as they did this, the clock kept ticking; and the end of the exam drew closer; and closer; and closer.

The moral of the story is – no, I’m not going to tell you the moral of the story. Consider this the final question of your exam: what is the moral of this story? If you get it right, you pass; if you get it wrong, you fail.

You can send me some cupcakes, if you think that will help.

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