121017-2052 EDT
__dan:
I liked zog's idea of getting rye to propose how he would solve the problem.
Zog's approach is the same method as one of my old prof's. On a final test I thought there was a problem with a question. In other words, in this case, I thought there was an inconsistency. All our tests were open book and on the honor system. Thus, the profs usually were not even in the room during tests. Dow, the department head was filling in for our regular prof, A. B. Macnee.
Dow's approach in various meetings, and teaching, was to ask questions to try to make the presenter or student more deeply think about the problem. So if you ask him a question it is likely he would not answer it, but try to get you to think a bit.
In this case Dow simply said that I should, for the answer, explain what I thought was wrong with the question and make a best effort to answer what I thought was the correct question.
An example of one of Dow's teaching methods was a homework question something like the following:
There is a rectangular space, physically defined. At a defined point on one face of the space was an electron beam of some initial velocity perpendicular to said face. On an opposite face is a point and the question is what are the uniform electric and magnetic fields in this space that will cause the electron beam to hit the point of the opposite face.
.
Yes, I did see the process of having the student get results by working the problem himself. I was thinking the problem was three weeks old and rye was long gone, the assignment was over.
The university I went to catered to people who had the old tests and homework to copy and hand in, study from. I was not there for that and something about my routine disagreed with the system. I thought it was a scam but that's what the competition was. Graduation rate of the program was much less than 50%. Workload was geared to copying but I'm sure it was great if you knew what was on the test and had a copy of it. Strangers not at class would show up for tests.
There was one question on a final, the question was like 25% of the final, and the final was like 45% of the grade. What was the convolution of two functions given. I was sure that convolution had not been taught in the class and it was not in the textbooks, I checked. This was in the days before wikipedia and I could not find it afterward. I did know that given the space for solving, the problem would resolve algebraically if set up right, but I had no idea what the word convolution meant. They could have printed it in chinese with the same result. This despite doing all first person work.
Had a professor, Bansal, who I thought was solidly in the great, brilliant, genius, range. Then he drew the hydrogen proton on the board and drew the electron as a point charge in orbit, explained the math then said the math could only be used for the hydrogen proton and would not work with anything more complex, like helium. I looked at it for an instant and saw if the electron moved in orbit it would radiate, radiation meant loss of energy, loss of stability, and collapse. I looked around that instant and saw the universe was not collapsing and the professor was saying the model was not useful for solving anything more than a single proton. I was sitting there to learn what the electron is, and this honest genius who knew his stuff was drawing a model that predicted the instability and collapse of all matter of the universe into radiation and random gas.
Convolution is the overlap or coincidence of two functions.
