I had to argue with with a graduate student over an ambigram. On two adjacent true/false questions, he wrote "yes" and "no" respectively, then very lightly drew arrows reversing them. The answers were wrong, and I refused to accept the reversal as a legitimate mark. He told me that in Germany, erasures and cross-outs are not allowed, and he had no choice but to use arrows. Nice to see that Americans are now learning to apply European techniques. As for the test in general, I strongly believe that these things are part of education in the broader sense. Thinking about ill-posed problems is an important skill, especially in math. Realizing that your teacher is deeply confused and coping gracefully with him is an important life skill. My grandfather was a sports writer, and he knew the difference between probable and possible. Hilarie
From: Bill Gosper <billgosper@gmail.com>
Apparently, possibility is the intersection of probability with Boolean algebra. A certain 4th grade teacher decided to enrich Saxon Math with a few days of re-education from a private copy of something called "Logic Liftoff", followed by a test supposedly copied therefrom, on which a certain confused 4th grader apparently was reduced to bluffing with ambigrams: gosper.org/logic.png <http://gosper.org/logic.png>. I don't understand how he got credit on the first five answers, since their correct answers are clearly "the sun will rise tomorrow." Or how he didn't lose 5 more points for "Febuary". I actually had to Google for reassurance that they weren't dumbing down the spelling. --rwg