One of the five major errors from the 2022 VCE mathematics exams concerned a question on the mass distributions of cans filled with liquid. The stuff up was that VCAA didn’t declare which two of the three mentioned variables – Can, Liquid, Total – were to be assumed independent. Although it was 0% students’ responsibility to do so, it was also not obvious what was a reasonable independence assumption to make, a non-obviousness that VCAA eventually steamrolled, in their three-months-later exam report (Word, idiots). The independence question led to a heated argument on this blog, so naturally I titled the subsequent blog post “Cannery Row”, playing on the title of Steinbeck’s famous novel.
John Steinbeck wrote a sequel to Cannery Row, titled Sweet Thursday. Steinbeck’s sequel is not very good but it has a memorable scene, which works very well as a sequel to VCAA’s exam stuff ups. The scene concerns Joseph and Mary (one person), a schemer who is always looking for an angle. Doc (pictured above), the main character of the novel, is teaching Joseph and Mary how to play chess:
One day, sitting in Western Biological, Joseph and Mary saw a chess-board and, finding that it was a game and being good at games, he asked Doc to teach him.
J. and M. easily absorbed the characters and qualities of castles and bishops and knights and royalty and pawns. During the first game Doc was called to the telephone, and when he returned he said, “You’ve moved a pawn of mine and your queen and knight.”
“How’d you know?” the Patron asked.
“I know the game,” said Doc. ”Look, Joseph and Mary, chess is probably the only game in the world in which it is impossible to cheat.”
Joseph and Mary inspected this statement with amazement. “Why not?” he demanded.
“If it were possible to cheat there would be no game,” said Doc.
J. and M. carried this away with him. It bothered him at night. He looked at it from all angles. And he went back to ask more about it. He was charmed with the idea, but he couldn’t understand it.
Doc explained patiently, “Both players know exactly the same things. The game is played in the mind.”
“I don’t get it.”
“Well, look! You can’t cheat in mathematics or poetry or music because they’re based on truth. Untruth or cheating is just foreign, it has no place. You can’t cheat in arithmetic.”
Joseph and Mary shook his head. “I don’t get it,” he said.
VCAA just doesn’t get it.
And the choice of which two random variables are independent matters. You get different answers depending on the choice (although the answers are the same when rounded to the accuracy required in the question).