The Surprise Quiz Paradox
When I was a student in grade school and high-school, I hated surprise quizzes. It wasn’t that I didn’t feel prepared or that I had any sort of test anxiety – rather, I believed the unpredictable pronouncements were cruel.
But then I stumbled upon the Surprise Quiz paradox and thought I had discovered a sure-fire method to prevent the teacher from ever administering such an unexpected test of our subject awareness.
Here’s the logic. On Friday afternoon, a teacher informs the class that there will be a surprise quiz someday next week. She won’t say which day of the week it will occur, only that it will be sometime before the week is out.
That means – with absolute certainty – there can’t be a quiz next week!
What?! How can that be?
If the quiz is supposed to occur “next week”, that means it must be on Monday, Tuesday, Wednesday, Thursday, or Friday.
Imagine we attend class the first four days without any quiz.
Then on Thursday night, we’d all know that the test must be on Friday. Clearly not a surprise.
So, if there really will be a surprise quiz, it can’t possibly be on Friday.
Thus the quiz could only be on one of the four remaining days.
However, if we get to the end of Wednesday and still no test, then we’d know the quiz must be on Thursday (since we already ruled out Friday). Again, no surprise. So, the test can’t be on Thursday either.
How about Wednesday?
By the same logic, if we got to the end of Tuesday, we’d know the test would have to be on Wednesday, so once again, no surprise.
Following the logic all the way through, it turns out that there is no day the teacher could give the quiz in which it would be a surprise.
Therefore, no surprise quiz. Ever!
Unfortunately, while the logic is perfectly sound, my teachers didn’t concur and continued to punish us with their unforeseen gifts of knowledge assessment.
The Surprise Quiz paradox is one of the oldest and most discussed philosophical paradoxes highlighting the nature of meta-knowledge and the limits of thinking we know what we know.
This paradox is made strikingly clear throughout A Course in Miracles, particularly in the following passage:
[You are convinced that] you are a body, and the body’s eyes can see. You also believe the body’s brain can think. If you but understood the nature of thought, you could but laugh at this insane idea. It is as if you thought you held the match that lights the sun and gives it all its warmth; or that you held the world within your hand, securely bound until you let it go. Yet this is no more foolish than to believe the body’s eyes can see; the brain can think.
The paradox is that we read these lines with our body’s eyes and process their meaning with our body’s brain. How can that possibly be, and how do we reconcile this enigma?
In our next class we’ll thoroughly dissect and resolve that riddle. Unfortunately, however, surprise quizzes will continue to torture unwitting students.