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William_Quixote comments on Harry Potter and the Methods of Rationality discussion thread, January 2015, chapter 103 - Less Wrong
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A spell to grade tests is probably not an old spell that's been around forever since no one else seems to use it, but QQ may have invented it for this purpose.
Either way, it's existence is a further hint to the nature of magic in the world of HPMOR. It involves some pretty sophiscated natural languge processing. The fact that magic can do natural language processing is hinted as significant in chapter 6 while Harry is studying the retrieval charm and trying diffent phrases that point to "bag of gold". If we knew how magic could read a test and predict what the ministry would give it, we would know a lot more about magic.
Note, we can reject the hypothesis the the spell just doing something simple like implements a big data style algorithm with 800 years of prior tests and grades as its training corpus because QQs students are going to be writing answers that are very different from the training set and so the model wouldn't have good predictive power
Quirrell is joking. He doesn't care about the results of the ministry-mandated test, as he already knew what grades his students had earned from him regardless.
At the beginning Quirrell had said any tests he gave would grade itself in real time so students could help each other for bonus points. So Some method of achieving a similar effect exists.
Assuming Quirrell did have the final grades already calculated before the test, did Quirrell know ahead of time how the students would score on the test and have the final grades reflect that, or did he use the grades up to that point in total indifference to the test scores?
ETA: Oops, I seem to have completely missed this discussion when I posted this here. My bad.
There's a much simpler explanation: The tests came pre-graded and QQ just cast a spell to reveal the invisible grades and ignored all the answers.
The spell might just be querying Quirrel or a confederate in real-time to grade the results.
Yes. Note that Q is terrifyingly fast; remember the scene where he speed-reads the newspaper.
Though now it's been pointed out by others, I agree it's pretty much certain that the actually intended meaning is that Q is joking, he ignored their answers to the official exam, and their grades were determined before they ever took it.
And even more relevantly, the scene where he sits in his office, grading papers, not moving anything but his eyes.
It's not clear he's doing it super-fast on that occasion, though, is it?
That's true.
If you accept the definition of the supernatural as a physical law that applies to ontologically basic mental things, then finding the answers to a test would seem to be something the supernatural can do without having to do natural language processing, the same way a spell can turn someone into a frog without having to process DNA. We think of "the answers to a test" as a concept.
That just means that the spell inventor doesn't need to know anything about or implement natural language processing. To get magical primitives like ontologically basic mental parts you still have to have complex and fully reducible algorithms running over the base physics outputs somewhere even if that somewhere is "parallel to or between frames of the simulation".
If "gets the answers to the test" is a primitive, no you don't. The magic just does it. That's the difference between magic and science. The spell is a black box with no parts inside.