It’s remarkable how little forgetting seems to happen for Quantum Country readers: Quantum Country users rarely forget after demonstrating five-day retention. How should we interpret this?
One response might be to radically extend the periods between reviews, making the system more efficient. In 2021-04 Quantum Country schedule experiment, I did just that, and found that for many questions, we can extend the schedule a great deal with little apparent penalty: QCVC questions are initially forgotten at very different rates. According to this data, readers who recall the easiest questions in-essay can wait two months for their first review in exchange for only a few percentage points of recall lost.
Maybe that’s true. But I think it’s pretty likely that something else is going on. Consider a question like this:
What is the product of the $X$ matrix with itself, $XX$?
The answer is “the identity matrix.” But my concern is that the question may cue the answer, at least a bit. That is: it communicates that there’s an important property of the X gate which occurs when it’s doubled; there are only a couple plausible such properties; a moment’s thought makes the answer relatively clear if you remember anything else about the X gate. If I could somehow test your memory without cueing you, would it have the same recall rate? Would you have named this relation if I’d instead asked you to tell me everything you knew about the X gate? If you were working on a problem which required you to know this fact? (This latter question connects to Retrieval practice and transfer learning)
I think it’s very possible that this cueing effect is masking some real forgetting that’s going on. And so if we stretch the schedules out a great deal, we’re actually creating large swaths of time in which the reader’s understanding is much shakier than it would be with more regular reviews.
I know that there’s some empirical literature testing Retrieval practice in “free” vs. cued contexts; I should review that literature to see what’s known here.
Something interesting about Quantum Country—and about the project of Spaced repetition memory systems can be used to develop conceptual understanding in general—is that its dynamics look quite different from most of the experimental literature on retrieval practice. I suspect this particular effect contributes: experiments on English–Swahili word pairs aren’t going to be troubled by cueing effects, or at least not nearly at the same rate.
As an informal experiment, I looked through QCVC’s questions and marked the ones which I felt were “uncued”—that is, those where I don’t expect the question context to artificially stimulate the memory. My coding is here, 48 questions of the 112. These do seem to be forgotten more rapidly 20211126172919:
… but it’s still just a 5% drop from 1 week to 2 months, which is still frankly unbelievable.
Another way to test this theory is to consider questions which I expect to be more “rote” and less conceptual. These should have a more pronounced forgetting curve. For example, here are the recall rates for the questions asking for the matrix values of the X, Y, Z, and H gates 20211130215624:
Another way to look at this cueing effect is in relation to the notion of Salience prompts. Consider this question:
After we measure a state $\alpha|0\rangle+\beta|1\rangle$ in the computational basis, is it still in the state $\alpha|0\rangle+\beta|1\rangle$?
It’s worth asking: is retrieval practice really the purpose of this question? Or is it more that these are Salience prompts? Is it a “reminder”—i.e. hey dummy, measurement is destructive! Every time you see this question, you’ll reliably remember that the answer is yes. Your accuracy rate is irrelevant. What matters is that if you hadn’t been asked this question, you wouldn’t behave in accordance with possessing this knowledge as reliably.