Retrieval check (from lesson 1, new setting). A chess engine can be described at three of Marr’s levels: computational (what problem is it solving, and why — e.g., “find the move that maximizes expected outcome under the rules of chess”), algorithmic (what representations and processes — e.g., minimax search over a game tree with alpha-beta pruning), and implementational (what physical substrate runs it — e.g., GPU tensor cores evaluating a neural network). A claim like “this engine runs the same search algorithm whether it’s on a phone or a data-center cluster” is making a claim that one of those levels stays fixed while another varies. Which level is being held fixed, and which is varying? Answer before reading on; the solution confirms it.
Two more terms, then the puzzle
Massed practice: concentrating all study or practice of one topic into a single session — cramming. Spaced (distributed) practice: spreading the same total study across multiple sessions, separated by real gaps of time. The spacing effect — one of the most replicated findings in memory research, documented since Ebbinghaus’s 1880s work — is that spaced practice produces better long-term retention than massed practice for the same total study time, with the advantage often small right after studying but large after a delay.
Interleaving: mixing practice of several related-but-distinct things within one session, instead of completing one fully before starting the next (“blocked” practice). It typically feels worse in the moment (more effortful, more errors) but produces better long-term retention and — specifically — better ability to tell which technique a new, unlabeled problem calls for.
The puzzle
Lesson 15 established that a chunk’s activation sums a term over every past use: B = ln(Σᵢ tᵢ^(−d)). Lesson 16 established that a genuine retrieval attempt — reconstructing something under effort, not just re-reading it — counts as one of those uses.
Here’s the question neither lesson answered: does it matter how far apart two uses of the same chunk are? Consider two review schedules for the same fact, each adding exactly one more retrieval attempt on top of the original encoding:
- Schedule 1: review the fact again 1 hour after first learning it.
- Schedule 2: review the fact again 3 days after first learning it.
Both add exactly one term to the activation sum. Using the mechanism from lessons 15–16 — specifically, what “retrieval” actually requires to count as effortful reconstruction rather than something closer to recognition — explain why Schedule 2’s review is a more valuable use-event than Schedule 1’s, despite both being, mechanically, “one more retrieval.” Then state the one concrete design rule this implies for when a review should be scheduled relative to how much the earlier trace has already decayed — not “spacing is good,” but the specific condition a good spacing schedule needs to satisfy.