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When you convey knowledge to a student, you rarely convey to them all of the complexity and detail that existed in your own understanding.

Knowledge tends to decay over time, accumulating compression errors. The thing you convey to your student is pared-down and simplified, and the thing they receive will contain additional leaps and connections as they integrate it into their own understanding, some of which may be unintended or inaccurate. When they attempt to pass the knowledge along to their student, this process will compound, resulting in serious drift.

This is especially problematic for domains of knowledge that are not well-pinned-down and explicit; if you are teaching someone multiplication and they accumulate misunderstandings, this is not a huge problem because various algorithms for multiplication are well-known and well-described; there's something of an anchor for the core concept, preventing excessive drift. But if what you are attempting to convey is original or pre-paradigmatic, such that no anchor exists, drift can be a serious problem.


When teaching, it helps to make your target "my student will correctly convey this to their student," i.e. to think in terms of heading off miscommunications and miscommunications in their future explanation of the topic at hand. This leads to more robust communication than directly focusing on the student in front of you.