Combinatorial explosion of questions and errors

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(there might be a more standard term for this)

Non-interactive explanations (e.g. textbooks, blog posts, and YouTube videos, in contrast to interactive explanations like classrooms and tutoring) face the problem of combinatorial explosion of questions and errors. As the length of the explanation increases, there will be more and more potential questions a learner could ask, as well as more and more potential errors in reasoning the learner could make (or misconceptions they could have). As the explanation is non-interactive, the explainer must anticipate in advance which questions and errors are most likely for the intended audience, and must decide how extensive the explanation will be.

Consider the experience of reading a mathematical proof. Each step in the proof is an opportunity for the reader to become confused, as they might not understand a calculation or reasoning that is being done.

Here is an example of this sort of thing, as related by Nate Soares:[1]

The problem is, most of the time that I get stuck, I get stuck on something incredibly stupid. I’ve either misread something somewhere or misremembered a concept from earlier in the book. Usually, someone looking over my shoulder could correct me in ten seconds with three words.

“Dude. Disjunction. Disjunction.”

These are the things that eat my days.

Some related phenomena (these problems also arise from the static/non-interactive nature of learning material):

  • the thing where course instructors reuse old exam/homework problems it's hard to come up with new problems
  • the problem with storing static example problems in spaced repetition software, because the user will just memorize the answer instead of treating it like a new problem

See also