Great post, Martin. Spot on. This is a big part of what I enjoy about teaching. Aside from all the usual stuff about not properly understanding something until

Great post, Martin. Spot on. This is a big part of what I enjoy about teaching. Aside from all the usual stuff about not properly understanding something until you've taught it to someone else, there's something else going on, which (by crude analogy to your analogy!) is a bit like the rsync algorithm: you have a large "bitmap" to sync, and limited bandwidth to sync it over, so you proceed by checksumming the receiver's existing copy and trying to figure out what diffs you need to communicate to bring them up to date. In practice this means that teaching is a deeply interactive activity which involves first exploring the contours of someone's existing understanding and then trying to move them to a richer understanding in the most direct way possible. Perhaps this is a more general case of what you're talking about: intuition is one thing that you can try to teach (or communicate) to another person, but maybe all you're trying to teach is something mundane and concrete like the difference between a Google account and a Google Apps account, which is less about intuition and more about having a simple but exactly correct mental model of the world in order to not be hopelessly confused by it.