Part of this reminds me of a project idea I've had in the past: figuring out how to teach people an 'abstract visual relationship' language. I'll quote from the

Part of this reminds me of a project idea I've had in the past: figuring out how to teach people an 'abstract visual relationship' language. I'll quote from the article: > ... he immediately responded that when he taught algebra courses, if he was discussing cyclic subgroups of a group, he had a mental image of group elements breaking into a formation organized into circular groups. Jacque Hadamard once conducted a study of how mathematicians approach their work, which can still be found in a book called "The Psychology of Invention in the Mathematical Field". Here's an excerpt: > Indeed, every mathematical research compels me to build such a schema, which is always and must be of a vague character, so as not to be deceptive. I shall give a less elementary example from my first researches (my thesis). I had to consider a sum of an infinite number of terms, intending to valuate its order of magnitude. In that case, there is a group of terms which chances to be predominant, all others having a negligible influence. Now, when I think of that question, I see not the formula itself, but the place it would take if written: a kind of ribbon, which is thicker or darker at the place corresponding to the possibly important terms; or (at other moments), I see something like a formula, but by no means a legible one, as I should see it (being strongly long-sighted) if I had no eye-glasses on, which letters seeming rather more apparent (though still not legible) at the place which is supposed to be the important one. It seems to me that this is a surprisingly common approach to dealing with highly abstract subject matter. I first noticed myself doing it while reading Structure of Scientific Revolutions and later used it intentionally in working on math and CS stuff. My experience with it so far leads me to believe it can be taught/strengthened. I've written a much more in depth essay on this in the past, but it's fairly unfinished. I still wonder about it though...