The perils of intuition

Look at me! I’m blogging from Cafe 1842 in Waterloo, like the cool kids do!

Last week at the conference, I blandly assured my old advisor (after several drinks on both of our parts) that a certain statement about objects called “trees” and “dominating sets” was clearly true. (More details available on request, but I assume that most of my readers don’t care about the technical details enough to parse through them.) He, naturally enough, asked me to write up a quick demonstration of this, as it’s closely related to a problem we’ve worked on in the past that he’s currently waving at one of his present grad students.

I’m still convinced that the result is true, but nailing down the particulars is looking to be a mite trickier than I’d hoped.

I’ve heard that most people think in either words or pictures, and I don’t think that’s the case for me. If I were thinking of this in terms of words, then the proof would be concurrent with the thought, right? And if I thought in terms of pictures, then I could just draw out a diagram showing the source of my convictions on this score, and then explain it by describing what’s going on where. Whereas with what I’ve got, I perceive how the proof has to work on some non-visual, non-verbal level, and converting that into things that other humans might understand is the sticking point.

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