This is interesting. I think the article would be at least slightly enhanced if the theorem is preceded by a rigorous definition of "know" (given a graph) -- even if the obvious guess is the right one -- and if the allusion to a Galois connection were accompanied by a definition thereof. (For example, I'd like to know whether a person automatically "knows" themself, even if this doesn't affect the theorem and its proof.) --Dan Jim wrote: << I'm thinking of submitting the following bit of silliness to Mathematics Magazine: http://jamespropp.org/galois.pdf Comments are welcome! In particular, I'm pretty sure that statements fairly close to "The people you know are the people who know all the people who know all the people you know" already occur in print, and I'd like to give credit where credit is due (even if that prevents my article from fitting onto one page).
Those who sleep faster get more rest.