Those make sense. I note they’re not just simple lines in a space of ideas, but use a wider gamut of the senses than I was aiming for. Probably, the sort of shapes I was going for are in an unhappy middle ground. Too impoverished compared to the senses, too rich compared to the austerity of diagrams in category theory. So this post should have been about the images different proof methods bring to mind.
Recursion/induction is like a loop with an off-ramp. Like a letter Q.
Maybe proof by contradiction is like an inverted house of cards. You make an assumption, and then look for ways to knock it down.
proof by probability feels like a gauge, like a line with an arrow that indicates a threshold.
Direct proof is a square. It just sits there on its own.
I don’t know one directly for contraposition, but it involves negative space like the image of the faces and vases.
Those make sense. I note they’re not just simple lines in a space of ideas, but use a wider gamut of the senses than I was aiming for. Probably, the sort of shapes I was going for are in an unhappy middle ground. Too impoverished compared to the senses, too rich compared to the austerity of diagrams in category theory. So this post should have been about the images different proof methods bring to mind.