The Ford Circles correspond only to the rational numbers, so there should be no expectation the tangent points would "cover" the real line. Still, I agree it is a good example, but for a different reason than you were thinking. It shows how Doron's "direct perception" can lead to false conclusions.
"Direct perception" from the diagram leads to the incorrect conclusion there would always be gaps. In fact, the rationals are everywhere dense, so there are no gaps. But after correcting for this mis-perception, "direct perception" leads to another incorrect conclusion that the rationals cover the real line.
I realized they only corresponded to the Rational Numbers, but still found the illustration cute, so to speak.
There's a Lewis Carrol quality to it.
But it seems I'm not only suffering from an ignorance of the subtlies of accepted mathematics, but I really wasn't directly perceiving in the illustration what Doron meant it to give a direct perception of.
It now has something to do with "Complexity" and "Simplicity," and I don't know what Doron means by this new word combo yet.
Well, I get half way to understanding him, but before I can close the gap, there is another halfway to be traversed. Then another, then another ....
But I'm sure he'd say that's because I'm going "step by step." and am a "verbal thinker."
I think he does have a basic frame he hangs everything on. And I sort of see it. It's the fractal partitioning or whatever you want to call it, that's generally based on two stand alone, contrary principles.
Every question about the frame requires an answer that articulates a new interacting word pair and partitions spawned by it.
The deeper you go, the more it fractures.
But heck, I have a handle with no bicycle attached to it. lol
