I always had a strong empathy with the Time Cube guy. I secretly hoped that it was all some sort of clever isomorphism with real math—he'd found some alternate way of thinking about things that while "correct," depended on a completely different intuitive basis. I'd always envisioned it as a joke that someone had spent way too much time on. I am sure you could do something like that. But my hopes were dashed at the MIT lecture when it became clear that no, he was just some guy that we were all making fun of. Really, my hopes had been dashed days before when I actually spent enough time looking at the website to think about it for a while.
Even so, there are days like today when I feel like giving up on this whole traditional sanity thing. I'd shout at the world that we were living time backwards; the answer asks the question; and the future chooses its own past. And I wouldn't be all that serious. At least not at first.
I don't actually see myself jumping off the deep end like that. It is fun to think about though as I think about all the "crazies" out their with their alternative maths and physicses, hoping that at least one of them is a perfectly sane (if twisted) person who has truly found a consistent system with a highly divergent intuitive model.