In my last two posts I talked about the Chiral Caterpillar, or the four different chiralities of reflection, and in Flyby Cones about the small correction to the unit sphere of reflection to account for the fact that the inside flyby angle is zero in half of the reflections. However, I also said that I had at least one rather major unanswered question remaining, but didn’t specify what it was.
In today’s post I reveal what this question was and present a rather feasible solution for it. In short, the first and last segments of the four-sphere-caterpillar didn’t seem to fit properly with the middle one. After toying around with the model, I realized today that I hadn’t reversed both of the hinges. In the post I think had stated something on the lines of the vertical hinge always opening upwards, or other such nonsense. I should have listened to Wittgenstein’s Proposition 7 from Tractatus Logico-Philosophicus:
"Whereof one cannot speak, thereof one must be silent"
Meaning that if I knew that I wasn’t able to say anything sensible, it would have been better off not to say anything.
So, the answer was to reverse both hinges so following from the nomenclature of the Chiral Caterpillar post, the four chiral options are: left/up-left, left/up-right, right/down-left and right/down-right. And this is what it looks like as a rotating 3D model:
I would so much like to say that this is the final answer and that there are no puzzles left to solve. However, the above model is still just an idea. If I’m not able to convert it into equations, there’s probably something wrong with it. But there’s already a tiny possibility that the above model is either the final model or so close to it that it doesn’t make a difference. I still prefer being a bit pessimistic and be positively surprised if this was the final solution.
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