The Other Fold

In my last post I presented a mathematically accurate way of describing the folding of two neighboring bikau quadrilaterals, so that the angle of reflection in one of the motion vectors is zero. In the post I said that I need to apply the idea to the whole Folded Reflection model before I can be sure that the theory is ready. I was hoping that it wouldn’t take too long, but I was apprehensive of the fact that I’ve made promises like this before.

However, just a day after the last post, I present the other fold. You see, the Folded Reflection model describes two types of reflections. The ‘vertical reflections’ is where there are twice as many true reflections on one side of the folded pair, due to the angle of reflection on the other pair being zero. This is the model of the previous post. In today’s post I present the ‘horizontal reflection’, where the two bikaus on either side of the plane of reflections are otherwise the same as in the ‘vertical reflection’ model, but where the bikaus are tilted in a way that there are (more or less) identical, reflections pattern for the two pair of motion vectors. Because of the complex shape of the folded bikau, the tilts have minor differences, but I won’t delve into those in this post.

Rather, here is the other folding pattern, where the two yellow cones should be nearly identical to the cones presented in my last post:

If you look very carefully, you can see that their sizes aren’t identical, as the circular bases of the cones are drawn on the surface of a sphere, meaning that that the circular base here is very slightly smaller than in my previous post. I’m hoping this won’t cause any problems in the future.

And if no problems arise in fitting these two folds together, this should be the mathematical basis of the Theory of Everything. However, I won’t make pronouncements stronger than this. It’s just so easy to be wrong, when extrapolating from incomplete data, even when the incompleteness doesn’t seem very big.