Sometimes mathematics can be brutal. I was relatively sure that the reflection model that I’d created for elementary particles of energy was finished. I said so in my last post “Three Reflection Spheres”. I thought the only thing left was to convert the reflection model into equations. However, pretty soon as I started doing this, I faced a stone wall. The model assumed that the distance between neighboring elementary particles of energy (the kaus along the same plane, not the ones reflecting) would be the same at each point of reflection. However, when I converted the shape with one hinge for three spheres into equations, the equations unequivocally showed that this wasn’t the case with the three-sphere-model.
This means once again that while I was correct in some parts of the theory, I was wrong in some rather major respects. But it’s not bad that I was wrong. After all, I was wrong in a useful way. I wasn’t wrong about the unit sphere of reflection, and I wasn’t about the hinge sphere. Rather, I was wrong in assuming that these were different spheres. What now seems almost inevitable is that there is just one sphere of reflection and hinging. I’m still working on the revision of the theory, but it seems most likely that the sphere of reflection holds two hinges: one for each path of kaus. In the 3D model below, I illustrate the concept: the red nodes denote the hinges, the red toruses the hinging paths and the blue toruses surrounding the green node B mark the circular planes of reflection. If you look closely, you see only a single yellow reflection connection between kaus J and K. When the hinging angle is increased above zero, only these two kaus remain in contact with each other.
If this model holds, there are always a pair of hinges between neighboring unit spheres of reflection that open in the same direction and a pair that opens in the opposite direction.
While this idea seems really solid in my head, take this with a hefty pinch of salt. I haven’t really had time to think about all of its weaknesses. So, be prepared to hear where I’ve found I’ve been wrong. I hope this is the final truth, but probably this is a bit too much to hope for.
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