In my last post on my quest to explain the Theory of Everything with the reflection of elementary particles of energy (dots), I talked about precision reflections. In the post I was able to apply the mathematical concept of the tetracone of reflection to the model with circular planes of reflection.
In today’s post, I once more introduce a new mathematical tool. While reflection was described by a tetracone, the full model requires a shape for the grazing of dots as well. In my original model I thought this might not be required, because I start by defining the central vectors that graze each other. When the whole shape is drawn around these two vectors, you don’t necessarily need a tool to describe them. But this isn’t he case for the shapes of the vectors that are reflected from the center of the reflection model. Thus far, I’ve only drawn half of the approaching and reflected vectors, and more or less ignored what happens to them after grazing.
Or to be frank, the shape that I’ve been building has thus far ignored that the geometry at the edges has to allow for grazing as well. To illustrate the problem, I’ve reinvented the wheel, at least figuratively. You see, the distance between the two grazing dots is by definition always 2r, or twice the radius of a dot. This distance, marked by a green cylinder, can be considered the axle for a wheel, whose diameter is the length of the grazing vector. While the two vectors grazing have a different angle of movement relative to each other, the two grazing wheels are identical. In the image below this axle-wheel combination is seen at the center (between the tetracones).
Because the wheels are drawn by rotating a grazing vector perpendicularly around the axle, this shape should never be wonky. However, if we draw an axle from the end of one reflection vector to the end of another and draw grazing wheels by rotating the reflection vector around the tip of the axle, we see that in the below image, the second grazing wheel is helplessly wonky.
When viewed from above, the grazing wheel looks even more helpless:
The curious thing is that while you might imagine that I’d be despondent seeing that there’s something wrong with my shape, I’m actually quite optimistic. The reason for this is that I had cut quite a few corners in creating the above image. I knew that I had made some assumptions that hadn’t been grounded on anything very tangible, but I had to start from somewhere. Only when these assumptions are in direct contradiction with the overall logic of the theory, can they be corrected. And this is exactly what my wonky grazing wheel allows.
I still don’t know how to solve the problem of the wonky grazing wheel, but I know that this is my topmost priority. The solution might be simple or hard but I’m quite confident that the solution exists. I’m not sure whether solving this problem will be the final big problem, or whether it just reveals a knew problem to be solved. Either case is possible. Only time will tell.
And to end this post, here is the rotating model with grazing wheels:
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