Spherical Reflection, or Bending it Like Beckham

 In my last post I talked about the mathematics of pushing a string. In the post I described the way two entangled helices of elementary particles of energy (dots) are reflected by either three dots (outside of the saint Hannes knot), or by four dots (in the saint Hannes knot). In the post I presented an image showing the reflection outside the saint Hannes knot but promised that I would soon talk about what happens in it.

So that’s what I’ll try to do today. After a lot of hits and misses I ended up with a 3D model that looks like this: 

If we stop the spinning, the model looks like this:

In this model, you don’t see the dots moving along their orbitals, which might be a bit confusing. There was no way for me to include their movement, as I’m not ready enough with my model. However, the movement of the dots is a crucial feature of the image. You see the dots in the left move towards the viewer and the dots away from the viewer (or vice versa: the important thing is that the direction of their movement is opposite. So, in the above image, you can image the 45-degree angles to be the golf-clubs of a left and right-handed players, hitting golf balls (or a string of them) in opposite directions. But as the golfers hit the balls, they also hit each other’s clubs, causing the balls to spin. In Finnish we used to call this a banana shot, but apparently the more common English term is a curl.

If we simplify the above image to a 2D projection of just the dots in the plane of reflection, we get this:

And if we include circular arced arrow for the spherical reflection, the image looks like this:

So, what is spherical reflection? Very simply put, it is the second reflection of the once reflected motion that cause dots to move in a continuously ‘curled’ orbital:

It will still take a while until I can convert this general idea to proper equations describing the curved motion of vectors. I can’t promise anything, but I wouldn’t be too surprised if it took days, rather than weeks or months. Then again, considering that I have worked on this for almost two and a half years, there’s always the possibility that there’s still something that I have overlooked.