A Teaser Twisted Knot

If I’m not mistaken, this is the longest pause between my posts. As regular readers know, I’ve been on a quest to explain the interaction of molecules (and elementary particles of energy) by reflection or fully elastic collisions. I’ve been really close to the final answer for a long time, but have time and time again hit a mathematical brick wall. This brick wall is that if I need to explain anything by any other means than reflection, I’ve lost the mathematical game.

You see, I can make all sorts of mathematical shortcuts to form a rough idea, but if I can’t eventually lose these crutches, the theory doesn’t hold.

I’ve tried so many different ways of forming closed-loop orbitals through reflections and each time these attempts have failed. For a while I presented these ideas as posts, but eventually decided that without something very solid, I just can’t keep on posting with minimal change.

These past days I’ve had quite a few insights that might turn into something very concrete. I’m not at all sure whether these ideas will pan out but at least after a long pause I can turn my ideas into equations. And these equations form a new kind of a twisted knot:

The above knot might still be just a cool image. Or it could be something much bigger.

Had I posted a lot lately, I wouldn’t have posted this yet. But as I’ve been under a dry spell idea-wise, I’m putting this idea into the public to force me to talk about it. Usually when I try to teach about something, I’m teaching myself as well. And reveal irrationalities in my logic much better than if all of the ideas were just in my head.

I still don’t know whether this idea amounts to anything but at least I have high hopes for it.