In my last post I presented a rather cumbersome-looking shape with circles and vectors, as well as tiny spheres. As regular readers know, these tiny spheres represent elementary particles of energy, or dots. In actual dot-to-dot interactions these spheres are larger and are connected to neighboring dots at the points in time where they experience reflections. However, if we shrink these dots to a fraction of their size, we can simplify both their connections and flightpaths into vectors.
In the post I laid the groundwork for the shape that defines all reflections. Or to be more specific, a shape that can be copied end-to-end, resulting in a closed-loop (never-ending) path for the dots. At the end of the post, I said:
Next, I need to do is to connect the future particles to their past and far-future. If I’m able to do this, I think I should be able very rapidly describe these connections with vectors and proper equations that I can put into Excel.
In today’s post I think I’ve managed to do this. First of all, I connected the rest of the unconnected dots to make the missing paths. While for a while I thought I would need to do something else, this was the only thing that was really left for the simple shape. However, there was still one more thing to do. I copied the whole shape, shifted it by √2r, where r is the radius of a dot, and then rotated it by 180 degrees around the general flightpath of the dots. This was almost enough to get the final shape, but because the original shape wasn’t fully cylindrical, I had to do minor tweaks to perfectly overlay the two cross-shaped collection of present and future dots in in the two shapes, reducing the overall number of rings in the new shape to five. I decided to ditch the rings around the dots as well, as they were more of a crutch and didn’t aid in the drawing of the structure once I understood the shapes.
And this is how it looks like as a static image:
And this is how it looks like when rotating:
The more astute observer might notice that I’ve made all future particles transparent, as well as all the vectors that do not depict connections between dots, or their flightpaths. I still can’t say with absolute certainty that this shape defines all interactions within particles of matter. To make this statement, I need to convert the shape into equations and see whether I can replicate it with Excel.
If before I’ve talked about Zeno’s paradox(es), this time I feel more like the tortoise in “The Tortoise and the Hare.” If you don’t remember the story, this is how Wikipedia describes it:
The story concerns a Hare who ridicules a slow-moving Tortoise. Tired of the Hare's arrogant behavior, the Tortoise challenges him to a race. The hare soon leaves the tortoise behind and, confident of winning, takes a nap midway through the race. When the Hare awakes, however, he finds that his competitor, crawling slowly but steadily, has arrived before him.
Despite me being extremely slow in every step of the way, I’ve been persistent and kept on going. The hare represents all the other scientists publishing tons and tons of papers, but not getting anywhere. I equate their naps to be the points where they decide to study things that they are sure to get published, instead of studying the most fundamental problems that will not yield easy papers that can be published with a few months of work.
Of course, if I realize that I cannot convert the above shape into equations, or that the equations lead to nonsensical results, I need to claim that failure as loudly as today’s proclamation that I might have the answer.
But I do hope that I’m right…
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