In my last post I talked about misunderstanding mathematics. In this post I’m talking about something that follows along the same path, but looking at the problem from a different perspective.
Today, I’m showing that my general logic holds with the vectors and their arrangement, but only on a rough level. I knew that I could draw a toroidal double-helix just like the Blender image from the last post. I just needed to go back to the electron equations that I had figured out almost three months ago.
These were the equations:
But this time we aren’t talking about electrons, so the constants had to be tweaked. First of all, as we aren’t talking about a charged particle that is quasi-spherical, we need to make Amin smaller than 1, and G to be zero. P was 5, not because it holds any particular significance, but because I was able to make the geometry work with P = 5 in Blender and I needed to replicate the exact conditions.
Then I did a lot of ‘dirty math’, or rough guesstimates to get the plotted dots to match what I had in Blender, but in the end, this is what I got:
Exactly what I wanted, with an average deviation of the vector length being just 0.7 %. The equations are written in a way that the distance between neighboring circles of the same color is always the same (0.2 in this case, just because this is the distance I used in Blender.
But then there is the question of how I ended up with points along a curve in the first place? Well, I just assumed that the distance between two dots along the same curve is always the same, so I just ended up tweaking the increments of θ I used in the equation. Nothing highly logical. Just brute force. But after I had done this, I had an array of dots, whose distance from each other I could just calculate using three-dimensional Pythagorean theorem. And by tweaking the point-to-point distance in one curve, I could make the distance two the closest neighboring dot of the neighboring curve to be also 0.2. Well, 0.2±0.0015, to be exact. So, not bad.
However, the curious thing is that each dot had four neighboring dots of the neighboring orbital and two of these dots could be described as the closest dot. And even when the length of the vector for either one wasn’t always 0.2., their deviation from 0.2 was pretty much identical. What this seems to very strongly indicate is that my origami became very interesting indeed. Instead of equilateral triangles, the double-helical orbital seems to be comprised of three-dimensional quadrilaterals, or rhombi, to be more precise. The comical thing is that looking at the structure more closely, I see that it is the same folded 2D ribbon that I had to reject before.
But even this shape is remarkably close to being accurate. The only problem is that as the dots need to touch, anything with a vector length smaller than 0.2 is impossible and a vector length higher than 0.2 would mean that the dots no longer touch.
What this exercise means is that while I can show the approximate accuracy of the theory just by brute force, I would prefer being fully accurate. And for this I need to figure out the mathematics.
I already know that one key to solving the mathematics is in splitting the formation of the helix into two increments of circular arcs (red arcs in the picture below). The first (larger) arc has a radius of the larger torus, plus/minus its location on the tubular surface of the torus. The second (much smaller) arc has a radius of half a dot. And the larger arc never has depth, as it always depicts a circular arc around the center of its rotation. This arc is pretty easy to describe mathematically. However, the second arc is much trickier to describe, as it is an arc of a circle, whose center is at a distance exactly the radius of the torus from its center (pretty much by definition). But it is angled, which means that its description with an equation is making my hair grey. I feel like calling it quits, but even though the problem is quite hard for me, it is clearly solvable. This is why I’m reluctant to submit the manuscript of the theory of everything as half-finished.
The almost comical thing is that I think I finally have enough evidence that I could already write what I know down and probably would be at least accepted for review. But I fear that the insatiable desire for mathematical precision would still allow reviewers to dismiss my manuscript.
I think my fear is based on no one saying that my theory is clear and that it makes so much sense. The reception has been relatively positive, but positive in the sense of “keep up the good work”, not in the sense of “I always wondered what quantum mechanics and gravity are, but now that you’ve explained it, I finally understand”.
But now I’m tempted to have a pause in the mathematics a start writing again. I’ll probably know when I continue writing, whether I know enough to finish the manuscript, or whether I’m forced back to figure out the rest of the mathematics. There is already a small chance that I allow myself to submit what I already know. Sometimes perfectionism is unhealthy. This is something everyone should know about, even if it’s not 100 % ready.
Comments