| The Nature of Dimensionality | ||||
|---|---|---|---|---|
| And so on... | ||||
| points 0 Space | lines 1 dim | triangles 2 dim | pyramids 3 dim | 4DStruct 4 dim |
| "Triangle Numbers" | ||||
| 1 | 0 | 0 | 0 | 0 |
| 2 | 1 | 0 | 0 | 0 |
| 3 | 3 | 1 | 0 | 0 |
| 4 | 6 | 4 | 1 | 0 |
| 5 | 10 | 10 | 5 | 1 |
| 6 | 15 | 20 | 15 | 6 |
| 7 | 21 | 35 | 35 | 21 |
| 8 | 28 | 56 | 70 | 56 |
| 9 | 36 | 84 | 126 | 126 |
I was browsing through the history of math and I happened on the idea of "triangle numbers" at Wikipedia, in the context of Fermat polygonal number theory. I had to say: "WTF is that!" When I realised what it was, I had an ephiphany . I had done this work long ago in trying to understand dimensionality itself. Those numbers show up in a table I created about 15 years ago to deal with n-Space and the nature of dimensionality and sets.
At that time I resolved some relationships with numbers that involve things like (1+1/n)^n and a host of other things that have to do with integers. This gets back to that number I hate and it is sqrt(-1). I know that everybody else accepts this as part of normal math, but I do not. To me it is the place between two numbers that does not exist. Well, in any case I am dealing with eiπ+1. It seems to me that even though this very useful and I can apply it and use it in context as well as anybody, I don't like the derivation and application. There is much more to this and the way i is defined gives rise to something that I use that is equivalent.
That is why I named the post "Alien Intellect" as the way I deal with science is truly alien. I don't mean that I am an alien, just that I devised methods that are more effective by not accepting that which was given. The math and physics is incomplete, this I always knew.
This table also has something to do with Fibonacci and life and genetics. There is a deeper something in all this that is perhaps in the realm of metaphysical.
I discovered another odd thing when doing an implementation of flock emergence with my n-Body math. I have to complete the code and test it, but I will post some results and videos.
| 1 | ||||||||
| 1 | 1 | |||||||
| 1 | 2 | 1 | ||||||
| 1 | 3 | 3 | 1 | |||||
| 1 | 4 | 6 | 4 | 1 | ||||
| 1 | 5 | 10 | 10 | 5 | 1 | |||
| 1 | 6 | 15 | 20 | 15 | 6 | 1 | ||
| 1 | 7 | 21 | 35 | 35 | 21 | 7 | 1 | |
| 1 | 8 | 28 | 56 | 70 | 56 | 28 | 8 | 1 |
It does relate to Pascal's triangle also. I had my own version of that also. There are many of these things that are completely new to me. Dimensionality and topology is one of the oddest and though there is no evidence of dimensions beyond 4, it does not mean they could not exist. It occurs to me on occasion that what we experience is just the shadow of something very strange. It does have something to do with eiπ.
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