The nature of the probability matrix is pivotal to understanding many different processes. The image shows what happens as the differential is integrated over time. The universe is best characterized by its changes and so are the relationships. Circuits, fields, momentum, and motion of all forms can be modeled and thus reversed to a model from its product. I think that I had not yet appreciated how this all related until now. The addition of logs, periodic, differential, and complex elements adds new aspects but does not change the basic principles. It relates to vector space in some very unusual ways. I feel that I have been here before when designing a solver for the "einstein" puzzle. It is easy to see how the rate of change is incorporated in the matrix multiplication process of a probability matrix. It does seem that interaction of sets and the vector rotation of a Rubik's cube could be defined in this framework as well as the solutions to the "einstein" game.
As time goes by it gets easier to use. I can see how it can be used for logic simulation (SPICE), though I had my own design with CAM that I feel was faster and easier to use. I wonder if the algorithms for matrix manipulation can be implemented in a type of CAM ( Content Addressable Memory). It would seem so at first glance. The Banach Tarski is still a bit sketchy for me and perhaps it is just a matter of relating it to what I know of the operation. There are some odd things that happen and action at velocities nearing the speed of light have a strangeness about them that rivals this. I can't say if what is said of that is the same as I only understand one of them. I am of the impression that quantum mechanics has some rough edges that may come from the math itself or from the way it is interpreted or applied. Frequentists and Bayesians. I was doing some LaGrange equations of gravity with other elements incorporated and simulating that and there was a realization there also. This is very much like the OpenGL cave logic world that I created. I am glad I learned all these things, they will be useful. I feel that I have ∇uated, ( scientific humor ).
I don't feel that anything can truly be learned and retained without seeing how it applies. That is certainly true for me and programming. Somebody can talk about OO programming and any number of algorithms, but until I write my first program to implement the effect, it just seems like noise. To me it just seems like teaching is a way to have a agreed upon name that describes something, but the learning comes from doing.
I have a good idea for a hole in gravity that comes from the many dimensions and I have also devised a universal language. The strange thing about the language is that it looks a lot like DNA and in my wild imagination it made me think of a communication system between advanced alien cultures that used DNA like communication and as a result it developed strange patterns in the communication channels some times and it had to be cleaned out. Like mold growing in the warm water of a nuclear reactor cooling tower. I would hope we aren't the fungus that fouls the universe, that would be an unfortunate position. Sounds like a good Twilight Zone episode to me.
I was thinking about Rubik's cube and matrices and decide that it would be possible to make a matrix tree solution and make it a solved game for number of moves. It seemed that 26! * 22 would do it and so I computed the flops to see if it was doable on my machine and 1030 flops is not in the range of any machine in this time or the near future. That is just a brute force, and I am guessing it could be finessed to 21! fairly easily. That is in the computable range of some super computers, but not my computer. I see that in the history of its analysis that sets and vectors have been used and even Hofstadter has had a hand on the cube. It seems that a divine solution could be had and perhaps I will consider that as it does apply to many other situations like possible quantum states or even nuclear physics and gravity in a round about way.
I think I am getting an idea of who knows what they are talking about and who is just tweeting their ignorance on the net. There are some real geniuses that have presence and some things I could learn.
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