Why do these Lagrange numbers work the way they do? They take advantage of their own nature, they reorganize sequences in separable groups, each group defined by a power series. The Lagrange number itself just divides sequence into single matches, then dual matches, and so on. When combined with the set calculus of hyperbolics we get powerful artificial intelligence.
The Lagrange just combine sequential sets. But within the hyperbolic system, they find the minimum redundant sequence, label then, then the system just jumps up to a higher number and finds the next sequential sets. That is a powerful artificial basis system. This idea of finite group calculus is very powerful, it is the next generation AI, and we barely passed the first.
Take speech understanding. What would the Lagrange hyperbolics do? Find the optimum groups of growth and decay processes. Do this recursively, get group powers of groups. They would actually learn speech.
isn't this idea, if developed, really finite discrete log? Or actually, decomposition into optimum groups. We move the higher Lagrange, and we squeeze the angle, but get an independent basis to obtain the next estimate of divergence. This is the missing theory I wandered upon about two years ago. I always though the Lagrange was the generalization of minimum redundancy encoding. If we are working with an existing group, the goal is to estimate the maximum divergence about the ring. Find its 'pi', this is the road to big stuff. I think this approach eventually solves this:
In probability theory, a balance equation is an equation that describes the probability flux associated with a Markov chain in and out of states or set of statesIt is an optimum decomposition of the probability flux. I think.It find the most divergent path about the ring, stepping between Lagrange power series.
The little thing itself, if done accurates, should be the prime group, a new and novel concept, and very powerful.
So hyperbolics, when used with the Lagrange angles, are doing group intersections, decomposing some group using prime groups. The diagram is the first prime group, it is a basis set of all other groups. So it is perfectly reasonable in particle physics to have a prime group, though we may never actually detect it. But, try taking a perfect sphere in a pure simple vacuum. then cool the vacuum down, way down until you are freezing gravity. The slowly compress the sphere, I think you might make some of these and the vacuum will get sloshy.
This is great stuff, it really is.