Continuous Hierarchy and Geometry

Here's how Continuous Hierarchy relates to geometry.

1. We are uncertain of either the velocity or the position of a point
2. We are uncertain of the ordering of points within a group.
3. We are uncertain of the points a group contains
4. A polygon is an uncertainly ordered group.

Reversible Computing

At the lowest level, reversible (quantum) computing (circuitry) can be done by maintaining the inputs from each computation. Thus there along with 2 inputs for an AND gate, there is an unknown input. There are 3 outputs as well, the 2 inputs, and the result from anding the two inputs. This allows computations to be reversed and checked as well. There is no loss of information, and unknowns progress into knowns. The only thing that you can't recover is the unknowns.

Continuous Hierarchical Turing Machine

So what would be a turing machine that could deal with continuous hierarchy?

1. First, it would have to deal with symbols changing slightly, with possible unknown symbols.
2. It would have to deal with tape that it doesn't know the contents of, and the tape may change suddenly under it. (I think currently turing machines have this).
3. It would have to deal with reordering of symbols on the tape.

I think that probablistic turing machines can handle 3. And a quantum computer is a a kind of probablistic turing machine.

I have to think more about the rest of the turing machine besides the tape perhaps.

Combinatoric Turing Machines

Combinatoric Turing Machines work on scales of the internet, where there are millions of symbols. Each step in the machine reads and writes millions of symbols. But for efficiency of processing, out of the millions of symbols being read, only a few are chosen to compute the value of a symbol under the read head. Once you have the chosen symbols, you would apply some criteria to chose one: average, max, min, lucky, first, last, sum, best, most terms covered, etc.

More on Fractal Turing Machines

Well, here's more on fractal turing machines. What I am thinking is that you can go both up and down the number of symbols being analyzed. Thus you could look at two symbols at the same time, four symbols at the same time .... Or you could look at 1/2 a symbol... As well as being able to advance fractional amounts. If you look at a lot of symbols at the same time, you would need some function to provide a final value, like, min, max, average, etc. What if you have millions of symbols, what do you do? The answer is to choose a certain number of symbols to represent the collection of symbols, or what you might call a combinatoric turing machine.