Double Helix Turing Machine

What if there was a twisting Turing Machine?

Fractal Turing Machines

So there is variable rate encoding of music. What about a variable rate Turing machine, such that the frequency and amplitude of each symbol are different distances apart on the tape.

Or how about a Turing Machine which divides a symbol into 2, 4, or 8 symbols (quadtree and octree).

These might be thought of as fractal Turing machines.

Criticisms of the Turing machine

Here are some criticisms of the Turing machine:

1. It doesn't allow for advancing a fractional amount along the tape
2. It doesn't allow for torn tape, or the machine falling off the tape
3. It might not allow for unknown symbols

What you might want to do with a Turing machine is:

1. Add new sections of tape
2. Delete old sections of tape

I think these can be handled with a Turing machine, through erasing and moving symbols

I think we need to advance to a fractal Turing machine

A Continuous Hierarchy

Composite functions in computers take a time to run. Each step takes time. Climbing up and down hills take time. Each step takes time. So how are steps in computer science like steps in a computer? We can often determine how long a step will take in a computer. A composite step however, may take different amounts of time. Thus we assign a range to the amount of time an algorithm takes, or a big O() notation. In real life, we can give a rough estimate to how long a step will take, but it depends on how fast the person is hiking, what kinds of obstacles there are, etc. Similarly, there might be obstacles in computer science. The hills in computers are circuits, and each step is a transistor. The circuit is continuous. If we use AND OR and NOT as primitives on the network, we can see even more time being spent between steps. Light bounces around the room a continuous fashion, and each collision with an object is a step.

Continuous Hierarchy as Continous Programming

Currently, computer programming, in a language like, say Lisp or Java, has a levels of hierarchy. I think we need to break the levels down into surfaces or curves, to achieve continuous programming. Then we can mix and match.

If you think of logic as a hierarchy of rules, then what is a fuzzy hierarchy of rules? What is a continuous hierarchy of rules? The rules must break out of their well confined structure of sets and be truly fuzzy. Thus decision trees become a pile of fuzzy fuzzy rules.

Defective Fuzzy Operators, Fuzzy Defective Operators

So what are defective fuzzy operators? They are the typical fuzzy operators, such as union/or intersection/and and complement/not but they don't return crisp fuzzy sets. Instead they return fuzzy fuzzy sets. So the boundaries of your resultant fuzzy set don't match the input fuzzy sets.

This appears to be a new technology. One may say that my model is wrong if the operators return the wrong results. I say that fuzzy operators as they typical are thought of are defective, and need to be replaced with more realistic, real world operators.

Perhaps there are fractal fuzzy operators or fuzzy fractal operators. And don't forget faulty fuzzy operators and fuzzy faulty operators

Something to think about.

Fractional and Transcendental Derivatives

So, if you have a fractal hierarchy that bends, its motion can be described with fractional derivatives. But what is a transcendental derivative? That seems very interesting, and I am pursuing information on it.

Continuous Hierarchy from a geographical perspective

We have artificial political boundaries that form from bivalent thinking. But the world is geographical. There aren't really lines where my property, city, county, state, or country begins or ends. Of course, you shouldn't trespass or steal--but that's a social idea, not a geographical idea. You would let your neighbor stand on your driveway to talk to you, but if he was just standing there all day long, you might be concerned for him.

As a youngster, I thought about what it meant to have a house that was on a state or country line. Would that mean you would have to pay taxes in both states? Neither state? The state of your choice? Whatever side of the house you spent the most time in?

Continuous Hierarchy, a new definition

So I don't think that set membership should be a quality of continuous hierarchy. Instead continuous hierarchy should be more like exploration. You wander around a "space" and find elements, without any set boundaries. There is no membership in sets. Sets are abstractions which don't belong in continuous hierarchy. What there is is relativity. You place elements relative to each other, not on coordinates like in a set or not in a set. The location of each element is uncertain, as well as the velocity.

Now how does this relate to speech? A sentence is a landscape of information.

Multidimensional Electricity

I know that direct current electricity runs from positive to negative. But what if there were more poles to electricity? There are 4 forces. Can we leverage the forces in these to generate other types of electricity? Maybe we can remotely control electricity? Alternating current can be thought of as a 2 dimensional wave. What about an ocean of electricity, a 3 dimensional wave? Or even more untapped dimensions. Light might be thought of as an ocean of electricity. How many dimensions are there to light? Complex numbers were perhaps invented to get rid of discontinuities between surfaces in space. What about the discontinuities between stars in space? Could some complex number system allow us to travel between stars?

Editor's Note: After viewing a lecture on Physics, I realize that there is a field of electricity.