Vibrating and Non-Vibrating Numbers

Every rational number that has an end vibrates with the repeating rational number right below it. Thus 2 vibrates with 1.99999999999..., 3.5 vibrates with 3.49999999... Note that rational numbers which do repeat, they vibrate as you calculate them to the number of decimal points you want, moving from gross vibrations, to much more fine vibration. The only rational number that doesn't repeat is 0. 0 doesn't vibrate. Transcendental numbers vibrate like repeating rational numbers.

metacontinuity (not transformers) and feedback

Stepping back from continuous hierarchy, perhaps we should take a look at metacontinuity. It appears that Transformers has taken this word for a roll, so I'll just refer to the universe as metacontinuous. It's not something about something, or stepwise recursion, it's feedback in movement. Perhaps it's a parser that has feedback built in. A self-critical aspect that's always running--figuring out how to improve itself.

Death of Continuous Hierarchy

It appears that my current definition of continuous hierarchy is very similar to differential propositional calculus, so I'm going to resign that definition.

Defining Universes, Reference versus Awareness, How to do Artifical Intelligence and build a web browser.

So how do you define a universe? A simple way might be "All there is." Which is perfectly acceptable. But does the abstract idea of a square exist in the universe? Does the idea of a universe exist in the universe? Is the universe of ideas somehow separate from the universe itself? Is there something which isn't the universe? Somehow there is a divide between the abstract and the concrete. The abstract may be used to describe the concrete. Art is one way of making the abstract concrete. One might say that reference is abstract, and awareness is concrete. People have spent hours and hours trying to create artificial intelligence and other programs out of reference. What they need to do is spend hours and hours trying to create artificial intelligence out of awareness. Record every mouse action and key press, network traffic and deltas between screen shots--and put them through a learning program (yes, I know it's difficult to learn through time). Learn how to predict input, and what output is expected from the input. Would it be possible to build a web browser just by using a learning program that learned by watching another web browser? How much would the human have to help?

A Universal Set and Illogical State-ments made Logical

So a universal set may only exist within one universe. It may not extend across universes. However, relationships (information) between sets may exist across universes. Thus a set A may be a member of a set B in one universe, and the set A not be a member of a set B in another universe. Russell's Paradox only exists if you are referring to a single universe. There must be something about Russell's Paradox which is an informatic way of creating separate universes. A paradox is when conflicting things can be held true at the same time. Each side of the paradox exists in one universe, and is a totally acceptable way of talking about it. If A holds in one universe, and not A holds in another universe, then one may say A and not A holds true. If you are only referring to one universe, then both A and not A can not hold true at the same time (but they may at different times). If you think about a single universe of logic, then A and not A must be a false statement, and A or not A must be a true statement. If you think about multiply present universes, then A and not A may or may not be true, and A or not A may or may not be true.

A basis for continuous hierarchy in space

The basis for continuous hierarchy in space is multiply present parallel universes (or massively parallel universes). Universes which cross over each other, and share atoms. A concrete set A in universe B may be different than the concrete set A in universe C. But A(B) and A(C) are the same set. Get it? Continuous hierarchy.

The basis for continuous hierarchy

The basis for continuous hierarchy is that things change in time. Anything in physical reality is different every time you measure it--every concrete set is different. The question is, do things we think of (abstract sets) change in time when we measure them. Our understanding of a situation may change. We may get more insight into ourselves or a situation. We have a set in our minds that is the set of all squares. There are an infinite number of squares in the square set--assuming our mental universe is unbounded in size. There is no such thing as a concrete set of squares...they are all imperfect examples of something in the abstract set of squares.

Continuous hierarchy is not about abstract sets, it's about concrete sets. I cannot argue about stuff that is infinite in nature. It would take me too long.

Measurement and Continuous Hierarchy

Since measurement is an essential component of continuous hierarchy, let us consider two measurements made at exactly the same time at a set. By the uncertainty principle, observation affects the measurements. So only one observer is different than two observers. The question is, will the two observers achieve the same measurement? We have set A, observer o1, and observer o2. They observe at time t. Thus:

A(o1, t) - A(o2, t) = {}(o1 - o2, t) Thus the effect of time is negligible (but it might affect the empty set), but the effects of the differences between the observers implies that we don't get the empty set. If o1 = o2, then we get the empty set.

Deltas between Sets Measured in Time

In continuous hierarchy, set subtraction computes a delta between sets. We don't yet know if this result is a set or not. For example, if you have a set A, and the subtraction operator -, the A - A is not the empty set. Each time you measure A, you get a different result, so the two references to A are references to different sets in time. So you might look at the equations A(t1) - A(t2) = {}(t2 - t1) As t1 approaches t2, A - A becomes the empty set.

Differential Recursion, Real Recursive Functions lead to Continuous Hierarchy

So, if you consider taking the time step in a recursive function to the smallest possible time, say dt, we get a smooth recursive function. This is "real recursive functions" or "differential recursion." I claim that if you apply this same technique to sets, you will get continuous hierarchy. What is the delta between sets? Reducing the delta between sets to something close to 0 will lead to continuous hierarchy.

Self-Reference versus Self-Awareness

It seems like I've been chasing after self-reference for quite a while, and now I need to chase after self-awareness.

Continuous Hierarchy: What we are trying to achieve

With continuous hierarchy, we are trying to get rid of recursion. The universe is not recursive, it is continuous. What we need is a continuous recursion, without levels. This works out to continuous self-reference, instead of leveled self-reference. Or no self-reference at all. No self-reference at all seems rather impossible at this point--people refer to themselves all the time, when they say "I", so let's attempt continuous self-reference. Continuous self-reference seems like narcissism, or schizophrenia, but without the mirror.

metaghastcar

So if you had a car that ran on meta, how far would it go?