The Evidence for and the Theory of Incompleteness

[Fredrick]

Incompleteness.

On the psychological level, it is a sense of 'incompleteness' that motivates all lifeforms to compete for the resources of life, and does not seemingly allow for an existence without this exchange of energy expended.

There is also a mathematical explanation, a summary......

In 1931, the Czech-born mathematician Kurt Gödel demonstrated that within any given branch of mathematics, there would always be some propositions that couldn't be proven either true or false using the rules and axioms ... of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules and axioms, but by doing so you'll only create a larger system with its own unprovable statements. The implication is that all logical system of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.

Gödel's Theorem has been used to argue that a computer can never be as smart as a human being because the extent of its knowledge is limited by a fixed set of axioms, whereas people can discover unexpected truths ... It plays a part in modern linguistic theories, which emphasize the power of language to come up with new ways to express ideas. And it has been taken to imply that you'll never entirely understand yourself, since your mind, like any other closed system, can only be sure of what it knows about itself by relying on what it knows about itself.

I love that you bring up Gödel, Labelwench.

Of course, he says something important, but at the same time it is really simple, too. When defining the entire world (or everything there is) then we cannot define the entire set of definitions in a similar way.

He points to the duality that exists at the Universal Framework: there is something incomplete, and we can fill that up with something else, but not with something that belongs to that level, even when the filling then appears to exist at that level.

I have been proclaiming the same/similar information that when using a framework, there is always an empty position within the whole set of positions. And the empty position can be taken in (by something else).

[labelwench]

I have been proclaiming the same/similar information that when using a framework, there is always an empty position within the whole set of positions. And the empty position can be taken in (by something else).
Originally posted by Frederick

Frameworks within frameworks, from the micro to the macro, the scale on each end beyond our ability to know. We are a species capable of conceptualizing that which can not be measured, as the scale is beyond what we can comprehend by the experiencing of it.

And yet we can think beyond the limitations of a lifetime........beyond what is known, and venture into that which has not yet been experienced but only arrived at through logic, intuition, and speculation.

Considering our basic inadequacies in the day-to-day treatment of our fellow beings, and the planet which supports all, I find the paradox quite amazing and baffling at the same time....

[austintorn@aol.com]

Escher Tames Infinity

But, not really,
For the space at the edge
Gets really compressed.

So, how many sides does a circle have?
Two. The inside and the outside.

We see many grand concepts,
But many can’t see beyond
The edge of their nose in real life.

That which is not can inform us, too,
Such as infinity never happening.

It tells us that time had to begin,
And could not have been forever,
At least for de-finite things.

Zero, the most important number,
Tells that there must be symmetry,
Lest a specific number of things
Become “special”, which it never can.


P.S. Fredrick, I have a new thread, too:

http://www.toequest.com/forum/genera...tml#post112198

[Fredrick]

While there are connections between the Frameworks, they should each be seen as independent. If we agree that at the overall level incompleteness is the norm, then there is no surprise that the frameworks are to be considered on their own terms.

Let's explore the simplest one — the Universal Framework — and view/discuss its own terms.

For this largest of frameworks, it is good to know that there is not much to be said about it. The most important aspect of this framework is that all that is contained within it is moving outwardly. Really, that is all there is to it.

And yet that is not all of it, because we can discuss this a bit more in detail. For instance, outward movement only exists as a reality of multiple parts. No single entity can move outwardly by itself. Even the blowfish has its limitations, but a school of fish could potentially scatter itself in all directions, outwardly, for as long as they desire and not run out of ocean. Because of the outward reality, we can state that:

1/ The Universal Framework is plural in nature.



The Universal Framework can only be understood when viewed from the collective perspective. Outward movement requires that multiple entities move outwardly from one another in some form of unison (though this does not necessarily require the perfect kind of unison, even when it is more recognizable for us that way). A pattern must be distinguishable, otherwise we do not have outward movement. While the universe's outward movement may not be too clear (especially when considering the first moments), the overall outward movement is well-established, and we can state that:

2/ The Universal Framework is collective in nature.



And yet, while there is only a Universal Framework when it is plural and collective in nature, there is no relationship between the parts that are moving outwardly away from each other. If there was a bond, then the outward movement would have slowed, stopped, and returned, or it would have at least shown signs of that bond. The information we have does not show such a bond, and we can state that:

3/ The Universal Framework is non-cooperative in nature.



When viewing the other frameworks, we can notice that they do not operate on an outward level. No galaxy has its parts move outwardly from itself, no solar system has its parts move outwardly from itself, and here on earth we are not moving outwardly either (only awkwardly sometimes). The outward movement in our universe occurs at the universal level, not at its parts.

4/ The Universal Framework is a distinct framework.



Still, if there are connections between all frameworks, then we may experience the Universal Framework at times. Stars are shining their bright light outwardly, away from themselves. Novas explode outwardly (though some claim black holes are also formed due to the opposite, the implosion). These are nevertheless examples from the center of the Solar Framework. From the Galactic Framework and from the Planetary Framework I cannot come up with any examples.

So, outwardly, there are two frameworks: one without an actual center (the Universal Framework) and one that arrived from a center, whether still existing or no longer existing (the center of the Solar Framework). From the Solar Framework's reality about outward movement, we may state that #3, the non-cooperative nature, may have once occurred at the Universal Framework at its very beginning. From the visual of a star shining its light outwardly, we can however also confirm that once the photon leaves the star, it does not return to the star.

The idea that somehow an entity such as a black hole can remain is not an enigma, but a desire of the human mind to fill in the blind spot where it lacks accurate vision.

I'd like to open this for discussion. In how far can we distinguish a Universal Framework that is unique? In how far can this framework be used; what are its limitations?

[Fredrick]

Frameworks within frameworks, from the micro to the macro, the scale on each end beyond our ability to know. We are a species capable of conceptualizing that which can not be measured, as the scale is beyond what we can comprehend by the experiencing of it.

And yet we can think beyond the limitations of a lifetime........beyond what is known, and venture into that which has not yet been experienced but only arrived at through logic, intuition, and speculation.

Considering our basic inadequacies in the day-to-day treatment of our fellow beings, and the planet which supports all, I find the paradox quite amazing and baffling at the same time....

Very good, Labelwench, we have capacities indeed that are astounding. I agree here fully with you. Yet they can trick us as well. Still, one does not need to contradict the other. We treat our fellow beings a certain way, because we are tricked into believing they are them and not us, we may be tricked to think that they are less worthy than us, and we have ensured that they are not equally represented like we are (or think we are, because some trickery may be used on the inside by, for instance, the elite on the rest of society).

[Fredrick]

Escher Tames Infinity

But, not really,
For the space at the edge
Gets really compressed.

So, how many sides does a circle have?
Two. The inside and the outside.

We see many grand concepts,
But many can’t see beyond
The edge of their nose in real life.

That which is not can inform us, too,
Such as infinity never happening.

It tells us that time had to begin,
And could not have been forever,
At least for de-finite things.

Zero, the most important number,
Tells that there must be symmetry,
Lest a specific number of things
Become “special”, which it never can.


P.S. Fredrick, I have a new thread, too:

http://www.toequest.com/forum/genera...tml#post112198

A nice start indeed, Austin, I visited your thread and if I have time I will visit more and post responses.

I see you regard the infinity as an entity, as a reality that is real within our universe. How do you counter me, when I state that infinity is a concept only? That there is no there there when viewed at the level of actual entities? Or was this a smart move on your side and have infinity tamed at the 2D level by no one less than Escher?

[austintorn@aol.com]

'Infinity' is not an entity, for it can never be achieved—and this is what tells us something. We should all bear in mind to replace it (as well as 'eternity" and "Nothing") in our sentences with "that which can never happen" and then see if the sentence still makes sense.

[austintorn@aol.com]

The Universal Framework
Is not all that important,
But for TOE enthusiasts,
Being that it is much older
And thus more basic and primitive
Than the composite complexities
Of us and our planet.

It is also fairly inaccessible directly,
Being so vast and far away.

Even its TOE is not so interesting,
This being some symmetric
And simple material spewed into
An outward movement
From some eventually causeless state.

Our existence trumps it in every way.

[Fredrick]

'Infinity' is not an entity, for it can never be achieved—and this is what tells us something. We should all bear in mind to replace it (as well as 'eternity" and "Nothing") in our sentences with "that which can never happen" and then see if the sentence still makes sense.

Excellent, Austin, we are on the same page then.

It functions very similar as an ideal does. In general, an ideal cannot be achieved, but we can certainly dream of it. By working towards an ideal, an improvement towards the ideal can get achieved, leaving some already satisfied, others still wanting more when setting their goals higher towards achieving the ideal. I, for one, am definitively satisfied with your reply.

[austintorn@aol.com]

OF QUIRKS AND QUARKS

Whatever physical laws lurked and larked,
Back then, parked, of the deep and dark,
Led to a very small excess of quarks
And leptons over their counterparts—
Of the order of 1 in 30 million sparks,
Resulting in the predominance of matter farts
In the present universe over antimatter arts.

From these marks we mammals harked,
With mind, soul, spirit, and hearts,
Although some other mammals barked
And some even quacked and quarked,
Floating in our wonderful Earthly ark
Upon life’s ocean of dangerous sharks.