Gödel's Incompleteness theorem versus Theory of everything

What Cantor demonstrated is that there is 'something' wrong with our mathematics.

Since the foundation of physics is mathematics it should come as no suprise that physicists have no idea what's going on.

Just look at quantum theory. It's enlesslesly convoluted. There are so many 'band aids' on the theory now it's ridiculous.

Certainly Godel fortifies the implications of Cantor's work.

It all - all of it - 'smoke and mirrors' !

I don't understand how it follows that, just because a finite, causal universe cannot be fully and consistently described, it cannot also be causally determined.

I agree that it means that we can't predict its causally determined outcomes accurately, but how does that deliver choice about future states to components and systems within the universe?

That exactly where the magic of Gödel comes in. Since our TOE's will always produce at least a few inconsistent situations it means the universe can never be pinned down in a finite system of rules (i.e. a TOE) as soon as we do it new problems will arise that challenges our main theories ad infinitum. And as soon as the TOE is expanded it allows more possibilities.
And well the more you describe something the more you can predict and since only certain parts of the TOE will be incomplete per revision it leaves open the possibility that certain phenomenon can be fully described and predicted.

reply to post by visible_villain

As I'm sure you know, before Gödel threw his 'monkey wrench' into the 'mix' of western science, Georg Cantor had already 'beaten him to the punch.'

Haven't done the research but the idea it seems is closely tied with what is called the Continuum Hypothesis. Yes it shows of certain weaknesses of mathematics but is nothing of the likes of Gödel's theorems since Gödel's theorems are applicable on all formal systems advanced enough to contain arithmetic. But his very dust theory is a result of the theorems, but I agree he did prove to a degree that theories will always be lacking.

reply to post by Incompleteness

Haven't done the research but the idea it seems is closely tied with what is called the Continuum Hypothesis.

Well, I don't know how much math you know ... I've you have the elementary calculus we could probably talk about 'whats wrong with math'

It get's somewhat technical, but the 'issues' are actually pretty simple - it's definately not 'rocket science' ...

reply to post by tobiascore

Math can describe the rules of our universe. But it does not explain everything. Western Sciences idea of a TOE would be to describe the 3 dimensions of a box using math. What that box is, where that box came from, what lies outside the box fundementally can not be described by math. Therefore a TOE that strictly uses math will be a flawed TOE. Math is what WE say about the universe, not how it fundementally is. To think otherwise is an anthrophomorphic flaw.

Well have you ever read the theories of Max Tegmark about his theories that the entire universe (and the multiverse) are essentially mathematical structures. No that means there exist other structures outside own allowing wildly different things to be possible. But what I am getting at is that EVERYTHING is mathematics inside and out the thing is exactly what Gödel is about we cant describe what is outside the box unless we go there only to discover that the box was in box thats in another box...

reply to post by visible_villain


Well i am still sixteen but have done some university level calculus so we could if you want to, if i don't understand anything I am sure to have cleared up soon, my father is a prof. of mathematics at our local university.

Originally posted by visible_villain
reply to post by Incompleteness

 

Haven't done the research but the idea it seems is closely tied with what is called the Continuum Hypothesis.

Well, I don't know how much math you know ... I've you have the elementary calculus we could probably talk about 'whats wrong with math'

It get's somewhat technical, but the 'issues' are actually pretty simple - it's definately not 'rocket science' ...

I would be very interested in hearing this too.

One of the greatest thinkers, and one of the most odd, was Nikola Tesla, who told Einstein in essence,

"Herr Einstein, you attempt to use mathematics to understand the universe, while Thomas Edison only uses trial and error with no basic understanding of what is possible and what is not. I, on the other hand use both mathematics to define what may be allowed, and then am able to engage in focused experimentation."

Tesla produced.

Originally posted by Incompleteness
Since our TOE's will always produce at least a few inconsistent situations it means the universe can never be pinned down in a finite system of rules (i.e. a TOE) as soon as we do it new problems will arise that challenges our main theories ad infinitum. And as soon as the TOE is expanded it allows more possibilities.

Certainly it implies that the universe cannot be fully described in terms of mathematics. And quantum mechanics does indeed set limits to a complete description of reality. However, reality at a macroscopic level does indeed exist, and functions in a fairly predictable way.

A deterministic universe is one in which all events that occur are determined by the initial conditions. A degree of randomness may be built into those conditions, so that a range of interim or final states is possible; however, for the universe to be nondeterministic, it is not enough that its state at a given time be unpredictable; it is necessary that an actor within the universe should be able to alter real outcomes (or a range of outcomes) in a way that is not determined by the initial conditions. In other words, what the actor chooses to do is not itself determined by the initial conditions but is a product of what we know as 'free will'.

Do Gödel's incompleteness theorems make possible free will? If you believe they do so, could you please explain how?

Originally posted by Astyanax
However, reality at a macroscopic level does indeed exist, and functions in a fairly predictable way.

Technology and understanding of physics refines our concepts of what is possible. For instance, I doubt many people would have predicted the atomic bomb. Electronics have enabled all sorts of other things that were only envisioned by science fiction writers. The more we know about it, the more possibilities become open to us. And both of these major discoveries came from looking at things at smaller and finer detail. Now tenured physicists (like William A. Tiller) are pioneering science that studies EM and subtler energies in the human body, and have demonstrated the human body's ability to heal itself and others through intention that manifests itself in the body as small electric currents that stimulate regeneration, etc. It's going to be interesting to see where things go.

Originally posted by tobiascore
Space and time are quantized. Thinking you can build a TOE off the current physical model is incorrect. The universe is not mechanical. Look towards digital physics, not Newtons idea of a clockwork universe. It just doesn't work with quantum mechanical systems.

Doesn't that imply that space and time are not quantized, then? Perhaps, in the 'real universe', at some level the underlying dynamics are not quantized, but the resulting effect of determinable measurability is. A TOE addressing such would, in its theoretical construction, account for multiple (or perhaps innumerable) possible quantum dynamics, with no definitiveness of which interpretation is actually 'true'. So it is possible for a model to construct with dynamics beyond the resolution of Planck-level. Provability within that extent, however, is something else entirely....

Originally posted by Astyanax
Wonderful, mind-stretching topic, by the way. Ian MacLean, come back!

I am here! I have been working on a personalized Theory Of Everything. Involving a woman, a ring, and a mountain:

i343.photobucket.com...
(Ian McLean and americandingbat at Castle Crags State Park near Mount Shasta, California)

reply to post by Ian McLean

My heartiest congratulations to you both.

Does this kind of thing happen often on ATS, I wonder.

Pardon the digression, moderators!

Originally posted by Ian McLean

Originally posted by tobiascore
Space and time are quantized. Thinking you can build a TOE off the current physical model is incorrect. The universe is not mechanical. Look towards digital physics, not Newtons idea of a clockwork universe. It just doesn't work with quantum mechanical systems.

Doesn't that imply that space and time are not quantized, then? Perhaps, in the 'real universe', at some level the underlying dynamics are not quantized, but the resulting effect of determinable measurability is. A TOE addressing such would, in its theoretical construction, account for multiple (or perhaps innumerable) possible quantum dynamics, with no definitiveness of which interpretation is actually 'true'. So it is possible for a model to construct with dynamics beyond the resolution of Planck-level. Provability within that extent, however, is something else entirely....

Simple, at the planck level, "reality" is just information. If you model it as data, then a whole new world opens up. Like neils bohr said:

"It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature". - Niels Bohr

Fundamentally, we MUST be looking for newer and newer ways of describing our universe. Digital is the BEST way to model it at this point.

Originally posted by tobiascore
Simple, at the planck level, "reality" is just information. If you model it as data, then a whole new world opens up. Like neils bohr said:

"It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature". - Niels Bohr

Fundamentally, we MUST be looking for newer and newer ways of describing our universe. Digital is the BEST way to model it at this point.

I agree - almost. I would say: "at the planck level, digital is the best way to model our determinable perceptions of reality". Since that seems to be the minimum granularity for such things. Modeling of dynamics generated with that information can certainly open up a whole new world of understanding of emergent effect (chaos is a really fascinating subject). I don't think that such models can contain the totality of a description of the universe's behavior, though. It's over my head, but I understand that there are sub-planck levels of interaction, in current unifying theories. For example:

Heisenberg's principle states that the product of uncertainties of position and momentum should be no less than the limit set by Planck's constant, ℏ/2. This is usually taken to imply that phase space structures associated with sub-Planck scales («ℏ) do not exist, or at least that they do not matter. Here I show that this common assumption is false: non-local quantum superpositions (or 'Schrödinger's cat' states) that are confined to a phase space volume characterized by the classical action A, much larger than planck, develop spotty structure on the sub-Planck scale, a = ℏ²/A. Structure saturates on this scale particularly quickly in quantum versions of classically chaotic systems—such as gases that are modelled by chaotic scattering of molecules—because their exponential sensitivity to perturbations causes them to be driven into non-local 'cat' states. Most importantly, these sub-Planck scales are physically significant: a determines the sensitivity of a quantum system or environment to perturbations. Therefore, this scale controls the effectiveness of decoherence and the selection of preferred pointer states by the environment. It will also be relevant in setting limits on the sensitivity of quantum meters.
www.nature.com...

Edit: fixed mathematical representation, and thanks Astyanax!


[edit on May 4th 2009 by Ian McLean]