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Gödel's Incompleteness theorem versus Theory of everything

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posted on Apr, 25 2009 @ 07:16 PM
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The entire discussion will rest on three main concepts:
Concept 1:
The Theory of everything(TOE) is the idea that since we can use mathematics to describe every phenomenon we see from the interplay of electrons between atoms to the movement of galaxies. We will reach a point where if we write down every law and equation in a book and say we call it The Hitchhiker's guide to Everything, now since every law and equation is in the book any and every phenomenon should be predictable from this book. Meaning we should never again be incapable of explaining any things that we witness in relation to the physical causes of the event. And all possible technologies would also be deducible from this book meaning FTL-drives or wormhole networks feasibility will all be determined by the final form of this theory. The TOE can be visualized as a fence around us, we are allowed to do anything within the fence's parameters but the outside is forever out of our reach. Such a view of reality is inherently the reason why most physicist do what they do- working to create a theory of all theories, no physical phenomenon should lay outside its predictive capability. Stephen Hawking was a major force in the preceding decades to create a TOE. Culminating in our latest TOE contestant : M-theory which is basically a combined form of different string theories. See wikipedia for more information pertaining to string theory if you are unfamiliar with it.
Concept 2:
Now to get to the second part of the argument. Kurt Gödel was a brilliant mathematician and a personal friend of Einstein. Now he proved was is known as Gödels Incompleteness theorem(GIT).


Two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest.

There are two different GIT's but both of them basically state that any finite formal system effectively generated and advanced enough to contain basic arithmetic is either incomplete or inconsistent.
Meaning statements can me made that cannot be proved within the theory itself.
The unproven sentence can be proved by admitting new axioms into the theory thus increasing the complexity of the theory and what is possible with it, but even thought the unproven sentence can no be proven in the stronger theory ,the new theory will have new unproven theorems unprovable using the current theory. Thus can an ever increasing frenzy of new axioms and new problems arise. An upshot of this is that no theory will ever be able to explain the whole of mathematics.
Concept 3:
Any TOE wll be a finite formal system. The distinction isn't as clear cut as this simple introduction would imply. But a number of prominent scientist including the recently converted Stephan Hawking have decided that because off the implications of GIT no TOM can ever be fully constructed, the best we can hope for is a theory of almost everything. It can go either way because since we have no idea of what the TOE might be it is almost paradoxical that we might never now.
Now that we have laid the foundation I would like to hear your comments on what side you are and why?
Resources:
Stephan Hawking:No theory of everything
Incompleteness Wikipedia Entry
Reformathica: Discussion about incompleteness implications
More technical discussion of the implications of the incompleteness theorems

[edit on 25-4-2009 by Incompleteness]

[edit on 25-4-2009 by Incompleteness]

[edit on 25-4-2009 by Incompleteness]




posted on Apr, 25 2009 @ 07:53 PM
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Ah: complete, consistent, finite: pick any two.


Good thread; heavy stuff. Haven't delved into the links yet, but one thought off the top of my head:


Originally posted by Incompleteness
Any TOE wll be a finite formal system.

A distinction may be in the application of that system. For example, the rules describing the system may be finite, but when applying those rules, the amount of data necessary to "completely" describe the resulting determinism might not. A (probably flawed) example: if gravitational attraction is not quantized, with no minimum granularity, and every particle in the universe exerts a force on every other particle, however small that force is, to completely and accurately describe the combined force exerted on a single particle would require an (almost?) infinite amount of data - complete knowledge of the instantaneous location of every other particle in the universe.



posted on Apr, 25 2009 @ 09:15 PM
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reply to post by Ian McLean
 

There is an inherit distinction between the theoretical aspect of the theory and the applicability. But assuming that our TOE is affected by the Incompleteness theorem -which I believe it is- then no amount of data or computation (even a theoretical infinite amount) can completely describe the 'determined' universe, it will forever be out of our reach. The reason for this is simply that by the definition of the incompleteness of the TOE that there will always be statements (when physically translated : experiments or observations) that are unprovable with the current TOE thus meaning no coherent form of determinism will ever be possible in such a universe. The theory will always need to be updated with the new data and as soon as the new data is incorporated the resulting theory will have its own inconsistencies that require new data ad infinitum. The resulting deduction is that no amount of data or computation will result in a coherent determined state of the universe. Infinite input=infinite output. And to get back to your question about applicability as I have said their is a distinction between theoretics and applicability. Meaning you can use the theory for example electro magnetism like we are doing now to produce predictions, products or knowledge but because of the incompleteness certain predictions will be false, certain products unfeasible and certain knowledge unprovable until you create a new theory that correct the errors but the new theory will once again contain its own shortcomings- this means we could potentially always discover new things that leads to new theories , plus we will never know that the predictions or products or knowledge are false until we get data proving them false or we do the experiment's which will produce data that is not predicted with current theory forcing us to upgrade it again ad infinitum. So it is not possible for a completely 'determined' universe-affected by incompleteness-to exist as you proposed.

[edit on 25-4-2009 by Incompleteness]



posted on Apr, 25 2009 @ 09:30 PM
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I think they're complimentary, and we need both. It's just part of the nature of our reality, which any TOE would try to approximate as closely as possible, that we can't deduce everything there is to know logically. It just breaks down at some point and requires "something else" we haven't figured out yet. Douglas Hofstadter has even suggested a new type of number be invented to express Godel-looping expressions, just like "imaginary numbers" that engineers use are really just coordinates of a point in 2D or 3D expressed as a single entity.

If you look at any fractal where there's "blank space" (where the actual logical, formulated lines of the fractal pattern don't exist), that fractal can withdraw into itself infinitely and become infinitely more complex using only the same self-repeating pattern, and the empty space will remain, and still can't be touched by the pattern of the formulated fractal. In some respect I think our entire universe is a fractal pattern. There has to be something "outside" of it for it to exist, and we have trouble describing that "something" within a logical framework, because it precedes everything in our reality that logic depends on. Thus we can't "prove" it with logic, like we can't prove calculus within calculus, and the same with any other formal recursive system. If we could, I think we would discovery something very primal about existence in general.



posted on Apr, 25 2009 @ 09:56 PM
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reply to post by Incompleteness
 

Good explanation, thanks - though I wasn't suggesting that a describable deterministic universe like that exists (where everything can be measured instantaneously with complete accuracy); I was sort of bringing it up as counter-example.

Here's another thought: what about continuity of determinability? What I mean by that is this: consider a theory that, given a certain amount of data, predicts that a particle will be at a particular location. But, the location it predicts isn't precise, rather, it's a range of contiguous locations, with varying probability. However, as you increase the amount of data that is 'plugged in' to the theory, the range narrows, and the prediction of the theory becomes more precise. Contrast this with a theory that says "the particle will, with a certain probability, be within a particular set or range of locations, but there an outside chance it will be somewhere else - we don't know", and when you plug more data into that kind of theory, the precision doesn't increase necessarily, but perhaps only the probability changes. I think there's an interesting contrast between these two types of theories that relates to what you're saying. A 'TOE' like the first type of theory is perhaps a practical sort of 'TOE', as it can, with increasing certainty, locate the universe state vector within a particular provable region of solution space, for variable size sets of input data. Thus, there's a kind of closure on applicability. Is there any kind of formal description for what I'm saying here?



posted on Apr, 25 2009 @ 10:42 PM
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I'm not a mathematician or a learned physicist, but fromm what I've read, the whole universe and all causation can be summed up by the manifestation of a single photon of light, and any TOE would have to describe that, which leads to Heisenburg's uncertainty principal. To solve for any TOE the physicist or mathematician would need to describe the manifestations of light from the perspective of the photon itself, and not apart from it.



posted on Apr, 26 2009 @ 06:13 AM
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I agree but incompleteness doesn't imply a fractal like nature is present in nature. It simply means our best theories will always just approximate reality. But you are right is saying that any system that contains incompleteness cannot prove its own consistency by using itself. The universe is a formal system of which we are a part. So we will never be able to completely prove the universe's consistency from the inside. We will always be lacking some important observed phenomenon. But I disagree with your view that there exists more primitive axioms or systems that logic (it is unclear if mathematics precede logic). But certain types of logic and mathematics are complete and thus sound to use without worrying about incompleteness like elementary geometry is complete and first order logic. So logic can be proven using logic. But by updating our TOE and by being creative we will always be able to deduce more and more out of our theories. It lets one wonder if our reality is not some transcendental object which can never be fully described but always allowing new things to be done within it.



posted on Apr, 26 2009 @ 06:26 AM
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reply to post by Ian McLean
 

If we call our theory A and its purpose is to predict the location op a particle with data input. Necessarily the greater the input the more approximate the output. Now after using A for a while with great accuracy of results we suddenly realize that the prediction was all wrong: theory A contains incompleteness. Now we create a new theory by accepting theory A shortcomings as an axiom. Thus B can predict precisely what A couldn't. But after using B for a while we realize... so incompleteness doesn't necessarily limit the ability of the theory to predict the location of the particle it merely says that certain predictions will be false and a new theory will need to be created. But the other shortcomings of the theory e.i. the probability of where the particle is located may also be attributed to the incompleteness theory or it my be attributed to the inadequacy of our theory. But realizing what is inadequacy and what is impossible might be impossible to distinguish. And yes nothings stops us from creating a practical TOE but again just certain predictions will be false. But applicability might be endless since we will always be creating a new theory. Well yes should look into algorithmic information theory- dealing with information and prediction with incompleteness.



posted on Apr, 26 2009 @ 02:16 PM
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Originally posted by Incompleteness
I agree but incompleteness doesn't imply a fractal like nature is present in nature.


But a TOE does. How else would it apply to everything, unless it was literally a single pattern (formula, etc.) that explains all phenomena?


But I disagree with your view that there exists more primitive axioms or systems that logic


I'm not sure what you're disagreeing with. If the universe as science knows it did not exist, logic would not exist. And you already agreed that we can't figure out everything about the universe from within the universe itself (at least as we know it, the physical universe I should say). Even if we could, we still don't know everything about it right now so it makes no difference at the moment. The universe exists despite us not knowing the "first cause," the TOE, but we assume it exists anyway. I didn't say whatever else is out there can be axiomatized, I think it's just the boundary where logic breaks down and one must realize that not everything in existence HAS to be logical (in our current sense of the word, at least), have space, time, volume, etc., because logic itself can't be solely responsible for the TOE since our logic can't even prove itself, and what's worse, Godel's theorem makes a mockery of it.


But certain types of logic and mathematics are complete and thus sound to use without worrying about incompleteness like elementary geometry is complete and first order logic.


Godel proved that any formal system that is powerful enough to be recursive can be forced to produce inconsistent results without breaking any rules. If you could make geometry recursive (I'm sure someone has) then you should be able to produce Godel's theorem with it. I'd actually like to see that myself. And any system that isn't powerful enough for recursion is just incomplete, like "elementary" geometry. You can have a closed system that is consistent, but it won't be very powerful and can't tell you much of anything about the universe.


So logic can be proven using logic.


Where do you get that? Have you ever read the book Godel, Escher, Bach by Doug Hofstadter? He's the one that introduced Godel to me, and it's a very informative book. Alfred Whitehead and Bertrand Russell tried proving every single axiom of our mathematics logically in a book called Principia Mathematica, but failed, because there is no way to "prove" an arbitrary function like addition or even the natural sequence of numbers or many of the other basic, common-sense concepts that make up our "logic" but yet no one usually even feels the need to "prove" them. They may "make sense" to us but they are apparently just as arbitrary as using base-10 instead of base-16 or any other system, none of which are more correct than any other, they all work. But they certainly tried to prove logic using logic, and not long afterwards Godel published his famous theorem.

Here's a quote relating to it from History of Mathematics, by Carl Boyer, just so you know I'm not just making all this up:


Gödel showed that within a rigidly logical system such as Russell and Whitehead had developed for arithmetic, propositions can be formulated that are undecidable or undemonstrable within the axioms of the system. That is, within the system, there exist certain clear-cut statements that can neither be proved or disproved. Hence one cannot, using the usual methods, be certain that the axioms of arithmetic will not lead to contradictions ... It appears to foredoom hope of mathematical certitude through use of the obvious methods. Perhaps doomed also, as a result, is the ideal of science - to devise a set of axioms from which all phenomena of the external world can be deduced.


www.miskatonic.org...

A quote from Godel, Escher, Bach on the same page:


All consistent axiomatic formulations of number theory include undecidable propositions ...

Gödel showed that provability is a weaker notion than truth, no matter what axiom system is involved ...


One more, from a book called An Incomplete Education (emphasis mine!) :


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.


So in the case of figuring out everything in our physical universe, we would have to go outside of our physical universe, according to Godel's theorem. If we can't do that then we can never truly know everything about the physical universe.


It lets one wonder if our reality is not some transcendental object which can never be fully described but always allowing new things to be done within it.


Something very much like that, I agree. Pretty much no different than a dream, with many dreamers.



posted on Apr, 26 2009 @ 04:24 PM
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But a TOE does. How else would it apply to everything, unless it was literally a single pattern (formula, etc.) that explains all phenomena?


What I had meant about why the TOE isn't necessarily a fractal is that the theory of everything will be a collection of ideas, concepts and equations describing the whole of existence but fractals aren't found in everything. Parts might be fractal in nature.



But I disagree with your view that there exists more primitive axioms or systems that logic


Sorry made a typing error meant to say that I disagree with your view that there exists more primitive axioms or systems 'than' logic. Which refers to that logic can be used to prove logic. And logic is independent of subjectivity unless you are implying that 1 + 1 =3 if no one exists to test it. And I am not quite certain what you are referring to when you say:



at least as we know it, the physical universe I should say


And the very meaning of the TOE is contradicted when you say:



not everything in existence HAS to be logical


Since its goal is to describe ANY phenomenon. And the TOE will be based on logic and mathematics. And what examples of phenomenon do you know of that are not logical barring certain mathematical objects (see below).




Godel proved that any formal system that is powerful enough to be recursive can be forced to produce inconsistent results without breaking any rules. If you could make geometry recursive (I'm sure someone has) then you should be able to produce Godel's theorem with it. I'd actually like to see that myself. And any system that isn't powerful enough for recursion is just incomplete, like "elementary" geometry. You can have a closed system that is consistent, but it won't be very powerful and can't tell you much of anything about the universe.


Well there is a error in argument in assuming that elementary geometry is incomplete, it might be made so, by as you said being made into an self-referencing statement but the error in that argument is that the underlying mechanism are as a fundamental property 'complete' and 'consistent' in contrast to Peano Arithmetic which is incomplete no matter one's attempt to 'cure' incompleteness.



And any system that isn't powerful enough for recursion is just incomplete, like "elementary" geometry


Well no. In fact any consistent formal system that is non-recursive will be complete. For example basic addition is complete.



You can have a closed system that is consistent, but it won't be very powerful and can't tell you much of anything about the universe.


Again no. Since it is full and well possible that the TOE is complete and consistent. And closed. But the amount of interaction between the laws are so high that it gives the impression of incompleteness. So the underlying principles of our universe might be complete and consistent and the possible amount of interactions very large.



posted on Apr, 26 2009 @ 04:36 PM
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reply to post by bsbray11
 


And heres a quote to prove my reply Stephan Hawking speculating on TOE from wikipedia:


Douglas S. Robertson offers Conway's game of life as an example:[14] The underlying rules are simple and complete, but there are formally undecidable questions about the game's behaviors. Analogously, it may (or may not) be possible to completely state the underlying rules of physics with a finite number of well-defined laws, but there is little doubt that there are questions about the behavior of physical systems which are formally undecidable on the basis of those underlying laws. Since most physicists would consider the statement of the underlying rules to suffice as the definition of a "theory of everything", these researchers argue that Gödel's Theorem does not mean that a TOE cannot exist. On the other hand, the physicists invoking Gödel's Theorem appear, at least in some cases, to be referring not to the underlying rules.


And to reply to:



Where do you get that?


I get it because first order logic is used in many domains including in mathematics :


First-order logic (FOL) is a formal deductive system used in mathematics, philosophy, linguistics, and computer science.A first-order theory consists of a set of axioms (usually finite or recursively enumerable) and the statements deducible from them given the underlying deducibility relation. Usually what is meant by 'first-order theory' is some set of axioms together with those of a complete (and sound) axiomatization of first-order logic, closed under the rules of FOL. (Any such system FOL will give rise to the same abstract deducibility relation, so we needn't have a fixed axiomatic system in mind.) A first-order language has sufficient expressive power to formalize two important mathematical theories: Zermelo–Fraenkel (ZFC) set theory and (first-order) Peano arithmetic. A first-order language cannot, however, categorically express the notion of countability even though it is expressible in the first-order theory ZFC under the intended interpretation of the symbolism of ZFC. Such ideas can be expressed categorically with second-order logic.


And it is unclear if you know that there is a distinction between mathematics and logic since they have not been proven to be deducible form each other as you have said the reason why they couldn't deduce math from logic might be because they were trying to derive apples from mangoes. But there exist sub-branches in each that contains part of each other.




All consistent axiomatic formulations of number theory include undecidable propositions ... Gödel showed that provability is a weaker notion than truth, no matter what axiom system is involved ...


There is no reason to assume that the TOE will use exclusively number theory.

And the reason why we will always be able to go outside the system will be discussed in a idea i will soon post based on incompleteness inexhaustibility and post humanism.
Sorry for the long reply. Cheers.



posted on Apr, 26 2009 @ 05:19 PM
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Originally posted by Incompleteness
Sorry made a typing error meant to say that I disagree with your view that there exists more primitive axioms or systems 'than' logic. Which refers to that logic can be used to prove logic. And logic is independent of subjectivity unless you are implying that 1 + 1 =3


I'm not sure you understood what I was talking about in my post. I have nothing to argue about. If you have personal opinions on what theories have shown, or what they haven't, etc., you are certainly entitled to them.


Well there is a error in argument in assuming that elementary geometry is incomplete


It's either incomplete or inconsistent, has to be one or the other, that's what Godel proved some decades ago.


In fact any consistent formal system that is non-recursive will be complete. For example basic addition is complete.


Addition is not complete. Do you really think all fields of science and engineering can be reduced to simple addition? If you feel inclined to try it, go ahead, but until someone actually does it the answer is "no." Simple addition is what's called "trivial," meaning it isn't a powerful system and you can't calculate much with it exclusively.




You can have a closed system that is consistent, but it won't be very powerful and can't tell you much of anything about the universe.


Again no. Since it is full and well possible that the TOE is complete and consistent.


You started this thread asking about the relation between Godel's theory and a possible TOE. No TOE has ever been proven. Godel's theory, on the other hand, has. So unless Godel has been refuted and you're the only one that knows about it, I have to say you don't know what you're talking about.

I thought it was an interesting OP, but I'm not going to argue the implications of Godel's theorem. Enough people have already figured it out that it's not even a matter of debate, it's just a matter of understanding what you are really talking about.

All I have to say, is that if you think you have a formal, complete, and consistent system, produce it. You'll be the first, and believe me, much greater minds than yours or mine have been trying for decades. I sincerely believe it will never happen because it's impossible, just as Godel demonstrated very rigorously so many years ago.

[edit on 26-4-2009 by bsbray11]



posted on Apr, 26 2009 @ 05:43 PM
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reply to post by bsbray11
 




I'm not sure you understood what I was talking about in my post. I have nothing to argue about. If you have personal opinions on what theories have shown, or what they haven't, etc., you are certainly entitled to them.


I merely wanted to point out that there is no system more primitive that logic or mathematics nothing logically possible exits outside them.



It's either incomplete or inconsistent, has to be one or the other, that's what Godel proved some decades ago.


No I don't think you fully understand Gödels theorem. Do some research only systems containing Arithmetic-not only arithmetic but also addition and multiplication as well as '0' and 'successor of'- are incomplete. Thus a system containing addition but no multiplication is complete and vice versa.


1st Theorem (Syntactic Version): Assuming that the axiom system A has the following two properties: A is sufficiently strong to be a plausible candidate for an axiom system for arithmetic; in particular, it is at least strong enough to permit the derivation, by correct reasoning, of any true elementary arithmetic statement involving the operations of addition, multiplication and successor-taking, and incorporates the principle of natural induction; A is consistent - i.e. it is not possible to deduce from it a contradiction;


I propose you carefully read through this link so that you can get a better idea of when Godels theorems are applicable :
An Introduction to Gödels incompleteness theorems



Addition is not complete. Do you really think all fields of science and engineering can be reduced to simple addition?


See above. You have a misconception pertaining to completeness. It simply means no statements will be produced that are false. Such as 1 + 1=3 or the like it in no way implies that all of science is reducible to addition.



So unless Godel has been refuted and you're the only one that knows about it, I have to say you don't know what you're talking about.


Again go and read the wikipedia entry on TOE then scroll down to the incompleteness section for a quick discussion on why it is full and well possible for a TOE to exist that is consistent and complete.

Wikipedia entry on TOE



All I have to say, is that if you think you have a formal, complete, and consistent system, produce it. You'll be the first, and believe me, much greater minds than yours or mine have been trying for decades.


Somewhere you are misunderstanding the whole theorem. As I have said go read about it go to wikipedia even their entry on the incompleteness theory will give you examples of systems that are complete. Only systems containing the necessary arithmetic (addition multiplication '0' and 'successor of' are incomplete). And as I have said i already have a example elementary geometry since it does not contain the required arithmetic to be incomplete. If you have read all those links we can debate further.

[edit on 26-4-2009 by Incompleteness]



posted on Apr, 30 2009 @ 07:10 AM
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Good thread. I don't frequent this board so I could have easily missed it.

I'm inclined to believe that an absolute TOE to be impossible, that is, a theory that can describe EVERY action/outcome with exact precision. I believe there is evidence to suggest there is inherent irreducible randomness involved in some physical phenomenon (polarization, decay, uncertainty principle etc). In the macroscopic world however, I think theories will come very close to describing reality.

That said, my knowledge of such things isn't strong. I've read GEB and study about am doing a PhD in statistics. I studied maths/physics in undergrad.



posted on Apr, 30 2009 @ 07:55 AM
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reply to post by Incompleteness
 


I trust you have read "Godel, Esher, Bach" by Douglas Hofstadter?

From Wikipedia:


Gödel, Escher, Bach: an Eternal Golden Braid (commonly GEB) is a Pulitzer Prize-winning book by Douglas Hofstadter, described by the author as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll".

On its surface, GEB examines logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, discussing common themes in their work and lives. At a deeper level, the book is a detailed and subtle exposition of concepts fundamental to mathematics, symmetry, and intelligence.

Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.

In response to confusion over the book's theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms. In the book, he presents an analogy about how the individual neurons of the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants.

en.wikipedia.org...


If not I highly recommend it... I just went back and reread it recently after decades... its not an easy read... and even though I've read it before it still took me three months.... but if you are interested in cognition it is definitely a must.

Like Julian Jaynes "The Origin of Consciousness in the Breakdown of the Bicameral Mind' there are flaws in his arguments but I am not smart enough to pin them down... I just know that they are there.

Still GEB is a profitable read as is Jaynes.



posted on May, 1 2009 @ 11:45 AM
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Hi, theory fans.

After a search and not finding it in here, here is a nice video:

www.ted.com...

Blue skies.



posted on May, 1 2009 @ 02:03 PM
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reply to post by Incompleteness
 


You said :
... that since we can use mathematics to describe every phenomenon ...


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.'


Cantor Dust

Also known as the Cantor set, possibly the first pure fractal ever found – by Georg Cantor around 1872. To produce Cantor Dust, start with a line segment, divide it in to three equal smaller segments, take out the middle one, and repeat this process indefinitely.

Although Cantor Dust is riddled with infinitely many gaps, it still contains uncountably many points. It has a fractal dimension of log 2/log 3, or approximately 0.631.

Source : DavidDarling.info

Cantor Dust


Source : Platonic Realms

Cantor basically proved a result along the same lines as Gödel, essentially that we may be able to use mathematics to describe a phenomenon, but sometimes that description won't make any sense.

That is to say, that in some situations the 'models' we derive via math are 'self-contradictory.'

A lot of mathematicians didn't like Cantor very much because he showed them ways that our mathematics could 'fail.'

Many others considered him a profound genius.

Interesting person who made very powerful contributions to mathematics and philosophy ...



posted on May, 2 2009 @ 02:52 AM
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I really don't think that Cantor result is that self-contradictory.



posted on May, 2 2009 @ 03:22 AM
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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.

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.



[edit on 2-5-2009 by tobiascore]



posted on May, 2 2009 @ 07:29 AM
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reply to post by Incompleteness
 


by the definition of the incompleteness of the TOE that there will always be statements (when physically translated : experiments or observations) that are unprovable with the current TOE thus meaning no coherent form of determinism will ever be possible in such a universe.

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?

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






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