Hawking: No 'Theory of Everything'

The hand of Godel? by Hatta · 2010-09-30 07:00 · Score: 3, Interesting

Godel proved that all formal systems are either incomplete or inconsistent. Perhaps that's what we're dealing with here.

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Re:The hand of Godel? by w0mprat · 2010-09-30 07:30 · Score: 5, Interesting

We work on the assumption that the laws of physics are perfect and complete, and we are just trying to reveal them. The laws of physics could work well enough but actually be incomplete and consistent as you point out. They could even bebe crappy, bloated and buggy with lots of missing chunks, unused bloat and even errors.

If the laws of physics emerged naturally, for example budding off from a parent universe, and subject to a process of evolution I would expect theories of everything to be 'just good enough' and barely work rather than somehow perfect and elegant and mystical. Much like the junk DNA, apendix and mens nipples that rides along with us because evolution didn't really have pressure need to get rid of them.

I would say we should by default expect a theory of everything a whole basket of seemingly clumsy unweildy theories that barely fit together - after all they only need to be just good enough for us to be here and not any better. If we expect flawless elegant unified symmetry and beauty, then we'd need to demonstrate why (without invoking God to explain etc).

Researchers have been seduced by subjectively elegant and simple equations all the way back to F=MA ... these worked well enough, but were ultimately wrong, the truth was more complex and nuanced, but now we're finding the universe is fuzzy, clumsy and possibly buggy (inflation, possible variations in c, other weirdness).

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Re:The hand of Godel? by luis_a_espinal · 2010-09-30 09:37 · Score: 4, Interesting

Prove it.
Easy. Proof by contradiction:
Assume there is a universal (and extremely long) string U that encodes a countable set containing all problems P_i (encoded as decision problems) that are possible in this Universe. We can trivially see that indeed U must contain all problems that exist for it to represent the Universe. Otherwise, it does not represent the Universe.
Furthermore, if every decision problem P_i in U is decidable, then there is a (not necessarily unique) Turing Machine T_i that halts in finite time for each problem P_i in U. With this assumption, then there would be a Universal Turing Machine T that is a chain of all turning machines T_i that can compute (and thus give meaning) to all problems P_i in U (the string encoding of the universe.) That is, T is the universe.
But the halting problem is not in U. In fact, U cannot contain neither semi decidable nor undecidable problems (which was our base assumption). However, the halting problem (and all other semi-decidable and undecidable problems) exists in the Universe. U then, cannot be an encoding of the universe, and T (a turing machine) cannot be the Universe either.
qed.
It may just be a matter of scale - we simply aren't able to take a large enough view. A turing machine, if you only look at one small part of it, is no longer turing-complete. And the presence of a turing-complete machine doesn't mean the enclosing reality suddenly is turing-complete. Think babushka dolls, as in Soviet Russia, Turing completes YOU!
Dude, the fact that there are problems in this Universe (and thus part of it) that are not turing computable (a mathematical fact indeed) does indicate that the universe is not a Turing complete nor Turing computable. The universe is naturally uncountable.
Re:The hand of Godel? by FrangoAssado · 2010-09-30 13:18 · Score: 2, Interesting

Here is a way it could possibly not apply.
Your argument seems to be this (please correct me if I'm misrepresenting it):
Take the formal system of the "theory of everything", call it TOE. By Godel's theorem, there exists a certain arithmetic statement (G) that is independent of TOE. Because the universe is Turing complete, it's possible to physically build a Turing machine (M) whose output (or, even better, whether it halts or not) depends on the truth value of G. Since G is undecidable in TOE, the "theory of everything" can't predict what would physically happen if we actually build M in the physical world. So, this means that the "theory of everything" can't actually predict everything.
One possible objection is the following:
When you follow Godel's proof, you notice that the arithmetic statement that the proof constructs involves huge numbers, and that the more axioms you put on your system, the larger the numbers involved must be (if you don't remember just how huge the numbers are, go back and check it: it's mind boggling, even for the relatively simple formal system used by Godel).
That in itself would not be a problem, since we're only talking about the theoretical possibility of the existence of the "theory of everything". But, it turns out that it's possible (and even probable) that our universe is not actually Turing complete because there's a limit to how much computation is possible even in principle. That is, it's possible that the formal system of the "theory of everything" is complex enough that in order to build the Turing machine that would be unpredictable, you'd either have put so much in too little space that it would become a black hole, or you'd have to spread it out so much (in order to prevent the black hole) that the universe expansion would make one end of the Turing machine inaccessible to the other end, and so the machine wouldn't be able to compute anymore.
In case that last point is not too clear, you can find a much better explanation in this lecture (search for "So what does any of this have to do with computation?").
I'm not saying that this is the case, but it's certainly a possibility that has not been ruled out (and maybe it's even true).

What kind of semantic bullshit is this? by RobinEggs · 2010-09-30 07:10 · Score: 2, Interesting

Instead, they propose a "family of interconnected theories" might emerge

Which, if you read them all at the same sitting and follow all the connections, just might read like one big...unified theory.

This seems very, very close to a distinction without a difference.

Emergence might be infinite... by RyanFenton · 2010-09-30 07:13 · Score: 5, Interesting

I don't actually mind if this is the case. What it means then, is that new properties of aggregated matter emerge as you go up, and up in scope and scale, and that there does not have to be a set relationship on what rules must emerge.

Other than aesthetics, those emergent rules don't have to carry a thread of logic visible at all scopes. Rather, you just need to have the large number of interactions actually occur in relationship to eachother to see the combined effect, with many aspects unforeseeable by only observing the elements many magnitudes smaller.

Whether this might make the universe a more or less beautiful puzzle to figure out is open to interpretation.

Ryan Fenton

Re:Emergence might be infinite... by entrigant · 2010-09-30 07:29 · Score: 2, Interesting

Correct me if I'm wrong, but isn't the very idea of emergent phenomenon the result of a complex system emerging from less complex interactions? I was always under the impression the idea of a "theory of everything" is to isolate those simple interactions that all emergent behavior stems with the idea being that perhaps, in time, the emergent behavior can be predicted or even constructed.
Perhaps emergence can go both ways.. somehow? There is no base set of rules, and no matter how far in either direction you look you find more? I don't know, but it does seem that was we increase scale the trend is one way. The larger scale systems that we can explain are explained by smaller scale systems (at least from our point of view) and not vice versa.
In the end and for all we know we may be so far from the truth that if and when we do discover it it will look nothing like what we currently understand. We have no scale or basis for comparison. I find it amazing anyone would even attempt make claims as to what "the end" of knowledge looks like.

Just a result of age by Troggie87 · 2010-09-30 07:15 · Score: 4, Interesting

As scientists age they become somewhat jaded, it happens to a lot of people. Hawking has seen a problem he thought was about to be solved get ever more complex while little new progress has been made. I don't blame him for changing his stance. I had a professor during my undergrad who had been a part of some of the first fusion research, and he would occasionally bring up that he didn't think it was possible. According to him, "the kids today are trying what we tried and couldn't get to work back then" (Paraphrased). Maybe doubting there is a solution to the problems you have struggled with all your life is the best way to find peace as your life winds down?

Oh, on a personal opinion note, I doubt we will ever find a *provable* theory of everything. Eventually someone will put together something that relates a lot of complex fields, but I suspect it will be something ad hoc and beyond the practical limits of humanity to test. (*cough* string theory variant *cough*)

Re:Past His Prime by Wannabe+Code+Monkey · 2010-09-30 07:17 · Score: 4, Interesting

Totally. He just likes to hear his own voice.

Now you're making me wish that I hadn't commented in this discussion just so I could mod you up. Although if I had never commented, then you wouldn't have been able to reply to me and I wouldn't have been able to mod you up anyway. Maybe some smart scientist could help us out with this paradox.

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Re:unified theory by the turn of the century by jd · 2010-09-30 07:38 · Score: 2, Interesting

Actually, no. I was at the talk and he actually stated that every time people predicted the end of physics, something new was discovered that revolutionized the field; that in this light he was going to predict the end of physics and the discovery of a theory of everything. As far as I'm concerned, he has achieved his objective. Something new has indeed been discovered and it does appear to have revolutionized the field.

To those who think Hawking is beyond his prime, I'll say maybe. No scientist likes to give up working in their field and Hawking has far fewer reasons than most to want to. One major contribution he can make is in describing how he models the physics in his mind. The depth of his mental agility is staggering and knowing how he achieves it would be extremely valuable. We know a little of Einstein's method, but it needs a team - I'd suggest at a minimum a physicist, an analyst trained in extracting specifications from experts whether or not the expert knows what the specifications are and an expert in thinking techniques. The idea would be that the physicist is the only one who knows what would be meaningful to ask and how to understand the answers, the analyst is the only person trained in using examples to unveil the underlying mechanisms and methods, and you still then need someone to turn this model into something that can actually be used by others.

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from a previous story by night_flyer · 2010-09-30 08:15 · Score: 2, Interesting

'If we discover a complete theory, it would be the ultimate triumph of human reason - for then we should know the mind of God.' Hawkins - 1988

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Inifinte States by Roger+W+Moore · 2010-09-30 09:53 · Score: 2, Interesting

And the same goes for the universe itself; it has a bounded number of observable states.

That is not clear. A free electron has no quantized energy and, since current evidence points to the universe expanding for ever, there is no limit to the accuracy with which we can measure that energy (as boring as that measurement may be). Hence a single free electron has an infinite set of states as long as the universe's lifetime is unbounded.

Feynman agreed...though much earlier by PerlHeadJax · 2010-09-30 13:05 · Score: 3, Interesting

From Gleick's "Genius: The Life and Science of Richard Feynman"...

"'People say to me, "Are you looking for the ultimate laws of physics?" No, I'm not...If it turns out there is a simple ultimate law which explains everything, so be it--that would be very nice to discover. If it turns out it's like an onion with millions of layers...then that's the way it is.' He believed that his colleagues were claiming more success at unification than they had achived--that disparate theories had been pasted together tenuously. When Hawking said, 'We may now be near the end of the search for the ultimate laws of nature,' many particle physicists agreed. But Feynman did not. 'I've had a lifetime of that,' he said on another occasion. 'I've had a lifetime of people who believe that the answer is just around the corner.... But again and again it's been a failure. Eddington, who thought that with the theory of electrons and quantum mechanics everything was going to be simple...Einstein, who thought that he had a unified thoeiry just around the corner but didn't know anything about nuclei and was unable of course to guess it...People think the're very close to the answer, but I don't think so....

Whether or not nature has an ultimate, simple, unified, beautiful form is an open question, and I don't want to say either way.'"

(From the epilogue of the book, pp. 432-433, emph. added.)

Re:Old news by Artifakt · 2010-09-30 16:30 · Score: 2, Interesting

Putting it into a single simple phrase means losing a lot, but it's pretty fair to say Godel's second great proof shows that Formal Systems (like mathematics) have statements that are true, but can't be proven within the system. The more powerful a system is, the more (in general) it has such truths, and doing something that extends such a system's power actually makes the situation worse, not better.

If you want to condense that to a single, clipped phrase: "Truth extends beyond provability."

By the way, Godel's third great proof shows that God exists - sorry to bother all the Atheist slashdotters with that bit of trivia.

For those of you who don't know who Godel was, Einstein kept him around at Princeton to check Einstein's calculations and help with the hard parts, and the greatest work on Math of the 19th century, the Principia Mathematica, was overturned entirely by that pesky second proof.

And it was the quantum mechanicians who 'disproved reality'. Google "Copenhagen Interpretation", "Many Worlds Theory" "Erwin Rudolf Josef Alexander Schrödinger", or "Werner Heisenberg" for details.

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Re:Old news by walshy007 · 2010-09-30 17:04 · Score: 2, Interesting

By the way, Godel's third great proof shows that God exists - sorry to bother all the Atheist slashdotters with that bit of trivia.

You fail to specify what godels interpretation of 'god' is, spoiler: it's not the anthropomorphic zombie human/spirit that has super powers like what most religions preach.

I would of course assume you are speaking of Godel's ontological proof. Which he himself did not publish until his dying days because he did not want people to mistakenly think he actually believed in god.

The proof starts off arguing that there are infinitely possible worlds, therefore in at least one of those infinitely possible worlds there must be a god etc.

There are numerous arguments against such a proof, not the least of which some of them predate godel himself by a few hundred years. (Immanuel Kant rejected existence as a property some time before this proof was made)

Not to mention the problems of incoherence in regard to god being considered omnipotent, omniscient, and omnibenevolent,

Those that have read the many problems with his proof (even theologians) have usually found at least one if not more that satisfy to them that it is flawed.

That you have not is most surprising, there really are that many.

Re:Oblig by EnsilZah · 2010-09-30 22:16 · Score: 3, Interesting

It got me to check 404 though, which actually displays a 404, given 403 and 405 do point to actual comics leads me to believe is actually intentional, geeze this guy is committed.

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Hawking: No 'Theory of Everything'

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