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Hawking: No 'Theory of Everything'
Flash Modin writes "In a Scientific American essay based on their new book A Grand Design, Stephen Hawking and Leonard Mlodinow are now claiming physicists may never find a theory of everything. Instead, they propose a 'family of interconnected theories' might emerge, with each describing a certain reality under specific conditions. The claim is a reversal for Hawking, who claimed in 1980 that there would be a unified theory by the turn of the century."
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
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*)
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.
We always knew Comcast was corrupt, here's the proof: http://tech.slashdot.org/comments.pl?sid=1909890&cid=34545432
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.
... 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).
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
After logging in slashdot still does not take you back to the page you were on. It's been that way for 20 years.
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.