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    Limits To Science: God, Godel, Gravity
    By Johannes Koelman | November 12th 2010 07:22 PM | 105 comments | Print | E-mail | Track Comments
    About Johannes

    I am a Dutchman, currently living in India. Following a PhD in theoretical physics (spin-polarized quantum systems*) I entered a Global Fortune

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    Stupid physicists, they are doomed. Spending their whole lives searching for a theory of everything, not knowing that some eighty years ago this was proven to be logically impossible. 

    The internet is full with sentiments like the above. Many such posts refer to Stephen Hawking's 2002 Dirac lecture Gödel and the End of Physics.

    With the publication of his new book 'The Grand Design', the Oracle of Cambridge is again adding to the confusion. However, due to all the fuzz surrounding a much less interesting claim by Hawking this issue has not received any attention whatsoever.

    What is Hawking telling us? In his Dirac talk he states:

    "Up to now, most people have implicitly assumed that there is an ultimate theory, that we will eventually discover. Indeed, I myself have suggested we might find it quite soon. However, M-theory has made me wonder if this is true."

    He continuous:

    "Maybe it is not possible to formulate the theory of the universe in a finite number of statements. This is very reminiscent of Gödel's theorem. This says that any finite system of axyoms, is not sufficient to prove every result in mathematics."

    and at the end of his talk concludes with:

    "Some people will be very disappointed if there is not an ultimate theory, that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind."



    Hawking, terminator of the TOE? Hawking's latest book must puzzle those who hailed his claim that TOE is dead.

    Clearly, the world's most celebrated Nobel-less physicist is giving the physics community a wake-up call: "guys, you may not have noticed it, but we have hit a brick wall in our search for understanding and knowledge. Stop the search for the ultimate theory!". Since 2002 Hawking has delivered his talk and this very message several times, and a multitude of copies of the text of his talk can be found on the internet. So why are hordes of physicists stubbornly persisting in their doomed quest?

    And even more amazingly: how on earth can Hawking himself end his most recent book with the very conclusion:

    "M-theory is the only candidate for a complete theory of the universe. [..] If the theory is confirmed by observation, [..] We will have found the grand design"

    Has Hawking again changed his mind? 

    No, he hasn't. But he does seem to have gotten himself in a mess. Stuck in a labyrinth of excessive claims out of which no escape is possible. Life ain't easy if your books sell by the million and publishers insist on one-liners that guarantee a media frenzy.*

    So let me try to help out here and give you my take on what Hawking is trying to convey. It all starts with this guy Gödel that Hawking refers to in his Dirac talk. 


    From God To Gödel

    Brilliant, perfectionist, obsessed and socially inept. Kurt Gödel was all of it to the extreme. A lively account of Gödel's social interactions with government officials as well as with his friend Albert Einstein, is given in a note from Oskar Morgenstern (a scan of the original can be found here). Gödel's friendship with Princeton Institute colleague Einstein lasted till Einsteins death. They both admired each other, and late in his life Einstein commented that "his own work no longer meant much, that he came to the Institute merely [..] to have the privilege of walking home with Gödel".



    The privilege of walking home with Gödel

    Both friends were titans of twentieth century science. Although Einstein is much better known to the wider public, without any exaggeration Kurt Gödel can be named the Einstein of logic. His famous 1931 article in the Monatshefte für Mathematik und Physik redefined the foundation of mathematical logic, and put clear limitations to what can be achieved by the methods of logic.   

    Gödel's article presents a clever meta-mathematical argument that, put in simple terms, proves there is no system of logic that is free from contradictions and at the same time free of gaps. In other words, there is no system of logic that is capable to separate all statements contained within that system in the two categories 'true' and 'false'. There is always a third category 'undecideable'.

    This incompleteness theorem** exploded as a bombshell and shook the whole world of mathematics. Eighty years later Gödels results continue to stand out as a key achievement that has forever redefined mathematical logic and continuous to influence its development.
     
    Gödel's brilliance is beyond any doubt, but his mind also played tricks on him. Gödel's perfectionism created obsessions that in his later years grew far beyond his control. He stopped publishing his work out of fear for imperfections. Gödel's paranoia thereby deprived the world of any further contributions of this great mind. Other obsessions, however, affected Gödel himself. One of these was a fear of getting poisoned. Gödel trusted only the food prepared by his wife. When in 1977 she got hospitalized for six months, Gödel refused to eat. Late December 1977 the giant of mathematics was admitted to Princeton Hospital, weighing no more than 65 pounds. He died two weeks later, with the diagnosis "malnutrition and inanition due to personality disturbance".

    Some forty years after Gödel's death, we are asking ourselves the question what the legacy of this man means for physics. 

    Present day physicists feel little limitations. Frankly, they are the least impressed by any statements that try to limit their future achievements. This has been very different. Galileo's insights got overruled by biblical statements that declared the earth to be immoveable. However, that time now lays far behind us. The concept of separation of church and state has given physicists free reign. Since Laplace replied "Sire, I had no need of that hypothesis" to Napoleon's questioning why 'the author of the universe' was missing from his theories, no church and no God seem capable to stop physicists making progress. Almighty or not, physicists don't allow any supreme being blocking the road to new horizons and further progress.

    Enter Gödel. Is he God's revenge? Is Gödel putting limits to what physicist can achieve?

    Physicists build theories that are based on mathematics. They use mathematics to derive conclusions from these theories. They make predictions about physical reality based solely on mathematics and logic. Surely Gödel's results put limitations on what can be achieved in theoretical physics!

    Wow, wow. Not so quick! 

    We will come back to the question what is the relevance of Gödel to physics. But let us first make sure we understand Gödel's incompleteness theorem and its impact on mathematics. 


    Gödel: God's Gift To Math

    Fueled by inaccurate popularizations, the wider public seems to hold erroneous views on what Gödel's results imply. Following the adage a picture tells more than a thousand words, let me try to visualize how the vast majority of the public seems to perceive Gödel's results:



    Visualisation of a popular myth of Gödel's impact on mathematics. In the space of mathematical propositions there are grey areas, statements that are not yet proven neither disproven. Mathematicians work hard to find proofs or disproofs for all statements, thereby reducing the grey areas. Gödel's results tell us that there will always remain grey areas.   
         
    The above picture is misleading as it focusses on one single system of axioms. Mathematicians are not bound to work in a single such system, and are free to construct novel and more powerful systems. It is a freedom that is almost a defining characteristics of mathematics. A more accurate picture is therefore the following:



    Improved visualisation of the impact of Gödel's results on mathematics. Each system of axioms leads to grey areas of propositions that are undecideable. Progress can be made by replacing the set of propositions by more powerful ones that have a wider range of application. This removes grey areas but at the same time opens up new horizons behind which new grey areas loom. This process can repeat endlessly.

    This improved picture gives a much more optimistic view on the impact of Gödel's work on fundamental mathematics: there is no end to mathematics, progress is always possible but requires new approaches. Gödel has given mathematicians the guarantee they will never be out of work!

    Since Gödel's 1931 publication, further work has elucidated the meaning of his incompleteness theorems. In particular, in 1936 Alan Turing*** gave a specific example of uncomputability: a problem that can not be answered by any computer no matter how powerful or how long one is prepared to wait. This uncomputability implies Gödel's incompleteness: the grey areas in above animations.

    Uncomputability is a notion that brings us closer to physics. A theory of the universe is nothing more ( and nothing less) than a computer program. A program that simulates the evolution of the universe starting from the moment of the big bang. Gödel's and Turing's results make it very doubtful uncomputability issues would not await a theoretical physicist who has managed to construct the ultimate computer program that will simulate the universe.

    So there you have it: Turing has made incompleteness issues entering physics.

    Let's investigate this closer. 


    From Gödel To Gravity

    Turing's uncomputability refers to the generic problem of deciding whether any given computer program with given inputs will stop. Turing demonstrated that there exist computer program's with given inputs that can not be predicted to ever halt. You simply have to start the program and wait. As long as it keeps running you have no clue if it ever will halt.

    So let's say we have a computer program that simulates the whole universe and that is started with inputs such that it will compute the universe of tomorrow. You start the giant computer that runs the program, and it starts cranking away. Huge amounts of data are processed. After an hour the computer is still running. Two more hours, still running. Twenty more hours, no sign the program will stop. Tomorrow passes by, and the computer is still running. Will it ever stop? You have no idea.  

    So what? 

    This basically shows that it is likely that physics will never be able to predict tomorrow in all its details. But we knew that already. Physicists can't predict a coin flip, let alone tomorrow's stock exchange prizes. So Gödel's incompleteness and Turing's uncomputability don't bring us any new results. 

    But there is more. 

    The above application of uncomputability to predicting the universe assumes we can in principle build a computer capable of simulating the universe. But we can not. Not even in principle. If you would attempt building such a computer, you would discover that it would collapse and form a black hole long before it reaches the size needed to be capable of simulating the universe. And this constitutes not just a practical problem, but a very fundamental limitation. Even if we would be capable of building a quantum computer out of smaller and lighter components, we would still hit the same problem. Make the compenents even less heavy until you hit the quantum limit and the Heisenberg uncertainty relations prevent you from further improving your computer. Even if you manage to built the ultimate quantum computer operating on the orchestrated motions of countless photons, all with zero mass, you would still witness black hole formation before you would reach the computational capacity that would alow you to predict tomorrow.

    So it is gravity, and not Gödel, that prevents us predicting the future. That actually makes into a nice bumper sticker: "Gravity is to physics as Gödel is to math". This is the point Hawking is referring to in his Dirac lecture where he states "quantum gravity is essential to the argument".

    But we are not done yet. 

    As far as the question "is a TOE possible?" is concerned, all of the above is absolutely irrelevant. Uncompuability does not imply that a Theory Of Everything can not be constructed. Gödel does not prevent physicists from doing so, and neither does gravity. Stating that Godel (or Turing, or gravity) implies the logical impossibility of a TOE, is the same as stating that because of the incompleteness theorem an axiomatic logic can not be constructed. This is simply wrong. Axiomatic logics can be constructed, but given an axiomatic logic not every result can be derived. Similarly, Gödel nor gravity prevents us from constructing a TOE, but gravity does prevent us from turning this TOE into a crystal ball. 

    Anyone a problem with that?




    Notes

    * It is a fun exercise to derive extreme headlines from the various 'Hawking one-liners'. My favorite one is derived from his most recent one-liner "God not needed!", combined with his book title "God created the integers", giving the headline: "Hawking: all of math wrong, integers don't exist!".
    ** Actually, Gödel derived two related theorems. I have not attempted to state precisely all relevant details and assumption behind Gödel's incompleteness theorems.
    *** Another example of a life with a tragic ending. The UK of the post-war years was not particularly tolerant toward homosexuality. In the early 1950's, Turing's homosexuality resulted in a criminal prosecution and chemical castration. Shortly thereafter, aged 41, Turing committed suicide by cyanide poisoning. 

    --------------------------------------
    The Hammock Physicist on: E=m.c2, Entropic Gravity, Entropic Force, Shut Down LHC?, Game Theory, Metric Vs Imperial, Big Bang, Dark Energy, Chaos And Time's Arrow, The Grand Arena, Square Root Of The Universe, Physics In A Nutshell, The Longest Path, Hotel Boltzmann, Quantum Telepathy, Quantum Viruses, QHD, Fibonacci Chaos, Counting A Black Hole, Entropic Everything

    Comments

    For a computer program, it reminds me of finding the exact value of pi

    show me the exact value of pi . cannot - need to jump to a higher level of reasoning - i.e. computable number

    Johannes Koelman
    Mfc, you're right that the job of computing all the digits of pi is an infinite - and therefore impossible - task. But astronomky is also right in saying that that in itself does not make pi uncomputable. Gödel nor Turing can prevent that every digit of pi can in principle be computed. For some other - truly uncomputable - numbers it is not even possible in principle to calculate any of its digits. But I agree with you and would be tempted to make your statement even stronger: gravity allows us to define a finite accuracy such that it fundamentally impossible to calculate pi with that accuracy.
    Seems like inventions such as computable numbers illustrates:

    ".... Progress can be made by replacing the set of propositions by more powerful ones that have a wider range of application. This removes grey areas but at the same time opens up new horizons behind which new grey areas loom. This process can repeat endlessly"

    Not sure about the process repeating endlessly, but this does seem to be the general direction. Like knowing more and more about less and less.

    I found somewhere on the internet a paper and a generator that claim it could calculate a specified digit of pi. I wish I knew where the link was.

    That formula opens an entire new prospect to the possibility of building a machine to simulate the universe given an appropriate TOE. Perhaps we couldn´t simulate the entire universe but parts of it; of course this is pure speculation and i'm septic about it since the digits of Pi are not correlated and the same isn´t true about the universe. A more prospect venue could be the Holographic principle, trouble is the universe is expanding so it´s difficult to define his boundary but we could take a snapshot; what do you think of it?

    Brilliant articles
    Hope you'll write a book on physics for non-physicists

    Johannes Koelman
    Thanks. Maybe some day (but don't hold your breath...). In the meantime you can read the separate chapters for free here. :)
    Thank you for a nice posting.

    One interpretation for the physics counterpart of Goedel's theorem is that there is an infinity of laws of physics to be discovered. The evolution of the Universe involves this process of discovery and after each quantum jump giving rise to such a discovery we have new Universe which is even more complex than its predecessor since it contains conscious information about this new law. A new meta level in the hierarchy of understanding would emerge. Only if the Universe were given once and for all (no quantum jumps recreating it) one could hope or fear that physics would come to an end some day.

    This kind of heureka quantum jump could be clearly seen as the counterpart for the extension of axiom system by a new axiom. To me (and even more the forthcoming generations of physicist) this is very comforting. Imagine how horrible it would be if all laws of physics had been discovered: this would mean the end of mankind!

    The existence of infinity hierarchy of physics laws of course has nothing to do with landscape misery.

    Johannes Koelman
    Thanks Matti. I think you are referring here to the many worlds interpretation of quantum mechanics. I'm personally not very impressed by this concept, and don't believe it adds in any way to our understanding of physical reality. So haven't really thought about how this would play out in terms of undecideability. But surely, a many world reality would not reduce the issue of undecideability.
    There's an interesting paper by Paterek et al., Logical Independence and Quantum Mechanics (arXiv:0811.4542) that suggests something that seems related: basically, if you encode an axiom system into a quantum state, a measurement corresponding to some proposition will yield a random outcome precisely if the encoded proposition is logically independent of the axioms.

    In principle, this is just quantum computing -- basically, any quantum computation could be performed with just one measurement on the prepared system, the tricky part is knowing which basis to measure in, which is usually not easily possible; however, formulated like this, it seems very suggestive of some deeper connection between logic and quantum mechanics.

    Samshive
    Hi Johannes

    I enjoyed reading your article, and I think to a large extent, you got it correct. To me, however, the question about the TOE is whether our descriptions and formulations actually represent the underlying nature of the universe, or whether it is only a description of it. I think that most physicists that search for a TOE, implicitly assume the later. And here is where I think Godel's work has an impact on it...

    To paraphrase what you have already described, Godel's work implies that in any axiomatic system, unanswerable questions relevant to that system will arise. Obviously any TOE will have a finite number of axioms, and so questions will arise that cannot be answered. The options available are then to accept the uncertainties or to extend the system. Obviously any new system will have the same constraints, and eventually you would just have to stop and accept the uncertainties (as you have already implied). But just because you arbitrarily accept uncertainties, it doesn't necessarily imply that it describes the nature of reality. At best you are left with a description of the universe.

    Don't get me wrong, I am not trying to belittle such an achievement and to achieve such a description would be phenomenal by any standards, but are we not really looking for the true nature of reality?

    P.S. Here is a Science2.0 article I wrote about the same topic that describes my views.

    Johannes Koelman
    Siju -- there is much more that can be said about uncomputability and its impact on physics. For instance, you write:

    "Obviously any TOE will have a finite number of axioms, and so questions will arise that cannot be answered. The options available are then to accept the uncertainties or to extend the system."

    You ignore here a third option: what if in our physical reality there is no place for the answers to the unanswerable questions? Or in loose terms: what if even Nature can not answer these questions other than by letting things 'play out'?


    Samshive
    Hi Johannes,

    Am I correct in assuming that you are refering to aspects in physics such as the uncertainty principle with your statement above?
    Johannes Koelman
    No, I am in fact making the same remark Fabrizio is making below. If we see physical reality as a computer program that computes the universe, then out TOE would be final if it would lead to the same program.
    Samshive
    Thanks, that clarifies a few questions I had. I would like to give proper thought to the implications of such a program before commenting further.
    Samshive
    Johannes, I still have a few queries about this postulated computer program... Specifically, I do not see how it actually gets around uncomputability. I would assume that such a program would be sufficiently complex to have internal uncomputabilites as suggested by Turing. So potentially, the program would try and compute an outcome and would not halt. Or are you suggesting that this uncomputability is analogous to something in physical reality?
    That is hidden dimensions? Loops?

    Johannes Koelman
    Siju -- sorry, have been busy and didn't watch all recent comments to this post. It is very well possible that the program we call 'universe' will keep running. But that is not the issue. The key point I try to make is that you have to follow each computational step the universe is making in order to predict future states of the universe. As Rob remarked in one of the comments below: there is no shortcut. Another commenter made reference to Conway's 'Game of Life'. Creatures 'living' in a game-of-life world can potentially find out their TOE: the basic rules for the game-of-life. This TOE is fully deterministic. However, in order for them to predict their future, they need to emulate the full game-of-life they are part of (their game-of-life universe) and for that they need things like gliders and glider guns. But this emulation is always slower than 'the real thing'. It is for them fundamentally impossible to predict their future.
    Thanks, a most fun reading. Physics cannot be done without infinities :) And they cannot find out from where those infinities come? Really? God must laugh at us.

    Matti, I fully agree. That is called differentation, the difference that make a difference. That is also negentropy. Surprice! Who said Universe is going against an entropic death? Who could stop evolution?

    The old alchemists was right. They talked of a ladder of complexity, and we went up the ladder, step by step.

    MSSM has bad days nowadays. Poor Lubosch. But he can hardly think of another scenario, can he?
    Ulla.

    Johannes Koelman
    Thanks Ulla. Keep in mind that computations that lead to the answer 'infinity' have nothing to do with the concept of uncomputability (which basically tells us certain computations can not be done in finite time).
    That is known. In fact humans have a tendency to turn everything upside down, so also this quantum question. The problem is not in the quantum world, but how the quantum world would realize itself in our classic world.
    arXiv:0901.1270 Nottale
    "to transform a classical fluid into a quantum-type fluid by the application of a quantum-like potential, either directly in a stationary configuration, or through a retro-active loop to simulate the time evolution. In this framework, the amplitude of the quantum potential depends on a macroscopic generalization of the Planck constant, which can be changed during the experiment, therefore simulating a quantum to classical transition. "

    It is to the classic transformation we need the quantization? To get things 'on shell' or finite. Otherwise they can freely stay infinite. Or in implicite order as Bohm said. The evolution then turn implicit orders explicit in a new complexity step.

    But I turned to another difficulty with my comment. It is differentiation versus complexity and fractalization.
    arXiv:0812.3857 also Nottale
    the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads
    (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and
    (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations.
    In analogy with Einstein’s construction of general relativity of motion, which is based on the generalization of flat space-times to curved Riemannian geometry, it is suggested, in the framework of scale relativity, that a new generalization of the description of space-time is now needed, toward a still continuous but now nondifferentiable and fractal geometry (i.e., explicitly dependent on the scale of observation or measurement). New mathematical and physical tools are therefore developed in order to implement such a generalized description, which goes far beyond the standard view of differentiable manifolds.
    One writes the equations of motion in such a space-time as geodesics equations, under the constraint of the principle of relativity of all scales in nature. To this purpose, covariant derivatives are constructed that implement the various effects of the nondifferentiable and fractal geometry.

    He puts differentiation and fractality in oppsite positions, but that cannot be the case. Also differentiation need an underlying structure, and it cannot be so totally different from its 'parents'. Can someone help me with this?

    Once again an article showing why this blog is one of the best physics blogs around. You have a gift for clarifying complicated concepts without distorting their essence; if more physicists, especially those talking to science journalists, had such an ability, we'd have less LHC doomsdays and godless gravity theories, and more, well, science journalism.

    Another author with a similar knack for clarity of thought and presentation (very often, you encounter one without the other) is (or, sadly, was) Torkel Franzén, whose book on Gödel's theorem is probably the best antidote to the Gödel mysticism rampant especially on the internet. As he points out, it is indeed true that a physical TOE is subject to incompleteness -- however, this just means that it doesn't decide every arithmetical statement, which doesn't necessarily have a bearing on whether or not it describes the world.

    As a simple example, consider a 'world' described by a very simple TOE, the famous cellular automaton known as Conway's Game of Life. Its behaviour is completely determined by the simple ruleset it obeys -- its TOE --, and yet, since it is computationally universal, certain statements about its evolution are undecidable because of their equivalence to the halting problem. And just like that, the supposed contradiction between Gödelian incompleteness and the possibility of a TOE disappears.

    Johannes Koelman
    Thanks for your very kind words Anon. And also for drawing my attention to Torkel Franzén's work (I have to admit that I wasn't aware). Will definitely read his book, in particular because this article of his is indeed inspiring.

    The Game of Life is indeed a good model system to explain undecidability and uncomputability (and why neither of these render a TOE inexistent or problematic).
    You're very welcome. I hope you'll find the read as enjoyable as I did -- for me, it really put Gödel's results into a better perspective, making an at first apparently artificial and counterintuitive result seem much more natural.

    In a way, incompleteness just highlights the failure of the assumption that there is some sort of rock solid, absolute background to mathematics from which all truth flows -- an assumption that isn't as natural as it first might seem, for where should this background come from? God? Some unexplained platonic realm?

    Gödel's theorems show that the background of mathematics is a much more dynamical entity -- speaking metaphorically, one might say that they did for mathematics what general relativity did for physics, in this regard.

    Far from putting a limit on our ability to understand the world, Gödel thus indeed removed one -- had there been some set of axioms from which all mathematical truths can be derived, then the question: "Why those axioms?" would seem to be completely unanswerable.

    Aitch
    Johannes, thanks,
    .....however I thought this to be a self evident truth

    Since we cannot compute infinity, zero, or explain the golden ratio without evoking a grand designer/creator.....

    It reminds me of a book 'The Mathematical Universe' by Max Tegmark

    http://space.mit.edu/home/tegmark/toe.html

    I didn't think the idea behind the TOE was to create a crystal ball?....however perhaps there is an element of this in the search...?

    1. If P were true then I would know it; in fact I do not know it; therefore P cannot be true.
    2. If P were false then I would know it; in fact I do not know it; therefore P cannot be false.
    3. Therefore P is either a logical fallacy, or an uncomputability

    I predict the search will go on, as long as we remain 'unenlightened'

    Aitch
    Johannes Koelman
    "I thought this to be a self evident truth"

    Indeed, I fully agree. Everything stated in the above post is absolutely self-evident.

    "Since we cannot compute infinity, zero, or explain the golden ratio without evoking a grand designer/creator....."

    Compute zero, explain the golden ratio? These are empty tasks. Do you need a Grand Designer for that?

    "I didn't think the idea behind the TOE was to create a crystal ball?"

    That is exactly the point.
    “So it is gravity, and not Gödel, that prevents us predicting the future.”

    Just because a black hole can form (as you predict), it is not so clear that that black hole itself “prevents us from predicting the future.” Where exactly is the breakdown in causality?

    Since it is now agreed that black holes do not violate UNITARITY and that they are perfectly good and faithful memory devices, then how can you be so adamant that these elephants that never forget cause a breakdown in predictability.

    It is no longer felt that black holes send matter and information to other universes … not in any naïve sense at least. They are instead rather good at preserving everything that goes into them … re-encoding it … but not fundamentally destroying causality. That’s my impression …

    If the physics of a black hole can be reformulated in a holographic manner in which its singularity is merely a vestige of classical general relativity …. then in this more advantageous arena with the right number of operational dimensions, predictability does not suffer … any more than it does in a matter-free flat space.
    “So it is gravity, and not Gödel, that prevents us predicting the future.”

    Just because a black hole can form (and as you predict), it is not so clear that that black hole itself “prevents us from predicting the future.” Where exactly is the breakdown in causality?

    Since it is now agreed that black holes do not violate UNITARITY and that they are perfectly good and faithful memory devices, then how can you be so adamant that these elephants cause a breakdown in predictability.

    It is not longer felt that black holes send matter and information to other universes … not in any naïve sense at least. They are instead rather good at preserving everything that goes into them … re-encoding it … but not fundamentally destroying causality. That’s my impression …

    If the physics of a black hole can be reformulated in a holographic manner in which its singularity is merely a vestige of classical general relativity …. then in this more advantageous arena with the right number of operational dimensions, predictability does not suffer … any more than it does in a matter-free flat space.

    Johannes Koelman
    "Just because a black hole can form (as you predict), it is not so clear that that black hole itself “prevents us from predicting the future.” Where exactly is the breakdown in causality?"

    The breakdown occurs at the black hole horizon. Even if you would manage to keep your collapsing computer running, you would not be able to communicare the result.

    "Since it is now agreed that black holes do not violate UNITARITY and that they are perfectly good and faithful memory devices, then how can you be so adamant that these elephants that never forget cause a breakdown in predictability."

    Good question. Unitarity is preserved, but the the result of the computation would be scrambled in the form of Hawking radiation.. You would need to build a giant computer to decode this message, this computer will become so large that it turns into a black hole. You may repeat this ad infinitum...
    Bonny Bonobo alias Brat
    Johannes, surely scientists should talk about hypothetical Hawking’s radiation? I thought the scientific method requires proof before people start believing that something exists, otherwise it just remains a hypothesis. See http://en.wikipedia.org/wiki/Black_hole
    Observational evidence

    By their very nature, black holes do not directly emit any signals other than the hypothetical Hawking radiation; since the Hawking radiation for an astrophysical black hole is predicted to be very weak, this makes it impossible to directly detect astrophysical black holes from the Earth. A possible exception to the Hawking radiation being weak is the last stage of the evaporation of light (primordial) black holes; searches for such flashes in the past has proven unsuccessful and provides stringent limits on the possibility of existence of light primordial black holes.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Bonny Bonobo alias Brat
    The only evidence for Hawking’s radiation that I can find is at http://www.technologyreview.com/blog/arxiv/25805/ and it doesn't look very convincing to my untrained eye. It is Hawking's radiation that Belgiorno and co say they've seen...
    By watching from the side as a high power infrared laser pulse ploughs through a lump of fused silica. Their pulse has frequency of 1055nm but the light they see emitted at right angles has a wavelength of around 850nm.

    Of course, the big question is whether the emitted light is generated by some other mechanism such Cerenkov radiation, scattering or, in particular, fluorescence which is the hardest to rule out. However, Belgiorno and pals say they can rule out all these sources of light for the radiation they see. In particular, they that the fluorescent light is well characterised and that it differs in various significant ways from the emissions they see. Therefore, they must be seeing Hawking radiation, they conclude.

    That's an astounding claim and one that many physicists will want to pour over before popping any champagne corks. Why is it important? One reason is that Hawking radiation is the only known a way in which black holes can evaporate and so a proof of its existence will have profound effects for cosmology and the way the universe will end.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Johannes Koelman
    Helen -- the fact that we do not have the technology yet to obseve Hawking radiation, is the very reason why Hawking is still Nobel-less. If this radiation gets observed during his lifetime, he will in no time become a Nobel laureate. So yes, in the end hard observation is the only thing that counts. You are right about that. On the other hand, it is quite unthinkeable that Hawking radiation would not exist. It is simply needed to make black hole physics consistent. I would be surprised if even 1% of the total population of cosmologists and astrophysicist would not consider Hawking radiation real. And mind you: I am talking here about scientists, people whose status gets the biggest boost by proving their peers to be wrong. Hawking radiation is not just a hypothesis, it is a necessary hypothesis.
    Bonny Bonobo alias Brat
    Hawking radiation is not just a hypothesis, it is a necessary hypothesis.
    That would be OK Johannes if scientists wrote hypothetical Hawking's radiation when they referenced it but they don't, and although you scientists all know that it is hypothetical, the average lay person doesn't know this, and can easily misinterpret it as something that has been proven to exist. After all it is one of the reasons given for not worrying about the creation of a mini black holes at the Large Hadron Collider, because hypothetical Hawking radiation would ensure that they quickly evaporated without causing any problems.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Johannes Koelman
    "the average lay person doesn't know this, and can easily misinterpret it as something that has been proven to exist."

    I'm ok with that. I would hope that my blogging and that of countless others contributes to lay people accepting Hawking radiation as something that is real although no-one has directly observed it. Adding the word 'hypothetical' would create the wrong connotation. For me Hawking radiation is like the spherical earth. I haven't seen it, but I can not imagine a consistent physical reality without it. (And that is not just me with my limited mental capabilities: no one can.)

    Strictly speaking, "proven to exist" has no place in science. If you are purist to the extreme, you would need to have the word 'hypothetical' appear in every sentence in a physics blog.
    Bonny Bonobo alias Brat
    I like the analogy of the spherical earth but I think that initially it worked in reverse didn't it? For thousands of years people looked at the world stretching away into the horizon and hypothesised that because the world appeared be flat it therefore must be flat. Of course, eventually this was proved or should I say shown to be wrong.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Bonny Bonobo alias Brat
    I would be surprised if even 1% of the total population of cosmologists and astrophysicist would not consider Hawking radiation real.
    Johannes, if less than 1% of these scientists question the existence of Hawking’s radiation that still could be quite a few scientists couldn’t it? Mario Rabinowitz describes how after over a quarter of a century Hawking radiation has neither been detected experimentally anywhere in the universe, nor has intense theoretical effort succeeded in predicting the time history of black hole decay. He also explains why in the past many reputable scientists have questioned the validity of Hawking radiation and then offers his own alternative to Hawking’s radiation called Gravitational Tunneling Radiation (GTR) at http://arxiv.org/ftp/astro-ph/papers/0412/0412101.pdf

    Many reputable scientists questioned the validity of the Hawking model (1974, 1975) not long after its introduction. Belinski (1995) is not the only one to question the existence of Hawking radiation in recent times. His is a compelling and recent challenge. Some of the other challenges have been both less manifest and less direct. De Sabbata and Sivaram (1992) suggest that "Thus one may observe the decay [Hawking radiation] only if one makes an infinite succession of measurements. So in a sense one may never be able to observe the Hawking effect." Balbinot (1986) concluded that highly charged black holes do not radiate. He concludes that “For an extreme Reissner-Nordstrom black hole... there is no Hawking evaporation.” As a black hole becomes more and more charged, the Hawking radiation decreases until there is none.


    Vladimir Belinski (1995), a noted authority in the field of general relativity, unequivocally concludes: the effect [Hawking radiation] does not exist…He argues against Hawking radiation due to the infinite frequency of wave modes at the black hole horizon, and that the effect is merely an artifact resulting from an inadequate treatment of singularities.

    Belinski objects to what is called the “backreaction on the metric” which is missing in Hawking's derivation. This objection was raised by many researchers, and from Belinski’s perspective has not really been laid to rest. Belinski shows that if done properly there is no real particle-antiparticle creation because of “The inability of the particle to cross the barrier between the two Dirac seas ....” Infinities are manipulated in ways that are not justifiable. Since there is no experimental verification of Hawking or Unruh radiation, they are not experimentally justified.

    Robert Wald (1992) makes incisive observations that can be interpreted as being critical of Hawking radiation, but not as critical as those of Belinski (1995). He points out that although Hawking has found a sophisticated mathematical way of associating a thermal state to Schwarzschild spacetime, actual physical thermal emission has not been derived. It has not been shown that the thermal state will arise by either a plausible or implausible process, even if the space-time were shown to be physically relevant.
    I also wondered what you thought about Mario Rabinowitzs Gravitational Tunneling Radiation hypothesis which has implications with regard to Little Black Holes and dark matter when he claims the following?

    Furthermore, the reduced radiation of GTR compared with Hawking radiation allows Little Black Holes (LBH) to be candidates for dark matter, i.e. the 95% of the missing mass of the universe(Rabinowitz, 1999 a, b, 2005).

    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Johannes Koelman
    "Mario Rabinowitz describes how after over a quarter of a century Hawking radiation has neither been detected experimentally anywhere in the universe, nor has intense theoretical effort succeeded in predicting the time history of black hole decay. He also explains why in the past many reputable scientists have questioned the validity of Hawking radiation and then offers his own alternative to Hawking’s radiation called Gravitational Tunneling Radiation (GTR)"

    1) The fact that Hawking radiation has not yet been detected shoud be no surprise
    2) Not sure what exactly he means with "predicting the time history of black hole decay". If it is to predict the evaporation rate as function of mass, then Rabinowitz is plain wrong
    3) In first reaction to Hawking's evaporation proposal, some physicists questioned the validity. I do not think you can find many such 'reputeable physicists' these days. Scientific insights simply have progressed.
    4) GTR, if properly implememted in a quantum relativistic framework, would in its bare essence not be different from Hawking radiation.

    Note also that Rabinowitz' discussion focuses on the issue of unitarity. In the past Hawking has created a lot of confusion by maintaining that his radiation is purely thermal, which when you look in more detail, it clearly isn't. But that does not take away from the fact that Hawking radiation itself is a healthy concept (for a real good theory it is mostly the case that it contains much more than the inventor puts in, and there are many instances in which the inventor does not understand the full content of his/her new theory). If you want to read more about unitarity (information conservation) and Hawking radiation: Lenny Susskind has written a pop-science book (the Black Hole War) on this very issue.
    Bonny Bonobo alias Brat
    Johannes, do you think that this report today, of the relatively nearby birth of a baby black hole, will make it easier to prove or disprove Hawking’s radiation in the near future?

    Larry O’Hanlon’s report of a ‘Black Hole Baby Spotted Being Born’ claims that for the first time ever, a black hole has been seen being born out of a supernova of a star perhaps 20 times the mass of our sun. See http://news.discovery.com/space/baby-black-hole-gamma-ray.html#mkcpgn=em...

    For the first time, a black hole has been seen being born out of an exploding star just 20 times the mass of our sun -- right in our cosmic neighborhood. The baby black hole is located in the M-100 galaxy, which is about 50 million light-years from Earth. This makes it far, far closer than the gamma ray blasts seen billions of light-years away at the edge of the visible universe, which are thought to be the newborn wailings of an entirely different sort of black hole -- those with millions of times the mass of our sun which reside at the centers of galaxies.

    That birth date is in April 1979, when the supernova explosion that signaled the collapse of the star was spotted flaring brightly in the M-100 galaxy by a school teacher using a telescope…."In essence, this object occurred almost in our backyard”

    There are a number of kinds of stellar explosions that can produce supernovae -- which are short-lived, extra bright stellar events. What makes this one -- dubbed SN 1979C -- special is that it has been observed over the years with a series of orbiting x-ray telescopes, most lately the Chandra X-Ray Observatory. Those observations have revealed that SN 1979C has not dimmed in the 31 years since its birth, as would be expected if this was anything less than a genuine black hole. This lack of dimming suggests the new black hole is gorging on as much matter as it can handle, said Avi Loeb of the Harvard-Smithsonian Center for Astrophysics. It's the tearing apart of that matter as it falls into the black hole that creates the X-rays.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    These are not the same rays as the hair balls of Hawking radiation. Different cat altogether.

    blue-green
    Normal 0 Since our host is still away, I’ll clarify a bit more about the two kinds of cats. Hawking Radiation will occur even when a black hole is not engorging itself with ordinary in-falling matter. For a collapsed star it is extremely weak. It is going to be near impossible to detect Hawking Radiation around an ordinary black hole that is absorbing matter and being the ultimate particle collider it is. It will be nigh impossible to find a black hole in an empty region of space in which there is nothing to absorb (except virtual particles). There is little chance for Hawking to get a Nobel when this fundamental radiation is observed. It is going to be too hard to distinguish the different kinds of whiskers … The task of taking apart the fur balls and determining which radiation is the elusive Hawking Radiation is … insurmountable. Just my gut feeling.
    ((I was going to edit the above, however signing in gives meaningless error messages .... ))

    The blackbody temperature for Hawking Radiation for a collapsed star is a minuscule fraction of the background temperature due to the expansion of the universe. It’s like comparing 0.0001 degrees Kelvin with 3 degrees. When Hawking first published his radiation calculations, because the temperature is inversely proportional (to some power) to the mass of the collapsed object, it was hoped that there might be PRIMORDIAL black holes that would be observable, which have already evaporated and left their calling card behind. These small-mass objects are not to be confused with the “baby” black holes mentioned in the article sited above.

    Bonny Bonobo alias Brat
    Thanks for explaining this so succinctly Blue-Green. Let's hope that Stephen Hawking's radiation is shown to exist one day and that he gets get his Nobel prize, even though it does look unlikely at present that it will ever be provable. Especially as the alternative of him being wrong doesn't seem to be considered an option by most 'reputable' or respectable scientists. I can't help still wondering though, if being a reputable or respectable scientist has in itself an inherent requirement to be 'characterized by socially or conventionally acceptable morals' see http://www.thefreedictionary.com/reputable or what could be called scientific community 'groupthink' .
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    sorry about doubling up ... maybe you can strike that from the memory ...

    Great article Johannes. Thanks for the effort.

    I don't think humans beings are going to run out of problems to solve anytime soon so while Godel is interesting just how relevant is his theorem to the everyday world of getting things done? (I'm asking this as a person ignorant of implications of Godel's Theorem for getting things done, not in any way to denigrate Godel.)

    Your approach reminds me of something Chaitin wrote. He stated that Godel was a blessing because it means mathematics can go on forever. My understanding is that Chaitin, by extension of Godel's Theorem, established that even if we did come up with a Theory of Everything we can never know if it is the final theory of everything. I'm quite ignorant about physics but Chaitin's comment seems to faintly echo one of the issues in String Theory, that being that there are potentially so many possible and valid theories.

    Interestingly, in one text Chaitin states he did not understand Godel, it wasn't until Turing presented his halting problem that Chaitin finally grasped the theorem. So if someone of Chaitin's stature can struggle so hard to come to terms with one of the seminal intellectual events of the 20th century perhaps others of less stature should refrain from proclaiming that Godel has doomed us to cease from our wandering, to stop asking questions, to stop trying to improve our understanding of the universe.

    Once again, great post Johannes. I am reminded of a TV program I saw some months ago in which Murrary Gell-Mann was being interviewed. He stated that Bohr was an obscurantist and that there was far too much mysticism in quantum mechanics. It is great to see people like yourself so clearly articulating and demythologising this very entertaining intellectual field.

    Johannes Koelman
    Thanks John. I believe it is Chaitin who made the link from undecideability (via uncomputeability) to Kolmogorov complexity. I think Chaitin is trying to convey the message that to 'grok' Gödel's results, uncomputeability and complexity are necessary concepts.
    Hfarmer
    There are a large number of computational cosmologist who would disagree with what you have written here.  In particular
    "_The above application of uncomputability to predicting the universe assumes we can in principle build a computer capable of simulating the universe. But we can not. Not even in principle. If you would attempt building such a computer, you would discover that it would collapse and form a black hole long before it reaches the size needed to be capable of simulating the universe."

    They feel that their little models do just that.  

    I agree with you.  I agree with you because the sum total of all that we don't understand in the universe has been clumped under the heading dark energy + dark matter = all the stuff we can't figure out.... but since we've given it a name we know what it is.  It's like knowing the name of a bird and therefore thinking we know all about it

    The problem really is M theory and before it string theory.  It's one candidate theory of everything.  The problem is that for a while it seemed the only way to get a job in theoretical physics was if you studied M theory.  Thus other area's that were just as worthy were left to hang.    

    As far as a TOE is concerned.  I would be happy if we could just come up with a internally consistent theory for all non-dark matter and how it interacts. 
    Science advances as much by mistakes as by plans.
    Johannes Koelman
    "They feel that their little models do just that." Hontas, you have to distinguish modeling some average properties of the universe from predicting the evolution of the universe in all its microscopic details. The uncomputability restrictions refer to the latter. Computational cosmologists are busy with the former.
    There is a recent ArXiv paper which goes beyond gravity in claiming that gravity, black holes, and QFT are all caused by the limited speed of information. Sorry, this is a repost on the previous post of Johannes. But it fits into this discussion.

    Physics from information
    http://arxiv.org/abs/1011.1657

    This is an ongoing review on my conjecture that information processing at causal horizons is the key ingredient of all physics. Assuming that information is fundamental and the information propagates with finite velocity, one can find that main physical laws such as Newton's second law and Einstein equation simply describe the energy-information relation (dE=TdS) for matter or space time crossing a causal horizon with temperature T for observers. Quantum mechanics arises from ignorance of the observers about matter crossing the horizon, which explains why superluminal communication is impossible even with quantum entanglement. This approach also explains the origin of Jacobson's thermodynamic formalism of Einstein gravity and Verlinde's entropic gravity. When applied to a cosmic causal horizon, the conjecture reproduces the observed dark energy and demands the zero cosmological constant.

    Johannes Koelman
    Thanks Rob, that abstract looks interesting. Need to read the full paper.
    I have always understood that one of the consequences following from Turing's work was that it is impossible to predict the outcome of a sufficiently complex program without actually running it. There are no shortcuts for Turing complete devices.

    This would mean that predicting the future implies that you run a full blown simulation of the relevant part of the universe (causal part of the light cone). Which, obviously, would have to take at least as much room and time as the original.

    A TOE can be formulated as a set of differential equations, eg, GR, Schroedinger equation, Maxwell's equations, Navier-Stokes. The fact that these equations fit reality perfectly and are valid everywhere does not mean they can be solved.

    Johannes Koelman
    You got it Rob. :) One minor point: the examples you give do not all describe fundamental degrees of freedom. For instance, Navier-Stokes gives an average description of aggregates of fundamental degrees of freedom. Such statistical description are effectively shortcuts to 'the real thing' but are limited to the prediction of average behaviors. (A most useful description by the way.)
    @Johannes:
    "For instance, Navier-Stokes gives an average description of aggregates of fundamental degrees of freedom."

    I know (low-energy and infinite number of particles limit etc.) However, the whole thing about the entropy of gravity is about dragging GR into the same realm as Navier-Stokes. And the paper I linked to tries to extend that to QFT.

    But, you are right, of course.

    "So let's say we have a computer program that simulates the whole universe and that is started with inputs such that it will compute the universe of tomorrow".
    In a sense the universe is that computer program.
    Or was Galileo wrong?

    Johannes Koelman
    "In a sense the universe is that computer program." Right! (see also Rob's last comment) Don't see how Galileo is linked to this?
    what I want say is that if Galileo was right, where are "grey areas" in the universe?

    Johannes wrote: "Thanks Matti. I think you are referring here to the many worlds interpretation of quantum mechanics. I'm personally not very impressed by this concept, and don't believe it adds in any way to our understanding of physical reality. So haven't really thought about how this would play out in terms of undecideability. But surely, a many world reality would not reduce the issue of undecidability."

    No, I am not referring to many worlds interpretation. I have a never understood it and regard it as a self deception. My starting point is the basic problem of quantum measurement theory: the conflict between non-determinism of the state function reduction and determinism of Schroedinger equation. I believe that this conflict cannot be resolved unless one extends physics to a theory of consciousness by mathematicizing the notion of conscious observer. Quantum states are identified as quantum superpositions of both classical histories and quantum histories as analogs of Schroedinger time evolutions rather than time=constant snapshots of single history. Quantum jump replaces this kind of superposition with a new one so that one avoids the conflict with the non-determinism of Schrodeinger equation's determinism and non-determinism of quantum jump. This however forces a radical revision of the beliefs about the relationship between experienced time and geometric time. Subjective time corresponds to the sequence of quantum jumps and its relationship to the geometric time is more complex than the naive identification (inconsistent with the irreversibility of subjective time and reversibility of geometric time) would suggest.

    The sequence of quantum jumps gives rise to a genuine evolution if one accepts a variational principle which I have christened Negentropy Maximization Principle. NMP states that the information content of conscious experience associated with the quantum jump is maxima. This does not mean inconsistency with second law of thermodynamics. This principle gives standard state function reduction as a special case. In living systems however something totally new emerges. This involves new mathematics provided by p-adic numbers allowing among other things to define number theoretic variants of Shannon entropy which can have negative values so that the interpretation is in terms of information rather than entropy. The entanglement with rational or even algebraic entanglement probabilities allows to define these number theoretic entropies and this kind of entanglement can be stable against NMP so that state function quantum jumps need not mean the increase of ensemble entropy. This kind of entanglement would have interpretation as conscious information representing a rule with the instances of the rule identified as the state pairs appearing in the superposition. Schrodinger cat which is a little bit dead would realize that it is better to keep the bottle closed;-). This kind of entanglement would characterize living matter.

    Johannes Koelman
    Thanks for clarifying, Matti.

    I agree that the way measurements are incorporated in quantum mechanics is ugly. But would prefer not to link to this issue an ill-defined concept such as consciousness. Will probably come back to this in a future post.
    Consciousness is really ill-defined, and everyone has his/her own version. To this soup is added the anthropic principle. Are we again making us, humans the center of the whole universe? If we really consider what consciousnes is we can also skip thinking about some anthropic principle.

    The first error we do is that we believe consciousness is born in our brains. But that is not consciousness at all, it is awareness, a wake-up state of attention.
    Freud is wellknown for introducing the unconsciousness. That would mean not conscious, but is it really so? No, it is not awared. We confuse things. Take as instance memories of abusement that is laid somewhere deep in the body, in unawareness, but it is conscious still to the body, because it invokes on our behaviour.

    Look at the perceptions, the sense organs have conscious states. So now we have small 'brains' all over the body.
    Hamerhoff is known for the quantum consciousness, the computative state of microtubulis. They are linked to every cell (membrane - nucleus) in the body as a 'cellbrain' of consciousness. And then we also know the chromosomes are fractal and topological microstates of our whole organism. Chromosomes have a 'head' and a 'foot'. They also have memory?
    This consciousness is born through perceptions (measurements, quantum jumps) but they can also be transferred in other ways, so consciousness is also outside the body?

    As I see it we only qualitatively amplify our awareness of what happen in our surroundings by a selective choise of what is valueable information, everything else is left without attention. This evaluation happen in steps, always, and in fact the main purpose of our nervous system is to INHIBIT the informational flow. Nerves SELECT by themselves what is useful information and what is not. One of the main inhibitory places is our brain, and especially our brainstem. Many also inhibit flow from the middle brain, but it is only awareness, not consciousness. Men especially have difficulties in feeling emotions. This feeling is transferred to wifes instead :)

    Most of us that say conciousness is born in cortex have simply not thought enough on the problem. It can de defined more clearly. But one very difficult thing with consciousness is the hard problem with qualias. Consciousness is dual.

    So if you write on that, think of this :)

    A link to the complexity behind evolution http://en.wikipedia.org/wiki/The_Major_Transitions_in_Evolution.
    It is phase transitions. In metaphysical texts it is described with chakras :) It is the same thing. Chakras means exactly those steps of complexity, and they are innumerous. It is only our ignorance that make us feel much superior.

    I must add that the amplified awarenss is what we call intelligence. It is a much restricted consciousness in reality, and maybe that's why our thinking is so troublesome. Human intelligence has created much problems :)
    At least quantum field theories :)

    Hank
    You make Hawking out to be more clever than he seems to be.  In endorsing "M-theory" I assume he just gave up on actual physics.   He wrote "People are still trying to decipher the nature of M-theory, but that may not be possible" meaning he endorsed a 'theory' that isn't even a theory. 

    Worse, in endorsing some multiverse he got the British public wondering why they are funding physicists out to debunk the existence of a deity philosophically but are doing so backed with no experimental evidence.  His call for a change to what is acceptable as a theory, in order to make "M-theory" a theory, borders on silly.
    Johannes Koelman
    Hank -- maybe you're right. After all, I am trying to interpret what Hawking is saying in such a way that it makes sense. There is always the danger that in doing so, one is turning nonsense into sense (which in itself is a useful thing to do).

    Hawking has done some magnificant things, but tends to be over-rated as the most brilliant physicist since Einstein. Whether or not he himself agrees with this qualification, it does create a burden. Hawking should better understand the responsibilities that come with being declared 'a hero of contemporary science' and being a public figure, and not allow himself to become a toy in the hands of greedy book publishers.

    Apart from the above criticism, there is little to blame Hawking for, and I think you are a bit too harsh on him. I am not particularly fond of M-theory myself (and you will probably not read much about this theory in my blog), but I would not label M-theory non-physics.
    Amateur Astronomer
    The debate between Hawking and Penrose is still continuing. Roger Penrose has responded to Stephen Hawking in a new book “Cycles of Time”. Already it is being reviewed in the UK, but will not be available in USA until April 2011. Penrose attempts in his book to develop thermodynamics for a cosmos that predated the universe and will presumably survive the end of the universe. I usually prefer the Penrose point of view over that of Hawking. On this occasion I believe they are both lacking something important for cosmology. More recently than Gödel’s work, mathematics has shown that comprehensible quantities can be assembled into incomprehensible postulates. Sometimes the answers to questions are false. Other times there are questions that are not true. Mathematics recognizes the class of impossible questions that are self contradicting. If Gödel’s incompleteness theorem is true, then it is incomplete and can never be proven, because it is part of the system that it describes. It can be thought of as a cleverly concealed logical contradiction. That argument hinges on whether or not logic is a part of mathematics. Einstein read Gödel’s theorem and said he found it interesting, but it seemed to lack something.
    We start from the constrained reality, our classic world, and try to adopt the quantum world to it, instead of the opposite way.
    If the world is dual, that is matter - antimatter, we know that only one solution is possible and the other has to go away in some way. Bohm talked of implicit facts, Kauffman talked of 'possibilities' etc. This is also seen in the wave-particle duality.
    The essence is that both cannot at the same time realize themself in classic forms. Because our classic world is only a few percent of total matter, not to talk of the energy. If we instead start from the energy and try to figure out how on Earth we can have matter, we are more on the right path? How did God when he created the world? He definitely not laid everything on one card only. He had a big bank account of possible solutions? Just like nature has with the diversity.

    God = Godel = Gravity (we may as well skip Godel): http://www.youtube.com/watch?v=8slGZ9XszmA

    Bonny Bonobo alias Brat
    Turing's uncomputability refers to the generic problem of deciding  whether any given computer program with given inputs will stop. Turing demonstrated that there exist computer program's with given inputs that can not be predicted to ever halt. You simply have to start the program and wait. As long as it keeps running you have no clue if it ever will halt.

    So let's say we have a computer program that simulates the whole universe and that is started with inputs such that it will compute the universe of tomorrow. You start the giant computer that runs the program, and it starts cranking away. Huge amounts of data are processed. After an hour the computer is still running. Two more hours, still running.Twenty more hours, no sign the program will stop. Tomorrow passes by, and the computer is still running. Will it ever stop? You have no idea.
    Johannes, is there a place for the computer programmer in this analogy? Having worked as a computer programmer I know that I would never write a computer program that did not display in some format what stage it was in the processing and what it was currently doing. You might not be able to create a computer big or small enough to complete the job, but you could write a computer program that tells you what its doing while its processing, even if it never finishes its computations because they're uncomputable.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Johannes Koelman
    Helen -- you make the implicit assumption that the computational task at hand can be split in a finite number of subtasks, each characterized by a well-defined computational effort. When you are programming the TOE, this is not necessarily the case. But even if it is, the same (but slightly more elaborate) argument would apply: You run your program to compute tomorrow, and this time you have implemented a counter that shows progress in units of 1/1,000 of the total computational task. You start the run and watch the progress counter: 0.0% complete, five minutes pass by: 0.0% complete, an hour passes by: 0.0% complete... Is the program stuck, or just very, very slowly progressing? There is no way for you to know for sure.
    Bonny Bonobo alias Brat
    Helen -- you make the implicit assumption that the computational task at hand can be split in a finite number of subtasks, each characterized by a well-defined computational effort. When you are programming the TOE, this is not necessarily the case.
    Sorry Johannes, I am not assuming that there are a finite number of subtasks, I'm actually imagining an infinite number of subtasks each with some sort of computational command to execute even if its just performing an error or display subroutine.

    Also, I would never program the computer to display the percentage completed when the computer doesn't have that information. Instead I would program it to display the inputs that it was receiving, a counter of how many transactions it had done, what the last equation was that it had performed every so many transactions, how many times each subroutine or formula had been performed and whether the program was stuck in a loop or was trying to compute something uncomputable, like dividing something by zero etc. This would mean that I would have at least some idea of what the computer program was trying to do with the input.

    Anyway I can see that the computer programmer doesn't fit well with the analogy so I'll leave her out. Thanks for considering her anyway.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Samshive
    Hi Helen
    I think you have missed the truly disturbing aspect of Godel's work, and Turing's extension of it into the computing world. Turing doesn't just say that uncomputable questions would occur, that was already known (like getting stuck in a loop and stuff), but rather that it is impossible to write an algorithm that would generally know if an answer can be found. In other words, no matter how much information can be known by the programmer about a task that the computer is executing, the programmer will not be able to know in general if any progress has been made. 
    Bonny Bonobo alias Brat
    OK thank you Siju, I think I understand. Although I might know which subroutine I have just performed and which formula and input I have just processed, I will have no idea how much closer in general I am to getting the final result because a) the result itself is uncomputable and b) no algorithm exists that will show whether an answer can even be found or not. Is that what you mean?
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Maybe another example will help clarify the issue. This is not about "normal" programs where you try to make sure things terminate or loop.

    Turing's results have two relevant consequences.

    First, take a program that claims to divide number A by number B and return the divisor and the remainder. To predict the outcome of the program, you will have to perform the computation yourself. Now, you can use a different program and algorithm to perform this particular calculations. However, given an unknown code, you cannot guarantee that you will be able to analyze it in such a way that you can perform the computation in any shorter way, say, the "Game of Life". In general cases, you will have to perform the exact same computations as the program you analyze.

    Turing's result was that the only way to be sure that you get the same output as the requested program for any program and input is that you have to run the program on an emulator.

    The next question is whether you can predict whether a program halts (this is simplified). You can only guarantee to predict the outcome of running a program by running it yourself on a simulation. Therefore, you can only guarantee that a program halts by running it on a simulation and see whether it halts. But if the original does not halt, the simulation will not halt either.

    In a real computer, this does not happen. As a real computer has finite memory, and therefore, a finite number of states, any program that does not stop will eventually end up in a loop when it enters in a state it already has visited. At that point you know it is in an infinite loop and will not terminate. However, Turing machines have infinite memory so they can indeed run an infinite number of operations without entering a loop.

    To make things more real, take as an example the following program:

    0 initialize the tape with the program and input data
    1 XOR the first half of the written text on the tape with the second half
    2 Append the result to the text on the tape
    3 If the result was zero, stop
    4 else go back to 1

    Can you predict whether this program will halt for some given random input?

    I can give a trivial input that halts. Given the program on tape, add a string such that the first and second half of the tape are identical. This can always be done. The program will halt after one cycle.

    Maybe it is possible to prove this will/will not halt given random input. But you get the point if you realize that the program can be self changing.

    Bonny Bonobo alias Brat
    Thanks Rob for explaining Turing's results and predictions. As a result I have been reading about Turing, what a shame he committed suicide so young at 42. Its unbelievable that Turing who admitted being a homosexual was given the choice of chemical castration or prison after reporting a burglary by a homosexual lover and therefore incriminating himself by admitting his own homosexuality isn't it? Like one of his Turing machines he was only able to keep living his life of a genius (inputting and reading the tape) until the last read that identified him as a practicing homosexual (zero) then halt (his suicide). Here is his epitaph that he wrote himself.
    Epitaph
    Hyperboloids of wondrous Light
    Rolling for aye through Space and Time
    Harbour those Waves which somehow Might
    Play out God's holy pantomime
    —Turing, A. M. (1954).
    Its also interesting that there are just six types of fundamental operation that a Turing machine performs in the course of a computation. See http://www.alanturing.net/turing_archive/pages/Reference%20Articles/What%20is%20a%20Turing%20Machine.html#func It can:
    • read (i.e. identify) the symbol currently under the head
    • write a symbol on the square currently under the head (after first deleting the symbol already written there, if any)
    • move the tape left one square
    • move the tape right one square
    • change state
    • halt.

    These are called the primitive or atomic operations of the machine. A complicated computation may consist of hundreds of thousands, or even millions, of occurences of these atoms.


    Commercially available computers are hard-wired to perform primitive operations considerably more sophisticated than those of a Turing machine--add, multiply, decrement, store-at-address, branch, and so forth. The precise constitution of the list of primitives varies from manufacturer to manufacturer. It is a remarkable fact that none of these computers can outdo a Turing machine. Despite the Turing machine's austere simplicity, it is capable of computing anything that any computer on the market can compute.


    Indeed, since it is an abstract or notional machine, a Turing machine can compute more than any physical computer. This is because (1) the physical computer has access to only a bounded amount of memory, and (2) the physical computer's speed of operation is limited by various real-world constraints.
    So, now its easy for me to understand Johanne's analogy about the universe and the computer program and even the computer programmer behind why uncomputability shows the generic problem of deciding whether any given computer program with given inputs will stop.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    @Helen Barratt

    Bigotry destroys human lives and culture. Think about what would have been if this would have happened to Shakespeare, Da Vinci, or Michelangelo (for whatever reason).

    A small addition to my horrible program.

    It is clear that the probability that the above program halts after K iterations drops of exponentially with K. No cycling is possible as no state can appear twice. Which (most likely) means that only a small fraction ( O(2**-(N/2 + e) ) ) of input sequences of length N lead to halting programs, the remainder running forever. This can be changed by inserting the following line:

    3a If the parity of the result == 0 and length(text) >= 18, remove the lower 5/9th of the tape text

    As a result, the length of the text sequence will perform a random walk around the starting length with a hard wall at 12 (or whatever bound you like). As a result, I suspect most, if not all, input sequences will eventually halt or start to cycle. The proportion of halting versus cycling programs might very well be a non-computable number because there is no upper bound to the growth of the text length.

    Bonny Bonobo alias Brat
    Wow, sounds like you enjoy programming Rob. I'm a bit rusty these days but I'm pretty sure that I accidentally wrote a few randomly halting and endlessly cycling programs in the past, that's why I became pretty expert at displaying what was going on, it was based on total necessity in my case.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    "Wow, sounds like you enjoy programming Rob."

    Indeed, it beats solving crossword puzzles.

    "I'm a bit rusty these days but I'm pretty sure that I accidentally wrote a few randomly halting and endlessly cycling programs in the past, that's why I became pretty expert at displaying what was going on, it was based on total necessity in my case."

    Haven't we all?

    Rob

    What do you think of this new Nature latter by Shoichi Toyabe, Takahiro Sagawa, Masahito Ueda, Eiro Muneyuki & Masaki Sano: http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys1821.html,

    It begins:

    In 1929, Leó Szilárd invented a feedback protocol1 in which a hypothetical intelligence—dubbed Maxwell’s demon—pumps heat from an isothermal environment and transforms it into work. After a long-lasting and intense controversy it was finally clarified that the demon’s role does not contradict the second law of thermodynamics, implying that we can, in principle, convert information to free energy2–6. An experimental demonstration of this information-to-energy conversion, however, has been elusive. Here we demonstrate that a non-equilibrium feedback manipulation of a Brownian particle on the basis of information about its location achieves a Szilárd-type information-to-energy conversion. Using real- time feedback control, the particle is made to climb up a spiral-staircase-like potential exerted by an electric field and gains free energy larger than the amount of work done on it. This enables us to verify the generalized Jarzynski equality7, and suggests a new fundamental principle of an ‘information-to-heat engine’ that converts information into energy by feedback control.

    Cheers, Peter

    I am going to try to summarize what is going on here …. Corrections are welcomed.

    Although the finger is usually pointed at quantum mechanics for there being a fundamental unpredictability in physics, it is here being aimed right back at Einstein’s theory of Gravity and the 1916 Schwarzchild solution for the curvature of spacetime around a simple star. This famous solution was one of those moments in which something much larger had been hatched then even mad scientists could imagine.

    Einstein was basically a Laplacian, firmly believing everything is on a predetermined course and in principle, predictable, however no one is going to take seriously the idea of charting the course of every particle in even a mole (e.g. 12 grams of carbon) and 10^23 number of particles. One instead does a course-graining in the spirit of thermodynamics.

    After Einstein died in 1955, a Princeton University professor by the name of John A. Wheeler, revisited over and over again the Schwarzchild solution and became the father of Black Hole physics. Wheeler had already spent some time trying to make Relativity part of the foundation for Freshmen physics. He even took his class to Einstein’s house in 1954 to visit with the living legend. Wheeler also visited with Einstein a few years earlier to share with him the Feynman’s Path Integral Approach to Quantum Mechanics that Johannes posted about in his previous blog. As I recall, this was Feynman’s thesis topic and Wheeler was the advisor.

    It was Wheeler who kept emphasizing the importance of studying the implications of a completely gravitational collapsed object. This was long before general relativity and black holes had become popular in the 1970’s. Particle physics was all the rage, along with nuclear physics …. and the Standard Model was incubating while physicists press-released a menagery of particles names that would make even a biologist blush.

    In addition to coining the word “black hole”, Wheeler had a phrase to sum up much of black hole physics as it was understood, BEFORE, Hawking came up with the quantum mechanical radiation in 1974.

    “A black hole has no hair.” That was the mantra. To diagram it, Wheeler would show a toaster, a hair dryer an aardvark …. whatever (the actual diagram was imprinted on a card that he used for brief correspondence) (I have one or more, but not in front of me, so I’m going partly by memory and inventing).

    “A black hole has no hair” was always intended for purely classical black holes. Wheeler was well aware and published much as to how a proper understanding of “this quantum business” would change everything fundamental about gravitational collapse and even the no hair theorem.

    One can see perhaps how in that little phrase there was the hint that predictability (and even unitarity) could be at it limits with anything that approached a Schwartzchild metric.

    Hawking’s derivation of how Black Holes can evaporate raised a lot of hairs. The conclusion has been reviewed and derived using many different approaches. The same fundamental algebraic equation comes out. It appears to be on sound thermodynamic grounds.

    The entropy of a black hole can be written down as an exact number based on its Mass, Spin and Charge. It’s a number, an integer even, so it has a connection with fundamental arithmetic. This is perhaps where the connection to Gödel is made rigorous …. Those three fundamental quantities, Mass, Spin and Charge are what Wheeler said was all that was needed to describe a black hole, regardless of what went into its formation. This is why he said it had no hair. It is also, why a black hole is sometimes equated with being a fundamental particle: it is simple and inscrutable.

    The quantum mechanical hairiness of black holes raised a lot of difficult fundamental questions. The debates came to a climax when John Preskill proved that a black hole is in fact predictable, or more precisely, unitary. Leo Susskind doesn’t mention Preskill much in his Black Holes war book …. He does point out that as matter approaches the Schwarzchild radius, the information that comes back from in falling objects is time delayed evermore while ever more complexly revealed information is smeared over the entire area of the horizon. Everything that happens, even inside a black hole, is writ on its outer wall, its horizon. This is old hat for relativists … then again, maybe Leo is just doing a play on a Simon and Garfield song from his youth in which they chime that “everything you need to know is written on the subway walls.”

    ,,, make that Garfunkel ...

    Aitch
    Now you've torn it....check out the names - they'll never be the same again

    http://club.doctissimo.fr/jacoline/musique-annees-70-50504/video/garfiel...



    Aitch
    I wanted to read your article, but I couldn't get past the pretentious picture of you with the sunglasses on a hammock reading a book. Sorry, I just couldn't do it.

    Way to make decisions! I myself won't read Einstein because I don't like his hairstyle, and won't listen to Feynman because of his ridiculous Brooklyn accent. Hasn't hurt me any either! Rock on brother.

    Hank
    And I didn't read his comment because he is anonymous.   The world is an easier place to understand when arbitrary, superficial silliness is all it takes.
    Amateur Astronomer
    Roger Penrose takes science a step forward while Hawking is making the same mistake Gödel made. What Gödel forgot to say was that there is no ultimate limit to the search for knowledge and understanding. There is always a local temporary limit. It might be mistaken for a final limit, but then one limitation is removed, and we find a new limit on a grander scale. It works this way both in theory and practice. The science is continually rewritten to account for the realm of things that are definitely false and the things that are definitely true in the current context. Then someone proposes a new science and some way to test it on the remaining things that are unknown. That leads to a new set of knowledge in which some new things are known, and some new things are found to be false. It also results in a new set of unknown things. Human science is at a level of development where the set of unknown things doesn’t get any smaller from one stage to the next. The set of unknowns actually gets bigger. To me that means our technical society has not discovered half of the physical laws or half of the potential knowledge. The readers can take the view of Hawking and give up the quest, or the view of Penrose and take the next step. Roger Penrose wrote a new book “Cycles Of Time” that takes the next step in scientific inquiries and looks at the cosmos before the universe began. For a rational mystic there is always a limit in the present knowledge, but never a final and absolute limit. We are no where close to having a final theory of everything, or even guessing at what it might look like.
    Many times when I read these treads I think to myself I know absolutely nothing. Then I see there is some real physicist that has not understood anything either and I feel comfort. Sometimes though I understand something :)
    Did this make sense at all ? I just wanted to say that often more questions are born than those getting the answers. So the unknown is growing or expanding like the dark energy :)

    Aitch
    ....What Gödel forgot to say was that there is no ultimate limit to the search for knowledge and understanding. There is always a local temporary limit. It might be mistaken for a final limit, but then one limitation is removed, and we find a new limit on a grander scale....

    When I was a kid and first heard that type of explanation, I wrote on my bedroom wall,

    Theory A = ∞
    Theory B = ∞ +1
    Theory C = ∞ +1, +1
    Until the next theory comes along
    ....and infinity is always there, ....waiting......

    Isn't that about it?

    Sir Roger Penrose also wrote about quantum consciousness, in 'The Emporer's New Mind', didn't he?

    Aitch
    I don't know from where you get your history Sir Henry Cox ...
    My reading is that almost every major advance in mathematical physics
    has involved the removal of one or more infinities ...
    They remain in the mathematics, yet they have no physicality ...
    that's the lesson.

    Amateur Astronomer
    Everyone has a different version of history. That’s one thing you learn when living in a foreign country. We don’t agree on what is happening now. So there is no way to have agreement on history later. A few names and dates are all that the histories have in common.
    Aitch
    Appreciate the Knighthood ;-)

    My history comes mainly from within, whereas other people's tends to come from without, i.e from books or other people

    I think however the difficulty is not history relating to infinity, but use of language as a communication tool

    My use of infinity and yours clearly mean different things to each of us, as you use the term 'infinities' as if there were more than one
    In my use and understanding of Infinity, it is simply that all-encompassing containing everything, I was going to say, dimension, but that would probably give rise to another difference of views, so I'll leave it at that

    The very fact that [Mathematical] Physicists like to put infinity into their theories and then go about 'proving' that that particular infinity isn't real, just proves that they are playing games within the minds of  gullible observers, to show superiority of thought process ....but you have to see the original 'theory' as flawed in using a false infinity originally, in order to understand why this is happening

    There are other names for trickery in history, I'm sure you've heard of, like Charlatan  or Shyster
    A good thesaurus will give you a few more
    They remain in the mathematics, yet they have no physicality ...
    that's the lesson.
    One of my favourite lessons is the story of a Zen master who observes the people of his village celebrating a young boy's new horse as a wonderful gift. "We'll see," the Zen master says. When the boy falls off the horse and breaks a leg, everyone says the horse is a curse. "We'll see," says the master. Then war breaks out, the boy cannot be conscripted because of his injury, and everyone now says the horse was a fortunate gift. "We'll see," the master says again.

    So, Infinity.......we'll see

    Aitch
    well, your reading is still of interest ...
    in case you'd to share.

    consciousness is fickle

    women is fickle

    ... stranger in a strange land ...

    Women can be fickle.

    (pardon my French)

    TOE is a nice abbreviation. There is unfortunately too much hubris in the title “Theory of Everything” or “Theory of Infinity” as Sir Henry gets it. It invites derision by anyone outside of physics. The original and more correct term for TOE is a unified field theory aUFT. Physicists sort of have one called “The Standard Model” -- a term that only those within physics can love and appreciate.

    What interests me is the new take on fundamental physics that got a turbo boost by Verlinde almost a year ago.

    Further up in these comments there is a link to the following article “Physics from information” posted to arXiv on November 7, 2010.

    http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.1657v1.pdf

    There have been quite a few articles along its same lines this year. Most of them, including this one, overstate their claims. And yet, I feel that they are much closer to a TOE that people can comprehend than say a jazzed up Standard Model or a unification coming from a mathematical object like E8 which is so complex that only a handful of humans and computers can navigate their way through it.

    Further up from here I gave some background info concerning John A. Wheeler. It was he who also coined the phrase “It from Bit”. Maybe later I can post the diagram that he used for “a [classical] black hole has no hair”.

    Wheeler’s favorite program was/is the search for a means to “derive the quantum”.

    The authors in the “Physics from information” article claim that they have succeeded in doing so. “Quantum mechanics arises from ignorance of the observers about matter crossing the horizon …”

    Not so fast. Are we really onto fertile new ground here? Have they derived the need for Hermitian Operators, complex-valued Amplitudes, Hilbert Space, spin, anti-matter and all that?

    I don’t know. From a pedagogical standpoint I think it all quite interesting. I hope the authors are right in claiming the following:

    “All these studies are not a simple reinterpretation of existing physics. If information really is the essence of the universe, this alters our very paradigm in looking at physics, and it may serve as a key to solving hard problems in the field such as a theory of everything, dark energy and quantum gravity.”

    We’ll see here how Johanness weighs in on all of this one year after Verlinde ….

    We’ll see …

    There is a simple interpretation of the idea that physics derives from information:

    To know about physics, we have to "extract" information from reality. Only those things we can obtain information about, can we actually describe and analyze in physics.

    So, there might be physics inside a black hole, just as there is physics behind a Rindler horizon, and there might be physics beyond the Heisenberg uncertainty limit. But we simply will never get information about this physics. Our description of physics has to be build on the principle that the laws of physics will honor only that which we can get information about.

    Our reality might be derived from information not because information is all there is, but because information is the only thing we can ever use to build a picture of reality with physics.

    Note that Gerard 't Hooft has tried to develop a view of quantum mechanics around this idea.

    Precisely. And the science of information is Mathematics (trough information science,of course), so that the limits in Mathematics that Gödel exposed are at a fundamental level maybe only limits of information; the same principle arises in quantum mechanics in the problem of the collapse of the wave function: only when an observer gathers complete (sort of) information about an event does the function (or seems to) collapse to a known state. So the question is to if our inability to gather information beyond the uncertainty principle and Planck scales would temper us from obtaining full knowledge of nature - is like the quadrature of the circle, the more data you have the better the approximation. Until comes a theory that overcomes the need of full data, but theories are nothing more than a systematization of patterns, and maybe some patterns in nature are elusive to the current available level of information, or maybe there's a fundamental level with the language (formal system) we use to deal with that information, or both; maybe what we need is a some sort of meta-language to overcome the paradox of the self that no known formal system seems to avoid, that Gödel so eloquently put in algebraic form in his theorem. Is this God's realm?

    @cris:
    "maybe there's a fundamental level with the language (formal system) we use to deal with that information, or both;"

    The "language" of information is Turing machines. Information is what can be computed. Probability theory can be merged with computability by way of algorithmic (Kolmogorov) complexity theory. As Chaitin already observed.

    So we arrive at the conclusion that "It from Bit" is the inevitable result of the restriction that every theory of nature must be symbolic and Turing computable for us to even be formulated.
    (ie, there can be, irrational, real numbers in a theory, but they are dealt with as symbols, not as the actual numbers which are non-computable)

    I would not restrict the language of information to Turing Machines since there are alternative models of computation like recursion or lambda calculus, but we can accept the formulation as valid based on the near-universal acceptance of the Church-Turing thesis. But the question i alluded before remains: no formal system is full-proof - meaning not simultaneously complete and consistent. The same with Turing Machines via the halting problem which is not computable, but as Rob pointed out if we consider this not to be information than could be that some kind of reality is outside the domain of information. Or else, we could, as Rob implies, incorporate some knowledge 'à priori' as axioms (symbols), derived from intuition or alike. Otherwise, if information is all that there is and possible, the Universe must be an Universal Turing machine or equivalent.

    8-) .. as you will tell from below, i'm a total novice when it comes to reasoning and physics. But this is all fascinating stuff. I hope there's something non-trivial in my comment.

    > "The above application of uncomputability to predicting the universe assumes we can in principle build a computer capable of simulating the universe. But we can not. Not even in principle."

    if the universe itself is a physical machine that's performing a perfect simulation according to the perfect theoretic form of the universe: - would this logically mean there certainly *is* a TOE (maybe or maybe not discoverable). And that TOE *is* the same perfect theoretic form simulated by the universe? (It would have to be wouldn't it? Could you have the universe simulating one theoretical form while a different theory is a perfect TOE?) Ie. actual reality is divided between a physical form and a mathematical theoretic form. Ie. mathematics has an abstract reality independent of minds to discover it. (.. ummm .. or maybe the universe itself is the abstract theoretic form. Why would it need a seperate reality to run it? .. and why would it need to "run"?)

    ps: has someone somewhere clearly presented a list of essential assumptions that would allow the existence of a Theory of Everything? (i'm not sure if that's a silly question - does it show i'm missing the point? Maybe it's a matter of just going for it and letting the result speak for itself.)

    Being a non-scientist, i just assume there isn't a theory of everything (i feel it in my water :). My completely baseless assumption is: the behaviour and form of all the bits and forces of the universe emerged out of random, incoherent, indeterminate circumstances - in my unscientific view of the world, laws of physics might be emerging or modifying as we speak (tho in an immeasurably subtle way) - very little chance of a TOE that way. But i have no idea if chaotic evolution of the universe has any validity in physics.

    An important question is whether or not a TOE will be finite in length. I am taking 'TOE' to be, as a working definition, a complete description of reality or a complete description of everything that exists. Reality is infinitely vast at least for the reason that it contains all the integers, not to mention the vastness of the physical multiverse. So a TOE can be an infinite document. But like the digits of pi, perhaps this infinitely long document can be computed to arbitrary precision in a finitely long program, set of instructions. Then one *might* consider this program which generates a TOE to arbitrary precision to be "the" TOE, a compression of an infinitely long document into a finitely long document, thus showing that reality at its core does not possess the trait of Kolmogorov randomness. Being that reality contains the uncomputable, it *seems* unlikely that everything can be finitely describable.

    However, I believe that there is a TOE (complete description of reality) whose *form* can be written down. This TOE has a "shape" to it, but without specifying any more details than that. It's an existence proof of a plausible form a TOE could be in. It is roughly based on Tegmark's article entitled the Mathematical Universe Hypothesis (available on arxiv.org) which can be broken down to rely on the axiom that reality is independent of humans which is possibly controversial.

    The argument is made that a TOE can be in the form of a logical structure which is a tuple consisting of an underlying set, a set of distinguished constants (like zero), functions (like successor), and relations (like less than) on this underlying set. Making the additional assumption that if there is a structure such that *all* logical structures can be "embedded" within it, then this type of universality endows such a structure with the same structure as reality. Thus this sort of ultimate structure would be in an intuitive sense like ultimate reality. Thus a description of this ultimate structure would be a description of reality.

    To do this, I employ a different-than-usual set theory called NFU which stands for new foundations with urelements as explained by Randal Holmes' textbook on NFU. The NFU has been shown to be consistent which cannot be said of the more famous ZF or ZFC set theories. The NFU also has a universal set (a set containing all sets) and a "stratified comprehension theorem" which essentially states that any object of the form {x : F} where F is any "stratified" formula is a set in NFU. An example of a *non*-stratified formula F is the infamous formula used in Russell's paradox: x is not an element of x. Thus the object considered in Russell's argument isn't a set and from this argument, no Russell-type contradictions can be derived from the universal set axiom + stratified comprehension.

    Within NFU, it is possible to see that the object which contains *all* structures is a set. Then one can form the "reduced product" of all structures, using this set as the index set. One feature of a reduced product is that it is a logical structure and another feature is that every structure used to form the product (in this case, every structure) is embedded within the reduced product.

    The reduced product of all structures is the ultimate structure as described a few paragraphs above.

    miles
    Nice article Johannes.  I wonder how it is related to the law of entropy and Murphy's?
    The goal of science is to empirically describe our world.

    The humble point of view of most scientists is to describe, and not to discuss about the true nature of reality.
    It's only a finite attempt to understand, and most of scientists ackowledge this.

    I don't see the point of dicussing about the fact that the TOE will cover it all. TOE is and will remain a description, not the reality itself. If you want to talk about the true nature of reality, head towards philosophy. But even phylosophy is and will remain incomplete because bound to the limitations of human mind.

    To my knowledge, only some inner and subjective experiences in a man's life can, once in a while, bring to a level of understanding, well far beyond description like science does. Grasping the true reality of the world is only possible within us. I believe persons like Einstein understood this.

    "A knowledge of the existence of something we cannot penetrate, of the manifestations of the profoundest reason and the most radiant beauty - it is this knowledge and this emotion that constitute the truly religious attitude; in this sense, and in this alone, I am a deeply religious man." (Albert Einstein)

    socrates
    Well said, Francis. Both science and philosophy, when practiced at their highest level (meaning with greatest devotion), are a deeply religious experience, in my opinion. Unfortunately, the reputation of religion has been badly tarnished due to the politicizing of religious institutions and the ramped and cynical abuse of the trappings of religion for economic and political gain.

    Let's hope authentic religion (some now would prefer to call it spirituality, so distasteful has the word religion become) can find its way back to its rightful place in our lives.
    Citizen Philosopher / Science Tutor
    Consider this one as well:

    "The most beautiful and most profound experience is the sensation of the mystical. It is the sower of all true science. He to whom this emotion is a stranger, who can no longer wonder and stand rapt in awe, is as good as dead. To know that what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty which our dull faculties can comprehend only in their primitive forms - this knowledge, this feeling is at the center of true religiousness."
    ( Albert Einstein - The Merging of Spirit and Science)

    Bonny Bonobo alias Brat
    My God, did Albert Einstein ever shut up? Science20 is full of his quotes, I think he has a lot to answer for.
    My latest forum article 'Australian Researchers Discover Potential Blue Green Algae Cause & Treatment of Motor Neuron Disease (MND)&(ALS)' Parkinsons's and Alzheimer's can be found at http://www.science20.com/forums/medicine
    Vladimir Kalitvianski
    I did not read your posts but I remember a note somewhere about how physics perception turned from determinism to relativity, uncertainty, and incompleteness.
    I think that the Grand Unification Theory of Everything is very simple and aleady universally known:

    shit happens