On Mon, Dec 1, 2008 at 4:55 AM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > But I don't get your point at all, because the whole idea of > "nondeterministic" randomness has nothing to do with physical > reality...
It has all to do when it is about quantum mechanics. Quantum mechanics is non-deterministic by nature. A quantum computer, even within the standard model of quantum computation, could then take advantage of this intrinsic property of the physical (quantum) reality (assuming the model correct, as most physicists would). > true random numbers are uncomputable entities which can > never be existed, and any finite series of observations can be modeled > equally well as the first N bits of an uncomputable series or of a > computable one... That's the point, that's what the classical theory of computability would say (also making some assumptions, namely Church's thesis), but again quantum mechanics says something else : The fact that quantum computers are able of non-deterministic randomness by definition and Turing machines are unable of non-deterministic randomness also by definition seems incompatible with the claim (or mathematical proof) that standard quantum computers compute exactly the same functions than Turing machines, and that's only when dealing with standard quantum computation, because non-standard quantum computation is far from being proved to be reduced to Turing-computable (modulo their speed-up). Concerning the observations, you don't need to do an infinite number of them to get a non-computable answer from an Oracle (although you would need in case you want to finitely verify it). And even if you can model equally well the first N bits of a non-deterministic random sequence, the fact that a random sequence is ontologically of a non-deterministic nature, makes it a priori a different one in essence from a pseudo random sequence. The point is not epistemological. In any case, whether we agree on the philosophical matter, my point is that it is not the case that there is a mathematical proof about quantum systems computing exactly the same functions than Turing machines. There is a mathematical proof that the standard model of quantum computation computes the same set of functions than Turing machines. > ben g > > On Sun, Nov 30, 2008 at 10:53 PM, Hector Zenil <[EMAIL PROTECTED]> wrote: >> On Mon, Dec 1, 2008 at 4:44 AM, Ben Goertzel <[EMAIL PROTECTED]> wrote: >>> OTOH, there is no possible real-world test to distinguish a "true >>> random" sequence from a high-algorithmic-information quasi-random >>> sequence.... >> >> I know, but the point is not whether we can distinguish it, but that >> quantum mechanics actually predicts to be intrinsically capable of >> non-deterministic randomness, while for a Turing machine that is >> impossible by definition. I find quite convincing and interesting the >> way in which the mathematical proof of the standard model of quantum >> computation as Turing computable has been put in jeopardy by physical >> reality. >> >>> >>> So I don't find this argument very convincing... >>> >>> On Sun, Nov 30, 2008 at 10:42 PM, Hector Zenil <[EMAIL PROTECTED]> wrote: >>>> On Mon, Dec 1, 2008 at 3:09 AM, Ben Goertzel <[EMAIL PROTECTED]> wrote: >>>>>> But quantum theory does appear to be directly related to limits of the >>>>>> computations of physical reality. The uncertainty theory and the >>>>>> quantization of quantum states are limitations on what can be computed by >>>>>> physical reality. >>>>> >>>>> Not really. They're limitations on what measurements of physical >>>>> reality can be simultaneously made. >>>>> >>>>> Quantum systems can compute *exactly* the class of Turing computable >>>>> functions ... this has been proved according to standard quantum >>>>> mechanics math. however, there are some things they can compute >>>>> faster than any Turing machine, in the average case but not the worst >>>>> case. >>>>> >>>> >>>> Sorry, I am not really following the discussion but I just read that >>>> there is some misinterpretation here. It is the standard model of >>>> quantum computation that effectively computes exactly the Turing >>>> computable functions, but that was almost hand tailored to do so, >>>> perhaps because adding to the theory an assumption of continuum >>>> measurability was already too much (i.e. distinguishing infinitely >>>> close quantum states). But that is far from the claim that quantum >>>> systems can compute exactly the class of Turing computable functions. >>>> Actually the Hilbert space and the superposition of particles in an >>>> infinite number of states would suggest exactly the opposite. While >>>> the standard model of quantum computation only considers a >>>> superposition of 2 states (the so-called qubit, capable of >>>> entanglement in 0 and 1). But even if you stick to the standard model >>>> of quantum computation, the "proof" that it computes exactly the set >>>> of recursive functions [Feynman, Deutsch] can be put in jeopardy very >>>> easy : Turing machines are unable to produce non-deterministic >>>> randomness, something that quantum computers do as an intrinsic >>>> property of quantum mechanics (not only because of measure limitations >>>> of the kind of the Heisenberg principle but by quantum non-locality, >>>> i.e. the violation of Bell's theorem). I just exhibited a non-Turing >>>> computable function that standard quantum computers compute... >>>> [Calude, Casti] >>>> >>>> >>>>>> But, I am old fashioned enough to be more interested in things about the >>>>>> brain and AGI that are supported by what would traditionally be >>>>>> considered >>>>>> "scientific evidence" or by what can be reasoned or designed from such >>>>>> evidence. >>>>>> >>>>>> If there is any thing that would fit under those headings to support the >>>>>> notion of the brain either being infinite, or being an antenna that >>>>>> receives >>>>>> decodable information from some infinite-information-content source, I >>>>>> would >>>>>> love to hear it. >>>> >>>> >>>> You and/or other people might be interested in a paper of mine >>>> published some time ago on the possible computational power of the >>>> human mind and the way to encode infinite information in the brain: >>>> >>>> http://arxiv.org/abs/cs/0605065 >>>> >>>> >>>>> the key point of the blog post you didn't fully grok, was a careful >>>>> argument that (under certain, seemingly reasonable assumptions) >>>>> science can never provide evidence in favor of infinite mechanisms... >>>>> >>>>> ben g >>>>> >>>>> >>>>> ------------------------------------------- >>>>> agi >>>>> Archives: https://www.listbox.com/member/archive/303/=now >>>>> RSS Feed: https://www.listbox.com/member/archive/rss/303/ >>>>> Modify Your Subscription: https://www.listbox.com/member/?&; >>>>> Powered by Listbox: http://www.listbox.com >>>>> >>>> >>>> >>>> >>>> -- >>>> Hector Zenil http://www.mathrix.org >>>> >>>> >>>> ------------------------------------------- >>>> agi >>>> Archives: https://www.listbox.com/member/archive/303/=now >>>> RSS Feed: https://www.listbox.com/member/archive/rss/303/ >>>> Modify Your Subscription: https://www.listbox.com/member/?&; >>>> Powered by Listbox: http://www.listbox.com >>>> >>> >>> >>> >>> -- >>> Ben Goertzel, PhD >>> CEO, Novamente LLC and Biomind LLC >>> Director of Research, SIAI >>> [EMAIL PROTECTED] >>> >>> "I intend to live forever, or die trying." >>> -- Groucho Marx >>> >>> >>> ------------------------------------------- >>> agi >>> Archives: https://www.listbox.com/member/archive/303/=now >>> RSS Feed: https://www.listbox.com/member/archive/rss/303/ >>> Modify Your Subscription: https://www.listbox.com/member/?&; >>> Powered by Listbox: http://www.listbox.com >>> >> >> >> >> -- >> Hector Zenil http://www.mathrix.org >> >> >> ------------------------------------------- >> agi >> Archives: https://www.listbox.com/member/archive/303/=now >> RSS Feed: https://www.listbox.com/member/archive/rss/303/ >> Modify Your Subscription: https://www.listbox.com/member/?&; >> Powered by Listbox: http://www.listbox.com >> > > > > -- > Ben Goertzel, PhD > CEO, Novamente LLC and Biomind LLC > Director of Research, SIAI > [EMAIL PROTECTED] > > "I intend to live forever, or die trying." > -- Groucho Marx > > > ------------------------------------------- > agi > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > -- Hector Zenil http://www.mathrix.org ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
