On Mon, Dec 1, 2008 at 4:53 AM, 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.
or at least by a model of physical reality... =) (a reality by the way, that the authors of the mathematical proof believe in as the most basic) > >> >> 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 > -- 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
