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...
I don't get it. You don't think that quantum mechanics is part of our physical reality (if it is not all of it)? > true random numbers are uncomputable entities which can > never be existed, you can say that either they don't exist or they do exist but that we don't have access to them. That's a rather philosophical matter. But scientifically QM says the latter. Even more, since bits from a non-deterministic random source are truly independent from each other, something that does not happen when produced by a Turing machine, then any sequence (even finite) is of different nature from one produced by a Turing machine. In practice, if your claim is that you will not be able to distinguish the difference, you actually would if you let the machine run for a longer period of time, once finished its physical resources it will either halt or start over (making the "random" string periodic), while QM says that resources don't matter, a quantum computer will always continue producing non-deterministic (e.g. never periodic) strings of any length independently of any constraint of time or space! > 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... > > 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
