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/?member_id=8660244&id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
