OTOH, there is no possible real-world test to distinguish a "true random" sequence from a high-algorithmic-information quasi-random sequence....
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/?member_id=8660244&id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
