Hi Ed, I am glad you have read the paper with such detail. You have summarized quite well what it is about. I have no objection to the points you make. It is only important to bear in mind that the paper is about studying the possible computational power of the mind by using the model of an artificial neural network. The question of whether the mind is something else was not in the scope of that paper. Assuming that the brain is a neural network we wanted to see what features may take the neural network to achieve certain computational power. We found, effectively, that either an encoding at the level of the neuron (space, e.g. a natural encoding of a real number) or at the neuron firing time. In both cases, to reach any computational power beyond the Turing limit one would need either infinite or infinitesimal space or time, assuming finite brain resources (number of neurons and connections). My personal opinion (perhaps not reflected in the paper itself) is that such super capabilities does not really hold, but the idea was to explore all the possibilities.
It is also very important to highlight, that such a power beyond the computational power of Turing machines, does not require to communicate, encode or decode any infinite value in order to compute a non-computable function. It suffices to posit a natural encoding either in the space or time in which the neurons work, and then make questions in the form of characteristic functions encoding a non-computable function. A characteristic function is one of the type "yes" or "no", so it only needs to transmit a finite amount of information even if the answer required an infinite amount. So a set of neurons may be capable of taking advantage of infinitesimals, and answer yes or no to a non-computable function, even if I think that is not the case it might be. That seems perhaps compatible with your ideas about consciousness. - Hector On Tue, Dec 2, 2008 at 5:31 PM, Ed Porter <[EMAIL PROTECTED]> wrote: > Hector, > > > > I skimmed your paper linked to in the post below. > > > > From my quick read it appears the only meaningful way it suggests a brain > might be infinite was that since the brain used analogue values --- such as > synaptic weights, or variable time intervals between spikes (and presumably > since those analogue values would be determined by so many factors, each of > which might modify their values slightly) --- the brain would be capable of > computing many values each of which could arguably have infinite gradation > in value. So arguably its computations would be infinitely complex, in > terms of the number of bits that would be required to describe them exactly. > > > > If course, it is not clear the universe itself supports infinitely fine > gradation in values, which your paper admits is a questions. > > > > But even if the universe and the brain did support infinitely fine > gradations in value, it is not clear computing with weights or signals > capable of such infinitely fine gradations, necessarily yields computing > that is meaningfully much more powerful, in terms of the sense of experience > it can provide --- unless it has mechanisms that can meaningfully encode and > decode much more information in such infinite variability. You can only > communicate over a very broad bandwidth communication medium as much as your > transmitting and receiving mechanisms can encode and decode. > > > > For example, it is not clear a high definition TV capable of providing an > infinite degree of variation in its colors, rather than only say 8, 16, 32, > or 64 bits for each primary color, would provide any significantly greater > degree of visual experience, even though one could claim the TV was sending > out a signal of infinite complexity. > > > > I have read and been told by neural net designers that typical neural nets > operate by dividing a high dimensional space into subspaces. If this is > true, then it is not clear that merely increasing the resolution at which > such neural nets were computed, say beyond 64 bits, would change the number > of subspaces that could be represented with a given number, say 100 billion, > of nodes --- or that the minute changes in boundaries, or the occasional > difference in tipping points that might result from infinite precision math, > if it were possible, would be of that great a significance with regard to > the overall capabilities of the system. Thus, it is not clear that infinite > resolution in neural weights and spike timing would greatly increase the > meaningful (i.e., having grounding), rememberable, and actionable number of > states the brain could represent. > > > > My belief --- and it is only a belief at this point in time --- is that the > complexity a finite human brain could deliver is so great --- arguably equal > to 1000 millions simultaneous DVD signals that interact with each other and > memories --- that such a finite computation is enough to create the sense of > experiential awareness we humans call consciousness. > > > > I am not aware of anything that modern science says with authority about > external reality --- or that I have sensed from my own experiences of my own > consciousness --- that would seem to require infinite resources. > > > > Something can have a complexity far beyond human comprehension, far beyond > even the most hyperspeed altered imaginings of a drugged mind, arguably far > beyond the complexity of the observable universe, without requiring for its > representation more than an infinitesimal fraction of anything that could be > accurately called infinite. > > > > Ed Porter > > > > -----Original Message----- > From: Hector Zenil [mailto:[EMAIL PROTECTED] > Sent: Sunday, November 30, 2008 10:42 PM > To: agi@v2.listbox.com > Subject: Re: >> RE: FW: [agi] A paper that actually does solve the problem > of consciousness > > > > 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 > > ________________________________ > agi | Archives | Modify Your Subscription -- 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
