RE: RE: FW: [agi] A paper that actually does solve the problem of consciousness
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
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
On Dec 2, 2008, at 8:31 AM, Ed Porter wrote: 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. The universe has a noise floor (see: Boltzmann, Planck, et al), from which it follows that all analog values are equivalent to some trivial number of bits. Since digital deals with the case of analog at the low end of signal to noise ratios, digital usually denotes a proper subset of analog, making the equivalence unsurprising. The obvious argument against infinite values is that the laws of thermodynamics would no longer apply if that were the case. Given the weight of the evidence for thermodynamics being valid, it is probably prudent to stick with models that work when restricted to a finite dynamic range for values. The fundamental non-equivalence of digital and analog is one of those hard-to-kill memes that needs to die, along with the fundamental non- equivalence of parallel and serial computation. Persistent buggers, even among people who should know better. Cheers, J. Andrew Rogers --- 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=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
RE: RE: FW: [agi] A paper that actually does solve the problem of consciousness
J., Your arguments seem to support my intuitive beliefs, so my instinctual response is to be thankful for them. But I have to sheepishly admit I don't totally understand them. Could you please give me a simple explanation for why it is an obvious argument against infinite values ... that the laws of thermodynamics would no longer apply if that were the case. I am not disagreeing, just not understanding. For example, I am not knowledgeable enough about the subject to understand why the laws of thermodynamics could not apply in a classical model of the world in which atoms and molecules have positions and velocities defined with infinite precision, which I think many people who believed in them for years thought before the rise of quantum mechanics. I addition --- although I do understand how noise provides a limit to what can be encoded and decoded as intended communication between an encoding and decoding entity even on a hypothetical infinite bandwidth medium --- it is not clear to me that, at least, that at some physical level, the noise itself might be considered information, and might play a role in the computations of reality. That is not an argument that proves infinite variability, but it might be viewed as an arguments that limits the range of applicability of your noise-floor argument. As anybody who has listened to noisy radio, or watched noisy TV reception can, hear or see, noise can be perceived as signal, even if not an intended one. To the extent that I am wrong in this devil's advocacy, please enlighten me. (Despite his obvious deficiencies, the devil is a most interesting client, and I am sure I have offended many people --- but, I hope, not you --- by arguing his cause too strenuously out of intellectual curiosity.) Ed Porter -Original Message- From: J. Andrew Rogers [mailto:[EMAIL PROTECTED] Sent: Tuesday, December 02, 2008 4:15 PM To: agi@v2.listbox.com Subject: Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness On Dec 2, 2008, at 8:31 AM, Ed Porter wrote: 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. The universe has a noise floor (see: Boltzmann, Planck, et al), from which it follows that all analog values are equivalent to some trivial number of bits. Since digital deals with the case of analog at the low end of signal to noise ratios, digital usually denotes a proper subset of analog, making the equivalence unsurprising. The obvious argument against infinite values is that the laws of thermodynamics would no longer apply if that were the case. Given the weight of the evidence for thermodynamics being valid, it is probably prudent to stick with models that work when restricted to a finite dynamic range for values. The fundamental non-equivalence of digital and analog is one of those hard-to-kill memes that needs to die, along with the fundamental non- equivalence of parallel and serial computation. Persistent buggers, even among people who should know better. Cheers, J. Andrew Rogers --- 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: 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=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
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
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
Suppose that the gravitational constant is a non-computable number (it might be, we don't know because as you say, we can only measure with finite precision). Planets compute G as part of the law of gravitation that rules their movement (you can of course object, that G is part of a model that has been replaced by a another theory --General Relativity-- and that neither one nor the other can be taken as full and ultimate descriptions, but then I can change my argument to whichever theory turns out to be the ultimate and true, even if we never have access to it). Planets don't necessarily have to encode and decode G, because it is given by granted, it is already naturally encoded, they just follow the law in which it is given. The same, if a non-computable number is already encoded in the brain, to compute with such a real number the neuron would not need necessarily to encode or decode the number. The neuron could then carry out a non-computable computation (no measurement involved) and then give a no/yes answer, just as a planet would hit or not another a planet by following a non-computable gravitational constant. But even in the case of need of measurement, it is only the most significant part relevant to the computation that is performing that is actually needed, since we are not interested in infinitely long computations, that's also why, even when noise is of course a practical problem, it is not an infrangible one. Now you can argue that if only a finite (the most significant part) of the real number is necessary to perform the computation, it would have sufficed to store only a rational (computable) number since the beginning, rather than a non-computable number. However, it is this potential access to an infinite number that makes the system more powerful and not the fact of be able to infinite precision measurements. For more about these results you can take a look at Hava Siegelman's work on Recurrent Analogical Neural Networks, which more than a work on hypercomputation, I consider it a work on computational complexity with pretty nice scientific results. On the other hand, I would say that I may have many objections, mainly those pointed out by Davis in his paper The Myth of Hypercomputation, which I also recommend you in case you haven't read it. The only thing that from my point of view Davis is trivializing is that whether there are non-computable numbers in nature, taking advantage of their computational power, is an open question, so it is still plausible. On Wed, Dec 3, 2008 at 12:17 AM, Ed Porter [EMAIL PROTECTED] wrote: Hector, Thank you for your reply saying my description of your paper was much better than clueless. I am, however, clueless about how to interpret the second paragraph of your reply (all of which is copied below). For example, I am confused by your statements 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. considering that you then state: 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. What I don't understand is how a system does not require to communicate, encode or decode any infinite value in order to compute a non-computable function if its answer required an infinite amount [of information]. It seems like the computing of an infinite amount of information was required somewhere, even if not in communicating the answer, so how does such a system not¸ as you said require to communicate, encode or decode any infinite value in order to compute a non-computable function even if only internally? Ed Porter -Original Message- From: Hector Zenil [mailto:[EMAIL PROTECTED] Sent: Tuesday, December 02, 2008 5:14 PM To: agi@v2.listbox.com Subject: Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness 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
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
Hector, Yes, it's possible that the brain uses uncomputable neurons to predict uncomputable physical dynamics in the observed world However, even if this is the case, **there is no possible way to verify or falsify this hypothesis using science**, if science is construed to involve evaluation of theories based on finite sets of finite-precision data ... So, this hypothesis has much the same status as the hypothesis that the brain has an ineffable soul inside it, which can never be measured. This is certainly possible too, but we have no way to verify or falsify it using science. You may say the hypothesis of neural hypercomputing valid in the sense that it helps guide you to interesting, falsifiable theories. That's fine. But, then you must admit that the hypothesis of souls could be valid in the same sense, right? It could guide some other people to interesting, falsifiable theories -- even though, in itself, it stands outside the domain of scientific validation/falsification. It is possible that the essence of intelligence lies in something that can't be scientifically addressed. If so, no matter how many finite-precision measurements of the brain we record and analyze, we'll never get at the core of intelligence that way. So, in that hypothesis, if we succeed at making AGI, it will be due to some non-scientific, non-computable force somehow guiding us. However, I doubt this is the case. I strongly suspect the essence of intelligence lies in properties of systems that can be measured, and therefore *not* in hypercomputing. Consciousness is another issue -- I do happen to think there is an aspect of consciousness that, like hypercomputing, lies outside the realm of science. However, I don't fall for the argument that X and Y must be equal just because they're both outside the realm of science... -- Ben G On Tue, Dec 2, 2008 at 6:54 PM, Hector Zenil [EMAIL PROTECTED] wrote: Suppose that the gravitational constant is a non-computable number (it might be, we don't know because as you say, we can only measure with finite precision). Planets compute G as part of the law of gravitation that rules their movement (you can of course object, that G is part of a model that has been replaced by a another theory --General Relativity-- and that neither one nor the other can be taken as full and ultimate descriptions, but then I can change my argument to whichever theory turns out to be the ultimate and true, even if we never have access to it). Planets don't necessarily have to encode and decode G, because it is given by granted, it is already naturally encoded, they just follow the law in which it is given. The same, if a non-computable number is already encoded in the brain, to compute with such a real number the neuron would not need necessarily to encode or decode the number. The neuron could then carry out a non-computable computation (no measurement involved) and then give a no/yes answer, just as a planet would hit or not another a planet by following a non-computable gravitational constant. But even in the case of need of measurement, it is only the most significant part relevant to the computation that is performing that is actually needed, since we are not interested in infinitely long computations, that's also why, even when noise is of course a practical problem, it is not an infrangible one. Now you can argue that if only a finite (the most significant part) of the real number is necessary to perform the computation, it would have sufficed to store only a rational (computable) number since the beginning, rather than a non-computable number. However, it is this potential access to an infinite number that makes the system more powerful and not the fact of be able to infinite precision measurements. For more about these results you can take a look at Hava Siegelman's work on Recurrent Analogical Neural Networks, which more than a work on hypercomputation, I consider it a work on computational complexity with pretty nice scientific results. On the other hand, I would say that I may have many objections, mainly those pointed out by Davis in his paper The Myth of Hypercomputation, which I also recommend you in case you haven't read it. The only thing that from my point of view Davis is trivializing is that whether there are non-computable numbers in nature, taking advantage of their computational power, is an open question, so it is still plausible. On Wed, Dec 3, 2008 at 12:17 AM, Ed Porter [EMAIL PROTECTED] wrote: Hector, Thank you for your reply saying my description of your paper was much better than clueless. I am, however, clueless about how to interpret the second paragraph of your reply (all of which is copied below). For example, I am confused by your statements 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
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
On Wed, Dec 3, 2008 at 1:51 AM, Ben Goertzel [EMAIL PROTECTED] wrote: Hector, Yes, it's possible that the brain uses uncomputable neurons to predict uncomputable physical dynamics in the observed world However, even if this is the case, **there is no possible way to verify or falsify this hypothesis using science**, if science is construed to involve evaluation of theories based on finite sets of finite-precision data ... So, this hypothesis has much the same status as the hypothesis that the brain has an ineffable soul inside it, which can never be measured. This is certainly possible too, but we have no way to verify or falsify it using science. You may say the hypothesis of neural hypercomputing valid in the sense that it helps guide you to interesting, falsifiable theories. That's fine. But, then you must admit that the hypothesis of souls could be valid in the same sense, right? It could guide some other people to interesting, falsifiable theories -- even though, in itself, it stands outside the domain of scientific validation/falsification. I understand the point, but I insist that it is not that trivial. You could apply the same argument against the automated proof of the four-color theorem. Since there is no human capable of verifying it in a lifetime (and even if a group of people try to verify it, no single mind would ever have the intellectual capacity to get convinced by its own), then the four-color proof is not science... and me, I am pretty convinced that it is, including computer science and proof theory. Actually I think that that kind of proofs and approaches to science will happen more and more often, as we can already witness. Just as the four-color theorem was proved and then verified by another computer program, the outcome of a hypercomputer could be verified by another hypercomputer. And just as for the finite case of the four-color theorem, you would not be able to verify it but by trusting on another system. I am not hypercomputationalist, all the opposite! but closed definitions about what is science and people trying to have the good definition of science, look to me pretty narrow. However, if I were director of a computer science department, I wouldn't probably put any money into hypercomputationism research. But even if it is just philosophy, that doesn't make it less valid or less plausible. On the other hand, the scientific arguments against it often sound very weak, perhaps just as weak as the arguments in favor, but sometimes even weaker. What if a hypercomputer provides you, each time you ask, the answer to whether a Turing machine halts. You effectively cannot verify that it works for all cases (it is of course a problem of induction very spread in science in general), but I am pretty sure you would believe that it is what it says it is, if for any Turing machine, as complicated as you may want, it tells you whether it halts and when (you could argue for example that it is just simulating the Turing machine extremely fast, but let's suppose it does it instantaneously). How this prediction power would make it less science than, let's say, quantum mechanics? To me, that would be much more scientific than people doing string theory... The same about noise. People use to think about it as a constraint, but some of recent results in computational complexity and serious interpretations suggest that actually, as I was telling before, if it nature is indeterministic, noise is actually a computation carried out by something more powerful (even if it seems meaningful) than a universal Turing machine, so by itself, rather than subtracting computational power, it might add up! One would need of course to conciliate this with thermodynamics, but there are actually some interpretations that would easily allow this interpretation of noise. However I don't think I will take that thread of discussion. Together with the bibliography I've provided before, I recommend also a very recent paper by Karl Svozil in the Complex Systems journal about whether hypercomputation is falsifiable. It is possible that the essence of intelligence lies in something that can't be scientifically addressed. If so, no matter how many finite-precision measurements of the brain we record and analyze, we'll never get at the core of intelligence that way. So, in that hypothesis, if we succeed at making AGI, it will be due to some non-scientific, non-computable force somehow guiding us. However, I doubt this is the case. I strongly suspect the essence of intelligence lies in properties of systems that can be measured, and therefore *not* in hypercomputing. Consciousness is another issue -- I do happen to think there is an aspect of consciousness that, like hypercomputing, lies outside the realm of science. However, I don't fall for the argument that X and Y must be equal just because they're both outside the realm of science... -- Ben G On Tue, Dec 2,
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
Hi Hector, You may say the hypothesis of neural hypercomputing valid in the sense that it helps guide you to interesting, falsifiable theories. That's fine. But, then you must admit that the hypothesis of souls could be valid in the same sense, right? It could guide some other people to interesting, falsifiable theories -- even though, in itself, it stands outside the domain of scientific validation/falsification. I understand the point, but I insist that it is not that trivial. You could apply the same argument against the automated proof of the four-color theorem. Since there is no human capable of verifying it in a lifetime (and even if a group of people try to verify it, no single mind would ever have the intellectual capacity to get convinced by its own), then the four-color proof is not science... So, the distinction here is that -- in one case, **no possible finite set of observations** can verify or falsify the hypothesis at hand [hypercomputing] -- in the other case, some finite set of observations could verify or falsify the hypothesis at hand ... but this observation set wouldn't fit into the mind of a certain observer O [four color theorem] So, to simplify a bit, do I define X has direct scientific meaning as I can personally falsify X or as Some being could potentially falsify X; and I can use science to distinguish those being capable of falsifying X from those that are incapable ?? If the former, then the four color theorem isn't human science If the latter, it is... I choose the latter... ben --- 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=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
We cannot ask Feynman, but I actually asked Deutsch. He does not only think QM is our most basic physical reality (he thinks math and computer science lie in quantum mechanics), but he even takes quite seriously his theory of parallel universes! and he is not alone. Speaking by myself, I would agree with you, but I think we would need to relativize the concept of agreement. I don't think QM is just another model of merely mathematical value to make finite predictions. I think physical models say something about our physical reality. If you deny QM as part of our physical reality then I guess you deny any other physical model. I wonder then what is left to you. You perhaps would embrace total skepticism, perhaps even solipsism. Current trends have moved from there to a more relativized positions, where models are considered so, models, but still with some value as part of our actual physical reality (just as Newtonian physics is not just completely wrong after General Relativity since it still describes a huge part of our physical reality). Well, I don't embrace solipsism, but that is really a philosophic and personal rather than scientific matter ... and, I'm not going talk here about what is, which IMO is not a matter for science ... but merely about what science can tell us. And, science cannot tell us whether QM or some empirically-equivalent, wholly randomness-free theory is the right one... 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/?member_id=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
2008/12/1 Ben Goertzel [EMAIL PROTECTED]: And, science cannot tell us whether QM or some empirically-equivalent, wholly randomness-free theory is the right one... If two theories give identical predictions under all circumstances about how the real world behaves, then they are not two separate theories, they are merely rewordings of the same theory. And choosing between them is arbitrary; you may prefer one to the other because human minds can visualise it more easily, or it's easier to calculate, or you have an aethetic preference for it. -- Philip Hunt, [EMAIL PROTECTED] Please avoid sending me Word or PowerPoint attachments. See http://www.gnu.org/philosophy/no-word-attachments.html --- 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=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
If two theories give identical predictions under all circumstances about how the real world behaves, then they are not two separate theories, they are merely rewordings of the same theory. And choosing between them is arbitrary; you may prefer one to the other because human minds can visualise it more easily, or it's easier to calculate, or you have an aethetic preference for it. -- Philip Hunt, [EMAIL PROTECTED] However, the two theories may still have very different consequences **within the minds of the community of scientists** ... Even though T1 and T2 are empirically equivalent in their predictions, T1 might have a tendency to lead a certain community of scientists in better directions, in terms of creating new theories later on However, empirically validating this property of T1 is another question ... which leads one to the topic of scientific theories about the sociological consequences of scientific theories ;-) 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/?member_id=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
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. 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. 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/?member_id=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
On Mon, Dec 1, 2008 at 11:19 AM, Ed Porter [EMAIL PROTECTED] wrote: You said QUANTUM THEORY REALLY HAS NOTHING DIRECTLY TO DO WITH UNCOMPUTABILITY. Please don't quote people using this style, it hurts my eyes. 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. I don't even know what you're saying here. Maybe you're trying to say that it takes a really big computer to compute a very small box of physical reality.. which is true.. I just don't know why you would be saying that. You said IT IS CERTAINLY THINKABLE THAT THE BRAIN IS INFINITE NOT FINITE IN ITS INFORMATION CONTENT, OR THAT IT'S A SORT OF ANTENNA THAT RECEIVES INFORMATION FROM SOME INFINITE-INFORMATION-CONTENT SOURCE This certainly is thinkable. And that is a non-trivial statement. We should never forget that our concepts of reality could be nothing but illusions, and that our understanding of science and physical reality may be much more partial and flawed than we think. It's also completely unscientific. You might as well say that magic pixies deliver your thoughts from big invisible bucket made of gold. 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. So why are you entertaining notions of magic antennas to God? 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. I wouldn't. It's untestable non-sense. Trent --- 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=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
RE: RE: FW: [agi] A paper that actually does solve the problem of consciousness
Regarding the uncertainty principal, Wikipedia says: In quantum physics, the Heisenberg uncertainty principle states that the values of certain pairs of conjugate variables (position and momentum, for instance) cannot both be known with arbitrary precision. That is, the more precisely one variable is known, the less precisely the other is known. THIS IS NOT A STATEMENT ABOUT THE LIMITATIONS OF A RESEARCHER'S ABILITY TO MEASURE PARTICULAR QUANTITIES OF A SYSTEM, BUT RATHER ABOUT THE NATURE OF THE SYSTEM ITSELF. (emphasis added.) I am sure you know more about quantum mechanics than I do. But I have heard many say the uncertainty controls limits not just on scientific measurement, but the amount of information different parts of reality can have about each other when computing in response to each other. Perhaps such theories are wrong, but they are not without support in the field. With regard to the statement science can never provide evidence in favor of infinite mechanisms I though you were saying there was no way the human mind could fully represent or fully understand an infinite mechanism --- which I agree with. You were correct in thinking that I did not grok that you were implying this means if an infinite mechanism exited there could be no evidence in favor of it infinity. In fact, it is not clear that this is the case, if you use provide evidence considerably more loosely than provide proof for. Until the advent of quantum mechanics and/or the theory of the expanding universe, based in part on observations and in part intuitions derived from them, many people felt the universe was infinitely continuous and/or of infinite extent in space and time. I agree you would probably never be able to prove infinite realities, but the mind is capable of conceiving of them, and of seeing evidence that might suggest to some their existence, such as was suggested to Einstein, who for many years I have been told believed in a universe that was infinite in time. Ed Porter -Original Message- From: Ben Goertzel [mailto:[EMAIL PROTECTED] Sent: Sunday, November 30, 2008 9:09 PM To: agi@v2.listbox.com Subject: Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness 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. 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. 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 --- 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=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
HI, In quantum physics, the Heisenberg uncertainty principle states that the values of certain pairs of conjugate variables (position and momentum, for instance) cannot both be known with arbitrary precision. That is, the more precisely one variable is known, the less precisely the other is known. THIS IS NOT A STATEMENT ABOUT THE LIMITATIONS OF A RESEARCHER'S ABILITY TO MEASURE PARTICULAR QUANTITIES OF A SYSTEM, BUT RATHER ABOUT THE NATURE OF THE SYSTEM ITSELF. (emphasis added.) I am sure you know more about quantum mechanics than I do. But I have heard many say the uncertainty controls limits not just on scientific measurement, but the amount of information different parts of reality can have about each other when computing in response to each other. Perhaps such theories are wrong, but they are not without support in the field. Yeah, the interpretation of quantum theory is certainly contentious and there are multiple conflicting views... However, regarding quantum computing, it is universally agreed that the class of quantum computable functions is identical to the class of classically Turing computable functions. With regard to the statement science can never provide evidence in favor of infinite mechanisms I though you were saying there was no way the human mind could fully represent or fully understand an infinite mechanism --- which I agree with. No, I was not saying that there was no way the human mind could fully represent or fully understand an infinite mechanism What I argued is that **scientific data** can never convincingly be used to argue in favor of an infinite mechanism, due to the intrinsically finite nature of scientific data. This says **nothing** about any intrinsic limitations on the human mind ... unless one adds the axiom that the human mind must be entirely comprehensible via science ... which seems an unnecessary assumption to make In fact, it is not clear that this is the case, if you use provide evidence considerably more loosely than provide proof for. Until the advent of quantum mechanics and/or the theory of the expanding universe, based in part on observations and in part intuitions derived from them, many people felt the universe was infinitely continuous and/or of infinite extent in space and time. I agree you would probably never be able to prove infinite realities, but the mind is capable of conceiving of them, and of seeing evidence that might suggest to some their existence, such as was suggested to Einstein, who for many years I have been told believed in a universe that was infinite in time. well, my argument implies that you can never use science to prove that the mind is capable of conceiving of infinite realities This may be true in some other sense, but I argue, not in a scientific sense... -- 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/?member_id=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
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 Zenilhttp://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=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
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 Zenilhttp://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=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
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 Zenilhttp://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 Zenilhttp://www.mathrix.org
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
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 Zenilhttp://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:
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
But I don't get your point at all, because the whole idea of nondeterministic randomness has nothing to do with physical reality... true random numbers are uncomputable entities which can never be existed, 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 Zenilhttp://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
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
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... It has all to do when it is about quantum mechanics. Quantum mechanics is non-deterministic by nature. A quantum computer, even within the standard model of quantum computation, could then take advantage of this intrinsic property of the physical (quantum) reality (assuming the model correct, as most physicists would). true random numbers are uncomputable entities which can never be existed, 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... That's the point, that's what the classical theory of computability would say (also making some assumptions, namely Church's thesis), but again quantum mechanics says something else : The fact that quantum computers are able of non-deterministic randomness by definition and Turing machines are unable of non-deterministic randomness also by definition seems incompatible with the claim (or mathematical proof) that standard quantum computers compute exactly the same functions than Turing machines, and that's only when dealing with standard quantum computation, because non-standard quantum computation is far from being proved to be reduced to Turing-computable (modulo their speed-up). Concerning the observations, you don't need to do an infinite number of them to get a non-computable answer from an Oracle (although you would need in case you want to finitely verify it). And even if you can model equally well the first N bits of a non-deterministic random sequence, the fact that a random sequence is ontologically of a non-deterministic nature, makes it a priori a different one in essence from a pseudo random sequence. The point is not epistemological. In any case, whether we agree on the philosophical matter, my point is that it is not the case that there is a mathematical proof about quantum systems computing exactly the same functions than Turing machines. There is a mathematical proof that the standard model of quantum computation computes the same set of functions than Turing machines. 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
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
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
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
On Sun, Nov 30, 2008 at 11:48 PM, Hector Zenil [EMAIL PROTECTED] wrote: 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)? Of course it isn't -- quantum mechanics is a mathematical and conceptual model that we use in order to predict certain finite sets of finite-precision observations, based on other such sets 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. Sure it does: but there is an equivalent mathematical theory that explains all observations identically to QM, yet doesn't posit any uncomputable entities So, choosing to posit that these uncomputable entities exist in reality, is just a matter of aesthetic or philosophical taste ... so you can't really say they exist in reality, because they contribute nothing to the predictive power of QM ... -- 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/?member_id=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
On Mon, Dec 1, 2008 at 6:20 AM, Ben Goertzel [EMAIL PROTECTED] wrote: On Sun, Nov 30, 2008 at 11:48 PM, Hector Zenil [EMAIL PROTECTED] wrote: 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)? Of course it isn't -- quantum mechanics is a mathematical and conceptual model that we use in order to predict certain finite sets of finite-precision observations, based on other such sets Oh I see! I think that's of philosophical taste as well. I don't think everybody would agree with you. Specially if you poll physicists like those that constructed the standard model of computation! We cannot ask Feynman, but I actually asked Deutsch. He does not only think QM is our most basic physical reality (he thinks math and computer science lie in quantum mechanics), but he even takes quite seriously his theory of parallel universes! and he is not alone. Speaking by myself, I would agree with you, but I think we would need to relativize the concept of agreement. I don't think QM is just another model of merely mathematical value to make finite predictions. I think physical models say something about our physical reality. If you deny QM as part of our physical reality then I guess you deny any other physical model. I wonder then what is left to you. You perhaps would embrace total skepticism, perhaps even solipsism. Current trends have moved from there to a more relativized positions, where models are considered so, models, but still with some value as part of our actual physical reality (just as Newtonian physics is not just completely wrong after General Relativity since it still describes a huge part of our physical reality). At the end, even if you claim a Platonic physical reality to which we have no access at all, not even through our best explanations in the way of models, the world is either quantum or not (as we have defined the theory), and as long as it remains as our best explanation of a the phenomena that characterizes one has to face it to other models describing other aspects or models of our best known physical reality. It is not clear to me how you would deny the physical reality of QM but defend the theory of computability or algorithmic information theory as if they were more basic than QM. If we take as equally basic QM and AIT, even in a practical sense, there are incompatibilities in essence. QM cannot be said as Turing computable, and AIT cannot posit the in-existence of non-deterministic randomness specially when QM says something else. I am more in the side of AIT but I think the question is open, is interesting (both philosophically and scientific) and not trivial at all. 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. Sure it does: but there is an equivalent mathematical theory that explains all observations identically to QM, yet doesn't posit any uncomputable entities So, choosing to posit that these uncomputable entities exist in reality, is just a matter of aesthetic or philosophical taste ... so you can't really say they exist in reality, because they contribute nothing to the predictive power of QM ... There are people that think that quantum randomness is actually the source of the complexity we see in the universe [Bennett, Lloyd]. Even when I do not agree with them (since AIT does not require non-deterministic randomness) I think it is not that trivial since even researchers think they contribute in some fundamental (not only philosophical) way. -- 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 Zenilhttp://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=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
Re: RE: FW: [agi] A paper that actually does solve the problem of consciousness
Hector Zenil wrote: On Mon, Dec 1, 2008 at 6:20 AM, Ben Goertzel [EMAIL PROTECTED] wrote: On Sun, Nov 30, 2008 at 11:48 PM, Hector Zenil [EMAIL PROTECTED] wrote: 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 ... ... Oh I see! I think that's of philosophical taste as well. I don't think everybody would agree with you. Specially if you poll physicists like those that constructed the standard model of computation! We cannot ask Feynman, but I actually asked Deutsch. He does not only think QM is our most basic physical reality (he thinks math and computer science lie in quantum mechanics), but he even takes quite seriously his theory of parallel universes! and he is not alone. Speaking by... when I do not agree with them (since AIT does not require non-deterministic randomness) I think it is not that trivial since even researchers think they contribute in some fundamental (not only philosophical) way. -- Ben G Still, one must remember that there is Quantum Theory, and then there are the interpretations of Quantum Theory. As I understand things there are still several models of the universe which yield the same observables, and choosing between them is a matter of taste. They are all totally consistent with standard Quantum Theory...but ...well, which do you prefer? Multi-world? Action at a distance? No objective universe? (I'm not sure what that means.) The present is created by the future as well as the past? As I understand things, these cannot be chosen between on the basis of Quantum Theory. And somewhere in that mix is Wholeness and the Implicate Order. When math gets translated into Language, interpretations add things. --- 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=8660244id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
