Re: Computation as an explanation of the universe (was Re: [agi] Recursive self-change: some definitions)
OK, then the observable universe has a finite description length. We don't need to describe anything else to model it, so by universe I mean only the observable part. But, what good is it to only have finite description of the observable part, since new portions of the universe enter the observable portion continually? Physics cannot then be modeled as a computer program, because computer programs do not increase in Kolmogorov complexity as they run (except by a logarithmic term to count how long it has been running). I am saying that the universe *is* deterministic. It has a definite quantum state, but we would need about 10^122 bits of memory to describe it. Since we can't do that, we have to resort to approximate models like quantum mechanics. Yes, I understood that you were suggesting a deterministic universe. What I'm saying is that it seems plausible for us to be able to have an accurate knowledge of that deterministic physics, lacking only the exact knowledge of particle locations et cetera. We would be forced to use probabilistic methods as you argue, but they would not necessarily be built into our physical theories; instead, our physical theories act as a deterministic function that is given probabilistic input and therefore yields probabilistic output. I believe there is a simpler description. First, the description length is increasing with the square of the age of the universe, since it is proportional to area. So it must have been very small at one time. Second, the most efficient way to enumerate all possible universes would be to run each B-bit machine for 2^B steps, starting with B = 0, 1, 2... until intelligent life is found. For our universe, B ~ 407. You could reasonably argue that the algorithmic complexity of the free parameters of string theory and general relativity is of this magnitude. I believe that Wolfram also argued that the (observable) universe is a few lines of code. I really do not understand your willingness to restrict universe to observable universe. The description length of the observable universe was very small at one time because at that time none of the basic stuffs of the universe had yet interacted, so by definition the description length of the observable universe for each basic entity is just the description length of that entity. As time moves forward, the entities interact and the description lengths of their observable universes increase. Similarly, today, one might say that the observable universe for each person is slightly different, and indeed the universe observable from my right hand would be slightly different then the one observable from my left. They could have differing description lengths. In short, I think you really want to apply your argument to the actual universe, not merely observable subsets... or if you don't, you should, because otherwise it seems like a very strange argument. But even if we discover this program it does not mean we could model the universe deterministically. We would need a computer larger than the universe to do so. Agreed... partly thanks to your argument below. There is a simple argument using information theory. Every system S has a Kolmogorov complexity K(S), which is the smallest size that you can compress a description of S to. A model of S must also have complexity K(S). However, this leaves no space for S to model itself. In particular, if all of S's memory is used to describe its model, there is no memory left over to store any results of the simulation. Point conceded. --Abram --- 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=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
Re: Computation as an explanation of the universe (was Re: [agi] Recursive self-change: some definitions)
To clarify what I mean by observable universe, I am including any part that could be observed in the future, and therefore must be modeled to make accurate predictions. For example, if our universe is computed by one of an enumeration of Turing machines, then the other enumerations are outside our observable universe. -- Matt Mahoney, [EMAIL PROTECTED] --- On Thu, 9/4/08, Abram Demski [EMAIL PROTECTED] wrote: From: Abram Demski [EMAIL PROTECTED] Subject: Re: Computation as an explanation of the universe (was Re: [agi] Recursive self-change: some definitions) To: agi@v2.listbox.com Date: Thursday, September 4, 2008, 9:43 AM OK, then the observable universe has a finite description length. We don't need to describe anything else to model it, so by universe I mean only the observable part. But, what good is it to only have finite description of the observable part, since new portions of the universe enter the observable portion continually? Physics cannot then be modeled as a computer program, because computer programs do not increase in Kolmogorov complexity as they run (except by a logarithmic term to count how long it has been running). I am saying that the universe *is* deterministic. It has a definite quantum state, but we would need about 10^122 bits of memory to describe it. Since we can't do that, we have to resort to approximate models like quantum mechanics. Yes, I understood that you were suggesting a deterministic universe. What I'm saying is that it seems plausible for us to be able to have an accurate knowledge of that deterministic physics, lacking only the exact knowledge of particle locations et cetera. We would be forced to use probabilistic methods as you argue, but they would not necessarily be built into our physical theories; instead, our physical theories act as a deterministic function that is given probabilistic input and therefore yields probabilistic output. I believe there is a simpler description. First, the description length is increasing with the square of the age of the universe, since it is proportional to area. So it must have been very small at one time. Second, the most efficient way to enumerate all possible universes would be to run each B-bit machine for 2^B steps, starting with B = 0, 1, 2... until intelligent life is found. For our universe, B ~ 407. You could reasonably argue that the algorithmic complexity of the free parameters of string theory and general relativity is of this magnitude. I believe that Wolfram also argued that the (observable) universe is a few lines of code. I really do not understand your willingness to restrict universe to observable universe. The description length of the observable universe was very small at one time because at that time none of the basic stuffs of the universe had yet interacted, so by definition the description length of the observable universe for each basic entity is just the description length of that entity. As time moves forward, the entities interact and the description lengths of their observable universes increase. Similarly, today, one might say that the observable universe for each person is slightly different, and indeed the universe observable from my right hand would be slightly different then the one observable from my left. They could have differing description lengths. In short, I think you really want to apply your argument to the actual universe, not merely observable subsets... or if you don't, you should, because otherwise it seems like a very strange argument. But even if we discover this program it does not mean we could model the universe deterministically. We would need a computer larger than the universe to do so. Agreed... partly thanks to your argument below. There is a simple argument using information theory. Every system S has a Kolmogorov complexity K(S), which is the smallest size that you can compress a description of S to. A model of S must also have complexity K(S). However, this leaves no space for S to model itself. In particular, if all of S's memory is used to describe its model, there is no memory left over to store any results of the simulation. Point conceded. --Abram --- 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=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
Re: Computation as an explanation of the universe (was Re: [agi] Recursive self-change: some definitions)
On Thu, Sep 4, 2008 at 10:53 AM, Matt Mahoney [EMAIL PROTECTED] wrote: To clarify what I mean by observable universe, I am including any part that could be observed in the future, and therefore must be modeled to make accurate predictions. For example, if our universe is computed by one of an enumeration of Turing machines, then the other enumerations are outside our observable universe. -- Matt Mahoney, [EMAIL PROTECTED] OK, that works. But, you cannot invoke current physics to argue that this sort of observable universe is finite (so far as I know). Of course, that is not central to your point anyway. The universe might be spatially infinite while still having a finite description length. So, my only remaining objection is that while the universe *could* be computable, it seems unwise to me to totally rule out the alternative. As you said, the idea is something that makes testable predictions. So, it is something to be decided experimentally, not philosophically. -Abram --- 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=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
Re: Computation as an explanation of the universe (was Re: [agi] Recursive self-change: some definitions)
--- On Thu, 9/4/08, Abram Demski [EMAIL PROTECTED] wrote: So, my only remaining objection is that while the universe *could* be computable, it seems unwise to me to totally rule out the alternative. You're right. We cannot prove that the universe is computable. We have evidence like Occam's Razor (if the universe is computable, then algorithmically simple models are to be preferred), but that is not proof. At one time our models of physics were not computable. Then we discovered atoms, quantization of electric charge, general relativity (which bounds density and velocity), the big bang (history is finite) and quantum mechanics. Our models would still not be computable (requiring infinite description length) if any one of these events did not occur. -- Matt Mahoney, [EMAIL PROTECTED] --- 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=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
Computation as an explanation of the universe (was Re: [agi] Recursive self-change: some definitions)
I think that computation is not so much a metaphor for understanding the universe as it is an explanation. If you enumerate all possible Turing machines, thus enumerating all possible laws of physics, then some of those universes will have the right conditions for the evolution of intelligent life. If neutrons were slightly heavier than they actually are (relative to protons), then stars could not sustain fusion. If they were slightly lighter, then they would be stable and we would have no elements. Because of gravity, the speed of light, Planck's constant, the quantization of electric charge, and the finite age of the universe, the universe has a finite length description, and is therefore computable. The Bekenstein bound of the Hubble radius is 2.91 x 10^122 bits. Any computer within a finite universe must have less memory than it, and therefore cannot simulate it except by using an approximate (probabilistic) model. One such model is quantum mechanics. For the same reason, an intelligent agent (which must be Turing computable if the universe is) cannot model itself, except probabilistically as an approximation. Thus, we cannot predict what we will think without actually thinking it. This property makes our own intelligence seem mysterious. An explanation is only useful if it makes predictions, and it does. If the universe were not Turing computable, then Solomonoff induction and AIXI as ideal models of prediction and intelligence would not be applicable to the real world. Yet we have Occam's Razor and find in practice that all successful machine learning algorithms use algorithmically simple hypothesis sets. -- Matt Mahoney, [EMAIL PROTECTED] --- On Wed, 9/3/08, Terren Suydam [EMAIL PROTECTED] wrote: From: Terren Suydam [EMAIL PROTECTED] Subject: Re: [agi] Recursive self-change: some definitions To: agi@v2.listbox.com Date: Wednesday, September 3, 2008, 4:17 PM Hi Ben, My own feeling is that computation is just the latest in a series of technical metaphors that we apply in service of understanding how the universe works. Like the others before it, it captures some valuable aspects and leaves out others. It leaves me wondering: what future metaphors will we apply to the universe, ourselves, etc., that will make computation-as-metaphor seem as quaint as the old clockworks analogies? I believe that computation is important in that it can help us simulate intelligence, but intelligence itself is not simply computation (or if it is, it's in a way that requires us to transcend our current notions of computation). Note that I'm not suggesting anything mystical or dualistic at all, just offering the possibility that we can find still greater metaphors for how intelligence works. Either way though, I'm very interested in the results of your work - at worst, it will shed some needed light on the subject. At best... well, you know that part. :-] Terren --- On Tue, 9/2/08, Ben Goertzel [EMAIL PROTECTED] wrote: From: Ben Goertzel [EMAIL PROTECTED] Subject: Re: [agi] Recursive self-change: some definitions To: agi@v2.listbox.com Date: Tuesday, September 2, 2008, 4:50 PM On Tue, Sep 2, 2008 at 4:43 PM, Eric Burton [EMAIL PROTECTED] wrote: I really see a number of algorithmic breakthroughs as necessary for the development of strong general AI I hear that a lot, yet I never hear any convincing arguments in that regard... So, hypothetically (and I hope not insultingly), I tend to view this as a kind of unconscious overestimation of the awesomeness of our own species ... we feel intuitively like we're doing SOMETHING so cool in our brains, it couldn't possibly be emulated or superseded by mere algorithms like the ones computer scientists have developed so far ;-) 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=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
Re: Computation as an explanation of the universe (was Re: [agi] Recursive self-change: some definitions)
Matt, I have several objections. First, as I understand it, your statement about the universe having a finite description length only applies to the *observable* universe, not the universe as a whole. The hubble radius expands at the speed of light as more light reaches us, meaning that the observable universe has a longer description length every day. So it does not seem very relevant to say that the description length is finite. The universe as a whole (observable and not-observable) *could* be finite, but we don't know one way or the other so far as I am aware. Second, I do not agree with your reason for saying that physics is necessarily probabilistic. It seems possible to have a completely deterministic physics, which merely suffers from a lack of information and computation ability. Imagine if the universe happened to follow Newtonian physics, with atoms being little billiard balls. The situation is deterministic, if only we knew the starting state of the universe and had large enough computers to approximate the differential equations to arbitrary accuracy. Third, this is nitpicking, but I also am not sure about the argument that we cannot predict our thoughts. It seems formally possible that a system could predict itself. The system would need to be compressible, so that a model of itself could fit inside the whole. I could be wrong here, feel free to show me that I am. Anyway, the same objection also applies back to the necessity of probabilistic physics: is it really impossible for beings within a universe to have an accurate compressed model of the entire universe? (Similarly, if we have such a model, could we use it to run a simulation of the entire universe? This seems much less possible.) --Abram On Wed, Sep 3, 2008 at 6:45 PM, Matt Mahoney [EMAIL PROTECTED] wrote: I think that computation is not so much a metaphor for understanding the universe as it is an explanation. If you enumerate all possible Turing machines, thus enumerating all possible laws of physics, then some of those universes will have the right conditions for the evolution of intelligent life. If neutrons were slightly heavier than they actually are (relative to protons), then stars could not sustain fusion. If they were slightly lighter, then they would be stable and we would have no elements. Because of gravity, the speed of light, Planck's constant, the quantization of electric charge, and the finite age of the universe, the universe has a finite length description, and is therefore computable. The Bekenstein bound of the Hubble radius is 2.91 x 10^122 bits. Any computer within a finite universe must have less memory than it, and therefore cannot simulate it except by using an approximate (probabilistic) model. One such model is quantum mechanics. For the same reason, an intelligent agent (which must be Turing computable if the universe is) cannot model itself, except probabilistically as an approximation. Thus, we cannot predict what we will think without actually thinking it. This property makes our own intelligence seem mysterious. An explanation is only useful if it makes predictions, and it does. If the universe were not Turing computable, then Solomonoff induction and AIXI as ideal models of prediction and intelligence would not be applicable to the real world. Yet we have Occam's Razor and find in practice that all successful machine learning algorithms use algorithmically simple hypothesis sets. -- Matt Mahoney, [EMAIL PROTECTED] --- On Wed, 9/3/08, Terren Suydam [EMAIL PROTECTED] wrote: From: Terren Suydam [EMAIL PROTECTED] Subject: Re: [agi] Recursive self-change: some definitions To: agi@v2.listbox.com Date: Wednesday, September 3, 2008, 4:17 PM Hi Ben, My own feeling is that computation is just the latest in a series of technical metaphors that we apply in service of understanding how the universe works. Like the others before it, it captures some valuable aspects and leaves out others. It leaves me wondering: what future metaphors will we apply to the universe, ourselves, etc., that will make computation-as-metaphor seem as quaint as the old clockworks analogies? I believe that computation is important in that it can help us simulate intelligence, but intelligence itself is not simply computation (or if it is, it's in a way that requires us to transcend our current notions of computation). Note that I'm not suggesting anything mystical or dualistic at all, just offering the possibility that we can find still greater metaphors for how intelligence works. Either way though, I'm very interested in the results of your work - at worst, it will shed some needed light on the subject. At best... well, you know that part. :-] Terren --- On Tue, 9/2/08, Ben Goertzel [EMAIL PROTECTED] wrote: From: Ben Goertzel [EMAIL PROTECTED] Subject: Re: [agi] Recursive self-change: some definitions To: agi@v2.listbox.com Date:
Re: Computation as an explanation of the universe (was Re: [agi] Recursive self-change: some definitions)
--- On Wed, 9/3/08, Abram Demski [EMAIL PROTECTED] wrote: From: Abram Demski [EMAIL PROTECTED] Subject: Re: Computation as an explanation of the universe (was Re: [agi] Recursive self-change: some definitions) To: agi@v2.listbox.com Date: Wednesday, September 3, 2008, 7:35 PM Matt, I have several objections. First, as I understand it, your statement about the universe having a finite description length only applies to the *observable* universe, not the universe as a whole. The hubble radius expands at the speed of light as more light reaches us, meaning that the observable universe has a longer description length every day. So it does not seem very relevant to say that the description length is finite. The universe as a whole (observable and not-observable) *could* be finite, but we don't know one way or the other so far as I am aware. OK, then the observable universe has a finite description length. We don't need to describe anything else to model it, so by universe I mean only the observable part. Second, I do not agree with your reason for saying that physics is necessarily probabilistic. It seems possible to have a completely deterministic physics, which merely suffers from a lack of information and computation ability. Imagine if the universe happened to follow Newtonian physics, with atoms being little billiard balls. The situation is deterministic, if only we knew the starting state of the universe and had large enough computers to approximate the differential equations to arbitrary accuracy. I am saying that the universe *is* deterministic. It has a definite quantum state, but we would need about 10^122 bits of memory to describe it. Since we can't do that, we have to resort to approximate models like quantum mechanics. I believe there is a simpler description. First, the description length is increasing with the square of the age of the universe, since it is proportional to area. So it must have been very small at one time. Second, the most efficient way to enumerate all possible universes would be to run each B-bit machine for 2^B steps, starting with B = 0, 1, 2... until intelligent life is found. For our universe, B ~ 407. You could reasonably argue that the algorithmic complexity of the free parameters of string theory and general relativity is of this magnitude. I believe that Wolfram also argued that the (observable) universe is a few lines of code. But even if we discover this program it does not mean we could model the universe deterministically. We would need a computer larger than the universe to do so. Third, this is nitpicking, but I also am not sure about the argument that we cannot predict our thoughts. It seems formally possible that a system could predict itself. The system would need to be compressible, so that a model of itself could fit inside the whole. I could be wrong here, feel free to show me that I am. Anyway, the same objection also applies back to the necessity of probabilistic physics: is it really impossible for beings within a universe to have an accurate compressed model of the entire universe? (Similarly, if we have such a model, could we use it to run a simulation of the entire universe? This seems much less possible.) There is a simple argument using information theory. Every system S has a Kolmogorov complexity K(S), which is the smallest size that you can compress a description of S to. A model of S must also have complexity K(S). However, this leaves no space for S to model itself. In particular, if all of S's memory is used to describe its model, there is no memory left over to store any results of the simulation. --Abram On Wed, Sep 3, 2008 at 6:45 PM, Matt Mahoney [EMAIL PROTECTED] wrote: I think that computation is not so much a metaphor for understanding the universe as it is an explanation. If you enumerate all possible Turing machines, thus enumerating all possible laws of physics, then some of those universes will have the right conditions for the evolution of intelligent life. If neutrons were slightly heavier than they actually are (relative to protons), then stars could not sustain fusion. If they were slightly lighter, then they would be stable and we would have no elements. Because of gravity, the speed of light, Planck's constant, the quantization of electric charge, and the finite age of the universe, the universe has a finite length description, and is therefore computable. The Bekenstein bound of the Hubble radius is 2.91 x 10^122 bits. Any computer within a finite universe must have less memory than it, and therefore cannot simulate it except by using an approximate (probabilistic) model. One such model is quantum mechanics. For the same reason, an intelligent agent (which must be Turing computable if the universe is) cannot model itself, except probabilistically as an approximation. Thus, we cannot predict what we
