Xref: utzoo comp.ai:6070 sci.philosophy.tech:2155 Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!usc!apple!sun-barr!newstop!sun!amdahl!kp From: kp@uts.amdahl.com (Ken Presting) Newsgroups: comp.ai,sci.philosophy.tech Subject: Re: Another letter to the New York Review Summary: General Simulation Strategy. Keywords: Penrose, Moravec Message-ID: <2al902Zg8bnn01@amdahl.uts.amdahl.com> Date: 24 Feb 90 02:13:47 GMT References: <18883@bcsaic.UUCP> <1589@skye.ed.ac.uk> <11488@venera.UUCP> <1754@skye.ed.ac.uk> <90Feb15.231415est.6212@neat.cs.toronto.edu> Reply-To: kp@amdahl.uts.amdahl.com (Ken Presting) Organization: Amdahl Corporation, Sunnyvale CA Lines: 125 In article <90Feb15.231415est.6212@neat.cs.toronto.edu> radford@ai.toronto.edu (Radford Neal) writes: >In article kp@amdahl.uts.amdahl.com (Ken Presting) writes: >>It is not correct that calculations or algorithms are less powerful >>than other mathematical notations (such as the differential equations >>used to express the laws of physics), as Penrose suggests. Any >>mathematical description of a physical object (such as the brain) may >>be directly translated into a computer program, with no loss of >>information. This claim is a consequence of mathematical theorems which >>are certainly familiar to Penrose. > >I think you have missed Penrose's point, here. I have only just >started reading _The Emperor's New Mind_, but from what I have read, >it is clear that Penrose believes that the (true) laws of physics are >_not_ computable, and that neurons somehow make use of these laws >to perform non-computable operations. Penrose is also quite aware that >the _currently accepted_ laws of physics _are_ computable, so pointing >this out is not an argument against his views. Maybe I need to extend this paragraph. If some hypothesis is proposed, then to test the hypothesis it is necessary to draw conclusions from it (combined with assertions regrading initial conditions, state functions, etc). The hypothesis is disconfirmed if the conclusions mismatch observation. Confirmation is harder to define, but we can say that the hypothesis is succesfully tested when conclusions based on it match observation. As Ray Allis has observed in this group, a computer simulation operates by drawing conclusions from the description of a system. Now, any conclusion which might be drawn by a physicist can also be drawn by a computer (by enumeration, if the theory is stated in a complete logic). Therefore, if a physical hypothesis has been successfully tested for a given system, the physicists have *nothing* to say about that system which the programmers can't match. So my point is not that a computer program can always update its variables to match the trajectory of any physical system through its phase space. Last month I argued to the contrary. My point is that whatever claims the physicists care to make about the trajectory must be stated in finite notations, and are therefore susceptible to automated enumeration of consequences. A related point holds for measurements of initial conditions - sure, there may be an infinite amount of info in a real analog system, but when you measure it, you get a finite amount of info. There is a problem with getting the enumeration to run in real time. The elapsed time for a physical system to traverse a trajectory is not related to the length of the enumeration of assertions *about* the trajectory. If the trajectory is chaotic, then there is no upper bound on the number of significant digits needed to represent the trajectory, and no upper bound on the length of the assertions in the enumeration. So if brain processes are chaotic, we can't use our deductive simulator to control a robot in a real time duplication of some human's behavior. But the finiteness of measurements and the need to test physical hypotheses is significant here also. Suppose we truncate our significant digits (ouch), and run our simulation in real time. Then we try to compare the behavior of the robot to the behavior of a real person. They won't match, but there's no way to tell if the mismatch is due to unmeasurable discrepancies in the initial conditions, or to inaccurate simulation of the trajectory. Of course, if we let slip to the testers that the robot is computer-controlled, they'll know for sure that there are inaccuracies in the simulation. But they could never figure that out by external observation - experimental runs on chaotic systems are inherently unrepeatable. The best they could do is run many tests, looking for statistical deviations between the real person and the robot. Eventually, they'll find some, but we can always add a significant digit and force them to make the testing process take longer than a lifetime. (To get the simulation to run in real time at all requires that a more efficient algorithm than enumeration of assertions be used. I'd rather stick with enumeration and assume that a non-deterministic TM do the enumeration, just for elegance. Associative memory will give us real machines with non-deterministic speed, for finite problems) It is especially interesting that the designers (and testers) of an AI constructed out of analog devices are protected (or hampered) by similar phenomena. The specifications for the analog hardware must be finitely stated, the accuracy of the construction can be verified only down to a finite tolerance, the components' behavior can be predicted with only finite accuracy, and the initial state can be measured with limited precision. So if there is something very very small, but very very important about being born (for example), and we don't notice it, and therefore we can't give the same property to something that we build, then it won't help us at all to have a non-symbolic AI. If nobody noticed and described "that certain something", then no way can we build it into anything. But if we can build it, we can also program it. To sum up, the hypothetical uncomputability of any hypothetical laws of physics is just irrelevant. We'll crunch the same symbols the *physicists* crunch. Who cares what the *particles* compute? I feel a little sheepish making this argument, after having fanatically argued against the "if all else fails, we can simulate the brain" view so recently. The key idea here - the finiteness of scientific method - had not occurred to me before I got into Penrose' book myself. Still, I think my position here is consistent with my former arguments. I see no way to be sure that any given simulation will capture *everything* about an arbitrary physical process. I also see no way to be sure that the inevitable inaccuracies in a simulation will not leave out something important. I agree with Penrose that a computer simulation necessarily diverges from the system it describes. I deny the possibility that the difference is necessarily significant. I guess I'll leave the paragraph as it was. >Unlike the Chinese Room, Penrose's argument makes perfect sense to me. >I don't believe it (as yet), but that's just because I think the >possibility that the real laws of physics are non-computable is remote, >and the possibility that this would make any difference to the operation >of neurons even if it was true is even more remote. They both make sense to me. Searle's are more useful, I think. >But who knows? Maybe he's right. The only way to refute him is to >succeed in creating an artificial intelligence. I certainly hope none >of the proponents of "strong AI" think they've proved _their_ position >in the absense of such a demonstration. > > Radford Neal Thank you for your comments. Ken Presting