tedrick@ucbernie.BERKELEY.EDU (Tom Tedrick) (10/16/85)
In article <272@umich.UUCP> torek@umich.UUCP (Paul V. Torek ) writes: >In article <10642@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes: >>...for any particular Turing machine there are certain >>statements that the human mind can recognize as true (again with >>the consistency assumption), that the machine cannot recognize >>as true. >> >>Does anyone dispute this? > >Yes. If the human brain is essentially a Turing machine, then for any >particular human (or group of them) there is at least one statement that >he (they) cannot recognize as true. Not very earthshattering, given that >there are probably lots of complex mathematical theorems which are true >but which no human will ever recognize as true. > >--Paul V Torek torek@umich I don't understand your argument. I claim that the human mind cannot be essentially a turing machine. If we assume that a partcular mind is equivalant to a particular turing machine, then we immediately get a contradiction, namely there exists a statement recognizable as true by that human mind which is not recognizable as true by that turing machine. Can anyone explain to me what if anything is wrong with my reasoning? Thanks very much, -Tom tedrick@ucbernie.ARPA
torek@umich.UUCP (Paul V. Torek ) (10/17/85)
In article <10671@ucbvax.ARPA> tedrick (Tom Tedrick) writes: >>there are probably lots of complex mathematical theorems which are true >>but which no human will ever recognize as true. > >I don't understand your argument. I claim that the human mind >cannot be essentially a turing machine. If we assume that a >partcular mind is equivalant to a particular turing machine, >then we immediately get a contradiction, namely there exists >a statement recognizable as true by that human mind which is >not recognizable as true by that turing machine. Which one? The statement that is not recognizable by the Turing machine may be *extremely* complex -- what makes you so damn sure you could recognize it as true? Tell me, Tom, is it true that every even number greater than two is the sum of two primes? What, you don't know? Then you get the point -- I hope. --Paul V Torek, making flames the old-fashioned way -- earning them.
lambert@boring.UUCP (10/18/85)
(I have missed most of the discussion, since American net philosophy does not make it to this side of the Atlantic.) > I don't understand your argument. I claim that the human mind > cannot be essentially a turing machine. If we assume that a > partcular mind is equivalant to a particular turing machine, > then we immediately get a contradiction, namely there exists > a statement recognizable as true by that human mind which is > not recognizable as true by that turing machine. > Can anyone explain to me what if anything is wrong with my > reasoning? The following attempt uses a device that is, unless I am mistaken, due to Quine. Consider texts (some of which represent statements, such as: "Two times two equals four" and "`Two times two equals four' is a true statement about natural numbers", and some of which do not, like "Who? Me?" and "Don't `Aw, mom' me".). Some of these texts contain *internal* quoted texts. If T is a text, then let Q(T), or, in words, T *quoted*, stand for another text, consisting of T put between the quotes "`" and "'". So if T is "Two times two equals for", Q(T) is "`Two times two equals for'". Let SQ(T), or T *self*quoted, mean: Q(T) followed by T. So if T is " contains no digits" then T, selfquoted, is "` contains no digits' contains no digits" (which is a true statement). Now consider the text S = "`, selfquoted, is not recognizable as true by the mind of Tom', selfquoted, is not recognizable as true by the mind of Tom". S is a statement, and states that some text T, selfquoted, is not recognizable as true by the mind of Tom. So can Tom (or his mind) recognize SQ(T) as true, and is SQ(T) true in the first place? If Tom can recognize SQ(T) as true, then S is apparently false. But note that T is the text ", selfquoted, is not recognizable as true by the mind of Tom", so SQ(T) = S. So Tom would have recognized a false statement as true. If we collectively assume that Tom would never do such a thing, then all of us non-Toms can now recognize S as true, something Tom can not. If "Tom" is consistently replaced by "human being", then the argument still goes through. Neither I, nor you, or anyone else, can recognize that statement as true without showing its falsehood (and human fallibility). We would have to wait for some non-human intelligence telling us it is true, but although we might believe it, we still could not recognize it as being true. (Now we might think that it is false, which may or may not be quite true, but than it follows again that not all humans can be infallible.) This may all seem shallow. But for me (to take an arbitrary example:-) to assert that the mind of a fellow human being can recognize something as true, with the same level of certainty as in mathematical proofs, requires a rather total understanding of that mind, that, at least for me, is still lacking. More so, if I would also have to recognize the infallibility of that mind (which is all the time an implicit argument). With my own mind, I thus far have not succeeded. I guess it is the same for other people. What the original reasoning really shows is that if we would, somehow, construct a Turing-machine description of the workings of our own mind, we could not with mathematical certainty recognize it as being that. Neither can a Turing machine do this for its own construction, or if it can, then it is either fallible or has glaring defects in its logical power. Applied to human beings, the conclusion is not a big surprise. It does not follow that human minds are not Turing machines (although their memory tapes seem not to be infinite:-). -- Lambert Meertens ...!{seismo,okstate,garfield,decvax,philabs}!lambert@mcvax.UUCP CWI (Centre for Mathematics and Computer Science), Amsterdam
tedrick@ucbernie.BERKELEY.EDU (Tom Tedrick) (10/18/85)
In article <299@umich.UUCP> torek@umich.UUCP (Paul V. Torek ) writes: >In article <10671@ucbvax.ARPA> tedrick (Tom Tedrick) writes: > >>>there are probably lots of complex mathematical theorems which are true >>>but which no human will ever recognize as true. >> >>I don't understand your argument. I claim that the human mind >>cannot be essentially a turing machine. If we assume that a >>partcular mind is equivalant to a particular turing machine, >>then we immediately get a contradiction, namely there exists >>a statement recognizable as true by that human mind which is >>not recognizable as true by that turing machine. > >Which one? The statement that is not recognizable by the Turing >machine may be *extremely* complex -- what makes you so damn sure >you could recognize it as true? Tell me, Tom, is it true that every >even number greater than two is the sum of two primes? What, you don't >know? Then you get the point -- I hope. No, I don't get the point. The complexity of the statement is not the issue. The issue is that humans seem to recognize that certain formal systems are consistent, but that this consistency cannot be proved within the system. This mysterious ability to recognize such things being something lacking in deterministic machines, I claim there is a distinction between the human mind and any Turing machine. Of course, I may be wrong in believing that these formal systems are consistent.
jwl@ucbvax.ARPA (James Wilbur Lewis) (10/18/85)
In article <10699@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes: > >No, I don't get the point. The complexity of the statement is not >the issue. The issue is that humans seem to recognize that certain >be proved within the system. This mysterious ability to recognize >such things being something lacking in deterministic machines, >I claim there is a distinction between the human mind and any >Turing machine. > >Of course, I may be wrong in believing that these formal >systems are consistent. Your points seem to be: (1) Humans can recognize consistency of certain formal systems, and machines lack this ability . (2) There is something mysterious about this ability, and nondeterminism has something to do with it; therefore (3) no Turing machine can be equivalent to a human mind. You are confusing two issues: reasoning *within* a formal system, and reasoning *about* a formal system. What is so mysterious about the latter kind of reasoning? All one needs to do is define a more powerful system, and then by reasoning within the new system you can show the incompleteness/inconsistency/whatever of the weaker system. Of course, the formal system for any given Turing machine is fixed, and that machine will be unable to 'jump out of the system' to reason about its own properties. But we can always design a more powerful machine which *will* be able to reason about the weaker one. Humans are subject to these constraints, too. Consider: "Tom Tedrick cannot consistently assert this proposition." I can prove it, but you can't do so and remain consistent. Does that make my mind more powerful than yours? Of course not, because you can exhibit the obvious proposition which *you* can prove but *I* can't (assuming I'm consistent! :-) Your mention of determinism is irrelevant; humans are just as deterministic as machines. Unpredictable, perhaps...since we are orders of magnitude more complex than any machines we know how to build....but subject to the same laws of physics. For a fascinating presentation of this and many other topics, check out any book by Douglas Hofstadter, especially "Godel, Escher, Back: An Eternal Golden Braid". Cheers, -- Jim 'down with human chauvinism' Lewis U. C. Berkeley ...!ucbvax!jwl jwl@ucbernie.BERKELEY.EDU "Lately it occurs to me What a long, strange trip it's been..."
tedrick@ucbernie.BERKELEY.EDU (Tom Tedrick) (10/18/85)
>>I claim there is a distinction between the human mind and any >>Turing machine. >Your points seem to be: >(1) Humans can recognize consistency of certain formal systems, and > machines lack this ability . >(2) There is something mysterious about this ability, and nondeterminism > has something to do with it; therefore [I didn't say anything about nondeterminism, just that the turing machines I am talking about are deterministic.] >(3) no Turing machine can be equivalent to a human mind. >You are confusing two issues: reasoning *within* a formal system, and >reasoning *about* a formal system. [I don't think that is what I am confused about.] >What is so mysterious about the >latter kind of reasoning? All one needs to do is define a more powerful >system, and then by reasoning within the new system you can show the >incompleteness/inconsistency/whatever of the weaker system. >Of course, the formal system for any given Turing machine is fixed, and >that machine will be unable to 'jump out of the system' to reason >about its own properties. But we can always design a more powerful >machine which *will* be able to reason about the weaker one. [Yes, this is exactly the point. Exhibit the turing machine that is claimed to be equivalent to the human mind, and the human mind can reason about the system in ways impossible within the system. Thus we contradict the assumption that the machine was equivalent to the mind.] >Your mention of determinism is irrelevant; humans are just as deterministic >as machines. Unpredictable, perhaps...since we are orders of magnitude more >complex than any machines we know how to build....but subject to the same >laws of physics. OK, we at least have a clear point of disagreement. I don't believe human beings are deterministic. I also don't accept the laws of physics as absolute. I accept them as an absolutely brilliant model but not as complete truth. I don't accept the notion that the human being is just a very complex machine. I originally asked whether anyone disputed my claim that the human mind is not equivalent to a turing machine. After all the negative response, I would like to change my question to: *IS THERE ANYONE THAT AGREES WITH ME THAT THE HUMAN MIND IS PROVABLY NOT EQUIVALENT TO A TURING MACHINE?* "Help, I'm trapped in a machine :-)" -Beleaguered and beseiged on all fronts by the upholders of the dignity of turing machines, I remain -Tom the Human tedrick@ucbernie.ARPA
jwl@ucbvax.ARPA (James Wilbur Lewis) (10/18/85)
In article <10702@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes: > >>What is so mysterious about the >>latter kind of reasoning? All one needs to do is define a more powerful >>system, and then by reasoning within the new system you can show the >>incompleteness/inconsistency/whatever of the weaker system. >>Of course, the formal system for any given Turing machine is fixed, and >>that machine will be unable to 'jump out of the system' to reason >>about its own properties. But we can always design a more powerful >>machine which *will* be able to reason about the weaker one. > >[Yes, this is exactly the point. Exhibit the turing machine that >is claimed to be equivalent to the human mind, and the human mind >can reason about the system in ways impossible within the system. >Thus we contradict the assumption that the machine was equivalent >to the mind.] Foo! By reasoning about an equivalent Turing machine, the human mind is *also* constrained to operate within the system. No fair jumping out of the system here. I ask again: what is your basis for claiming that human reasoning can't be duplicated by a 'mere' machine, at least in principle? Are you saying that machines are incapable of the kind of reasoning involved in, say, the proof of Godel's Incompleteness Theorem? > >OK, we at least have a clear point of disagreement. I don't believe >human beings are deterministic. I also don't accept the laws of >physics as absolute. I accept them as an absolutely brilliant >model but not as complete truth. I don't accept the notion that >the human being is just a very complex machine. > I'm not sure why this is relevant. Are you saying the laws of physics are incomplete (because we don't know them all yet?) Or that certain phenomena are inherently inexplicable by ANY laws of physics, a la religious arguments? Whatever those laws of physics are, humans and machines both must obey them. > > -Tom the Human > tedrick@ucbernie.ARPA -- Jim Lewis, a Lean Mean Computing Machine! U. C. Berkeley ...!ucbvax!jwl jwl@ucbernie.BERKELEY.EDU
mj@myrias.UUCP (Michal Jaegermann) (10/19/85)
I am afraid that a lot confusion comes from a simple mix-up (which took quite a while for logicians to sort out :-) ). When somebody speaks about Turing Machines, Goedel Theorem and things of that sort truth and provability is understood >>within confines of a given FORMAL system<<. You may always give answer to some "unanswerable" questions if you will get out and look from "outside" (meta-reasoning). In everyday use of logic and truth we are mixing freely different meta-levels - which creates a lot of interesting and often funny paradoxes. Which probably indicates that formal logic and Turing Machines are only quite simple MODELS of our reasonig and that a human brain is not a Turing Machine (this goes far beyond mathematics, so I better stop). If you are finding "Goedel, Escher, Bach" too wordy and muddy. though funny and inspiring, and you do not want to wade through monographies on formal mathematical logic then find a book by R. Smullyan with a name "What is a name of this book?" to find a lot answers and questions related to the problem. So how is that book really called? Michal Jaegermann Myrias Research Corporation ....ihnp4!alberta!myrias!mj
rlr@pyuxd.UUCP (Rich Rosen) (10/20/85)
>>Your points seem to be: >>(1) Humans can recognize consistency of certain formal systems, and >> machines lack this ability . >>(2) There is something mysterious about this ability, and nondeterminism >> has something to do with it; therefore >>(3) no Turing machine can be equivalent to a human mind. >>You are confusing two issues: reasoning *within* a formal system, and >>reasoning *about* a formal system. > [I don't think that is what I am confused about.] [TEDRICK] If you understand what you're confused about, you're not confused about it. > [Yes, this is exactly the point. Exhibit the turing machine that > is claimed to be equivalent to the human mind, and the human mind > can reason about the system in ways impossible within the system. > Thus we contradict the assumption that the machine was equivalent > to the mind.] > OK, we at least have a clear point of disagreement. I don't believe > human beings are deterministic. I also don't accept the laws of > physics as absolute. I accept them as an absolutely brilliant > model but not as complete truth. I don't accept the notion that > the human being is just a very complex machine. The only reasons for doing so would be that you either have some evidence that this is not so, or you simply refuse to believe it because you don't like that conclusion. The first possibility (which I doubt is true) would be reasonable. The second (which is engaged in by a large number of people in this very newsgroup) is fallacious. > I originally asked whether anyone disputed my claim that the human > mind is not equivalent to a turing machine. After all the negative > response, I would like to change my question to: > > *IS THERE ANYONE THAT AGREES WITH ME THAT THE HUMAN MIND IS PROVABLY > NOT EQUIVALENT TO A TURING MACHINE?* I could care less about the exact type of machine that the human mind really is, but I have no disagreement with the notion that the mind and brain are represented as some sort of machine. To throw yet another bone into this mix, I will quote from the oft-misquoted (at least here) John Searle, from his "Minds, Brains, and Programs": I want to try and state some of the general philosophical points implicit in the argument. For clarity I will try to do it in a question and answer fashion, and I begin with that old chestnut of a question: "Could a machine think?" The answer is, obviously, yes. We are precisely such machines. "Yes, but could an artifact, a man-made machine, think?" Assuming it is possible to produce artificially a machine with a nervous system, neurons, axions, and dendrites, and all the rest of it, sufficiently like ours, again the answer to the question seems to be, obviously, yes. If you can exactly duplicate the causes, you could duplicate the effects. And indeed it might be possible to produce consciousness, intentionality, and all the rest of it using some other sorts of chemical principles than those human beings use. [ALL THIS, MIND YOU, FROM A "CRITIC" OF AI!] "OK, but could a digital computer think?" If by "digital computer" we mean anything at all that has a level of description where it can be correctly described as the instantiation of a computer program, then again the answer is, of course, yes, since we are the instantiations of any number of computer programs, and we can think. "But could something think, understand, and so on *solely* in virtue of being a computer with the right sort of program? Could instantiating a program, the right program of course, by itself be a sufficient condition of understanding?" This I think is the right question to ask, though it is usually confused with one of the earlier questions, and the answer to it is no. "Why not?" Because the formal symbol manipulations themselves don't have any intentionality... I think at this point Searle destroys his own argument. By saying that these things have "no intentionality", he is denying the premise made by the person asking the question, that we are talking about "the right program". Moreover, Hofstadter and Dennett both agreed (!!!!) that Searle's argument is flawed. "He merely asserts that some systems have intentionality by virtue of their 'causal powers' and that some don't. Sometimes it seems that the brain is composed of 'the right stuff', but other times it seems to be something else. It is whatever is convenient at the moment." (Sound like any other conversers in this newsgroup?) "Minds exist in brains and may come to exist in programmed machines. If and when such machines come about, their causal powers will derive not from the substances they are made of, *but* *from* *their* *design* *and* *the* *programs* *that* *run* *in* *them*. [ITALICS MINE] And the way we will know they have those causal powers is by talking by them and listening carefully to what they they have to say." Readers of this newsgroup should take note of how a non-presumptive position is built, and of how someone quoted right and left in this newsgroup doesn't even agree halfheartedly with the notions of those quoting him. -- Anything's possible, but only a few things actually happen. Rich Rosen pyuxd!rlr
laura@l5.uucp (Laura Creighton) (10/20/85)
In article <10702@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes: >*IS THERE ANYONE THAT AGREES WITH ME THAT THE HUMAN MIND IS PROVABLY > NOT EQUIVALENT TO A TURING MACHINE?* Me. But not for the reasons that you give. Aristotle propsoed the definiton ``man is a rational animal''. In recent years we have worked very hard on the ``rational'' part but not very hard on the ``animal'' part. I think that the concept of ``living'' is very important to the concept of ``mind''. This does not meant htat it is impossible to construct a living turing machine, but this is not where the efforts in AI have been spent so far. I fear that intelligence may be the easy part, and that it is AL (artificial life) which is the tough one. Laura Creighton l5!laura what's life to an immortal? -- Laura Creighton sun!l5!laura (that is ell-five, not fifteen) l5!laura@lll-crg.arpa
matt@oddjob.UUCP (Matt Crawford) (10/22/85)
In article <10702@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes: > >*IS THERE ANYONE THAT AGREES WITH ME THAT THE HUMAN MIND IS PROVABLY > NOT EQUIVALENT TO A TURING MACHINE?* Sure, I agree with you. A Turing machine has unlimited memory. _____________________________________________________ Matt University crawford@anl-mcs.arpa Crawford of Chicago ihnp4!oddjob!matt
mcewan@uiucdcs.CS.UIUC.EDU (10/24/85)
> [Yes, this is exactly the point. Exhibit the turing machine that > is claimed to be equivalent to the human mind, and the human mind > can reason about the system in ways impossible within the system. > Thus we contradict the assumption that the machine was equivalent > to the mind.] As far as I can see, your complete argument is: assumption: The human mind can do things that no machine can do. oconclusion: The human mind can do things that no machine can do. I can't argue with your reasoning, but I can't say that I'm impressed. Scott McEwan {ihnp4,pur-ee}!uiucdcs!mcewan "There are good guys and there are bad guys. The job of the good guys is to kill the bad guys."
dim@whuxlm.UUCP (McCooey David I) (10/25/85)
> In article <10702@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes: > > > >*IS THERE ANYONE THAT AGREES WITH ME THAT THE HUMAN MIND IS PROVABLY > > NOT EQUIVALENT TO A TURING MACHINE?* > > Sure, I agree with you. A Turing machine has unlimited memory. > _____________________________________________________ > Matt University crawford@anl-mcs.arpa > Crawford of Chicago ihnp4!oddjob!matt Matt's reply goes along with my line of thought. Consider the situation realistically: The human mind has a finite number of neurons and therefore a finite number of states. So I propose that the human mind is equivalent to a finite state machine, not a Turing machine. (I agree with Tom, but for the opposite reasons). Note that my comparison does not belittle the human mind at all. Finite can still mean very, very large. The operation of a finite state machine with a very large number of states is, for humans, indistinguishable from that of a Turing machine. Dave McCooey AT&T Bell Labs, Whippany, NJ ihnp4!whuxlm!dim or ...!whlmos!dim
cleary@calgary.UUCP (John Cleary) (10/26/85)
> > [Yes, this is exactly the point. Exhibit the Turing machine that > > is claimed to be equivalent to the human mind, and the human mind > > can reason about the system in ways impossible within the system. > > Thus we contradict the assumption that the machine was equivalent > > to the mind.] This is a very crucial point in this discussion I think. This is only true IF we assume that the human mind that is doing the reasoning is not itself part of the Turing machine being exhibited. The problem is that the physical boundary about a human is most unclear. The wiggling of an electron on Alpha Centauri might via changes in gravitation affect the firing of one of my neurons and so alter my behaviour. From this (extreme) example we have to include the whole universe in the description of the human. That is anything which can affect us (and so observable by us) must be included in a complete description of our behaviour. The set of all things observable by us (or potentially observable by us) can validly be called the whole universe. Unfortunately the whole universe includes all entities that can observe us and hence reason about us (remember Heisenberg, if it can observe you then it can affect you). The interesting thing about digital computers is that we confuse two things, the actual physical machine and its abstract description. The physical machine just like a human needs the whole universe included in it to describe it. The abstraction (what is described in the manuals) is an approxiamtion only. It is proably unclear from the abstract description what happens when a high energy gamma ray passes through the CPU chip. So I agree with those who say a digital computer AS DESCRIBED BY A FORMAL SYSTEM cannot have the same status as a human. However there is no reason we know of at the moment why a physical system cannot, indeed as the description of the physical computer includes the whole universe and the humans in it, it already has the same status as the human. This then raises some fascinating questions: 1) Church's thesis that all computers are equivalent to a Turing machine. This is actually a PHYSICAL law (like law of gravitation) potentially subject to a physical experiment. It is conceivable for example that some of the pecualiar effects of quantum mechanics could allow calculations faster than any possible Turing machine. 2) Is the entire universe a Turing machine? 3) Is it conceivable that any thing part of the universe could verify or refute 2)? I am also struck by the similarity of the conclusions of some philosophers from the Eastern tradition that we are all intimately connected with the whole universe. > > I originally asked whether anyone disputed my claim that the human > > mind is not equivalent to a turing machine. After all the negative > > response, I would like to change my question to: > > > > *IS THERE ANYONE THAT AGREES WITH ME THAT THE HUMAN MIND IS PROVABLY > > NOT EQUIVALENT TO A TURING MACHINE?* See above. I think this is a question for the physicists, and potentially subject to physicl experiment. > > "OK, but could a digital computer think?" > > If by "digital computer" we mean anything at all that has a level > of description where it can be correctly described as the instantiation > of a computer program, then again the answer is, of course, yes, since > we are the instantiations of any number of computer programs, and we > can think. No I disagree, here he talks about the abstract machine. > > "But could something think, understand, and so on *solely* > in virtue of being a computer with the right sort of program? > Could instantiating a program, the right program of course, > by itself be a sufficient condition of understanding?" > > This I think is the right question to ask, though it is usually > confused with one of the earlier questions, and the answer to it is no. > > "Why not?" > > Because the formal symbol manipulations themselves don't have > any intentionality... I agree. > ... If and when such machines come about, their causal powers will > derive not from the substances they are made of, *but* *from* *their* *design* > *and* *the* *programs* *that* *run* *in* *them*. [ITALICS MINE] And the way > we will know they have those causal powers is by talking by them and listening > carefully to what they they have to say." This is a fascinating argument, incorrect I think. Certainly in humans much of their abilities come from there experience of the world, learning adaptation. That is much of their state and behaviour is a result of their experience not their genes. I suspect any really interesting computer will be similar. Much of its behaviour will be a result not of its original programming but of its subsequent experience of the world. Unfortunatly again to describe the machines that result we must describe not only their original programming but all their later possible experiences. But they can potentially be affected by anything in the universe. The problem with the current state of computing, robotics and AI is that most computers have little or no interaction with the real world. They have no bodies. Hence they can to a very good approximatin be described by some formal system. Thus many people have a gut feeling that computers are fundamentally different from humans. In their guise as formal systems I think this is indeed true. I think there is also a practical lesson for AI here. To get really interesting behaviour we need open machines which get a lot of experience of the real world. Unfortunately we arent going to be able to formalize or predict the result. But it will be interesting. Sorry about the length of this, but the question seemed too fascinating to let alone. John G. Cleary, Dept. Computer Science, The University of Calgary, 2500 University Dr., N.W. Calgary, Alberta, CANADA T2N 1N4. Ph. (403)220-6087 Usenet: ...{ubc-vision,ihnp4}!alberta!calgary!cleary ...nrl-css!calgary!cleary CRNET (Canadian Research Net): cleary@calgary ARPA: cleary.calgary.ubc@csnet-relay
tedrick@ernie.BERKELEY.EDU (Tom Tedrick) (10/26/85)
Thanks very much for the responses about the mind-turing machine problem. They were very interesting and educational. The most interesting was from our distinguished mathematical colleague from Amsterdam. I have the highest respect for the Amsterdam mathematicians (having gone through some of the Lenstras' papers and heard their talks, for example) so I will defer to his superior knowledge, and only thank him for taking the time to reply. I suspect some of the responses were from people not sufficiently familar with the subject to have an informed opinion, but most were quite good. I didn't appreciate the responses that treated the problem as a joke, or subjected me to personal ridicule. For lack of time I am unable to respond to all the messages I received. I should mention that I saw a film where Godel said something to the effect that either mathematics was inconsistent, or there was some mysterious, not formally explainable process going on in the human mind. Anyway that was my understanding of what he said ... -Tom
jwl@ucbvax.BERKELEY.EDU (James Wilbur Lewis) (10/27/85)
In article <859@whuxlm.UUCP> dim@whuxlm.UUCP (McCooey David I) writes: >> In article <10702@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes: >> > >> >*IS THERE ANYONE THAT AGREES WITH ME THAT THE HUMAN MIND IS PROVABLY >> > NOT EQUIVALENT TO A TURING MACHINE?* >> >> Sure, I agree with you. A Turing machine has unlimited memory. >> _____________________________________________________ >> Matt University crawford@anl-mcs.arpa >> Crawford of Chicago ihnp4!oddjob!matt > >Matt's reply goes along with my line of thought. Consider the situation >realistically: The human mind has a finite number of neurons and therefore >a finite number of states. So I propose that the human mind is equivalent >to a finite state machine, not a Turing machine. (I agree with Tom, but >for the opposite reasons). Note that my comparison does not belittle the >human mind at all. Finite can still mean very, very large. The operation >of a finite state machine with a very large number of states is, for humans, >indistinguishable from that of a Turing machine. Not at all! I see two problems with your line of reasoning. First, your assertion that a finite number of neurons --> a finite state machine. This assumes that neurons have discrete states; however when you consider the continuous, analog nature of activation thresholds, this argument breaks down. A second, *major* flaw is the notion that humans must rely on their brains alone for 'storage'. Ever since the invention of writing, this hasn't been true; literature can be viewed as a Turing machine tape for humans! I stand by my claim that minds and Turing machines are equivalent. -- Jim Lewis U.C. Berkeley ...!ucbvax!jwl jwl@ucbernie.BERKELEY.EDU
marv@ISM780.UUCP (10/29/85)
>Not at all! I see two problems with your line of reasoning. First, your >assertion that a finite number of neurons --> a finite state machine. This >assumes that neurons have discrete states; however when you consider the >continuous, analog nature of activation thresholds, this argument breaks >down. >A second, *major* flaw is the notion that humans must rely on their brains >alone for 'storage'. Ever since the invention of writing, this hasn't been >true; literature can be viewed as a Turing machine tape for humans! >I stand by my claim that minds and Turing machines are equivalent. >-- Jim Lewis > U.C. Berkeley I claim that a finite sized human (not all information processing is done in the brain) *does* imply a finite state machine machine. I think that human information processing involves chemical reactions (a finite number atoms) and energy tranformations (a finite number of photons) and therfore only a finite (albeit very large) number of states. And surely you don't mean to imply that the amount of information stored in a finite sized set of librarys is infinite. I conclude that the human processing is *not* equivalent to a Turning machine. Humans are clearly physically realizable. Turning machines being infinite are not physically realizable. Therefore, I think a more reasonable question to ask is: can a physically realizable machine be built that can mimic human information processing? I am not aware of any laws of physics that disallows the construction of such a machine. It seams to me this is an open question to be answered (hopfully) in the future. Marv Rubinstein -- Interactive Systems.
creedy@cca.UUCP (Christopher Reedy) (11/15/85)
In article <> marv@ISM780.UUCP writes: > >I claim that a finite sized human (not all information processing is done in >the brain) *does* imply a finite state machine machine. I think that human >information processing involves chemical reactions (a finite number atoms) >and energy tranformations (a finite number of photons) and therfore only a >finite (albeit very large) number of states. > Unfortunately, at this level of interaction, quantum mechanics applies. I.e. results of interactions are non-deterministic. I am not enough of a theoretical physicist to know whether the simulation is still possible using probability distributions. However, it seems like a more sophisticated argument is needed here. > >And surely you don't mean to imply that the amount of information stored in >a finite sized set of librarys is infinite. > A Turing Machine does not have infinite memory in the sense you imply. The amount of memory that is in use at any point in time by a Turing machine is finite, even though it can grow without bound over the life of the computation. I am not convinced that this is any different from the memory that is available to a person who has the capability to research for any information that is available in any library anywhere. Chris Reedy