Path: utzoo!utgpu!watserv1!watmath!att!pacbell!pacbell.com!ucsd!swrinde!zaphod.mps.ohio-state.edu!uwm.edu!ux1.cso.uiuc.edu!ux1.cso.uiuc.edu!uxa.cso.uiuc.edu!xhg0998 From: xhg0998@uxa.cso.uiuc.edu Newsgroups: comp.ai Subject: Comments on "The Emperor's New Mind Message-ID: <47000003@uxa.cso.uiuc.edu> Date: 7 Sep 90 00:32:00 GMT Lines: 217 Nf-ID: #N:uxa.cso.uiuc.edu:47000003:000:12588 Nf-From: uxa.cso.uiuc.edu!xhg0998 Sep 6 19:32:00 1990 Comments on "The Emperor's New Mind" Written by Xiaoping Hu Copy Right 1990 All Rights Reserved << Any modification or distribution of this comment must have the full consent of the author. >> This comment provides an alternative view on the central question in Penrose's book: can computer have a mind? I wish it would be helpful to the readers' making their own minds after they read the book. Please forgive me for the lengthy comment. But I think it is worth time thinking these problems carefully and independently. Prof. Penrose summarized the most important recent discoveries in sciences and drew his own conclusion from his own insights. As a humble computer student, however, I disagree with most of the arguments that Prof. Penrose uttered in the book, although I may well be classified into the strong AI group by Penrose, despite that I had never heard the name before I read the book. Since I think that the topics in the book could be very controversial and Dr. Penrose's arguments could be misleading to those who do not have the patience or will to independently ponder such remote things as decidability, an inner voice, as Einstein used to say, invokes me to take the torture to append some comments to the introduction of this book. I have to confess that I finish reading the book and writing this review in a hurry, upon the request of the editors of Book & Journal. Therefore I may not well capture the genuine ideas and implications of Penrose. If this were true, I had to beg pardon from both the readers and Dr. Penrose. So I solemnly suggest that the readers read the related original books instead of taking short cut to listen to the opinions in the main stream. I am sure that Dr. Penrose will be happy at your reading his book. But you don't take my contention seriously, do you? Let us pick up some examples to elaborate here. Maybe I should not mention that the example in Page 255 (Fig. 6.18) can be well explained with classic Maxwell electromagnetic wave theory, without troubling us with the uncomfortable belief that a photon can appear in two distant locations at once (Qigung Master Yen Xin even thinks that an eminent Qigung master can do such miracles). Or maybe I should not helplessly argue that even an idiot could invent some intelligent machine simply by chance! Let us talk about more detailed problems in depth. First, many of the argument that Penrose holds against computer may well be applied to human beings. But still we consider that human beings have intelligence. Second, even we don't know everything about the world, in particular, about the quantum states, we are still intelligent as long as our brains are properly constructed somehow (to discover this really requires genius). A farmer may not know anything about how the solar energy is transformed into biological energy, but he can still raise crops as long as he follows some rules obtained by experience. Therefore all the quantum mechanics stuff may have nothing to do with intelligence. One simply may not need to know everything detail about quantum states to work out some mechanisms which possess some kind of intelligence, although the optimistic attitude of the proponents of strong AI seems naive enough to invite mockings. Third, an eunuch is no less intelligent than a normal man. Therefore, sex desire is not necessary for intelligence. Maybe friendship is a must? Also an uneducated farmer may not well understand the beauty of Picaso's paintings (frankly, even I myself do not quite understand. Do you?). But this does not prevents the farmer from possessing intelligence. Then, is sense of beauty pertinent to intelligence? Fourth, human has successfully created new plants by implanting and new animals by mixbreeding. These new creatures are not the products of the Nature's selection. They are neither evolved. They are created in a revolution. Is there any reason that prevents human from creating an artificial life of artificial intelligence? (You know that a new branch of science called artificial life has just be born. People are taking it seriously.) Fifth, consciousness is only one component of intelligence. Even up to day, intelligence is not well defined (such qualities like learning, memorizing, adaptivity, reasoning, are not even mentioned in Penrose's book). Then what's the deal to argue if AI is possible or not? Intelligence reflects the quality of understanding the nature and overcoming the nature. As long as machine can simulate human in this quality, there is no reason to say that machine has no intelligence because it does not make love. So I find many of the dispute are caused by the confusion in the definition of intelligence. What is Genuine Intelligence, really? Is a dog more intelligent than a pig? At last, let us spend length to go over the core problem: undecidability. Penrose piled up Goedel's theorem, Turing's Theorem, Russell paradox together, but, I would shout that in this particular important point he lacks genuine and original understanding of the meaning of these theorems and paradoxes. Actually, Goedel's incompleteness theorem and Turing's theorem on unceasingness of Turing Machine, can all reduce to Russell paradox, which again is another formalised version of the knight and knave story of the ancient Greek sophists. Actually as Penrose mentioned, both Goedel and Turing obtained their theorems after studying the Russell paradox. This paradox can be stated as follows: 1. S: Statement S is not true. * ==========#=============== In any two value (TRUE-FALSE) logic system, we can neither assign a TRUE nor a FALSE value to S, therefore, "for each self-consistent logical system", or "for each mathematical system as large as encompassing natural numbers", there exist propositions which can neither be proven true nor false. For, if S is assigned TRUE, then what S says must be correct; but what S says is just the opposite: Statement S is not TRUE. Again, we cannot assign a FALSE to S, otherwise, what S says must be wrong; therefore "Statement S is not true" must be wrong. Consequently S must be true. Where is the problem in the above paradox? Up to now, all the logicians, following Russell, conclude that there are something which just cannot be determined within the logical system we use. Everything is perfect there except that the Nature didn't allow us a perfect logical system. Is This True? Let us reexamine the statement and ask what the hell is S? S is not defined! S is self-contradicting by definition and involves infinite cycle. If one plugs S (Statement S is not true) into S * # # he would get 2. S: The Statement "that statement S is not true" is not true. * # Using the negation law in logic, statement 2 actually says that 2'. S: Statement S is true. contradicting statement 1. Such substitution can still go on to get more alternate negative and positive statements. Therefore, the very definition of S has violated the law that a variable can have exactly one value at once in a two value logical system. The Goedel's proposition involves such a definition, so does Turing's theorem. It is nothing else but to say "yes = no, and yes and no are two different values". Why this later statement is so ridiculously nonmeaningful, but the S statement racks the brains of all great logicians? Because S is so trickily constructed such that it consists of a cycle and can be anything else. Does there exist any other solution than claiming undecidability or incompleteness of any logical system? One way, as some earlier logicians suggested is that such self-contradicting propositions are not permissible for this logical system. Therefore another rule "propositions leading to self-contradiction by definition are not permissible" well solves the problem. However, this will again cause new paradoxes which I will not discuss further here. To get around this paradox and correctly understand the philosophical implication of it, we need to check again the logical system. A logical system comprises some operation rules such as AND and OR, as well as some definitions including symbols (A,B,C,D), domain of value (TRUE and FALSE), and original assignment to the variables in an expression. An expression containing unvalued variables may not be determined, not because the logical system is unable to, but because the expression is changing with the assignment of the variables. When you carefully check all existing paradoxes, you can find out that either a paradox is self- contradicting by definition or it comprises an infinite cycle such that it does not have a constant implication -- it is always changing its meaning! Do you remember how we define INFINITE? "An INFINITE is a number which is larger than any natural number". Is Infinite a constant? Is infinite an objective existence or simply a product of pure reason? I like to ask this question to Dr. Penrose, who tells me in his book that the world is of finite size and is dominated by quantum mechanics. We know that in a finite system, we can always include necessary rules to make it complete. In an infinite system since many things are changing with finite or infinite rules, it is necessary to have an infinite number of systems to encompass all propositions such that if a proposition cannot be determined in this system, it may be determined in some other system, although not all the systems need to be mutually consistent. From this point of view, Goedel's theorem only shows that there are some propositions which are not meaningful by definition, or cannot be determined because they do not have constant implications, or need infinite time to determine since they may involve infinite cycles like the Mandelbrot set. It does not say anything wrong about the logical system! Again, the logical system coming from the Nature must return to the Nature to make it meaningful. For example, from logic we know that 1 + 1 = 2. But in nature, 1 dog + 1 cat != 2 pigs, and 1 light speed + 1 light speed != 2 light speeds. We actually do not need to worry about if our logical system is complete enough to understand everything. What we need to worry is if we have enough time or luck to find out what is pertinent to our interests. Although life is finite, it is still not sure if a "genuine" intelligence requires infinite knowledge or mechanisms. Therefore it would be too early to conclude that human cannot work out a computer which simulates human in everything so perfectly that even human cannot distinguish it. If the very Quantum Mechanics is true, then Intelligence can involve only finite mechanisms. Therefore even one computer can simulate all the qualities of human intelligence, leaving alone that the computers may well be organized into a computer society in which each computer has different expertise and capacity, and even personality. The limitedness of a single man's ability suggests us that we need to group together to overcome the nature. Therefore, we need democracy and free speech and belief. Not only because life is limited, the capacity of a man's brain is also limited. No one can be right in everything every time. Therefore we must allow coexistence of different opinions. Otherwise, human society will certainly goes into some extreme, leading to self-destruction. One important feature of human inetelligence is its flexibility and freedom. To some degree, one can freely change his mind. Therefore any human brain in principle is a universal Turing Machine or Neumann Machine. Therefore, 4 billions people own 4 billions universal Turing Machines. That's still not all. Each brain can change the range in which it gives right answers. Such freedom allows the potentiality of solving unsolved problems. So, my conclusion is clear: I do not even need an uncertainty principle to convince Penrose that he will never exactly know the weight of his own head, but I still regard him as one of the human beings of highest intelligence. To conclude the past is wise, but to conclude the future is not. One can has his own belief on the future, but to use one's own belief to mock other people's believes does not seem a respectful and truth-loving way. Well, enough is enough. My little finger tells me that, as Einstein would say (Oops, Einstein again), I have got to stop now to keep my rice bowl. I am sure that some of you must be honest and naive enough to find out who is the true Emperor.