1 00:00:00,090 --> 00:00:10,830 Before I start on today's lecture, I just want to point out something from the last lecture there was, as I pointed out at the time, a misprint. 2 00:00:10,830 --> 00:00:16,440 I've not corrected it. It should say X prime equals x plus one. 3 00:00:16,440 --> 00:00:24,600 That's in slide one five two one five three and one five four. 4 00:00:24,600 --> 00:00:29,400 It previously said X equals x prime plus one, which was the wrong way round. 5 00:00:29,400 --> 00:00:33,390 This is clearly saying X Prime is the successor of X. 6 00:00:33,390 --> 00:00:47,230 That was correct. My gloss on it was mistaken. Sorry about that. 7 00:00:47,230 --> 00:01:00,850 Seems to be fine, Andy. Today we move on from the 1936 paper to the 1950 paper even more famous. 8 00:01:00,850 --> 00:01:07,900 It's one of the most cited philosophical papers ever published computing, machinery and intelligence. 9 00:01:07,900 --> 00:01:13,510 It was published in the prominent journal mined in 1950. 10 00:01:13,510 --> 00:01:17,650 You'll find that there are quite a lot of allusions back to the 1936 paper, 11 00:01:17,650 --> 00:01:28,700 so watch out for those quite a lot of what Turing says is alluding to results that he had proved then. 12 00:01:28,700 --> 00:01:35,420 I'm just putting on the slides here some useful books on the philosophy of AI on the Chinese room argument, 13 00:01:35,420 --> 00:01:42,440 as well as on Turing, will be dealing with cells Chinese room argument next time. 14 00:01:42,440 --> 00:01:46,760 Some useful collections of papers. This one we've already seen. 15 00:01:46,760 --> 00:01:55,400 There's a collection that I edited with Andy Clock back in 1996 that was from a conference commemorating Turing. 16 00:01:55,400 --> 00:02:02,450 And there are seven papers in there that are relevant to the Turing test and also my introduction. 17 00:02:02,450 --> 00:02:07,610 And there's a book devoted to the Chinese room argument that I mention there. 18 00:02:07,610 --> 00:02:13,550 Stanford Encyclopaedia of Philosophy is often very useful on philosophical things quite generally, 19 00:02:13,550 --> 00:02:20,000 and it's got an article on the Turing test and on the Chinese room, and there are some useful web resources. 20 00:02:20,000 --> 00:02:28,070 Andrew Hodges, who wrote the monumental biography of Alan Turing, has a website devoted to him. 21 00:02:28,070 --> 00:02:32,990 Lots of good stuff there and a very long paper with some useful stuff. 22 00:02:32,990 --> 00:02:36,800 I think of more mixed quality, but not all the points made. 23 00:02:36,800 --> 00:02:41,840 There are ones that I'd agree with, but it's got a lot of scholarly material on the Turing test. 24 00:02:41,840 --> 00:02:47,680 They're well worth looking at. OK. 25 00:02:47,680 --> 00:02:58,510 The 1950 paper is perhaps often taken more seriously than it ought to be, and this is a point worth starting with. 26 00:02:58,510 --> 00:03:05,110 This is a quotation from Robin Gandy I think may be the last thing he ever published. 27 00:03:05,110 --> 00:03:16,390 This was in our collection in 1996. The 1950 paper was intended not so much as a penetrating contribution to philosophy, but as propaganda. 28 00:03:16,390 --> 00:03:21,460 He wrote this paper, unlike his mathematical papers, quickly and with enjoyment, 29 00:03:21,460 --> 00:03:29,170 I can remember him reading aloud to me some of the passages always with a smile, sometimes with a giggle. 30 00:03:29,170 --> 00:03:35,410 Some of the discussions of the paper loaded with more significance than it was intended to bear there. 31 00:03:35,410 --> 00:03:39,430 Robin Gandhi was an intimate friend of Turing's. 32 00:03:39,430 --> 00:03:48,190 He was his Ph.D. student. He was Turing's literary executors of Turing left his papers to Gandhi. 33 00:03:48,190 --> 00:03:53,920 He also, interestingly ended up at Oxford, where one of the things that he did was to start the maths and philosophy degree. 34 00:03:53,920 --> 00:04:02,470 Back in 1969, in 1972, modern languages philosophy, modern languages was started in the next degree. 35 00:04:02,470 --> 00:04:07,750 To be started after that in philosophy was computer science philosophy in 2012. 36 00:04:07,750 --> 00:04:13,810 So a bit of a legacy then. 37 00:04:13,810 --> 00:04:20,620 OK, The Imitation Game is Turing's way of reworking the question. 38 00:04:20,620 --> 00:04:30,400 Can machines think? And this is a bit confusing, a bit odd. 39 00:04:30,400 --> 00:04:36,520 I proposed to consider the question Can machines think if the meaning of the words machine and thing? 40 00:04:36,520 --> 00:04:43,510 Could it be found by examining how they commonly used? The answer is to be sought in a statistical survey, but this is absurd. 41 00:04:43,510 --> 00:04:51,280 Instead, I shall replace the question by another, which is closely related to it, but relatively unambiguous. 42 00:04:51,280 --> 00:05:02,920 Now that's a bit peculiar, isn't it? Philosophers are constantly asking questions about the meaning of things like knowledge free will and so on. 43 00:05:02,920 --> 00:05:10,030 And we don't standardly think, well, we could go and do a statistical survey and find out what people say. 44 00:05:10,030 --> 00:05:14,680 But actually the only alternative is to replace it with a completely different question. 45 00:05:14,680 --> 00:05:23,950 So there's something a little bit odd about Turing's procedure, but let's see where it leads. 46 00:05:23,950 --> 00:05:36,160 His replacement question is in the context of an imitation game, and he introduces this in the context of a question over identity. 47 00:05:36,160 --> 00:05:49,090 We have an interrogator in one room who is sending questions to two individuals in two other rooms. 48 00:05:49,090 --> 00:05:56,200 The questions are being sent in text, so Turing suggests a teletype machine. 49 00:05:56,200 --> 00:06:03,850 Here I've actually got Turing statue, and that's an Enigma machine, but it's close enough to a teletype that I've put it in there. 50 00:06:03,850 --> 00:06:10,930 And here we've got Charles Babbage and Ada Lovelace, who I've taken as my sample man and woman it. 51 00:06:10,930 --> 00:06:18,190 When the game is played, the interrogator doesn't actually know the identity of the people concerned has no idea who they are. 52 00:06:18,190 --> 00:06:29,650 Just knows that there's one man and one woman in separate rooms and is sending questions to them in text and is receiving them back in text. 53 00:06:29,650 --> 00:06:36,760 And the interrogators job is to try to work out which is the man, which is the woman. 54 00:06:36,760 --> 00:06:42,280 But the twist on it is that the man is pretending to be a woman. 55 00:06:42,280 --> 00:06:48,670 So if, as Turing says, he asks, How long is your hair? 56 00:06:48,670 --> 00:06:55,570 The man might reply, My hair is shingled, and the longest strands are about nine inches long. 57 00:06:55,570 --> 00:07:03,110 Meanwhile, the woman may be saying, I'm the woman, don't listen to him, and you can imagine other questions that might be asked. 58 00:07:03,110 --> 00:07:09,310 I mean, in the modern context, one might ask who won the Premiership this year? 59 00:07:09,310 --> 00:07:15,010 And the man will respond, Oh, I don't know anything about football. I'll have to ask my boyfriend. 60 00:07:15,010 --> 00:07:18,520 So you can imagine it could be quite fun. 61 00:07:18,520 --> 00:07:25,750 I mean, it seems to have its origin in the sort of Victorian parlour game now. 62 00:07:25,750 --> 00:07:38,050 What the man is trying to do remember is to pretend successfully to be the woman he succeeds in that if the interrogator can't tell who's who. 63 00:07:38,050 --> 00:07:45,970 So if the interrogator ends up essentially tossing a coin, or suppose you play this game repeatedly with different interrogation? 64 00:07:45,970 --> 00:07:52,900 It is, and the man scores about 50 per cent, so the interrogator is only able to get him half the time. 65 00:07:52,900 --> 00:07:54,880 That's pretty much as good as it gets. 66 00:07:54,880 --> 00:08:01,120 It would be a bit peculiar if the man was able to impersonate a woman better than a woman can represent herself. 67 00:08:01,120 --> 00:08:20,150 But. So the interrogators in a different room, tones of voice are ruled out because the answers are purely by text, as you see. 68 00:08:20,150 --> 00:08:33,460 Turing is suggesting a tele printer. And then we get the computer being introduced. 69 00:08:33,460 --> 00:08:38,350 We now ask what will happen when a machine takes the place of a. 70 00:08:38,350 --> 00:08:41,110 That is the deceitful man in this game. 71 00:08:41,110 --> 00:08:49,600 Will the interrogator decide wrongly as often when the game is played like this, as he does when the game is played between a man and a woman? 72 00:08:49,600 --> 00:08:56,360 These questions replace our original can machines think? 73 00:08:56,360 --> 00:09:01,450 That's again, rather peculiar. They replaced the original question. 74 00:09:01,450 --> 00:09:11,740 What does that mean, then the machine? The question was can machines think that looks like it's got a yes or no answer? 75 00:09:11,740 --> 00:09:22,930 Or maybe the answer would be possibly yes. Machines could in principle think, are we really supposed to replace that with the question, 76 00:09:22,930 --> 00:09:29,920 can a machine play The Imitation Game as well as a man can against a woman? 77 00:09:29,920 --> 00:09:38,290 That seems a bit peculiar. Moreover, it's not clear exactly what the computer's job is. 78 00:09:38,290 --> 00:09:47,560 Here is the job to pretend to be a woman, or is the job to pretend to be a human? 79 00:09:47,560 --> 00:09:52,300 That actually does become clear later in Sections two and five of the paper. 80 00:09:52,300 --> 00:09:58,840 It becomes obvious that Turing is seeing the computer as trying to imitate a person. 81 00:09:58,840 --> 00:10:06,040 I mean, he often says a man, but that in 1950, when you say man, you often mean person. 82 00:10:06,040 --> 00:10:13,570 That's changed considerably. So this is the way the Turing test is normally understood. 83 00:10:13,570 --> 00:10:21,370 We've still got the interrogator. We've got the teletype communicating to two different rooms, if you like. 84 00:10:21,370 --> 00:10:30,100 One of them contains a computer running a programme. The other one contains a person could be either man or woman doesn't matter. 85 00:10:30,100 --> 00:10:35,500 And the computer is trying to impersonate a person. 86 00:10:35,500 --> 00:10:47,320 Either man or woman doesn't matter. And the result that Turing seems to be hinting at, he doesn't state it very explicitly. 87 00:10:47,320 --> 00:10:54,340 But this seems to be the drift of his paper that if the interrogator can't reliably distinguish the computer from the human, 88 00:10:54,340 --> 00:11:07,750 then the computer programme must be judged to be intelligent for thinking that that seems to be where he's going. 89 00:11:07,750 --> 00:11:13,900 In Section two of the paper, Turing's idea about what he's doing is clarified. 90 00:11:13,900 --> 00:11:22,270 The interrogators questions can be used to elicit the computer's knowledge about almost any of the fields of human endeavour. 91 00:11:22,270 --> 00:11:29,380 And he gives some examples we'll see in a moment and notice that the set up has the advantage as he points 92 00:11:29,380 --> 00:11:36,610 out of drawing a fairly sharp line between the physical and the intellectual capacities of a person. 93 00:11:36,610 --> 00:11:47,560 So one great advantage of the test is, as we've seen before, the tone of voice isn't taken into account, nor is the physical appearance. 94 00:11:47,560 --> 00:11:57,610 The interrogator doesn't actually see who is responding. All all he gets is the textual responses and has to judge on that basis. 95 00:11:57,610 --> 00:12:01,930 But as Turing says, those textual responses could cover a wide range of things. 96 00:12:01,930 --> 00:12:07,420 So here's an illustrative conversation that he gives. 97 00:12:07,420 --> 00:12:13,120 Please might write me a summit on the subject of the fourth bridge that comes the answer. 98 00:12:13,120 --> 00:12:20,170 Count me out on this one. I never could write poetry. It seems, may seem a rather strange thing to ask. 99 00:12:20,170 --> 00:12:27,520 As your first question, please write me a sonnet, not the sort of thing you would expect to happen in an interactive conversation. 100 00:12:27,520 --> 00:12:32,080 We'll see why Turing gives the example of a sonnet later. 101 00:12:32,080 --> 00:12:38,830 He's responding to Geoffrey Jefferson at thirty four thousand nine hundred fifty seven to 102 00:12:38,830 --> 00:12:45,010 seventy thousand seven hundred sixty four poles about 30 seconds and then give his answer, 103 00:12:45,010 --> 00:12:48,070 other than 5000 621. 104 00:12:48,070 --> 00:13:02,080 Notice Turing is here deliberately having the system pretend to take longer than it needs, so there's a clear element of deception playing a role. 105 00:13:02,080 --> 00:13:13,300 Do you play chess? Yes. And he gives a very simple chess set up, and after a pause of 15 seconds to educate Mate, 106 00:13:13,300 --> 00:13:20,350 I conclude that Turing was not particularly expert at chess if he thought it took 15 seconds to work that one out. 107 00:13:20,350 --> 00:13:24,760 There we go. Yeah, OK. 108 00:13:24,760 --> 00:13:33,160 An obvious objection to the Turing test. It seems to be biased in favour of human thought, and Turing says may not. 109 00:13:33,160 --> 00:13:40,330 Machines carry out something which ought to be described as thinking, but is very different from what a human person does. 110 00:13:40,330 --> 00:13:44,440 And indeed, this seems to be an obvious objection. 111 00:13:44,440 --> 00:13:53,990 I mean, suppose an alien comes down from the planet Zog and takes place that takes part in this test and. 112 00:13:53,990 --> 00:13:59,300 The alien is asked this question and comes back with an answer immediately. 113 00:13:59,300 --> 00:14:04,070 We just know it isn't a human. Certainly not in any sort of normal human. 114 00:14:04,070 --> 00:14:06,290 Does that mean it's not intelligent? No. 115 00:14:06,290 --> 00:14:16,010 On the contrary, if the alien is able to do arithmetic much more quickly than we can, if anything, that suggests it's more intelligent, not less. 116 00:14:16,010 --> 00:14:21,440 And likewise, if you if you ask it, you know, how long is your hair? 117 00:14:21,440 --> 00:14:30,830 What hair? Maybe the aliens on Zog don't have any hair that wouldn't count against its being intelligent. 118 00:14:30,830 --> 00:14:39,020 So it seems odd to have a test which depends on mimicking humans. 119 00:14:39,020 --> 00:14:42,950 Turing's response is that the objection is indeed a very strong one, 120 00:14:42,950 --> 00:14:49,130 but at least we can say that if nevertheless a machine can be constructed to play The Imitation Game satisfactorily, 121 00:14:49,130 --> 00:14:58,010 we need not be troubled by this objection. Now again, he doesn't say very explicitly where he's driving here, 122 00:14:58,010 --> 00:15:09,440 but I take it that this is a strong suggestion that he wants us to take the the test as a sufficient proof of intelligence, but not a necessary test. 123 00:15:09,440 --> 00:15:14,060 So if something passes the Turing test, then we are to deem it intelligent. 124 00:15:14,060 --> 00:15:27,480 The fact that it doesn't pass the test, e.g. because it responds more quickly than a human would should not mean that we counted as unintelligent. 125 00:15:27,480 --> 00:15:32,130 Now I want to just now refer to something later in the paper. 126 00:15:32,130 --> 00:15:34,890 I mean, I'm generally going in this lecture I'm going through, 127 00:15:34,890 --> 00:15:42,720 as you see in sequence through the paper to guide your reading of it, and I please do read it before the next lecture. 128 00:15:42,720 --> 00:15:48,870 I hope you know this will help you to identify the principal points in it. 129 00:15:48,870 --> 00:15:58,990 But later on in Section six, Turing is going to give an example, which I think probably is the best argument for the Turing test. 130 00:15:58,990 --> 00:16:07,840 And it concerns the choice of words in a poem. And here is the dialogue. 131 00:16:07,840 --> 00:16:10,180 So again, we've got this sonnet. 132 00:16:10,180 --> 00:16:20,980 We imagine the interrogator questioning what Turing calls a witness that is one of the people in one of the rooms in the first line of your sonnet, 133 00:16:20,980 --> 00:16:28,300 which reads, Shall I compare this to a summer's day? Wouldn't a spring day do as well? 134 00:16:28,300 --> 00:16:34,300 Or better back comes the answer. It wouldn't scan. 135 00:16:34,300 --> 00:16:39,160 In other words, it would have the wrong rhythm. Shall I compare this to a spring day? 136 00:16:39,160 --> 00:16:43,990 Not enough syllables. How about a winter's day that would scan? 137 00:16:43,990 --> 00:16:53,350 All right. Shall I compare it to a winter's day? Yes, but nobody wants to be compared to a winter's day. 138 00:16:53,350 --> 00:17:01,390 Would you say Mr. Pickwick reminded you of Christmas, then we had an allusion to Shakespeare and a Shakespearean sonnet? 139 00:17:01,390 --> 00:17:08,860 Now we get Dickens, OK? Just pick Mr. Pickwick, remind you of Christmas in a way. 140 00:17:08,860 --> 00:17:14,190 Yeah, Christmas is a winter's day, and I don't think Mr. Pickwick would mind the comparison. 141 00:17:14,190 --> 00:17:23,100 I don't think you're serious by a winter's day. One means a typical winter's day rather than a special one like Christmas. 142 00:17:23,100 --> 00:17:35,400 OK, now let's suppose that that conversation took place and we were completely assured that these responses had not as it were being built in, 143 00:17:35,400 --> 00:17:36,930 there wasn't any trickery involved. 144 00:17:36,930 --> 00:17:50,070 You know, canned responses just coming out and supposed conversations of similar levels of sophistication came across quite a range of topics, 145 00:17:50,070 --> 00:17:58,740 not just on poetry, a number of things. The force of Turing's argument here is to say surely. 146 00:17:58,740 --> 00:18:04,110 Surely we would then have to say that this is exhibiting intelligence. 147 00:18:04,110 --> 00:18:15,060 This would be pretty strong evidence. And in the context of 1950, where obviously Turing cannot appeal to achievements in robotics, 148 00:18:15,060 --> 00:18:22,500 for example, or simulation of human behaviour, physical behaviour or anything like that, 149 00:18:22,500 --> 00:18:30,420 this kind of achievement, if if it were to be achieved in verbal response, 150 00:18:30,420 --> 00:18:35,940 would be pretty much a strong evidence of intelligence, as perhaps you could get. 151 00:18:35,940 --> 00:18:41,460 So it's propaganda. It's quite effective. 152 00:18:41,460 --> 00:18:51,660 OK, section three Turing goes onto the machines concerned in the game, and you will see that there is another bit of humour coming in. 153 00:18:51,660 --> 00:18:58,920 We want to allow all sorts of different engineering techniques to be used to create these machines. 154 00:18:58,920 --> 00:19:04,080 However, we wish to exclude from the machines men born in the usual manner. 155 00:19:04,080 --> 00:19:05,280 In other words, 156 00:19:05,280 --> 00:19:15,570 we're not going to treat biological reproduction as an appropriate way of producing a thinking machine because otherwise that would include all of us. 157 00:19:15,570 --> 00:19:24,760 So Turing is obviously pushing towards saying our restriction is going to be digital computers, right? 158 00:19:24,760 --> 00:19:32,490 We don't. We don't want to rule out a machine on the grounds that it's made of one thing rather than another. 159 00:19:32,490 --> 00:19:36,720 We do want to rule out biological organisms. 160 00:19:36,720 --> 00:19:46,290 So what we're going to do is go for digital computers, which of course, is exactly the domain of his 1936 paper. 161 00:19:46,290 --> 00:19:53,400 The idea behind digital computers is that these machines are intended to carry out any operations which could be done by human computer. 162 00:19:53,400 --> 00:19:58,410 That's a clear echo of section nine of the 1936 paper, 163 00:19:58,410 --> 00:20:07,890 where he argues for the Turing machine as a way of encapsulating all the things that a human computer could do. 164 00:20:07,890 --> 00:20:13,440 He then gives an outline of how they work. 165 00:20:13,440 --> 00:20:21,540 He considers some particular cases. He suggests that a digital computer could contain a random element. 166 00:20:21,540 --> 00:20:26,820 You could have a computer with an unlimited store and that has special theoretical interest. 167 00:20:26,820 --> 00:20:37,380 Obviously, Turing machines have an unlimited store, and he alludes to Charles Babbage showing that digital machines needn't be electrical. 168 00:20:37,380 --> 00:20:42,780 They could be mechanical. Charles back Babbage designed the analytical engine. 169 00:20:42,780 --> 00:20:48,000 It was never built. Unfortunately, it's far too complex and expensive. 170 00:20:48,000 --> 00:20:53,310 But the idea of an analytical engine was that showing that a digital computer 171 00:20:53,310 --> 00:20:58,950 could be made in principle as a physical machine rather than a mechanical machine, 172 00:20:58,950 --> 00:21:05,250 rather than an electronic universality of digital computers. 173 00:21:05,250 --> 00:21:09,720 Again, a clear echo of the 1936 paper. 174 00:21:09,720 --> 00:21:17,790 And here, bear in mind that Turing is addressing an audience of probably mainly philosophers and general readers, 175 00:21:17,790 --> 00:21:24,900 not people who would be familiar with the results of his 1936 paper. 176 00:21:24,900 --> 00:21:33,210 So processes in the world are really continuous and indeed chaotic. 177 00:21:33,210 --> 00:21:41,610 And Turing gives an illustration of what we now call the butterfly effect, which was quite prescient in 1950. 178 00:21:41,610 --> 00:21:51,360 But even where processes are continuous, they can usefully be modelled by discrete systems and discrete state machines, 179 00:21:51,360 --> 00:21:58,020 as he describes them, is utterly predictable. There is no reason why this calculation should not be carried out by means of a digital computer, 180 00:21:58,020 --> 00:22:00,570 provided it could be carried out sufficiently quickly. 181 00:22:00,570 --> 00:22:09,120 The digital computer could mimic the behaviour of any discrete state machine, so digital computers are, in a sense, universal. 182 00:22:09,120 --> 00:22:15,690 Again, we've seen his model of the universal Turing machine from 1936. 183 00:22:15,690 --> 00:22:28,140 He's pointing out now that not only can you have a computer that can mimic any digital system and any system of axioms rules, etc. of inference, 184 00:22:28,140 --> 00:22:42,090 but also any continuous system can generally at least be modelled with arbitrary, accurate accuracy by some corresponding digital system. 185 00:22:42,090 --> 00:22:44,550 So because digital computers are universal, 186 00:22:44,550 --> 00:22:50,610 the Imitation Game question reduces to this Let's just fix our attention on one particular digital computer. 187 00:22:50,610 --> 00:22:56,550 See? Is it true that by modifying this computer to have an adequate storage, 188 00:22:56,550 --> 00:23:01,950 suitably increasing its speed of action and providing it with an appropriate programme, 189 00:23:01,950 --> 00:23:06,960 C can be made to play satisfactorily the part of a in The Imitation Game. 190 00:23:06,960 --> 00:23:12,840 The part of B being taken by a man person right here. 191 00:23:12,840 --> 00:23:20,790 It's it's obvious that the Part B is not meant to be taken by a woman, specifically with the computer pretending to be a woman. 192 00:23:20,790 --> 00:23:40,020 All right. OK, now we come to section six and in section six of the paper, Turing considers and rejects nine different objections to his thesis. 193 00:23:40,020 --> 00:23:47,460 And some of these he treats rather humorously, not terribly seriously. 194 00:23:47,460 --> 00:24:01,350 Some of them he discusses more seriously. But I think he also in doing so makes some significant mistakes, which we will see. 195 00:24:01,350 --> 00:24:09,120 But before he considers the objections, he offers a couple of predictions we'll be coming back to these in a later lecture, 196 00:24:09,120 --> 00:24:15,780 but they're quite significant and I think quite prescient. 197 00:24:15,780 --> 00:24:20,550 I believe this in about 50 years time. OK, about 2000, 198 00:24:20,550 --> 00:24:30,540 it will be possible to programme computers with a storage capacity of about 10 to the nine to make them play The Imitation Game so well that 199 00:24:30,540 --> 00:24:40,940 an average interrogator will not have more than 70 per cent chance of making the right identification after five minutes of questioning. 200 00:24:40,940 --> 00:24:51,770 OK. So in 2000, would it have been possible to programme a computer with a storage capacity of about a gigabyte to make them 201 00:24:51,770 --> 00:25:04,300 play The Imitation Game so well that the average interrogator will go wrong at 30 percent of the time? 202 00:25:04,300 --> 00:25:08,560 I think actually that's rather a plausible prediction. 203 00:25:08,560 --> 00:25:16,690 I think if artificial intelligence research had focussed on achieving that, I think it would have achieved it. 204 00:25:16,690 --> 00:25:22,690 Not true that it did. But I think it could have. We'll come back to that in a later lecture. 205 00:25:22,690 --> 00:25:29,620 Look at the second one. The original question? Can machines think, I believe, to be too meaningless to deserve discussion? 206 00:25:29,620 --> 00:25:32,200 Nevertheless, I believe that at the end of the century, 207 00:25:32,200 --> 00:25:37,870 the use of words and general educated opinion will have altered so much that one will be expected to be. 208 00:25:37,870 --> 00:25:45,720 One will be able to think speak of machines thinking without expecting to be contradicted. 209 00:25:45,720 --> 00:25:52,960 I'm in a more authoritative position to discuss that than most of you, but I will tell you this in 2000, 210 00:25:52,960 --> 00:26:01,240 I think it was quite plausible that one could talk of machines thinking without expecting to be contradicted. 211 00:26:01,240 --> 00:26:05,290 I think now it happens all the time anyway. 212 00:26:05,290 --> 00:26:17,800 That's another thing we'll come back to. But do note that as you go through the paper, those are quite significant predictions and important ones. 213 00:26:17,800 --> 00:26:23,110 OK? The theological objection thinking is a function of man's immortal soul. 214 00:26:23,110 --> 00:26:28,000 God has given an immortal soul to every man and woman, but not to any other animal or to machines. 215 00:26:28,000 --> 00:26:40,480 Hence, no animal or machine can think. I'm not going to spend long on Turing's discussion of this, which seems somewhat flippant. 216 00:26:40,480 --> 00:26:47,350 Certainly, Turing is not sympathetic to such religious doctrines. 217 00:26:47,350 --> 00:26:55,470 He highlights the absurdity of some religious views, e.g., women don't have souls. 218 00:26:55,470 --> 00:27:00,580 Suppose God gives cells. Why shouldn't he give a soul to a computer? 219 00:27:00,580 --> 00:27:10,000 I mean, if one thought that this was a serious discussion, there is a lot that could be said here. 220 00:27:10,000 --> 00:27:14,350 Turing rather skips over it. I'm going to as well. 221 00:27:14,350 --> 00:27:21,430 I think whatever is significant about that objection can be wrapped up in the problem of consciousness, 222 00:27:21,430 --> 00:27:25,420 which will come to light in their heads in the sand. 223 00:27:25,420 --> 00:27:30,670 Objection again, rather flippant. The consequences of machines thinking would be too dreadful. 224 00:27:30,670 --> 00:27:33,940 Let us hope and believe that they cannot do so. 225 00:27:33,940 --> 00:27:44,560 And Turing is suggesting that this lies behind many people's opposition to the idea of machines thinking they just don't want to think about it, 226 00:27:44,560 --> 00:27:53,500 bury their heads in the sand. Consolation is more appropriate than refutation, perhaps in the transmigration of souls. 227 00:27:53,500 --> 00:28:00,880 Yeah, sure. I think again, Turing is having some fun. 228 00:28:00,880 --> 00:28:09,580 I don't actually think the paper could possibly be published in the journal like mind in its current form today. 229 00:28:09,580 --> 00:28:18,490 It would have had a lot heavier editing for some of this stuff, but it does add to the entertainment of reading it. 230 00:28:18,490 --> 00:28:25,210 OK, number three, we come to the mathematical objection and this is a serious objection. 231 00:28:25,210 --> 00:28:37,990 It's been raised in recent years. Well, John Lucas many years ago now, actually and Roger Penrose, the idea is that results like girdles, 232 00:28:37,990 --> 00:28:44,230 but also, you see, Turing is alluding to other results that we looked at in the last lecture church. 233 00:28:44,230 --> 00:28:52,580 Clearly, Rosser Turing results that demonstrate the limited power of discrete state machines. 234 00:28:52,580 --> 00:29:05,050 And does that show actually that humans have an ability that no discrete machine can because we can run through, for example, the Turing? 235 00:29:05,050 --> 00:29:15,430 That's sorry, the girdle proof. We can see that the girdle formula is true, but the girdle formula cannot be proved by the formal system. 236 00:29:15,430 --> 00:29:19,960 Therefore, we are able to do something that the formal system cannot. 237 00:29:19,960 --> 00:29:26,800 Therefore, the human brain has a power that discrete make state machines cannot. 238 00:29:26,800 --> 00:29:34,280 That's a sketch of the kind of argument that Lucas and Penrose suggest. 239 00:29:34,280 --> 00:29:44,290 So it's interesting that cheering anticipates this. Here you can see a clear reference back to the 1936 paper. 240 00:29:44,290 --> 00:29:49,690 Consider the machine specified as follows Will this machine ever answer yes to any question you can see? 241 00:29:49,690 --> 00:29:53,560 That's a bit like will the machine ever print a zero on the tape? 242 00:29:53,560 --> 00:30:01,180 He knows these proved that you cannot have a general machine that will do that. 243 00:30:01,180 --> 00:30:10,060 But in answer to the question, does that show that these machines are less powerful than the human mind? 244 00:30:10,060 --> 00:30:17,350 Not necessarily, no, because humans have limitations too, and superiority over one particular machine. 245 00:30:17,350 --> 00:30:28,000 I mean, suppose we have some Turing machine implementing some axiomatic system and then we do a girdle on it and find a formula that it cannot prove 246 00:30:28,000 --> 00:30:39,490 that just shows we're superior to that machine in that respect doesn't show we are superior to all machines in all respect or even in one. 247 00:30:39,490 --> 00:30:44,920 Okay, so I'm going to put that to one side, but that is potentially an important objection. 248 00:30:44,920 --> 00:30:49,510 So it's one that has been taken seriously down the years. 249 00:30:49,510 --> 00:31:00,430 The argument from consciousness, I think, is probably the most important objection, and it's where I'm going to suggest Turing goes most wrong. 250 00:31:00,430 --> 00:31:05,980 He quotes from Geoffrey Jefferson's list oration of 1949. 251 00:31:05,980 --> 00:31:14,770 So here is Jefferson saying why computers can't think not until the machine can write a sonnet or 252 00:31:14,770 --> 00:31:22,210 compose a concerto because of thoughts and emotions felt and not by the chance for all of symbols? 253 00:31:22,210 --> 00:31:30,340 Could we agree that machine equals brain that is not only write it, but know that he had written it. 254 00:31:30,340 --> 00:31:41,290 So you can see Jefferson is putting a lot of emphasis on that writing of a sonnet, and Turing is responding to this with his examples of sonnet. 255 00:31:41,290 --> 00:31:53,650 No mechanism could feel and not merely artificially signal an easy contrivance pleasure that it successes grief when it's valves fuse, 256 00:31:53,650 --> 00:32:01,240 be made miserable, be charmed. Be angry or depressed. OK, so you get the idea. 257 00:32:01,240 --> 00:32:05,710 The computer can't genuinely feel anything. 258 00:32:05,710 --> 00:32:16,170 So when the computer produces a sonnet, say it's not doing it through genuine thinking. 259 00:32:16,170 --> 00:32:24,420 Now, Turing's response to this is amusing, but I'm going to suggest dubious. 260 00:32:24,420 --> 00:32:31,560 This argument appears to be a denial of the validity of our test, according to the most extreme form of this view. 261 00:32:31,560 --> 00:32:37,260 The only way to know that either a machine or a man thinks is to be that particular man. 262 00:32:37,260 --> 00:32:46,200 It is, in fact, the solipsistic point of view. It may be the most logical view to hold, but it makes communication of ideas difficult. 263 00:32:46,200 --> 00:32:51,120 A is liable to believe anything, but B does not. 264 00:32:51,120 --> 00:32:56,010 Meanwhile, B is liable to believe B thinks, but it is not. 265 00:32:56,010 --> 00:33:05,190 Instead of arguing continually over this point, it is usual to have the polite convention that everyone thinks. 266 00:33:05,190 --> 00:33:12,270 OK. Solipsism, by the way, is the theory that I am the only thing that exists in the world, right? 267 00:33:12,270 --> 00:33:17,520 Everything else is a figment of my imagination, including all of you. 268 00:33:17,520 --> 00:33:24,480 So if I'm a solipsistic right, I genuinely think that I am the only thing that's thinking. 269 00:33:24,480 --> 00:33:37,680 And Turing is suggesting that if we follow the logic of Jefferson's objection, we would actually come to the conclusion that solipsism is true. 270 00:33:37,680 --> 00:33:42,780 Now, he then gives his viva voce example. 271 00:33:42,780 --> 00:33:49,020 So I think the previous point will come back to it in a moment I think is highly dubious. 272 00:33:49,020 --> 00:33:54,360 But I think some of what he says about the sonnet example is strong. 273 00:33:54,360 --> 00:33:59,580 So just to remind you, that's the conversation about the sonnet. 274 00:33:59,580 --> 00:34:04,620 You can see it's quite a sophisticated conversation. 275 00:34:04,620 --> 00:34:11,130 What would Jefferson say if the sonnet writing machine was able to answer like this in the viva voce? 276 00:34:11,130 --> 00:34:17,640 I do not know whether he would regard the machine as merely artificially signalling these answers. 277 00:34:17,640 --> 00:34:27,300 But if the answers were satisfactory and sustained as in the above passage, I do not think he would describe it as an easy contrivance. 278 00:34:27,300 --> 00:34:31,920 In short, then, I think that most of those who support the argument from consciousness could be 279 00:34:31,920 --> 00:34:38,620 persuaded to abandon it rather than be forced into the solipsistic position. 280 00:34:38,620 --> 00:34:49,810 OK. I think there's a good point there, but I think there's a confusion of two quite distinct lines of thought. 281 00:34:49,810 --> 00:34:58,360 So one of those is that Jefferson is denying the validity of the Turing test because it does not test for genuine consciousness. 282 00:34:58,360 --> 00:35:05,230 And according to Jefferson, genuine consciousness, rather than artificial signalling is necessary for intelligence. 283 00:35:05,230 --> 00:35:13,060 OK, that's one line of thought. A different line of thought is that artificial signalling of apparent emotions 284 00:35:13,060 --> 00:35:18,480 is unworthy of being deemed intelligent because it's an easy contrivance. 285 00:35:18,480 --> 00:35:25,150 OK, so those are two different points. One is saying consciousness is crucial has got to be genuine feeling. 286 00:35:25,150 --> 00:35:31,480 The other one says Easy contrivance isn't enough. 287 00:35:31,480 --> 00:35:35,740 Now Turing runs those together in his response. 288 00:35:35,740 --> 00:35:46,120 And I think his answer to the easy contrivance point is much stronger than his response to the first unconsciousness, 289 00:35:46,120 --> 00:35:47,630 what he'd have been better saying. 290 00:35:47,630 --> 00:35:55,000 And we'll talk about this more in the next two lectures after he gave the sonnet example and others write not just the sonnet, 291 00:35:55,000 --> 00:36:00,010 but examples of similar sophistication of conversation, 292 00:36:00,010 --> 00:36:08,800 he should have said something like this if the answers were satisfactory and sustained, as in the above passage direct quote from him, 293 00:36:08,800 --> 00:36:15,910 then there would be reason to call the machine intelligent, irrespective of whether or not it has genuine feelings. 294 00:36:15,910 --> 00:36:23,440 Intelligent need not require consciousness. That, I think is the way he should have argued. 295 00:36:23,440 --> 00:36:32,830 Obviously, there's a lot more to say about this, so we'll come back to this in, well, the next sector and especially the one after that. 296 00:36:32,830 --> 00:36:39,850 Okay, so we'll put consciousness on one side for now. We then get two arguments from various disabilities. 297 00:36:39,850 --> 00:36:46,210 Again, Turing is obviously being humorous because he includes amongst the disabilities, being kind, 298 00:36:46,210 --> 00:36:52,780 beautiful, friendly, having initiative, having a sense of humour, telling right from wrong making mistakes. 299 00:36:52,780 --> 00:36:54,980 Okay, that's a disability. Maybe fall in love. 300 00:36:54,980 --> 00:37:03,040 Well, maybe that his enjoy strawberries and cream, learn from experience, use words properly, be the subject of its own thought. 301 00:37:03,040 --> 00:37:05,950 Do something really new. 302 00:37:05,950 --> 00:37:15,370 Now, obviously, the limited machines of 1950 couldn't do these, but it requires some argument to show that no machine could allow. 303 00:37:15,370 --> 00:37:19,510 Some of these just seem to take us back to the argument from consciousness. 304 00:37:19,510 --> 00:37:24,560 Okay, I'm being kind, you might say, to be genuinely kind. 305 00:37:24,560 --> 00:37:34,390 Do you actually have to have feeling for the other person or a robot is not kind, even if it does the kinds of things that kind people would do? 306 00:37:34,390 --> 00:37:38,740 Enjoy strawberries and cream? Well, presumably you need to be conscious to do that. 307 00:37:38,740 --> 00:37:48,940 So quite a lot of this just takes us back to that argument when we are actually talking about disabilities, like making a mistake, Turing remarks. 308 00:37:48,940 --> 00:37:55,960 This is a very old complaint. I mean, to say computers can't be intelligent because they can't make mistakes would be very odd. 309 00:37:55,960 --> 00:38:03,130 We normally think of the intelligent person as making fewer mistakes than the unintelligent person. 310 00:38:03,130 --> 00:38:12,820 But also, he points out that you could programme a machine to make errors in the same in a humanlike way, potentially. 311 00:38:12,820 --> 00:38:20,140 But again, it would be odd to say that worst performance makes it more intelligent. 312 00:38:20,140 --> 00:38:28,660 Number six, we come to Lady Lovelace's objection. This can seem quite a strong objection, or it's a very popular one. 313 00:38:28,660 --> 00:38:32,740 But I think Turing deals with this reasonably well. 314 00:38:32,740 --> 00:38:40,810 He quotes Ada Lovelace saying that Charles Babbage's analytical engine has no pretensions to originate anything. 315 00:38:40,810 --> 00:38:45,670 It can do whatever we know how to order it to perform. 316 00:38:45,670 --> 00:38:49,720 So a computer programme essentially just follows orders. 317 00:38:49,720 --> 00:38:56,860 Therefore, it can't be intelligent and you can see there are there are interesting issues raised here. 318 00:38:56,860 --> 00:39:02,800 For example, if we discuss the relation between intelligence and free will. 319 00:39:02,800 --> 00:39:11,200 But on the point about not originating anything, Turing points out that we can often be surprised by the outcome of things. 320 00:39:11,200 --> 00:39:23,500 I mean, it's perfectly possible, for example, to write a computer programme which experiments you can write a computer programme, 321 00:39:23,500 --> 00:39:28,480 which compares different strategies against each other. 322 00:39:28,480 --> 00:39:32,140 So, for example, you could write a computer programme to play a game, 323 00:39:32,140 --> 00:39:37,090 maybe that you've never played before something like three dimensional noughts and crosses or something like that. 324 00:39:37,090 --> 00:39:43,140 Maybe you've never. That but you could write a programme that learns strategies for playing that 325 00:39:43,140 --> 00:39:47,160 simply by trying different strategies and comparing them against each other. 326 00:39:47,160 --> 00:39:53,220 And then at the end of it, you've got a programme that plays the game far, far better than you could yourself. 327 00:39:53,220 --> 00:39:59,760 It's odd to say that it's just doing what it's told. No, it's actually learning. 328 00:39:59,760 --> 00:40:00,660 Now you might say, yeah, 329 00:40:00,660 --> 00:40:07,950 but it's not genuinely learning because the learning mechanism itself is under the control of an algorithm that you have written. 330 00:40:07,950 --> 00:40:15,450 Well, OK. But then if you're going to push this argument, I suspect that it's taking us back to issues about consciousness. 331 00:40:15,450 --> 00:40:26,380 Genuine agency again free will, but apparently tied in with the idea that one needs to be conscious of what one's doing. 332 00:40:26,380 --> 00:40:29,590 And I want to be fair to Ada Lovelace. 333 00:40:29,590 --> 00:40:41,110 She wrote some famous notes on Babbage's analytical engine in virtue of which she's often spoken of as the first computer programmer. 334 00:40:41,110 --> 00:40:52,930 And the quotation from Turing he was he was quoting from Note eight note gee, sorry of her 1842 notes, 335 00:40:52,930 --> 00:41:00,730 but Note A includes this interesting statement the operating mechanism might act upon other things. 336 00:41:00,730 --> 00:41:10,540 Besides, no were object found whose mutual fundamental relations could be expressed by those of the abstract science of operations 337 00:41:10,540 --> 00:41:18,370 and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine. 338 00:41:18,370 --> 00:41:24,430 Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and 339 00:41:24,430 --> 00:41:29,440 of musical composition was susceptible of such expression and adaptations, 340 00:41:29,440 --> 00:41:37,480 the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent. 341 00:41:37,480 --> 00:41:42,760 So it's a little unfair to Ada Lovelace that because of Turing's paper, 342 00:41:42,760 --> 00:41:50,710 she is very widely known as someone who denied that computers could originate anything when actually more prominently in that document, 343 00:41:50,710 --> 00:41:54,430 she was saying, uh, again. 344 00:41:54,430 --> 00:42:03,130 Very prophetically, the Babbage's analytical engine had the potential to operate in lots of different spheres, 345 00:42:03,130 --> 00:42:12,950 music as well as numbers, and to be creative in the sense of coming out with new compositions. 346 00:42:12,950 --> 00:42:23,210 OK. Just to finish the last few sections of Turing's paper, we get the argument from continuity in the nervous system. 347 00:42:23,210 --> 00:42:30,680 The nervous system is not a discrete state machine. A small error in the information about the size of a nervous impulse impinging 348 00:42:30,680 --> 00:42:36,200 on Neurone may make a large difference to the size of the outgoing impulse. 349 00:42:36,200 --> 00:42:45,200 And again, we he makes the point about how a discrete state machine can mimic a continuous system. 350 00:42:45,200 --> 00:42:49,430 The argument from informality of behaviour, 351 00:42:49,430 --> 00:42:56,840 if each man had a definite set of rules of conduct by which he regulated his life, he would be no better than a machine. 352 00:42:56,840 --> 00:43:03,860 But there are no such rules. So men cannot be machines. And he points out that this is a fallacy. 353 00:43:03,860 --> 00:43:04,760 And in any case, 354 00:43:04,760 --> 00:43:12,000 it's hard to establish that we're not in fact governed by laws of behaviour and laws of behaviour are not the same as rules of conduct. 355 00:43:12,000 --> 00:43:14,780 OK, rules of conduct tell you what you ought to do. 356 00:43:14,780 --> 00:43:24,170 Laws of behaviour are natural laws or consequences of natural laws, which determine how we do, in fact, behave. 357 00:43:24,170 --> 00:43:33,470 So, for example, many of you will have read section eight of Hume's first enquiry, where he discusses liberty and necessity. 358 00:43:33,470 --> 00:43:36,560 And Hume clearly takes the view that although we don't know what they are, 359 00:43:36,560 --> 00:43:48,420 there are underlying laws of behaviour that we are determined in what we do. 360 00:43:48,420 --> 00:43:53,670 Finally, in this section, we get the argument from extrasensory perception. 361 00:43:53,670 --> 00:43:58,770 This seems very odd. You might. What's that doing there? 362 00:43:58,770 --> 00:44:12,720 Well, first of all, Turing seems to think that the statistical evidence for telepathy and psychic Karnezis and so on is strong, indeed overwhelming. 363 00:44:12,720 --> 00:44:20,460 Most of us now inform people would not think this was true, but a guy called J.B. Rhine at the time was quite influential. 364 00:44:20,460 --> 00:44:32,290 He was doing a lot of experiments, and Hodges, in his biography of Turing, points out that Turing seems to have been impressed with that. 365 00:44:32,290 --> 00:44:37,950 And the sad fact is on either sad or happy, depending on how you look at it, I suppose. 366 00:44:37,950 --> 00:44:47,220 But the evidence simply hasn't stood up very well. I don't think many would say that there is compelling evidence for these phenomena. 367 00:44:47,220 --> 00:44:53,490 But anyway, during thought there was let suppose that there was, 368 00:44:53,490 --> 00:45:01,560 then you can see why cheering might be concerned because if extrasensory perception were possible, 369 00:45:01,560 --> 00:45:12,960 then that's something that a machine probably couldn't mimic. It could mean that we have going into the processing of our conversation forms 370 00:45:12,960 --> 00:45:22,740 of perception that Turing is not going to be able to imitate in his machine. 371 00:45:22,740 --> 00:45:37,500 Just by the way, I've alluded to Hodges biography. It does seem plausible that Turing's great interest in things like spiritualism and 372 00:45:37,500 --> 00:45:43,290 clairvoyance and that kind of thing were influenced by the death of Christopher Morcombe, 373 00:45:43,290 --> 00:45:54,390 his intimate friend when he was very young. I'm thinking about life after death, hoping that the soul continues to exist and so forth. 374 00:45:54,390 --> 00:46:02,820 So it's perhaps not surprising that it has, you know, that it features in in this paper. 375 00:46:02,820 --> 00:46:12,330 The finally, we get on to learning machines where Turing starts off saying, 376 00:46:12,330 --> 00:46:19,830 I have no very convincing arguments of a positive nature to support my views. 377 00:46:19,830 --> 00:46:24,990 The only really satisfactory support that can be given for the view expressed at the beginning of 378 00:46:24,990 --> 00:46:31,650 Section six will be that provided by waiting for the end of the century and then doing the experiment. 379 00:46:31,650 --> 00:46:36,480 So he's now referring back to those predictions that I drew your attention to. 380 00:46:36,480 --> 00:46:41,550 And he's basically saying, Well, I can't prove that what I say is right here. 381 00:46:41,550 --> 00:46:52,110 But wait and see. Well, I think there is a lot to be said for seeing his paper as. 382 00:46:52,110 --> 00:46:59,140 If you like propaganda, largely what he's doing is. 383 00:46:59,140 --> 00:47:08,980 You're saying you may naturally be very disinclined to think that computers can be intelligent? 384 00:47:08,980 --> 00:47:19,790 Let me give you a thought experiment. Suppose they could perform this well, would that not force you to revise your view? 385 00:47:19,790 --> 00:47:26,780 I actually think it would force you to revise your view. I think if computers could do this, general use of language would change. 386 00:47:26,780 --> 00:47:32,000 We would come to call them intelligent and so on. That's my prediction. 387 00:47:32,000 --> 00:47:40,850 Let's wait and see. But it gives a way of addressing the question which takes it away from all these 388 00:47:40,850 --> 00:47:46,010 what he thinks of as irrelevant issues like the theological objection and so on. 389 00:47:46,010 --> 00:47:50,120 And it potentially also takes it away from issues like consciousness, though, 390 00:47:50,120 --> 00:47:58,430 as we've seen, Turing doesn't separate those as much as perhaps he should. 391 00:47:58,430 --> 00:48:02,990 We've seen he's ending with the section on learning machines. 392 00:48:02,990 --> 00:48:09,960 He actually suggests that the way to get a machine that can perform to the desired standard might 393 00:48:09,960 --> 00:48:16,130 be to try to simulate a baby's mind rather than an adult and provide it with the ability to learn. 394 00:48:16,130 --> 00:48:17,060 OK. 395 00:48:17,060 --> 00:48:27,410 This seems frankly very unrealistic, but it's easy for us to say that because we've seen a lot of experience, you know, of artificial intelligence. 396 00:48:27,410 --> 00:48:29,600 We know how difficult it is to learn. 397 00:48:29,600 --> 00:48:36,020 We know how difficult it is to interact with the physical environment, something that babies do very effectively. 398 00:48:36,020 --> 00:48:42,950 They learn huge amounts through their physical senses to get a computer, 399 00:48:42,950 --> 00:48:51,710 to be able to learn in anything like that way so far beyond us and likely to be for some time. 400 00:48:51,710 --> 00:48:55,820 An important point that Turing makes here is that learning machine is highly likely to behave 401 00:48:55,820 --> 00:49:00,890 in ways that its programmers could neither foresee nor understand and also to make mistakes. 402 00:49:00,890 --> 00:49:06,680 So he's bolstering up points he's already made in the paper. 403 00:49:06,680 --> 00:49:15,260 Many people think that a very abstract activity, like the playing of chess might be a good place to start in attempting to match human intelligence. 404 00:49:15,260 --> 00:49:23,840 Chess was indeed seen as a paradigm case for artificial intelligence for many, many years. 405 00:49:23,840 --> 00:49:30,620 But perhaps instead, it's best to provide the machine with the best sense organs that money can buy and then teach it to 406 00:49:30,620 --> 00:49:36,530 understand and speak English so that it could then follow the normal teaching of a child again. 407 00:49:36,530 --> 00:49:43,400 This now seems incredibly naive. General natural language understanding is extraordinarily difficult, 408 00:49:43,400 --> 00:49:48,650 and progress in things like machine translation has tended to come in recent years, 409 00:49:48,650 --> 00:50:00,720 from humungous amounts of data analysed statistically, rather than the kind of formal methods that may initially have seemed more promising. 410 00:50:00,720 --> 00:50:04,850 Okay, on that uncertain note, as I say, the paper ends. 411 00:50:04,850 --> 00:50:10,160 Please make sure you read it carefully before the next lecture. 412 00:50:10,160 --> 00:50:18,920 I hope that what we've covered today will help you to appreciate both its virtues and its some of its vices. 413 00:50:18,920 --> 00:50:23,543 Thank you.