1. How do minds work? What does it mean to think? Can airplanes fly? Can submarines swim? Can computers think? What does it mean to think? Can airplanes fly? Can submarines swim? Can computers think?

2. What is the relation between mind and brain? Traditional view: Locke Matter, incogitative Matter and Motion, whatever changes it might produce of Figure and Bulk, could never produce Thought. I appeal to everyone’s own thoughts, whether he cannot as easily conceive Matter produced by nothing, as Thought produced by pure Matter, when before there was no such thing as Thought, or an intelligent Being existing. Traditional view: Locke Matter, incogitative Matter and Motion, whatever changes it might produce of Figure and Bulk, could never produce Thought. I appeal to everyone’s own thoughts, whether he cannot as easily conceive Matter produced by nothing, as Thought produced by pure Matter, when before there was no such thing as Thought, or an intelligent Being existing.

3. Descartes’ view Mind and Brain are separate But connected at the pineal gland Mind and Brain are separate But connected at the pineal gland

4. What can Computer Science tell us about these questions?

5. Stuart M. Shieber Division of Engineering and Applied Sciences Harvard University Stuart M. Shieber Division of Engineering and Applied Sciences Harvard University Resurrecting the Turing Test

6. Turing’s Goal Alan Turing, Computing Machinery and Intelligence, 1950: Can machines think? How could we tell? Flashback to the 17th century: Do animals have souls? How could we tell? Alan Turing, Computing Machinery and Intelligence, 1950: Can machines think? How could we tell? Flashback to the 17th century: Do animals have souls? How could we tell?

7. Descartes on the Singularity of Verbal Behavior “In fact, none of our external actions can show anyone who examines them that our body is not just a self-moving machine but contains a soul with thoughts, with the exception of spoken words, or other signs that have relevance to particular topics without expressing any passion.” — Rene Descartes, Letter to the Marquess of Newcastle, 1646 “In fact, none of our external actions can show anyone who examines them that our body is not just a self-moving machine but contains a soul with thoughts, with the exception of spoken words, or other signs that have relevance to particular topics without expressing any passion.” — Rene Descartes, Letter to the Marquess of Newcastle, 1646

8. Cordemoy on Indistinguishability “That if the Bodies, which are like mine, had nothing but the facilness of pronouncing Words, I should not therefore believe that they had the advantage of being united to Souls: But then, if I finde by all the Experiments, I am capable to make, that they use speech as I do, I shall think, I have infallible reason to believe that they have a soul as I.” — Geraud de Cordemoy “That if the Bodies, which are like mine, had nothing but the facilness of pronouncing Words, I should not therefore believe that they had the advantage of being united to Souls: But then, if I finde by all the Experiments, I am capable to make, that they use speech as I do, I shall think, I have infallible reason to believe that they have a soul as I.” — Geraud de Cordemoy

9. Turing’s Agenda “I propose to consider the question, ‘Can machines think?’ This should begin with definitions of the meaning of the terms ‘machine’ and ‘think’. The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous. If the meaning of the words ‘machine’ and ‘think’ are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to the question, ‘Can machines think?’ is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words.” — Alan Turing, Computing machinery and intelligence, 1950 “I propose to consider the question, ‘Can machines think?’ This should begin with definitions of the meaning of the terms ‘machine’ and ‘think’. The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous. If the meaning of the words ‘machine’ and ‘think’ are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to the question, ‘Can machines think?’ is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words.” — Alan Turing, Computing machinery and intelligence, 1950

10. Division of Engineering and Applied Sciences Harvard University Division of Engineering and Applied Sciences Harvard University Turing’s “Imitation Game” InterrogatorB (a person)A (a machine)

11. Necessary versus Sufficient Conditions Is ability to pass a Turing Test a necessary condition of intelligence? “May not machines carry out something which ought to be described as thinking but which is very different from what a man does? This objection is a very strong one, but at least we can say that if, nevertheless, a machine can be constructed to play the imitation game satisfactorily, we need not be troubled by this objection.” — Turing, 1950 Is ability to pass a Turing Test a sufficient condition of intelligence? Is ability to pass a Turing Test a necessary condition of intelligence? “May not machines carry out something which ought to be described as thinking but which is very different from what a man does? This objection is a very strong one, but at least we can say that if, nevertheless, a machine can be constructed to play the imitation game satisfactorily, we need not be troubled by this objection.” — Turing, 1950 Is ability to pass a Turing Test a sufficient condition of intelligence?

12. Turing: Replace the Question “Instead of attempting such a definition I shall replace the question by another.... The original question, ‘Can machines think?’ I believe to be too meaningless to deserve discussion.” — Turing, 1950 “If Turing intends that the question of the success of the machine at the imitation game replace the question about machines thinking, then it is difficult to understand how we are to judge the propriety and adequacy of the replacement if the question being replaced is too meaningless to deserve discussion. Our potential interest in the imitation game is aroused not by the fact that a computer might learn to play yet another game, but that in some way this test reveals a connection between possible computer activities and our ordinary concept of human thinking.” — Moor, 1976 “Instead of attempting such a definition I shall replace the question by another.... The original question, ‘Can machines think?’ I believe to be too meaningless to deserve discussion.” — Turing, 1950 “If Turing intends that the question of the success of the machine at the imitation game replace the question about machines thinking, then it is difficult to understand how we are to judge the propriety and adequacy of the replacement if the question being replaced is too meaningless to deserve discussion. Our potential interest in the imitation game is aroused not by the fact that a computer might learn to play yet another game, but that in some way this test reveals a connection between possible computer activities and our ordinary concept of human thinking.” — Moor, 1976

13. The Turing Test is not a sufficient condition for intelligence. Gundersonflexibility of behavior Davidsonsemantics Searleintentionality Blockrichness of information processing... The Turing Test is a sufficient condition for intelligence. Dennett The Turing Test is not a sufficient condition for intelligence. Gundersonflexibility of behavior Davidsonsemantics Searleintentionality Blockrichness of information processing... The Turing Test is a sufficient condition for intelligence. Dennett Current Views

14. Dennett: The Turing Test is Sufficient “The Turing test in unadulterated, unrestricted form, as Turing presented it, is plenty strong if well used. I am confident that no computer in the next twenty years is going to pass the unrestricted Turing test. They may well win the World Chess Championship or even a Nobel Prize in physics, but they won't pass the unrestricted Turing test. Nevertheless, it is not, I think, impossible in principle for a computer to pass the test, fair and square. I'm not running one of those a priori ‘computers can't think’ arguments. I stand unabashedly ready, moreover, to declare that any computer that actually passes the unrestricted Turing test will be, in every theoretically interesting sense, a thinking thing.” — Dennett, 1985 “The Turing test in unadulterated, unrestricted form, as Turing presented it, is plenty strong if well used. I am confident that no computer in the next twenty years is going to pass the unrestricted Turing test. They may well win the World Chess Championship or even a Nobel Prize in physics, but they won't pass the unrestricted Turing test. Nevertheless, it is not, I think, impossible in principle for a computer to pass the test, fair and square. I'm not running one of those a priori ‘computers can't think’ arguments. I stand unabashedly ready, moreover, to declare that any computer that actually passes the unrestricted Turing test will be, in every theoretically interesting sense, a thinking thing.” — Dennett, 1985

15. I conclude that the capacity to emit sensible responses is not sufficient for intelligence, and so the neo-Turing Test conception of intelligence is refuted (along with the older and cruder Turing Test conceptions). I also conclude that whether behavior is intelligent behavior is in part a matter of how it is produced. Even if a system has the actual and potential behavior characteristic of an intelligent being, if its internal processes are like those of the machine described, it is not intelligent. — Block, 1981 I conclude that the capacity to emit sensible responses is not sufficient for intelligence, and so the neo-Turing Test conception of intelligence is refuted (along with the older and cruder Turing Test conceptions). I also conclude that whether behavior is intelligent behavior is in part a matter of how it is produced. Even if a system has the actual and potential behavior characteristic of an intelligent being, if its internal processes are like those of the machine described, it is not intelligent. — Block, 1981 Block: The Turing Test is Insufficient

16. If an agent passes a Turing Test, then it produces a sensible sequence of verbal responses to a sequence of verbal stimuli. The Turing Syllogism

17. If an agent passes a Turing Test, then it produces a sensible sequence of verbal responses to a sequence of verbal stimuli. If an agent produces a sensible sequence of verbal responses to a sequence of verbal stimuli, then it is intelligent. If an agent passes a Turing Test, then it produces a sensible sequence of verbal responses to a sequence of verbal stimuli. If an agent produces a sensible sequence of verbal responses to a sequence of verbal stimuli, then it is intelligent. The Turing Syllogism

18. If an agent passes a Turing Test, then it produces a sensible sequence of verbal responses to a sequence of verbal stimuli. If an agent produces a sensible sequence of verbal responses to a sequence of verbal stimuli, then it is intelligent. Therefore, if an agent passes a Turing Test, then it is intelligent. If an agent passes a Turing Test, then it produces a sensible sequence of verbal responses to a sequence of verbal stimuli. If an agent produces a sensible sequence of verbal responses to a sequence of verbal stimuli, then it is intelligent. Therefore, if an agent passes a Turing Test, then it is intelligent. The Turing Syllogism

19. If an agent passes a Turing Test, then it produces a sensible sequence of verbal responses to a sequence of verbal stimuli. If an agent produces a sensible sequence of verbal responses to a sequence of verbal stimuli, then it is intelligent. Therefore, if an agent passes a Turing Test, then it is intelligent. If an agent passes a Turing Test, then it produces a sensible sequence of verbal responses to a sequence of verbal stimuli. If an agent produces a sensible sequence of verbal responses to a sequence of verbal stimuli, then it is intelligent. Therefore, if an agent passes a Turing Test, then it is intelligent. The Turing Syllogism The Turing Test conception of intelligence:

20. If an agent produces a sensible sequence of verbal responses to a sequence of verbal stimuli, then it is intelligent. The Occasional Conception

21. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli, whatever they may be, then it is intelligent. The Capacity Conception Promissory Note The Turing Test needs to demonstrate Capacitya general capacity for sensible response to verbal stimuli Promissory Note The Turing Test needs to demonstrate Capacitya general capacity for sensible response to verbal stimuli

22. The Aunt Bertha Machine

23. Exponential Growth Assume each time the judge asks a question, she picks between two questions based on what has happened so far Questions Asked Possible responses 12 24 38 416 532 664 n 2 n Assume each time the judge asks a question, she picks between two questions based on what has happened so far Questions Asked Possible responses 12 24 38 416 532 664 n 2 n

24. Storage versus Length exponentia l

25. Length versus Storage logrithmic

26. Intelligence is the capacity to emit sensible sequences of responses to stimuli, so long as this is accomplished in a way that averts exponential explosion of search. (Block, 1981) If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli, whatever they may be, and without requiring exponential storage, then it is intelligent. Intelligence is the capacity to emit sensible sequences of responses to stimuli, so long as this is accomplished in a way that averts exponential explosion of search. (Block, 1981) If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli, whatever they may be, and without requiring exponential storage, then it is intelligent. The Compact Conception

27. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli, whatever they may be, and without requiring exponential storage, then it is intelligent. The Compact Conception

28. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli, whatever they may be, and without requiring exponential storage, then it is intelligent. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli that is of length at least logarithmic in the storage capacity of the agent, whatever they may be, then it is intelligent. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli, whatever they may be, and without requiring exponential storage, then it is intelligent. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli that is of length at least logarithmic in the storage capacity of the agent, whatever they may be, then it is intelligent. The Compact Conception Modified ^ Modified ^

29. The Turing Test needs to demonstrate Capacity: a general capacity for sensible response to verbal stimuli Complexityof length at least logarithmic in the storage capacity of the subject under test. The Turing Test needs to demonstrate Capacity: a general capacity for sensible response to verbal stimuli Complexityof length at least logarithmic in the storage capacity of the subject under test. Promissory Notes

30. Proofs based on interaction and randomization. Interactive Proofs

31. P[rover] examines the jar to obtain bean count b 0 V[erifier] privately removes d jelly beans (0 or 1, chosen randomly) and shakes the jar P examines the jar to obtain bean count b 1 P reports b 1 – b 0 If d = b 1 – b 0, V accepts; otherwise V rejects P[rover] examines the jar to obtain bean count b 0 V[erifier] privately removes d jelly beans (0 or 1, chosen randomly) and shakes the jar P examines the jar to obtain bean count b 1 P reports b 1 – b 0 If d = b 1 – b 0, V accepts; otherwise V rejects Jelly Bean Counting

32. Probabilistic proof condition No false rejections False acceptance 1/2 the time Exponential confidence For k rounds, false acceptance 1/2 k Only verifier receives proof Verifier can generate accepting protocols unilaterally Probabilistic proof condition No false rejections False acceptance 1/2 the time Exponential confidence For k rounds, false acceptance 1/2 k Only verifier receives proof Verifier can generate accepting protocols unilaterally Properties of the Interactive Proof Protocol

33. Division of Engineering and Applied Sciences Harvard University Division of Engineering and Applied Sciences Harvard University The Turing Test as an Interactive Proof Space of all possible verbal stimuli Space of all possible verbal stimuli Subspace of verbal stimuli with sensible responses Subspace of verbal stimuli with sensible responses

34. Division of Engineering and Applied Sciences Harvard University Division of Engineering and Applied Sciences Harvard University Run k rounds of Turing Tests. Observe that sensible responses are generated on a fraction of inputs greater than the threshold t s. Then, with probability of error exponentially small in k, sensible responses are generated on at least a fraction t l of all inputs. The Turing Test as an Interactive Proof

35. The Turing Test needs to demonstrate Capacitya general capacity for sensible response to verbal stimuli Complexityof length at least logarithmic in the storage capacity of the subject under test. The Turing Test needs to demonstrate Capacitya general capacity for sensible response to verbal stimuli Complexityof length at least logarithmic in the storage capacity of the subject under test. Promissory Notes

36. Division of Engineering and Applied Sciences Harvard University Division of Engineering and Applied Sciences Harvard University Size of the Universe Here, now Big bang 15*10 9 light-years Time

37. Storage Capacity of the Universe Volume: (15*10 9 light-years) 3 = (15*10 9 *10 16 meters) 3 Density: 1 bit per (10 -35 meters) 3 Total storage capacity: 10 184 bits < 10 200 bits < 2 670 bits Critical Turing Test length: 670 bits < 670 characters < 140 words < 1 minute Volume: (15*10 9 light-years) 3 = (15*10 9 *10 16 meters) 3 Density: 1 bit per (10 -35 meters) 3 Total storage capacity: 10 184 bits < 10 200 bits < 2 670 bits Critical Turing Test length: 670 bits < 670 characters < 140 words < 1 minute

38. If an agent passes a Turing Test, then it produces a sensible sequence of verbal responses to a sequence of verbal stimuli. If an agent produces a sensible sequence of verbal responses to a sequence of verbal stimuli, then it is intelligent. Therefore, if an agent passes a Turing Test, then it is intelligent. If an agent passes a Turing Test, then it produces a sensible sequence of verbal responses to a sequence of verbal stimuli. If an agent produces a sensible sequence of verbal responses to a sequence of verbal stimuli, then it is intelligent. Therefore, if an agent passes a Turing Test, then it is intelligent. The Turing Syllogism

39. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli, whatever they may be, and without requiring exponential storage, then it is intelligent. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli that is logarithmic in the storage capacity of the agent, whatever they may be, then it is intelligent. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli, whatever they may be, and without requiring exponential storage, then it is intelligent. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli that is logarithmic in the storage capacity of the agent, whatever they may be, then it is intelligent. The Compact Conception Modified ^ Modified ^

40. If an agent passes k rounds of a Turing Test of at least one minute in length, then with probability of error exponentially small in k, it has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli that is logarithmic in the storage capacity of the agent, whatever they may be. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli that is logarithmic in the storage capacity of the agent, whatever they may be, then it is intelligent. Therefore, if an agent passes a Turing Test, then it is intelligent. If an agent passes k rounds of a Turing Test of at least one minute in length, then with probability of error exponentially small in k, it has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli that is logarithmic in the storage capacity of the agent, whatever they may be. If an agent has the capacity to produce a sensible sequence of verbal responses to a sequence of verbal stimuli that is logarithmic in the storage capacity of the agent, whatever they may be, then it is intelligent. Therefore, if an agent passes a Turing Test, then it is intelligent. The Turing Syllogism The modified compact conception of intelligence:

41. The Turing Test can be viewed as an interactive proof of intelligence: In form In performance How might it not be exponentially hard? Does the Turing test answer the question of whether computers can think? The Turing Test can be viewed as an interactive proof of intelligence: In form In performance How might it not be exponentially hard? Does the Turing test answer the question of whether computers can think? Discussion