1. Lecture # 39 What Can’t Be Computed?

2. Computability Tractable problems (P): Can be solved by a a computer is some deterministic (reasonable) polynomial time –What is a ”reasonable” running time? Intractable problems (NP): 1. Guess the solution 2. Answer must be verifiable in polynomial time

3. Goal: transfer all n disks from peg 1 to peg 3 Rules: –move one disk at a time –never place a larger disk on top of a smaller one Example: Towers of Hanoi Simonas Šaltenis, Aalborg University, simas@cs.auc.dk 1 2 3

4. How Long? (http://www.mathcs.org/java/programs/Hanoi/index.html) Towers of Hanoi

5. How Long? 64 disks Move 1 disk per second 585 billion years Is that tractable/reasonable? Towers of Hanoi

6. What are some other hard problems?

7. Traveling Salesman Problem A traveling salesperson needs to visit n cities Is there a route of at most d length? (decision problem) Simonas Šaltenis, Aalborg University, simas@cs.auc.dk

8. TSP Algorithms Naive solutions take n! time in worst-case, where n is the number of ”legs” or ”hops” on the trip No polynomial-time algorithms are known –TSP is an NP-complete problem Longest Path between cities A and B is also NP-complete Simonas Šaltenis, Aalborg University, simas@cs.auc.dk

9. Can Computers Think? What is thinking? (http://www.youtube.com/watch?v=VSdxqIBfEAw)http://www.youtube.com/watch?v=VSdxqIBfEAw How can you measure thinking? Does it involve cognition? How do you measure/evaluate intelligence?

10. One Measure of Thinking Type a question on a computer - send a copy to a human - send a copy to computer If, after a reasonable amount of time you can’t tell which is which, does that mean the computer is thinking (is intelligent?)

11. Can Computers Express Emotion? Which is harder? Thinking or Expressing Emotion?

12. Can Computers Play Chess? What constitutes playing chess? How about beating a grand master? How can a computer do this without being able to think?

13. Can Computers Play Chess? Use a big table of possible moves given a specific board configuration Look ahead as far as possible Use a database of opening and end games

14. Can Computers Play Chess? Kasparov won IBM’s “DEEP BLUE” in ‘96 DEEP BLUE beat Kasparov in ‘97

15. Can Computers be Creative? Can computers do art work? (http://www.soban-art.com/)http://www.soban-art.com/ Can computers write stories, compose music? Can computers perform medical diagnoses? What is Artificial Intelligence?

16. Can Computers be Creative? What is the essence of creativity? Is it following procedures or rules? Is it unpredictable departure from rules? What is the role of agency in creativity?

17. Can Computers be Creative? Is creativity random? Is creativity entropic? Is creativity algorithmic?