1. CSC – 332 Data Structures Dr. Curry Guinn

2. Today Go over Homework 2 Godel, Escher, Bach

3. Homework 2 – Problem 1 See White Board

4. Homework 2 – Problem 2 See White Board

5. Homework 2 – Problem 3 See white board

6. Homework 2 – Problem 4 a)

7. Problem 4a with bigger values for n

8. Homework 2b up to 1000

9. 2b for, ahem, larger values

10. Problem 4 c and d

11. Problems e

12. Problem f

13. Problem g

14. G ö del, Escher, Bach: An Eternal Golden Braid What is the relationship between Bach, Escher, G ö del? What does this have to do with Computer Science?

15. J. S. Bach (1685-1750) The “Old Bach” Story Describe some ways a theme can be played against itself What is the “Endlessly Rising Canon”? –An Example, although not Bach’s Canon which is a bit longer and more complexAn Example, although not Bach’s Canon which is a bit longer and more complex –Music.zipMusic.zip –http://www.youtube.com/watch?v=A41CITk85jkhttp://www.youtube.com/watch?v=A41CITk85jk Music puzzles were the Sudoku of the day –Musical composition followed such precise rules such that with training a person could complete a score that someone else began.

16. M. C. Escher (1902-1972) Dutch (Netherlands) Explored –Perspective –Perception –Impossible objects –Tessellations –Infinity

22. Kurt G ö del (1906-1978) Incompleteness Theorem (1931) What does it mean for a mathematical or logical system to be consistent? What does it mean for a mathematical or logical system to be complete?

23. Principia Mathematica Bertrand Russell, Alfred North Whitehead 1910-1913 There are true statements in the number theory described in the Principia Mathematica that do not have a proof within that number theory.

24. Some Bothering Paradoxes This statement is false. Russell’s paradox of sets –Sets can contain sets –A set could contain itself –Define a “run-of-the-mill” set to be one that does not contain itself –Look at the set of “run-of-the-mill” sets –Does it contain itself?

25. Computers Can Only Do What They Are Programmed To Do Can computers ever be intelligent? Creative? Flexible? Synthesize new concepts? If so, that seems a paradox.

26. Three-Part Invention Dialogue parodying Lewis Carroll Achilles and the Tortoise Who is Zeno? What are Zeno’s Paradoxes?Zeno’s Paradoxes

27. Chapter 1: The MU-puzzle Hofstadter is setting up a syntactic logical system Proofs are “mechanical” – you must follow rules What does it mean to jump out of the system? What is a decision procedure?

28. Which Box Contains the Gold? Two boxes are labeled "A" and "B". A sign on box A says "The sign on box B is true and the gold is in box A". A sign on box B says "The sign on box A is false and the gold is in box A". Assuming there is gold in one of the boxes, which box contains the gold?

29. For Next Class, Thursday Homework 3 due February 06Homework 3 For Thursday –Weiss, Chapter 3 ArrayLists (Chapter 3)