bobgian@psuvax.UUCP (01/01/84)
1. What is the sum of the first N positive integers? That is, what is: [put here the sigma-sign notation for the sum] 2. Prove that the your answer works for any N > 0. 3. What is the sum of the squares of the first N positive integers: [put here the sigma-sign notation for the sum] 4. Again, prove it. 5. The proofs you gave (at least, if you are utilizing "traditional" mathematical background,) are based on "mathematical induction". Briefly state this principle and explain why it works. 6. If you are like most people, your definition will work only over the domain of NATURAL NUMBERS (positive integers). Can this definition be extended to work over ANY countable domain? 7. Consider the lattice of points in N-dimensional space having integer valued coordinates. Is this space countable? 8. Write a program (or express an algorithm in pseudocode) which returns the number of points in this space (the one in #7) inside an N-sphere of radius R (R is a real number > 0). 9. The domains you have considered so far are all countable. The problem solving methods you have used (if you're "normal") are based on mathematical induction. Is it possible to extend the principle of mathematical induction (and recursive programming) to NON-COUNTABLE domains? 10. If you answered #9 NO, why not? If you answered it YES, how? 11. Problems #1 and #3 require you to perform INDUCTIVE REASONING (a related but different use of the term "induction"). Discuss some of the issues involved in getting a computer to perform this process automatically. (I mean the process of generating a finite symbolic representation which when evaluated will return the partial sum for an infinite sequence.) 12. Consider the "sequence extrapolation" task: given a finite sequence of symbols, predict the next few terms of the sequence or give a rule which can generate ALL the terms of the sequence. Is this problem uniquely solvable? Why or why not? 13. If you answered #12 YES, how would you build a computer program to do so? 14. If you answered #12 NO, how could you constrain the problem to make it uniquely solvable? How would you build a program to solve the constrained problem? 15. Mankind is faced with the threat of nuclear annihilation. Is there anything the field of AI has to offer which might help avert that threat? (Don't just say "yes" or "no"; come up with something real.) 16. Assuming mankind survives the nuclear age, it is very likely that ethical issues relating to AI and the use of computers will have very much to do with the view the "person on the street" has of the human purpose and role in the Universe. In what way can AI researchers plan NOW so that these ethical issues are resolved to the benefit of the greatest number of people? 17. Could it be that our (humankind's) purpose on earth is to invent and build the species which will be the next in the evolutionary path? Should we do so? How? Why? Why not? 18. Suppose you have just discovered the "secret" of Artificial Intelligence; that is, you (working alone and in secret) have figured out a way (new hardware, new programming methodology, whatever) to build an artificial device which is MORE INTELLIGENT, BY ANY DEFINITION, BY ANY TEST WHATSOEVER, that any human being. What do you do with this knowledge? Explain the pros and cons of several choices. 19. Question #9 indicates that SO FAR all physical symbol systems have dealt ONLY with discrete domains. Is it possible to generalize the idea to continuous domains? Since many aspects of the human nervous system function on a continuous (as opposed to discrete) basis, is it possible that the invention of CONTINUOUS PHYSICAL SYMBOL SYSTEMS might provide part of the key to the "secret of intelligence"? 20. What grade do you feel you DESERVE in this course? Why? What grade do you WANT? Why? If the two differ, is there anything you want to do to reduce the difference? Why or Why Not? What is it? Why is it (or is it not) worth doing? -- Spoken: Bob Giansiracusa Bell: 814-865-9507 Bitnet: bobgian@PSUVAX1.BITNET Arpa: bobgian%psuvax1.bitnet@Berkeley CSnet: bobgian@penn-state.csnet UUCP: allegra!psuvax!bobgian USnail: Dept of Comp Sci, Penn State Univ, University Park, PA 16802