Problem Set 1

Due Monday Sept. 29

1. (~1 page) Discuss the nature of the concept of "memory" in Plato's "Meno". In particular, in what ways do the dialogue between Socrates and the slave boy illustrate (or fail to illustrate) what you regard as a definition of memory?

2. (a) (~1.5 pages) In Turing's paper "Computing Machinery and Intelligence", Turing offers a variety of potential arguments against the possibility that a computer could (eventually) pass the Turing test for intelligence. Which (if any) of these arguments do you find particularly provocative? (You may or may not actually *agree* with the argument, but the issue is whether you find it interesting.)

(b) (~1.5 pages) Searle's paper "Minds, Brains, and Programs" has a similar structure to Turing's, offering a variety of counterarguments to his "Chinese Room" thought experiment. Again, which (if any) of these arguments do you find particularly provocative?

3. (~1.5 pages) Consider the following water transfer puzzle. You have three jars--one whose capacity is 8 quarts, one of 5 quarts, and one of 3 quarts. At the start of the puzzle, the 8 quart jar is filled, and the other two jars are empty. Your job is to transfer water (without measuring) between jars so that eventually there are 4 quarts in the large jar, and 4 quarts in the 5-quart jar. Each transfer must either fill the target jar or empty the source jar (or both).

3a. List all the possible achievable states of this puzzle, using a format like the following:

A. 8 0 0

B. 5 0 3

C. 3 5 0

and so forth. In other words, use three numbers to designate a state in which the first number is the amount in the 8-quart jar, the second number is the amount in the 5-quart jar, and the third number is the amount in the 3-quart jar. (Hint: if you label each state with a letter, as I've done for the three states listed above, you won't need the entire alphabet to list them all!)

3b. Show the solution to the problem by listing a sequence of states from part 3a. For instance, if your first move is to transfer the 8-quart jar to the 5-quart jar, then your solution will begin A --> C --> and so forth, if you use the labeling scheme above.

3c. Show a possible order of states that would be encountered in breadth-first search for this puzzle. For instance, if the start state is A, then the next two states encountered would be one move away--namely, states B and C. Show all the new states (i.e., the ones we have not yet encountered) that are two moves away; three moves away; and so forth. [Note: we will discuss breadth-first search in class on Monday 9/22.]