CSCI 1240: The Computational World Problem Set 1: Week 1 ...

CSCI 1240: The Computational World
Problem Set 1: Week 1
Problem 1. (5 points) Write a brief (~300 words) response to the Turing paper selecting
one of the objections mentioned in the paper and explaining why you think that objection
either is or is not particularly provocative.
Problem 2. (5 points) Write a brief (~300 words) response to John Searle's "Chinese
Room" thought experiment, selecting one of the objections mentioned in Searle's paper
and explaining why you think the objection, or Searle's response, is particularly effective.
Problem 3. (4 points) Find an implementation of Weizenbaum's "Doctor" program on
the Web (you might also find it under the name of "Eliza"), and act the role of the patient
for at least a dozen or so exchanges. Analyze the program's responses along the following
lines: would you be led to believe that the program actually knows anything about
psychiatry? About you and your problems in particular? Point to a particular response
and discuss how that response could be made by a program that knows some syntactic
rules (such as changing first-person sentences to second-person sentences) without
actually knowing any semantics (meaning) about the topic under discussion. Do you
think the Doctor program might have any therapeutic value (for instance, if you were
actually feeling troubled about something, would you derive any comfort from a
"conversation" with the program)?
Problem 4. (3 points) In lecture, we discussed the difficulty that computers have in
understanding simple stories, and we suggested that part of that difficulty is because it is
hard to program in "common sense knowledge". Recently, there have been impressive
attempts to use the vast knowledge base of the Web as a source of all sorts of factual
information (including, perhaps, some "common sense" knowledge)–a source that
computers can automatically search. Take a look at IBM's hot-off-the-press "Watson"
Jeopardy-playing system, as described in the New York Times:
http://www.nytimes.com/2010/06/20/magazine/20Computer-t.html?hp
Try playing "Jeopardy!" against Watson, and see how you do (I beat the program, but just
barely):
http://www.nytimes.com/interactive/2010/06/16/magazine/watson-trivia-game.html?hp
On what sorts of questions did you do better than the computer? On what sorts did you do
worse? Discuss your impressions of the sort of "knowledge" that Watson appears to have.
Problem 5. (8 points) For each of the following sets, identify whether the size (or to be
technical, "cardinality") of the set is finite, infinite-and-countable, or infinite-anduncountable.
Explain your answer in each case. For extra credit: if the set is finite, write
an expression that gives the number of items in the set.

a. The set of all rational numbers between 0 and 0.001
b. The set of all irrational numbers between 0 and 0.001
c. The set of all distinct ways of ordering a deck of 52 cards.
d. The set of all possible ways of assigning either 0 or 1 to 40 distinct slots. (Another way
of thinking of this: imagine 40 blanks. How many distinct binary numbers can you write
in those 40 blanks?)
e. The set of all possible ways of assigning either 0 or 1 to a countably infinite number of
slots. (Another way of thinking about this: how many possible infinite-length binary
numbers can you write?)
f. The set of all perfect squares (1, 4, 9, 16…).
g. The set of all distinct pairs from an overall set of 100 items. (Another way of thinking
of this: there are 100 people in a room. How many distinct handshakes are possible?)
h. The set of all points in the interior of a unit circle (the circle of radius 1).
i. The set of all possible (syntactically correct) Turing machine programs that can be
written in at most 500 standard alphabetic characters.
j. The set of all possible programs for a Turing machine.