From the Princeton Weekly Bulletin, April 28, 1997
What is learning?
Philosopher, electrical engineer examine the question from different viewpoints--in the same course
By Caroline Moseley
What is learning? This question, central to the enterprise of any university, is being examined in an innovative interdisciplinary course called Learning Theory and Epistemology, taught by Professor of Philosophy Gilbert Harman and Assistant Professor of Electrical Engineering Sanjeev Kulkarni.
This union of apparently disparate approaches to the study of learning theory makes perfect sense, say the instructors.
"In recent years," observes Harman, "aspects of the philosophical problem of induction have been studied by logicians, computer scientists, psychologists, engineers and statisticians -- among others. While much of the work has been technical, the ideas are simple and can be understood by anyone, regardless of background."
Harman's broad interests within philosophy include theoretical and practical reasoning and cognitive science. Currently director of the Program in Cognitive Science, he has been a member of the faculty since 1963. When Kulkarni, who studies statistical pattern recognition and machine learning, came to Princeton in 1991, Harman contacted him immediately "to explore areas of common interest. We agreed that there are fundamental advances that cover so many areas, they should be made accessible to a wide audience. The richer the mix of students, the better."
The result is ELE 218/PHI 218, on which both professors have been working for about a year and half, with support from the President's 250th Anniversary Fund for Innovation in Undergraduate Education.
The course meets three times a week, for two lectures and a precept. "This is truly 'team teaching,'" says Andrew Houck '00. "In each lecture, professors Harman and Kulkarni both speak, often alternating, presenting differing views on the same material. It's rare when one professor talks for more than five minutes without comment by the other."
"One of the nice things about 218 is that it's really rather spare: An over-head projector, a blackboard and two professors are all we need," says John Griffin '99, an English major who hopes to earn a certificate in Theater and Dance.
Can't guarantee sun will rise
In the course, "We're attempting to develop as precise as possible a definition of the nature and limits of learning," says Harman. "There are a number of paradigms that can be used to explore the issue, and what ties them together is the urge to formalize."
"How to draw inferences from data and how to decide if we're justified in drawing those inferences, are philosophical problems," explains Kulkarni, "but there are technical methods that allow us to quantify those problems."
For example, among the tools the class studies are Bayesian statistics. In the 18th century, mathematician Thomas Bayes developed a method of inference from probability that allows prediction. Ian Hunter Todd '99, a civil engineering major, explains it this way: "You can't guarantee the sun will rise tomorrow just because it has risen every day so far, but Bayes said if you've seen the sun rise for a number of days, you can claim with greater confidence that it will, in fact, rise again."
Course readings are in textbooks such as Clark Glymour's Thinking Things Through: An Introduction to Philosophical Issues and Achievements (1992) and Tom Mitchell's Machine Learning (1997), as well as excerpts from numerous other sources, including articles by both professors.
In addition to a term paper, there are also weekly problem sets.
Try this. "A process produces a sequence of numbers as output. Supposing that the first three numbers produced are 2, 4 and 8, name two of the most likely rules for the sequence. What would you predict as the next number? What justification could be given for that prediction? (Supposing the next three numbers are 14, 22 and 32, what would you predict for the seventh number?)
"A similar question arises about the justification for scientific inquiry. For example, when scientists accept an inverse square law of gravitation rather than some more complicated law that would account equally well for the data, is there a way to justify their conclusion without supposing that nature is simple? Explain."
Variety enhances value to all
The course, by its nature, has attracted students of varied interests and backgrounds--thereby enhancing its value to all, according to participants.
"As you take more and more courses within your major," Houck observes, "you become less and less open to the contributions everyone in other departments has to offer. Here, the engineer can gain a philosophical perspective, while the nonmathematical oriented people can get a taste of how learning applies to machines. It wakes everybody up."
The professors have learned along with the students in this new course. It's a challenge, Kulkarni notes, "to make the technical level suitable for everyone, yet maintain the rigor of the course."
Apparently they have been successful in creating what Kulkarni calls "a bridge between humanities and engineering." Griffin says that "equations that made me run for cover in high school" have become clear, because "Harman and Kulkarni have a way of teaching the math that I can understand."
Learning Theory and Epistemology is probably unique, the teachers believe. "As far as we know, there is no course anywhere that talks about these matters at the level we do," says Kulkarni. "There are certainly more advanced courses in many related areas in many universities (including Princeton), but nothing this accessible."
In fact, says Harman, "We tried to find a course like this somewhere, so we could look at the materials, but there just wasn't anything. We may end up writing our own text."