Close X

# Computers Are Precise - That's Their Problem

THE trouble with computers, say Daniel McNeill and Paul Freiberger in their engaging new book "Fuzzy Logic," is that they're programmed as yes-no, on-off, black-and-white machines in a complex world where nothing is so clear-cut. What computers need, the authors say, is a healthy dose of fuzziness.

Fuzzy logic sprang into being 29 years ago when Lotfi Zadeh, an Azerbaijani-born professor at the University of California at Berkeley, discovered it in a flash one evening. Fuzzy logic confounds conventional logic because it deals with set theory in a new way, the authors say.

If you had New Math, you may remember sets. Imagine a set of men. Jim is 6 feet, 6 inches, Tom is 5 feet, 11 inches, and Bob is 5 feet, 9 inches. Draw a circle around the men who make up the tall men set. Clearly Jim belongs in the set. Does Tom?

Conventional logic forces you to create a definition of tall. If it's 5 feet, 10 inches, then Tom is in the set. If it's 6 feet, he's not.

The problem with this logic is that its precision is artificial, the authors argue. The line that separates tall men from others is not so clear in the real world. If Tom is tall, then Bob, who is only two inches shorter, is pretty close to tall, too.

Even the ancient Greeks questioned conventional logic with their famous paradox of the heap. Remove a grain of sand from a heap, and it's still a heap. Remove another grain and another, and the heap remains. Eventually, though, there is only one grain left. Is it a heap? If not, at what point did it stop being a heap?

Zadeh said objects could be partial members of a set. At some point, the Grecian sand pile becomes a 0.5 member of the set of heaps. Tom is maybe a 0.6 member of the set of tall men. Even Bob, at 5 feet, 9 inches, retains 0.4 membership, while Jim is almost a full member at 0.95.

Such ideas contradict a long line of logicians and mathematicians who claim that A can't be both B and not-B (Aristotle's Law of Contradiction) and that A has to be either B or not-B (Aristotle's Law of Bivalence). Making up mid-points, say critics of fuzzy logic, lacks scientific rigor.

McNeill and Freiberger, who write about computers, quote these critics at length and try to answer them in a forceful way. They largely succeed. But one can't help feeling at certain points in the book that maybe the critics are onto something. Some of the examples of fuzzy theory the authors cite sound a little loose.