Mathematician Seeks Way to Mimic the Human Mind

MORAGA, Calif. — It’s a long way from Lancaster, England, to this tiny Northern California town--a spot so remote that no one bothers to lock their doors because “burglars don’t know it’s here,” says mathematician Keith Devlin, dean of sciences at St. Mary’s College of California.

Five years ago, Devlin was an esteemed professor of mathematics at the University of Lancaster, a well-respected logician firmly ensconced in the mainstream of his field.

He was pressured to leave Lancaster, he says, when he became obsessed with the search for an entirely new kind of mathematics, one that would mimic the human mind. “Why would I take a perfectly good mathematical career and ruin it?” he asks.

The answer is that Devlin is one of those rare scientists who risk their reputations and livelihoods to push the fringes of knowledge beyond the bounds of conventional wisdom. Like others of his kind, he does not seem unduly bothered by the prospect of failure. “The worst thing people can say is, ‘This guy’s gone crazy,’ ” he says.

The possible payoff is profound: If he succeeds, he could break through the logjam that has kept true progress toward artificial intelligence at a virtual standstill for decades. His goal is to understand the underlying mathematics of thought well enough to develop computers more in synch with human thoughts and emotions.

Traditional mathematics got humanity to the moon and outer space. But it is not up to grappling with the inner world of the mind. For today’s mathematicians, he says, “inner space is the final frontier.”

Even if his work doesn’t produce human-like computers like Stanley Kubrick’s Hal in the movie “2001,” it could lead to everything from more user-friendly automated teller machines and safer automatic pilots to better personal computers and medical diagnostics.

“How do you design and build a computer that can respond well to the often nonscientific and decidedly nonmathematical human beings that use them?” Devlin asks. “Somehow, the desires, practices and foibles of people need to find their way into the precise blueprints.”

Dramatists and poets and sociologists and psychologists produce insights about the human condition that are difficult to analyze, says Devlin. “They’re essentially fluid and plastic and fuzzy, because that’s what people are like.”

At the other end of the spectrum is the absolute precision of mathematics and science. Devlin’s goal is to bridge the gap.

When he first started talking about his ideas in England, colleagues thought he had “lost it.”

“For a mathematician to break rules is an oxymoron,” he says. “It’s part of the discipline. Precision is so important. Being right is so important. You’re never supposed to publish until you’re sure.”

In fact, the ideas he’s working on are so radical he fears they might not ultimately be considered mathematics. His new “soft” math is not even precise, its results not true or false, but shades of gray--a lot like those fuzzy social sciences pure mathematicians often disdain: psychology, sociology, economics, linguistics.

He calls it “the mathematics of the people” and expects it to be taught routinely in the classrooms of the 21st century. Such drastic measures are called for, he says, because human intelligence is not logical and cannot be captured by computers that “think” by logical deduction.

‘Dropping a Way of Thinking’

Although Devlin swears there’s nothing Irish about him but his name, the twinkly-eyed Englishman looks every bit the leprechaun. He clearly gets a kick out of finding something new in a field that has been around for millenniums. Since his abrupt change of life, “my views of what mathematics is have changed dramatically,” he says.

The hardest part has been unlearning everything he has learned. “It meant dropping a way of thinking I’d been holding onto for 25 years. I didn’t realize how tight those blinders were.”

Like most other mathematicians, Devlin’s education was built on the mainstream study of logical thought, which goes back at least to ancient Greece. Logical deduction, the Greeks taught, always leads to truth. To borrow an example from Aristotle, if all men are mortal, and Socrates is a man, then one can conclude without doubt that Socrates is mortal.

The beauty of logic is that the subject matter is irrelevant. Instead of Socrates, men and mortality, the statement could be about anything at all. If all Xs are Y, and Z is X, then Z is Y. Apples and oranges. War and peace. Or the intrinsically meaningless ones and zeros of computer language.

In the language of logic, truth doesn’t depend on context. The answer is always pure, simple, definitive. Socrates is either mortal or he isn’t. There is no in between.

This way of thinking received an important boost from a different front in the 1960s when Massachusetts Institute of Technology linguist Noam Chomsky suggested that language followed a similar logic. That is, language could be distilled into a series of abstract patterns, or rules, that “make sense” regardless of context. That’s why a “nonsense” poem like Lewis Carrol’s “Jabberwocky” “makes sense,” even though it has no sense.

For example, people can easily identify the nouns, verbs and adjectives in the sentence “The flabberjom scringingly swinkered the ralidous snig,” even though it has no meaning.

Devlin for one isn’t surprised that two seemingly disparate disciplines--mathematics and language--seem to have so much in common.

“Of all the species that have ever been on the Earth, there’s only one species that’s had language, and there’s only one species that is capable of abstract deductive thought. And it’s the same species. . . . Now the mathematician in me says [that can’t be a coincidence].”

The evidence from both linguistics and logic seemed to point to the same conclusion--that the mind thinks, and talks to itself, in a coldly logical manner. But chinks appeared in this edifice.

First, mathematicians could not explain the logic of paradoxical statements such as: “This sentence is false.” If it’s false, it’s true. And if it’s true, it’s false.

They could not account for the way the brain correctly figures out the nouns and verbs in sentences like: “Time flies like an arrow. Fruit flies like a banana.” The most elementary mind can make sense of them, but no computer in the world can do it. For one thing, computers don’t do metaphors. For another, they can’t keep up with the changing context that turns nouns into verbs, and verbs into prepositions.

Brain scientists such as Antonio Damasio of the University of Iowa discovered that a lack of emotion leads to irrational behavior. Emotion is part and parcel of human reasoning. When the emotional parts of their brains are damaged, people can’t think straight. “Logic alone does not produce intelligent behavior,” says Devlin.

Finding Those of Like Mind

So it was, more or less, in 1980 when logician Devlin was asked to consult on a British team of scientists investigating ways that mathematics could capture intelligence. Devlin left the project after a few months, he said, because he realized he wanted to completely rethink his ideas about logic and thinking.

The more he talked about his ideas with his colleagues at Lancaster, the more isolated he became. “I couldn’t find anyone to talk with,” he says. “I would give talks. People would walk away shaking their heads. What is this guy talking about?”

His lectures were almost all words, few symbols. “People would say: Where is the mathematics?”

It was a grim time for Devlin. “I was very disheartened,” he says. “I was on the point of giving up.”

Meanwhile, shrinking science budgets in England forced the university to focus on projects that would pay off, that might produce “useful” results. “They couldn’t afford to support some guy off on what might be a wild goose chase,” Devlin says.

So he sort of understood when Lancaster started pressuring him to leave in the mid-1980s. At the same time, he was angry: “A university is supposed to provide the one environment where you can do these kind of things.”

The turning point came when he heard a talk by Stanford University mathematician Jon Barwise that echoed many of his own ideas. Devlin was elated. “I thought: If I’ve gone crazy, at least there’s this other great mathematician and he’s crazy too!”

Barwise had just become director of a cutting edge interdisciplinary group at Stanford called Center for the Study of Language and Information, where Devlin remains a senior researcher. It was founded in 1983 to study the fertile intersection of information science, computing and thought. Barwise invited Devlin to join him. Devlin describes his days there as “endless seminars with some of the smartest people in the world. These people wanted to know how the mind works, not how to prove theorems. There was no fear. It was like a drug.”

He realized he would never go back--either to Lancaster or to academic math. A colleague suggested that a liberal arts college, where the boundaries between disciplines are less rigid, might be just the place for him. Eventually, he found St. Mary’s and fell in love with it. He has been dean of science there since 1993, free to step over the lines that separate academic categories and “play. . . . It’s a monastery, where you can retire and think thoughts.”

Importance of Context

The new math that Devlin is working on is called “situation theory” because it tries to make the situation, or context, paramount. For example, he envisions a conversation as a meeting of two overlapping fuzzy auras--each representing everything the person brings to the interchange, including emotional attachments, personal history, whatever he or she ate for breakfast, current moods and preferences in reading and movies.

His goal is to create a symbolic notation that captures this entire cloud of unspoken context, something he compares to musical notes. If he can develop a workable symbolic vocabulary for these auras, he can get them down on paper so other people can use them.

“Anyone who can read the music can get some notes out of a piece of Mozart and can play something that everyone else will recognize as Mozart,” he explains. Putting situation theory into symbols will amount to much the same thing.

That could make a big change for computers. Now, all computer languages depend on the kind of formal logic that is used to prove theorems. But the brain does not use formal logic. “This thing between our ears didn’t evolve to manipulate symbols,” he says. That’s why, even though the IBM computer Deep Blue can defeat world champion Garry Kasparov in chess, it doesn’t think. “It doesn’t play chess,” says Devlin. “It does something else. It’s doing its thing and a human is doing its thing, but they’re doing two very different things.”

Doubts, but No Regrets

Even Devlin isn’t sure he will succeed. “You honestly don’t know whether your way is going to lead to anything or whether it’s going to be garbage,” he says.

Fortunately, he is also in demand as a popularizer of mathematics, with half a dozen popular books under his belt, television programs for PBS and BBC, and radio programs for National Public Radio. It was hard breaking away from academic math at first, mainly because it meant giving up the pats on the back from colleagues who thought highly of his work. “My existing feedback was gone,” he says. “But you know, the world didn’t fall apart in the next day or so. And it may not, and I’m still enjoying it 10 years later. I go to bed each night, and I think: That [day] was fun.”

If his work is successful, it probably won’t be judged by mathematical standards, but by what he calls engineers’ standards. Mathematicians like solutions to be beautiful and elegant as well as “right,” he says. But engineers only care about whether the thing works. He expects his first efforts to be awkward and inelegant, but he will be happy if they manage to produce some results.

He is already working with several large corporations to see if “situation theory” can grease the wheels of corporate communication. It should definitely make it easier to communicate with the next generation of computers responsible for everything from ATM transactions to airline scheduling by making the ways computers think more in sync with the way their users do.

Devlin acknowledges that what he’s doing is backward from the way he is used to working. Mathematicians are trained to get rid of the messy ambiguity of everyday life to see the underlying patterns. Now he has to learn to see the patterns in the mess.

“All of existing mathematics that I know about forces you to be very precise about everything right at the beginning. It has to be defined.”

His new soft math would start with the messy reality of real conversation and human thinking, and try to encode that into a regular mathematical framework.

This kind of revolution has occurred in mathematics many times before, Devlin says. The global age of exploration required trigonometry to build ships and navigate. Einstein’s theory of gravity required an entirely new kind of geometry. “The Information Age,” says Devlin, “is no different.”