FROM THE UPSTAIRS PORCH window of his split-level house in the Puente Hills, Bart Kosko enjoys a view of the largest Buddhist temple in the Western Hemisphere. Others can keep their manicured lawns, swimming pools, hot tubs, nearby golf courses and sundry suburban amenities. For Kosko, a 30-year-old assistant professor of electrical engineering at USC, it is enough to be able to gaze at one of the few buildings in the country where his concept of reality would not be denounced as scientific heresy, as well as an affront to common sense.
"You have to have a great belief in the truth of your own statements," says Kosko, whose mathematical ideas continue to encounter resistance and outrage from the scientific community in this country despite their widespread acceptance and application in Asia. "You may have stumbled, humbly, upon a universal truth, but if the world, everyone from Aristotle to Bertrand Russell, says you're wrong, it takes immense ego not to agree with them."
The universal truth to which he refers is called fuzziness. Developed by Polish mathematician Jan Lukasiewicz during the 1920s and expanded (and named) 40 years later by UC Berkeley computer scientist Lotfi A. Zadeh, fuzziness refutes the traditional Aristotelian theory of absolutes, arguing that the world is full of things that defy categorization by Western logic, things whose definitions are a little fuzzy. Its applications are, among other things, revolutionizing the computer world by creating systems of machine intelligence that compute in terms of humanlike reasoning.
Kosko, a Zadeh protege, is the veritable St. Paul of Fuzziness. The American scientific community does not always take kindly to his devotions, however. Telling a modern scientist that there can be logic without Aristotelian tenets is like telling a Catholic there can be Christianity without Christ--some scientists have apoplectic fits at the mention of Kosko's name. Yet in this time of technological competition with the East, Japanese and Chinese scientists embrace fuzziness; with its acceptance of universal ambiguity, fuzziness is the mathematical equivalent of Taoism and Zen Buddhism. In Japan, especially, Kosko is the Carl Sagan of fuzzy technology. Indeed, as many Western scientists begin rethinking Kosko, this mathematical doctrine may force the first actual confrontation, and eventually a melding, of Eastern and Western philosophical and scientific ideology.
Kosko is, in essence, the quintessential scientific cyberpunk--a hip, street-smart prophet of life in the Information Age. He's also a musician, an essayist, a screenwriter--and a pugnacious sort. He just may be able to pull it off.
ZADEH EXPERIENCEDhis first flash of fuzzy revelation in a hotel bed; Kosko did his mentor one better--he worked out key facets of the geometry of fuzziness while soaking in the hot tub behind his house.
The hot tub is a fitting place for lambasting Aristotle. The baths were an ideal setting for ancient Greeks to debate the merits of the philosopher's world view. In his hot tub, Kosko contemplates his longstanding frustration with the way those theories continue to prejudice Western imagination. Aristotle, Kosko says, was just too rigid in his thinking.
"Aristotle was never one to split hairs," he explains. "He believed you were either hairy or you weren't. If I were inclined to start plucking my own--which I'm not--I would eventually pull out the one hair that he would have argued separates hairy people from non-hairy people. Say that hair is number 5,000. With it, I'm hairy. Without it, I'm not."
In science, Kosko says, this absurd yet inviolable rule--that everything must fit one category or another at all times--is called the Law of the Excluded Middle. In it, there can be no shades of gray, no concepts such as "partly" or "mostly."
"We've all been conditioned to behave as if this was true," Kosko says. "But it isn't--not in the real world. These binary assumptions offer a handy first approximation of reality. But sooner or later they break down."
Computers, symbols of pure logic, offer a good illustration of the difference between fuzzy and non-fuzzy thinking. Non-fuzzy computers, the technological epitome of Western thought, rely entirely on binary thinking. Everything they do is the result of combining ones and zeroes with and , or and not . The only thing programmed into the system is yes or no, categories of equality and inequality, and that's all that will come out.
A traditional computer would have difficulties accommodating the concept of a platypus, for example, because it is an animal that is and is not, in equal measure, a mammal. Faced with this peculiar creature, the computer, like Western thought, is reduced to spinning its figurative gears. It simply cannot grapple with a world in which reality does not come prepackaged in crisp binary packages.
Western scientists have tried to account for inherent ambiguities of the universe with probability theory--the mathematical expression of the chance that a specific event will or will not occur. It usually takes the form of a number between one and zero. In the case of a set of tall people, for instance, individuals always would be categorized as tall or short. But a 5-foot-tall person might be described as having a 50% probability of belonging to the set, a 6-footer 90% and a 7-footer 100%. In other words, probability reflects the statistical averages of the population--50% are below 5 feet, 90% are shorter than 6 feet and 99% are shorter than 7.
Probability works with large statistical populations, Kosko says, but is incapable of dealing with most individual situations.
"It assumes the world is black or white," Kosko says, "but it's never sure which one. There's uncertainty in fuzziness, too, but it's deterministic uncertainty."
Fuzziness, he says, measures the degree to which an event occurs. In other words, it models reality, basically providing a shortcut that probability cannot. A computer programmed with fuzzy chips can deal with degrees. It may, for instance, be drizzling slightly outside. A fuzzy computer chip will not try to categorize it as raining or not because it relies on a user-defined alphabet of functions rather than the usual ones and zeros. It can compute variations of measurement from light to heavy, small to large or slow to fast.
An ordinary air conditioner, for instance, kicks in when it senses the environment is either too hot or too cold. It either will begin blasting at full power or shut down. But this isn't efficient or conducive to maintaining maximum levels of comfort. A fuzzy air conditioner, however, would be able to identify the more-comfortable temperature ranges. Instead of shutting down, the fuzzy air conditioner would taper off its activities as the area being cooled became more comfortable.
So when a fuzzy computer is charged with control functions such as, say, docking a space shuttle with a space station, these translate into a smoothness of performance in control systems that cannot be replicated otherwise.
Although many of Kosko's theories revolve around computer applications, he has dozens of everyday examples to explain the difference between fuzziness and probability: Whether or not an article is published, to use one of his favorites, is a matter of probability. The degree to which it is published--it may or may not have been heavily edited--is one of fuzziness. Or suppose, he says, there is a 50% chance that there is an apple in your refrigerator. That is probability. But what if there is half an apple in the refrigerator? That half an apple has a 50% degree of membership in the set of whole apples. Numerically, these two situations are equivalent. Physically, however, they are distinct.
KOSKO HIMSELF embodies the fuzzy idea of many things concealed in one. A former farm boy who escaped the Midwest on a full music scholarship to USC in 1978, Kosko straddles the disparate, and often antagonistic, cultures of science and art. As a neural networks expert and a fuzzy theorist, he has organized several important international conferences and is about to publish the first college textbook about neural networks--computer systems that emulate an organism's ability to learn by experience. NASA uses him as a consultant on the space shuttle, as did the Strategic Defense Initiative Office. Outside the realm of science, Kosko is an accomplished composer who scores his own videotaped lectures and a published writer and essayist. Currently, he is collaborating with Bill Gray, co-writer of "The Philadelphia Experiment," on a science-fiction screenplay.
"I realize that many people within academia frown upon my outside pursuits," Kosko says. "I suppose they view it as a dissipation of energy. I see it as a stimulant. I have a lot of energy."
Kosko is a "bewildering combination of talents," says Marvin Minsky, an artificial intelligence pioneer at MIT. George Klir, editor of the prestigious International Journal of General Systems (soon to publish Kosko's latest paper, which details the theorems proving fuzziness) calls Kosko's mathematical ideas "quite profound." And Zadeh, his mentor, calls him "one of the most unusual and most highly gifted individuals I have ever met."
Beneath it all lies obduracy that prevents Kosko from ever backing down from a fight. Bart Kosko is cocky and tenacious and driven by the belief that time is the enemy of all things. And to keep up with the exponential rate of change engulfing the world, he is prepared to do without sleep--Kosko puts in a mere four hours of sack time nightly. Uncharacteristically for one so young, Kosko feels the clock ticking deep in his gut.
Kosko grew up in a largely Slavic, working-class Kansas City neighborhood called Strawberry Hill. His childhood was an odd mixture of "Little House on the Prairie" and the "Lord of the Flies." The woods behind his house were great for woodcraft, hunting and trapping and amateur rocketry. But they were also the scenes of sometimes vicious B B gun, wrist-rocket and Molotov cocktail battles between warring neighborhood kids. Bart, his friends recall, could always be found in the front lines.
"Bart was the most passionate person I ever met," recalls childhood friend Kevin Helliker, an author and journalist who lived two houses down from him as a boy. "Our sense of the Koskos was that they had more fun than anybody."
That changed tragically in Bart's 10th year, when their house burned down because of an electrical short. A few months later, Bart's father, a building contractor, was killed in a car accident.
"All kids have a keen sense of what's fair and not," Helliker says. "But Bart had this tremendous, inborn outrage at injustice. That outrage only increased after the death of his father."
The financially strapped Koskos moved to a farm near Lansing, Kan., where Bart threw himself into a variety of pastimes to escape his loneliness and anger. He gobbled up books on science, philosophy, literature, art and politics. Along with improving his karate, he taught himself how to play the mandolin, guitar, balalaika and piano. His friends never knew of his musical acumen until they read in the newspapers that he had won a national Young Composers Contest. Then in 1977, he won a full scholarship to USC, having composed an orchestral overture to "The Count of Monte Cristo" in high school.
As an undergraduate at USC, Kosko decided to supplement his income by writing for pay. Learning that the men's adventure market was wide open, he placed short pieces in magazines such as Oui and Gallery.
What motivates Kosko? "You have to understand that Bart is indignant over the ultimate imminence of his own death," says Helliker in an attempt to analyze his friend's drive to succeed in so many areas. "Last year, when we spent some time together, he advised me almost daily to reflect on the fact that the coroner would be cutting out my guts sooner than I imagine. Death was never far off--it should be stared in the face on a daily basis, he said, to remind us we don't have time to waste."
Kosko agrees that he views "with dread" the prospect of his own demise. Mortality is, in fact, what makes Bart run as if someone--or something--were chasing him.
KOSKO'S STAY at the USC School of Music was short-lived. Although he had passed his graduate placement exams, he and the school differed over what he should be studying. "I just hated atonal music," he says.
Kosko kept his scholarship for a year, but he was strongly urged to find another major. He chose philosophy and economics, eventually becoming a fan of free market economist Milton Friedman and a campus libertarian activist. But he soon ran into conceptual difficulties that might not have fazed his fellow students.
"In philosophy," he explains, "one does logic. But the Aristotelian theories underlying it hadn't changed in 3,000 years. That is never symptomatic of a healthy theory.
"I eventually abandoned philosophy because I felt that there was no room in academia for philosophers in the classical sense that Kant, Aristotle, Hume and Descartes had been. They had done their best to master all the science and mathematics of their day. In many cases they actually contributed to it. I began checking out math books." Kosko went on, in fact, to secure a master's degree in mathematics and a Ph.D. in electrical engineering, which he viewed as a field in which most of his scientific interests converged.
Kosko's fuzzy road to Damascus ran through Austin, Tex., where he met Zadeh at an artificial intelligence conference in 1984. A year before that, he first saw the word fuzzy in a scientific paper. Kosko recalls being struck by revelatory wonder. "This really seemed to tie together many of my concerns," he recalls.
At the conference, Zadeh was fiercely attacked for his ideas. Kosko, a young graduate student, without a doctorate much less professional standing, stood in front of a room filled with the Pharisees of the scientific community and mounted an impassioned defense of a concept of fuzziness, although the mathematical questions had not been asked or answered. (Two years later at another conference, this same fervor would induce one scientist to bang on a table in Kruschevian fury, yelling that "a set is a set is a set.") Zadeh was impressed. Immediately afterward, Kosko mailed Zadeh a theorem supporting fuzziness. Zadeh eventually became Kosko's thesis adviser.
A year later, Kosko attended another conference at which a well-known probabilist insisted publicly, and almost persuasively, that Zadeh was violating some inherent law of nature with his theories.
"I remember a chill going through the audience," recounts Kosko. "I suddenly had the sinking feeling that maybe there really is no fool like an old fool. At that point, I decided I had to know definitively if fuzziness was true. I was like a theist impelled to establish the existence of God. If it were so, I'd become a priest. If not, I'd be the biggest atheist that ever lived."
After conscientious deliberation and much back-to-the-basics mathematical formulation, Kosko eventually decided in favor of fuzziness. His dedication marked him as both maverick and dangerous iconoclast. Notoriety came during the mid-'80s, when he began to vigorously champion neural networks. Now an accepted part of the computer world, they were as scientifically outre then as fuzziness is now.
IN ADDITION TO being its prophet, Kosko has made a unique contribution to fuzzy set theory. He geometrized fuzziness, gave it concrete form and functionality, just as Einstein geometrized space and time.
Kosko pictures the set of fuzzy sets as a Rubik's cube. Each set becomes a point in the cube. Conventional sets occupy the corners of the cube with fuzzy sets occupying the rest of the cube. Each element in the fuzzy sets belongs to the set to a different degree. The farther the set is from the corner, the more it resembles its own opposite. At the midpoint, the set equals its own opposite. That's where the world's classical paradoxes reside, Kosko says. The points within the cube model ambiguity. Once within the cube, he says, we can accept and understand the paradoxes and ambiguities of life.
Kosko calls this "the black hole of set theory, where a thing can be its own opposite." Here, for instance, you will find the proverbial cup that is half empty and half full, the Taoist concept of yin yang, the liar from Crete who said all Cretans are liars, Bertrand Russell's set of all sets that are not members of themselves, and Russell's barber.
Russell's barber, Kosko explains, is a bewhiskered man who lives in a town and who shaves a man if and only if he does not shave himself. So who, one might ask, shaves the barber? If he shaves himself, by definition he does not. But if he doesn't, he does.
This kind of speculation is enough to drive most Westerners crazy, and according to the annals of mathematical history, many have despaired over resolving such enigmas. But, Kosko says, despair only sets in if one rigidly ascribes to an arbitrary insistence on bivalence. People in the Far East, he says, would not likely fall into such a trap. In societies where Buddhism is common, such as Japan--which he visits frequently as consultant, conference organizer and general representative of what many Japanese corporations consider the future of technology--the idea of a thing containing its own opposite is not hard to accept. It may, in fact, be a characteristic of mature civilizations that they are simply more capable of recognizing fundamental limits in man's ability to know the real world.
"In the end," he says, "the insistence on either / or interpretations of reality, which Western science relies upon, is merely a cultural preference."
Fuzzy proponents believe that fuzzy thinking may hold the key to the development of the kind of artificial intelligence suggested by HAL, the computer in Stanley Kubrick's film, "2001: A Space Odyssey." Katsushige Mita, president of Hitachi Ltd. and chairman of the board of LIFE, Japan's new Laboratory for International Fuzzy Engineering Research (which is funded by the Ministry of International Trade and Industry and more than 45 of Japan's largest high-tech corporations), believes that "fuzzy artificial intelligence will play an important role in the future intimate relationship between men and computers."
Already, manufacturers in Japan are spinning off a host of applications, from air conditioners, camcorders and automobile transmissions to subway trains and stock-trading programs. All use fuzzy chips that enables control systems to smooth out functions that otherwise might oscillate between minimum and maximum values.
Many American scientists insist that probability can do anything fuzziness can, and generally with better results. Only one U.S. company, Togai Infralogic of Irvine, designs and produces fuzzy chips. Some critics argue that the concept of fuzziness has never been articulated in a manner scientists could validate. Judea Pearl, a professor of computer science at UCLA, says he is "still waiting for a good definition of what a fuzzy system actually is. I haven't yet seen one that is divorced from jargon."
"Any problem which fuzzy technique is designed to handle can be solved just as well, if not better, within a probabilistic framework," adds Peter C. Cheeseman, a researcher at the Research Institute for Advanced Computer Science now on contract with NASA Ames Research Center near San Francisco. Scientists there are exploring fuzzy control techniques for space-shuttle docking maneuvers. Cheeseman is not impressed by these efforts. According to Cheeseman and other digital purists, Kosko and other fuzzy advocates have vastly oversold the benefits of their reasoning. Fuzziness, by its very nature, may lead to unreliable systems.
"I wouldn't want to be on a spacecraft being docked by fuzzy techniques," he says. "It may work well 99% of the time until, whoops, hey, no space station!"
KOSKO'S CRITICS must wonder how long he can remain so brash. Burnouts are no rarity in science, and Kosko, who for five years has been passionately campaigning for fuzziness, seems to be pushing his luck. Those who know him well, however, have few such qualms.
"In Einstein's day," recalls Robert Hecht-Nielsen, a former colleague of Kosko's who is now owner and president of a high-tech firm in San Diego, "there were a number of great intellects who did amazing things. But they never achieved Einstein's prominence, despite their talent, because they had no staying power. I'm not comparing Bart to Einstein in any definitive sense, but I do think he can hang in there."
So, Kosko believes, can fuzziness. He says that it will ultimately make possible genuine reasoning systems in machine intelligence, where artificial intelligence and neural network approaches have failed. Working a fundamental change in the way people regard the world, however, will take decades, if not longer.
To this day, Westerners have not yet faced, in any deep sense, the inherent screwiness of the physical universe as demonstrated by physicists during the early decades of this century. Eventually, Kosko says, "our physical explorations of subatomic reality, antimatter, and the space-time fabric will probably lead us to entirely different times and places, different definitions of reality."
"There may be no God but the Mathmaker," Kosko has written. "And Science is his prophet." Kosko's own prophecies, he prefers to make known in his upcoming science-fiction movie. The one thing we can count on, he says, is that fuzziness is here to stay.
The question, however, is to what degree.