In search of a scientific revolution: controversial genius Stephen Wolfram presses onward.

Plenty of people claim to have theories that will revolutionize science. What's rare is for other scientists to take one of these schemes seriously. Yet that's what's happened since May 2002 when theoretical physicist Stephen Wolfram self-published a book in which he alleged to have found a new way to address the most difficult problems of science. Tellingly, he named this treatise A New Kind of Science. The book, which Wolfram sent to hundreds of journalists and influential scientists, sparked a firestorm of criticism. Detractors charged that the author was peddling speculations as discoveries, asserting that decades-old research was new, and pirating the research of others without giving due credit. Many commentators concluded that the author's promise of a revolutionary upheaval in science was grandiose and unbelievable, even as they allowed that the book contained some incremental scientific discoveries, as well as intriguing ideas.

Fast-forward to this summer: Wolfram's book is in its fifth 50,000-copy printing, despite being a $45, 1,200-page, technically dense hardback. Dozens of scientific papers have cited the book. Wolfram has hosted the first international conference on his work.

What's going on? Has the man discovered a secret that will cause science textbooks to be rewritten or merely found a formula for mass-marketing science--or something in between? Science News takes a look at Wolfram's enterprise 15 months after the book's debut.

EQUATION EVASION At the heart of Wolfram's work is the observation that extremely simple computer programs can generate patterns of extraordinary complexity. Among such programs are a type known as cellular automata, which scientists have studied for 50 years (SN: 7/3/99, p. 8).

To understand what a cellular automaton is, consider a sheet of graph paper on which a pattern can be marked by darkening selected boxes. The top row may have one or more boxes blackened. A simple cellular automaton draws a pattern by beginning with the second row and working its way down the page.

As it considers each box in a row, the automaton observes the box above and those on either side of that higher box. Then, on the basis of a specific rule that depends on which, if any, of those three boxes are dark, the automaton blackens its current box or leaves it blank--and moves on.

Most simple cellular automata generate boring, repetitive patterns. However, one day more than 20 years ago, Wolfram was observing the behavior of a cellular automaton known as Rule 30 when the program created an unpredictable pattern of stunning complexity on a computer printout. That event began a journey of discovery, Wolfram says, that ultimately led him to realize that elementary computer programs offer a way to solve problems in many branches of science without the drudgery and limitations of conventional equations and equation-based simulations.

Although equations have formed the foundation of math and theoretical science for centuries, they often become insoluble when applied to complex phenomena. By contrast, Wolfram contends, simple, complexity-generating programs are the tools of "a new kind of science" that, more accurately and easily than the old one, can simulate complicated phenomena, from the growth of snowflakes to the workings of the universe.

According to Wolfram, this style of simulation will be successful because it mimics how the universe works: Computational processes underlie phenomena from elementary particle interactions to life.

Wolfram has spun off a lot of exhilarating ideas about where this new approach can lead. For example, rather than needing Darwinian evolution to explain the complexity of living creatures (SN: 6/10/00, p. 382), Wolfram says that a biological computation process based on a few simple rules could do the trick. In physics, Wolfram's approach suggests that space itself may not be a continuous entity but rather some sort of network of interconnected fragments. The unpredictability of patterns generated by simple programs, he says, explains how people can exercise free will while their brains obey strict physical laws.

Although Wolfram calls his approach a new kind of science, some elements of it, such as cellular automata, have been investigated for decades. His new work also has links to earlier theories of fractals (SN: 2/2/02, p. 75), of chaos (SN: 10/31/98, p. 285), and of complexity theory (SN: 5/6/00, p. 296). In fact, Wolfram has in the past made notable contributions to research on cellular automata and complexity.

For that reason among others, the man behind A New Kind of Science isn't easily labeled a crackpot. A British-born prodigy, he received a Ph.D. in theoretical physics from the California Institute of Technology at age 20 and won a MacArthur Foundation "genius" award 2 years later, in 1981, for his work in physics and computing. Later, he created Mathematica, a software package for scientists, engineers and mathematicians, and developed it into a highly profitable business--Wolfram Research of Champaign, Ill.--which he still leads.

Because of Wolfram's credentials, heavy hitters of science and technology have paid attention to his book, though not necessarily praised it. In the New York Review of Books last October, physics Nobel laureate Steven Weinberg of the University of Texas at Austin concluded that Wolfram had written a "failure," albeit "an interesting one" Weinberg found that "not one real-world complex phenomenon ... has been convincingly explained by Wolfram's computer experiments." Still, he added, Wolfram may have taken a first step toward a much-needed theory of complexity.

A critique by inventor and artificial intelligence pioneer Ray Kurzweil of Kurzweil Technologies in Wellesley Hills, Mass., hails Wolfram's work as a "tour de force" on the topic of cellular automata. Nonetheless, Kurzweil says that Wolfram seriously overstated the complexity that simple programs produce. On the topic of living organisms, for instance, Kurzweil asserts that unless factors beyond simple rules are invoked, one can't explain "insects or humans or Chopin preludes."

Fans of Wolfram's work say that much of the negative reaction has stemmed more from the author's self-aggrandizing writing style than from his science. For instance, Wolfram says in his book, "I have discovered vastly more than I ever thought possible, and in fact what I have now done touches almost every existing area of science, and quite a bit besides."

Fans look beyond his habit of frequently and brashly proclaiming the historic importance of his findings. "I believe that some of the ideas in A New Kind of Science are going to be very valuable to us in developing predictive models," says medical researcher Elaine L. Bearer of Brown University in Providence, R.I.

RITE OF ASSEMBLY Compared with the harsh treatment Wolfram endured from many reviewers last year, the recent conference on his work was a love fest. More than 200 men and women, paying up to $325 apiece, attended the event June 26-29 at a hotel in Waltham, Mass. They ranged from college students to retirees and represented an eclectic mix of professions and interests, including physics, biology, psychology, medicine, computer science, engineering, economics, business, art, and music. Attendees came from as far away as Norway, Israel, and Australia.

Some people said they were drawn by their admiration for Wolfram; others, by the allure of participating in what could be a historical shift in scientific thought.

"This guy is the closest thing to [Isaac] Newton in 350 years," says Stanley Ruby, a physicist who retired from Stanford (Calif.) Linear Accelerator Center 9 years ago. "I think he's onto something hugely important."

Others, like Carl E. Lippitt of Sandia National Laboratories in Albuquerque, came looking for help with applying Wolfram's concepts to engineering designs.

For instance, Lippitt and his Sandia colleagues are exploring control schemes for proposed battlefield robots that would aid soldiers, for example by carrying extra gear. Because the battlefield is such a complex environment, those robots would require intricate behavioral repertoires. That's where Wolfram's ideas of generating complexity from simplicity seem to fit in, Lippitt says. Yet Lippitt couldn't find in Wolfram's book guidance for developing practical devices.

"It's somewhat difficult to understand, from an engineering perspective, how you go about implementing these ideas," Lippitt says.

During the two-and-a-half-day "minicourse," Wolfram did most of the talking--about 15 hours' worth of lectures--although there were a few panel discussions.

The meeting was too one-sided, says mathematician and science fiction author Rudy Rucker of San Jose (Calif.) State University, even though he's a fan and friend of Wolfram's. "It would be a better conference if somebody besides Stephen was organizing it. Then it could be more of a full spectrum" of opinions, he says.

Kurzweil Tech's vice president of business development Celia Black-Brooks says the meeting's science was over her head, but she had no trouble appreciating the business savvy of Wolfram's firm. "He certainly has a well-oiled marketing machine behind him," she adds.

Wolfram unveiled no new developments in his own work at the conference because there haven't been any to speak of since the book was finished, he told Science News. He says he's been too busy giving talks at campuses and laboratories, responding to the 30,000 or so e-mails prompted by the book, and striving to build a scientific movement based on his work. Wolfram predicts that it will be another year before he can get back to the science.

On the other hand, at the conference's poster session, about 10 of the conference goers unveiled projects in which they had used Wolfram's style of computer modeling to explore areas as diverse as explosion dynamics, quantum mechanics, data visualization, and cultural identity.

Among those projects was a cellular automaton created by physicist Larry G. Hill of Los Alamos (N.M.) National Laboratory. The algorithm yields an animation that may mark the first step toward realistic computer models of explosions caused by superheated liquids, Hill says. The dynamics of those fluids have proved too complex for today's conventional equation-based simulations, he adds.

In another project, electrical engineer Rodrigo G. Obando of Fairfield (Conn.) University statistically analyzed cellular automata patterns and translated the results into three-dimensional forms resembling disks, bowls, and hats. Comparing the shapes of those forms may reveal relative degrees of symmetry, complexity, and randomness of automata patterns, Obando says.

VENUE MENU Besides hosting the conference, Wolfram and his associates are moving ahead on other fronts to foster a new scientific movement.

At the meeting--which planners say will be repeated next year--Wolfram distributed a booklet summarizing more than 170 problems and projects that he considers next steps for the field that he has launched: for instance, to "develop automated ways to find 'interesting' cellular automata" and to consider "what might history have been like if cellular automata had been investigated in antiquity."

Wolfram also announced the start of an online clearinghouse for related research (http://atlas.wolfram.com) and to found an institute devoted to the approach. What's more, he said he's planning to transform Complex Systems, a journal that he founded in 1987, into the flagship publication for the new field.

Although the scientific establishment has largely rejected Wolfram's revolution, academia features a few courses on the topic. For instance, San Jose State's Rucker has been teaching a graduate course on it since the fall of 2002, and Wolfram and his assistants taught a 3-week graduate course in early July at Brown University.

"One of the things universities should do is to be a home for ideas that are controversial, whose long-term potential is uncertain, and that generate a lot of interest and excitement," says Brown's provost, mathematician Robert J. Zimmer. He invited the Wolfram program onto the campus after a Wolfram talk at the school last October proved so popular that people had to be turned away.

One effect of Wolfram's campaign for a new science has been to intensify interest in some longstanding ideas that don't mesh with prevailing theories. For instance, in the early 1980s, Edward Fredkin originated the idea that the universe itself may be a cellular automaton and that energy and mass are just information (SN: 8/2/97, p. 76). In Fredkin's model, both space and time are grainy rather than continuous, so space is permeated with exquisitely small, discrete cells whose states change at extremely brief, discrete intervals, just as patterns generated by computers' cellular automata do.

Fredkin, now of Carnegie Mellon University in Pittsburgh, complains that Wolfram has taken credit for some of his ideas. At the same time, he says, his now-famous friend and rival has "done me a favor because a lot more people are interested in what I do because of Wolfram's notoriety."

Wolfram says he's pleased with the his enterprise's progress, which is "a little ahead of schedule." Looking ahead, he predicts that the "first round of serious extensions to the book" will come in 2 to 3 years.

To skeptics and enthusiasts alike, Wolfram readily declares that the revolution has begun. Nonetheless, "it's going to be a while," he admits--another 10 years or so--before his approach will take the place he thinks it deserves at the forefront of science.