One fine spring day in May 2002, the English-born physicist Stephen Wolfram was at long last ready to present his book, A New Kind of Science, to the world. Its publication had been a long time in coming, having been announced, and postponed, several times during the preceding three years. A few months prior to its actual publication a review already hailed the book as a pathbreaking work that would have worldwide significance. This review, incidentally, had, just like the book, been published by Wolfram’s own publishing house. If you tend to believe an author’s own pronouncements, or take kindly to the media spin put out by public relations firms, then you would have to assume that this book was on a par with Isaac Newton’s Principia and Charles Darwin’s The Origins of Species. One may be forgiven for thinking that the author would have no qualms whatsoever in comparing his book to the Holy Bible.

Given the brouhaha surrounding the publication, it was not surprising that A New Kind of Science quickly became the Number 1 best-seller at Amazon.com and kept this sales rank for a couple of weeks. The five-pound tome comprises no less than 1,197 pages, and they are not easy going. The intrepid reader quickly realizes that Wolfram’s intention was nothing less than to turn the entire body of science on its head. In his book Wolfram offers solutions to a broad spectrum of topics, including, to name just a few, the second law of thermodynamics, the complexities of biology, the limitations of mathematics, and the conflict between free will and determinism. In short, the book is hailed as nothing less than the definitive answer to all questions, bar none, with which generations of scientists have been struggling, often in vain. A New Kind of Science, the author says in the pref-

ace, redefines practically all branches of the sciences. This is what Stephen Wolfram believes or, rather, wants us to believe.

Who is this man who is so convinced of his near-divine gifts? Stephen Wolfram was born in London in 1959 into a well-to-do family. His parents were a professor of philosophy and a novelist. (A note for the chauvinists, if there are any, among the readers: The mother was the professor and the father the novelist.) The young lad was sent to boarding school at Eton. There, at the tender age of 15, Stephen wrote his first paper in physics. It was promptly accepted by a reputable scientific journal. In keeping with the ways of the British academic elite, Wolfram went on to Oxford University, whence he graduated at 17, an age when other boys only just about start writing their university applications. By the age of 20 he had not only gained a Ph.D. from the California Institute of Technology, he could look back on a publication list with close to a dozen articles.

Two years later, in 1981, Wolfram won a fellowship from the MacArthur Foundation, the youngest ever recipient of this award. Commonly called “genius awards,” these fellowships, given to exceptional individuals who have shown evidence of original work, allow scientists complete financial independence over the course of five years. For reasons having to do with copyrights and patent laws, the somewhat irascible Wolfram then had a falling-out with CalTech and moved on to the Institute for Advanced Study (IAS) in Princeton, New Jersey. His interests, at the time, spanned cosmology, elementary particles, and computer science.

Eventually he hit on a topic that would provide the foundation for his current and—if you believe his public relations machine—revolutionary discovery: cellular automata. Years earlier, in the 1940s, the legendary John von Neumann, one of Wolfram’s predecessors at IAS, had come up with the idea of cellular automata. But that was only in passing and he had soon lost interest in them. Indeed, von Neumann’s article on this subject was pub-

lished only posthumously. Nobody pursued the idea. The topic, in fact, was all but lost.

Then in the 1970s, on the other side of the ocean, John Conway, a mathematician in Cambridge, England, came up with a prototype for cellular automata. It was dressed in the guise of a computer game called “The Game of Life,” which actually is not really a game but a concept. “Life” uses a grid that resembles a checkerboard, the difference being that the black and white squares do not necessarily alternate but are distributed randomly. One could interpret these squares as the initial population of a colony of bacteria. A few very simple rules determine how the population procreates. Certain bacteria survive, others die off, and new ones develop.

Despite the fact that the simplest rules—such as “If the bacterium has more than three neighbors, it dies”—determine survival and reproduction, the happenings on the checkerboard are anything but simple. Complex population patterns develop, with some colonies dying off, others appearing seemingly out of nowhere, and still others continuously oscillating between two or more states. Then there are those that simply crumble away until only a few small islands are left. What is so surprising is the fact that a very small number of rules succeed in generating such an enormous number of varying and different phenomena and consequences. When Scientific American published an article on “Life,” the game became so popular that, according to one estimate, more computer time was spent on it than on any other program. It was all the rage.

Stephen Wolfram was no exception. But he did not simply while away his time with “Life.” He went a few steps further. Putting the game through rigorous analytical tests, he cataloged the evolving patterns. His article entitled “Statistical Mechanics of Cellular Automata,” published in 1983 in the Review of Modern Physics, is to this day considered the standard introductory text to the subject of cellular automata.

Wolfram had in the meantime turned 24 and was still

pursuing an academic career, having moved from the IAS to the University of Illinois. He was convinced that his work was the beginning of what would be renewed public interest in cellular automata. But only very few of his colleagues were interested, and Wolfram—apparently unable to thrive without public accolades and recognition—was quite disappointed. However, never short of ideas, he embarked on a new career. He became an entrepreneur.

Of course, Wolfram did not venture into the field of management unprepared. During his years as a scientist, he had developed a piece of software that does symbolic mathematics: That is, it does not simply perform numerical calculations but manipulates equations, gives the solutions to complicated integrals, and accomplishes a host of other neat things. Within two years he developed it into a commercial product and launched it under the brand name “Mathematica.” It became a hit in no time. Today there are approximately 2 million professionals—engineers, mathematicians, and industrialists—throughout universities and large corporations who use “Mathematica.” Thanks to this innovative and widely used piece of commercial scientific software, Wolfram, Inc., a firm with around 300 employees, still flourishes today.

Wolfram’s newly found fortune gave him the independence to return to scientific work. For the next 10 years he spent each and every night on his research. He was firmly convinced that the grid with its small black squares held the key to the secrets of the universe. Wolfram was convinced he had found the answers to all of life’s secrets.

It is not uncommon for natural scientists to believe that all phenomena in physics, biology, psychology, and evolution can be explained through mathematical models. Wolfram was no exception. However, he believes that it is not always possible to explain phenomena by means of formulas, where all one has to do is insert variables and parameters into appropriate slots. Instead, he argued, a series of simple arithmetic computations—so-called algorithms—are repeated over and over and over again. While observing the developing string of intermediate results, it

would usually not be possible to predict the outcome. A final result will eventually arise simply by allowing the algorithm to run its course.

By looking at the results of algorithms that simulate cellular automata, Wolfram discovered that they mimic patterns one encounters in nature. For example, the development of certain cellular automata is similar to the development of crystals or to the emergence of turbulence in liquids or to the generation of cracks in material. Hence, he argues, even quite simple computer programs can simulate the characteristics of all kinds of phenomena. From there it is only a small step—for Wolfram, that is—to explain the creation of the world: A few computations, repeated millions or billions of times, would have produced all the complexities of the universe. The thesis, which he develops in the book, is incredibly simple and as such also rather disappointing: Cellular automata can explain all of nature’s patterns.

In the course of the years of nocturnal research, Wolfram managed to simulate an increasing number of natural phenomena with cellular automata. Sometimes he had to run through millions of versions until he hit on the suitable automaton. But eventually it always worked, whether it was in thermodynamics, quantum mechanics, biology, botany, zoology, or financial markets. Wolfram even asserted that the free will of human beings was the result of a process that can be described by cellular automata. He was convinced that very simple behavioral rules—similar to cellular automata—determine the workings of the neurons in our brains. Seemingly complex thought patterns emerge by repeating these behavior patterns billions of times. Hence, what we have hitherto considered intelligence is, in principle, no more complex than the weather. He also posited that a very simple set of calculations could reproduce our universe to its last and smallest detail. It was only a matter of allowing the algorithm to run for a sufficiently long period of time.

Over the years Wolfram worked entirely on his own, sharing his ideas with only a few trusted colleagues. This had both advantages and disadvantages. On the one hand,

Wolfram did not risk exposing himself to any criticism or, worse still, ridicule. On the other hand, nobody could check his propositions or suggest improvements. But Wolfram did his job well. After reading close to 1,200 pages, even the most skeptical reader will be convinced that cellular automata are able to simulate patterns of innumerable natural phenomena exceedingly well.

But does that mean that automata are indeed at the origin of the patterns observed in nature? No, not by a long stretch of the imagination. It is simply not acceptable to let analogies and simulations act as substitutes for scientific proof. If, for example, we visit Madame Tussaud’s Wax Museum and stand in front of a figure that looks exactly like Elvis Presley, must we conclude that Elvis Presley was made of wax? Certainly not. Wolfram would disagree. For him it is all a question of what one demands from a model. In his view a model is good if it is able to describe the most important characteristics of a natural phenomenon. Even mathematical formulas only provide us with descriptions of the observed phenomena and not with their explanations, he argues. If Elvis’s most important characteristic was what he looked like, then the wax figure can, for all intents and purposes, be considered a good model, Wolfram claims.

Whether such arguments can convince other scientists remains to be seen. But this is of no concern to Wolfram. He intends for his book to be read by the wide public, not by only the select few, and in this aim he does a very good job indeed—not least because of the well-oiled publicity machine.