Posted on 07/09/2002 4:37:11 PM PDT by Nachum
THE TASK IS SIMPLE but impossible. You are standing on the 50-yard line inside the Louisiana Superdome in New Orleans, and your job is to tile the field with 1-inch-square bathroom floor tiles, half of them black, the other half white.
Billions of tiles await you on wooden pallets in each end zone.
And so you begin. One tile. Fifty tiles. Ten thousand tiles barely cover the insignia at the center of the field. So far to go. It hits you that if you are ever going to finish with your sanity intact, you'd better start making this job more interesting. So you start devising rules—say, that no two black tiles can touch another unless they are on a diagonal or are surrounded by six white tiles; or that white tiles can line up to make an L shape but not a T. You come up with a half dozen of these arbitrary rules, and because the work is otherwise so relentlessly boring, you stick with them.
The work lasts for years. Then one day you find yourself putting the last tiles down in a small patch by the groundskeeper's entrance. Three tiles. Two. One. Catching your breath, you kneel at the last open spot. There, it is done. Four billion tiles. A life's work.
Stiffly, on worn-out knees, you shuffle toward the exit ramp. Passing the locker rooms, you decide to look at your work one more time but from a different vantage point. Slowly, you make the long climb up the ramp, from field seats to upper deck, and finally to the top of the dome. You look down, expecting a sight like sand on a beach, or the surface of polished marble...
Instead, you see a flower.
Not just the shape of a flower. Not just the idea of a flower. But the very embodiment of a flower: a rose in bloom, every feather of its petals, the odd twists of its pistil, all as perfect as if you were kneeling down beside it in the sunny corner of a garden. That it is black and white and two-dimensional and 100 yards long doesn't diminish the flower that displays itself beneath you. Nor does it keep the hairs on the back of your neck from standing up.
Your work suddenly has meaning. Your life has meaning. In some inexplicable way, the universe has meaning.
The secret of how simple tiles could create a rose has hidden in plain sight for 5,000 years. The Egyptians, while stacking more than 2 million giant stone blocks to build the Great Pyramid, almost looked it in the eye. The Arabs, great pattern makers and mathematicians that they were, should have seen the secret. Mandated by the strictures of their faith, discouraged from using anything but abstract, repeating forms in their decoration, the clues were right before them every day on tile walls and copper trays and in the backgrounds of their miniatures. But their eyes were on Allah, as the eyes of Irish monks were on God the Father, as they painted intricate repeating patterns to illuminate the Book of Kells.
Then, in the Middle Ages, Roman mosaicists, whose art is known as "cosmatesque," found the pattern within a pattern. They left their designs in floors, stairs, columns, and porticos all over Italy, and in two marble floors in London's Westminster Abbey. But they were craftsmen, not scientists or mathematicians. So for generations, they pieced together large designs made up of identical, smaller designs and saw only the beauty of the resulting symmetry, not a window to a new world. For 800 or 900 years, millions passed by these designs, marveled at their complex beauty—and walked on.
A ROSE BY ANY OTHER RULES
On a blistering night in late May, I find myself lost on the gritty streets of South Side Chicago. A young man named Ben is driving me to the man who claims to understand how billions of tiles could make the image of a rose on the floor of a football stadium. In fact, how simple rules such as those represented by the tiles might create the whole universe—and along the way, change how we think about everything from physics to philosophy, from stock markets to weather prediction.
The rental car lurches from one stoplight to the next. "I think we missed the turnoff," Ben says, looking over his shoulder at a street sign. He pulls into a crumbling driveway to turn around. Driven out by the heat, families slump on front porches as shopkeepers clang iron gates together in front of their stores.
As we pull away in a new direction, I consider how strange it is that after two years of chasing this story, only to be denied access again and again, I've now suddenly been summoned by this mysterious man. What happened to instigate this change? And what role am I playing in this man's calculated plan to explain to the world how the world works?
My first contact with Stephen Wolfram came 12 years ago. I was living by my wits as a freelance writer when a friend of my parents, a senior editor at Addison-Wesley, asked if I could write press releases to help promote one of his new authors.
This was not, the editor explained, a standard book promotion. "This guy Wolfram is a genius," he said, "the real thing," and handed me a stack of magazine clippings to help convince me.
The clippings told a remarkable story. Stephen Wolfram was born in London in 1959. His father is a moderately successful novelist; his late mother was an Oxford don in philosophy. A brilliant child, he earned a scholarship to Eton College at age 13. There, forced to play cricket, he found the best place on the field to read books. By 14, he had written his own book on particle physics; by 17, he had a scientific paper published in the journal Nuclear Physics.
He attended Oxford University on a scholarship and, during the summer after his first year, went to work in the Theoretical High-Energy Physics Groups at the Argonne National Laboratory. That summer Wolfram wrote a scientific paper on heavy quark production that soon became a classic in the field—and he turned 18.
A year later, in 1978, Wolfram was invited to the California Institute of Technology (Caltech) by legendary scientist Murray Gell-Mann. There his brilliant reputation gathered momentum: He invented the Fox-Wolfram variables in particle physics, discovered the Politzer-Wolfram upper bound on the mass of quarks, and published more than 25 scientific papers. The work he did in just his first year at Caltech earned him a Ph.D. in theoretical physics. In 1980 he joined the Caltech faculty, and in 1981, at age 21, he was awarded a MacArthur "Genius" Fellowship—not for any single piece of work but for the "breadth of his thinking."
I returned the clippings to the book editor and accepted the job. "People talk about this guy like he could be the next Newton," the editor said. He explained that Wolfram had recently invented a new mathematical software program that could quickly perform mathematical calculations and produce three-dimensional graphic images. The results were spectacular: the first great mathematical program for the personal computer. Anyone from a curious 12-year-old to a NASA scientist could use it to perform ultracomplicated calculations or simply for the pleasure of watching mathematics arc across the screen. To announce the launch of Mathematica, Wolfram wanted the full PR treatment: press conference, press kit, interviews, everything.
For the next three weeks, Stephen Wolfram was an English accent on the other end of the phone, endlessly unsatisfied ("This simply will not do!"), tearing up my copy, demanding an A-list of Silicon Valley leaders be invited, and remotely managing every tiny aspect of his press conference.
We got him everything he asked for. Apple's Steve Jobs attended, as if he were a Wolfram groupie, as did three dozen members of the press. Now there was only the matter of preparing Stephen Wolfram.
He arrived the afternoon before the event with a beard and near-shoulder-length hair, wearing sandals, dark socks, greasy corduroys, and a torn and unraveled brown sweater. "Oh God," said the PR person in charge of the press conference. "We can't let him out in public like that." So, during the next 24 hours we undertook a frantic makeover, ferrying Wolfram to the nearest department store for a button-down shirt, a new sweater, gray slacks, and dress shoes.
The next day, the conference room was filled with reporters, camera crews, and VIPs. The presence of the charismatic Jobs guaranteed the event would be a success. Then Stephen Wolfram stepped onto the dais—in the same ratty clothes he'd worn the afternoon before.
The Mathematica introduction was a huge success, earning media coverage ranging from the New York Times to Dr. Dobbs' Journal. But we never got a word of thanks from Wolfram and only heard secondhand that he was pleased his product had gotten its due.
Ten years later, I heard Stephen Wolfram's name again over a holiday drink with the book editor. He told me he'd put off retirement to work with Wolfram again on his next project. "It's too complicated to explain what Wolfram's doing," he said, "but I think it's going to be huge."
TRUE BELIEVER
We're still lost. Ben shifts uncomfortably in his seat. "I'm really sorry about this," he says. "There was some construction on the freeway, so I thought it would be quicker to take surface streets." Another hour goes by as we aimlessly drive around South Side Chicago.
My young guide is 26 years old and a recent graduate in linguistics from the University of Iowa. Ben updates Wolfram's eccentric Web site (www.stephenwolfram.com), which mixes interesting glimpses of his research with a scrapbook of photos and, occasionally, even graphs of how much email he receives. Ben tells me that he has been to Wolfram's house a dozen times, usually late at night because that's the only time Wolfram is awake and working. "It's kind of weird meeting your boss in the middle of the night," says Ben, with the solemnity of a true believer, "But then, Stephen is a very remarkable man."
The trip has taken two hours, and I find myself completely disoriented, without any idea where I am. Wolfram has agreed to visit with me, but he clearly doesn't trust me enough to let me know where. In order to talk with him at his home, I've had to agree not to divulge where he lives or anything about his family. To guarantee the former, I learn by accident, months later, that Wolfram told Ben to get us lost before coming to the house.
I'm startled out of my thoughts when Ben suddenly swerves into a driveway. "We're here," he announces.
A clean-shaven, balding man answers the door on the first knock. "Hello, Michael. It's been a while," says Wolfram, extending his hand from the darkness. I barely recognize him. Wearing wire-rimmed glasses and a striped dress shirt, he is a chubby, 41-year-old suburbanite. Only the corduroys, tennis shoes, and an English accent exuding confidence remind me of the younger Wolfram. Still looking at me, he makes a hand motion for Ben to move into the first-floor library and suggests that I follow him up the spiral stairs to his office.
THE HUMMING AERIE
The second-floor office is all white and so brilliantly lit it could be an operating room. Georgian bookcases line the walls broken by posters that are blowups of abstract patterns that prove to be Wolfram's work. In the corner, I note an odd sight in this room of pure intellect: a glass case filled with seashells. Against one wall is a large flat-screen monitor.
Wolfram has hidden in this upstairs office for the past nine years, working in secret every night until dawn on a new kind of science. By day he runs a software company, and in the eyes of the public, he is a successful chief executive. To his scientific peers, he is a brilliant could-have-been, a young man who set the world on fire by reinvigorating an obscure scientific field called cellular automata—and in the process kicked off Chaos Theory—before selling out to the blandishments of corporate life.
Wolfram drops into his chair, spins around to face me, and announces wryly, "You wanted to see me in action. But I fear that this is all there is"—he gestures at the computer screen—"all night, every night."
I notice the bookshelf next to him is crammed with the immortal works of the greatest scientists who ever lived: Euclid's Elements, Malthus' Essay on the Principle of Population, Newton's Principia, Maxwell's Treatise on Electricity and Mathematics, Darwin's Origin of Species—each turning the world upside down and making the author's name sing through history.
"Let me give you an example of my work," he says, and types in the conditions of Rule 107 of cellular automata on the computer. A black square appears on the screen, and a fraction of a second later a salt-and-pepper triangle made of individual black and white tiles appears beneath it.
This unprepossessing image is the heart of Wolfram's new science. To understand why it is so important—indeed, why it may touch off a revolution in science—you have to go back to the early 1950s, before Wolfram was born. As a sideline to his work, the great mathematician John von Neumann had investigated how to take simple structures, like tiles, and arrange them in such a way that, given a few rules, they could reproduce themselves indefinitely. After constructing a self-reproducing mathematical rule that accomplished this, von Neumann moved on to other challenges, such as inventing the modern computer.
His work contributed to a scientific field called cellular automata—"cellular" because it deals with units on a larger grid, "automata" because they automatically followed a simple rule. The theory languished as little more than a mathematical novelty for two decades, the kind of topic an ambitious grad student might pick up, write a paper about, and then drop to pursue another topic. In fact, by 1970 only about 50 papers had been written about cellular automata.
But in the 1960s things began to change—not in the world of theory but, ironically, because of a computer software game. It was called Life and was devised by John Conway, a Cambridge University mathematician.
Life was stunning both in its simplicity and its profundity. The rules were simple: Start with a grid, such as a sheet of graph paper or a checkerboard, and mark on it an arrangement of dark squares. These dark squares—cells—are "alive"; the rest are dead. Each cell has eight neighbors, four adjoining and four on the corners. Cells stay alive if they have an optimum number of neighbors (two or three); they die if they are left alone or overcrowded. If conditions are just right (three neighbors), they will give "birth" to a live cell nearby. It sounds like the recipe for a very boring and static game. But, on the contrary, whole worlds unexpectedly open up. If you play Life, you discover rather quickly that everything depends upon the initial conditions. Begin with too few live cells or space them too far apart, and the system dies. Put them too close together or in too symmetrical a pattern, and they sit there and do nothing.
But arrange the cells in a kind of T and all hell breaks loose. The cells breed like rabbits, live and die, and fill all the available space with patterns of remarkable complexity. Life is aptly named: As you watch the game develop, especially in high speed on a computer, the little cells seem alive as they evolve into ever more complex forms. It is impossible not to consider that what you're seeing is some kind of insight into the natural world.
The influential science writer Martin Gardner heard about Life and wrote it up in his popular "Mathematical Games" column in Scientific American, thereby setting off a Life-playing craze in university computer departments all over the world. Life fanatics, including Conway himself, soon began to wonder if a giant game of Life played on an equally giant computer wouldn't create its own living, breathing universe—in Conway's words, "genuinely living, evolving, reproducing, squabbling-over-territory" creatures. Perhaps, Conway and his acolytes mused, we are merely cells on God's great grid.
Wolfram first heard about Life around 1973, when he was still in high school. He even wrote a program that implemented it, ignoring the metaphysical mumbo-jumbo, but found Life "neither very interesting nor particularly dynamic." Still, the idea of the universe being computational—a notion first proposed by H-bomb coinventor Stanislaw Ulam in the 1950s and picked up by Conway with Life—started wheels turning in Wolfram's brain.
But he put the idea aside for the moment. Wolfram had enough to keep himself busy. By the time he landed at Caltech in 1978, he had become interested in one of the supreme problems of astrophysics: How are complex structures like galaxies formed? Like many scientists before him, Wolfram was finding that the biggest obstacle to an answer was mathematics itself.
This was, and remains, a minority view—in some camps even heresy. Mathematics, after all, is one of the supreme achievements of the human mind. It is the defining tool of civilization, the dynamo of the scientific revolution, the very heart of modern life. Mathematics has conquered nearly everything it has encountered for the past 2,300 years, since Euclid first decreed the postulates of geometry.
But for all of its power, mathematics, even armed with the power of calculus, has failed to fully answer the problem of complexity. The universe is far messier and more unpredictable than any equation can capture. Mathematics, as the language of physics, enables science to describe the movement of bodies in space, but what it cannot do is describe the full complexity of those bodies in anything but equations as complex as the subject itself. No equation can capture the essence of a fly, much less explain how the whole universe was created from a point of singularity.
In pondering this problem during 1980 and 1981, Wolfram began to pull together different threads of his life's work—neural networks that model how the brain might function, the Ising model from statistical physics, the Life game—to ask the question: What if the universe itself is a kind of computer? And what if that computer operates from a simple beginning and a dozen basic rules?
Wolfram later recalled this breakthrough when he told author Ed Regis in 1987, "It was sort of amusing. I was thinking about these models of mine for a month or so, and then I happened to have dinner with some people from MIT, from the Lab for Computer Science, and I was telling everybody about them...and somebody said, 'Oh yeah, those things have been studied a bit in computer science; they're called cellular automata.'
Wolfram rushed out and dug up every paper on the subject he could find. He was stunned. "They were so boring! They were a sad illustration of a sad fact about science, which is that if someone comes up with an original idea, then there will be 50 papers following up on the most boring possible application of the idea, trying to improve on little pieces of details that are completely irrelevant." So Wolfram went back to the source: von Neumann's own papers on his discovery of cellular automata. To his dismay, Wolfram discovered these founding documents were boring as well. The great mathematician had apparently come up with a "thoroughly arcane and complicated" proof that solved the problem to his satisfaction, and then moved on.
So Wolfram took up the challenge with his characteristic combination of brilliance, single-mindedness, arrogance, and entrepreneurship. Soon he was at an informal conference on the physics of computation. It took place in January 1982 on a small Caribbean island privately owned by computer scientist/physicist Ed Fredkin, then an MIT faculty member. Fredkin had grown rich enough to buy an island by founding his own computer graphics company and taking it public—a lesson not lost on the 22-year-old Wolfram.
Gregory Chaitin, now a researcher at IBM's Thomas J. Watson Research Center, first met Wolfram at the conference. He remembers seeing him walking along the beach, wearing a suit and lost in thought. "He looked like a student just arrived from Oxford," he says.
What was on Wolfram's mind was something he'd seen at the conference: a computer programmed to become a cellular automata machine. The Life game was on that machine, as was every other recent attempt to generate two-dimensional automata. Wolfram could sit at the keyboard and put in various conditions, and the cells would grow across the screen. "I find it really remarkable that such simple things can make such complicated patterns," he told Computing magazine. The experience would set the trajectory of his life for the next 18 years.
Wolfram went home with his head full of ideas. He knew not only the limits of the research to date into cellular automata but also where to take it next. He began publishing a flood of inventive papers on the subject, igniting new interest among mathematicians in cellular automata. At the end of 1982, after a feud with Caltech over the commercial potential of his work, Wolfram packed up and moved to the Institute for Advanced Study at Princeton. Soon after, he had a suite of rooms for himself and his team of four scientists and a host of powerful computers. Day and night, Wolfram played with cellular automata. Scandalizing the institute, he even went into business selling the most interesting of the printouts of cell patterns as postcards.
At the center of Wolfram's research was a quest for a new level of simplicity, beyond even that of the Life game—a simplicity that, in a strange irony, could produce infinite amounts of complexity. To do this, he moved beyond the two-dimensional grid of things like Life to the one-dimensional world of the line. In the process, he moved from the limited number of fixed rules for two-dimensional cellular automata found in Life to an almost unlimited number of potential rules. If Life could theoretically create a universe, albeit a primitive one, one-dimensional cellular automata might create our universe—if the patterns could be shown to exhibit enough complexity. Wolfram's genius was not only in making this intellectual leap, from two dimensions to one, but also in knowing where to look for the answers. Why one dimension? Because, like the universe itself in the beginning, it is cellular automata in their most elemental form. If Wolfram could find complexity in one-dimensional cellular automata, the simplest construction imaginable, he knew he could find it anywhere.
For years Wolfram worked through the night to determine the unfolding of hundreds of thousands of possible rules, typically going to bed around 5 a.m. and getting up in time for lunch.
Most of the rules quickly devolved into predictable, endless patterns. A few exhibited anomalies—zigzags that resembled cracks in cement, lines that looked like one of the air shafts in the Great Pyramid, even patterns that looked like gathered lace curtains—but ultimately all were too simple to capture the complexity of nature.
He began to fear that he had been lured into one of science's many dead ends. He could foresee working late into the night for a lifetime, painstakingly running computer models and squinting into the monitor, failing to ever divine a revealing pattern.
But then one night in May 1984, an epiphany: Wolfram realized his mistake. He had entered into this project with a predetermined idea of how nature worked, assuming that natural systems begin with randomness and move toward order. That assumption had colored everything he did thereafter. Looking only for emerging order, he had tossed aside every rule that hadn't exhibited those characteristics.
But, he now asked himself, what if you turned the whole idea upside down? What if you began with ordered conditions and looked at which rules spun out greater complexity? Through a long night, Wolfram tore through all his past work, papers flying, looking for examples that would prove his new model. Finally, close to dawn, he found it: Rule 30, a pattern that grew more intricate and unpredictable with each step. It was stuffed with what mathematicians call "emergent effects": events that cannot be predicted in advance. From the simplest of parts, Wolfram had created infinite complexity. The aha! moment had arrived. "The Rule 30 automaton is the most surprising thing I've ever seen in science," Wolfram told London's Daily Telegraph. "'Even though it starts off from just one black cell, applying the same simple rule over and over again makes Rule 30 produce [an] amazingly complex pattern.
"It took me several years to absorb how important this was. But in the end, I realized that this one picture contains the clue to what's perhaps the most long-standing mystery in all of science: where in the end, the complexity of the natural world comes from."
The more Wolfram studied Rule 30, the more incredible it became. For example, though the black-and-white triangle, the product of 2 million calculations, seemed to exhibit a certain symmetry, it was, in fact, chaotic. In particular, following the single line of black and white tiles that ran vertically from the peak of the pyramid, Wolfram found perfect chaos—i.e., a pure random number generator. He showed it to his old Caltech physics mentor, the late Nobel laureate Richard Feynman. Feynman was convinced there had to be some regularity in Rule 30. He took off for Hawaii on vacation and, for fun, spent the time there bent on proving Wolfram wrong. When he returned, he admitted he'd failed to find any sign of order.
On fire, Wolfram redoubled his research. For the next few years, he studied the results of one rule after another, with each new generation of computer speeding up the process. He found other dazzling, open-ended rules that seemed to create infinite complexity. During this period, Wolfram published a series of papers—from "Cellular Automata as Simple Self-Organizing Systems" in 1982 to "Cellular Automaton Supercomputing" in 1988—that became instant classics. Wolfram was the toast of the scientific world. He was a superstar at conferences. Scientific American published his writing. Nature ran his cellular automata pictures on its cover. Omni called him "the new Einstein."
But even as Wolfram's fame grew, his work was already going sideways. When he found Rule 30, Wolfram was convinced that all he had to do was unveil it and its potential would be recognized in all its glory. At that point, thousands of mathematicians and scientists, armed with Wolfram's sacred texts, would race and revolutionize science.
It didn't work out that way. The world took his ideas and ran off in a different direction, especially toward fields like Chaos Theory. To Wolfram, this was not only pop science but also a narrowing of perspective, when cellular automata had the potential to be fundamental and all-inclusive. "Most people used them only to reinforce [rather than destroy] their own disciplines. They got the technical stuff but missed the deep concepts. It was frustrating for me," he says with bitterness.
To set the cellular automata train back on track, Wolfram wrote a manifesto, established a technical publication called the Complex Systems Journal, founded an institute at the University of Illinois, and influenced a think tank at the Santa Fe Institute—all for naught. "I was basically reduced to a theory in the cellular automata textbook," he says. "Looking back, I was naive. So I opted out. Soon I became a sort of Old Guard. And after that, I was forgotten."
Wolfram, as usual, didn't help his case by being arrogant and pushy. He "stepped on a lot of toes," says Norman Packard, former director of the Center for Complex Systems Research that Wolfram founded in Illinois. "The political game of the university is a complex one and is not always amenable to the brash, demanding whiz kid interloper."
Walking away wasn't hard at all. In the course of his work with cellular automata, Wolfram had grown frustrated with the inability of existing software to deal with abstract mathematics. It could perform prodigious feats of arithmetic but was cumbersome at integrating programming, graphics, formulas, and numerical calculations.
So, in his typical manner, Wolfram sat down and wrote a new software program to do the job. In 1986, frustrated with re-search and academia, his entrepreneurial juices flowing, Wolfram decided to turn his program into a marketable product.
It took two years to complete, but the program, called Mathematica, proved to be the most popular scientific software ever made. Wolfram won't release exact figures but estimates that Mathematica's numerous versions (the latest is 4.0), have more than 2 million users in 90 countries. Mathematica has been used for everything from designing the flow rate of shampoo to calculating the Nielsen TV ratings to designing the cycling arena at the Atlanta Olympics.
Mathematica also turned Wolfram Research, which Wolfram funded with the last of his MacArthur money, into a privately held company with 300 employees and $50 million in estimated annual revenues, in the process making him a very wealthy man. In his new persona, Wolfram was still mobbed and cheered but now by teachers at Mathematica conferences. In business magazine profiles and newspaper reports, he appeared a contented businessman running a prosperous midsize company in Champaign, Illinois.
But he was also a man with a secret. Despite his bitterness at how his theory was being perverted, despite seeming to have walked away from cellular automata research forever, Wolfram could not leave it behind. It called to him because he felt he'd left something undiscovered—and before long, Wolfram was working later and later at night exploring his new ideas in the field, arming himself with the latest computers and servers to speed up his quest. Soon Wolfram Research became the company Wolfram ran while waiting for his computers to crunch millions of cellular automata calculations. And it's been that way for nine years.
AN EMERGING UNIVERSE
Back in Wolfram's office, Rule 107 continues to unfold before us as the computer knits a great skein of black and white on the screen. This rule produces a series of parallel lines traversed by a staircase-like design—a wild crazy quilt like Rule 30. In Wolfram's words, it is merely "interesting." He points out several diagonal slashes on the screen. "Let's see what those stripey bits do."
Soon Wolfram has forgotten me as he types away at the keyboard, glancing up over his glasses at the screen. "Hmmm. Not clear. Not clear," he mutters, his British accent growing deeper with his concentration.
Having read some of the early chapters of his manuscript on the subject, A New Kind of Science, I understand the basics of what Wolfram has found. I also know that Wolfram long ago learned enough about these rules to prove his case about the potential role of cellular automata as a universal computer capable of producing patterns for everything from quasars to bumblebees, hurricanes, stock markets, and rose petals. So why hasn't he published? Why has A New Kind of Science swelled from the 300 pages he would need to make that case to about four times that size? Most of all, why hasn't Stephen Wolfram come down from the attic?
One answer comes from an old friend, IBM research scientist Chaitin, who is part of a small circle of people with whom Wolfram has shared his work over the past 20 years or so. Says Chaitin, "Stephen is an exceptional man, and to his credit he's trying to do something revolutionary. He's trying to uncover the building blocks with which God decided to build the universe. But," he quickly adds, "such an ambition creates not one goal but two: one mathematical and the other scientific.
"In the end, mathematicians will judge this work on its intellectual merits. The question for us will be: Is his model interesting and does it play together in a compelling way? But that doesn't answer the second question, which is: Did God, or nature, actually decide to use this model? That's another matter entirely. The physicists are likely to say, 'Interesting, but is the world really built that way?'
"That's why the book is so long. He's looking for evidence in nature. I think he keeps hoping to make a few final breakthroughs before publishing."
It is in search of that evidence that Wolfram is revisiting Rule 107 tonight, and why he has revisited other rules in each of the past thousand nights. Is there something else there he can see? Some connection to the natural world? He's uncovered at least a dozen rules that produce randomness. One rule, whose number he refuses to disclose, is a "universal computer," apparently capable of creating the complexity found in the universe, not to mention possibly revolutionizing the way computers are built.
It sounds clever, but is it right? After all, it's a long way from something that looks like a crack in a sidewalk to the hundreds of billions of stars and all their accompanying planets, and every molecule on every one of them, in the Milky Way. "Is there any other evidence," I ask, "that this process takes place in the real world?" Wolfram makes a small smile. He takes me over to a bank of printers and terminals and pulls out a large sheet of paper. On it are the results of a rule that creates great triangles within triangles. "Now," he says, "look at this." He pulls open a drawer, takes out one of those odd seashells, and hands it to me.
A chill runs down my back. On the cold, shiny surface of the conical shell, in light brown, is etched the exact same pattern as in the printout. "It's called a Textile Cone Shell," whispers Wolfram. "Extremely poisonous. It mostly lives deep in the mud, so there may be no adaptive reason for it to have developed this pattern."
For Wolfram, this is his equivalent of Darwin's finch, Mendel's sweet pea—that shocking piece of evidence from the natural world that makes a radical, all-encompassing theory seem intuitively true. Rule 30 set Wolfram on his search; the Textile Cone Shell told him he was on the right path.
But the Textile Cone Shell, even Rule 30 and the rest, aren't enough. Not for Wolfram. Not now. He tried once before to show the world how important cellular automata could be—only to see the whole field race off on an unworthy tangent. This time, Wolfram won't allow science to hide. Never again will scientists be able to look at cellular automata through the biases of their own disciplines—he will force them to look at their fields through the lens of cellular automata.
And they won't like what they see. For at least four years now, Wolfram has been challenging the mathematical center of each of the major scientific disciplines in turn: biology, chemistry, physics, philosophy, evolution, fluid dynamics, cosmology, human cognition, music theory, the material sciences—the list grows by the night. He even takes on mathematics itself. There is practically no corner of the scientific world that, in Wolfram's mind, can't be revolutionized by his model. And so chapter after chapter of the new book sets down new paths—or more accurately, throws down gauntlets—challenging scientists in those fields to rewrite their disciplines according to Wolfram's new rules.
In case the world still chooses not to listen, Wolfram also tosses in one more bomb to make sure he isn't ignored: He demolishes some of the foundational theories in many of the fields. This last, he says, wasn't planned but occurred because, "I was surprised to find errors at the heart of many of these disciplines."
Take seashells. One of the most esteemed documents of modern paleontology is Stephen Jay Gould's doctoral thesis on shells. According to Gould, the fact that there are thousands of potential shell shapes in the world, but only a half dozen actual shell forms, is evidence of natural selection. Not so, says Wolfram. He's discovered a mathematical error in Gould's argument, and that, in fact, there are only six possible shell shapes, and all of them exist in the world.
In other words, you don't need natural selection to pare down evolution to a few robust forms. Rather, organisms evolve outward to fill all the possible forms available to them by the rules of cellular automata. Complexity is destiny—and Darwin becomes a footnote. "I've come to believe," says Wolfram, "that natural selection is not all that important."
The more sciences he probes, the more Wolfram senses a deeper pattern—an underlying force that defines not only the cosmos but living things as well: "Biologists," he says, "have never been able to really explain how things get made, how they develop, and where complicated forms come from. This is my answer." He points at the shell, "This mollusk is essentially running a biological software program. That program appears to be very complex. But once you understand it, it's actually very simple."
Wolfram won't describe all of his discoveries, but he does toss out a few extraordinary examples:
A challenge to natural selection as the defining force in evolution
Why time goes only one way
How to grow artificial organisms
An explanation of stock market behavior
How complex systems, from thunderstorms to galaxies, exhibit intelligence
New ways to design and build integrated circuits and computers at the atomic level
Why leaves, trees, seashells, snowflakes (and almost everything else) take the shapes they do
Wolfram confidently predicts, "Within 50 years, more pieces of technology will be created on the basis of my science than on the basis of traditional science. People will learn about cellular automata before they learn about algebra."
This list alone should give the scientific (and business, religious, and political) world pause. If Wolfram is right, a decade from now investors may be developing models that truly capture the unpredictability of Wall Street; urban planners may be devising blueprints that account for the complexity of human behavior; biologists may be modeling forms of life that have never lived before; we may know an end to traffic gridlock; even reliably predict the weather. Everything from cars to cartoons, from farms to pharmaceuticals, may reflect the richness of the natural world as seen through Wolfram's cellular automata.
There is one implication of Wolfram's work that he chooses to dismiss, but others may not. Is it a coincidence that the designers of the Life game began to talk of God when they saw the implications of their creation? Wolfram says "there's no place for God" in his new science. But what about just outside? What will theologians say when they see a theory that proposes that the entire universe—with its perplexing combination of good and evil, order and chaos, light and dark—could have been started by a First Mover using a dozen rules?
NOTHING TO CHANCE
Undermining Darwin, humiliating one of the most popular science authors alive in Gould, relegating mathematics to the bargain counter—Wolfram knows the scientific community may savage him. He has, he says, intentionally tackled each scientific discipline only enough to pique the interest of its members but not enough "to spoil everybody's fun." Still, he predicts, "People in specialties will be convinced I missed the point." That's why, he says, he's included in the book "a complete history of their field"—as if that's going to do anything but infuriate them more.
For all of his scientific brilliance and real-world success, there is something shockingly naive about Wolfram. He honestly thinks that he can attack the foundation of the modern world, the life's work of millions of scientists, and the heart and soul of academia—and not suffer more than a brief, grumpy backlash before he is lauded as the new King of Science. He also is convinced that his New Science is so simple and so self-evident that he will be invited on talk radio shows all around the country—no doubt explaining the nuances of cellular automata to Howard Stern and his fans.
Gregory Chaitin groans when he hears this. "Academic politics and scientific politics are as hardball as anything in Washington. When someone goes off in a different direction like this, people get upset. It's the same in every field. It's only after they are good and dead that we declare them geniuses." But when I ask if running a software company, all the while secretly working at night on a magnum opus no one will see until its completion, is a good strategy, Chaitin pauses, then says solemnly, "I don't know whether he's doing the best job being Stephen Wolfram or not."
Noted science writer Timothy Ferris has his own concern: whether Wolfram will get a fair hearing at all. "Academic intellectuals," he says, "tend to underestimate the intelligence and creativity of their peers in the corporate sector, who they too often assume to be sellouts simply because they make more money." Did Wolfram, in buying his freedom by becoming a corporate CEO, sell his credibility?
But then, I tell myself as I sit beside him, maybe Wolfram knows exactly what he's doing. The drumbeat is already growing in the technical community. Across the Web, from search results found on Google.com to Deja.com newsgroups, you can follow strands with titles like "Searching for Stephen Wolfram." On Amazon.com, despite the fact that it is already past Wolfram's announced publication date, A New Kind of Science recently was getting enough preorders to bounce it to the middle of the sales list—surely a record for an unpublished book of arcane theory by a nocturnal physicist.
In the end, after all of Wolfram's pronouncements and all of the scientific world's anticipation, the proof will be in the work itself. And that work lies on the desk in front of me: the mountainous 1,200-page manuscript of A New Kind of Science, including 300 pages of endnotes and hundreds of spectacular illustrations. Every word was not only written but also edited by Wolfram. Every chart and graph and image is his creation. So are the endnotes, even the index. He is going to publish the book himself because no publisher is willing to produce a book of this size, with such intricate graphics, to Wolfram's exacting standards of quality, at a price of $39.95, which is affordable to a mass audience. It will be the most ambitious vanity book since, well, Copernicus' On the Revolutions—a fact he knows well. That's why A New Kind of Science is four years overdue.
Terry Sejnowski, a computational neuroscientist at the Salk Institute for Biological Studies in La Jolla, California, is another of Wolfram's friends who has been given a peek at the new book. He defends Wolfram's delay. "Steve Wolfram is the smartest scientist on the planet, and if anyone is capable of creating a new science, he is the one." Remember, he adds, "Newton also isolated himself for decades before he published the Principia."
But Chaitin isn't sure. He sighs and says, "I keep telling him, 'Stephen, this is a lifetime activity. Put the book out now, then publish additional books. I still want to be alive when this thing gets published.'"
Wolfram assures me that the book will be published sometime in 2001. But as I watch him still tinkering with each detail of Rule 107, I wonder if that date is any more reliable than all the ones that came before it.
INTO OUTER DARK
It's 2 a.m. and Wolfram is just warming up. As he talks to me about his marketing plans, I realize he's running a model in his head about how the book will be received and what the reaction will be, and the reaction to that reaction. Like a chess master, he's thinking five moves ahead.
"Some people will try to ignore it, but they won't be able to. They'll say, 'Isn't it interesting how far he can get with such simple ideas?' Others, I think, young scientists and mathematicians, and older professionals looking for something new in their careers, will take my ideas and run with them." In his mind, whole trees of knowledge will blossom from individual pages in the book. But, like complexity theory, after a decade, the new science will become "encrusted" with misdirected efforts, faulty ideas, and speculation. Then a new generation will strip away this encrustation and return to the simple building blocks.
And where will they find them? In his book, of course. "My guess is that my examples and pictures will survive for a very long time," he says. And that's important to Wolfram because, as much as he wants his to be one of those great books on the shelf, he doesn't want it to share their fate of being respectfully unread. There are no global scientists left in the world. The last to own that title was Albert Einstein. Wolfram confides in me that he wants to wear that crown.
It's now 3 a.m. As I sit listening to Wolfram, I finally understand the reason for this late-night meeting. I am just one tiny detail, a tile if you will, among the thousands of pieces that Wolfram is preparing for the world. I am to be Stephen Wolfram's cellular automata—as are you—operating by Wolfram's rules, sent out into the world to create ever larger waves of complexity and discord. He is about to be the world's most famous thinker, or its biggest fool, and I have no way of knowing which one.
The irony—and perhaps the tragedy—is that Wolfram thinks he can control the impact of his work. Yet the whole point of his New Science is that nothing can be controlled. The unexpected always lies waiting at the next step, ready to destroy the best-laid plans of even the most brilliant men.
There is nothing more to say. Wolfram leads me down the stairs to the library, where a tired Ben has dutifully remained awake studying Linux programming. Wolfram walks us to the front door and wishes us a brisk "Good night."
The door closes behind us. There is no porch light. No moonlight. Young Ben and I are left to stumble down the darkened path through the black night, as Wolfram returns to his brilliantly lit aerie.
"You sure you know the way home?" I ask Ben.
monkey, it interests me! Though I'm only half-way through so far. The author seems to have given an excellent description of some of Feigenbaum's original insights -- E.g., sensitive dependence on initial conditions; simple, "self-replicating," periodically iterated rules.
I gather the simple rule is a mathematical equation into which numbers are "fed." Except I don't think the word "self-replicating" is quite accurate because, in Feigenbaum's original experiment, the next successive number generated by the equation refers back to the iteration immediately preceding it, and must take that number into account (i.e., by adding it to itself). Then comes the next iteration, with the new number "fed" into the equation, etc., etc. It's a "feedback loop." Ad infinitum.
This is fascinating stuff, monkey. Give me some time to digest it a bit. I may be back. best, bb.
That's the gist of it. Cellular Automata are the same concept, maybe even simpler, since equations aren't required to appreciate them. It's good to remember occasionally that nature doesn't do math, but really excels at recess.
The social movements of the 20th century - feminism, racial diversity, sexual freedom, the welfare state - were all deconstructive. Using these movements to create a new society is like building a house with dynamite. It's why Derrida is so flip; he can't answer the dumb s--- question by the science major fulfilling an elective: If you deconstruct everything, what's left?
One answer to that question is a dark age, perhaps the end of man. But chaos gives a strange hope. The world is not descending, but breaking up (who cares how) to rebuild again. There are patterns and structures, swirls and eddies all around us, jousting, combining, most fading away, but something is filling the landscape.
Very interesting observation, monkey. I agree with you that the social movements to which you refer were all deconstructive, and moreover reductionist and disordering. But this leads to a question: What, exactly, are these movements deconstructing, reducing, and disordering?
I have my own speculations about that, of course. For I do understand the question and have been thinking about it for a while now. Without getting into a whole lot of details here, IMHO the “what” can be summed up by what Eric Voegelin has termed the millennial constant: which has to do with the ways man historically has understood himself in relation to God and man, the world and society. My speculation is that what we are seeing in Western society today is a kind of “end stage” of a social process that began to gather steam in the eighteenth century. Generically, the process is called Progressivism, which is itself a complex of ideas (e.g., materialism, phenomenalism, positivism, utilitarianism, scientism, atheism).
There are other precedents in history for this type of general breakdown in the social order — Athens, Rome, nineteenth-century Europe in the throes of the Industrial Revolution, et al. Inevitably, once these things have run their course (and we’re still living in the time of the last, though even that is changing before our very eyes), then man has had to search for, and restore, the order of himself and society.
What these smelly little deconstructionists are trying to do is simply to expunge the idea of society (you can just forget about God) as having any particular legitimate claim on human beings. For them, the “radical individual” is all there is. (And then they set to deconstructing that.) Yet there is no way to reconstruct a decent human society from that premise alone. But then, isn’t that the entire point of the deconstructionist exercise? As you say, it’s like trying to build a house with dynamite….
Gleick’s Chaos suggests that there are deep structures of order “hiding under” the apparent disorder that we see in the world. I gather that Cellular Automata suggests the same also. The message seems to be that, in any dynamic, non-linear system, disorder left to itself long enough will eventually recur back to the fundamental structured state.
We assume the universality of entropy, the tendency of things to disorder and decomposition, to falling apart into their elemental constituents. I gather that the deconstructionists are in the entropy business. Yet chaos theory suggests something altogether different about the way nature (and presumably human nature and human societies), “left to her own devices,” operates. I, too, see chaos theory as a strangely hopeful development.
LOL monkey, “…nature doesn’t do math, but really excels at recess”! Of course nature doesn’t do math. But I’m beginning to wonder whether she must execute a certain program, which the equations are attempting to penetrate and describe in a suitable human language. Perhaps all that nature does at recess is to generate complexity from a small set of simple, universal rules. Diversity in unity.
IMHO Chaos was an odd book in a certain way. I imagine an atheist reading it might find ways to account for a universe without God in its pages. Yet a theist might view it as furnishing evidence of the hand (or rather, the mind) of God at work in all things. Remarkably, Gleick cites Plato twice, delighting this reader. He even touched on the millennial constant once. I suppose there are few works written these days that could/would draw such a variety of reactions…. This is really heady stuff! I’m looking forward to A New Kind of Science, which should arrive Monday. Thanks, monkey – bb.
Did he say something new? Or not?
Heh heh heh! That's for sure -- it weighs six pounds. Have you read it, monkey? I'm about 300 pages into it; so far it's a beautiful thing....
Here's an FR review you might like.
That it is, monkey. I understand the book was composed using proprietary pagination/layout software of Wolfram's own design. The technology that went into the physical production of this book is most impressive. The fineness of the screens needed to render those graphics is not something one normally encounters in the offset press environment. So I have a hunch this was output on a very "advanced" and very large-scale digital press. Plus Wolfram (or his firm -- don't know how to tell the two part) even designed the typeface used for the mathematical symbols/notation. And when was the last time you saw a dust cover that exactly matched the (full-color) hardcover binding?
Everything about this book is "unusual." :^) It's certainly been an education so far!
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