-Caveat Lector-
Good article for those interested in "IT."
AKE
God, Stephen Wolfram, and Everything Else
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.
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