Một thế hệ khoa học mới của thế kỷ 21

IV. Ý tưởng, nội dung của cuốn "Một loại hình khoa học mới"
Như chúng ta biết, trong 300 năm qua, hầu như toàn bộ khoa học tự nhiên được xây dựng dựa trên một quan điểm mà quy tới cùng là: mọi sự vật trong vũ trụ đều vận động theo các quy tắc (định luật) mà có thể biểu diễn theo các phương trình toán học truyền thống.
Còn ý tưởng cơ bản nằm sâu trong "A New Kind of Science" lại xuất phát tự nhận định rằng con đường mô tả các hiện tượng trong tự nhiên bằng các phương trình toán học truyền thông không phải là cách duy nhất, và đến thời đại chúng ta khi khoa học & công cụ công nghệ đã pt như hiện nay thì phương pháp đó bắt đầu bộc lộ nhiều nhược điểm, hạn chế...
Có thể chỉ ra các cách mô tả quy luật khác, đặc biệt có thể mô tả tập hợp các quy tắc bằng các chương trình may tính và chúng mang một tính khái quát hơn, rộng lớn hơn các phương trình toán học truyền thống. Do đó vấn đề được đặt ra là: bằng cách nào để chúng ta có thê dùng các chương trình máy tính để mô tả các quy luật của tự nhiên?
Trong khi nghiên cứu mô hình toán học Cellular Automata S. Wolfram đã phát hiện ra rằng: có những quy tắc tiến hoá là các chương trình máy tính rất đơn giản nhưng chúng lại có thể tạo nên các vật thể phức tạp như mọi vật thể khác trong toàn bộ thế giới xung quanh ta. Phải chăng đây là cách tiếp cận đơn giản cho những vấn đề phức tạp bậc nhất? Và đây có thể là một chìa khoá bí mật vạn năng, một công cụ hùng mạnh giúp loài người mở ra một con đường mới cho tư duy nhằm giải đáp vô số các câu hỏi rất cơ bản trong triết học, khoa học và đời sống.
Nhằm chứng minh cho ý tưởng đó, trong cuốn sách "Một loại hình khoa học mới", S. Wolfram đã áp dụng mô hình và phương pháp tiếp cận mới để thu được nhiều kết quả có ứng dụng lớn trong các ngành khoa học đang tồn tại.
Có thể kể đến vào vấn đề được ông đề cập: bản chất định luật thứ 2 của nhiệt động lực học, về sự phát triển của các cấu trúc phức tạp trong sinh học, sự hạn chế về mặt tính toán của toán học, về khả năng xây dựng 1 lý thuyết thực sự cơ bản cuả vật lý học và cả đến vấn đề triết học rất trừu tượng như sự tác động qua lại giữa ý chi tự do và thuyết tiền định.
Nội dungcủa cuốn sách bao gồm các mục và 12 chương sau:
Mở đầu
Những ý tưởng cơ bản của "Một loại hình khoa học mới"
Phần 1. CƠ SỞ CỦA LÝ THUYẾT
Chương 1. Sự cần thiết của một loại hình khoa học mới
Chương 2. Thí nghiệm cơ bản
Phần 2. MÔ HÌNH
Chương 3. Thế giới của những chương trình đơn giản
Chương 4. Những hệ thống dựa trên những con số
Chương 5. Các hệ 2 chiều và hơn nữa
Chương 6. Xuất phát từ sự không trật tự
Phần 3. ỨNG DỤNG
Chương 7. Những cơ chế trong các chương trình và tự nhiên
Chương 8. Áp dụng cho những hệ thống thông thường
Chương 9. Vật lý cơ sở
Chương 10. Các quá trình của nhận thức và phân tích
Phần 4. TÍNH TOÁN ĐIỆN TỬ
Chương 11. Khái niệm về tính toán điện tử
Chương 12. Nguyên lý về sự tương đương của tính toán điện tử
Phần Kết. Tương lai của khoa học trong quyển sách này
Nhiều người đã hỏi S. Wolfram: Anh viết cuốn sách "Một loại hình khoa học mới" cho ai?
Anh trả lời: "Một loại hình khoa học mới" là một cuốn sách nói về các tư tưởng lớn và phát minh lớn. Do đó bất cứ ai quan tâm đến các vấn đề nêu trên đều có thể đọc và tìm thấy ở đây nhiều diều thú vị.
Có rất nhiều cuốn sách nói về những cái mới. Và trong thời gian qua đa số các vấn đề mới trong khoa học được trình bày mang tính kỹ thuật. Nhưng tác giả đã viết cuốn sách hoàn toàn là dễ hiểu đối với đông đảo bạn đọc. Sách có đầy các tranh minh hoạ (hơn 1000) và qua những bức tranh đó tác giả đã trình bày khá đầy đủ toàn bộ lịch sử của bộn môn khoa học mới bằng ngôn ngữ thông thường (phần kỹ thuật được đưa vào phụ lục)
Các kết quả thu được trong ?oMột loại hình khoa học mới? có nhiều ứng dụng lớn cho các ngành khoa học đang tồn tại: Vật lý học, sinh học, toán học, khoa học tính toán. Do vậy, những người quan tâm đến các bộ môn khoa học trên, là nhà chuyên môn hay người bình thường sẽ đều có thể tìm thấy trong đó nhiều điều thú vị và quan trọng.
Trong ?oMột loại hình khoa học mới? tác giả đã phát triển một con đường hoàn toàn mới về cách tư duy các vấn đề khoa học và theo tác giả cách tiếp cận mới này có ý nghĩa quan trọng không chỉ cho các nhà nghiên cứu mà còn cả cho tất cả những ai quan tâm đến lý thuyết nói chung và triết học nói riêng.
Các nhà vật lý quan tâm đến một câu hỏi khác: Có phải là trong ?oMột loại hình khoa học mới? đã đưa ra một đề nghị về một lý thuyết cơ bản cho vật lý không?
Wolfram đã trả lời: Quả là có nhiều lời đồn đại như vậy, và mặc dù chưa đưa ra một lý thuyết cuối cùng, nhưng tác giả cũng đã vạch một phương hướng đầy triển vọng cho những ai muốn làm việc đó. Tác giả tin rằng, những khuôn khổ mà được mô tả trong ?oMột loại hình khoa học mới? sẽ giúp mọi người xây dựng nên một lý thuyết vật lý thực sự là cơ bản.
Điều mà tác giả thực hiện ở đây là hoàn toàn khác với những điều tương tự đã làm trong vật lý hạt cơ bản, lý thuyết trường hay lý thuyết dây. Con đường mới này được dựa trên linh cảm mà tác giả có được qua việc nghiên cứu các chương trình máy tính đơn giản và sự nhận biết sâu sắc về những điều nó có thể làm được.

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Được CaChep sửa chữa / chuyển vào 16:49 ngày 01/08/2003

Xin lỗi vì chen ngang khi anh chưa viết hết, nhưng tôi chưa hiểu cái hiện tượng mẫu hình pt sinh học.... nghĩa là vấn đề gì vậy?
Thân ái
Hà Nội - Sài Gòn đường dài như nỗi nhớ
ai gọi tên em tha thiết mấy cho vừa
Được LG sửa chữa / chuyển vào 14:51 ngày 01/08/2003

Vâng, thú thực tôi đã viết quá ngắn và tối nghĩa. tác giả cuốn sách đã đưa ra ~ ví dụ thuyết phục chứng minh 2 điều sau:
- Quá trình từ loại sinh vật A chuyển dần thành loại B diễn ra ntn nhìn theo lý thuyết phức tạp.
- Quá trình biến đổi đường xoắn trôn ốc của 1 con ốc biển theo thời gian diễn ra ntn?
Tôi thực sự kinh ngạc về sự mô phỏng đó

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V. Kết luận
Trên đây là những nét giới thiệu về mô hình toán học ?oHệ tự hành dạng tế bào? và quyển sách ?oMột loại hình khoa học mới? của Stephen Wolfram. Dự báo đây sẽ là một sự kiện xuất bản lớn nhất kể từ tác phẩm ?oNguồn gốc của mọi loài? của Darwin 140 năm trước đây. Quyển sách này sẽ làm cho nhiều nhà khoa học suy nghĩ lại từ đầu về phương pháp tiếp cận của họ trong công việc. Và hơn thế nữa, tác giả cũng theo gương Darwin trong việc trình bày toàn bộ tư tưởng của mình trong có một cuốn sách mà mọi người đều có thể hiểu được.
Hy vọng sẽ có nhiều người trong chúng ta quan tâm, theo dõi để bắt nhịp được với một hướng phát triển mới đầy lý thú nhưng cũng đầy hứa hẹn của khoa học nói chung và vật lý học nói riêng này.
Phải chăng đây là một ngôn ngữ, một phương pháp tư duy mới của khoa học trong thế kỷ 21, kỷ nguyên Văn minh thông tin của loài người?!

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Xin post bài viết cùng chủ đề sau:
God, Stephen Wolfram, and Everything Else
Michael S. Malone, Forbes ASAP, 11.27.00
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 e***or at Addison-Wesley, asked if I could write press releases to help promote one of his new authors.
This was not, the e***or 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 e***or and accepted the job. "People talk about this guy like he could be the next Newton," the e***or 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 e***or. 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."
(Continue)

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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 automatâ?"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 con***ions 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 sciencê?"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 automatâ?""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 changê?"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 profun***y. 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 con***ions 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 con***ions. 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 universê?"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 Lifê?"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 gamê?"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 con***ions, 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 gamê?"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 universê?"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 con***ions 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 Institutê?"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.
(Continue)

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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 cre*** 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 peâ?"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 bê?"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 tra***ional 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 universê?"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 academiâ?"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 e***ed 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 ad***ional 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 automatâ?"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.

Đf tri thức ngỈời Vi?t giàu hỈn, trí tu? sáng hỈn !

The Man Who Cracked The Code to Everything ...
... But first it cracked him. The inside story of how Stephen Wolfram went from boy genius to recluse to science renegade.By Steven Levy
Word had been out that Stephen Wolfram, the onetime enfant terrible of the science world, was working on a book that would Say It All, a paradigm-busting tome that would not only be the definitive account on complexity theory but also the opening gambit in a new way to view the universe. But no one had read it.
Though physically unimposing with a soft, round face and a droll English accent polished at Eton and Oxford, Wolfram had already established himself as a larger-than-life figure in the gossipy world of science. A series of much-discussed reinventions made him sort of the Bob Dylan of physics. He''d been a child genius, and at 21 had been the youngest member of the storied first class of MacArthur genius awards. After laying the groundwork for a brilliant career in particle physics, he''d suddenly switched to the untra***ional pursuit of studying complex systems, and, to the establishment''s dismay, dared to pioneer the use of computers as a primary research tool. Then he seemed to turn his back on that field. He started a software company to sell Mathematica, a computer language he''d written that did for higher math what the spreadsheet did for business. It made him a rich man. Now he had supposedly returned to science to write a book that would make the biggest splash of all. And, as someone who''d followed his progress since the mid-1980s, I was going to see some of it.
We agreed to meet for dinner in Berkeley. As I drove to the restaurant, rain started coming down in sheets; on the pavement, water ran toward the gutter in twisted, chaotic rivulets - seemingly unfathomable patterns that I would never view in the same way after Stephen Wolfram was done with me. We chatted through dinner, remembering some of our history. And then he handed over a stack of papers. The type was set and the diagrams were sharp - apparently he was almost at the page-proof stage, with publication pending. I''d known about his work in a former backwater of physics called cellular automata, and as I read the first few paragraphs, it was clear he was using that research as a background to make more profound statements. Very profound statements. As best I could make out in my quick flip through the pages, he seemed to be saying that the key to the universe was computation: The entire cosmos, from quantum particles to the formation of galaxies, was a perpetual runtime flowing from simple rules. Yet despite all our learning, human beings have missed the point of it all, because of the elusive nature of complexity. That is, until Stephen Wolfram came along and uncovered what a few millennia''s worth of scientists had somehow failed to comprehend. Whoa.
I wondered if the pages I was holding would actually be a part of history. Or would they be regarded as folly, an act of hubris by a brain-punk who''d been thumbing his nose at the scientific establishment even before he began to shave? I handed it back to him, with the assurance that upon its completion within a few months, I''d get a chance to go through it at my own pace. And so would the world.
That was 10 years ago.
What happened to Stephen Wolfram in the interim has become sort of an urban legend in the scientific community. Not long after our dinner, which occurred in the spring of 1992, he became, in his own words, a "recluse." He moved, with the woman he had recently married (a mathematician), to the Chicago area and started a family. He rarely made the two-hour drive to Wolfram Research, his thriving software company. Instead, he put himself in a kind of voluntary house arrest, single-mindedly devoted to the completion of the book. "He dropped totally out of the scene in every sense of the word," says his friend Terrence Sejnowski, a neuroscientist at the Salk Institute. "He hasn''t published a word, he doesn''t go to meetings. He''s in a self-made isolation center." To maximize his concentration, Wolfram became nocturnal: He worked at night, when the world was asleep, and retired at 8 in the morning.
As the Web emerged and exploded, as dotcoms boomed and busted, as the White House went from Bush to Clinton to Bush, he worked. At some point he had decided that no conventional publisher would provide the attention and exacting standards that his book demanded. (He had no lack of offers.) So he decided to do it himself, using the resources of his software company. It would result in one of the most expensive vanity projects in history. Or as one friend, Gregory Chaitin, an information theorist at IBM, puts it, "He reminds me of the noblemen who worked in science during the 1800s - they did it for the love of it."
Wolfram''s days would begin in mid-afternoon. He''d usually do an hour or two of official business, operating a multimillion-dollar company by email and conference call. Early evening hours offered an opportunity for some family time. Then, as the world retired and distractions fell away, he''d enter the professionally soundproofed, wood-lined office on the top floor of his house and immerse himself in the act of remaking science.
He spent hours running thousands of computer simulations and noting the results. Because part of his project involved nailing down the conceptual history of dozens of scientific branches, he''d surf the Web. "One can devour lots of papers in very short amounts of time in the middle of the night," he would later explain to me. He''d begin with an idea, and start downloading papers. Eventually, "you feel kind of depressed that it''s too big a field and you''re never going to understand it." But then, "usually in a few days it all starts to kind of crystallize and you realize that there really are only three ideas in this field, and two of them you don''t believe. And sometimes at that stage, when I''m checking that I''ve really got all of the ideas, I find it useful to chat with people. Sometimes you hear about something else. And sometimes you don''t."
Wolfram''s friends came to know the drill. "You get a call at 2 in the morning," says Sejnowski. "By the morning he knows more than you do." Every two weeks or so, Wolfram would call an outside expert, but usually found these sessions unsatisfying. All too often he''d be disappointed that the alleged master couldn''t provide him with the information he needed.
He pressed on, never a day off. "I wanted a straight line from where I started to where I wanted to get to," he says. "I cut off interaction with the outside world - not that it wouldn''t have been fun, I personally like it - but those little perturbations would make the thing take longer." On a good night, he''d get a page written, and he''d be a few hundred words closer to finishing. And so it went, night after night, a lone explorer inventing his own brand of science while the world slept.
At various times, it appeared publication was imminent. Those who purchased a collection of his scientific papers, issued in hardback in 1994, saw an image of the cover art for his book, then titled A Science of Complexity ("coming soon," the caption said, "sure to become a landmark in the history of modern science"). Over the next few years, Wolfram teased his public by hinting at the contents in occasional interviews. But the publication date kept moving back. Wolfram''s friends seriously feared that it would never be completed.
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Wolfram predicts an algorithmic key to the universe that can compute quantum physics - or, say, reality TV - in four lines of code.
Early last year, Wolfram told me he was almost finished, this time for real. He promised to send me an early copy, if I would sign a nondisclosure agreement. A few days later, A New Kind of Science arrived. My copy (number 26) was broken up into three thick sections. Together they dwarfed a phone book. A sticker on the otherwise blank cover was printed with my name on it. There was a disconcerting warning: "CONFIDENTIAL: Receipt and perusal of this document permitted pursuant to nondisclosure agreement ... If you do not have such an agreement please return this immediately...."
If I thought that the draft I had glimpsed in 1992 was provocative, it was nothing compared with the scope and sheer chutzpah of the finished product. Scheduled to reach stores in May, A New Kind of Science will ignite controversy in the scientific world. The self-conscious comparisons with Newton''s 1687 Principia will undoubtedly earn Wolfram both attention and derision. Some early readers are drawing analogies instead to Galileo - not in terms of scientific achievement, but heresy.
At 1,280 pages, the book pushes the limit of what can be physically bound between two covers. Inside, it recognizes no boundaries, not only ranging through tra***ional fields of science but venturing into the realms of philosophy, theology, the social sciences, and even extraterrestrial policy. There are two sections, the larger being a main text of 12 chapters written in everyday English, with almost no equations, in order to reach an audience of nonspecialists. (One of his friends, Carnegie Mellon mathematical logician Dana Scott, complained to Wolfram that A New Kind of Science reads like USA Today. As if.) Just as important as the text are hundreds of detailed diagrams, the majority of them visual representations of experiments run from Mathematica programs.
The second section is a collection of notes, which includes a piecemeal yet concise history of science through the filter of a didactic middle-aged, MacArthur-winning Jedi mind-warrior. It also contains personal notes, bits of Mathematica code, various mentions of previous work (though bibliographic comments are scrupulously avoided), and an index of 15,000 entries.
To Wolfram, adopting a relatively readable style also meant jettisoning all pretense of humility, a trait that in any case he believes is a waste of time. In a note titled "Clarity and modesty," he admits to having once subscribed to the "common style of understated scientific writing" but concluded that unless he explicitly identified his findings as the earth-shattering concepts he believed them to be, readers wouldn''t grasp their significance. Of course, the very nature of his approach - laying his theory out in one Brobdingnagian salvo - is by nature immodest.
By rejecting the standard protocols of scientific publication - the release of findings in a series of refereed, jargon-laden papers with rigorous mathematical proofs - Wolfram is consciously bypassing the establishment, engaging in a form of retail science that aims straight for the people. Wolfram insists that "doing a small piece and telling the world about it" would have taken him three times longer, and besides, "if you give them little pieces, they''re not going to come up with grand conclusions."
The book begins with a thunderclap:
"Three centuries ago science was transformed by the dramatic new idea that rules based on mathematical equations could be used to describe the natural world. My purpose in this book is to initiate another such transformation, and to introduce a new kind of science that is based on the much more general types of rules that can be embodied in simple computer programs."
He goes on to explain that by applying a single key observation - that the most complicated behavior imaginable arises from very simple rules - one can view and understand the universe with previously unattainable clarity and insight. The idea of complexity arising from simple rules - and that the universe can best be understood by way of the computation it requires to grind out results from those rules - is at the center of the book. The big idea is that the algorithm is mightier than the equation. "Stephen makes the point that Newton developed calculus before Babbage invented computing - but what if it had been the other way?" says Rocky Kolb, a physicist at the Swiss physics laboratory CERN.
Wolfram is not satisfied with simply explaining and justifying his contentions, but instead makes substantial efforts to apply his insights to dozens of fields. "What''s basically happened is that I had this idea of how to use simple programs to understand things about nature, the universe, other stuff," he says. "And you can start looking at questions that have been around forever, and you really get somewhere." He invariably introduces each topic in a similar fashion: Curious to know about _______ [CHOOSE ANY SCIENTIFIC DISCIPLINE] and how his new theories might apply, he decides to take a look at the history of the field. Amazingly, he concludes, for hundreds of years so-called experts have failed to answer key questions that should have been easily resolved centuries ago. (Wolfram''s disappointment in his predecessors is bottomless.) But when Wolfram applies the ideas from A New Kind of Science, he begins making progress and expresses the hunch that not long after his ideas are understood, the biggest problems will quickly be resolved, transforming the field.
To list only a few examples: Wolfram finds an exception to the second law of thermodynamics; conjectures why extraterrestrials might be communicating with us in messages we can''t perceive; explains seeming randomness in financial markets; defines randomness; elaborates on why the "apparent freedom of human will" is so convincing; reconstructs the foundations of mathematics; devises a new way to perform encryption; insists that Darwinian natural selection is an overrated component in evolution; and, oh, theorizes that there''s a "definite ultimate model for the universe." What might this be? The mother of all rules; a single, simple "ultimate rule" that computes everything from quantum physics to reality television.
The climax of the book is the principle of computational equivalence, which may as well be called "Wolfram''s law." After hundreds of pages of laying groundwork, presenting case after case of visual examples where simple rules generate counterintuitively complex results, Wolfram concludes that this phenomenon is overwhelmingly commonplace - it''s at the base of everything from morphology to traffic jams. Then he goes further, stating that once a system achieves a certain, easily attainable degree of complexity, it''s reached the point of maximum complexity, as measured by the computation required to crank out the end result. Everything at that level of complexity - and that means almost everything you can think of, from human thought to rain hitting pavement - is exactly as complex as anything else.
It''s an idea that is at once liberating and humbling. Wolfram himself considers it the logical next step from earlier scientific revolutions, each of which disabused humanity of the notion that there is something "special" about our species and its place in the scheme of things. (Copernicus showed we weren''t the center of the universe; Darwin proved we were just another product of evolution.) Basically, he''s saying that all we hold dear - our minds, if not our souls - is a computational consequence of a simple rule. "It''s a very negative conclusion about the human con***ion," he admits. "You know, consider those gas clouds in the universe that are doing a lot of complicated stuff. What''s the difference [computationally] between what they''re doing and what we''re doing? It''s not easy to see."
The principle of computational equivalence also puts limits on science itself, ruling many questions unanswerable because the only way to discover the consequences of many complex processes is to let things proceed naturally. There''s no shortcut, since our own computational tools are at best only as powerful as the complicated systems we hope to study.
On the other hand, if the concept is valid, it portends amazing technological developments. "You might think machines can''t capture nature because these programs are too simple," Wolfram says. "But the principle of computational equivalence says that''s just not true. These programs can do all the stuff that happens in nature." By that reasoning, no barriers exist to prevent machines from thinking as humans do. "I have little doubt," he writes, "that within a matter of a few decades what I have done will have led to some dramatic changes in the foundations of technology - and in our basic ability to take what the universe provides and apply it for our own human purposes."
Only a few people - mainly friends of his in the scientific community - have read the book before its publication. They are vastly impressed, but at this point generally reluctant to endorse all of it; they say people will take decades to absorb everything Wolfram is proposing. Not heard from yet are the voices of the establishment, which undoubtedly will have problems with the unconventional work and its author. "Most scientists will find it difficult to believe that there''s a better way to do science," says CERN''s Kolb. "It''s not the way we''ve been trained to think."
Probably the toughest criticism will come from those who reject Wolfram''s ideas because the evidence for his contentions is based on observing systems contained inside computers. "When it comes to computer experiments," he says, "I can just do them and can know absolutely - definitively - I got the right answer and understand what''s going on." Wolfram can argue at length why this is a valid approach. Ultimately, he believes, he and his future followers will generate a wealth of computer-related systems that create phenomena identical to those found in the natural world - and the weight of the evidence will convince all but the most hardened skeptics that his ideas are dead-on. The beginnings of this are rules that seem to produce on a computer the same results as pigmentation patterns on jaguars and seashells, the behavior of financial markets, or the growth of leaves.
For now, the skeptics aren''t having it. "Worthless!" says renowned physicist Freeman Dyson, who received an early copy of A New Kind of Science and required only a glance before dismissing it. "It''s a case of style over substance."
If Wolfram''s ideas ultimately are refuted, he will be remembered as one more brilliant guy who went overboard, verging on megalomania. But even if he is wrong, A New Kind of Science is an incredible achievement, one that will richly reward adventuresome readers. Of course, if he is right, his book indeed belongs to history. Either way, the world is about to reckon with a scientist who''s making the biggest leap imaginable: remaking science itself, with only his computer and his brain.
In a sense, A New Kind of Science is the result of a journey that began with a computer printout produced by an early Sun workstation on June 1, 1984. Stephen Wolfram, then 25, was already on his second career. Born in 1959 to a father who was both a textile manufacturer and a minor novelist, and a mother who taught philosophy at Oxford, the young Wolfram was clearly a prodigy - and a handful. "I guess I was not a very easy kid," Wolfram told me when we first met in 1984. His baby-sitters would typically leave after a week or so "because I was terrible to them."
At age 10, he decided to become a scientist and began operating in much the same isolated manner that would characterize his later methodology. Almost from the start, he developed an allergy to the establishment. At 12, he won a scholarship to Eton, where he astonished teachers with his brilliance and frustrated them by taking no instruction whatsoever. He made money by doing other kids'' math homework. At 14, he became interested in a particle physics problem and wound up writing a paper that was accepted by a prestigious professional journal. He entered Oxford at age 17, but it is an exaggeration to say he attended it - by his account, he went to first-year lectures on his first day and found them "awful." The next two days he dropped in on second- and then third-year lectures, quickly deciding "it was all too horrible - I wasn''t going to go to any more lectures." So he worked independently, making no secret of his disdain for the professors he considered his intellectual inferiors. When he took end-of-year exams, he finished at the top of his class.
Eventually, after publishing 10 papers, he left Oxford for Caltech, which presented him with a PhD in theoretical physics just weeks after he turned 20 and hired him as a faculty member alongside luminaries like Richard Feynman and Murray Gell-Mann. A year later, he won the MacArthur award. He considered the surrounding hubbub an annoyance, and during a network TV interview he conspicuously picked his nose.
At Caltech, he ran into his first serious professional flap. Wolfram had become interested in how computers could help the scientific process; he developed SMP, a computer language that performed tasks like algebra. Because of Caltech''s patent rules, an ugly dispute broke out, and Wolfram was forever embittered that he was denied sole ownership of what he considered his creation. He left Caltech for a sinecure at the Institute for Advanced Study, the Princeton, New Jersey-based former home of Albert Einstein. But by that time, he was no longer interested in particle physics. Instead, he began pursuing what he viewed as more creative areas, "things that people would consider crazy." Specifically, he became interested in cellular automata.
At the time, the field of cellular automata, or CAs, oscillated between a science and a computer geek''s plaything. CAs themselves are abstract systems that pose a spreadsheetlike universe in which individual cells move from one con***ion to another - for example, from dark to light - one click at a time, according to what rules have been set for this evolution. These rules determine the color of the cells in the next iteration, depending on the con***ions of the current pattern. The word automata refers to the nature of the process, in which the patterns on the grid evolve depending not on human intervention but on the rules themselves: Once the initial con***ion and those rules are set, all a person can do is sit back and watch.
The field was the brainchild of the legendary mathematician John von Neumann, at the suggestion of his friend Stanislaw Ulam. Von Neumann was interested in the idea of artificial life, particularly self-reproduction. His claim - which would be echoed by those who went on to study CAs - was that these systems should not be seen solely as mathematical abstractions but as stripped-down versions of the universe itself, wherein the pageant of cells turned on and off on a checkerboard (or computer screen) could actually stand for the mechanisms in the physical world. One computer scientist, Ed Fredkin, the former head of MIT''s famous Project MAC, bent some minds by suggesting that the universe itself was a giant cellular automaton.
Not surprisingly, Wolfram regarded the early work in the field as "just awful" and proceeded to brand the category as his own, somewhat to the dismay of the small CA community, which appreciated the attention Wolfram brought but resented his imperious attitude. ("Wolfram is an absolutely brilliant guy, and he''s right about the new kind of science that underlies everything," says Fredkin. "But he can''t escape a compulsion to take cre***.") Wolfram methodically analyzed sets of rules, developing a classification system that rated the complexity of various CAs - all with the intention of clarifying the way we view complexity in the real world. He did this by studying and numbering all possible rule sets in one-dimensional CAs. These were elementary systems in which the CA grows one line at a time; the state - dark or light - of each cell on the new line is determined by a rule that depends on the con***ions on the previous line.
Wolfram also began to build a case that the same mechanisms that determined the outcome of cellular-automata experiments were omnipresent in nature itself. He was often photographed with seashells whose pigment displayed a pattern that was eerily similar to those produced in his computer printouts of simple CA experiments.
Wolfram was a controversial figure at the Princeton institute in the mid-1980s. Established scientists considered his operation on the third floor of Fuld Hall, where he and his assistants sat in front of workstations and performed digital experiments, as somehow unseemly, not the way serious research should be conducted. "I''m not sure that what he does can be called science," the institute''s Dyson told me around that time. "It''s more in the nature of mathematical games. He clearly is not a physicist anymore." And Heinz Pagels, the late physicist who headed the New York Academy of Sciences, told me, "The wunderkind has no clothes."
For his part, Wolfram felt he could have used more outrage - it would have meant people were thinking about those ideas and taking them seriously. In Wolfram''s mind, studying the results of cellular-automata runs on the computer could unlock deep truths about the universe itself. The proof for him came one fateful day in June 1984 when he printed out the results of a 2-D cellular-automata experiment using Rule 30.
When Wolfram studied the printouts on an airline flight from New York to London, he was thunderstruck. This experiment used the simplest of initial con***ions - one darkened cell on the top row. And the process of generating future states was elementary. Yet Rule 30 yielded an eruption of the most complicated, seemingly random output imaginable. (See page 135.) In fact, there seemed no end to it. As Wolfram studied it, he began to realize that there was something profound about how such complexity would arise from a simple program and began to wonder about the implications. Eventually, he would conclude that Rule 30 was not an anomaly but a crucial window onto the way the world operated.
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Wolfram''s cellular-automata work came to be cited in more than 10,000 papers. He felt, however, that even his enthusiasts were missing the point - that CAs held the key to a vast understanding of the world. Aware that the Institute for Advanced Study was not eager to host his explorations, he left for the University of Illinois at Urbana-Champaign, which gave him his own institute, the Center for Complex Systems Research. But after two years, he left the center - among his many complaints, he says, "the goofiest thing was that I was supposed to be the guy who went out to raise money, while other people got to do science." By then, he had seemingly been diverted by another project - creating a computer language called Mathematica, which took his SMP work at Caltech to a much higher level. He started Wolfram Research and hired top scientists and mathematicians to staff its Champaign headquarters. The software came out in 1988 and was an instant success. By 1995, more than a million people were using it.
Mathematica turned out to be invaluable to Wolfram, allowing him to pursue his real dream of making a mammoth contribution to scientific understanding. On a mundane level, the company brought him the wealth and resources to proceed with his book without having to worry about income or research grants - since Wolfram Research was a private company, with the majority of shares owned by its founder, there was no problem spending millions of dollars on a personal science project. More significantly, the creator of the software turned out to be its most avid consumer. Mathematica was a powerful tool to run the experiments that formed the basis of his "new kind of science." A couple of years after the program was finished, Wolfram gushed to me that "I''ve been going back and redoing problems, and it''s spectacular - things that once took me a week to do now take a half hour." Wolfram had given himself the ammunition to remake science, and in 1991, he withdrew his physical presence from the company to concentrate on the book. So began his days as a recluse.
On a crisp morning in February this year, I am off to Champaign to sit down with Wolfram for the first time since that night in Berkeley a decade ago. Only a few days before, he absolutely, positively completed A New Kind of Science. Still trying to acclimate himself to the weird circumstance of being awake at 9 in the morning, the CEO is making a rare appearance at Wolfram Research, located in an six-story office building not far from the university campus, to review some projects. (The book itself - 50,000 copies - is about to roll off presses at a Canadian printer, the only operation in the western hemisphere that Wolfram judged capable of rendering the high-definition graphics and illustrations. It will cost $12 a copy to print - five or six times that of a conventional book - making its $45 cover price somewhat of a bargain.) What was a mop of unruly hair when we last met is now a balding pate. He wears a tweed jacket, slacks, and sneakers, the picture of a software executive.
For someone with so little patience for human failing, his management style is fairly loose, though clearly his employees are deferential to him. At a Mathematica design review, he flirts with sarcasm - "Why would anyone want to do this?" he says of a proposed feature - but listens to the answer and finally concludes that the proposal is impressive. "I wouldn''t have been here for 11 years if he was the terror that people say he is," says marketing exec Jean Buck, who assumes a maternal tolerance toward the quirks of her employer. (She finds it humorous that when she told her boss she''d be busy on Super Bowl Sunday, he asked, "What''s that?") The 300 people at Wolfram Research know they are free to act independently, but only in the spirit of their leader. Though during the Internet boom some hoped that Wolfram Research would go public, Theo Gray, a scientist who helped Wolfram form the business, says that was never a possibility. "It wouldn''t be Stephen''s company then," he says.
Later in the day, I meet with a group who assisted Wolfram on A New Kind of Science. There are perhaps a dozen people in the room, and like prisoners shown the open gate after serving a long sentence, everybody is a little stunned that the book is actually finished. There are fact checkers, proofreaders, graphics specialists, PhDs who helped run the computer experiments, the art director, the production manager - a disparate collection who were part scientific staff, part publishing staff. Each day, while Wolfram was sleeping, this contingent would be busily generating graphics, securing permissions, and looking for the perfect photograph of broccoli. (One tells a story of when Wolfram rejected a picture of a panther "because it had a funny expression.") As the book got bigger, there were conflicts over how to handle its complexity. At one point there was actually a debate about whether there should be notes to the notes.
In some ways, A New Kind of Science was run like a software project. The work was always to be delivered as a digitally typeset file with all the graphics included: one massive load of bits. So instead of drafts, there were frequent "builds," some of them buggier than others. There were alpha versions and beta versions. Some of the engineers are developing A New Kind of Science Explorer, a PC application with a mini-Mathematica program that allows people to run the experiments in the book and begin to do research projects of their own. Wolfram feels very strongly that "his" kind science is one through which amateurs will unearth major discoveries, and he has been thinking of various ways to assist them.
Suddenly, it occurs to me that someone might be missing in this group. "Who actually e***ed the book?" I ask. There is a puzzled silence in the room. An e***or? Finally Wolfram says, "No one." Except, of course, the author. Later on, he explains. "I think in terms of ''This is my book and I''m fully responsible for it.''"
After Wolfram''s day at his software company, we drive through town to a nondescript steak, chicken, and salad house in Urbana to continue our discussion. I ask him what he thinks the reaction will be to A New Kind of Science. He doesn''t guess, and in a sense doesn''t care. "I think when I started this project I was still very interested in saying, ''What will other people think?'' After a while I realized, ''Why am I really doing this? Is it really worth my while to spend 10 years of my life doing something to get other people to say positive things about it?'' No, it''s not. Absolutely not. And actually, from some very cynical point of view, my opinion of the world at large isn''t high enough for me really to be interested in what they have to say."
So when people complain - and they will - that Wolfram''s "new kind of science" is built not on proofs but on looking at computer readouts, he''ll see their complaints as the howling of dinosaurs. "They''ll probably talk derisively about little programs and games," he says. "But it''s not really engagement, it''s like, ''Let''s just hope it goes away.'' It''s like the print publishers hoping the Web goes away." He prefers to take the long view. He''s absolutely confident that his work is sound and is ready to let people absorb it over a period of decades. He believes that in each area he discusses, other researchers will confirm his findings. He thinks that eventually the principle of computational equivalence will be as commonly accepted as gravity.
Meanwhile, he says, his main concern is that people actually read the book, and he professes to fear not those who will attack him but bandwagon-riders who will scan a chapter or two and then generate garbage based on their misimpressions.
As the meal progresses, our talk turns to an enigma that is almost certainly a computational equivalent of the mysteries of the universe: Wolfram himself. I point out that in a strange way, this 1,200-page tome with pictures and diagrams of computer experiments and animal skins and seashells and axioms is an extremely personal book. Presented in the guise of science are passionate contentions about religion and free will and the nature of humanity. The discoveries track its author''s obsessions. In a sense, A New Kind of Science is Stephen Wolfram''s autobiography.
"There are definitely elements of expression there," he admits. "I think 10, 15 years ago, I could not have done a decent job. I''ve seen more of people''s lives now. Back then, I would have said, ''I don''t care about theology, that''s not my thing.'' But as I kept looking at the historical context, I started realizing that I actually did care about these things and had something to say about them."
The book also is arguably a rite of passage for him as a man. When I first met Wolfram in 1984, he insouciantly dissed his parents'' careers. "I''ve never read [my father''s] novels.... They get good reviews, but they don''t sell terribly many copies," he told me. Ironically, A New Kind of Science is not just a scientific excursion but also a literary excursion. Like James Joyce, Wolfram believes his ideal reader is one who will devote a lifetime to reading his book, and like Joyce the novelist, Stephen Wolfram (a novelist''s son) has produced an encyclopedic world.
If the expression of the book represents his father''s craft, the application of his ideas to the riddles of human existence reflects the concerns of his mother, the Oxford philosophy professor, who died in 1993. Back in 1984, he said of her, "I have no idea what she does, and the only consequence of her being in that profession is that I will never consider doing anything that''s labeled philosophy." But A New Kind of Science is nothing if not a book on philosophy. One of his friends suggests it should be called Principia Computatus. And in another irony not lost on the author, Wolfram''s research led him to a textbook on logic written by his mother. "I actually cared about the answers to the questions," he says.
I think back to Wolfram as a brash, trash-talking 25-year-old. Now he''s a family man ("Having kids has made him much more of a human being," says a Wolfram Research exec) whose new work, while as iconoclastic as ever, turns out to be a homecoming for him, an outcome that seemed totally unpredictable. Only by nature running its inscrutable computations could the result become apparent.
As dessert is served, I bring up the secret-of-the-universe question. Wolfram''s theory that there is a single rule at the heart of everything - a single simple algorithm that, in effect, generates all the rules of physics and everything else - is bound to be one of his most controversial claims, a theory that even some of his close friends in physics aren''t buying. Furthermore, Wolfram rubs our faces in the dreary implications of his contention. Not only does a single measly rule account for everything, but if one day we actually see the rule, he predicts, we''ll probably find it unimpressive. "One might expect," he writes, "that in the end there would be nothing special about the rule for our universe - just as there has turned out to be nothing special about our position in the solar system or the galaxy."
this rule of the universe to be?"
"I''m guessing it''s really very short."
"Like how long?"
"I don''t know. In Mathematica, for example, perhaps three, four lines of code."
"Four lines of code?"
"That''s what I''m guessing. I mean, I don''t really know, but I think there''s no obvious evidence that it''s any longer than that. Now, in a sense, it will be short if Mathematica was a well-designed language. It will be longer if it doesn''t happen to be as well-designed, in the sense that that doesn''t happen to be the way the universe works. But we''re not looking at 25,000 lines of code or something. We''re looking at a handful of lines of code."
"So it''s not like Windows?"
"No." Wolfram laughs. "It''s not like Windows. It''s going to be something small, I think. I''ve certainly wondered. You ask about the theological questions and things. I think there will be a time when one will sort of hold those lines of code in one''s hand, and that is the universe. And what does this mean? You know, how do we then feel about things, if this whole thing is just five lines of code or something? And in a sense, that is a very unsatisfying conclusion, that sort of everything that''s going on, everything out there, is all just this five lines of code we''re running."
There is a moment of silence between us. In the background are the clatter of dishes and silverware, noises that come from a restaurant in Urbana, Illinois, preparing for closing time. The mundane but complex stuff of equivalent computational processes.
"Well," I say finally, "I guess we''d feel really bad if it wasn''t well-written."
Wolfram grins. "Yes, right."
Another pause. "So do you believe we''ll find this code in your lifetime?"
"I hope so. Yeah."
"Do you want to find it?"
"Sure. That''d be nice."
"Is that your next thing to do?"
The self-styled Newton of our times smiles, as if to himself. "I''d like to think about that. Yeah.?
Just over twenty years ago I made what at first seemed like a small discovery: a computer experiment of mine showed something I did not expect. But the more I investigated, the more I realized that what I had seen was the beginning of a crack in the very foundations of existing science, and a first clue towards a whole new kind of science.
This book is the culmination of nearly twenty years of work that I have done to develop that new kind of science. I had never expected it would take anything like as long, but I have discovered vastly more than I ever thought possible, and in fact what I have done now touches almost every existing area of science, and quite a bit besides.
In the early years, I did as I had done before as a scientist, and published accounts of my ongoing work in the scientific literature. But although what I wrote seemed to be very well received, I gradually came to realize that technical papers scattered across the journals of all sorts of fields could never successfully communicate the kind of major new intellectual structure that I seemed to be beginning to build.
So I resolved just to keep working quietly until I had finished, and was ready to present everything in a single coherent way. Fifteen years later this book is the result. And with it my hope is to share what I have done with as wide a range of scientists and non-scientists as possible. In modern times it has been almost unheard of for genuinely new science to be presented for the first time in a book that can be read by non-scientists. For progress in science has mostly tended to take place in small steps that cannot reasonably be explained without relying on specialized technical knowledge of what has gone before.
But to develop the new kind of science that I describe in this book I have had no choice but to take several large steps at once, and in doing so I have mostly ended up having to start from scratch--with new ideas and new methods that ultimately depend very little on what has gone before. In some ways it might have been easier for me to present what I have done in some kind of new technical formalism. But instead I have chosen to spend the effort to take things to the point where they are clear enough to be explained quite fully just in ordinary language and pictures.
Unfortunately, however, this will no doubt mean that there are some--particularly from the existing sciences--who will at first assume that their existing technical knowledge must somehow already cover whatever is in this book. And a few, I fear, will stop at that point, and choose to learn no more. But many, I hope, will at least look at the book long enough to begin to be surprised by what it actually says.
At first probably they will think that parts of it cannot possibly be correct--for they seem so at odds with existing science. And indeed if I myself were just to pick up this book today without having spent the past twenty years thinking about its contents, I have little doubt that I too would not believe many of the things it says.
But the computer experiments on which the science in the book is ultimately based are easy to check on any modern computer. And almost all the arguments in the book--while often not conceptually simple--require no specialized scientific or other knowledge to follow.
Yet it has certainly taken me years to come to terms with the conclusions I have reached. And while I hope that all the effort I have put into presentation in this book will make it easier for others, I do not expect it to be a quick process. For to absorb in any real way what the book has to say requires a fairly major shift in intuition and thinking.
But the most important first step, I believe, is just to recognize what is involved. For though there are connections of all sorts, this book is first and foremost about a fundamentally new intellectual structure, that needs to be understood in its own terms, and cannot reasonably be fit into any existing framework.
It has been a great challenge for me to capture the things I have discovered over the past twenty years in a book of manageable size. And to do so I have often ended up compressing into a page or even a paragraph the essence of what a chapter or even a book could have been written about.
In the quarter million or so words of the main text my emphasis is on communicating the core of my ideas and discoveries--as well as indicating a little of how I came to them. The last three hundred or so pages of the book--themselves another quarter million or so words--supplement the main text with many historical and technical notes, and also summarize more discoveries. The notes that begin on page 849 address some specific issues about reading this book.
Throughout the book my primary concern is with basic science and fundamental issues. But building on the foundations in the book there are a vast array of applications--both conceptual and practical--that can now be developed. No doubt some will come quickly. But most will probably take decades to emerge. Yet in time I expect that the ideas of this book will come to pervade not only science and technology but also many areas of general thinking. And with this its methods will eventually become a standard part of education--much as mathematics is today. And in the end most of what now seems surprising and remarkable in the book will come to seem familiar and commonplace.
But for me what has always been most important is the actual process of discovery. For I know of nothing as profoundly exciting as to glimpse for the first time some new and basic truth. And now that I have finished building the intellectual structure that I describe in this book it is my hope that those who read these words can share in the excitement I have had in making the discoveries that were involved.
Stephen Wolfram, January 15, 2002

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