'A New Kind of Science': You Know That Space-Time Thing? Never Mind

AMONG a small group of very smart people, the publication of ''A New Kind of Science,'' by Stephen Wolfram, has been anticipated with the anxiety aroused in literary circles by, say, Jonathan Franzen's recent novel, ''The Corrections.'' For more than a decade, Wolfram, a theoretical physicist turned millionaire software entrepreneur, has been laboring in solitude on a work that, he has promised, will change the way we see the world. Adding to the suspense, the book has been announced and withdrawn as the artist returned to his garret to tinker, ignoring the bad vibes and hexes cast by jealous colleagues hoping to see him fall flat on his face.

Now, weighing in at 1,263 pages (counting a long, unpaginated index) and 583,313 words, the book could hardly be more intimidating. But that is the price one pays for a first-class intellectual thrill. While experimenting with a simple computer program 20 years ago, Wolfram stumbled on something rather eerie: ''the beginning of a crack in the very foundations of existing science.'' Ever since, he has been following it deeper as it widens into a crevasse.

The normal thing would have been to dispatch regular reports from the field -- unreadable papers published in fashionable zines like Physical Review Letters or Physica D. Instead, Wolfram decided to do what Darwin did (and he would not shun the comparison). He is springing loose his vision all at once, in a book intended for nonscientists and scientists alike.

From the very beginning of this meticulously constructed manifesto, the reader is presented with a stunning proposal: all the science we know will be demolished and reassembled. An ancient error will be corrected, one so profoundly misguided that it has led science down the wrong avenue, until it is approaching a cul-de-sac. The mistake (as everyone who hated calculus will be happy to hear) is trying to capture the richness of the universe with mathematical equations -- Newton's, Maxwell's, Einstein's. All are based on an abstract, perhaps dubious idea -- that time and space form a seamless continuum. Whether dealing with an inch or a second, you can chop it in half and the half in half, ad infinitum. Thus things can be described with unlimited, infinitesimal precision.

This conceit works fine for simple phenomena like a planet's trajectory around the sun or a weight falling from the Leaning Tower of Pisa. But as scientists try to explain systems of greater complexity -- a hurricane, the economy of Portugal, a human or even a reptilian brain -- the calculations become ever more elaborate until one is left with an unwieldy array of symbols that do not explain much at all.

Wolfram believes that even his own field, theoretical physics (he got a Ph.D. from Caltech when he was 20), suffers from the problem. Equations can capture characteristics of individual particles with breathtaking precision. But put three or four particles together and the complications begin to overwhelm. The problem, he proposes, is that equations are the wrong tool for the job. They should be replaced with computer programs -- more specifically, the little snippets of software called algorithms.

That sounds absolutely ridiculous. Programs are just human inventions, marching orders for a machine. They serve well as a quick and dirty means of tricking a computer into approximating the smoothness of nature, roughing out reasonably good facsimiles of a scientist's perfect equations. But computers understand nothing but 1 or 0, with no gradations in between. Algorithms can mimic reality's grain as finely as the engineers can manage, but the simulation can never be as sharp as the real thing.

Wolfram contends that this, the common wisdom, gets things upside down: the algorithm is the pure, elemental expression of nature; the equation is an artifice. That is because the continuum is a fiction. Time doesn't flow, it ticks. Space is not a surface but a grid. A world like this is best described not by equations but by simple step-by-step procedures. By computer programs.

The universal operating system Wolfram imagines is not something horribly complicated like Windows. The key idea in the book is that simple, byte-size programs have the surprising ability to produce endlessly intricate behavior. His most basic example is a group of elegant little algorithms with a clunky name: cellular automata.

These have been kicking around in the popular science press for years. Start with a row of squares (the cells), some white and some black. Then transform the pattern according to a mindlessly simple rule. Here is an example: if either of a cell's neighbors is black, then make the cell itself black in the next round; otherwise, make it white. That is the whole program. Print each new generation below its progenitor and a pattern unfolds like a piano roll. Automate the procedure with a computer and watch what scrolls down the screen.

Most of these experiments -- Wolfram has tried them all -- settle into numbing repetition, churning out the same configuration again and again. But every now and then a rule takes flight and soars. What Wolfram calls Rule 30 sounds about as dull as can be: if a cell and its right-hand neighbor are white, the next time around make the cell the same color as its left-hand neighbor is now; otherwise, make it the opposite. Apply the rule to a single black square and the pattern that emerges looks every bit as random as the snow on a television tuned to an empty channel. You have to see it to believe it, and Wolfram obliges with stunning illustrations (including the book's goldenrod endpapers, spattered with output from Rule 30). The implication is that some computation like this may be the engine of entropy in the universe.

Other rules have the opposite effect: seed them with a random jumble of cells and, after a few iterations, they begin generating complex order. Some of the output resembles intricately varied stalactites; some looks like tracks of colliding particles in a high-energy accelerator lab. Think of stars and galaxies emerging from the confusion of the Big Bang, or life from the primordial sea.

Most pleasing to the eye are rules generating nested patterns like those of a crystal or a snowflake, or the markings on a seashell, the branching of a leaf, the spiral of a pine cone. Other patterns swirl like clouds, smoke or turbulent streams of water.

Wolfram believes he has clinched the deal with what, for many scientists, will be the meat of the book: a proof that a simple cellular automaton can be programmed to perform any conceivable computation (making it equivalent to what the British mathematician Alan Turing called a universal computer). If you buy all this, then a simple algorithm like those described in the book could constitute the machine code of the universe, the platform on which all the other programs run.

One idea after another comes spewing from the automata in Wolfram's brain. Maybe it is not evolution but algorithms that generate biological complexity. Maybe, if everything arises from computations, it makes perfect sense to think of the weather and the stock market as having minds of their own. Maybe free will is the result of something called ''computational irreducibility'' -- the fact that the only way to know what many systems will do is to just turn them on and let them run.

All this is laid out clearly and precisely. Any motivated reader should be able to plow through at least a few hundred pages before the details become too burdensome. Then one can just marvel at the pictures. (It's evident why Wolfram, who adds depth to the term ''control freak,'' published this work himself. Some illustrations contain hundreds of checkered cells per inch, requiring ''careful sheet-fed printing on paper smooth enough to avoid significant spreading of ink.'')

Probably only scientists will read the 348 pages of notes (though these can be very amusing, providing us with Wolfram's thoughts on subjects like ''clarity and modesty,'' ''whimsy'' and ''writing style''). Many may already be thumbing through the index, whetting their knives. At least in the main text, Wolfram often gives the impression that he has the field -- sometimes called physics of computation -- all to himself. Some of his colleagues will find their work acknowledged in the notes; others may not.

Yet Wolfram has earned some bragging rights. No one has contributed more seminally to this new way of thinking about the world. Certainly no one has worked so hard to produce such a beautiful book. It's too bad that more science isn't delivered this way.

George Johnson contributes science articles to The Times. His new book, ''A Shortcut Through Time,'' will be published next year.

Here is another pathetic, desperate straw for egghead atheists to cling to, in their never-ending quest to talk themselves out of the existence of God, so that they can be Real Important.

It might actually show the opposite -- especially if the code snippit for the universe contains a copyright statement ... 8-)

I can't imagine writing anything without =
Oh, yes I can: (eq force(* mass acceleration)).
Did I remember it right?

'eq' is test for equality, assign is 'setq'.
(setq force (* mass acceleration))

"Very clothes, but then I don't Lispth."

Here is another pathetic, desperate straw for egghead atheists to cling to, in their never-ending quest to talk themselves out of the existence of God, so that they can be Real Important.

Don't worry. Every prediction that whizbang scientific discoveries from great thinkers would force believers into atheism has failed thusfar. The latest was the Human Genome project, which ended up turning the dangling legs of some labcoated fence-sitters over to the Intelligent Designer side.

"The world expressed by the language of math always seemed somehow not quite right to me after I found out that the circumference of a circle divided by the diameter is an irrational number."

I've always felt the same way. The number that did it for me was i, the square root of -1. It's called imaginary, because it can't exist in the world of real numbers and yet is critical to higher math equations. I always saw that as the chink in the armor of science.

At any rate I think Wolfram, and those mentioned by others here, have hit upon a more accurate dscription of EVERYTHING because it is non-linear. Now if they can do it in about 42 dimensions, 264 colors, and modulating terabit bandwidths they might be getting somewhere. As a start.

Thanks for the great LINK on # 67, Smithee! Don't you sense, amongst the science-types, not merely a desperation to disprove the Bible account of Creation, but a palpable TERROR that it might be true?

After the Genome shocker, they should have started asking hard questions about what thin ice "evolution" now sits on, but instead, they merely latch onto the next lame-brained "theory" like this one, which will be chewed over for awhile, then discarded with all the others.

After each one of their lil' "theories" is cast aside as useless, they always express relief that there is now a brand-new one which gives them "hope" to still disbelieve God's Word.

In LISP, "eq" tests for identical symbols. Nothing to do with equations. To test for identical value, especially numerical value and type, you could use eql, or equal, or equalp. Still, none of these has anything to do with an equation, i.e. the result could be "nil" indicating the arguments are not the same ("same" depending on which comparison operator you use).

Equations are things you can use algebra and calculus on to solve for a particular variable, and obtain a function that tell you the value of that variable based on other values. The vast majority of computer programs do no symbolic manipulation on equations. They calculate, they compare, they store, and they branch. In fact it is a key result of Wolfram's work that once a fairly low level of complexity is reached, a program (in the very very general sense of the word) is hopelessly specialized, and that only very simple combinations of rules result in unexpected and interesting outcomes.

From my understanding of the article, it sounds to me like the author has discovered the not too particularly earth shattering idea that the universe is non-linear.
All of those books on fractals as Chaos theory said the same thing a few years ago without this authors grand sounding claim to have re-defined the universe. Can you, or anyone one else tell me why I should invest my copious (not) free time in reading his work? Most of the published reviews seem to gloss over the concept as they usually do with similar topics.

I'm an Economist, so while I may lack the specific training, I can usually muscle through the math if given time, so I'd appreciate any explanation from someone with a better understanding than the average book reviewer.

Thanks.

Wolfram is not claiming to have "re-defined" the universe. He is claiming to have come up with a new set of tools that can be used to better understand specific parts of the universe. The ultimate proof of the validity of the theories presented will be if someone is able to create a wholly new technology, application, equation or science using these theories. We should find out within the next thirty years or so.

And this is another pathetic, desperate straw for mush-for-brains religionists to cling to, in their never-ending quest to talk themselves into believing everything they've been told, so they don't have to criticaly think about the universe.

I agree! People shouldn't believe everything they are told...like:

"We are the Scientific Community and we attest that the universe has three dimensions... Anyone who says anything other should be ridiculed"...

"Wait-- make that FOUR dimensions...anone who says anything other must be laughed at..."

"Wait, make that TEN dimensions..."

"The Speed of Light is ALWAYS 186,000 mps. It can NEVER be anything less..."

"Oh, wait, some guys in a laboratory slowed it to 0 mps??... er...well...uh..."

"The theory of Evolution is a FACT... We're gonna find those missing links any day now... Anyone who says anything else must be ridiculed thoroughly..."

We shouldn't believe stuff like that?

"The Speed of Light is ALWAYS 186,000 mps. It can NEVER be anything less..."

Hey rocket scientist, the speed of light IS always 186,000 miles per second IN A VACUUM. It moves slower in any other media. Using your broken understanding, you would say that Cerenkov radiation proves that things can move faster than the speed of light.

It is interesting how someone who knows so little about science thinks they know what science actually says.

You are uniquely suited to understand it better than I. A few years ago, another "new" book came out, as another derivative of Chaos, and Economics studies and projections figured _prominantly_ in it. The book was titled "Complexity".

I felt that the touting of a "Bold new Science" on the jacket was a bit like a Geo Metro equipped with a speedometer that maxes at 165.

Chaos was the "New paradigm shift". It did influence me and my career greatly, presenting me with a new way to look at engineered material structures and surfaces. It appears it greatly influenced the current author, also. But I doubt the derivatives of the pioneering work of Lorenze,Sierpinski, Kock, Mandelbrot, et al will amount to as much of a real world everyday impact.

Now, if I ever find certain Strange Attractors in the Stock Market and the Lottery, I shall be on here with a more pretentious Freepname! :-)

It is interesting how someone who knows so little about science thinks they know what science actually says.

I see. That would be kind of like people who've never seen the inside of a Bible who think they know what IT says, huh?

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