'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 Adding to the suspense, the book has been announced and withdrawn as the artist returned to his garret to tinker, ignoring the bad vibes and hexes cast by jealous colleagues hoping to see him fall flat on his face.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.

Not to sound arrogant, but duh! Cytosine, thymine, adenine, or guanine.

Incidentally, "A New Kind of Science" has 85 reviews at Amazon.com. Average rating: 3 stars. This rating indicates either a mediocre book or a very controversial one. I'd guess the latter. I haven't read the reviews, but I bet there are a lot of extreme ones (one star or five stars). Maybe I'll wait until it gets to the library. I've got about two or three dozen books I'm in the middle of, not exaggerating. I don't need another one just yet! Especially one that demands so much of the reader.

I cannot explain it. But I think the problem he addresses may answer a question that I have had running around this brain for about 25 years.

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. Something as simple as that ratio between geometric shapes should not create something as profound as p. I have always felt that complexity of describing the world using math was way too complicated. In engineering much of math is simply the use of tricks. tables and transforms to make the complex manageable. Perhaps it should never have been so complex to begin with.

It should be an interesting book.

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.

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.

Alas, I am geek...

Sounds kind of like "Hello, my name is Bill W." I'm kind of a renaissance geek. Majored in Math, minored in C.S., yet won the literature prize at graduation in high school, and sang in my college's chamber choir; Currently, I maintain a gardening web site, hike, bike, kayak, write poetry, maintain an online diary, spend way too much time on FR, managed my divorce, maintain a long-distance relationship, and oh, hold down a full-time job. That all sounds good, like I'm well-rounded, but often the way it feels to me is that in any given one of those areas, many or most people in the group are better than I at the given skill.

But still, like Johnny 5 in the movie "Short Circuit", my motto would be "IIIIInnnnnput!" It would be cool to be the Tiger Woods or Pavarotti of SOMETHING. I guess I just find too many things too interesting to set aside for one thing. I 'spect there are a lot like me on FR. Viva generalism!

I think this guy is on to something. As an eternal computerist (since punched cards), I've often observed how snippets of code made for one purpose can be put together with code that served some other purpose (even though it is completely irrational to do so) to create amazing and elegant solutions to problems. It sounds to me just from reading this article that is what he is proposing. I'll have to get the book and get my wife to read the really big words to me.

Stephen "The sourcecode of the Universe is about five lines" Wolfram's book will look especially good on the coffee table during Mensa meetings.

Someone at Amazon has a "How to be Pretentious" list of books. I qualify for Mensa, and because my father and grandfather were members (my father only briefly), I went to some get-togethers. Some very self-involved people. I decided to deliberately not join the group, because I never wanted to be the kind of person who is only tolerable within that narrow group, and insufferable to EVERYBODY else.

There is so, so much I don't know and will never know. I was blessed with a decent brain (and cursed with it, too...depression, anxiety, shyness, etc.). But I value a firefighter more than a professor by default, whatever his IQ or 'credentials'. That's the conservative in me. I'm still somewhat amazed at how many really smart conservatives there are at FR. I guess I bought the liberal party line for too long, that smart people were liberal (and conversely, average and not-so-smart people were conservative).

Actually, there is a lot more to what Wolfram is proposing. First of all, he gives some very elegant examples showing how "cellular automata" can be applied to problems like fluid dynamics. Secondly, he demonstrates (rather convincingly, to my mind) a proof that explains why there are only five kinds of basic shell shapes used by every creature that has a shell. It's not evolution, it's the manner by which shells are extruded, and the possible "rules" that can be applied as the shell grows. Thirdly, he demonstrates that additional complexity in the initial algorithims does NOT result in more complex systems. In fact, once a basic threshold of functionality is crossed adding additional complexity to the starting algorithm seems to actually detract from having complex systems as a result. This is a rather remarkable and wholly counterintuitive conclusion.

Perhaps the most poignant thing he has to say in the book comes towards the end, where he talks about how we may be able to figure out the basic "patterns" of the universe, yet will will never really be able to know where they are heading, we will just have to watch them iterate and see how they shape up. I've only read the first two chapters, and skimmed the rest, now I'm ready to go back and dig in for round two.

As an eternal computerist (since punched cards), I've often observed how snippets of code made for one purpose can be put together with code that served some other purpose

Do you program in PERL by any chance? I still remember the punch card days on an HP myself, though I was in the 8th grade then. Started out with a trash 80...ahhh those were the days. Block graphics, 4-8mhz processor, 16k ram, z80 processor...

I guess I have to read the book, because I can't believe the above summary. If the above statement is true, the book is a gigantic hoax. First, becuase Wolfram's alleged "proof" was proved back in 1966 by Arbib. Secondly, because Deutch proved in 1985 that a "Turing Machine" could not simulate our actual universe. Indeed, it cannot even simulate a photon.

I grant that many of the forms we see in Nature could be the result of simple interactions iterated many times. But gee, that was first demonstrated in 1917, no less, in D'Arcy Thompson's magnificent book On Growth and Form.

In sum, nothing mentioned in the above review is in any way novel. So I guess I suspend judgement until I can read the whole thing.

A couple of points:

1. This work is eerily familiar to Wieschaus' and Nüsslein-Volhard's work where they discovered a very simple and universal rule for embryonic development.

"Remarkably, the phenotypes could be easily classified into three distinct categories. They called them gap, pair-rule, and segment-polarity, depending on what was missing from the embryo: a large domain of the body, smaller domains spaced every other segment, or even smaller domains within each segment. As they continued to accumulate more mutants, it became clear that they all fell into one of these three distinct categories, even if details (e.g. the exact borders of the missing domains) differed.

They suggested that these three types of genes were responsible for a progressive subdivision of the embryo, starting with a rough sketch of the embryo body pattern and then filling in finer and finer details as two new waves of genes become active.

To everyone's surprise, virtually all the genes involved in early development of Drosophila turn out to be represented also in vertebrates, proving an amazing conservation of regulatory mechanisms across over 600 million years of evolution."

2. Let us never forget that it was another young man playing with a cheap pocket calculator who saw into the fabric of the universe, discovered the fingerprints of God and created the field of Chaos Theory - Mitchel Feigenbaum.

3. From the simple to the complex - works for me...

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.

Hofstader's magnus opus Goedel, Escher, Bach.

Fret not that this will somehow prove that humans are nothing more than sophisticated computers. Kurt Godel proved otherwise in 1931 with his paper "On Formally Undecidable Propositions of Principia Mathematica and Related Systems".

Godel proved that there are things we know are true, but cannot be arrived at given a starting set of rules like a computer program.

Ernest Nagel in his 1958 book "Godel's Proof" correctly concludes this, "Godel's conclusions bear on the question whether a calculating machine can be constructed that would match the human brain in mathematical intelligence...the brain appears to embody a structure of rules of operation which is far more powerful than the structure of currently conceived artifical machines. There is no immediate prospect of replacing the human mind by robots."

Godel's proof is a killer logical problem for atheists like Hofstader who want to reduce man to nothing more than a sophisticated machine. It's mathematically proven that our thinking brains are outside the system. Hofstader trys to get around Godel's proof by suggesting that machines can change their own logical set of rules they function by. The end result is Hofstader spiriling down to nowhere in his book "Godel, Escher, Bach".

The word from the trenches of mathematics and similar is that while the book has some very interesting ideas, it is not revolutionary by any means. Some points worth mentioning:

1.) Most of the really interesting ideas that he posits are conjecture. He provides scant mathematical proof for these and there is some skepticism in the mathematical community that some of his conjectures are actually true.

2.) He appears to take credit for a number of ideas that are not his. Some of the concepts he waxes eloquent on as though they were created by him pre-date him in publication by a decade or more and were definitely developed by others.

3.) It is an excellent treatise on complexity theory, but the hype exceeds the actual intrinsic value. It is a brilliant work but spotty, and falls well short of earth-shattering.

4.) Wolfram is an egomaniac with delusions of grandeur writ large. Make no mistake, he is a very bright fellow, but he attributes far more value to his original ideas than they actually warrant. But then, this personality flaw is well-known and documented.

My take is that you should read it and learn, but take some of it with a grain of salt. The basic mathematics is well done, but some of his conjecture is more sketchy. I'll add that going into what makes it sketchy requires a fair bit of mathematical background or you likely won't see it. Overall, it is an interesting book but no bible by any means.

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