I read about this book in Scientific American a few years ago. Algorithms instead of evolution. He's certainly going to get the scientific community buzzing...
Posted on 06/09/2002 5:39:56 PM PDT by aculeus
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 Adding to the suspense, the book has been announced and withdrawn as the artist returned to his garret to tinker, ignoring the bad vibes and hexes cast by jealous colleagues hoping to see him fall flat on his face.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.
I read about this book in Scientific American a few years ago. Algorithms instead of evolution. He's certainly going to get the scientific community buzzing...
It sounds fascinating, but I think I'll wait for the video!!:)
If your translation is understandable, I will make another FR donation for the FReepathon.
BTW, the Wired article is linked here.
One fundamental claim elaborated on in the article posted here is that equations, e.g. calculus equations for motion, are paradoxically limiting in their complexity: they only work for a narrow set of problems. Wolfram claims this is why so much undiscovered terrirtory remained undiscovered for so long.
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.
Please make your check payable to FreeRepublic, Fresno Ca.
The game of life, as it existed on computers way back when, is a good illustration of what he is talking about. Mathematical rules not necessarily being over complicated. The article points out some great observations, and after being up late working on the stuff was I was very happy to see it posted! Great read!
PS - I am no mathematician or physicist, I do however play with number theory alot for amusement. So I cannot get overly technical answering questions :) I am a hobbyist.
I'm looking forward to the rest the book.
Jack
That is, the book may be revolutionary. But what the Times reports about the book, is not.
Maybe I am just tired and stupid tonight, but this just seems to be a philisophical exansion of Chaos.
A simple equation, reiterated and fed back over and over can produce the limitless complexity of the Mandlebrot Set, for example.(Do a google search for the term if you have not read Gleik's book "Chaos").
Most forms in Nature are chaotic in origin, and represent the self-similarity of some basic algorithm that expands to overall complex form from a simple fractal.
Diabolical structures with seemingly infinite circumference with fixed area, like the Koch snowflake, or shapes with unlimited internal area in a fixed volume like the Sierpinski gasket have been around for ages.
At the time (80's) nonlinear systems like Chaos were being introduced into popular reading, it did seem like a "Paradigm shift", and could give insights into how Nature did things, and why.
A bifurcation series (one branches to two, branches to 4, 8, 16...)gives a good approximation of a branching tree, or the human circulatory system.
So it does not surprise me at all that someone would take the principles and run with them, extending them.
The only thing that does surprise me is the claim of novelty.
But as I said, maybe I am just tired from the weekend, and tomorrow morning I shall slap myself in the forehead.
You realize I shall have to READ this huge thing now!!!? :-)
They definitely expand your mind. His stuff on self-referential sentences and the like is a big influence on me -- I've come up with dozens of my own. For a little more approachable popular math books, John Allen Paulos' books are great, too. I love "A Mathematcian Reads the Newspaper". It's essentially a long series of articles illustrating different ways in which people are misled by the media's use of statistics, or ways in which people themselves misinterpret simply presented statistics. "Innumeracy" is another, about how people understand (or don't understand) mathematics and numbers.
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