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A New Kind of Science 530

Posted by timothy
from the want-to-have-read dept.
cybrpnk2 writes: "The story is one of epic proportions: Boy genius gets PhD from Cal Tech at age 20, is the youngest recipient ever of the MacArthur Foundation Genius Grant, writes the Mathematica simulation software used by millions of people, makes millions of dollars in the process, becomes enticed by the seductive lure of the Game of Life, and goes into a decade of seclusion to discover the secrets of the universe. You can catch up on the resulting speculation and hype here. The years of anticipation and publication delays came to an end Tuesday, May 14, 2002 with Stephan Wolfram's release of his opus, A New Kind of Science." Read on for cybrpnk2's review of Wolfram's much-heralded work.
A New Kind Of Science
author Stephen Wolfram
pages 1197 (plus 62 page index)
publisher Wolfram Media, Inc.
rating 10
reviewer cybrpnk2
ISBN 1-57955-008-8
summary A long awaited treatise that cellular automations, not mathematics, holds the key to understanding reality

First things first - have I read this book? Hell, no, and if anybody else says THEY have in the next year, they're lying thru their teeth. This book is so dense that if Wolfram had added a single additional page, the whole thing would have imploded into a black hole. That's got to be the only reason he quit writing and finally went to press.

I've been waiting for years for ANKOS to come out. I ordered my copy Tuesday when it was released, got it on Thursday and I've been skimming it like mad since. To give you some idea of how engrossing this book is, I was reading it Friday morning at 4 AM in the bathroom of a Motel 6, curled up in a bedspread on the tile floor to keep from disturbing my wife and stepdaughter during a trip to my stepson's graduation. I've got four college degrees, one in math and two from MIT, and bottom line - this sucker's gonna take a while to digest. However, it's theoretically straightforward enough that anybody with a high enough level of obsession and a few years to stay glued to it can follow it in its entirety. In ANKOS, Wolfram certainly comes across as arrogantly cocky but in the final analysis is he a crank or a revolutionary genius? Who knows, but it's going to be a new nerd pastime for the next decade to argue that point.

ANKOS is 1250+ pages divided into 850 pages of breezy exposition followed by 350 pages of fine-print notes. The exposition is composed of 12 chapters and the notes have about a paragraph per page of topic- and name-dropping technobabble to let you know where to go next for more details on whichever of Wolfram's tangents strike your fancy. Topping the whole thing off is a 60+ page index with thousands of entries in even smaller typeface than the notes.

Despite its length, ANKOS is not a rigorous mathematical proof of anything as much as it is a superficial survey of a vast new intellectual landscape. And what a landscape Wolfram has laid before us. It's all about cellular automations, which have traditionally been relegated to the realm of mathematical recreations. Start with a black square in the center grid square (cell) on the top line of a sheet of graph paper. Think up a few rules about whether a square gets colored black or white on the next line down depending on the colors of its neighbors. Apply these rules to the squares on the next line of the sheet of graph paper. Repeat. Watch what happens. Sounds simple. It isn't.

The first short chapter outlines Wolfram's central thesis: That three hundred years of mathematics based on the equals sign have failed to provide true insight into various complex systems in nature, and that algorithms based on the DO loop can succeed in this endeavor where mathematics has failed. The reason, claims Wolfram, is that deceptively simple algorithms can produce heretofore undreamed of levels of complexity. He claims that while frontier intellectual efforts such as chaos theory, fractals, AI, cybernetics and so forth have hinted at this concept for years, his decade of isolation studying cellular automata has taken the idea of simple algorithms or rules embodying universal complexity to the level of a new paradigm.

The second chapter outlines what Wolfram calls his crucial experiment: the systematic analysis of the 256 simplest rule sets for the most basic cellular automatons. He discovers this "universe" of rules is sufficient to produce his four so-called "classes" of complex systems: order, self-similar nested patterns, structures and most importantly, true randomness. The first two lead to somewhat familiar checkerboard-type patterns and leaf-type fractals; the last two, unforeseen unique shapes and unpredictable sequences. Wolfram stresses that the ability of simple iterative algorithms to produce complex and unique non-fractal shapes as well as truly random sequences of output is in fact a revolutionary new discovery with subtle and profound implications.

The third chapter expands his initial 256-rule-set universe of simple algorithms with many others Wolfram has researched for years in the dead of night while others slept. Rule sets involving multiple colors beyond black-and-white, rule sets that update only one grid square instead of a whole row, rule sets that embody full-blown Turing machines, rule sets that substitute entire sets of patterned blocks into single grid cells, that tag end point grid squares with new patterns, that implement "registers" and "symbols" - Wolfram has examined them all in excruciating detail. And no matter how complex the rule set is he explores, it ends up generating still more and more unexpected complex behavior with many notable features as the rule sets are implemented. This ever-escalating spiral of complexity leads Wolfram to believe that cellular automatons are a viable alternative to mathematics in modeling - in fact, embodying - the inherent complexity of the natural world.

In chapter four, he begins this process, by linking cellular automatons to the natural world concept of numbers. Automatons that multiply and divide, that calculate prime numbers and generate universal constants like pi, that calculate square roots and even more complex numerical functions like partial differential equations - Wolfram details them all. Who needs conscious human minds like those of Pythagoras or Newton to laboriously work out over thousands of years the details of things like trigonometry or calculus? Set up dominos in just the right way, flip the first one and stand back - nature can do such calculations automatically, efficiently and mindlessly.

Chapter five broadens the natural scope of cellular automations from one-dimensional numbers to multi-dimensional entities. Simple X-Y Cartesian coordinates are left behind as Wolfram defines "networks" and "constraints" as the canvas on which updated cellular automatons flourish - always generating the ever-higher levels of complexity. More Turing machines and fractals such as snowflakes and biological cells forming organs spontaneously spring forth. So far we've seen some really neat sleight-of-hand that Martin Gardner or Michael Barnsley might have written. But we're only on page 200 of 850 with seven chapters to go, and Wolfram is just now getting warmed up.

Chapter six is where Wolfram begins to lay the foundation for what he believes is so special about his insights and discoveries. Instead of using rigid and fixed initial conditions as the starting points for the cellular automations he has described, he now explores what happens using random and unknown initial conditions in each of his previously defined four "classes" of systems. He finds that while previously explored checkerboard (Class 1) and fractal (Class 2) systems yield few surprises, his newly-discovered unique (Class 3) and random (Class 4) cellular automaton systems generate still higher levels of complexity and begin to exhibit behavior that can simulate any of the four classes - a telltale hint of universality. Furthermore, their behavior starts to be influenced by "attractors" that guide them to "structure" and self-organization.

With the scent of universality and self-organization in the air, Wolfram begins in chapter seven to compare and contrast his cellular automations to various real-world topics of interest. Billiards, taffy-making, Brownian motion, casino games, the three-body problem, pachinko machines - randomness is obviously a factor in all of these. Yet, Wolfram notes, while randomness is embedded in the initiation and influences the outcomes of each of these processes, none of them actually generate true randomness in the course of running the process itself. The cellular automations he has catalogued, particularly his beloved Rule 30, do. The realization that cellular automations can uniquely serve as an initiator or generator of true randomness is a crucial insight, leading to the difference between continuity and discreteness and ultimately to the origins of simple behaviors. How, you ask? Hey, Wolfram takes most of the chapter to lay it out in a manner that I'm still trying to follow: no way can I summarize it in a sentence or two.

By chapter eight, Wolfram believes he has laid out sufficient rationale for why you, me and everybody else should think cellular automations are indeed the mirror we should be looking in to find true reflections of the world around us. Forget the Navier-Stokes equations - if you want to understand fluid flow, you have to think of it as a cellular automation process. Ditto for crystal growth. Ditto for fracture mechanics. Ditto for Wall Street. Most definitely ditto for biological systems like leaf growth, seashell growth and pigmentation patterns. This is very convincing stuff - tables of Mathematica-generated cellular automation shapes side by side with the photos of corresponding leaves or seashells or pigment patterns found in nature. Yes, you've seen this before in all of the fractals textbooks. The difference between fractals and cellular automations: fractals are a way to mathematically catalog the points that make up the object while cellular automations are a way to actually physically create the object via a growth process. It's a somewhat subtle difference - and a key Wolfram point.

Having established some credibility for his ideas, Wolfram stretches that credibility to the limit in chapter nine, where he applies his cellular automation ideas to fundamental physics. It was practically inevitable he would do this - his first published paper as a teenager was on particle physics, and that's the field he got his PhD in from Cal Tech at age 20 before going on to write the Mathematica software program and make his millions as a young businessman. Despite his solid background in physics, this seems at first blush to be pretty speculative stuff. He shifts his focus on the cellular automations from randomness to reversibility, and describes several rule-sets that both lead to complexity and are reversible. This behavior is an apparent violation of the Second Law of Thermodynamics. From Wolfram's way of thinking, if the universe is indeed some kind of ongoing cellular automation, then it may well be reversible and the Second Law must not be the whole story, so there must be something more we have yet to learn about the nature of the universe itself. He continues extensive speculations on what this may be, and how space, time, gravity, relativity and quantum mechanics must all be manifestations of this underlying Universal Cellular Automation. The rule set for this ultimate automation, which Wolfram believes might ultimately be expressed as only a few lines of code in Mathematica, takes the place of a mathematically-defined unified field theory in Wolfram's world. This is mind-blowing stuff, but ultimately boils down to Wolfram's opinion. I have great difficulty in comprehending space and time and matter and energy as "mere" manifestations of some cellular automation - if so, what is left to be the "system" on which the automation itself is running? I'm reduced to one of Clarke's Laws: The universe is not only stranger than we imagine, it is stranger than we CAN imagine ...

Wolfram shifts from Kubrick-style religion back to mere philosophy in chapter ten, where he explores how cellular automations are perceived by the human mind. Visual image perception, the human perception of complexity and randomness, cryptography, data compression, statistical analysis, and the nature of mathematics as a mental artifact are all explored. The chapter ends on a discussion of language and the mechanics of thinking itself. Wolfram reaches no real concrete conclusions on any of these, except that once again cellular automation is a revolutionary new tool to use in achieving new insights on all of these topics.

Chapter eleven jumps from the human mind to the machine mind by exploring not the nature of consciousness but the nature of computation instead. He goes here into somewhat deeper detail on ideas he has introduced earlier, about how cellular automations can perform mathematical calculations, emulate other computational systems, and act as universal Turing machines. He focuses on the implications of randomness in Class 4 systems and the universality embodied in systems like that of his Rule 110. His arguments lead up to a closing realization, what he does not call but may one day be named Wolfram's Law.

The final chapter, chapter twelve, discusses what all of Wolfram's years of isolation and work have led him to conclude. He calls it the Principle of Computational Equivalence. What follows is an unavoidably oversimplified distillation of Wolfram's thoughts on the PCE. If indeed cellular automations are somehow at the heart of the universe around us, then the human effort to reduce the universe to understandable models and formulas and simulations is ultimately doomed to failure. Because of the nature of cellular automation computation, there is no way to come up with a shortcut method that will deduce the final outcome of a system in advance of it actually running to completion. We can currently compute a rocket trajectory or a lens shape or a skyscraper framework in advance using mathematics merely because these are ridiculously simple human efforts. New technologies based not on mathematics but instead on cellular-automations like wind-tunnel simulators and nanobot devices will be exciting technological advances but will not lead to a fundamentally new understanding of nature. Issues that humans define as undecidability and intractability will always limit the level of understanding we will ultimately achieve, and will always have impacts on philosophical questions such as predestination and free will. To conclude with Wolfram's own final paragraph in the book:

"And indeed in the end the PCE encapsulates both the ultimate power and the ultimate weakness of science. For it implies that all the wonders of the universe can in effect be captured by simple rules, yet it shows that there can be no way to know all the consequences of these rules, except in effect just to watch and see how they unfold."

As noted above, 350+ pages of notes follow this exposition, and trust me, there's no way they can be summarized. To mention one nugget I found amusing as I envisioned Wolfram working towards endless dawns on ANKOS, he thinks sleep has no purpose except to allow removal of built-up brain wastes that cannot be removed while conscious. So much for dreaming.

So what is the bottom line on ANKOS? It is a towering piece of work and an enduring monument to what a focused and disciplined intellect can achieve. It is very thought provoking. It will definitely lead to new work and progress on cellular automation theory and some interesting technological applications we should all look forward to with anticipation. But is it the next Principia, the herald of a new scientific revolution?

Read and decide for yourself. Only time, and a lot of it, will tell.


To read it yourself, you can purchase A New Kind of Science at bn.com. You can read your own book reviews in this space by submitting your reviews after reading the book review guidelines.
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A New Kind of Science

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  • by BoyPlankton (93817)
    I've got four college degrees, one in math and two from MIT, and bottom line - this sucker's gonna take a while to digest.

    1 + 2 = 4?
    • Re:One in math? (Score:2, Redundant)

      by kryzx (178628)
      The degree in math was from Enron Community College. The actual degree name is "Baccalaureate of the Fine Arts in The Flexible New Math of the Quasi-Legal Gray Areas". At MIT he only studied history and phys. ed.
    • Re:One in math? (Score:2, Informative)

      by cybrpnk2 (579066)
      Ahem....and one non-math, non-MIT degree...
      • by skroz (7870)
        It was Sociology, wasn't it. Nobody wants to admit to a sociology degree. Stupid, stupid social science majors.
        • It was Sociology, wasn't it. Nobody wants to admit to a sociology degree. Stupid, stupid social science majors.

          One of my college's courses in Sociology was entitled "Studies of a Contemporary American Subculture." It was a six credit 400 level course that met all summer.

          The actual content: the students followed the Grateful Dead for six weeks, then wrote a paper about it.

          I'm still convinced this is the single greatest course in all of college history: not only for the actual "Be a Deadhead" bit, but they got *six* credits for it.

          I'm no longer convinced soc majors are dumb at all.

        • Re:One in math? (Score:3, Interesting)

          by meehawl (73285)
          It was Sociology, wasn't it. Nobody wants to admit to a sociology degree.

          I have a Sociology degree, and a Robotics/AI degree. Robotics was far easier, and dealt with simpler logical models. Sociology was harder because it dealt with people and social networks -- easily the most complex systems ever discovered in the universe (and I have a background in theoretical physics).

          Yes, Sociology attracts flakes, but it also attracts people who like to get to grips with the really difficult, interesting questions that can't be abstracted away into pseudo-code, automata, and heuristics.
    • Hey, if you had four degrees, you'd understand that math....
    • "... one in math and two from MIT" is -- obviously, I think -- not a complete description/list of his degrees. He's just making the point that the degrees that he has probably aren't shallow, and by implication neither is the book.
      • How can the degrees of the reviewer implicate anything about the book? If that's a consequence of this new kind of science, I'm a bit dubious to the whole thing :)
        • The degrees of a reviewer don't prove but do imply a certain level of intellectual ability. Combined with the admission that the reviewer that the book will "take a while to digest", this doesn't not prove but does imply that it's a challenging book.
          • Ah, there's the source of my confusion: In this mathematical context you're misusing the concept of implication. In everyday English your distinction between the words "prove" and "imply" makes sense, but in the language of mathematics an implication is simply the logical relation which is false only if the premise is true and the conclusion is false.
            • Ah, there's the source of my confusion: In this mathematical context you're misusing the concept of implication.

              You are the source of your confusion. The review is not a mathematical context, nor are our posts about it a mathematical context.

              • After a few weeks of studying for my exam in discrete mathematics, I'm seeing everything in a mathematical context :)

                Which, incidentally, brings up a point: The Wired article keeps setting Wolfram's theories up as an alternative to mathematics as a tool for modelling the universe. But automata such as the CAs which form the basis of ANKOS is exactly the sort of thing which has traditionally fallen within the field of discrete mathematics. Probably just a case of the Wired journalist using a too-narrow definition of the word mathematics, but I'm having trouble seeing where the fundamental line goes between the two definitions.
    • The unmentioned 4th degree was a degree in Windows 98 Workgroup Administration from DeVry Technical Institute.
  • by phwiffo (139975) on Tuesday May 21, 2002 @10:50AM (#3558295) Homepage

    I suggest seeing pi [pithemovie.com] if you like this story.

    Great soundtrack too.

  • by mikester911 (223866) on Tuesday May 21, 2002 @10:54AM (#3558338)
    "Can you give us the answer to life?", they asked the computer.

    Deep Thought pondered their question.

    "Yes," he said. "But it will be tricky. And first I have to write Mathmatica."

    (apologies to Mr. Adams fans)

  • Kurzwiel's Review (Score:5, Informative)

    by Hartree (191324) on Tuesday May 21, 2002 @10:59AM (#3558389)
    Well thought out review [kurzweilai.net]

    Wolfram is looking at a piece of the puzzle, IMHO. Though his book seems to be a tour de force of applying specific cellular automata to generate all sorts of neat things, I don't see it as being particularly new. This is more a book to bring it to the attention of people in other fields who may be able to make use of it. Rather like Mandelbrot's The Fractal Geometry of Nature.
    • by Bearpaw (13080) on Tuesday May 21, 2002 @11:11AM (#3558472)
      Wolfram is looking at a piece of the puzzle, IMHO.

      Have you read the book? Or just reviews of the book?

      (No offense meant, but there are a lot of people who seem to think that one can somehow form a meaningful opinion of something just by exposure to other folks opinions of it.)

    • Well thought out review [kurzweilai.net]

      Great. If there's egomaniac bigger than Wolfram, then it's Kurzweil. Actually, Kurzweil is on his own level, constantly inventing goofy terms to expound upon his wacky brain-in-a-jar theories that completely and utterly ignore the fact that both AI researchers and brain theorists aren't making the slightest bit of headway toward his vision of the near future.
  • We were discussing this at work yesterday. As some of my collegues were quick to point out, this is all most likely toss. For cellular automata to be relevant you'd have to assume the universe has a finite number of 'states'. Quantum physics currently is pretty certain it is not.

    The analogy used by the super math junkie of the group was that you can describe all physics with 2 equations; it doesn't mean that sheds any insight to anything though.

    The one thing that is of interest to me is perhaps using the methods used to create fractals in factoring (since the numberline is self deriving from many many number lines masking one another).
    • Re:Talking at work (Score:4, Insightful)

      by FreeUser (11483) on Tuesday May 21, 2002 @11:40AM (#3558695)
      As some of my collegues were quick to point out, this is all most likely toss. For cellular automata to be relevant you'd have to assume the universe has a finite number of 'states'. Quantum physics currently is pretty certain it is not.

      Actually, quantum physics does imply there are a finite number of states. Time, space, energy, motion, even Heisenberg's uncertainty are all descreet, quantisized values. The number of eigenstates that exist before an observation is made that collapses into one observed "event" is not infinite, it is merely a very, very, very big number (made much bigger when one considered the true vastness of the universe on a macro scale, and the number of quantum processes thus contained, many of which are not observed and thus, arguably, never collapsed into one given state or another).

      We tend to think of quantum clouds of probability and "alternate universe" scenerios as containing an infinite number of possible states, but that isn't really true. Consider the plank constant (a measure of the smallest possible increment of space, time, or energy, the base unit of the universe, if you will [and if you normalize it to whatever units you are working with]). Now consider a cloud of probability that contains, for example, all possible locations and vectors of an electron within a hydrogen atom, for example. That volume has some descrete limit (though depending on one's interpretation, that limit may be the entire volume of the universe, or more commonly, some small volume around that atom's nucleus). Either way, that volume has an upper limit. We thus have a system with an upper and lower limit on where the electron can be at any moment, and what vectors it may have. This means there is a finite number of possible states that can exist, and while that number is impossibly huge to contemplate, it is not infinite.

      Therefor, while Wolfram may or may not be right in his thesis, quantum physics does not in any way conflict with that thesis. Indeed, it might even lend his thesis some support (I have no idea if it does ... I haven't received my copy of his work yet, much less begun reading it).

      This isn't to say Wolfram can't be wrong ... he might be very wrong for all I know. I am merely saying that your coworkers' arguments for dismissing his work out of hand are very, very mistaken.
      • It is not a thought of wrong or right, we're just perhaps wary of the "Earth shattering" connotations everyone seems to be placing upon the work. And as the review reads, it doesn't seem to prove or describe things as much as try to get people interested in the field.
        • It is not a thought of wrong or right, we're just perhaps wary of the "Earth shattering" connotations everyone seems to be placing upon the work. And as the review reads, it doesn't seem to prove or describe things as much as try to get people interested in the field.

          First, I wouldn't trust any reviewer of the work. I would read it yourself and draw your own conclusions. That is exactly what I intend to do when I receive my copy.

          Second, I agree, skepticism is what any critically thinking person should have when approaching any work, particular a work which claims to offer a new paradigm shift in scientific thought. I disagree with uninformed people lauding his work before they've read it (as you allude to) as much as I do people who are dismissing it because it doesn't map to their preconceptions. Both extremes are wrong ... I don't have an opinion (and neither should you or your co-workers, unless you've managed to snag a copy sooner than I) because I haven't read it yet. I've read some articles on it, and some reviews, by people that may or may not understand it (likely the latter ... most reviews, including this one, contain disclaimers about "I didn't get this part" and such), and while that whets my appetite, it should not form any kind of predisposition or opinion IMHO.

          That having been said, the claim may very well be right. I really don't know (and I may not even know after I've read his work ... for all I know it may require years of remedial education before I can even understand it, much less comment intelligently on it). One thing is certain, most groundbreaking work is initially rejected out of hand by a conservative establishment ... an indication of one of the weaknesses inherent in our current system. Which isn't to say it doesn't have many strengths, what I am rather trying to say is that to assume one conclusion or the other ahead of time is a mistake.

          Your coworkers used an inaccurate argument (which exposed some commonly held misconceptions about quantum physics that was the foundation of their argument) to argue for dismissing his work outright, or at least starting it with a fairly closed mind and a rather strong predisposition regarding its contents. That IMHO is a mistake...the work will stand (or fall) on its own, but it should be considered from a skeptical, but ultimately neutral, position.

          It is not you I am arguing against, it is against dismissing his work without reading it, which the fallicious argument I rebutted seemed to imply would be justified.

          By all accounts this guy (Wolfram) can be arrogant and annoying. He is also indesputably a genius, and his past performance, scientific and mathematical work, and achievements more than justifies that this work, however revolutionary in its arguments, however anti-establishment in its creation, however controversial in its conclusions, at least be considered fairly and not dismissed out of hand.

          He really could be on to something ... and he isn't the only one to have done work in that field that has led to hints of something very profound wrt information theory, cellullar automata, and the underlying nature of our reality. Right or wrong in its final conclusions, this work is likely to sparc a great deal of productive activity and research if it even lives up to a fraction of its billing.

          I am waiting impatiently for my copy for this very reason: whether I agree or disagree with the guy, I'm going to enjoy having my mind challenged in ways it hasn't been for far too long.
      • That volume has some descrete limit (though depending on one's interpretation, that limit may be the entire volume of the universe, or more commonly, some small volume around that atom's nucleus). Either way, that volume has an upper limit.

        This is the Menger Sponge problem. Fractals are the same way -- Sure, they may have a finite derivable volume, but try and calculate the area and you're wasting your time. It's infinite. Koch Curves are the same way.

        So although you may have a finite problem space to work in, the number of viable solutions is surely not finite.

        Unless of course quantum mechanics has no basis in the "real world" of physical manifestations. :)

        .anacron

        • This is the Menger Sponge problem. Fractals are the same way -- Sure, they may have a finite derivable volume, but try and calculate the area and you're wasting your time. It's infinite. Koch Curves are the same way.

          In mathematics, that is true. However, there is emperical evidence that does indicate the basic notions of quantum mechanics are more or less correct. What this means is that the smallest unit by which position can change or be defined is defined by the plank constant (normalize it to the plank constant for simplicity sake if you like), the smallest increment of time is defined by the plank constant (again, normalize if you like), ditto for energy, which means ditto for veloocity and acceleration, etc.

          Thus, for an electron orbiting [bad word, but traditional] a nucleus there is a lower limit to the number of descrete positions it can have (because at that level space itself becomes granular), and a lower limit to its vector (say, at reast, ie. V=0).

          There is also an upper limit, namely the size of the universe (assuming no other constraints on the electron to keep it bound to the nucleus) to its position and the speed of light to its velocity respectively.

          We already know that the possible states are defined by two values which are essentially quantum values (i.e. grunular in nature at the smallest level), thus there is a finite number of velocities the electron can have between being at rest and travelling at the speed of light, just as there are a finite number of places it can be, defined by the granular nature of spacetime itself at plank lenths.

          Infinities within these constraints are artifacts of mathematics, not physical properties, assuming, of course, quantum mechanics has a basis in the "real world." Mathematically you can define a fractal down to levels well beneath the plank length, but that doesn't mean you can lay points out in space at that resolution. Again, assuming QM is an accurate picture of what is going on (it seems to be at this point based on empiracal evidence, but as with all theories, it is only an approximation of what is really going on). Mathematics, on the other hand, contains the notion of infinitely divisiable continuities, which appear not to be reflected in our physical reality. This is one example where the math doesn't appear to map correctly to the physical world, and where the math can come up with infinities that, to the best of our knowledge, simply are not there in the physical world.
      • Re:Talking at work (Score:5, Insightful)

        by dragons_flight (515217) on Tuesday May 21, 2002 @01:13PM (#3559456) Homepage
        BBzzzt. Wrong.

        The quantum simple harmonic oscillator (SHO), a baby among useful quantum phsyics problems has an infinite number of states. The states it may occupy have energies, (1/2 + n)*h-bar*omega_0, for all non-negative integers n. [omega_0 is a property determined by your configuration.] Virtually every useful quantum physics problem also has an infinite number of states, including the electron configuration of atoms.

        Higher energy states occur with increasing rareness, and thus for practical purposes scientists often truncate and only deal with the first several states. This does not however mean that nature doesn't concern itself with all of them. (Perhaps, nature truncates too, but Wolfram sure hasn't shown that, and QED experiments would imply that nature sure doesn't truncate early on.)

        This has NOTHING to do with a state's spatial extent. Of course everything has to fit inside the universe. So what? Suppose I only cared about a 1x1 square, there are still an infinite number of ways to draw a curve from one corner to the opposite corner while staying inside the box. Likewise, you can have infinite variety in quantum states in only a limited volume.

        It sounds like you want to cheat and invoke the quantitization of space and say that the electron has some position in space. This simply isn't true, the various proofs of the "No Hidden Variables Theorem" shows that the electron really has no position when not being "measured" and that you truly do have to work in terms of the whole (usually infinite) array of wave functions. The universe simply doesn't operate in terms of point particles.

        Actually it's never even been shown that time and space are discrete, though a number of theorists would like them to be. On the other hand though, I don't see any reason why the universe having infinite numbers of states would be an impediment to the use of CAs. Anything being modelled on computer has to be an approximation anyway.
      • I'm bored, so I'm going to keep you honest. :)

        Actually, quantum physics does imply there are a finite number of states. Time, space, energy, motion, even Heisenberg's uncertainty are all descreet, quantisized values.

        We thus have a system with an upper and lower limit on where the electron can be at any moment, and what vectors it may have. This means there is a finite number of possible states that can exist, and while that number is impossibly huge to contemplate, it is not infinite.

        But 'discrete' and 'finite' and 'bounded' are not the same thing.

        Counterexample: Consider the available electron energy states of Hydrogen. [gsu.edu] Discrete? Yes. Bounded? Yes. Finite? No - the energy levels (n>0) go like -1/n^2. COUNTABLY infinite, but definitely infinite. The electron can always be pushed into your favorite higher energy state (asymptotically approaching the ionization energy) by absorbing a photon of the right frequency.

    • Sorta like how for math to be relevant you need to assume the universe has a finite number of numbers? After all my computer could never really represent all the numbers there are, and thus it will never do useful mathematics.
    • For cellular automata to be relevant you'd have to assume the universe has a finite number of 'states'. Quantum physics currently is pretty certain it is not.

      Really? Do your workmates think that the word "quantum" is just put in their for decoration?

    • We were discussing this at work yesterday. As some of my collegues were quick to point out, this is all most likely toss. For cellular automata to be relevant you'd have to assume the universe has a finite number of 'states'. Quantum physics currently is pretty certain it is not.

      From the review, wolfram claims to have addition, subtraction, multiplication, and division... with these he can generate all rational numbers... plus he claims to be able to generate trancendental numbers like pi, that seems to imply that he can make all real numbers. I haven't read the book, but I see nothing in the review that would preclude these methods from describing an infinite number of quantum states or even a continuum of states.

      By the way, saying that the universe has an infinite number of quantum states is basically just saying that there is no maximum entropy for the universe. (the entropy of a system is a measure of the number of quantum states in a system). However some cosmologies have a 'big crunch' ending the universe which would imply some maximum entropy and therefore a finite number of quantum states in the universe.

      What is clear (from the Big Bang theory) is that there currently is a finite number of quantum states in the universe that is increasing with time. That is, the universe currently has some finite entropy that we can assign a number to and that entropy is increasing with time. The entropy is finite because the universe had a set beginning where the entropy was zero (if the universe didn't exist, it didn't have any quantum states).

      There are theories other than the big bang (like steady state cosmology) that have no fixed beginning to the universe. However, these all have a finite value for entropy in the universe (at least locally) for other reasons (see the "Heat death of the universe")
  • Article header made it seem like this lopsided prodigy had discovered the real world. Instead he's just shifting his focus a few microns over.

    I would love to read a book about more mundane concerns written by someone whose education was accelerated like that, to try to see what a world I already know looks like to them.
  • by Fnkmaster (89084) on Tuesday May 21, 2002 @11:09AM (#3558453)
    Disclaimer: I haven't read the book yet but I plan on doing so. I have read some of Wolfram's scrawling notes and have a bit of an idea what the general gist of the book is likely to be.


    I am disappointed that a Physics PhD could miss out on some fundamental issues here. First of all: anybody who has worked their way through an undergraduate curriculum in Physics understands in a visceral fashion that there is an extreme difference between MODELLING the world with a construct, mathematical, computational or otherwise, and saying that the world IS such a construct. We are in possession of many equations that model certain interactions between different kinds of substances via different forces in the world. Traditional mathematics has yielded many useful tools for modelling these processes. Stating that computational theory or cellular automata may yield useful models as well is an obvious inference. Saying that all physical processes are fundamentally composed of elements that ARE cellular automata seems to me to be a non sequitor. Hell, we don't KNOW what anything in quantum physics or beyond IS really, we just know that certain relationships hold mathetmatically that we can translate in physical conceptions and understanding.


    Now, the concept of emergent complexity and complexity theory in general - as I understand it, this is stuff that folks at the Santa Fe Institute and elsewhere have been working on for years, and that the understanding has been around for years that you can model many real-world processes well by systems such as cellular automata or other rule-based systems with complex emergent behaviors.


    So... I am left wondering what to make of this book. Ultimately, it will speak for itself when I read it. But it sounds like it's a mix of already known fact with ego and some intuitionist insights into certain physical processes in a monolithic volume. If he PROVES anything interesting and fundamental about certain areas of physics or fluid dynamics, or presents models more useful and meaningful (i.e. that provide information NOT obtainable through current models) than he has produced a valuable scientific work. Otherwise, it's just an interesting treatise that may inspire more meaningful work by others who are more willing to work within the establishment and processes of the mainstream scientific world (not to say that those outside it CAN'T do excellent work, just that I'm not sure if Wolfram can).

    • He isn't saying it's the "truth" -- he's just saying he's come up with a better framework for working these things out. We all know how trying to solve problems in the wrong framework makes things much more complicated (a trivial example would be the old Physics 101 problem set question of solving problems in the right frame of reference). Coming up with a better framework for solving problems is a huge step forward, if it is in fact true.

      Personally, I'm going to read the book BEFORE i decide.
      • Fully agreed. If it's a better framework than that's wonderful. I agree that there are many degrees of improved models that sort of stack on top of each other in physics. Up to some level of accuracy, the more detailed models have to match up to the predictions of the less detailed ones, to the extent that they describe reality.


        My point is that I want to hear about what new predictions or results he's obtained from his models, or which interesting existing results he's replicated using a new method (the method of Cellular Automata) before I can accept that this is a "better" framework for describing the world. If he can provide an alternative derivation for the curvature of space-time or for QED or even for something MUCH more simple, than there's some merit here. If he can just wave his hands (like I hear others doing) and say "this behavior is complex, complex behavior is modelled by CAs, look at my CA that makes patterns sort of similar to this thing" than he's not providing me with the kind of results I need to accept the model as useful.


        Like I said, I haven't read the book yet so I am reserving my judgement. But I haven't heard ANYBODY mention ANY interesting results or derivations done in the book, just handwaving about how great and interesting Cellular Automata are and how simple rulesets can have complex emergent behavior (this has been known for years and people have been working on such models for quite a few years now).

    • by jamesmartinluther (267743) on Tuesday May 21, 2002 @11:41AM (#3558699) Homepage
      "Otherwise, it's just an interesting treatise that may inspire more meaningful work by others who are more willing to work within the establishment and processes of the mainstream scientific world (not to say that those outside it CAN'T do excellent work, just that I'm not sure if Wolfram can). "

      There's a good chance that Wolfram is attempting to do much more than provide support for the work of others (although that is certain to occur). The sheer number of axioms, the amount of supporting "data", and the numerous instructions to build supporting "instruments" (via his software) leads me to that conclusion.

      Thomas Kuhn proposed that mainstream science is based on an ongoing process of shattering and creating scientific worldviews. I would say that that the most meaningful work is performed by people who are able to support a new theory with new data and cause a paradigm shift [uoregon.edu].

      Copernicus, using the latest instruments and the latest data acquired from those instruments, argued that it is the Sun at the center of the solar system (and not the Earth as most scientists in his era argued). I think that Wolfram is trying to be a Copernicus as opposed to a Hawking. So the real question here is: what is Wolfram getting at with this book? Well, he probably is not done yet.

      On a lighter note, we can't blame such talented (and often obsessed) individuals for perceiving everything within the context of their paradigm - especially when it could lead to more software sales ;)

    • First of all: anybody who has worked their way through an undergraduate curriculum in Physics understands in a visceral fashion that there is an extreme difference between MODELLING the world with a construct, mathematical, computational or otherwise, and saying that the world IS such a construct.

      Maybe you should read the book. It sounds to me from the review that Wolfram is saying that CA's and the Universe are like the way an airplane is like a bird, not the way a bird is like a bunch of feathers glued to a paper-towel roll.

      Thus, an airplane can be viewed as a model of a bird in the way that some of Wolfram's CAs can be viewed as models of the universe...

      However think of the philosophical implications if it turns out we're all just lightened grid squares being generated by a few lines of code in Mathematica?

      • But if all he's saying is that fundamentally we can be modelled by a bunch of units with mostly local interactions that come together to have global effects and can be described by a set of rules - well, shit, physics has known that for years. Cellular automata also have other characteristics like a finite number of states (is that accepted by modern quantum theory? Is it even consistent to describe the world in that manner?). Given that we can construct a Turing Machine from the Game of Life (i.e. it is Turing complete), we can already describe all computational processes via CAs, and if we believe that the universe could be simulated in finite time via a TM, then it makes some sense that there could be some model equivalence.


        In order to be USEFUL, though, there needs to BE an actual model that can make useful predictions. If Wolfram constructed a model for some physical processes that made useful and non-obvious predictions (i.e. better than some existing models for the process) than I think he'd get a lot more credit. Otherwise, it amounts to a metaphysical statement that the Universe IS a CA. If, as you say, he's not making this claim, than I hold him to the same standards of usefulness, insight and predictions that I hold any other theory.

    • I think it's the issue of universality.

      That is, you're right -- we can define equations and systems of mathematics and the like to model or describe the universe we exist within.

      I think (and no I haven't read the book, I'm extrapolating from the review) that Wolfram is claiming that 1) ANYTHING can be modeled with cellular automata; and therefore that 2) If 1 is true, then whether or not the universe really IS an "assemblage" of automata or not, we shouldn't care -- can you really do better (or do you CARE to do better) than a perfectly accurate model "Of Everything"?

      Of course, I still would debate how you can tell when you have the RIGHT model -- presumably multiple models can predict all of the universe that we currently comprehend, but when there's a new area to understand, how do you tell which of those is right? It's the whole infinite-possibilities paradox, just one layer removed.

      Xentax
  • by mobydobius (237311) on Tuesday May 21, 2002 @11:13AM (#3558488) Homepage
    ...goes into a decade of seclusion to discover the secrets of the universe

    I worry about that. Science isn't practiced very well in a vaccuum. One feature of the scientific act of discovery that makes it so effective is that the scientists involved are constantly examining each others musings, to keep any one of them from going off the deep end. Genius and madness go hand in hand, after all, and nothing can drive you nuts quite like being alone with your own thoughts. Especially if those thoughts are exceptional.

    I just hope this book doen't show that dear Dr. Wolfram has lost it.
  • "Bit String Physics" (Score:4, Interesting)

    by Baldrson (78598) on Tuesday May 21, 2002 @11:15AM (#3558499) Homepage Journal

    From the introduction to Bit String Physics [amazon.com]:

    This interest of mine in scientific revolutions remained casual, until I heard Ted Bastin talk about the combinatorial hierarchy in 1973. This remarkable construction, "discovered" by Fredrick Parker-Rhodes in 1961, yields algorithmically the sequence 3, 10, 137 (~hc/e**2), 2**127 + 136 (~1.7*10**38 ~ hc/Gm(p)**2) and cannot be extended past the fourth term for reasons intrinsic to the construction. Why a simple mathematical algorithm should have anything to do with two of the fundamental dimensionless constants of modern physics remained unexplained, and so far as I am concerned remains unexplained to this day. It could -- as the prevailing paradigms in theoretical physics seem to require -- just be a coincidence, like the "prediction" by Swift that Mars has two satellites. To make it plausible that, although still mysterious, the fact that the number of entities calculated for the third and fourth levels of the combinatorial hierarchy correspond closely to the two dimensionless numbers which characterize the two long range, macroscopic forces observed in nature (electromagnetism and gravitation) is probably something more than a coincidence is a main objective of this book.
  • Here's an excellent review (both critical and favorable at the same time) of Wolfram's book by someone of similar stature and experience - AI pioneer and successful entrepreneur Ray Kurzweil:

    Reflections on Stephen Wolfram's "A New Kind of Science" [kurzweilai.net]

  • Phenomenal (Score:2, Insightful)

    by ForExportOnly (529923)
    A book review written by a guy who hasn't read the book. Personally, I went through the first chapter of the book last night and I am pretty sure it is going to be tough reading (and I don't even have any degrees from MIT). I think a book review based on skimming the book is exactly what Wolfram is worried academia might do. Rather than listening to what he had to say, they have traditionally only listened long enough to gather ammunition against him.
    • I am pretty sure it is going to be tough reading (and I don't even have any degrees from MIT)

      Actually, once you get through the first chapter, things aren't so bad.

      If you make it a point to follow along, it's not so hard - the pictures/diagrams (of which there are many) get the salient points across, and do a pretty decent job of showing what's going on. Not many equations, and the ones there are are pretty easily followed. (and this from a biology grad from Illinois Tech - I'm definitely a resident of the foothills of mathematical academia).

      This guy has some -serious- ego, though - the first chapter seemed to be nothing but (as yet unsubstantiated, but then I'm only on the 4th chapter) blowhard hubris promise-the-world-in-a-simple-program promises.

      Nevertheless ...

      I work with computers these days, and have gotten used to the idea that people with huge egos not only exist, but often have the results to back them up. So I'm trying to reserve judgement about his revolutionizing the world of science until I read a bit more.

      But cellular automata are much better observed in action than in the static pictures he provides. A quick search on the web yielded this fine program [wisc.edu] that has given me a lot to play with over the last few days too.

      A fun book, overall. Not expensive. Worth poking around in, once you get past Wolfram's ego.
  • Crank, crank, crank (Score:5, Interesting)

    by gonerill (139660) on Tuesday May 21, 2002 @11:23AM (#3558568) Homepage
    but in the final analysis is he a crank or a revolutionary genius? Who knows, but it's going to be a new nerd pastime for the next decade to argue that point.

    This means he's almost certainly a crank. If actual scientists were arguing heavily about it, there might be a bit more uncertainty. But if the debate is happening amongst people whose knowledge of physics comes mainly from Star Trek, then that pretty much settles the matter in advance.

    Wolfram will probably end up having a place on the intellectual fringes, worshipped by people who are often smart but who haven't bothered/aren't trained well enough to see why specialists don't really pay attention to them. In nerd idea-space Ayn Rand is the other main example of this type.

    The best comment I've read about Wolfram's book comes from Cosma Shalizi, a physicist working at the Santa Fe institute, who specializes in cellular automata. He comments [santafe.edu] [scroll down on link]:

    Dis-recommended: Stephen Wolfram, A New Kind of Science [This is almost, but not quite, a case for the immortal ``What is true is not new, and what is new is not true''. The one new, true thing is a proof that the elementary CA rule 110 can support universal, Turing-complete computation. (One of Wolfram's earlier books states that such a thing is obviously impossible.) This however was shown not by Wolfram but by Matthew Cook (this is the ``technical content and proofs'' for which Wolfram acknowledges Cook, in six point type, in his frontmatter). In any case it cannot bear the weight Wolfram places on it. Watch This Space for a detailed critique of this book, a rare blend of monster raving egomania and utter batshit insanity.]

    I await solid arguments to the contrary --- ie, arguments that don't start from any of the following premises:
    1. But he was a boy genius at CalTech and Feynman said so!
    2. But he wrote Mathematica, which is obviously really hard!
    3. But if he's right this will change the world!
    4. But other Scientists are ignoring/laughing at/refuting him only because they are jealous of his enormous brain!
    5. But he only ignored peer review because he's so brilliant!
    6. But every work of genius always seems crazy when it first appears!

    I leave it was an exercise to the reader to show why Wolfram's supporters shouldn't rely on these points (although Wolfram himself apparently does).

    • Funny...after reading Cozma Shalizi's notebooks, I can come to the same conclusion about him that he makes about Wolfram: he's a pompous, insufferable egotist. He should stick to physics and stop arrogating about disciplines on which he is a patent amateur. Funny how most physicists consider themselves experts on everything...
    • You seem to have forgotten the story of Einstein and how his insights were first received.

      In academia, there are factors that lead people in established positions of authority to be highly skeptical of new ideas. Most graduate students are experts in this kind of skepticism.

      Why not let the experts read over Wolfram's work for a few weeks and repeat some of his experiments (like good scientists do) before you get appalled about the book...

      • You're thinking about this the wrong way. This is a problem of false positives. As I've pointed out before [slashdot.org], we all know that given something is a work of genius the probability that it will look bizarre is very high. However, given that something looks bizarre, the probability that it is a work of genius is very low. Wolfram's work, right now, has all the hallmarks of the crank. Note that Einstein's ideas were radical -- and took a long time to be properly understood -- but he didn't exile himself from scholarly debate or claim that any initial skepticism about his ideas was evidence that they were right. The ideas stood up by themselves. I'll be surprised if Wolfram's do --- though of course I'm not ruling it out as impossible.
        • by greenrd (47933)
          but he didn't exile himself from scholarly debate

          Er, I think you'll find that Einstein didn't publish his ideas on special relativity until they were good and ready. The fact that Wolfram's book took so longer than expected to come out, shows he was still revising it for a long time - and what on earth is wrong with wanting to make sure your ideas are polished before publishing them? Given the perceived significance of this book, it makes perfect sense to me that he wouldn't want anything too significant to leak out ahead of time - especially if it contained mistakes!

          Peer review comes now. To suggest that there will be no peer review, with Wolfram's book currently #1 on Amazon.com, is beyond ludicrous. If he had published it posthumously, now that might fairly be described as "exhiling himself from scholarly debate".

          or claim that any initial skepticism about his ideas was evidence that they were right. Maybe not - but Einstein did say something to the effect of "if experiments don't agree with me, experiments are wrong" - which is far more arrogant on the face of it. However, perhaps he was just joking.

    • by EccentricAnomaly (451326) on Tuesday May 21, 2002 @01:46PM (#3559706) Homepage
      I've gone through peer-review several times and it's mostly an exercise of massaging the egos of people in the field who are 'respected' just for being in the field for so long and who haven't really produced anything new in their lauded carreers. You go through a ton of busywork making sure you have the right damn font and you have all of the right people referenced (whehter or not you actually used their papers) and you get paid nothing, the journal takes your copyright and charges you $10 to make fair use copies of your own damn paper.

      In academia, if you have a good idea someone will steal it, if you have a great idea they will dismiss you without listening to it. If you don't believe me, look into whether or not Watson and Crick _really_ discovered the structure of DNA or if it was a grad student who's ideas they orginally dismissed.

      In academia there's this absurd notion that if someone understands your explanation of a new idea that they somehow helped you come up with it.

      So Bravo to Wolfram for thumbing his nose at academia! I just hope he can back it up.
    • by cnladd (97597) on Tuesday May 21, 2002 @03:39PM (#3560548) Homepage
      The parent poster either didn't read the review much, already had a strong bias against the book (or author), or doesn't have much of an open mind. My point of view, anyways. :)

      From the original review: but in the final analysis is he a crank or a revolutionary genius? Who knows, but it's going to be a new nerd pastime for the next decade to argue that point.

      The reply: This means he's almost certainly a crank. If actual scientists were arguing heavily about it, there might be a bit more uncertainty. But if the debate is happening amongst people whose knowledge of physics comes mainly from Star Trek, then that pretty much settles the matter in advance.

      I didn't come away with that point of view at all. When the review said "nerds", I didn't take it to mean the folks "whose knowledge of physics comes mainly from Star Trek." And the bit about him being a boy genius and the author of Mathematica didn't sounds like the beginnings of any sort of argument to me. I'm sorry, but it just didn't seem like the reviewer said "He was a boy genius, wrote Mathematica, so he must be absolutely correct."

      I had no idea who Wolfram was before reading this - to me, it served as an introduction as to who the author was. That I feel, combined with his 10-year solitude, says quite a bit about the author's personality - something that the reviewer acknoledged in a number of places.

      In fact, the reviewer was critical at a number of points, especially when talking about the arrogant tone of the writing and the vagueness of some of what was presented. Didn't sounds to me as if this was one of Wolfram's "followers", but someone who got a very interesting book (that he happened to have been hearing about for awhile and was anxiously awaiting), and was trying to digest it and understand it so as to be better able to form an opinion.

      As far as the bit about other scientists ignoring him (and several other statements along similar lines), your post really sounds a bit condescending. The reviewer himself stated that he had a few degrees (one physics, I believe?) and that the reviewer himself didn't fully understand all that was in the book. That right there speaks quite well for the reviewer. I've also read other reviews from other scientists, and I've seen a pretty decent amount of debate so far. Some truly hate it and feel it's pure crap. Others like some of the ideas, but feel it's not enough. It doesn't even seem as if this reviewer thought this book was the be-all-end-all text, the answer to everything.

      So far, it looks as if the primary intent (at least of the review - possibly even the book, though who knows?) was to spark a discussion. Not a bunch of namecalling (crank!), but honest discussion.
  • To conclude with Wolfram's own final paragraph in the book:

    Guess I don't need to buy it now...

  • by ellem (147712) <<moc.liamg> <ta> <25melle>> on Tuesday May 21, 2002 @11:25AM (#3558586) Homepage Journal
    Pfft!

    I could have done it in 2 Lines with Perl!

    • Well, that would explain a lot of things...

      Sure, it's a 2-liner, but is anybody going to be able to maintain it 20 billions years from now? Huh?
    • I could have done it in 2 Lines with Perl!

      Actually the new version of the C++ STL will have a universe container. It's just that it will take forever for any of the compiler suites to implement it correctly...
  • I found this written in one of the margins...

    There are no positive integers such that x^n + y^n = z^n for n>2. I've found a remarkable proof of this fact, but there is not enough space in the margin to write it.

    What does this mean?

  • The review begins with a a grand statement about how the author hasn't even read the book -- the first inidcation that the reviewer is reviewing reactions and interviews, and not Wolfram's actual words.

    But then again, this is Slashdot... ;)

    • by Fjord (99230) on Tuesday May 21, 2002 @12:34PM (#3559148) Homepage Journal
      The review goes on to say how he has been skimming it but the text it too dense to have read within the time of release and the present time -- the first inidication that the poster is responding to very little of the actual review, and not cybrpnk2's whole essay.

      But then again, this is Slashdot... ;)
  • by kryzx (178628) on Tuesday May 21, 2002 @11:31AM (#3558630) Homepage Journal
    Great review. It's hard to convey complex concepts clearly, but cybrpnk2 did an excellent job.

    What this most made me think of is DNA. DNA is just oodles of four-state variables that represent some kind of program. It is exactly like the cellular automata he's been working with. Looking at the code (the DNA itself) and the output (the organism produced) perhaps we can understand the underlying algorithm that uses the code to produce the output. Unravelling, understanding, decompiling, reverse engineering, or whatever you want to call it, the secrets of how the DNA code is executed could be the biggest scientific advance ever, and Wolfram may have provided the tools to do it.

    Suprisingly there was no reference to this in the review, which probably indicates no discussion of it in the book. Cybrpnk2, is it true that he did not discuss DNA?

    • I was surprised by this point, too. Wolfram mentions DNA (he MENTIONS just about everything) but not anywhere near as much as I would have thought he coulda/shoulda/woulda. If he'd spent ten years analyzing the various genome databeses out there [nippur.irb.hr] with the same level of intensity, I think he would have REALLY come up with something spectacular. But that would make him a biologist, and he considers himself first and foremost a physicist...
    • DNA is just oodles of four-state variables that represent some kind of program. It is exactly like the cellular automata he's been working with.

      I can see why DNA would remind you of the sort of CA that Wolfram is working with: it's 1D, linear, and can take on one of several states at each position. However, DNA is not a cellular automaton. With a true CA, the state of the system at iteration i is dependant on the state of the system at iteration i-1 (or earlier). You can describe it as a Markov chain, I think (please correct me if I'm wrong about that). On the other hand, if we consider an "iteration" of the DNA system to be a single round of DNA replication, then the state of the system at iteration i is identical to the state of the system at iteration i-1, with some noise thrown in. If, on the other hand, we consider an iteration to be a single generation of reproduction of the species, then the state at i is dependant on all sorts of things unrelated to i-1: mostly the choice of a mate, which is heavily determined by chance and environment.
    • Unravelling, understanding, decompiling, reverse engineering, or whatever you want to call it, the secrets of how the DNA code is executed could be the biggest scientific advance ever, and Wolfram may have provided the tools to do it.

      Not sure what you mean by that. The genetic code is understood perfectly well: we know exactly how bases map to codons map to amino acids, and we've known for over 40 years. The mechanisms of DNA replication and transcription are also understood to exsquisite detail, as is the mechanism of translation from mRNA to protein. Protein folding is poorly understood, as is the complex cellular feedback loop between protein content, cellular environment, and DNA transcriptional control. I don't see the immediate application of Wolfram's CA ideas to these problems. CA have been around for over 20 years now, and people have certianly tried to apply them to biological processes, with no groundbreaking results.
      • Not true. We have the genetic code, but it is *not* well understood.

        We don't understand why certain cells become blood cells and others become skin cells, or how all the cell of the brain know which other cells to attatch themselves to, or why at a certain stage of development the heart starts pumping, or why cells divide and divide until there are just the right number, then stop.

        We are just beginning to study some of these things, and we're still looking at effects, not at the underlying mechanism. Somehow this DNA code contains instructions for every cell at every stage of development. We have not even begun to understand how cells use those instructions.

        • We have not even begun to understand how cells use those instructions.

          My point above was that we, in fact, understand very well how the genetic instructions encoded in DNA are used by cells. The map from gene sequence to protein sequence is understood perfectly. The most pressing outstanding problems in cellular and systems biology are simply not genetic: they center, rather, on complex interactions between the various components of cells and the cellular environment. Answering the questions you cite will require a detailed understanding of these complex interactions.
          • Fascinating. I get the distinction: DNA to protein translation as opposed to multiple protein interaction at the cell level. That kinda kills the fun, puzzle-like quality of starting with something simple and trying to find the algorithm that gets you to the real results. But maybe that's why that part has already been worked out.

            While you seem to be quite knowledgable I retain some skepticism (hey, this is the internet :-), but it piques my curiosity, so I'm planning to read up on this some. Good links and refs would be welcome.

            I am sure Wolfram would argue that it's still a CA problem, just at a different level. Life, the universe and everything, it's all CA. Or maybe he's a wacko.

  • I thought that the game of life lost some of it's "wonder" once spacefillers [radicaleye.com] came about..... Oh well.

    Until it can be determined that everything in the universe consists of a binary nature, I probably wont see the point in continued cellular automata research ;)

    After all, the meaning of life, the universe, and everything is 42. Duh.
  • A little trivia - both were in the first MacArthur "Genius" class [macfound.org] and both produced huge tomes released this year. Does this mean that Wolfram should watch his back [slashdot.org]?
  • by Minter92 (148860)
    and have known several others who have worked for him and I wouldn't put much stock in anything he says.

  • Maybe Douglas Adams was right about the Earth computer!
  • There's extensive coverage of this book, maybe even by someone who's read it, in this week's Nature (16 May issue).

    Sadly they have a closed subscription list.

    Key quotes include:

    Gene Stanley, a physicist at Boston University, has used other mathematical methods to study some of the same systems that Wolfram considers in his text. Stanley does not believe that cellular automata can do everything that Wolfram ascribes to them, but says that the book has persuaded him that they are more than just a curiosity. "This is a much-needed complementary approach," he says. "It's a profound book, perhaps the book of the decade."

    And:

    But to many, the fact that Wolfram's ideas still lack the predictive power of established theories built on more conventional mathematics is a sign that the wunderkind has come up short. With the book's publication date having been repeatedly pushed back, some speculate that Wolfram has been striving, but never quite succeeding, to pull off his promised scientific revolution. Michael Berry, a theoretical physicist at the University of Bristol, UK, remains unconvinced that Wolfram has done more than embellish the basic idea that simple systems such as cellular automata can generate complexity. "We've known this for 20 years," says Berry. "He'll have some fans, but I think others are going to react strongly against him."

    Their bottom line - the jury is still out how much this is hype and how much real advance. There are also some interesting insights into how Wolfram conducts himself too.

  • by jafuser (112236) on Tuesday May 21, 2002 @12:15PM (#3559005)
    I ordered my copy Tuesday when it was released
    I ordered my copy on January 2, 2001 and have frequently been lamenting to my co-workers every time it got put back. I was well known for shouting out "where the hell is my fuc*ing wolfram book?" in the office in moments of temporary insanity brought on by yet another delay.

    I eventually wrote Wolfram Science an email, partly out of jest:

    Where's my ####ing wolfram book!!??? I ordered it on Amazon a year ago...
    Only problem was that I originally wrote it without censoring myself, then corrected the censor in my email body, but not my subject. Despite the vulgarity, I still managed to get a very professional response:

    Dear Mr. Faulkner,

    Well, your emotions might be shared by Dr. Wolfram as well given the fact that the time frame in his case is ten years and, when he started writing he did not know that it would take him this long. He has literally been working on this book full time for the entire decade (and running his company).

    [... clipped ...]

    Thank you very much for interest in "A New Kind of Science."

    Sincerely,

    David Reiss, Ph.D.
    Scientific Communications Director
    Stephen Wolfram Science Group

    Oops... ]:)

  • I would love to have one of my submissions actually make it to the front page. So why does this guy get his book review posted, when he didn't even read the book. Let's establish some kind of standards here.
    Rules:
    1. Book Reviews: You must actually read the book.
    2. Movie Reviews: You must see the movie.
    etc.
  • Emergent systems (Score:4, Interesting)

    by vohlish_n (261634) on Tuesday May 21, 2002 @12:21PM (#3559056) Homepage
    There was an article in NewScientist on the 9th February (subscription required to view the article), "What Lies Beneath", about emergent systems. It discusses that we may never know the true nature of the universe; of what it is made of.

    Robert Laughlin (Stanford University) is researching this. What we observe in the universe is model-independent, and we cannot actually see the model itself.

    "The laws that govern large-scale phenomena will not be deduced from the laws that govern tiny particles, he says. "It's in the same way that flocking behaviour can be characterised without understanding everything about birds, or superconductivity without understanding atomic theory."

    This idea is called emergence. It's a familiar phenomenon in the theory of condensed matter, which is Laughlin's background. Solids and liquids sometimes play host to strange entities that bear little resemblance to the atoms making up the substance."
    ...
    "If what you see is model-independent then you can't learn anything about the underlying equations by observing it," says Laughlin. "You could call this the dark side of emergence."
    ...
    "What we emerge from is unknowable," says Laughlin. "The underlying equations of the Universe cannot be determined from what we know."

    The article goes into greater detail than I can here, but it definitely an interesting read.

    If all this is true, we can never really know the true mechanics of the universe. It may actually be a simple "4-line" automaton. It could be a billion other things - we'll probably never know.
  • by peter303 (12292) on Tuesday May 21, 2002 @12:24PM (#3559076)
    Science is a cooperative enterprise- building on the insights and mistakes of others. Even fellow eccentric-recluse-genius Isaac Newton said "If I have seen farther than others, it is because I have stood on the shoulder's of giants". Wolfram's insight may be a way of describing things, but it may not be the best way, or the most comprehensive. He's got to work with others.
  • Perhaps this is a dumb, ignorant question, but what is the difference between Wolfram's Cellular Automata and the relatively old conceptual tool used in artificial life [susx.ac.uk] (and maybe used for other things?).

    Is Wolfram's idea a generalized theory of the tool used for ALife? A new application for that tool? Something completely different?

  • INTERVIEW WOLFRAM! (Score:5, Insightful)

    by guanxi (216397) on Tuesday May 21, 2002 @12:37PM (#3559184)
    Since, according to the reviewer, nobody will be able to digest this book for at least a year, perhaps we could get a Slashdot interview with Wolfram?
    • by cybrpnk2 (579066)
      Now THIS is a really good idea. Taco, Timothy...or anybody else that just wants to go straight to The Big Guy...the contact info for Wolfram is here [wolframscience.com]...
    • by FreeUser (11483)
      Since, according to the reviewer, nobody will be able to digest this book for at least a year, perhaps we could get a Slashdot interview with Wolfram?

      I think we should wait a year, perhaps two.

      And I think the questioners should be required to have read the book in question, and pass a test on the subject as an (admittedly imperfect) assurance that they have done so.

      Otherwise the questions are likely to be an emberrassment, and the answers rather scathing. :-)

      Then again, that might be worth it, just for entertainment value. [grin]
  • It seems that product of the simplicity of the rules involved and the predictability of the phenomena being modeled is a constant. Simple, cellular automata rules CAN produce the same models, but are unpredictable. High-order differentials can produce predicable results, but are hell to calculate. Somewhere near the middle, we hope we can find equations we can perform, that still provide reasonably accurate predictions.

    I hope that this book gets wide spread. Not because I think that Wolfram is correct, I don't presume to know that answer. But I do believe that this book will spur on a great deal of scientific inquiry, that cannot help but to lead us somewhere extraordinary.

  • Wolfram shifts from Kubrick-style religion

    <honoured bow>
    Thank you, thank you...
    </honoured bow>

    Seriously, it looks like I'll be buying this when I can find a copy. It looks pretty damn interesting, whether or not the guy's a kook. :) I've just been reading about Wolfram in Steven Levy's Artificial Life... very surfacey magazine style treatment, but good stuff nonetheless.
  • For those curious (or who know already) about Conway's Game of Life, the best implementation I've seen is a Java applet [lifepatterns.net] by Alan Hensel. It has numerous popular patterns preloaded (including a Turing machine, IIRC). It's primary characteristic, though, is blazing speed - an order of magnitude faster than any other implementation I've seen, including compiled ones.
  • by Animats (122034) on Tuesday May 21, 2002 @01:48PM (#3559717) Homepage
    When I first heard about this book, I expected more. The big announcement would have been that Wolfram had found a cellular automaton that generated physics. But he hasn't. He merely speculates that one exists. It's a plausible conjecture, but no more than that.

    Fredkin went down this road a few years ago, but didn't succeed either. He and Wolfram used to work together, but they seem to have split up.

    If anybody ever finds a simple CA that results in a system that behaves like physics, there will be a short, world-famous paper that will put them down in history with Newton and Einstein. But this isn't it. To Wolfram's credit, he isn't claiming that it is.

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