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The Universe in 4 Lines of Code? 502

Posted by michael from the where-the-sidewalk-ends dept.
serendigital writes "Stephen Wolfram, founder of Wolfram Research and creator of Mathematica has, after 10 years+ finished his book, "A New Kind of Science." In a "Wired" article entitled: The Man Who Cracked The Code to Everything ...," Steven Levy talks about how and why the book was written and more importantly, what it is about. The best part of the article is in this exchange: 'I've got to ask you,' I say. 'How long do you envision this rule of the universe to be?' ... 'I don't know. In Mathematica, for example, perhaps three, four lines of code.'" This book seems a little... nutty. But it's been submitted a bunch of times. If anyone wants to review it, go right ahead.
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The Universe in 4 Lines of Code? More

The Universe in 4 Lines of Code?

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  • Silly mathematicians. (Score:5, Funny)

    by zzendpad ( 84506 ) on Saturday May 18, 2002 @08:02PM (#3544220)
    This is silly. The universe is far too simple to be explained by mathematics.
    • but 42 is an integer!
    • Perhaps, but so far mathematics has given us a far more accurate picture of the universe than anything else we have. In the future we may find phenomena that are not accuratly explained with math but so far its proven to be the best language for describing the world around us (when we get it right of course).
      • It gives an accurate picture of physics, but not an accurate picture of anything with meaning, i.e. - relationships, love, peace, etc.

        When it does, call me.
        • It gives an accurate picture of physics, but not an accurate picture of anything with meaning, i.e. - relationships, love, peace, etc.

          When it does, call me.

          Ah, one at a time now.

          relationships

          Sure it does, in fact logical and mathematical modeling of relationships between groups and even between individuals is widely used and has been for sometime.

          Just ask the CIA or FBI. :) Establishing the probability (yes probability IS MATH, I know it is only a /chance/ of something happening, but it is still math!) of a person belonging to ideological group Y based upon that persons relationships with persons of interest A, B, and C (along with D, E, F, and G. ;) ) is a rather complicated field of study that is very much so within the sciences.

          Granted we can't yank information out of a person's head;

          yet.

          :)

          Discovering and mapping out these such relationships is a precursor to the eventual complete mapping out of all interpersonal human emotions and thoughts, but hell, the human mind has had up to 2 million years to evolve (depending on who you want to listen to) complex ways to fudge things up;

          you expect things to get done when we have only recently even learned at the very HINTS of what causes the mind to work?

          Bah. Give it time. But do not say it is not a science, Science is by definition All That Exists.

          If it exists Science will find it out. If the current methodologies or languages of Science cannot be used to describe whatever it is that is discovered, then new languages will be developed and new methods of research will be created.

          Science may be full of crotchety old inflexible men, but those crotchety old men die sooner or latter, and even better some of them are not as inflexible as you may think.

          love

          Science has already identified the cause for love (inherently necessary in order to keep the two parent long term system of child baring functional, not that hard to figure that one out), and is well on its way to discovering the various causes.

          Already Science has isolated various chemicals that are responsible for a few of the physical incarnations of love ('that tingly feeling' and such), and soon hopefully science shall discover the remaining information as well.

          Peace

          Depends on what kind of peace you want.

          If you mean peace as in 'no guns shooting people' then simple statistical analysis will give you the rates of death by various causes.

          If you mean peace as in not being stressed out to hell then Science has had that one for quite some time, tons of chemicals involved ya (actually not that many) but hardly a secret.

          Hell even the hippies had that one down. :P

          If you mean peace as in inner wellbeing;

          well heck then you are asking for bare level metaphysics, and that is just a state of mind any ways;

          And science knows the causes of self delusion as well. :)
        • read this book:

          Shadows of Forgotten Ancestors by Carl Sagan and Ann Druyan...

          Love, relationships and most defintely peace is explained by math. Why? Because of DNA, Natural Selection and simply who we are.
    • The universe is far too simple to be explained by mathematics.

      Well, it can. Sort of. Pure mathematics is great for predicting a single event of a simple system. For modeling the complex behavior of many interacting systems (nuclear reactions, protein folding, sociology), we've got no single equation that can do it. You can't predict it, but you can simulate it, using the basic equations to predict one event at a time. We don't have an equation of gravity that works for more then two bodies of mass, but what we can do is model each pair interaction for a short time interval, modify the system accordingly, advance the timer one tick, and repeat.

    • And the worst part is probablly you and Wolfram are both right at the same time.

      ... as if there's something meaningful in knowning those "4 lines of code". You can even presuppose that those rules exist and we can find them. What do you have? The entire premise is "the Wolfram worldview focuses on simple rules that generate counterintuitively complex results...".

      Does there exist math to go from those simple rules to complex results? The problem is, and this part of it was as at least elluded to in the Wired article, that the complexity doesn't exist inherently in the system but in our perceptions of the system. And our definition of complexity is about as slippery as snot on teflon -- implicitly defined by our own analogies of our experiences of being human and our colored perceptions of everything in nature.

      To go from "simple rules" to "complex results" seems intractible. You still may be reduced to discovering complex and interesting results in the crufty scientific way. And those 4 rules may just be sitting up on the mantle doing the only thing they can do: looking pretty.

      • There is such a thing as "complexity inherent in a system". In fact, computer scientists (the ones who work for universities, not the ones who build web pages) have been working on this for 30 years. Complexity theory is a very well defined, but not very well understood, discipline.

        A good place to get started with complexity theory is the book Computational Complexity by Papadimitriou, if you're interested. The definitions of a "complex system" are given in this book, and they have nothing to do with analogies of our experience of being human. Complexity is a mathematical object.

        By the way, one of the open problems in complexity theory is the famous P=NP problem, and if you solve it, you will win $1 million.

        • The article attributes Wolfram to saying the "algorithmic complexity" of all natural process are all equivalent. So all problems would just appear up as, say, NP-hard -- hardly a tool for distinguishing any one result from any other.

          That is if the complexity you and I are referring to were even semantically equivalent. But, the complexity in the way both Wolfram and I mean is more akin to "structure". For instance, in the Game of Life [math.com], the "emergence" of, say, gliders and producers from its simple rules cannot be expressed with algorithmic complexity semantics.

          And my original assertion is that I believe it's probably unlikely that there will ever be mathematics to describe that kind of complexity. Because, what we find complex or interesting in that context is merely a reflection of the bias we gain from our environment ("things that fly", "things that cycle", etc).

    • Actually... (+ my own little biased review) (Score:4, Informative)

      by lonedfx ( 80583 ) on Sunday May 19, 2002 @12:39PM (#3546282)
      This is silly. The universe is far too simple to be explained by mathematics

      Actually the book has more to do with cellular automatons than with mathematics,

      although, arguably, you could describe cellular automatons using link theory (which is a theory of structure, logic and math, and Wolfram's automatons are specially well suited for it) and with more classic mathematical tools.

      Here is my little biased review (biased because I have a take [causaregosum.net] in that kind of stuff, only more mind related).

      I wont reiterate the claims of the book because you can find all sorts of review that do that (oh wait, now that I reread this it appears I'm doing just that later, oh well, still not bad an intro, heh), suffice to say, this book could become the "Bible of Reductionism" for many generations of scientists to come. I do not use the word Bible trivially here, this book is about belief, and that is the biggest problem anybody will have with it. You can agree or disagree with Wolfram as to wether or not the boradness of his conclusions will hold up to scrutiny, but the transfer of those conclusions to to the real world is a completely different step. It is a matter of belief.

      If you torture data sufficiently, it will confess to almost anything. (Fred Menger, Emory University Organic Chemist)

      Nobody is immune to this mistake, a good part of the field of artificial intelligence research is faulty of the same (I myself do it often, but I don't publish), it is the reason why connectionism as a paradigm was so succesful among the community even if it still has to deliver on some of its most basic promises.

      In a nutshell, Wolfram found a set of simple rules for cellular automatons that lead to complex behavior. The second part of his discovery is the principle of computational equivalence, again, summed up, it means that passed a 'threshold' (more or less), two computational processes can be regarded as equally complex. This is a BIG claim, one that will be investigated thoroughly by mathematicians. But the point is that if it holds, you have explained many things : randomess, free will, and you have put in terms that are all but vague what it means for connectionism to cross the threshold of self awareness (in a broad sense).

      How, you aks, can he do that with cellular automatons ? Simple once you drop the concept of linear time. What he realized along with many other researchers (and I'll grab the opportunity to pat myself in the back and include myself in that group), is that time is a poorly defined concept today, until you dive into quantum physics when it starts to make sense. What is needed is to redefine causality. Again in a nutshell, classical causality says that an effect always follows a cause, but that is a definition that itself includes time, and since causality is supposed to define the arrow of time, this definition is not acceptable.

      The new definition becomes "an effect always has a cause", now you can immediately see that the idea of causal directionality has been removed, but that doesnt mean that time flows backward, just like things didnt start falling up once Newton realized up and down were foolih concepts. Shortly put both future and past exert constraints on a local event (think about Marov states in the future and in the past). When equally balanced, those consraints map to classical quantum physics.

      So Wolfram's cellular automatons integrate that concept, you can link events to cells that are in the same discrete time slice as your event. You can link to events in the past, or (like in classical physics), link to events in the future. That itself assumes that time is a discrete phenomenon, it is again a BIG assumption, it is a statement of Wolfram's belief (he uses that word) that time in the physical universe IS indeed discrete, and that thus, his discoveries about causal networks map directly to our world. Lets make it clear here that if he is wrong, then none of these claims map to the physical universe, and the book is just about having fun (a lot of it, tho) with computers and the concept of time (now of course that in itself could be very useful for quantum computing).

      And then he goes on to describe how you can then use this stuff to make elemetary particles, or even space-time itself.

      All in all this is genius stuff, if not completely revolutionary. I would describe it as the Game of Life meets Link Theory. It is a brilliant reformulation of Link Theory in terms of cellular automatons, and since Link Theory is a bit hard to work on, an easy way to use it with computers is extremely welcomed. For my part, I cannot wait for a version of Mathematica that integrates non-linear time processes. My own neural net models would become that much easy to write as I wouldn't have to deal with C++ journaling memory templates, and once quantum computers are out, I can just run the thing and not wait an arbitrary long time.

      But again the flaw is one that we often make, if usually not that publicly: we start to believe in our stuff. Yes, it could work that way, but everything here is the result of a computer experiment, and that is the hard truth of it. It is a beautiful theory, easy to understand, even for the non scientist, but its predictions are minimal, distinguishing it from a physical model of reality in order to test it is going to be a hard task.

      Arguably connectionism's biggest problem is that its promises are quite vague, and thus, it is hardly disprovable as a paradigm, and the same problem applies to Wolfram's work, it is very apealing, but things are explained in very tiny details or in broad strokes. There is no equation that will tell you the bigger picture because there is no bigger picture, the world is a soup of events, and as apealing as this might be, as natural as the patterns the simulation generated seems to be, this does not mean that the physical world is actually operating like this.

      Even going further, it is worthless as a replacement for 'bigger laws', laws that supervene other laws, gaz propagation can be predicted by such laws, but Wolfram's laws are too tiny, their nature is to lead to chaos and non predictibility, to actually generate the supervenient laws, but again, predictive power is non existant or lower than current science.

      But again, this will not prevent many from holding this book quasi religiously, even unknowingly (as many people do today with broad connectionism), because it is simple, elegant, and accounts for a lot, or so it seems (but again, some people think that the pyramids were built by aliens because they think it's simple, elegant, and explains a lot). This book will be about belief, in the next decades and centuries, it will be held as the Bible of Reductionism, because it provides the self consistent argument some philosophers like Dennett needed to explain away consciousness as a pure illusion.

      This is my second problem with this book, Wolfram basically says he is presenting us with a theory of everything, but there is not much about perception, qualias, and more generally, the phenomenal aspects of consciousness. Wolfram, as the Priest of Reductionists I think he is going to become, simply leaves the matter out, talking about perception in terms of representational spaces (even if not in quite those terms), but the phenomenal aspect of those spaces is let out, as if we actually were Chalmers' zombies.

      To conclude, this will be a delightful read for most slashdoters, at least, all of those with a scientific 'way of life' (no strong backround needed), they will see it as the crystalization of their materialistic views. Religious people might have a problem with this book as it depicts us as automatons, literally.

      And then there are people like me, lost between the duality of phenomena and matter and the universe being-causally-closed-sad-state-of-affair. To us, sometimes known as naturalistic dualists (qualia as part of natural laws), the strong deterministic framework that Wolfram imposes seems to point to a strong epiphenomenalism for consciousness, where other theories based on quantum indeterminacy (and quantum theory has been throughly tested for 60+ years) do open possibilities of weak epiphenomenalism. In a few words, I'm not completely convinced by Wolfram's version of free will.

      I'm a bit more than two third into the book, reading it quickly at first to grasp the feel of it, and then to read it slowly a second time, so it is possible that some of the things I have said may not be fair, and for this I apologize in advance.

      I'm loving every part of it, and if you feel my remarks are too harsh, just assume that I'm jealous I didn't write it. If anything this will make mentioning reverse causation much easier in academia without being laughed at, and Link Theory is going to get a huge boost. Having made 4 computer languages already, I plan to have my fifth be able to run reverse causation in typical link theory problems or simulate my causal backpropagation neural network model. If I can use some of Wolfram's formalism to help this task and if he has cleared up the mess with causality, or helped people make the distinction between predictability and determinism for the rest of us too, then I'll be eternally grateful.

      lone, dfx.
      http://www.causaergsum.net/

  • 4 Lines? Bleh... (Score:5, Funny)

    by number one duck ( 319827 ) on Saturday May 18, 2002 @08:02PM (#3544222) Journal
    A *real* god would do it in but a single line of Perl.

  • I'm reading the book (Score:4, Interesting)

    by Anonymous Coward on Saturday May 18, 2002 @08:03PM (#3544229)
    I managed to get it a week ago because I work at a bookstore. I'm about halfway through, and so far it's overrated. The demonsrated cellular automata are very cool, but Wolfram constantly confuses similar behavior for causation. After the first 300 pages describing various kinds of CAs, he slips into pure "I suspect" and "Probably" and "Very likely" mode without really explaining why he suspects the things he does. The wildest thing he's stated so far (without any real evidence, just lots of "It is my strong belief") is that space and time are discrete on a very small scale, and are stuctured as a network of nodes. He doesn't (yet) go so far as saying that the universe is actually a simulation running in a computer. Maybe he will later in the book. Most of the rest of it seems to be concerned with the limits of computation.

    In his credit, he does make a good argument that much of nature is based on processes analogous to CAs, particularly the growth of plants and pigmentation patterns on animals. But again there's lots of "I believe" and practically no "I've observed."

    • Re:I'm reading the book (Score:5, Informative)

      by GMontag451 ( 230904 ) on Saturday May 18, 2002 @09:12PM (#3544425) Homepage
      The wildest thing he's stated so far (without any real evidence, just lots of "It is my strong belief") is that space and time are discrete on a very small scale, and are stuctured as a network of nodes.

      Quantum Mechanics has already suggested that both space and time are discrete on small scales, and I believe there is quite a bit of indirect evidence to support this claim. The discreteness is based on Planck's constant, and the unit length and unit time are approx.10^-33 cm and 10^-43 sec respectively (which if you do the math are equivalent if you equate 1 year and one 1 light year). All lengths of space or time are either multiples or one over a multiple of length.

      The claim that they are structured as a network of nodes is certainly speculation, but it is at least a logical speculation. The points would probably have to be connected somehow.

    • does. The wildest thing he's stated so far (without any real evidence, just lots of "It is my strong belief") is that space and time are discrete on a very small scale, and are stuctured as a network of nodes. He

      The discrete nature of space and time is neither new nor particularly controversial. Maybe the network of nodes is (new that is), but it doesn't even seem that controversial to me.

      Just my 2 cents ... or 3.9 cents here.

  • Chaos (Score:3, Interesting)

    by QuodEratDemonstratum ( 569501 ) on Saturday May 18, 2002 @08:04PM (#3544233) Homepage
    Looks like he's rediscovered chaos theory - simple input intp simple equations give complex outputs; he thinks he can find the simple input which generates the universe from a chaos producing equation.

  • Fabric of Reality (Score:3, Informative)

    by EricBoyd ( 532608 ) <mrericboyd@yahoo. c o m> on Saturday May 18, 2002 @08:06PM (#3544244) Homepage
    The book sounds superficially like David Deutsch's "The Fabric of Reality", which tries to try everything together using a computational theory of reality + the multiverse intrepretation of quantum mechanics.

    Deutsch believes that the simulation of something at a deep enough level is entirely equivalent to the real thing -- which is another way of stating this authors belief that reality is just an algorithm. I personally think it's at least as good a metaphysics as anything else I've read...

    Websurfing done Right! StumbleUpon [stumbleupon.com]

  • He's rediscovered Fractals... (Score:4, Interesting)

    by crovira ( 10242 ) on Saturday May 18, 2002 @08:13PM (#3544262) Homepage
    Big deal. Benoit Mandlebrot did it years ago.

    He's just trying to 'spin' it his way.

  • Nathan and company, be prepared for the slashdotting!

    May your MaxClients be well :)

    I miss you all. Right now I'm stuck answering phones and being talked down to by developers and SySAdmins :(

  • Don't hold your breath for reviews! (Score:5, Informative)

    by Raetsel ( 34442 ) on Saturday May 18, 2002 @08:15PM (#3544270)

    • "If anyone wants to review it, go right ahead."
    Ouch... It'll be a while before any reviews get submitted, Michael -- it's HUGE! (Page 2 of the article: "At 1,280 pages, the book pushes the limit of what can be physically bound between two covers.") Levy talks about it dwarfing (!!!) a phone book... though it would depend on what phone book you're trying to dwarf.

    Wolfram's demands regarding publishing are interesting -- the book is going to cost $12 to actually produce (5x to 6x that of a "normal" book, though the extra size certainly has to be a factor!), and be priced at $45 -- it includes large quantities of high-rez graphics. Also, it went through alphas and betas, like software -- not versions or revisions as writers are familiar with.

    Definitely something I'm going to read... although I doubt I'll achieve full comprehension. The "A New Kind of Science Explorer" software should be fun to play with -- but will I have to wait another 10 years for that?

    • Levy talks about it dwarfing (!!!) a phone book... though it would depend on what phone book you're trying to dwarf.

      I have the book, and I just glanced over at it here on my shelf. It does not "dwarf" a phone book. My denver metro yellow pages is taller, wider, and about a quarter inch thicker, and the phone book is paperback while this book is hardcover.

      I'd have dived in already, but unfortunately I have some other books I have to plow through first. The graphics (black and white grids which are essentially "game of life" snapshots with varied rules and starting conditions) are pretty cool.
    • Just think of it as a physics textbook. As college textbooks go, it's not exceptionally large. My favorite basic physics text is bigger than any phone book I've seen.
  • I think Wolfram means something similar to the idea that E = m * c ^ 2 is one "line of code", yet that has profound implications from everything to the structure of atoms to the eventual fate of the universe. That's what I suspect he means by "code". Not printf("Hello World");

    Sig: What Happened To The Censorware Project (censorware.org) [sethf.com]

  • related (Score:5, Funny)

    by bilbobuggins ( 535860 ) <bilbobuggins@[ ]tjunt.com ['jun' in gap]> on Saturday May 18, 2002 @08:21PM (#3544289)
    In related news,
    Bill Gates concurred while noting that those four lines of course referenced msie.dll to get the job done.
  • In Python, of course:
    class Universe:
    def life_the_universe_and_everything(self):
    return 42
    if __name__ == '__main__': print Universe().life_the_universe_and_everything()

  • I can do it in one. (Score:5, Funny)

    by dstone ( 191334 ) on Saturday May 18, 2002 @08:23PM (#3544301) Homepage
    Four lines?! I don't know where this Wolfram guy was trained, but I can declare the constant 42 in a single line. Well, I suppose that does leave 3 lines for comments. And if anything was worth commenting...
    • One to declare the constant. Another to print it - if your program can't tell anyone the Secret of Life, the Universe, and Anything, it's useless. The remaining two lines are a loop allowing you to either exit the program, or print the Ultimate Number again (if for some reason the user wants to double-check).
    • Hey,

      Four lines?! I don't know where this Wolfram guy was trained, but I can declare the constant 42 in a single line.

      Dude, it won't compile if it doesn't have a 'main' routine, thus:

      Const int Universe = 42

      main {
      // Do Nothing
      }

      You could trim it down, but you want to keep it readable.

      -M

  • He brilliant alright (Score:5, Insightful)

    by Theodore Logan ( 139352 ) on Saturday May 18, 2002 @08:33PM (#3544329)
    I've been waiting eagerly for this book ever since I first heard about it (some years ago).

    Stephen is an amazing guy, and I'm sure what he's done is something absolutely marvellous. I'm also sure, however, that his attitude will continue to suck for great lengths of time. He's probably one of the most arrogant people on this planet. I think he said it best himself regarding what he thinks people will say about his book:

    my opinion of the world at large isn't high enough for me really to be interested in what they have to say

    Now, if that's not a bad attitude I don't know what is. I suppose he could be excused though. He's pretty much as close to the stereotype mad scientist recluse as anyone will ever get.

    • my opinion of the world at large isn't high enough for me really to be interested in what they have to say

      Now, if that's not a bad attitude I don't know what is.

      The opinion that counts is his own opinion of himself. He does not put himself at the mercy of the opinions of the twerps.
    • 'What will other people think?' After a while I realized, 'Why am I really doing this? Is it really worth my while to spend 10 years of my life doing something to get other people to say positive things about it?' No, it's not. Absolutely not. And actually, from some very cynical point of view, my opinion of the world at large isn't high enough for me really to be interested in what they have to say."

      Arrogant? Maybe. But you need the full quote to bring perspective to this issue. He spent 10 years of his life not to please people, but to do the right thing.

      It doesn't matter if people think it's wrong or right. What it matters to him is being right (in the objective sense and not the subjective sense). So he DOES care. But his motivation is not "acceptance" biased. That is a good thing.

      I have always found economics to be a stagnated field. By? Because you can only try to "extend" or complicate the "orthodoxial" core. Everything else will be filed to the trashcan without further analisis.

      What this guy is doing is the way to go. If nobody believes in you, then you need selffinancing. That means you need to reach 3 achievements:
      1) Be a genius (natural)
      2) Make money (luck)
      3) Think different and question mainstream if need be

      That's hard. And it's really noteworthy that someone has met the requirements. I wish I could make some money so that I can begin to work in the way I believe (as oposed to the way "to please other people, so i get food").

      Thanks!

  • Easy... (Score:3, Funny)

    by commonchaos ( 309500 ) on Saturday May 18, 2002 @08:37PM (#3544338) Homepage Journal
    just remove all but 4 cr-lf's (\n)

  • Bug (Score:5, Funny)

    by DeadBugs ( 546475 ) on Saturday May 18, 2002 @08:37PM (#3544341) Homepage
    "The Universe in 4 Lines of Code?"

    Do you ever get the feeling there is a bug in one of those lines?

    • Re:Bug (Score:3, Funny)

      by Tablizer ( 95088 )
      (* Do you ever get the feeling there is a bug in one of those lines? *)

      Probably line #3 which says:

      male.libidoLevel := 6000;

      It was supposed to read:

      male.libidoLevel := 60.00;

      • Re:Bug (Score:3, Funny)

        by shayne321 ( 106803 )

        It was supposed to read:

        male.libidoLevel := 60.00;

        Which is SOO tragic, considering line 4:

        female.bitchFactor *= male.libidoLevel;

        Imagine how much better Universe SP1 will be. :)

        Shayne

  • Useless. (Score:2, Interesting)

    by Man of E ( 531031 )
    So say he's right, and we can describe the entire universe in four lines of code. Lovely, we can generate little simulated universes inside our computers, with little simulated particles, planets, mice, people, vogons, whatever. The behaviour of these systems will look remarkably like that of our own universe, and everyone will be most impressed. And then?

    Perhaps I'm being too rash (haven't read the book, but I certainly will), but it seems we cannot apply this theory to predict anything about our own universe, simply because applying cellular automaton methods would require incredibly detailed measurements of initial conditions. We can't measure the positions and momenta of all particles (thank you dear Heisenberg) in order to predict weather or cosmology, and the innumerable factors affecting theories of finance, politics, biology and others are likely to be beyond the reach of measurement as well. Pity.

    Perhaps if combined with some sort of Monte Carlo simulation, it might have some applications: specify a million scenarios and compute probabilities for visible effects. Still, the same thing can be achieved with current computational models at lower computing cost than the tiny scale of a CA model would require.

    Lastly, if found, the rule will be beyond proof. It will just be a rule that generates systems within computer simulations that are similar to observed phenomena. Good enough for some perhaps, but anything that's beyond proof tends to take on a theological flavor. Not my kind of thing.

    • Re:Useless. (Score:3, Insightful)

      by tsarina ( 456482 )
      He got these ideas when one day he found that extremely complex events can be expressed in relatively simple equations. Seeing that complex events can be so reduced, that's where is '4 lines of code' is coming from. He believes that the falling of a raindrop is of equal complexity as the behavior of gases in a nebula - a single equation can predict both.

      Maybe it can't be proven, per se, but nothing scientific can be. All scientific theories are that - just theories. None of it should be dogma, for that would violate the principles of science. There's nothing lost if such equations must be considered hypotheses that have yet to be proven wrong.

      This isn't meant to create a tidy artificial universe. It's to prove that the real universe can be predicted by simple equations. Whether he succeeds or not - that's the problem. There's no middle ground. Either this will be the waste of a brilliant mind (read his background in the latest Wired) or the greatest revolution in the history of science and a certain Nobel Prize.

      • Re:Useless. (Score:2, Insightful)

        by qeL3-i ( 577868 )
        It won't be a "waste of a brilliant mind". If he succeeds, it's not a waste. If he fails, he's shown that there are no easy answers in that direction, so then other people will try other directions of research which might be more fruitful.
  • In say C++ it would look something like this (I assume they mean 4 lines of code in the body itself):

    #include <everything>
    #define ANSWER 42
    void Universe::main(int argc, char* argv[]){
    while(this.ANSWER == 42){
    doStuff();
    }
    }

    ....

    now, as for void Universe::doStuff() however, that can NOT be represented in 4 lines of code.

  • Mathematica (Score:5, Interesting)

    by gbnewby ( 74175 ) on Saturday May 18, 2002 @08:48PM (#3544372) Homepage
    There are probably far fewer slashdotters familiar with Mathematica than PERL, so I wanted to write a few lines about Mathematica. From what he's said, Wolfram wrote Mathematica a lot like Larry Wall wrote PERL: to solve lots of problems by hiding complexity behind the scenes.

    As PERL is the swiss army chainsaw of computer programming, Mathematica is the swiss army chainsaw of mathematics. The syntax isn't as forgiving as PERL, but it's not bad. Here's a snippit I use for singular value decomposition:

    • svout = SingularValues[N[mydata],Tolerance->0];

    • {u, md, v} = svout;
      Print["u is ", u//MatrixForm];

    I've done the same thing with LAPACK and CLAPACK (scientific programming libraries) and in 3 lines of FORTRAN, C or C++ you haven't even started to define your data. In Mathematica, you're already done.

    Then there's visualization. Running on a PC or via XWindows, Mathematica can do stunning graphics -- including interactive graphics -- with almost no coding. It's not entirely flexible (sort of like using SAS or SPSS' graphics routines), but again you can do astoundingly great things with almost no code.

    In short, Mathematica is very close, for mathematics, to what PERL is for programming (or insert your favorite programming language or toolkit - but I think PERL fits best). While in the olden days of CGI everyone would have their own copy of cgi-lib.pl, now PERL has this functionality built in -- we just do stuff like do stuff like "my $query = new CGI;". In Mathematica, the language has evolved similarly so that stuff you needed to write lots of code for previously is now abstracted to a few functions. Like PERL's ability to use modules, you can write your own add-ons for Mathematica. Like PERL's POD, Mathematica can be used for documentation (and *was* used to write the Mathematica Book, and presumably Wolfram's new book).

    Just a few words about Mathematica. Give it a try, if you're remotely interested in how this stuff works. You'll probably like it!

    • While in the olden days of CGI everyone would have their own copy of cgi-lib.pl, now PERL has this functionality built in -- we just do stuff like do stuff like "my $query = new CGI;"

      This is not true, actually. In this last line, you're using the CGI module by Lincoln Stein, instead of the cgi-lib.pl module. Neither are built into Perl.
      • If you mean strictly Perl the Language, or strictly Perl the Interpreter, you're correct. However, if you just mean Perl, which includes the language, the intreptutor, the debugger, it's standard libraries, etc. then Perl does come with CGI.pm built in.

        -Bill

    • Re:Mathematica (Score:3, Interesting)

      by CheshireCatCO ( 185193 )
      Speaking as someone who has Mathematica installed on his laptop as well as his workstation (and has it currently, actively working on both machines at the moment), I have to disagree with your review, if only in the light in which you cast MMA.

      Mathematica (aka MMA) is a life-saver for some kinds of symbolic manipulations and is great for plotting up formulae. But it has a lot of weak flanks. I refuse to use it for writing things, [La]TeX is much better for that. You might lose a bit of WYSIWYG, yes, but MMA gets really slow after a few pages of serious 2D mathematics. And it's a lot easier to type straight text.

      MMA also is far from ideal for data plotting and manipulation. While I knew MMA long before IDL (from RSI), I have long since started doing all of my data I/O, plotting and manipulation in IDL.

      Finally, MMA is pretty slow about serious number crunching. Much has been made about doing modelling in MMA, but my observation and my experience is that if you want to use commercial software (as opposed to writing your own C/FORTRAN/whatever code), Matlab and even Maple are better than MMA.

      Still, Mathematica is very strong in its niche. I'm not sure it's worth $700+, which is the usual cost. But since I'm still a graudate student, I got my copy for $150 or so. It's been worth that.

      All that said, this far from proves that Wolfram has a clue about anything other than MMA.

      • Re:Mathematica (Score:2, Insightful)

        by chemguru ( 104422 )
        Speaking as a former student that learned Mathmatica in Calculus labs ( for I, II, and III ) and Maple for engineering classes...

        I completely agree with you about how powerful Mathematica is, but when I started doing PChem research on Fourier transforms I found MathCAD to be the easiest for documentation. I have since only used MathCAD, as it doesn't require learning the cryptic code... just learning the interface which is fairly intuitive.

        As far as speed... We pitted two PPro 200s of equal specs: one with Mathematica, one with MathCAD. We calculated the Riemann Sum of several functions, and MathCAD appeared to be the quickest.

        But... just a suggestion that you MAY wanna try... if you haven't already...

        --JamesT

      • Re:Mathematica (Score:3, Insightful)

        by Glorat ( 414139 )
        I'd just like to contend that Mathematica does actually handle documentation remarkably well. I've documented my entire Elementary Number Theory course using MMA including all the really really nasty formula (2^(p^(p-1.....))) in nice 2D. There is no performance loss in its display and creating them is such a breeze if you know the keyboard shortcuts (Ctrl^6 etc.). The Mathematica file format is based on Latex so anything you can do in Latex you can probably do in Mathematica too. (Well, enough anyway) I'll choose Mathematica whenever possible

        Don't try serious number crunching with Mathematica. True! Tbe Runge-Kutta's and P-C methods for solving ODE's run about 100 times slower than the same in fortran. But it only took 10 lines of code so I didn't mind too much ;)

        Finally, for those who want to see just how good (better IMO) Mathematica is at WYSYWIG Latex like editing, check out my ccourse notes [ic.ac.uk] (800kbs gzipped postscript). It has impressive formatting

    • Re:Mathematica (Score:3, Interesting)

      by mcelrath ( 8027 )
      I wonder if Steven Wolfram himself has to call up Wolfram tech support when he gets a new laptop, dig up his registration number, license number, and hardware ID, and explain to them that he wants to transfer his license to a new computer and why he wants to transfer his Mathematica license to a new computer and assure them that yes he will delete the old copy and give them the hardware identifier for his new machine and install a new Big Bro^H^H^H^H^H^H^H^H License Manager...yadda yadda

      Sure it's a useful piece of software. But it's an absolute pain in the ass, Wolfram is a paranoid bastard, and it's not worth half the price they ask for it. For my professional work, I choose Maple [maplesoft.com]. Go away Wolfram and annoy someone else. I don't want to talk to you after I have legally purchased your product. It's NONE OF YOUR BUSINESS!

      Remember dongles? The things you put on your serial port to keep you running Autocad on only one machine? Mathematica is one big software dongle.

      --Bob

  • Instead of ads on pages, why not have a slashdot referrer thingy for links to amazon.com in book reviews/discussions?

  • What Wolfram is driving at (Score:4, Interesting)

    by vkg ( 158234 ) on Saturday May 18, 2002 @08:50PM (#3544378) Homepage
    is that the observable universe is defined by calculus and differential equations in very small areas: planetery motion, for example, or atomic physics.

    Phenomena like life, geology and the like are very badly behaved with respect to our standard mathematical tools and we all know this.

    Wolfram is suggesting that cellular automata provide a simple framework for examining the phenomena outside of the "magic circle" of the calculus: i.e. most of life and the universe.

    Of course, for a long time we've confused hard science with the application of calculus, which has effected what we consider "science" to be: if it is not an equation, we don't think it's scientific.

    Well,

    1> go talk to some biologists

    2> get used to it: equations got us this far, but after this it may be increasingly about computation.

    Consider, for example, the Four Color Theorem [wolfram.com] - the only existing proof of which requires a lot of computer power to grind through cases. Is it a valid proof? Probably - but not to the standards of mathematicians who grew up in the pre-computer age, to whom an exhaustively checked list of cases does not look like mathematics at all.

    We'll see how Wolfram's work fares over time, but my bet is that it will fare Quite Well.
    • is that the observable universe is defined by calculus and differential equations in very small areas: planetery motion, for example, or atomic physics.

      No. The universe can be described by calculus and difficult equations.

      Phenomena like life, geology and the like are very badly behaved with respect to our standard mathematical tools and we all know this.

      No they're not. It's just that in order to model biological phenomena very well, you have to do finite state analysis on a very fine scale - and getting even the most powerful supercomputer to do the (calculus and difficult equations) calculations on ALL those elements is...unrealistic.

      Still don't believe me? Ask IBM - according to their Blue Gene Project, given all the computing power available on the planet right now, it would still take several hundred years to calculate the structure of human proteins.

      Still not convinced? OK. The human body is around a trillion cells. Each of these cells has millions of molecules in it. Each of those molecules can be accurately modeled by calculus and DifEq...but you've got trillions of millions of equations to worry about. There's not enough RAM on the planet to hold that matrix. Also consider that you also have trillions of millions of possible boundary conditions.

      Wolfram is suggesting that cellular automata provide a simple framework for examining the phenomena outside of the "magic circle" of the calculus: i.e. most of life and the universe.

      Wolfram is also supplying the code for the book in Mathematica. I submit to you that Wolfram is trying to sell more software. Which isn't to say I don't own his books, or that I don't have 4.1 minimized on my desktop right now. Because I do. But when someone comes out and says that his book is the be all and the end all of our scientific quandries, I am...skeptical.

      You've hit a sort of soft spot here. I love the alternative ways of thinking - wavelets, fuzzy logic, neural networks, AI, and yes cellular automata. Each of these fields has been able to solve (or simplify) problems that have plagued researchers. But every time a researcher uses one of these methods to solve a problem, he or she starts evangelizing it, and hurts its credibility. It's a problem of HYPE - and there's HYPE written all over this book. He should have just published it, sent a copy to some respected scientists, and let THEM speak about it. I could care less when I see fervent hype on the MTV. But I get sick when I see it in scientific publications.

      Of course, for a long time we've confused hard science with the application of calculus, which has effected what we consider "science" to be: if it is not an equation, we don't think it's scientific.

      1> go talk to some biologists

      Biologists are friggin crazy. I know this because I am one :)

      2> get used to it: equations got us this far, but after this it may be increasingly about computation.

      Consider, for example, the Four Color Theorem [wolfram.com] - the only existing proof of which requires a lot of computer power to grind through cases. Is it a valid proof? Probably - but not to the standards of mathematicians who grew up in the pre-computer age, to whom an exhaustively checked list of cases does not look like mathematics at all.

      You seem to be unfamiliar with mathematical proofs. Grinding through many cases does not a valid proof make. In order to prove a theorem, you have to verify its validity for ALL cases, and in order to disprove a theorem, you only have to find one case where it is not valid. Just because you ran your theorem on a supercomputer for three months does not mean you have proved its validity for all cases. Example: You are trying to prove some theorem, and you use only positive integers. The supercomputer runs for a year and finds no holes in your theorem. Then your girlfriend comes over and enters -1, and your supercomputer barfs at you.

      We'll see how Wolfram's work fares over time, but my bet is that it will fare Quite Well.

      I HOPE it fairs well - I'd love to understand WHY the second law of thermodynamics works as well. But whether it fairs well or not, it would have faired much better without all of the hype and simply on the merits of the work itself.

      • You seem to be unfamiliar with mathematical proofs. Grinding through many cases does not a valid proof make. In order to prove a theorem, you have to verify its validity for ALL cases, and in order to disprove a theorem, you only have to find one case where it is not valid. Just because you ran your theorem on a supercomputer for three months does not mean you have proved its validity for all cases. Example: You are trying to prove some theorem, and you use only positive integers. The supercomputer runs for a year and finds no holes in your theorem. Then your girlfriend comes over and enters -1, and your supercomputer barfs at you.

        You seem to be unfamiliar the concept of proof by cases. A proof by cases is valid if and only if the cases are exhaustive. For example, if you prove something for all even numbers and all odd numbers, you have proven it for all integers. The proof of the Four Color Theorem broke the problem, or some lemma used in the problem, into around 1000 cases. The cases were exhaustive, or it would not have been a proof. Some curmudgeons didn't like the fact that the cases were checked by computer.

    • Consider, for example, the Four Color Theorem [wolfram.com] - the only existing proof of which requires a lot of computer power to grind through cases. Is it a valid proof? Probably - but not to the standards of mathematicians who grew up in the pre-computer age, to whom an exhaustively checked list of cases does not look like mathematics at all.

      This was a subject of debate twenty years ago. Currently the computer proof is generally well accepted by mathematicians. What Wolfram proposes is neither new nor revolutionary.

      Computer Science itself has spent a good portion of its young life moving away from equation descriptions to constructive, computable descriptions. They are called algorithms. You don't need cellular automata to make a switch from equations to computing. Moreover, I was reading a famous physicist (whose name escapes me) state that physics had move beyond the equation as description and considers now computational descriptions as valid.

  • "With patience, insight, and self-confidence to spare...."

    Most intersting was his claim that the single rule of the universe could be defined in a few lines of code if it were a well-designed language (so stop coding in C++ *grin*). I would suspect that the rule, if it exists, looks much like an obfuscated C program - subtle, with side-effects that have important ramifications a few iterations later.

    Now, what penatly does God traditionally hand out for hubris? Still, I can't wait to read it.
  • Ray Kurzweil, the inventor, AI theorist, and author of The Age of Spiritual Machines, has a long review of the book available here [kurzweilai.net].

    One of the key points of the review is that while Kurzweil agrees that certain levels of complexity can be achieved, higher levels of complexity are simply not derivable from cellular automaton, the generator of Wolfram's complexities.

    To quote Kurzweil: There is a missing link here in how one gets from the interesting, but ultimately routine patterns of a cellular automaton to the complexity of persisting structures that demonstrate higher levels of intelligence. For example, these class 4 patterns are not capable of solving interesting problems, and no amount of iteration moves them closer to doing so.
  • From what I've seen in various places, he's trying to describe everything in terms of cellular automata.

    But a cellular automaton is just the discrete version of a differential equation. Physics has been described in terms of differential equations for 150 years.

    So is he getting any new insights? Simplifying the calculations? Or is he just rearranging the the mathematical furniture?

  • Complexity Theory (Score:5, Informative)

    by kmellis ( 442405 ) <kmellis@io.com> on Saturday May 18, 2002 @09:21PM (#3544441) Homepage
    Salon published a sort of a review [salon.com] of Wolfram's book recently titled "The Next Newton?". Talk about hyperbole.

    As a letter writer to Salon points out, it seems that Wolfram thinks that he's discovered Complexity Theory all by himself. The Salon article certainly gives that impression -- not having read the book, I can't make my own judgment.

    The Salon writer writes as if cellular automata were some silly mathematical curiosity (or worse, the writer thinks that CA is recent to computing) that Wolfram "rediscovered" and took seriously for the first time. Of course that's absurd.

    The Santa Fe Institute [santafe.edu] was founded jointly around 1984 by the eminent Nobel Laureate, physicist Murray Gell-Mann, and several others. Stuart Kauffman [santafe.edu] has researched and written on complexity for many years.

    I myself have been following, as a layperson, complexity theory for about fifteen years. In 1991 I had the opportunity to be an undergraduate intern -- an opportunity I didn't follow up on because of my severe academic workload, but an opportunity I will always regret not taking advantage of. Undergraduate intern positions are much more competitive now. This eleven years has made the difference between "bleeding edge" and "cutting edge". Or perhaps complexity theory is even mainstream. I've noticed a burgeoning graduate school interest in complexity studies programs.

    Complexity theory intersects many disciplines, and it involves several related ideas such as chaos theory, modeling, self-reference, artificial life, and others. It's evolved into a fairly rigorous discipline, and the more formalized idea of "complex adaptive systems" forms the core. For those who have read Douglas Hofstadter's book, Godel, Escher, Bach [amazon.com], (a very influential book for many of us) published around '82, many of these ideas will be familiar.

    Wolfram's quip that seems so risible is really only an overstatement of the central idea of complexity theory: that a limited number of "rules" can give rise to extremely complex behavior. This was the surprise of cellular automata, exemplified by Conway's "Life" [brunel.ac.uk], invented in 1970. But the underlying idea goes as far back as John von Neumann. Wolfram has done some interesting work in CA. But it sure as hell isn't his idea. For many in the Slashdot community, this is all as familiar as the back of their hands. But apparently there's still a lot of people that should be aware of this stuff that are not.

    Finally, many people here would probably be interested to know that SimCity's designer, and Maxis, have had some association with SFI. This makes sense because the emergent behaviors of complex systems are not (as a practical matter) deductively predictable -- their behavior must be studied. The techniques of systems modeling are requisite. SimCity was the general public's first accessible insight into just how fascinating and educational systems modeling can be.

  • That dosen't make the complexity that exists in the universe unimportant. It's the RAM that counts. The massive storage and corresponding computation, the size and scale of it, that matters.

    After all, an Alpha, a K7, and the microcontroller in my digital waltch, are all made from a few types of logic gates, but an Alpha can calculate a lot more. It has more capacity. The universe, assuming that it is all based on a few lines of code, can exhibit so much more still, due to being so vast.

  • The book sounds like a belated promo for cellular automata (that stuff was cool a few decades ago when Conway at Princeton was playing around with the game of Life on his computer ... Conway is a real mathematician by the way who has done some very legitimate work.)

    The real genius of Wolfram is not his "formula" that claims to explain the world, but how he has bilked universities and research institutes around the world in the untold millions for Mathematica site licenses.

    It is not an understatement to call Wolfram the Microsoft of scientific computing software. Both Gates and Wolfram dropped out of academia to create their respective computing empires. Both use proprietary data formats to lock in their customers. Both go to school campuses and offer students the "first hit" for free.

    Gates' used a little of Dad's money (wealthy Washington lawyer) to get his start. Wolfram, in a stroke of true genius, used his McArthur grant to set up shop.

    The book is just a farce to make the hungry PhD Computer Science students who bang their heads trying to fix the bugs in Mathematica (and there are many) feel like Wolfram is doing something useful for his hefty paycheck while they sweat over their mundane chores. Can't you just hear them whispering to each other "When is Stevie Wonderboy going to tell us how the universe got started?"

    If you are at a university that has a site license for Mathematica, ask the university to consider canceling the license and purchasing the open-source REDUCE system instead. It is an older product than Mathematica and lacks a slick GUI interface. This is no longer a problem though because REDUCE interfaces nicely with TeXmacs, and if you haven't heard about the latter, check out this Metafont-based WYSIWYG scientific editor at www.texmacs.org.

    Just my 2 cents worth; done ranting :)

  • Digital Mechanics (Score:3, Interesting)

    by ROBOKATZ ( 211768 ) on Saturday May 18, 2002 @09:47PM (#3544499)
    This sounds a lot like Ed Fredkin's Digital Mechanics [digitalphilosophy.org] theories. Which isn't surpising, considering that Wolfram and Fredkin used to work together.
  • Guess Erwin's six lines isn't so impressive after all...

  • Bah! (Score:2, Funny)

    by metacell ( 523607 )

    Wolfram is wrong! Einstein is wrong too! And newton also! They're all wrong!

    All of the universe can be described as a single atom of plutonium.

    http://www.newphys.se/elektromagnum/physics/Ludwig Plutonium/ [newphys.se].

  • The Journal Nature ran an article on this book, mainly on the reactions its getting (both good and bad):

    http://www.nature.com/cgi-taf/DynaPage.taf?file=/n ature/journal/v417/n6886/full/417216a_fs.html [nature.com]
  • If they send me one then you should see my review here... maybe even before the end of the year :-).

    Danny.

  • What is a cellular automaton? (Score:2, Informative)

    by Anonymous Coward
    People here seem to be making comments without knowing what a cellular automaton (the central theme in his book) is. Here's my humble attempt at attempting to redress this situation.


    Well, we start with a differential equation, in particular, a partial different equation (pde): A pde is an equation that describes how a quantity changes with respect to several variables (which we will take to be time and space). Imagine when someone farts in a corner of a room. We want to describe how the concentration of farted gas (the quantity we are interested in) changes when time advances, as well as how the concentration of farted gas changes with space. Using molecular dynamics arguments, we can write down an equation
    dc/dt = D (d^2c/dx^2 + d^2c/dy^2 + d^2c/dz^2)
    where c is the concentration of farted gas, and t represents time and (x,y,z) represent three-dimensional space. The actual form of the equation is not important (but it is the diffusion equation in case you are interested). The point to note here is that we have written down a pde for c as a function of t and (x,y,z). We can then proceed to solve for c at any t and (x,y,z) that we are interested in, using techniques from calculus. This, in a nutshell, is the basis of many equations of physics -- Newton's, Maxwell's, Schrodinger's, and Einstein's equations are all pde's.


    Now, imagine a discretized version of a pde, in which time t, space (x,y,z), and the quantity itself c, are all discretized. Discretized in the sense that they take discrete values, i.e., we measure time in "time steps" t=1,2,3,etc. and space in "space units" x=1,2,3,etc. and the quantity c in, for example, "smelly", "moderate", "not too smelly", etc. Then the discretized version of a pde is a cellular automaton.


    By considering only two dimensions (one time and one space), and by explicitly enumerating all possible rules that one can get, Wolfram found that there are several automata that cen generate extermely complicated behavior.


    Now, what his book seem to be proposing is that, by moving away from the calculus of a pde, and venture instead into discrete space, he seems to have uncovered a profund law governing all cellular automata. This in itself is a cool result! However, add that to his belief that everything (including the universe) is a cellular automaton, and people get less enthusiastic. Anways, hope this brief treatise on cellular automata helps!

  • My first college physics professor used to say that Maxwell's 4 equations do a nice job of summing up the Universe...

  • See Fredkin's Digital Physics book draft online (Score:3, Interesting)

    by hqm ( 49964 ) on Saturday May 18, 2002 @10:40PM (#3544645)
    People interested in the concept of the universe
    as a digital computer should look at

    http://www.digitalphilosophy.org [digitalphilosophy.org].

    Fredkin was thinking about this stuff long before Wolfram was born.
  • The concept is deceptively simple. Every interaction in the universe can be reduced to a series of mathmatical equations of iteration that can be represented in two dimensional space. The clustering of solution follow extrememly simple rules, that even a child could learn in a few minutes. The reprocussions if this is proven to be true would be nothing short of revolutionary. Imagine the paradigm shift when the world finally realized that the earth revolved around the sun... this beats that by a factor of 100.

    And he's got lots of hard data to back up his claim. Sampling from dozens of sciences, he shows the same patterns emerging over and over again. It's stunning to see some of the work because it becomes intuative after only a few examles and you can see the patterns in so many different places.

    So either he's a complete nut, who has taken something that's absurdely simple and mis-applied it to all the major scientific endeavours, or he's a certifiable genius who has just opened the window to understand the universe in the most basic of ways.

    I'll let you know after I read the book. ;-)

  • Want to learn more about Cellular Automata? (Score:3, Informative)

    by marhar ( 66825 ) on Saturday May 18, 2002 @11:23PM (#3544706) Homepage
    Rudy Rucker and John Walker (themselves pretty amazing guys) have released their Cellular Automata lab, originally written as part of Autodesk's science series. You can download it at http://www.fourmilab.ch/cellab/ [fourmilab.ch]

    Wolfram's first CA book (the collection of his papers) is out of print but available for download at http://www.stephenwolfram.com/publications/books/c a-reprint/ [stephenwolfram.com]

  • As others have mentioned, Fredkin's Digital Mechanics [digitalphilosophy.org] is a similar idea.

    The idea that there's an underlying structure to the universe that's executing on some finite-state machine has come up a few times. It's a reasonable conjecture. But until somebody finds a program, automaton, or a set of rules that yields physics, it's no more than a conjecture. If somebody finds such a set of rules, they get a Nobel Prize and go down in history with Newton and Einstein. But neither Fredkin nor Wolfram have done that.

  • The article says that the book has in it a way to violate the second law of thermodynamics (or at least that the author claims such.)

    Uh, any confirmations on this? I mean if it IS true wouldn't that alone be like one of the biggest contributions so science, err, well, uh, ever? Heh.

    (or at least it would cut down my power bill. :) )
  • In one of the articles on him, I read about him pointing out this seashell, and how it closely resembled one of his automata. Well, duh. How else would cells organize themselves? They don't line up in neat grids, and they move around sometimes, but of course the growth (and practically everything else) of cellular organisms will be closely related to cellular automata.

    I don't think anyone has been disputing that.

    Could the basic building blocks of the universe be modeled this way? Maybe. But it's not going to matter. The universe we see and measure would be emergent properties, anyway, and it's pretty well established that perfect measurement is impossible.

    The problem with cellular automata is that they're hard to approximate. You can't predict the general behavior of a million-square game of Life with a thousand grey squares.

    You could have your model of the universe in 4 lines of code, and not be able do a damn thing with it. A finite system can't contain a copy of itself (let alone one running at a higher speed) in one corner. So we could neither confirm such a model nor apply it.

    I'm sure of only one practical application of this admittedly revolutionary development of cellular automata: this is going to form the foundations of some terrific computer games. I want a copy of that book. It's no 42, but I'm sure it's awfully interesting anyway.
  • While the concepts in his book certainly seem interesting in the mathematical sense, they have nothing to do with physics and science. Science revolves around experiments and facts, which Wolfram's book is lacking. There are several arguments against a "turing machine" style universe:
    • The best we can tell so far, time is infinitely divisible. There doesn't seem to be a fundamental quantum of time, like the clock rate of a computer.
    • While a grid of simple computers could accurately simulate a Newtonian universe with a few simple rules and variables, simulating a universe with both quantum mechanics and relativity is an entirely different kettle of fish. A fixed grid would be just ilke the aether -- a fixed reference frame. We now know that this is not the case in our universe.
    • Most existing theories assume a continuous universe with "infinite precision". That is, most theories are expressed in terms of real or complex valued differential equations, which can be simulated only to a finite precision on a computer. So far, there has been no evidence of any such error, if there were, images of distant stars and galaxies would be blurred, spectral lines spread out, etc...

  • Useful Links (Score:4, Informative)

    by guanxi ( 216397 ) on Sunday May 19, 2002 @12:44AM (#3544858)
    The book
    http://www.wolframscience.com/

    The downloadable code (4 lines, I suppose)
    http://www.wolframscience.com/nks/progra ms/

    Stephen Wolfram
    http://www.stephenwolfram.com/about-sw/
  • I haven't read the book (already ordered it), but I have a bone to pick with it. The first thing that is new about it is that it avoids peer review prior to publication.
    We all know that the best way to advance in an area of knowledge is by getting criticism to our new ideas. The reason to do so before publication is that any scientists know how easy it is to fool one self and tries to avoid it, not by asking a few friends to read our stuff, but by asking the biggest experts in the best magazines (or by posting for free in a web site so everybody gets a crack at it).
    By failing to follow this procedure Dr. Wolfram has open himself up to criticism that his book is not a scientific enterprise, but a commercial one...
    Disclosure: I am a mathematician...

  • Algorithms without Context (Score:3, Insightful)

    by ChaoticCoyote ( 195677 ) on Sunday May 19, 2002 @11:08AM (#3545983) Homepage

    An algorithm is a pure expression of process; it has no meaning with execution and data contexts. Thus, I think Wolfram has gone beyond science into faith and religion... he may answer "how", but that is only part of an entire description of the universe that also asks "why" and "what."

    Be that as it may, I am fond of heretics who shake the foundations of science with unorthodoxy. Wolfram is brilliant, if erratic, and I'll read his book simply to have my viewpoints challenged.

  • Autodidact (Score:3, Insightful)

    by gonerill ( 139660 ) on Sunday May 19, 2002 @01:49PM (#3546513) Homepage
    The book has all the marks, both positive and negative, of the very smart autodidact. On the positive side: enormous ambition, singular vision and determination to innovate. On the negative side: monomania, evangelical tone, and contempt for/unwillingness to engage with one's peers.

    That last one is the most problematic. Wolfram says he doesn't expect people to understand him, or to get a negative reaction from the scientific community, and -- worse -- that this negative reaction is only to be expected etc. These are the early hallmarks of the crank.

    Things to expect soon: A legion of amateur readers proclaiming him a genius and arguing that the indifferent reaction of mainstream science is somehow evidence that the book is right. Just remember: P(Cranky and Weird | Work of Genius) = High. P(Work of Genius | Cranky and Weird) = Very low.

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