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[P]
Wolfram publishes A New Kind of Science

By CitAnon in News
Wed May 15, 2002 at 10:24:10 PM EST
Tags: Science (all tags)
Science

Stephen Wolfram has finally published his A New Kind of Science. The culmination of twenty years of private and furtive work by the creator of Mathematica, A New Kind of Science purports to revolutionize science and mathematics through the application of cellular automata. Normally, claimants with such hubris are laughed off by serious scientists, but Wolfram is arguably one of the brightest minds in science. With this book, Wolfram begins his attempt to take his science to the mainstream and put his name besides those of Einstein and Newton. Here are several articles from Forbes, the New Scientist and the New York Times on the book and Wolfram.


Why should you care about this guy's ideas? Here's an excerpt on Wolfram from the Forbes article:

Stephen Wolfram was born in London in 1959. His father is a moderately successful novelist; his late mother was an Oxford don in philosophy. A brilliant child, he earned a scholarship to Eton College at age 13. There, forced to play cricket, he found the best place on the field to read books. By 14, he had written his own book on particle physics; by 17, he had a scientific paper published in the journal Nuclear Physics.

He attended Oxford University on a scholarship and, during the summer after his first year, went to work in the Theoretical High-Energy Physics Groups at the Argonne National Laboratory. That summer Wolfram wrote a scientific paper on heavy quark production that soon became a classic in the field--and he turned 18.

A year later, in 1978, Wolfram was invited to the California Institute of Technology (Caltech) by legendary scientist Murray Gell-Mann. There his brilliant reputation gathered momentum: He invented the Fox-Wolfram variables in particle physics, discovered the Politzer-Wolfram upper bound on the mass of quarks, and published more than 25 scientific papers. The work he did in just his first year at Caltech earned him a Ph.D. in theoretical physics. In 1980 he joined the Caltech faculty, and in 1981, at age 21, he was awarded a MacArthur "Genius" Fellowship--not for any single piece of work but for the "breadth of his thinking."

In A New Kind of Science, published on May 14, Steven Wolfram presents the centerpiece of his push for a new infrastructure of science based upon the extensive and diverse application of cellular automata to study complex or non-perturbative processes in sciences ranging from particle physics to systems biology to the study of the human brain. He claims that he will provide a concerted case with important, previously unreported insights backed up by large amounts of experimental evidence gleaned from twenty years of largely private and secretive work.

In his own words, from an interview with the New Scientist:

So, what have you discovered?

Enough to fill hundreds--maybe thousands--of scientific papers. I've amassed a huge amount of evidence for my idea that simple programs--like the cellular automata--are the key to lots of important phenomena in nature. In physics, for instance, I can finally explain why the second law of thermodynamics works--that is, why many physical systems tend to become irreversibly more random as time progresses. In biology, I now know how a lot of the complexity arises. I've discovered that many things we might have thought were special about life and intelligence, for example, can also emerge in all kinds of physical systems. Consequently, I don't believe "anthropic" arguments that say that for us to be here it's necessary for there to be stars, galaxies and so on. There can be things just as complex as us without any of that.

Why haven't you published any of this?

Because it's all part of a big picture that can be communicated properly only by showing everything together. I guess if someone else had been paying for my work, I might have had to give progress reports. Fortunately, I've been able to concentrate on putting everything together in a nice coherent way, as a book called A New Kind of Science. It's been a huge project. I've devoted about 100 million keystrokes to it. I've taken a lot of trouble to polish my ideas so they're as clean as possible. Usually, new directions in science begin far more gradually, with lots of people involved. But the things I'm doing now are different enough that I've had to build up a whole new intellectual structure by myself.

Undoubtedly, an unstated reason for Wolfram's silence has been the control of information about his work. Consequently, there are, at this time, few well informed and objective reviews of his work. The trickle of information that I have seen come from comments, here and here, by k5 readers who have found reviews or begun reading the book.

For a flavor of the material in the book, you can find the example programs from his book at http://www.wolframscience.com/nks/programs/. The codes run as Mathematica notebooks. However, they are intuitive enough that, even if you don't have Mathematica, you can glean some understanding by simply reading them with the free Mathreader.

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Poll
A New Kind of Science will
o Revolutionize science and mathematics. 14%
o Have significant, but not revolutionary impact. 18%
o Have some impact. 51%
o Make Stephen Wolfram the laughing stock of the scientific community. 14%

Votes: 27
Results | Other Polls

Related Links
o Stephen Wolfram
o A New Kind of Science
o several articles
o New Scientist
o here
o here [2]
o begun reading the book
o http://www .wolframscience.com/nks/programs/
o Mathreader
o Also by CitAnon


Display: Sort:
Wolfram publishes A New Kind of Science | 191 comments (166 topical, 25 editorial, 0 hidden)
About the book (4.44 / 9) (#8)
by cameldrv on Wed May 15, 2002 at 12:53:33 AM EST

Having read a draft of the book, I will say first off that the book has received massive hype and it would be quite hard for any book to live up to it. However, I found the book certainly quite interesting. IMO, the most important result published in the book is that of the Turing completeness of rule 110, by explicit construction. The book will get a lot of criticism for not being mathematically rigorous, however, I think it's best to see it as a survey of computational analogs in nature. If you have an interest in CA, you should find it a good read.

just asked for a review copy (4.00 / 4) (#9)
by danny on Wed May 15, 2002 at 12:53:46 AM EST

Well, I just mailed them asking for a review copy! Wait a few months (depending on whether they ship air or surface and how readable the work is) and I should have a review for you.

Danny.
[900 book reviews and other stuff]

Looking forward to your review (1.00 / 1) (#11)
by CitAnon on Wed May 15, 2002 at 01:02:41 AM EST

Hopefully I'll get my copy soon.

[ Parent ]
huh? you haven't even read it yet? (none / 0) (#168)
by bhouston on Fri May 17, 2002 at 04:42:46 PM EST

> "Hopefully I'll get my copy soon."

You haven't even read the book yet but you already have unquestioning adoration for it?  Come on... you have to be on someone's payroll.

-ben
www.exocortex.org/~ben

[ Parent ]

I take it, then, (5.00 / 1) (#169)
by MrMikey on Fri May 17, 2002 at 04:58:37 PM EST

that you didn't read CitAnon's story (which included links to several articles, and excepts from two of them)? He hasn't read the book, but he appears to be familiar with Wolfram's work. As for "unquestioning adoration", you must have read a different story from this one. Given that CitAnon just finished saying that "Actually, many people who have worked with him have said privately that he is a control freak, a thoroughly arrogant SOB and a rotten scoundrel." in the very post you are responding to, I am forced to question your reading comprehension skills.

[ Parent ]
Damn! (1.00 / 1) (#52)
by DesiredUsername on Wed May 15, 2002 at 08:19:42 AM EST

I should have thought to ask my wife to do the same thing!

Play 囲碁
[ Parent ]
Wolfram's error (3.70 / 10) (#12)
by tiger on Wed May 15, 2002 at 01:59:30 AM EST

Although I agree that the universe is best explained as being computerized, and this idea is already many decades old, and I have written my own online book on the subject here, the big problem I have with Wolfram’s approach is the same big problem that others have already pointed out: Wolfram insists on the underlying program for the universe being very simple.

In the June 2002 issue of Wired magazine which I got today, there is an article about Wolfram and his book. In that story, Wolfram is quoted as saying, in answer to the question low long the program would be: “I don’t know. In Mathematica, for example, perhaps three, four lines of code.” [page 148]

Wolfram is great with the math, and has a strong physics background. However, he seems stupid to me on this subject, because he believes in a free-ride that gives great complexity from great simplicity. My own background is computer science (PhD), and there are no free-rides like that in computer science.

--
Americans :— Say no to male genital mutilation. In Memory of the Sexually Mutilated Child



well.. (3.66 / 3) (#15)
by Rainy on Wed May 15, 2002 at 02:28:29 AM EST

One could say that you have a processor with very simple structures like gates, switches and if you look at a personal computer with all the software running on it, scanner, adobe photoshop, 3d studio max, game of life simulator, quack 3, etc. it apparently looks much more complex than what you see on basic logic level it's all built upon.
--
Rainy "Collect all zero" Day
[ Parent ]
Sure he might be wrong, but.... (4.00 / 3) (#16)
by Spork on Wed May 15, 2002 at 02:43:47 AM EST

We still have to assume that the simplest theory which explains all our data is the most likely to be true. Of course it's not a sure bet--I mean, the fundamental laws in the universe could be Byzantine. For example, there could be laws of nature about how fundamental constants change with time, even pretty abrupt ones. For all we know, all electrons will become positively charged in the next minute, and we'll all implode. We can never be sure that it won't happen; we can't even say it probably won't happen. The only reason why we don't believe that it won't is because we think that the universe is basically simple, and that there aren't any "extra" laws about charge shifting during the next minute and other wacky stuff.

That's why I think that scientists must assume the "program" of the universe, if there is such a thing, is simple. If you don't require simplicity, you might as well stick ghosts and elves and magic spells in your theory. (Of course, there might be undiscovered ghosts and elves and magic spells, but doesn't it seem like a safer guess to think that there aren't any? In the same way, the fundamental laws might be convoluted, but it should seem more likely that they are elegant and simple.)

[ Parent ]

Conway's Life is Turing-Complete (4.00 / 6) (#33)
by _Quinn on Wed May 15, 2002 at 05:37:47 AM EST

Implying that a four-line Mathematica program (or so; I don't know Mathematica that well, but Conway's life is pretty simple) can compute any computable funtion.

It's not unreasonable to suggest that simple rules lead to great complexity; the Turing machine itself is pretty simple.

-_Quinn
Reality Maintenance Group, Silver City Construction Co., Ltd.
[ Parent ]

but Turing machines want an infinite tape (4.00 / 6) (#36)
by martingale on Wed May 15, 2002 at 06:05:02 AM EST

I think what misleads people who read the four line comment is that it isn't enough to build a Turing machine (or the Game of Life), you have to have an initial configuration of the tape (or the planar grid for Life) which can be arbitrarily complex depending upon the function you wish to compute. There is no finite configuration of the tape which computes every computable function.

So Wolfram's comment is misleading people by implying four rules are enough. You need four rules and an arbitrarily large computer "memory" (tape, grid, whatever) which must be filled with the proper initial conditions (arbitrarily long program) to allow the CA to evolve a solution. Think of the four rules as a (very) reduced instruction set processor.

There is no magical program which computes all answers (halting problem paraphrased).

[ Parent ]

hmm? (5.00 / 2) (#94)
by _Quinn on Wed May 15, 2002 at 05:32:58 PM EST

I think what misleads people who read the four line comment is that it isn't enough to build a Turing machine (or the Game of Life),

Well it depends if you're a reductionist, doesn't it?  That there are known problems which can not be treated from first principles does not detract from the value and simplicity of those principles.

you have to have an initial configuration of the tape... which can be arbitrarily complex depending upon the function you wish to compute

Actually, the tape only contains the input, unless you're talking about UTMs, for which it's relatively easy to prove that even exponential-time complete problems have algorithms which can be written in a (relatively small) constant space.

There is no finite configuration of the tape which computes every computable function.

Actually, there is (of course, since the set is infinite, it'll take forever):

function = '';
nextFunction() {
if( function == '' ) { function = '0'; return function; }
else { int fnIndex = binaryToInteger(function);
fnIndex++;
function = integerToBinary(fnIndex);
return function;
}
}

UTM(x, '');
while( true ) {
UTM(x, nextFunction());
}

This is obviously a finite program (in fact, it can be embedded in the UTM's finite control) which will enumerate all possible functions, and simulate the UTM executing that function on input x.  Most of the strings aren't valid encodings of functions, but that doesn't matter; UTM() will just halt (or crash) immediately, and we'll move on.

Now, if you mean "need an arbitrarily large amount of memory to compute all computable functions", well, of course it does: a given computable function can be arbitrarily large and work on arbitrarily large input!

Furthermore, you only need one initial condition on the tape: that it continues for a sufficiently large distance to the right.  The contents of the tape don't matter at all: you can embed the input in which you're interested in the finite control, as well.

-_Quinn
Reality Maintenance Group, Silver City Construction Co., Ltd.
[ Parent ]

thanks for the example (5.00 / 2) (#103)
by martingale on Wed May 15, 2002 at 08:39:41 PM EST

Now, if you mean "need an arbitrarily large amount of memory to compute all computable functions", well, of course it does: a given computable function can be arbitrarily large and work on arbitrarily large input!
That's exactly what I meant. Nothing fancy, just a counterpoint to the naive idea that four rules alone (or whatever) would encode the universe. I am a reductionist, but I put laws and initial conditions on an equal footing. Either one without the other is useless. That may be obvious to you, but I've also met people who think the laws alone are more important.

Thanks for the TM counterexample to my sweeping statement. I'll make sure to watch my mouth if you're reading :-)

[ Parent ]

Ahh, OK. (none / 0) (#124)
by _Quinn on Thu May 16, 2002 at 03:47:51 AM EST

When you said "Wolfram insists on the underlying program for the universe being very simple," I assumed you meant the dynamics of the universe as a physical system, not the state and its transition function.

The reason to be more concerned with the laws than the conditions is the unknowability of some large part of the conditions; and the value of theory is its predictive power, that is, its applicability outside of the current conditions.

That's not to say, however, that a layman might read Wolfram's statement to include the state, and thereby be decieved.

And thank you: it's not often that theoretical computer science comes in handy on K5. :)

-_Quinn
Reality Maintenance Group, Silver City Construction Co., Ltd.
[ Parent ]

the universe is not computerized (2.33 / 3) (#42)
by martingale on Wed May 15, 2002 at 06:32:21 AM EST

I haven't read Wolfram's book, so I'm not sure what exactly he claims. Although, while I'm at it, I wouldn't expect either Forbes, New Scientist or the NYT to properly review his book. I'll wait for a scientist or two to give his opinion before I pick up the book.

With the above disclaimer, the general idea that the universe is explainable as a giant computer (or CA or whatever) is bunk as far as modern physics sees it. According to Quantum Theory, physical states evolve continuously until a measurement occurs, when a completely random jump into a new state is made (the set of possible states can be computed). This randomness is inherent, it is not merely an approximation to the output of a very complex hidden mechanism (the Bell experiments were designed to test precisely this). So any computing system which could replicate Physics would replicate Quantum Physics and the Bell experiments and so would be nondeterministic, ie it would constantly flip coins.

This result obviously extends to Turing machines or cellular automata. None of them can simulate the Universe unless their rulesets include truly random choices. That's not the case for classical TMs or CAs.

This isn't to say that with sufficient effort, a given physical system can't be approximated arbitrarily well by a deterministic TM or CA; there are plenty of theoretical physicists doing just that. But the fundamental reality of the universe doesn't work that way.

[ Parent ]

randomness and programs (3.66 / 3) (#79)
by tiger on Wed May 15, 2002 at 03:36:54 PM EST

With the above disclaimer, the general idea that the universe is explainable as a giant computer (or CA or whatever) is bunk as far as modern physics sees it. According to Quantum Theory, physical states evolve continuously until a measurement occurs, when a completely random jump into a new state is made (the set of possible states can be computed). This randomness is inherent, it is not merely an approximation to the output of a very complex hidden mechanism (the Bell experiments were designed to test precisely this). So any computing system which could replicate Physics would replicate Quantum Physics and the Bell experiments and so would be nondeterministic, ie it would constantly flip coins.

There are many different algorithms to generate random numbers, and there are many computer programs that use random-number generators. To do quantum mechanics with a program, that program would, in effect, include calls to a subprogram that uses an algorithm to generate random numbers.

So, your argument fails, unless one requires that the underlying program for the universe be very simple, as Wolfram does. Your argument provides support for the idea that the underlying program for the universe is complex, not simple.

--
Americans :— Say no to male genital mutilation. In Memory of the Sexually Mutilated Child



[ Parent ]
random generators (3.66 / 3) (#107)
by martingale on Wed May 15, 2002 at 08:58:43 PM EST

There is no deterministic computer program for producing random numbers. Nobody has one (or it's a really well guarded secret). What you are referring to is pseudo-random number generation, which isn't quite the same.

Pseudo-random number generators are designed to produce a nonrandom sequence of numbers which pass any given set of statistical tests chosen more or less in advance. But there will always be a statistical test of randomness which the generator fails.

There are also physical sources of randomness which can be wrapped around computer functions, for example here. But these random number generators do not generate anything computationally. They simply translate the physical world's randomness into bits.

So the point stands. No computer can, on its own, simulate the Universe because it cannot produce, on its own, a sequence of independent random numbers.

[ Parent ]

More importantly (none / 0) (#114)
by X3nocide on Wed May 15, 2002 at 09:35:35 PM EST

There is a way to predict what the next value will be. If you have the initial conditions to the generator and the algorithm, you will be able to predict the results amazingly well ;)
I suppose you could call it the "follows the pattern created by this code" statistical test instead.

pwnguin.net
[ Parent ]
yep, you can actually formalize this (none / 0) (#116)
by martingale on Wed May 15, 2002 at 09:53:20 PM EST

and you end up definining a truly random (finite) sequence as a sequence for which there is no computer program which is shorter to write down than the original sequence. Quite a neat tie-in between probability theory and computer science there.

[ Parent ]

physical measurements (none / 0) (#127)
by tiger on Thu May 16, 2002 at 04:18:22 AM EST

So the point stands. No computer can, on its own, simulate the Universe because it cannot produce, on its own, a sequence of independent random numbers.

All physical measurements that physicists make are finite and limited, and whatever degree of randomness can be measured in physical processes, can easily be exceeded by the randomness produced by any of many random-number generators running on our own computers and using a large-enough bit size.

So, believe what you want, but physical experiments will never support your claim that the randomness in physical processes cannot be the result of a computer program making use of some random-number generator.

--
Americans :— Say no to male genital mutilation. In Memory of the Sexually Mutilated Child



[ Parent ]
uh...what? (none / 0) (#129)
by martingale on Thu May 16, 2002 at 04:52:43 AM EST

All physical measurements that physicists make are finite and limited,
I'm with you so far...
and whatever degree of randomness can be measured in physical processes, can easily be exceeded by the randomness produced by any of many random-number generators running on our own computers and using a large-enough bit size.
Do you even know what randomness means? Pseudorandom number generators do not generate any randomness whatsoever. That doesn't mean they aren't useful, but all of them are limited. Don't believe me? Be my guest: write a small C program which given a positive number n generates a sequence of n independent coin flips (50/50 probability). If you solve that one, be sure to let me know so I can take credit for giving you the idea. Hint: the trouble is making the coins flips truly independent.

So, believe what you want, but physical experiments will never support your claim that the randomness in physical processes cannot be the result of a computer program making use of some random-number generator.
I don't need to believe. Physicists have done the experiment already. Do a Google search on Bell's Theorem and Hidden Variable experiments. When you suggest that there is an underlying computer program which simulates physical reality, you are postulating a so called hidden variable model. Togheter with Quantum Mechanics, it is possible to derive certain probability inequalities which must always hold. These can be tested in an experimental setting, and that's precisely what has happened.

I'm afraid you're wrong on this one (bugged me too the first time I heard about it).

P.S. I expect you might also be interested in reading about the EPR paradox, on the same site.

[ Parent ]

Nonlocality (none / 0) (#133)
by x31eq on Thu May 16, 2002 at 06:33:44 AM EST

The first page you link to correctly states that Bell's theorem depends on two conditions:

The first condition means that the probability for a measurement at A is only a function of A's variables. This condition is known as the "locality" condition. The second condition means that one can "separate" the probabilities for measurements on A and B (ie: the probabilities for measurements at A and B are two independent functions). This is the "separability" condition.

Physicists generally prefer a random system to a nonlocal one, but this is a matter of preference. There's no proof that the "fundamental reality of the universe" is local and separable. Not having read the book either, I can't say what Wolfram is proposing. But ignoring this problem would be an uncharacteristic attack of imbecility. Let's assume his automata aren't bound by locality or seperability, or he takes a true random number generator as given.



[ Parent ]
nonlocality -> paradoxes (none / 0) (#134)
by martingale on Thu May 16, 2002 at 06:45:57 AM EST

Correct me if I'm wrong, I am under the impression that nonlocality introduces problems with causality, because it implies instantaneous information transfer, thus possible time paradoxes. That's why physicists prefer the random explanation, I'm told.

[ Parent ]

No (none / 0) (#135)
by spiralx on Thu May 16, 2002 at 07:41:40 AM EST

The whole point of Bell's Inequality was that you either kept quantum mechanics local while sacrificing causality or you allowed nonlocality and preserved causality. Oddly enough, scientists preferred to keep causality.

More info here.

You're doomed, I'm doomed, we're all doomed for ice cream. - Bob Aboey
[ Parent ]

am I confused or are you? (none / 0) (#156)
by martingale on Thu May 16, 2002 at 08:58:47 PM EST

Nice article by the way. I don't get your comment though. Didn't you mean realism when you wrote causality?

If you keep QM local (ie don't allow FTL communication) and accept Bell you cannot have hidden variables (ie realism according to the essay).

If you make QM nonlocal (allow FTL communication) and accept Bell you can find frames of reference which differ on which of two spacelike separated events came first (destroying causality in general, the idea that two inertial observers always agree on the ordering between events).

If you want hidden variables and locality, you reject Bell (the joint measurability objection is interesting, but I don't really understand it).

If you want hidden variables and Bell, you reject locality and come up with a weird preferred reference frames scheme.

Personally, I'm totally happy to throw out realism and keep both locality and Bell. Anything else looks much too tentative.

[ Parent ]

Wolfram claims true randomness (none / 0) (#143)
by CitAnon on Thu May 16, 2002 at 02:47:40 PM EST

Wolfram claims that he has created truly random processes using CA that have passed every known statisitcal test. This is different than a normal pseudo-random number generator, which only gives you numbers that look random for a limited sample size.

[ Parent ]
aargh, now I'm going to have to buy the book! [nt] (none / 0) (#153)
by martingale on Thu May 16, 2002 at 07:28:32 PM EST



[ Parent ]
But... (none / 0) (#131)
by MalcolmCleaton on Thu May 16, 2002 at 05:59:29 AM EST

...we don't know that quantum stuff is genuinely random, just that it appears to be random.

Imagine that every quantum decision anywhere is made by a very bad RNG on the computer simulating the universe, which chooses alternate 1's and 0's. How would we tell? There's so much unknown in how many other decisions would have occurred between any two events we measured that it would be effectively entirely random.

Thanks,
Malcolm.

[ Parent ]

that's called hidden variable theory (none / 0) (#132)
by martingale on Thu May 16, 2002 at 06:14:20 AM EST

Your comment is perfectly valid and sensible, but you're not the first to think of it. See my other comment for a link to what the physicists have done about it. The short of it is that Bell's theorem works out what we could observe if some deterministic (hidden from us, hence it's called hidden variable theory) RNG was doing the quantum decisions. It turns out there's an experiment which can decide the issue (does there exist a deterministic RNG or not?) and the result is there isn't. Now quantum mechanics itself could be seriously wrong, invalidating all this, but there's no evidence AFAIK.

[ Parent ]

There are no local hidden variables (none / 0) (#142)
by CitAnon on Thu May 16, 2002 at 02:43:01 PM EST

In other words, there are no hidden variables that do not violate general relativity. On the other hand, if you take away that constraint, then all bets are off.

[ Parent ]
QM and pseudorandomness (5.00 / 1) (#165)
by sigwinch on Fri May 17, 2002 at 03:09:40 PM EST

According to Quantum Theory, physical states evolve continuously until a measurement occurs, when a completely random jump into a new state is made (the set of possible states can be computed).
No. Quantum mechanics says
  1. Particles can interact at events. You can build experiments and watch them interact.
  2. If you run many identical experiments, you can draw a 4D histogram of the number of interactions.
  3. The shape of the histogram is determined by the wavefunctions of the particles involved.
  4. A particle's wavefunction evolves over time according to the Schrodinger equation. It also has to obey some conservation and boundary condition rules.
QM does not propose *any* description of how or why a particle interaction event occurs. It merely predicts how often that event will occur if identical conditions are created numerous times.
This randomness is inherent, it is not merely an approximation to the output of a very complex hidden mechanism (the Bell experiments were designed to test precisely this).
No, those experiments had nothing to do with randomness. What they demonstrated was that QM cannot be explained by *local* phenomena of any kind, either random or deterministic. Instead, QM is a nonlocal and/or noncausal phenomenon.

Incidentally, it doesn't take multi-particle entanglement to create nonlocality/noncausality. It's trivial to "stretch" a particle's wavefunction to enormous sizes, easily meters. Yet a stretched particle can interact at a nanoscopic event, and once it interacts the wavefunction instantly shrinks to a smaller size.

This result obviously extends to Turing machines or cellular automata. None of them can simulate the Universe unless their rulesets include truly random choices.
Even a trivial digital system can produce output that passes any randomness test you care to name, except for comparison with an identical digital system. A digital system with Planck-energy bits and a few eV of total energy would be random enough for God.

--
I don't want the world, I just want your half.
[ Parent ]

sigh (none / 0) (#170)
by martingale on Sat May 18, 2002 at 12:41:31 AM EST

I feel like I'm repeating the same thing over again and again (but not always to the same people). What's so hard to understand?

1. Particles can interact at events. You can build experiments and watch them interact.

2. If you run many identical experiments, you can draw a 4D histogram of the number of interactions.

3. The shape of the histogram is determined by the wavefunctions of the particles involved.

4. A particle's wavefunction evolves over time according to the Schrodinger equation. It also has to obey some conservation and boundary condition rules.

My description is pretty much the same as yours, given that both are wishy washy. 4) is a continuous evolution of the state, and 2) and 3) are an imprecise way of stating the measurement postulate, in which the only values ever observed are the eigenvalues of the operator which represents the observable. Right after the measurement, the state is identical to the eigenfunction corresponding to the eigenvalue obtained as a result of the measurement. If you represent the state as a normalized vector (point on the 1-sphere in Hilbert space) then the evolution of this vector experiences a discontinuous jump at the moment of the measurement. Your statement 1) can either be seen as a tautology (interactions must necessarily occur at spacetime events or they wouldn't be physical) or as a postulate that QM interactions are indeed observable (I'll take it that's what you meant).

So we come to the problem of whether the jump or collapse of the state into one of the eigenfunction states (I'll assume the spectrum of the observable operator is at most countable) is random or else occurs as the deterministic (ie perfectly repeatable in principle) consequence of an internal mechanism not directly modeled by the postulates of QM.

QM does not propose *any* description of how or why a particle interaction event occurs. It merely predicts how often that event will occur if identical conditions are created numerous times.
As you point out, QM does not describe *why* the interaction occurs, although it certainly describe *how* the interaction occurs: you can calculate it.

No, those experiments had nothing to do with randomness. What they demonstrated was that QM cannot be explained by *local* phenomena of any kind, either random or deterministic. Instead, QM is a nonlocal and/or noncausal phenomenon.
Here's what Bell's conclusion is, taken from this discussion (courtesy spiralx). Bell says "In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant."

So if you insist on a local physical mechanism to explain the apparently random choice of eigenfunction after the measurement, you must accept nonlocality and/or noncausality. But I specifically insist on no mechanism (ie it's a purely random choice as far as can be ascertained, even in principle), which it appears to me is a postulate perfectly compatible with Bell's theorem. There certainly might be a different experimental setup which invalidates my viewpoint, but I'm not aware of it, which means I can't take it into account here (*). In my argument, I use Bell only to dismiss the hidden variable point of view, ie if deep down you believe there's some local physical mechanism, you must contend with Bell's theorem.

Even a trivial digital system can produce output that passes any randomness test you care to name, except for comparison with an identical digital system. A digital system with Planck-energy bits and a few eV of total energy would be random enough for God.
No trivial (or nontrivial) digital system can produce output that passes any test I care to name. Give me such a system and I will, upon inspection, find a test which this system fails. Assuming you give me the underlying dynamical system, all I need do is find a function of the output variable whose autocorrelation function decays slowly enough. That's the pedantic way. In actual fact, it's often possible to deduce the period of the random number generator from an analysis of the algorithm. If you don't give me the dynamical system, I'll define a Turing machine which will try all functions out until it finds one. There always is one, otherwise the algorithm must be the same size as the output sequence.

Now if all you want to do is approximate randomness, I have no problem with your statement. But then if all you want to do is approximate the current model of the observed universe, we've just left philosophy and entered pragmatic engineering. I'm perfectly happy with that, but it kind of makes the current discussion void (which is probably good, I'm tiring of it).

(*) There appears to be a way of replicating the wave function collapse through unitary evolution only, by jointly analysing the composite system of observer+observed, which is a quite promising idea. Somebody pointed me to the paper by Albrecht "Following a collapsing wavefunction", but I can't remember who did so. If this idea can be expressed more universally I might become a believer.

[ Parent ]

Link to the article (none / 0) (#171)
by CitAnon on Sat May 18, 2002 at 06:45:50 AM EST

Look at comment #159

[ Parent ]
Here's a working link (none / 0) (#172)
by CitAnon on Sat May 18, 2002 at 06:48:32 AM EST

Albrecht's article

[ Parent ]
perfect, thanks to you and a clockwork llama [n/t] (none / 0) (#173)
by martingale on Sat May 18, 2002 at 07:01:47 AM EST



[ Parent ]
reply (none / 0) (#177)
by sigwinch on Sun May 19, 2002 at 03:24:33 AM EST

Your statement 1) can either be seen as a tautology (interactions must necessarily occur at spacetime events or they wouldn't be physical)...
That really is what I meant. It's the critical distinction between classical forces and quantum forces. The former interact over unbounded space and time, while the latter interact over finite spacetime volumes.
As you point out, QM does not describe *why* the interaction occurs, although it certainly describe *how* the interaction occurs: you can calculate it.
Terminology mismatch: by "how" I meant the internal evolution of the particle that resulted in the interaction event.
So if you insist on a local physical mechanism to explain the apparently random choice of eigenfunction after the measurement, you must accept nonlocality and/or noncausality.
My point was that the very concept of instantaneous wavefunction collapse implies 1) that the universe permits phenomena that are not Lorentz invariant and/or 2) that the wavefunction is a non-physical approximation.
No trivial (or nontrivial) digital system can produce output that passes any test I care to name. Give me such a system and I will, upon inspection, find a test which this system fails. Assuming you give me the underlying dynamical system, all I need do is find a function of the output variable whose autocorrelation function decays slowly enough.
There exist cryptographic cipher algorithms that have extremely long repetition periods (e.g., 2256), and ridiculously low autocorrelations as measured with a variety of mathematical functions. On a practical level, these algorithms are far more random than any measurements you can make. If a particle is governed by such an algorithm, the only way to predict its evolution is to observe most of its internal state (without disrupting its state in the process).

The Quantum Entanglement and Causality paper you mentioned points out that it isn't even necessary for the function to be complex. A simple sinewave will suffice: its sign a large distance from the origin is critically dependent on the exact frequency and the exact distance. If the wavelength is extremely short, even sub-proton-radius length variations between experimental runs will produce seemingly random results, as will tiny frequency variations.

--
I don't want the world, I just want your half.
[ Parent ]

ok, and more on rngs (none / 0) (#178)
by martingale on Sun May 19, 2002 at 04:46:18 AM EST

Terminology mismatch: by "how" I meant the internal evolution of the particle that resulted in the interaction event.
Ok, but note that your definition of "how" implicitly assumes there is a hidden internal mechanism inside the particle, if I understand you correctly. In that sense, I certainly agree with you that QM doesn't predict the how.

There exist cryptographic cipher algorithms that have extremely long repetition periods (e.g., 2256), and ridiculously low autocorrelations as measured with a variety of mathematical functions.
Sure. The Mersenne Twister for example has a period of 2**19937-1 and is equidistributed in 623 dimensions up to 32 bits per dimension. That looks almost like overkill, until you think about what it means. The output of MT guarantees at most a uniform random vector within the unit cube in 623-space. That's a pretty small physical system. Think of an Ising type model, maybe spin glass. The energy function alone is a joint function of N real variables, where N is the number of sites. With a square lattice, the side length is going to be SQRT(N). So if for example you want to pick a random starting point for a dynamical simulation, MT limits you to a lattice of 24x24 with single precision floating point numbers.

This is just an example and you might argue that the starting point should be chosen differently. My point is that arbitrary functions on the N-space unit cube crop up very easily, eg in stat mech. We don't have rngs which can rigorously handle many of the cases, ie when you want a uniform multidimensional quantity, it's not uniform except for small values of N. Instead, we pretend.

[ Parent ]

rngs and stuff (none / 0) (#179)
by sigwinch on Sun May 19, 2002 at 07:02:20 AM EST

Ok, but note that your definition of "how" implicitly assumes there is a hidden internal mechanism inside the particle, if I understand you correctly.
Correct.
In that sense, I certainly agree with you that QM doesn't predict the how.
Sure it does: God plays dice. ;-)
We don't have rngs which can rigorously handle many of the cases, ie when you want a uniform multidimensional quantity, it's not uniform except for small values of N. Instead, we pretend.
Is that just because you need speed more than anything else? Modern cipher algorithms can produce very large and uniform outputs, but they are rather slow. (E.g., the Twofish algorithm would take 0.5 milliseconds on a 100 MHz Pentium for your 24 X 24 X 32 bit example.) I guess you could compromise and periodically reseed the fast RNG using the crypto RNG.

--
I don't want the world, I just want your half.
[ Parent ]

an rng for all occasions (none / 0) (#180)
by martingale on Sun May 19, 2002 at 11:39:48 AM EST

Is that just because you need speed more than anything else? Modern cipher algorithms can produce very large and uniform outputs, but they are rather slow. (E.g., the Twofish algorithm would take 0.5 milliseconds on a 100 MHz Pentium for your 24 X 24 X 32 bit example.) I guess you could compromise and periodically reseed the fast RNG using the crypto RNG.
The Mersenne Twister is comparable in speed to the standard unix rand(3) random number generator, which incidentally is absolutely awful. Never use it for anything other than flipping a coin for what movie to go see at the cinema. I believe some implementations are up to four times faster than rand(), but in truth that's not really what I worry about. If you run rand 24x24 times on your machine you'll get a meaningful comparison.

Basically, I'm not very knowlegdeable about crypto, but here's my understanding: Crypto rngs are usually much too slow for any simulation work (and conversely simulation rngs like MT aren't high quality enough for crypto). The selection criteria are different. For crypto, you care about an unpredictable seed for a specific encryption algorithm, while for simulation you really need particular geometric properties (equidistribution in several dimensions).

In the latter case, you can bias (throw into doubt) all the random quantities you generate, uniform or otherwise, if you don't have the proper geometric properties; in my example, a 25x25 lattice would potentially be fatally crippled because the supposed uniform sequence was geometrically in some thin subspace of the cube rather than filling it completely. The program code would be the same, but simulating 24x24 would be more or less correct while 25x25 would be wrong. Of course there would be no way to know this except indirectly. Moreover, this has nothing to do with the actual period of the rng.

Now even if you had the time to use a crypto rng, it is likely that such an rng doesn't have a sufficiently large equidistribution property (not surprising, it's not designed for that).

One thing that some people do is use a physical source of randomness and store the observations on a CD. Then they read the bits from a file whenever they need them. It's a good idea, won't have any equidistribution problems, but the bits are very quickly used up.

Basically, what I'm saying is that even a reasonable toy physical system, unless it has special structure, is likely orders of magnitude beyond the capabilities of current random number generators. If you want to simulate the whole universe, you have no hope (but for that you'd probably need to use a quantum computer anyway, due to other complexity issues).

[ Parent ]

RNGs (none / 0) (#181)
by sigwinch on Sun May 19, 2002 at 08:25:45 PM EST

For crypto, you care about an unpredictable seed for a specific encryption algorithm, while for simulation you really need particular geometric properties (equidistribution in several dimensions).
The whole point of a cipher is that the output data has no detectable patterns. If it had patterns, you could use them to break the code. Being plotted in N dimensional spaces is nothing compared to the other mathematical torture tests a cipher has to endure before it is considered good.

--
I don't want the world, I just want your half.
[ Parent ]

perhaps (none / 0) (#182)
by martingale on Sun May 19, 2002 at 09:12:19 PM EST

As I said, I'm not sufficiently knowledgeable about crypto rngs to know their weaknesses, I guess it all comes down to the particular encryption method.

If you encrypt blocks of data using random numbers, you'll be fine for a range of block sizes depending on the rng, and then the number of blocks you can encrypt is proportional to the period of the generator divided by blocksize. However if you choose the blocksize too large, I'd expect problems. It all comes down to how many consecutive random numbers you use for the same block/calculation.

Another potential objection is that the output of the rng may not be completely uniform; that shouldn't necessarily matter for encryption, especially if you use up few (I don't know, less than 500) random numbers per block. I don't know what else to say. Perhaps if they can be speeded up, they'll be used more widely.

[ Parent ]

Tiger's Book (none / 0) (#189)
by maveness on Mon Jun 10, 2002 at 06:14:09 PM EST

It's hard for me to take at face value anything said by a person who wrote the following in (apparently) all sincerity:
There are three commonly recognized races: african, caucasian, and oriental. And there appears to be a strong correlation between the comparative traits of these three races, and the comparative traits of the two human genders: man and woman. Briefly, the correlation is that on a scale from masculine to feminine, the three races are ordered: african, caucasian, and oriental. Consideration for specific traits follow--and when speaking of specific traits, as they appear in each gender and race, the average case is assumed.
It goes on from there getting progressively more and more problematic. And this was just a section of his book I picked more or less at random.

Caveat lector.

*********
Latest fortune cookie: "The current year will bring you much happiness." As if.
[ Parent ]

stephen wolfram is a fucking badass (4.20 / 10) (#13)
by sayke on Wed May 15, 2002 at 01:59:45 AM EST

i've been fascinated by CAs since i first heard about them from an article he wrote, and his work pretty much defines the study of them. john conway did some cool stuff with em (most notably and popularly with his game of life ruleset), but wolfram has really done all of the interesting research in the area.

ya know, i shouldn't say that. lots of other people besides wolfram have been involved in making some truly awe-inspiring stuff - like, for example, this. fuckin aye that owned me. i spent two weeks dissecting it.

when i was reading the elegant universe i tried very hard to think of physics in terms of cellular automata. i gave up after i got about 90% of the way through elegant universe, though, because physics is just too bizarre and nonintuitive for me. i'd like to think i gave it a good whack, though ;)

then i read greg egan, and bewm, i started thinking about it again.

here's hoping wolfram does it right... a grand unified theory stated in non-traditionally computational terms!!()@#)(@#)(@# how much more hyped can you get? awww man, a new cosmology in terms of things i might actually have a chance in hades of understanding. holy fucking jesus shit, that would rule! =)


sayke, v2.3.1 /* i am the middle finger of the invisible hand */

Wolfram, Life, the Universe, and Everything (3.50 / 2) (#18)
by Lode Runner on Wed May 15, 2002 at 02:59:50 AM EST

TM implemented in Life? Now, where have I seen that before?

Ah yes, there was a slashdot conversation about it 18 months ago. One of the more entertaining /. moments, IMHO. Lots of links to that sycophantic Forbes article and lots of people belittling Conway's accomplishment while displaying their own ignorance re CA (Wolfram vs. von Neumann, turing machines vs. universal turing machines, and Life in general.



[ Parent ]

i think i came across it by way of... (4.00 / 2) (#27)
by sayke on Wed May 15, 2002 at 04:20:24 AM EST

this list, a couple of years ago or so, but i can't find the specific post. i didn't see the slashdot article.

interestingly enough, ray kurzwiel has a review and some reflections on wolfram's book here. cool shit, all right, but i don't understand what he means by "orders of complexity"... ah well.

cool forbes article, btw. hadn't seen that before. i think i'll show it to my friends if they want to know what i'm ranting about next time i'm trippin' daisies with em' ;)


sayke, v2.3.1 /* i am the middle finger of the invisible hand */
[ Parent ]

He he! It's always entertaining when... (3.40 / 5) (#14)
by SIGFPE on Wed May 15, 2002 at 02:15:36 AM EST

...someone who works in a tiny niche in a subject thinks it's the most important thing in the universe and publishes a book saying so.

Still, I'll probably order the book. Watch this space for a review.
SIGFPE

Wolfram's Big Head (4.76 / 13) (#20)
by Spork on Wed May 15, 2002 at 03:34:32 AM EST

In your only link to something other than Amazon, you refer us to a page on the dude's own website. After looking carefully, I found this page is a linkorama of worshipful articles in the popular press, all hailing Wolfram as a genius for his adolescent accomplishments.

I'm sorry, but the fact all of this is on stephenwolfram.com makes me think that the guy has lost any perspective of the fact that he is a fallible being. Boy geniuses, when they grow up, often assume that anything they pull out of their ass is the holy truth itself.

To be quite honest, I'd be a lot more impressed with Wolfram if he, on his site, stuck to the subject that he was researching, making it look like his conclusions can stand up on their own merits. Instead, he chooses to prop them up not because of anything in the content, but merely by declaring that these ideas sprang from the mind of the great Wolfram (like we should all drop to our knees and hail the revelation). This looks to me like a good sign that he lost all critical judgement about what springs from his own mind. That's not to say he's become dumb, but perhaps too arrogant to seriously consider that his wishful thinking might be wrong. Pedestian physicists usually have enough humility to censor themselves when they are spinning out into mere speculation (they know what it's like to be shut down and made to feel like shit by their once-professors and colleagues). This keeps them honest, careful and self-critical.

One gets the impression that Wolfram is so smart that no one ever managed to make him feel like a total idiot. If so, he probably never acquired the self-critical instinct to deeply question his conclusions in a fundamental way.

I say this probably makes him more prone to error than the average Cal Tech physicist.

Not quite (5.00 / 2) (#21)
by streetlawyer on Wed May 15, 2002 at 03:41:40 AM EST

One gets the impression that Wolfram is so smart that no one ever managed to make him feel like a total idiot

I would imagine that the shitkicking publishing company lawyers who massacred Wolfram over the Mathworld website might have introduced him to the phenomenon of street-smarts as opposed to book learning.

Btw, that's a useful general lesson; nobody in the entire world is smarter or more aggressive than a media industry lawyer.

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]

That had nothing to do with Wolfram (5.00 / 1) (#22)
by Kalani on Wed May 15, 2002 at 03:56:11 AM EST

That was Eric Weisstein's mistake. I doubt that it was much more than an annoyance for Wolfram. Wolfram's "street smarts" are rather well established I think, at least if the success of his company is any indication.

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
Wolfram supported him (none / 0) (#23)
by streetlawyer on Wed May 15, 2002 at 04:07:03 AM EST

True. But the size of Wolfram's company owes more to the fact that Mathematica is a fantastic product than to any triumphs of management. In my limited experience, they make it an absolutely painful experience trying to give them money.

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]
What were you trying to purchase? (none / 0) (#25)
by Kalani on Wed May 15, 2002 at 04:13:51 AM EST

I haven't had any problem getting a copy of the student version of Mathematica from them (and that requires even more effort on the part of the buyer than normal purchases).

I agree that Mathematica is a great product, and it's come quite a long way since Wolfram's original development of it. From what I've read, he's been spending most of his time on the management side of the development of Mathematica. He may be involved in public relations or even sales to some extent, but even if he isn't I don't think that detracts from his "street smarts." His company has lots of nice deals with universities and research institutions, so somebody's been doing a good job there. If it isn't Wolfram then at least Wolfram is wise for choosing good businesspeople.

Anyway, from Eric's notices on mathworld, I think that the problem was introduced long before he went to work for Wolfram Research. It seems a little silly to fault Wolfram for that.

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
Venture capitalists (none / 0) (#77)
by ucblockhead on Wed May 15, 2002 at 03:17:06 PM EST

What, they didn't want to bend over and give anyone with a checkbook control?
-----------------------
This is k5. We're all tools - duxup
[ Parent ]
addendum (4.00 / 3) (#24)
by streetlawyer on Wed May 15, 2002 at 04:10:57 AM EST

Sorry; my reply above looks rather churlish and gives the impression that I'm trying to cover up the fact that I misremembered the important detail of the identity of the guy in the Mathworld fiasco. That wasn't my intention; thanks for the correction.

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]
Smarter? (4.00 / 1) (#34)
by dipipanone on Wed May 15, 2002 at 05:51:16 AM EST

Btw, that's a useful general lesson; nobody in the entire world is smarter or more aggressive than a media industry lawyer.

More aggressive, I'll definitely give you. Better financed than everyone else is true as well. But smarter? Really?

Not that they're dumb, of course. But they do spend an awful lot of time using their paid-for intelligence to defend dumb ideas and impoverished arguments, and inevitably at least half of them will be wrong at any given time.

Having said that, as someone married to a lawyer, I'm well aware of the importance of avoiding personal litigation. If you're the person footing the bills, eating shit is invariably far less unpleasant and a damn sight more palatable than going to law.

--
Suck my .sig
[ Parent ]
Yes, smarter (none / 0) (#38)
by streetlawyer on Wed May 15, 2002 at 06:10:14 AM EST

Media industry lawyers are among the brightest people I know. They're the modern equivalent of the rabbinical scholars whose commentary fills up the Torah.

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]
Well.. (5.00 / 2) (#43)
by dipipanone on Wed May 15, 2002 at 06:49:04 AM EST

Media industry lawyers are among the brightest people I know.

I have to say I've only known one, and she's not dumb having gone to Harvard Law, but she's a bit of a whore (not a comment on her sexual habits) and didn't seem to me to have the sort of critical, enquiring intelligence that transforms the world. She's just started working for a Hollywood firm, and sees her job as a foothold into production.

I can't help thinking though, that for people who are possessed of that kind of intelligence, IP law doesn't seem like the most fruitful place to expend one's energies.

They're the modern equivalent of the rabbinical scholars whose commentary fills up the Torah.

Heh. Now I *know* you're trolling me. You wouldn't happen to *be* a media lawyer by any chance?

--
Suck my .sig
[ Parent ]
Mathworld flap (5.00 / 1) (#66)
by nucal on Wed May 15, 2002 at 01:57:25 PM EST

Couldn't figure out what you guys were talking about, so I looked it up. Here is Eric's version.

[ Parent ]
bingo (4.50 / 2) (#31)
by tiger on Wed May 15, 2002 at 05:31:55 AM EST

One gets the impression that Wolfram is so smart that no one ever managed to make him feel like a total idiot. If so, he probably never acquired the self-critical instinct to deeply question his conclusions in a fundamental way.

I think you have hit the nail on the head. And one can also add the fact that he is so rich that he is probably surrounded by sycophants who praise his ideas and his book.

--
Americans :— Say no to male genital mutilation. In Memory of the Sexually Mutilated Child



[ Parent ]
Wolfram (none / 0) (#46)
by CitAnon on Wed May 15, 2002 at 07:05:23 AM EST

Yes, Wolfram has a big head. Actually, many people who have worked with him have said privately that he is a control freak, a thoroughly arrogant SOB and a rotten scoundrel. Then again, people have said the exact same things about about Isaac Newton, Steve Jobs, Ahmed Zewail, Edward Teller, Norman Schwarzkhof, David Geffen.... Assholes abound. Once in a while, one of them shakes the world.

[ Parent ]
Not to say that this is one of those times (none / 0) (#47)
by CitAnon on Wed May 15, 2002 at 07:06:36 AM EST

But we don't know that this isn't one of those times either.

[ Parent ]
And with his credentials (5.00 / 1) (#48)
by CitAnon on Wed May 15, 2002 at 07:07:48 AM EST

One should at least give his ideas an honest and thorough look before dismissing them outright.

[ Parent ]
wow! (none / 0) (#49)
by martingale on Wed May 15, 2002 at 07:09:20 AM EST

I was about to reply but you caught yourself just in time. Congrats!

[ Parent ]

Precious list (4.00 / 1) (#73)
by medham on Wed May 15, 2002 at 03:08:43 PM EST

Teller and Schwarzkopf. Outstanding. To think that people told Teller he was nuts for wanting to nuke anything that moved (and many large things that didn't). Or how those damn Washington bureaucrats didn't want to let Schwarzkopf win the war against the I-raqis.

The real 'medham' has userid 6831.
[ Parent ]

Different ways to be an ass (4.80 / 5) (#85)
by Spork on Wed May 15, 2002 at 04:08:12 PM EST

The smart people that you list do screw up sometimes. For example, Jobs had his cube, or for that matter, NeXt. Despite the fact he's an asshole, these lessons have surely taught him enough humility to second-guess his impulses and have everything double-checked by colleagues (and not merely sycophantic ones).

I think we also need to make a distinction between mere assholes and know-it-alls. For example, one asshole I know understands that she is not the smartest person in the world, but pretty smart nonetheless. She sucks up to the few people smarter than her, but if she doesn't think you're one of them, she'll treat you like garbage. Still, she is aware of her limitations and so doesn't try to revolutionize her field in a single swoop, because she knows that she'd swiftly be put in her place by superior intellects. So, she is very careful to publish only the stuff that she has the capacity to defend, and these tend to be pretty small contributions that don't step on too many toes.

If Wolfram is an asshole, he is an asshole of an entirely different sort. He takes himself to be at the absolute top of the intellectual heirarchy (comparing himself to Newton and Einstein), and he has already said that small-mindedness among physicists and mathematicians (and biologists and philosophers!) will mean it will take a while for his analysis to take over these fields. He's just a priori sure that his speculations contain only truth, and that the only thing preventing his immediate takeover of academia are the psychological flaws of the present academics. It's like he can't even conceive of the possibility that there might be some cogent scientific and conceptual objections to his program.

This is indeed an "asshole" attitude, but it is also one that basically destroys everything that is good about science and academics. Most scientists put their ideas "out there" and see how well they stand up under the scruitiny of their colleagues. They hope the some of the ideas will make some impact, and that most will not contain glaring errors. I fear that Wolfram has been away from the academy too long, and he has forgoten that you can't do science by standing on a mound and making grandiose proclemations.

All this said, I still think the book might be interesting, but Woflram's very unscientific attitude will very much hurt it in the long run. From the few pages I have read, he clearly makes some mistakes (in matters outside of his field of physics) and you just know that he won't approach criticism with the attitude "alright, the book has a couple of mistakes, but also a couple of really good ideas that would be important to discuss." Just watch, when his first responses to reviews come out, they will basically be ad homminem attacks on the reviewer. This will create an atmosphere among scientists that the whole package is of marginal scientific value (a bunch of pretty pictures and grandiose declarations). I think this is too bad. There will probably be some really interesting stuff in there. Publishing it all in a shiny "popular" book means, however, that the stuff won't get distilled out and incorporated into general scientific debates for a long time to come.

[ Parent ]

scientistic knob (5.00 / 3) (#128)
by streetlawyer on Thu May 16, 2002 at 04:23:05 AM EST

I fear that Wolfram has been away from the academy too long, and he has forgoten that you can't do science by standing on a mound and making grandiose proclemations.

Wasn't there a patent clerk from Zurich, I forget the name, who did more or less exactly that?

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]

No way! (2.00 / 1) (#160)
by Spork on Fri May 17, 2002 at 06:16:18 AM EST

If it's the patent clerk I'm thinking of, then you're way off. He published three papers in 1905 alone (while still working in the patent office), all on quite different subjects. (One of those, the one on Brownian motion, won him the Nobel Prize.) He was in constant contact with the important scientists and was always exchanging data with them. And (this is important) he used the goddamn journals, like a serious scientist is supposed to.

It's a good thing, too. If he had isolated himself from top physicists and then tried to present his data in a coffee-table book, I seriously doubt anyone would have cared.

[ Parent ]

So, are you saying (none / 0) (#175)
by delmoi on Sat May 18, 2002 at 06:14:13 PM EST

That if you don't "use the god damn jornals" that you're ideas are not going to be right? Presumably if einstine did what wolfram did his e would still equal mc2
--
"'argumentation' is not a word, idiot." -- thelizman
[ Parent ]
credibility and "scientific process" (none / 0) (#183)
by visigoth on Mon May 20, 2002 at 02:42:17 AM EST

Well, of course the truth or falsehood of his theories in and of itself wouldn't change, but they would be far less likely to be evaluated and tested by the very people they need to be (the community of practicing scientists), which process is necessary for any theory to be widely accepted as "science".


[ Parent ]
15 years on the sidelines (none / 0) (#185)
by Spork on Tue May 21, 2002 at 08:19:13 AM EST

Seriously, we are supposed to think that Wolfram's book will be important to science after he has basically been missing in action from the scientific community for 15 years? Sure, he may have been a lurker and an observer, but that is a far cry from being a participant. The comparison to the famous patent clerk was totally off base, because that guy stayed in constant contact with the people at the cutting edge of physics. Wolfram, on the other hand, has been on the CEO circle jerk circut. See the difference?

[ Parent ]
Things you sort of already knew... (4.50 / 2) (#137)
by Lonath on Thu May 16, 2002 at 11:30:43 AM EST

I have read some of the book, and there are a few interesting things in it, but most of it seems like stuff I've seen before or at least thought about some, and I'm sure you have, too. His big result seems to be that all complex processes can be expressed in terms of the same simple pieces. Well, if you ever studied physics (like he did) you probably noticed that there were a finite number of fundamental particles and that the universe is made up of lots and lots of these things and that energy comes in packets and whatnot. This is known. He then shows that a simple CA can be used to create a Universal turing machine, and so therefore science has been looking at things in the wrong way and they need to look for simple solutions..simple calculations that can be used to represent everything. This is true. I believe this, but it isn't useful. When was the last time you programmed something with a Turing machine? Last week? Last month? Never? Why? Because it's a pain in the ass to use. The other idea that certain things have to be calculated and cannot be proved is well known such as in halting, incompleteness, uncertainty principle. However, I think most people get this idea. This is what scientists do. They have a huge body of knowledge and calculations that have already been done and they use them to do more complex things without having to rework all of the details over and over. We all know that there are only a few things that a computer can do, but the point is that you write code that does complex things, then you never have to again. You calculate things and store them so you don't have to calculate them over and over again. You won't build an entire model of something complex by using a CA. You learn about it and compute things in your mind and come up with models and formulas that represent a huge number of calculations in your mind so you don't have to constantly redo the same stuff over and over. I guess I'm disappointed. He seems to have stumbled upon something that many others have done before, and he seems to fail to recognize that science and thinking is the process of doing simple calculations piled upon each other until they get complex enough that you can see something interesting and then that causes you to be able to avoid those calculations and thought from now on. So you can't just reduce things to the simplest level of complexity because they would take too long to compute. You have to build on the complex generalizations created in order to advance.

[ Parent ]
Why do you love Wolfram so much? (1.00 / 1) (#167)
by bhouston on Fri May 17, 2002 at 04:38:19 PM EST

Hi Citanon.

Obviously you adore this Wolfram guy.  I can not understand why -- most of the talk about his "theories" are just PR stuff and not (yet?) substance.  Are you being paid to promote this guy's stuff?

Cheers,
-ben houston
http://www.exocortex.org/ben

[ Parent ]

I'm ignorant, but I must also wonder... (1.00 / 1) (#125)
by Bnonn on Thu May 16, 2002 at 04:08:01 AM EST

...why such a smart guy has a .com website. Is he running a company under his own name?

[ Parent ]
In two minds (4.25 / 8) (#26)
by streetlawyer on Wed May 15, 2002 at 04:17:06 AM EST

I'm in two minds on this. On the one hand, it has to be taken seriously, and my inclination is always to err on the side of controversial innovations, particularly when established opinion of scientists (usually the least open minded and most judgemental of people) is set against them.

On the other hand, the author's constant references to Principia Mathematica remind me uncomfortably of Newton's other great work, which took up a great deal of his intellectual life after Principia. This work was .... approximately 32 crates of utterly worthless meanderings on the subject of alchemy.

One thing I would have to say is that (using Amazon's excellent freebie take-a-peek feature), the patterns which he claims "explain the workings of the stock market" look remarkably similar to Eliott Waves, a theory of the market which is generally regarded as crank economics within the profession, but which certainly has its adherents. Hmmmm ...

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever

I don't know how well it works in predicting ... (5.00 / 2) (#29)
by Kalani on Wed May 15, 2002 at 04:49:45 AM EST

... the stock market, but there really is quite a bit to cellular automata (and related subjects). For instance, they can often be the testing ground for genetic algorithms. It's also been used to generalize complex systems that were previously special-case curiosities (I'm thinking of Craig Reynold's boids in particular -- that's actually been implemented as a cellular automata system).

There has been quite a bit of research done in CA-generated (or CA-based) neural networks, which have often been applied to certain subsets of stock market data. My textbook on nnets has a classic example of that, in fact.

You're right that his book could be pure quackery though. It's a bit too early to tell really (that's why the poll for this story kind of bothers me, there's no "I have no idea" option). I look forward to reading it though. :)

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
Principia... (3.33 / 3) (#53)
by sebpaquet on Wed May 15, 2002 at 08:54:07 AM EST

Just to set the record straight:
  • Philosophiae Naturalis Principia Mathematica (1687 or so) is Newton's seminal book on physics.
  • Principia Mathematica (1910-1913) is Whitehead and Russell's landmark work on mathematical logic and the foundations of mathematics.

----
Seb's Open Research - Pointers and thoughts on the evolution of knowledge sharing and scholarly communication.
[ Parent ]
pedant (4.28 / 7) (#54)
by streetlawyer on Wed May 15, 2002 at 09:03:04 AM EST

Those of us who can cope with the concept of two books having the same title (ie, the whole funky world) refer to Newton's book as "Principia Mathematica", or if we're feeling cool and hip in an unbuttoned kind of way, "Principia". Are you going to try to make the claim that there was any danger at all of confusion here, or were you just showing off?

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]
Confusion (none / 0) (#187)
by sebpaquet on Fri May 24, 2002 at 11:50:46 AM EST

Well, I was confused by the comment. I'm used to seeing Principia refer to Newton's work and Principia Mathematica refer to Russell and Whitehead's. I didn't know that the latter was actually used to refer to Newton. Google confirms that it is the case, although R&W have a clear edge.
----
Seb's Open Research - Pointers and thoughts on the evolution of knowledge sharing and scholarly communication.
[ Parent ]
Hey! Don't sneer at Newton's alchemy! (4.00 / 2) (#57)
by porkchop_d_clown on Wed May 15, 2002 at 10:34:16 AM EST

Those crates of meanderings were the basis for a whole series of lousy books by Piers Anthony!

Worthless. Harrumph!


--
I feel like I've lived my live in screensaver mode....


[ Parent ]
Which series? [nt] (none / 0) (#64)
by mcherm on Wed May 15, 2002 at 01:05:45 PM EST



-- Michael Chermside
[ Parent ]
The Incarnations of ??? (3.00 / 2) (#65)
by porkchop_d_clown on Wed May 15, 2002 at 01:10:41 PM EST

"To Ride a Pale Horse", etc...

The basic premise of that world was that Newton did the same thing for magic that he did for science: put it on a sound mathematical basis. In the books, technology is as likely to be based on magic as it is on science.


--
I feel like I've lived my live in screensaver mode....


[ Parent ]
Ah... that one (none / 0) (#184)
by mcherm on Mon May 20, 2002 at 01:15:08 PM EST

I'd missed or forgotten the reference to Newton as the basis for that world. But I have to say, I found it to be a VERY fun world... the odd mix of science and technology together was fun. (Although it waned in favor of pure magic as the series progressed.)

-- Michael Chermside
[ Parent ]
Crank economics (2.66 / 3) (#75)
by medham on Wed May 15, 2002 at 03:15:05 PM EST

You don't really think that economists can be cranks, do you? Have you ever seen how much math is an economics paper nowadays?

And it's quite wrong to say that Newton's alchemical work is worthless. As cultural documents of the thought of his generation, they will prove to be of far more worth to future psycho-dialectical historians than his soon-to-be-outdated physics.

Also, don't forget, that Newton solved the mind-body problem by rendering the concept of "body" meaningless. HNIC A. Koyre has some interesting things to say about this.

The real 'medham' has userid 6831.
[ Parent ]

wasn't that Descartes? (5.00 / 2) (#110)
by martingale on Wed May 15, 2002 at 09:12:42 PM EST

I always thought he had some mind-body "issues" himself.

[ Parent ]

Differing views (4.00 / 1) (#80)
by SIGFPE on Wed May 15, 2002 at 03:40:41 PM EST

On the one hand, it has to be taken seriously, and my inclination is always to err on the side of controversial innovations
Funny. Your self-perception is different from my perception from reading your posts to K5 Mr Copenhagen-man.
SIGFPE
[ Parent ]
Hahahaha (4.50 / 4) (#89)
by streetlawyer on Wed May 15, 2002 at 05:05:51 PM EST

I always love it when somebody turn out to still be nursing wounds from an encounter with me that I'd entirely forgotten.

You are, of course, still wrong. The Copenhagen Interpretation was the genuinely radical step in quantum physics, because it 1) introduced a distinction between observers and observed, 2) introduced genuine metaphysical (as opposed to epistemological) indeterminism and 3) suggested that there might be limits to knowledge (Bohr's positivism implies that the thing-in-itself is unknowable).

The Many-Worlds interpretation can only be seen as a reactionary move, aimed at making the universe safe for classical physicists by suggesting that all the scary quantum phenomena are simply the result of there being extra space-like and time-like dimensions. It gets rid of all the truly radical implications of quantum theory by shoving them off into an unexplained "somewhere else". The combination of wild unsupportable metaphysical assertions with utterly conservative physics is part of what makes the MWI such a repulsive fudge. Bohr struck exactly the right mix by being bold in his willingness to reinterpret physical law, while maintaining an admirable positivism about the scope of his claims. And that's why the Many Worlds Interpretation is for cunts.

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]

He he (4.00 / 2) (#91)
by SIGFPE on Wed May 15, 2002 at 05:11:20 PM EST

I've watched you defend the orthodox view of many things to many people (memes, sociobiology, memetics, QM). I had you marked down as Mr. Straight. I still do.
SIGFPE
[ Parent ]
Hahahaha (4.20 / 5) (#90)
by streetlawyer on Wed May 15, 2002 at 05:05:58 PM EST

I always love it when somebody turn out to still be nursing wounds from an encounter with me that I'd entirely forgotten.

You are, of course, still wrong. The Copenhagen Interpretation was the genuinely radical step in quantum physics, because it 1) introduced a distinction between observers and observed, 2) introduced genuine metaphysical (as opposed to epistemological) indeterminism and 3) suggested that there might be limits to knowledge (Bohr's positivism implies that the thing-in-itself is unknowable).

The Many-Worlds interpretation can only be seen as a reactionary move, aimed at making the universe safe for classical physicists by suggesting that all the scary quantum phenomena are simply the result of there being extra space-like and time-like dimensions. It gets rid of all the truly radical implications of quantum theory by shoving them off into an unexplained "somewhere else". The combination of wild unsupportable metaphysical assertions with utterly conservative physics is part of what makes the MWI such a repulsive fudge. Bohr struck exactly the right mix by being bold in his willingness to reinterpret physical law, while maintaining an admirable positivism about the scope of his claims. And that's why the Many Worlds Interpretation is for cunts.

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]

What is the fuss about? (3.57 / 7) (#28)
by jope on Wed May 15, 2002 at 04:49:09 AM EST

I didnt read the book, but from what info is
available from third parties, I am not too impressed. First, there is no fundamental difference between formulae and programs. Read any book on computational theory for this. Using stuff like CAs to model complex behavior has been the big buzz of chaos theory and not too much revolutionary stuff came out of this. (Some *usable* stuff, came out of chaos theory yes, but just read all the articles  from that time about the revolution it will be). I agree that it might be refreshing to go and just try to use different classes of models in some scientific areas. But this is already happening, and it sure is an evolution, not a revolution.

Yes it's good not to get too caught up (4.00 / 1) (#30)
by Kalani on Wed May 15, 2002 at 05:00:41 AM EST

And a CA system could be expressed as a mathematical formula anyway. I doubt that Wolfram is really fixated on ditching math as much as he is interested in describing old problems in new ways. I think that he probably takes issue with the "overapplication" of linear equations (or systems of such equations) to some classes of natural phenomena. Even if his method turns out to be very useful for predicting the shapes of galaxies and such, our traditional way of expressing natural processes will still probably be used as much as possible I think. Iterated functions are neat in that you can get complex behavior out of simple rules (the mandelbrot fractal and such, as very basic examples) but in the analysis of some problems I think that the method would be overkill. It's just a couple of multiply instructions to calculate the position of a falling ball after t seconds, but deducing that from a large CA system that simulates the physical world would take much much more time.

I'm going to read his book though. I'd like to know if there are any problems that benefit greatly from his method of analysis. I'm sure that there are bound to be at least some things (the possible explanation of the specific formation of galaxies, for instance, seems very interesting to me).

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
you've hit the nail there (4.80 / 5) (#32)
by streetlawyer on Wed May 15, 2002 at 05:37:33 AM EST

The big thing in this book, and the reason I'm going to buy it, is that Wolfram and his cellular automata might have come up with a way of making nonlinear modelling tractable. If that is the case, then he will certainly deserve to be put right up there with Newton and the rest.

The critique he appears to be making is slightly misplaced; everyone knows that linear assumptions are an approximation, and usually a very bad approximation indeed, but nobody knows any other way to go ahead. Particularly, nobody in the mainstream statistics community has really got behind neural nets and genetic algorithms because they are such a f'kng black box; a neural net will usually give a "good fit" to the data, but it doesn't deliver rigorous measures of goodness of fit or anything analagous to a standard error. which makes it more or less unusable. If Wolfram is opening up that black box, he's done a hell of a thing.

On the other hand, I suspect that what he will end up doing is asking us to buy Mathematica and trust in his methods, replacing a black box with a Stephen Wolfram-shaped one.

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]

I don't think that you need to worry about that (none / 0) (#35)
by Kalani on Wed May 15, 2002 at 05:55:02 AM EST

On the other hand, I suspect that what he will end up doing is asking us to buy Mathematica and trust in his methods, replacing a black box with a Stephen Wolfram-shaped one.

That would make him an awfully smart businessman though wouldn't it?

Seriously though, if you check out his website, you'll find that you can freely download all of the programs that he goes over in the book (they're Mathematica notebooks but you can download the free MathReader program to execute them). Also, Mathematica isn't at all required to test cellular automata. If you can program one in Mathematica then you can program one in C++ too. The only extra work you'd have to do would be in drawing the grid yourself (but that's not a difficult task at all).

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
the website, ach (5.00 / 2) (#37)
by streetlawyer on Wed May 15, 2002 at 06:07:51 AM EST

This was the root of my frustration with Wolfram the company. Their website just simply does not seem to work for me. I'm sure it's my fault, but by browser/connection just does not seem to acknowledge the existence of anything remotely Wolfram-related. Feh.

I was being a bit flippant above; not so much accusing him of following a proprietary solution as suggesting that if the "New Kind of Science" relies on trusting the uninterpreted results of long iterative computer simulations, it's never going to take off. People don't even really like the proof of the four-colour theorem.

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]

Oh (none / 0) (#40)
by Kalani on Wed May 15, 2002 at 06:16:45 AM EST

People don't even really like the proof of the four-colour theorem.

Yes, you're right. Unfortunately I think that people (mathematicians specifically) are just going to have to eventually come around to embracing computing devices. Hopefully I'll have more to say on the nature of his programs when I read the book. Luckily I have no such biases about CA or the four-color theorem. :)

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
don't bet on it (4.00 / 1) (#44)
by martingale on Wed May 15, 2002 at 06:58:39 AM EST

Unfortunately I think that people (mathematicians specifically) are just going to have to eventually come around to embracing computing devices.
Mathematicians embrace computing devices just fine, thanks. We do latex, dvips and lp, not to mention the odd pine or mutt. Oh yeah, and netscape on Solaris :-)

There is a world of difference between a proof and an observation. Physics is about observation. "Mathematical" investigations with computers tend to be about observation. But real mathematics is about insight into the system which you don't get from a black box, which your computing device represents. If you need Mathematica to prove a result and it takes 200,000 pages of printouts to write the proof down, that's no good. Lesson 101 is: a mathematical result is useless if you can't figure out what makes it tick within your own lifetime. Then there is the notorious fact that all programs have bugs. This is an invariant even against Moore's Law.

If you want to see what real mathematics with computers is/will be like, open Knuth's TAOCP. Now that's a treatment of computers in the mathematical style.

[ Parent ]

Well I'm not trying to start a flame-war (4.00 / 2) (#50)
by Kalani on Wed May 15, 2002 at 07:17:08 AM EST

There is a world of difference between a proof and an observation. Physics is about observation. "Mathematical" investigations with computers tend to be about observation.

Yes yes of course, but that doesn't mean that computers aren't valid tools for proof either. Pythagoras proved his theorem about the length of the hypotenuse of a right triangle with a simple picture, but that was all that was necessary in that case. It could be that there are a large class of problems that require you to exhaust all possible combinations of some set of things. Whether you do that by hand or with a computer, proof is proof. You don't even need to hand-check the printout or anything silly like that. The check for whatever properties you're looking for can be a part of the algorithm.

But real mathematics is about insight into the system which you don't get from a black box, which your computing device represents.

You know very well that it's not just a black box. It has well-defined mathematical properties and has been used thoroughly as a theoretical device to solve all sorts of problems (but use it as an actual device to solve some problems and you're suddenly heretical).

If you need Mathematica to prove a result and it takes 200,000 pages of printouts to write the proof down, that's no good. Lesson 101 is: a mathematical result is useless if you can't figure out what makes it tick within your own lifetime.

OK, it's not ideal, but if it is a solution and it's proven beyond any doubt then it simply must be accepted. It may very well be that there are no other ways to solve the problem but to exhaust every possibility (or some other such analogous situation). In cases like that, you just need to understand the algorithm ... even the output can be weighed analytically to determine whether or not it's what you want.

Then there is the notorious fact that all programs have bugs. This is an invariant even against Moore's Law.

That's untrue (although I'm sure you're just being cheeky). It does seem to be the case that more bugs are introduced as programs get larger and larger, but then most programs that are used to prove some thing or another aren't usually very large. Besides, if it is a complicated process that you're modelling then the computer will have a better chance of executing it flawlessly than a human would.

If you want to see what real mathematics with computers is/will be like, open Knuth's TAOCP. Now that's a treatment of computers in the mathematical style.

Thanks, I own the whole set (and am anxiously awaiting the next three books). Knuth enumerates many of the mathematical properties of computing devices and problems for which computing devices are ideally suited. Really, he goes out of his way to explain how the "black box" you mentioned earlier works. Knuth's work only adds to the idea that computers can be used as analytical tools.

I'm not trying to turn this all into a religious war or anything. I'm lighthearted about it all. I just dislike seeing an idea dismissed solely on the basis of its inelegance. If the (undeniably true) answers to the questions of life come out of my dog's nose, I'm OK with that -- just as long as the nose provides sufficient proof.

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
me neither (5.00 / 1) (#51)
by martingale on Wed May 15, 2002 at 08:13:38 AM EST

Okay, I'll tone down the rhetoric. We agree on some points. I was afraid you were some kind of experimental mathematics weenie who thinks that running the 3x+1 (Collatz) problem 5000 times "proves" it.

Yes yes of course, but that doesn't mean that computers aren't valid tools for proof either.
Agreed. In fact, they are becoming essential not just for combinatorics problems. Symbolic computation packages and tools such as Mathematica/Matlab are perfectly allowable and used in proofs provided much care is taken to check that the results are valid. That's the hard part. If you want to check that your computationally arrived result is valid, you need insight and understanding of the limitations of the computer: double precision arithmetic, valid or invalid limits, exponential growth of the number of computations, continuous dependency on initial conditions, whatever. There's a good chance that if you understand all this and how it applies to your problem that you can then find another, more elegant way to prove the result. All you really need is for the computer to tell you what the result looks like.

if it is a solution and it's proven beyond any doubt then it simply must be accepted.
Sorry to quote you out of context, but the hard part is always to prove beyond doubt. Sure exhaustive combinatorics searches can often be phrased that way, but dynamical systems for example is a different kettle of fish. In that case, it's the algorithm we don't understand (well it might be simple to write down) and simulating on a computer won't usually *prove* anything interesting.

It does seem to be the case that more bugs are introduced as programs get larger and larger, but then most programs that are used to prove some thing or another aren't usually very large.
It is a sad fact that complicated systems like Mathematica are used more and more frequently even for simulating small systems for which a C program would do. That's a problem because unrelated bugs can muck around with your program. It also means, in the case of Mathematica, that the exact *way* your problem is solved can sometimes be hidden. When finding the roots of some function for a subsequent calculation, which exact method is Mathematica using, and does it impact the approximation? Another source of error might be the hardware (Pentium bug) or the software layers (does the C library have an elusive bug?). Only abstract computers (like Knuth's MIX) don't have implementation bugs.

In summary, I'd say that I'm weary about proving results by computer, mainly because of the awareness of all the things that might go wrong. That doesn't mean the computer doesn't have its place like you said. But I'm not prepared to trust a system if I can't keep a good overview of it. Give me the detailed overview, and I'll accept the proof.

[ Parent ]

Mathreader (4.66 / 3) (#39)
by cameldrv on Wed May 15, 2002 at 06:11:13 AM EST

Unfortunately for the purposes of the code from the book, Mathreader isn't going to do you a whole lot of good. You can view the code, but you can't execute it. Furthermore, unless you know Mathematica, you're going to have a pretty hard time deciphering some of the programs as they are quite dense. There are one-liners that can expand to 20-30 of C++. I understand that WRI will be releasing "A New Kind of Science Explorer" which will include a simple interface and a restricted Mathematica kernel to execute the code.

[ Parent ]
Yes I just discovered that (none / 0) (#41)
by Kalani on Wed May 15, 2002 at 06:21:43 AM EST

I guess I should have actually looked at some of the notebooks before I opened my big fat mouth huh? :)

Maybe the book will explain the significance of parts of that code in more detail than you get from the little notebook files. If not, I'm sure that some programmers will eventually implement the CA systems he covers in his book (I'll certaintly give it a shot if there aren't any decent free simulations).

You're right about the expansion too. Some of the code in these notebooks uses symbolic integration, which would require LOTS of code in C++. ;)

Hopefully the centerpiece of his work will be CA systems though, and that'll be painless to duplicate in environments other than Mathematica. I guess I shouldn't really say anything more until I read the damn book. :)

PS: I think the MathReader program does already have a restricted Mathematica kernel. I remember using it to listen to the audio output of a CA system on his website a year or so ago by running a little applet in a Mathematica notebook.

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
A little tale of Wolfram. (5.00 / 5) (#58)
by doop on Wed May 15, 2002 at 10:38:35 AM EST

[...]Wolfram and his cellular automata might have come up with a way of making nonlinear modelling tractable.
Already have, for certain important cases, and quite some time ago.

A lot of effort has been invested in the last century or so by physicists and mathematicians, in order to understand the Navier-Stokes equations. These are the equations describing fluid flow: in order to have a quantitative understanding of anything from the water running out of a faucet to the swirly shapes made by cigarette smoke, you need to be able to solve these equations. Unfortunately, they are nonlinear, and difficult to solve in all but the most simple cases. Even trying to find numerical solutions or approximations using computers is difficult.

Enter Wolfram:- around 1986, he discovered that you could simulate the Navier Stokes equations using cellular automata. You aren't directly solving the equations -- they are never explicitly entered into the model -- but you can write down a set of CA rules which, if followed on a computer, will produce large-scale behaviour conforming to the NS equations -- physically realistic fluid flow is an emergent property of Wolfram's CA, in the same way that smoke rings are an emergent property of the smoke and air molecules of which they are composed. It had a lot of advantages over conventional methods for solving Navier-Stokes: it was always numerically stable and didn't crash or overflow, it didn't require floating-point calculation, since you could implement the CA with entirely Boolean operations, and it could very easily be split across many nodes of a massively parallel computer.

Now, as I understand it (I only became involved in this field a few years ago, and what follows is the best I've managed to glean -- I'd be grateful for clarification), Wolfram wrote this all up, and submitted a paper describing what he'd done to a journal, only to have it delayed or rejected. In the mean time, three other scientists published a paper describing exactly the same method, and to this day the technique is often referred to as "the FHP method", after the initials of these three.

Wolfram then set up his own journal, Complex Systems, to deal with ideas similar to his; as far as I know, he also stopped publishing in conventional journals. How much this is due to a fit of pique at the FHP incident, how much is due to his personal quirkiness, and how much is due to anything else seems to depend on who you ask. The impression that I've been given is that since then he's been very private and secretive (to the extent of paranoia) about his work, intending to blow the world away with this new book. Wolfram's paper (which is much larger and more in-depth than the FHP paper) is tantalisingly entitled "Cellular Automaton Fluids 1: Basic Theory". I'm not aware that a follow-on paper has ever been published.

Anyhow, the CA he described gave birth to its own little subfield: although it turned out to not be the revolution it initially promised (some thought it would solve the problem of modelling turbulence once and for all, but the CA fluid was found to have certain unrealistic properties), it and its progeny have a wide variety of applications to things that conventional fluid dynamics can't touch: there is at least one commercial outfit selling software based around this idea, and many more are using similar techniques for in-house modelling.

Oh, and Wolfram has a patent on his CA fluid dynamics technique. I don't believe that it has ever been enforced. It would certainly be very interesting if the book describes a way of doing for another field what the Wolfram/FHP CA has done for certain areas of fluid dynamics.

[ Parent ]

Very interesting, thanks (5.00 / 2) (#59)
by streetlawyer on Wed May 15, 2002 at 11:08:17 AM EST

I don't suppose you know of any mirror of that paper on a webserver not connected to the Wolfram organisation? As I mentioned elsewhere, for some reason I can never get anything but "Connection timed out" from them.

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]
Wolfram's papers (5.00 / 1) (#60)
by doop on Wed May 15, 2002 at 11:28:47 AM EST

Sorry, I don't know offhand of any public mirrors of his paper. It was published in the Journal of Statistical Physics, Vol. 45, nos. 3/4, p471--526 (1986) , which you should be able to find in your friendly neighborhood university library. There is a book, Lattice Gas Methods for Partial Differential Equations, which contains Wolfram's Paper, the FHP one, and a lot of other stuff.

The FHP paper is in Physical Review Letters, Vol. 56 no. 14, p1505--1508 (1986): you can view the abstract online, and download the paper if you have a subscription. Otherwise, there are lots of web pages on the method -- it's evolved considerably since 1986.

[ Parent ]

If you don't mind buying a book intead (none / 0) (#123)
by Kalani on Thu May 16, 2002 at 02:08:51 AM EST

Cellular Automata and Complexity by Stephen Wolfram from amazon.

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
Things are tough all over (5.00 / 2) (#84)
by epepke on Wed May 15, 2002 at 04:06:57 PM EST

Disclaimer 1: I know Wolfram very slightly, have hung out with him at some parties, and he was tight with Tony Kennedy, with whom I used to work. Disclaimer 2: I used to work at a cross-disciplinary research institute, now defunct (which is where I worked with Tony)..

I feel his pain. It is almost impossible to get a cross-disciplinary paper published unless you are already known in the target (not the source) field. Wolfram is best known for math. He didn't have a chance.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
Shouldn't have been that tough, though. (4.66 / 3) (#95)
by doop on Wed May 15, 2002 at 06:08:14 PM EST

It is almost impossible to get a cross-disciplinary paper published unless you are already known in the target (not the source) field.
I don't think the paper was particularly cross-disciplinary -- it seems to fit fairly nicely into the general category of mathematicical physics. Besides, he'd already published in both mathematics and physics.

I've heard people suggesting (here we go, hearsay mode on...) that one of Frisch, Hasslacher or Pomeau, or a colleague, might have been the referees for Wolfram's paper, and deliberately delayed it, or worse. Or at least that Wolfram suspected this, giving rise to his rather less communicative behaviour since.

Why did the FHP paper get published first? Maybe because it was shorter and went to a high-turnover letters-type journal, maybe it was just normal referee arsiness. Amidst the murk, I've no idea what the real story is: it could just be a fairy story told to innocent young graduate students.

I'm still rather surprised that papers on lattice gases tend to cite FHP in preference to Wolfram. Science? Apolitical? Hmmm.

[ Parent ]

A new Godel Escher Bach? (4.00 / 6) (#56)
by Paul Johnson on Wed May 15, 2002 at 09:21:42 AM EST

Reading about this book, I'm reminded of Godel, Escher, Bach. That was another huge magnum opus encompassing the authors personal interest in a wide range of stuff, and also revealing a deep unity between three apparently diverse subjects.

I don't know if Wolfram is a genius or nutter, but I'm certainly looking forwards to finding out.

Incidentally he sounds a lot like Newton, who also considered his contemporaries to be idiots, was obsessively secretive about his work, and was generally an unpleasant person to anyone who dared to disagree with him. I want to read his book, but I don't particuarly want to meet the guy.

Paul.
You are lost in a twisty maze of little standards, all different.

hofstadter and jewish mysticism (2.77 / 9) (#83)
by disney on Wed May 15, 2002 at 03:58:26 PM EST

the real purpose behind GEB was that it transmitted hidden Kabbalistic Hebrew symbols in a mathematical language, by a process of semi-theological rational hermeneutics. The fugue conceit was simply a diversion.

[ Parent ]
Huh? (1.00 / 2) (#100)
by jazzido on Wed May 15, 2002 at 06:59:49 PM EST

Explain, please.

--
"Patriotism is the last resource of scoundrels" (Samuel Johnson)

[ Parent ]
shh... (none / 0) (#112)
by martingale on Wed May 15, 2002 at 09:21:13 PM EST

I expect he could, but then he'd have to kill you ;-)

[ Parent ]

No reply.... (none / 0) (#117)
by CitAnon on Wed May 15, 2002 at 09:59:59 PM EST

Poor Jazzido must already be a gonner!

[ Parent ]
GEB (3.50 / 2) (#140)
by Wildgoose on Thu May 16, 2002 at 01:11:30 PM EST

I loved Godel, Escher, Bach an Eternal Golden Braid as well.

And I've had "A New Kind of Science" on order from Amazon for well over a year, ever since I first heard of it.

Maybe now the damn thing will finally arrive...

[ Parent ]

the difference was (4.25 / 4) (#163)
by kubalaa on Fri May 17, 2002 at 11:05:55 AM EST

Hofstadter didn't have the conceit to claim he'd invented "A New Kind Of Philosophy."

[ Parent ]
I'm reading A New Kind of Science (4.75 / 12) (#62)
by KnightStalker on Wed May 15, 2002 at 12:35:48 PM EST

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."

Interesting (4.00 / 2) (#68)
by CitAnon on Wed May 15, 2002 at 02:30:35 PM EST

Space and time are discrete on a small scale.
Don't know about what's meant by a network of nodes. However, one of the results of string theory is that there is a lower bound in the "fine grainedness" with which one could probe spacetime.

[ Parent ]
Casuation vs. similarity (3.00 / 1) (#69)
by CitAnon on Wed May 15, 2002 at 02:31:55 PM EST

Empahsizing the latter without going into the former would disappoint me too.

[ Parent ]
Causation (4.50 / 4) (#78)
by KnightStalker on Wed May 15, 2002 at 03:22:28 PM EST

Wolfram gets closest to establishing an actual causative link between CA phenomena and nature when he describes the growth of stuctures in plants that have Fibonacci properties (like the swirls in the center of sunflowers and daisies, or the way branches can grow in a spiral pattern around tree trunks, and also when he describes the growth of snowflakes. When he talks about particle physics and the structure of space, however, it looks like nothing more than wild speculation. It seems plausible to me, but then Christianity also once seemed plausible to me. ;-)

He describes the growth of plants, for example, by saying that certain plant cells take on certain growth characteristics (like branching, or starting a new sunflower seed) when the local concentration of certain chemicals reaches some limit. When the cell changes in response to the chemical, however, it depletes the local concentration, which affects the cells nearest it. This produces emergent behavior which works according to similar rules as cellular automata.

Again, I'm not finished with the book, so my thoughts might change by the time I finish.

[ Parent ]

Network of nodes (4.50 / 2) (#74)
by KnightStalker on Wed May 15, 2002 at 03:13:13 PM EST

As opposed to a fixed, graph paper style grid of cells, which is what you usually run a CA on, a network of nodes would consist of individual, separated cells that have multiple outgoing and incoming connections to other cells. Wolfram draws it as sort of a scaffold-like framework, where the intersections are nodes with three connections to adjacent nodes. The difference between the two is very significant when you're writing a program to store large numbers of data items. Networks can be set up with various structures, such as linear lists, hierarchical trees, a two-dimensional array with ragged edges, or pretty much any other form. From the point of view of data inside Wolfram's structure, though, I'm not sure what the difference is. There still is no way for a cell to "communicate" with any cell other than its neighbors.

[ Parent ]
network (none / 0) (#162)
by codemonkey_uk on Fri May 17, 2002 at 08:48:01 AM EST

I've not read the book, so I'm thinking on my feet here, but how about links in the network representing each of the "forces" described by modern physics, so that links have strengths, like you'd set up in a neural network.

It sounds all very cross domain and speculative, but even if it has no connection to reality, some interesting, and practical applications are bound to arrise from it.
---
Thad
"The most savage controversies are those about matters as to which there is no good evidence either way." - Bertrand Russell
[ Parent ]

after more reading... (5.00 / 1) (#164)
by KnightStalker on Fri May 17, 2002 at 11:58:06 AM EST

Disclaimer: I had to skip over a lot of stuff that was way over my head, and I don't even partly understand Wolfram's network model. :-)

It seems that I was thinking about it wrong. The important thing in these networks is the pattern of connections, not the intersections. His particles, including force carrying particles like photons and gluons, are manifested as stable irregularities in the pattern of connections between nodes.

The more I think about this, the more sense it makes. The only problem is, I'm probably thinking about it wrong, and it all seems to be speculation anyway.

[ Parent ]

His point abou tthe universe (4.66 / 3) (#70)
by CitAnon on Wed May 15, 2002 at 02:36:42 PM EST

His point about the universe, which is also something that more and more people are coming to believe and really, an idea that has been around for a long time before his book is that everything that everything in the universe is computation, or, at least, that's a way of looking at the universe that gives you deep insights.

[ Parent ]
To a bricklayer, the universe is made of bricks (4.50 / 8) (#63)
by StephenThompson on Wed May 15, 2002 at 01:01:47 PM EST

It is almost certain that future physics and cosmologies will look like computer algorithms and bits. This is because of the nature of man to confuse familiar things with fundamental things.

If you have a hammer, everything looks like a nail. If you are a programmer, you understand the world in terms of programs. If you are a mathematician, math. Priest..souls and angels. Cow herder..cows. Heck, when I play a video game too much, I start to model my world after the game, not always to bad effect either.

This isnt a totally bad thing, but we should be clear that the tool is not the subject being studied.

Yes... (4.50 / 2) (#67)
by Rocky on Wed May 15, 2002 at 02:21:57 PM EST

...I live on a weird electric carousel.

That's why I think of everything in terms of spin, charge, color and strangeness...

If we knew what it was we were doing, it would not be called research, would it?
- Albert Einstein (1879 - 1955)
[ Parent ]

But.... (5.00 / 1) (#71)
by Rk on Wed May 15, 2002 at 02:43:57 PM EST

You missed one: mass. All objects, well at least most objects, have a mass. Normal stuff has a positive mass, tachnyonic matter, if it exists, has an imaginary mass, and "exotic matter", if it exists, has a negative mass. Quarks have a mass, AFAIK, and so electrons. Basically, there are fermions and bosons, the latter being restricted by the Fermi exclusion principial, which states that two fermions can not have identical quatumn properties (= can not be at the same place, at the same time etc). Fermions have a spin which is a fracture of an integer (such as 1/2 or 1/3) and bosons have an integer spin (0, 1, 2). Colour is to the strong nuclear force as charge to the electromagnetic force. A quark is a fermion, while an electron is a boson (excuse me if I'm wrong on that point).

Strangeness, by the way, is not an attribute of any fundamental particles I know of. It might be an attribute of some K5 readers, however.

[ Parent ]

Never... (5.00 / 1) (#81)
by Rocky on Wed May 15, 2002 at 03:53:33 PM EST

...let the truth get in the way of a good story.

Besides, mass isn't in the Standard Model: that the whole problem.

How about flavor?

If we knew what it was we were doing, it would not be called research, would it?
- Albert Einstein (1879 - 1955)
[ Parent ]

fwiw, you completely miss the point (none / 0) (#190)
by momocrome on Sat Jul 13, 2002 at 12:46:37 PM EST

I know this is an old comment, you may or may not ever see this, but I thought it was important to point out the flaw in your comparisons: Certainly one's specialty or preoccupation shapes one's worldview. This phenomenon extends to every branch of human pursuit. The working concept here is that it is a process of finding the most accurate world-view that is the pursuit. It is entirely inconsequential and irrelevant whether this 'most accurate' world-view blossoms forth from the mind of someone pre-disposed to perceiving the world around them in the typifed manner of their field. What is important is the utility of the new point-of-view.

The value and validity of the world view is not tied to any aspect of the personal quirks or professional outlook of the originating theorist. Frankly I find your thoughts on the matter to be pessimistic in the extreme. I believe it is the act of cultivating this extreme conceptual bias that empowers the theorist and extends the sciences. From the tone of your spot above, you'd seem to reject the product of such a selfless personal sacrifice. The professional you dismiss for bias has in fact devoted their entire being towards the pursuit of more coherent understanding. To dismiss them for this is ridiculous and perverse!

"Give a wide berth to all that foam and spray." - - Lucian, The Way to Write History
[ Parent ]

negative evaluation (2.33 / 3) (#72)
by xah on Wed May 15, 2002 at 03:03:25 PM EST

For the entire known history of science, each successful new theory has provided us with the ability to ask more questions about the universe, not fewer. To the extent that Wolfram says he has found a simple concept that explains many complex concepts, Wolfram's theory would decrease the number of questions we can ask. Thus, he has either made the definitive statement of science for all time, or his theory is mistaken. I suspect the latter.

Untrue (2.00 / 1) (#86)
by trhurler on Wed May 15, 2002 at 04:17:52 PM EST

The entire known history of science consists in theories that were ALWAYS simple concepts that explain many complex concepts, and the reason the questions have always expanded is because the more general concept always led to lots more specific investigations, some of which suggested that there might be an even more general concept than our present one.

As such, Wolfram is either wrong or else the next rung on the ladder. We probably won't definitively know which for at least a few decades, unless he's truly wasted the last 20 years of his life.

--
'God dammit, your posts make me hard.' --LilDebbie

[ Parent ]
still negative (none / 0) (#96)
by xah on Wed May 15, 2002 at 06:11:25 PM EST

Here's a fascinating Wolfram interview.

It seems to me that Wolfram is caught in a dilemma between saying either: as I have supposed he said, that he has found the four-line computer program that controls the universe, and as a result many scientific endeavors now become only derivatives of his "new kind of science," and the pool of available scientific questions decreases; or he has found that in the many complex things of the universe can be found similarities, but not any similarities that might be useful to science. Either he has the god-principle or he does not.

Alternatively, he might be saying that the methodology of biology is superior to the methodology of particle physics. Why write a long book to say that, when many scientists have said the same thing for years? See A Tour of the Calculus.

I guess my major point of resentment is that he claims to have overthrown all sciences, apparently including the human sciences while no doubt ignoring them.

[ Parent ]

I think you misunderstood him (4.75 / 4) (#97)
by trhurler on Wed May 15, 2002 at 06:26:59 PM EST

I don't believe he claims to have overthrown anything in any meaningful sense; what he appears to be saying is that he has a better language in which to discuss things, and that more things can be discussed in his language. Maybe he's right. He specifically says he doesn't know "the program of the universe," but believes(not knows) that it exists. That's no bold claim; most physicists would say the same thing in different terms.

In any case, getting all huffy and saying "oh, he can't be right because I don't like his tone and his claims are too much" is the mark of a turf warrior bureaucrat, not an honest scientist. When you have real criticism to level, do so, but as long as you're speculating on 20 years of a man's life based on a 20 minute interview, maybe you should find something more profitable to do?:)

--
'God dammit, your posts make me hard.' --LilDebbie

[ Parent ]
still, it doesn't seem right (none / 0) (#118)
by xah on Wed May 15, 2002 at 11:08:39 PM EST

I stand by my statements, though I didn't realize they had so much power. Giving science a new language sounds like adopting the methodology of biology over the mathematically intensive methodology of the hard sciences. If that is all he's saying, that's not revolutionary. See A Tour of the Calculus. If his conclusion is wider, then perhaps he is suggesting that there is a god-principle without identifying what it is. If that is his suggestion, unless he has actually got that god-principle by the horns, or is increasing the range and kinds of questions we can ask, it's not a scientific advance. Without coming to a firm conclusion on the book, I've registered my doubts.

[ Parent ]
Well, (none / 0) (#139)
by trhurler on Thu May 16, 2002 at 11:50:56 AM EST

Biology certainly does not use a programming language paradigm to describe things in any sense that I'm aware, so I think he's onto something new here, if indeed his method produces useful results. I would say the only way to judge whether it produces useful results is to examine his claims in detail. I personally would find it remarkable if his method did not improve matters, and am mainly surprised that nobody has tried it before more than that he has tried it. After all, one of the fundamental beliefs of science is that things follow rules and have properties. The best, most flexible way we know to describe those properties is programming languages - not math.

--
'God dammit, your posts make me hard.' --LilDebbie

[ Parent ]
again, unconvincing (none / 0) (#144)
by xah on Thu May 16, 2002 at 02:48:28 PM EST

So, is he just trying to mathematize language and logic; or, in other words, complete the project Wittgenstein said could not be done, the project that Bertrand Russell could not finish? We do agree that we need to read the book to say something more firmly than we already have.

Should be interesting.

[ Parent ]

I think... (none / 0) (#149)
by trhurler on Thu May 16, 2002 at 04:00:23 PM EST

That rather than try to "mathematize" language, he is swapping mathematics out and language in - but not natural language. I want to read his book.

--
'God dammit, your posts make me hard.' --LilDebbie

[ Parent ]
Eh? (5.00 / 1) (#155)
by Kalani on Thu May 16, 2002 at 08:11:24 PM EST

So, is he just trying to mathematize language and logic; or, in other words, complete the project Wittgenstein said could not be done, the project that Bertrand Russell could not finish?

I assume that you're talking about Russell's Principia? If that's the case then I think that you've got it rather backwards. Russell wanted to construct a system from which all truths could be derived (that's not an incredibly satisfactory description of it but I think it's approximately right). That's the mess that Godel ended, but it hasn't got much to do with what Wolfram is putting together as far as I can tell.

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
More profitable (none / 0) (#186)
by Rasman on Thu May 23, 2002 at 06:53:47 AM EST

You mean there's something more profitable we could be doing with our time than reading K5???


If only I could break away from the intellectual masturbation that is K5 and do some real work...sigh...

[ Parent ]
Question (2.25 / 4) (#76)
by medham on Wed May 15, 2002 at 03:16:59 PM EST

Has anyone ever played D&D with Wolfram?

I've heard reports that his worlds are very magic-poor and that he doesn't have much patience for rules-lawyering.

The real 'medham' has userid 6831.

All I want to know is, (3.00 / 2) (#82)
by disney on Wed May 15, 2002 at 03:55:13 PM EST

is he D and D or is he a canary?

[ Parent ]
my POV (1.57 / 7) (#88)
by disney on Wed May 15, 2002 at 04:37:40 PM EST

I've accepted the fact that if I am to matter at all, I must matter to me. This realization, fearful though it may be to most people, has set me free. I may or may not matter to other people, and I do not matter outside of the context of a human being's consideration(be it mine or someone else's.) Why are we here? There is no purpose. Teleological investigations into things not caused by human efforts are mere foolishness, and while you might use words like "purpose" outside that context, you must remember their meaning to be something other than teleological in nature when put to that use.

Does it hurt to realize that there may be nothing more to it than what you see? Not really. There's so much to be done, and so many good reasons to do it... life as an end in itself is not life without purpose.

Salon Article (3.00 / 5) (#92)
by EraseMe on Wed May 15, 2002 at 05:15:00 PM EST

Salon also has a write-up.

What's the big deal? (3.50 / 4) (#106)
by naugerrooger on Wed May 15, 2002 at 08:56:31 PM EST

If the guy has set up some stuff to show that complex patterns can come from simple rules, I mean what's so different about what he's doing. I tried to use Mathematica one time, but it made my head spin. What can it do that a graphing calculator can't?

And what's his picture doing on the cover? I don't think it'll help sell many copies.
-- "Would?" Alice in Chablis

Lots, but one fun one is ... (5.00 / 1) (#119)
by Kalani on Thu May 16, 2002 at 01:10:44 AM EST

What can it do that a graphing calculator can't?

N[Pi,$MaxPrecision=50000000]

-----
"Nothing says 'final boss' like a giant brain in a tube."
-- Udderdude on flipcode.com
[ Parent ]
i already had this idea and so did lots of others (2.80 / 5) (#111)
by turmeric on Wed May 15, 2002 at 09:20:04 PM EST

its called 'demos'. the 'demo scene' in the 80s.

anyone with a basic grasp of physics and a little experience writing a water demo would realize there was something here untapped by the academic school system approach to the phenomena.

there are astrophysics folks starting to do something kind of the same. its not like he invented it.

but anyways, me, and im sure lots of others, we knew this was out there. but i knew that our society is too perverted and sick with violence and hatred and warfare, and that this technology would surely plunge us into some disgusting world war or some horrific eugenics project. so i didnt do anything with it.

to really progress we need spirituality not more science.,,, new scientific theories grow on trees.

spirituality and suicide bombers (2.00 / 2) (#113)
by boy programmer on Wed May 15, 2002 at 09:28:51 PM EST

The suicide bombers are 'spiritual'

[ Parent ]
Uhhh... (4.00 / 1) (#146)
by gmol on Thu May 16, 2002 at 02:54:01 PM EST

Bumpmapping some waves on an image doesn't exactly show that something is "untapped by the academic school system approach to the phenomena"...it's a cool effect but understandable to anyone with highschool math.

[ Parent ]
A new kind of arrogance (2.85 / 7) (#120)
by merkri on Thu May 16, 2002 at 01:23:34 AM EST

Ah, yes ... everything I love about science. An arrogant man with a high IQ toying around with his computer and declaring his impressions to be the one original truth. Never mind that what he writes about have been described in detail many times over in various ways by other individuals. He was a prodigy, so we have to listen to him, and give credit to whatever he says as his.

This sort of thing is exemplary of Kuhn's big mouth factor to a frightening extent.

What is so frustrating to me is the number of individuals who will attribute god knows what to this man just because he claims it to be so and because he was a prodigy. Meanwhile, everyone who has either passed into history or is too humble to take credit for more than their contribution gets no credit.

As someone else pointed out, this tome is full of Wolfram's speculation and narcissism. It is full of "seems to me" and whatnot, without real credit to those who have already expressed whatever ideas may have merit. Wolfram's egotism knows no bounds: of course there's no one else smart enough to have such ideas, so there's no point in considering the fact that many of his ideas may be old, and thus no reason to bother citing anyone.

Ridiculous. It's almost as if the idea of Monte Carlo simulation was unknown to him, because he's too arrogant to bother stop playing with the computer and read what other people have to say. Maybe if he listened to others for the past 20 years rather than bask in the glory of Mathematica (overrated perhaps? Need I say MATLAB? Octave? S? R? Lisp? FORTRAN?), he wouldn't sound so absurd.

I say it's a joke. It's the story of one arrogant, albeit intelligent, man's realizations of things that have been known to others for some time. It reads like a cautionary tale to those who think they don't need to pay attention to the "stupid people around them".

Quick to judge, aren't you? (4.00 / 4) (#121)
by greenrd on Thu May 16, 2002 at 01:33:15 AM EST

I say it's a joke.

Have you read the book?


"Capitalism is the absurd belief that the worst of men, for the worst of reasons, will somehow work for the benefit of us all." -- John Maynard Keynes
[ Parent ]

Kuhn's big mouth (4.33 / 6) (#126)
by streetlawyer on Thu May 16, 2002 at 04:16:04 AM EST

A classic example of what's wrong with philosophy of science these days. You understand fuck-all about the underlying maths, and you've got ignorance leaking from every pore on this one. Kuhn's theory is a good one; your application to this case is an embarrassment.

First up, "everyone who has either passed into history or is too humble to take credit for more than their contribution gets no credit.". That's ridiculous. This is a book about cellular automaton theory. Cellular automaton theory began with von Neumann, and the next person to write anything substantial about it was ... Wolfram. That's it. This is well documented in the literature, and your suggestion that "many of his ideas may be old" is ludicrous. Wolfram's failure to cite a pre-existing literature on cellular automata has nothing to do with arrogance and everything to do with a literature search.

The fact that you have confused cellular automata with Monte Carlo simulation is absolutely breathtaking. You might as well have written in bold letters at the top of your post that you were talking out of your arse. You just read the interviews where they said that he had carried out computer simulations, and assumed that they were the kind of simulations you knew about rather than anything else. The iteration of deterministic cellular calculations has absolutely nothing to do with pseudo-random smapling of a complex function, other than that von Neumann invented both techniques.

The idea that MATLAB, FORTRAN and LISP might be a substitute for Mathematica probably pushes you over the boundary into intentional trolling. But what you've actually done is to provide a perfect example of the behaviour Kuhn actually identified in scientists; a mixture of two parts cowardly intellectual conservatism to one part professional jealousy.

--
Just because things have been nonergodic so far, doesn't mean that they'll be nonergodic forever
[ Parent ]

Mathematica (5.00 / 1) (#136)
by Miniluv on Thu May 16, 2002 at 10:33:32 AM EST

If Wolfram had written it, you could use it as something he accomplished. Instead he fucked around on U of I funds whilst forcing grad students into doing 100% of the coding, then turning around and selling the product, to which he had no legal, or even moral, right, without paying the University a penny.

Brilliant, sure. Respectable? I think not.

Broken links suck, so this sig does too.
[ Parent ]

Do you work for Wolfram? (4.00 / 2) (#138)
by merkri on Thu May 16, 2002 at 11:47:59 AM EST

First, one comment: you may think that philosophers of science lack a proper understanding of the underlying math or whatnot, but one could just as easily assert a major problem with scientists having a lack of awareness of the sociological-psychological  processes involved in their decision making processes. It's simply poor self-awareness and an arrogance that assumes that their reasoning is somehow "pure" of what affects the rest of humanity.

No, I didn't just assume that both are simulations.

This is a book about cellular automata. True. And a wonderful book in that regard. But note that the press about this book (much of it pushed by Wolfram himself), and indeed, the title--"A New Kind of Science"--insists on pushing the scope of relevance into much larger domain. It is the grandiosity of the scope of the claims, not the cellular automata content itself that bothers me. It's not so much that Wolfram is writing about cellular automata, nor even that he's making suggestions about their relevance or importance to other areas of science, but that this perspective on science is somehow a fundamentally "new kind" of perspective that is revolutionary in nature and he is the new king.

Once Wolfram went beyond the scope of cellular automata, and (1) implicitly or explicitly made the book about nondeterminism (combinatorialism?) in logico-scientific explanation, and (2) equally implicitly or explicitly deemed himself its creator, he crossed a line for me. You're right: Monte Carlo simulation is not the same as cellular automata. However, it is extremely relevant to claims that someone has invented a "New Kind of Science", based on recognition that not everything can be predicted well a priori.

Maybe I am reacting to inappropriate hype about this text. But if so, it's a hype that Wolfram himself has helped create.

[ Parent ]

I'm gonna have to agree with streetlawyer (5.00 / 3) (#141)
by CitAnon on Thu May 16, 2002 at 02:28:42 PM EST

Have you actually READ the book? The press and Wolfram have hyped wide application of cellular automata because that is in fact what the entire book is about. You may find his attitude disturbing. Personally, I don't like his attitude either. However, that doesn't mean that it isn't a new perspective. It IS. It doesn't necessarily mean that it won't form the basis for much new insight. It could. And it doesn't mean that Wolfram won't be remembered as one of the greatest scientists of our generation. He has a shot. Of course, all this doesn't mean that you shouldn't poke fun at Wolfram's overflowing exhuberance for his own work or his shameless narcissism. What you shouldn't do is launch into a diatribe full of insulting generalizations without even giving the man's ideas a chance.

[ Parent ]
Ok (5.00 / 2) (#174)
by delmoi on Sat May 18, 2002 at 08:28:11 AM EST

So he's an arrogant bastard. Great. So was Newton.

I don't see how his 'attitude' has any relevence to whether or not he's right
--
"'argumentation' is not a word, idiot." -- thelizman
[ Parent ]
and they are achieving something we don't... (1.00 / 1) (#130)
by joto on Thu May 16, 2002 at 05:31:44 AM EST



Reversibility in particle physics (4.00 / 1) (#145)
by KnightStalker on Thu May 16, 2002 at 02:52:25 PM EST

One of the things Wolfram bases his "the universe functions as a cellular automaton" idea on is that particle physics is inherently reversible. That is, that given the state of a set of particles at any one time, you can find out exactly what their state was a moment before, and work backwards in that way.

See page 435 if you have the book. The quote is "Can one deduce from the arrangement of black and white cells at a particular step what the arrangement of cells must have been on previous steps? . . . . All current evidence suggests that the underlying laws of physics have this kind of reversibility." (the ellipsis only covers the start of a new paragraph.)

I'm no physicist, but my meager understanding of quantum physics is that the future positions of particles are defined by probabilities, and that this is not just because we can't predict what the particle might bump into, but because they actually don't necessarily travel in predictable paths. Am I right, and doesn't this imply exactly the opposite of what Wolfram claims?

Quantum physics (none / 0) (#148)
by fluffy grue on Thu May 16, 2002 at 03:47:50 PM EST

The thing about quantum physics is that it's at such a scale that you can only figure out the position or the velocity of a particle (never both), and observing it will affect its future anyway. Thus, you can't trace its path backwards, because you don't know what its path was; instead, you can only make a probability assesment saying "Well, it's 75% likely that it was previously over here, and assuming it was, then it's 75% likely that it was previously over there, but if it was really over there then it's 75% likely that it was over there before" and so on. It's not like tracking a pool ball, which is at such a scale that the various effects of photons bouncing off of it are insignifigant and mostly cancel out anyway.

Incidentally, I sometimes wonder if the laws of physics can be mapped to something like Conway's Game of Life in some sense. Filling a field with random data and then seeing it "evolve" into a field of elementary units of stuff seem very much like the current theories of the beginning of the universe...
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[ Parent ]

CA universe (5.00 / 2) (#151)
by KnightStalker on Thu May 16, 2002 at 04:16:42 PM EST

Incidentally, I sometimes wonder if the laws of physics can be mapped to something like Conway's Game of Life in some sense.

That's Wolfram's thesis, basically, although he goes into far more detail. What makes my head hurt is that Wolfram says that space has been experimentally verified to be continuous down to 10-20 meters, or 1/100000 of the width of a proton. (I'll have to take his word for it.) That sort of implies that a single actual proton would take terabytes of grid space to model.

[ Parent ]

CA element size (5.00 / 1) (#166)
by sigwinch on Fri May 17, 2002 at 03:44:07 PM EST

That sort of implies that a single actual proton would take terabytes of grid space to model.
Indeed! The fundamental quantization scale is determined by Planck's constant: 6.63*10-34 J*s. By comparison, even a puny photon of visible light has an energy of around 2*10-19 J, 15 orders of magnitude larger than the Planck energy. The energies, and by extrapolation the distances and times, are *very tiny*.

I've thought quite a bit about CA physics, and my conclusion is that particles have to be extremely sparse to be simulatable on a realistic computer. And even then it all goes to hell if you throw in 10 extra dimensions.

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[ Parent ]

Reversibility in QM (5.00 / 1) (#157)
by a clockwork llama on Thu May 16, 2002 at 10:29:51 PM EST

...my meager understanding of quantum physics is that the future positions of particles are defined by probabilities, and that this is not just because we can't predict what the particle might bump into, but because they actually don't necessarily travel in predictable paths.

Your confusion is a common one, and it comes from a misunderstanding of what a "measurement" is in quantum mechanics. It's only in the past few decades that physicists have begun to understand this subtlety of quantum mechanics, and I haven't seen many good accounts of it in lay expositions.

Here's a short version. Consider a quantum mechanical system A. If A is isolated, it evolves in a reversible way. However, if A is in contact with a big noisy system B, you can make approximations to the behavior of A which are not time-reversible. This is what the probabilistic "observations" of quantum mechanics are; in this case, A is the observed system and B is the measuring apparatus. Instead of making an approximation, you can consider A and B together as a single, isolated quantum mechanical system. Finding the behavior of this combined system is generally a very difficult problem, but when you solve it you will find that all the processes involved are reversible.

The situation gets a little hairier in quantum field theory. Some quantum field theories turn out not to be time-reversible, unless you replace all particles with their antiparticles and perform a reflection in space. You may have heard of this as "parity violation." Anyway, the combined symmetry is known as CPT (for charge-conjugation, parity, time reversal), and all the widely-accepted field theories have this property.



[ Parent ]
What do you mean by A and B as an isolated system? (none / 0) (#158)
by CitAnon on Fri May 17, 2002 at 12:09:50 AM EST

When you perform any type of measurement on a coherent quantum system, the sytem will collapse to one of its eigenstates. In your post, if the system you measure is A, then does that mean that B must not only include the mearsuring aparatus but the concious experimenter as well? If so, then one would not be able to fully understand quantum measurement without first coming up with a theory of the human conciousness. This is not a fringe view and is actually a view point espoused by many physicists. However, people don't normally talk about this in a technical context as this subject is currently more philosophy than science.

[ Parent ]
Modelling measurement (none / 0) (#159)
by a clockwork llama on Fri May 17, 2002 at 01:59:17 AM EST

In modern interpretations of quantum mechanics, there is no special role of consciousness in measurement. Consciousness seems to require a big system with lots of degrees of freedom, which is exactly how we describe measuring apparatuses; but really any other big system will do.

Of course, it is practically impossible to describe an ammeter quantum mechanically, let alone a human. However, simplified computer models have been created. For example, if the system being measured is one spin, we can model a measuring apparatus composed of ten spins. Under these circumstances, the computer simulations demonstrate the phenomena of "wavefunction collapse" very convincingly.

I'm not sure I'm doing such a good job of explaining this; it's difficult without resorting to math. If you have a quantum mechanics background, I would recommend reading "Following a "Collapsing" Wavefunction".


[ Parent ]

I've glanced over the article (none / 0) (#176)
by CitAnon on Sat May 18, 2002 at 09:51:56 PM EST

Just found the time to briefly look over the article. It demonstrates that entanglement with A can cause B to "collapse" into an apparently incoherent probability distribution over eigenstates. However, it does not actually provide a mechanism for choosing one state over the other. Instead, it takes the multi-worlds point of view.

To me, this offers some fresh insights into quantum measurement and perhaps represents a substantial step forward in understanding the phenomenon. However, it does not satisfactorily explain why we experience one eigenstate, or one world, over others.



[ Parent ]
The Emperor Has No Clothes (4.66 / 3) (#147)
by gmol on Thu May 16, 2002 at 03:22:59 PM EST

Disclaimer: I have not yet read the book, but if it smells like a duck...

I'll admit that I am in fact very jealous of Mr. Wolfram. He can claim some prodigous success at a young age and has produced a widely used product that aids scientific progress in many fields; and got rich doing it (what else can you ask for?).

But I can just smell it from the snippets that I've seen so far, that the book is more or less a pretty picture gallery of CA gems (which are always fun to look at). Although my estimate on Stephen's crackpot index isn't that high, I still say that he's displaying symptoms of crank-itis...

Running down that list... (4.00 / 2) (#150)
by KnightStalker on Thu May 16, 2002 at 04:05:45 PM EST

Wolfram may not peg the meter but he gets a pretty solid positive score. Particularly from items 19, 20, and 33.

[ Parent ]
Crackpot Index is very useful! (3.50 / 2) (#161)
by Spork on Fri May 17, 2002 at 06:22:09 AM EST

Thank you for that link. And yes, it's a good call to bring it up in this context.

[ Parent ]
Already Been Done? (3.00 / 1) (#152)
by ewhac on Thu May 16, 2002 at 04:31:42 PM EST

Didn't Autodesk spend a farkload of money on their own Cellular Automata division not so many decades ago?

I remember seeing them at the late lamented West Coast Computer Faire showing off their stuff at the time; a package of various cellular automata "games" which you could play with. It wasn't clear to what end they were working. The division was disbanded without fanfare years ago.

Schwab
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Editor, A1-AAA AmeriCaptions. Priest, Internet Oracle.

look up Rudy Rucker and John Walker (3.00 / 1) (#154)
by martingale on Thu May 16, 2002 at 07:45:42 PM EST

here

[ Parent ]
Discussion on bottomquark.com; Kurzweil's review (4.00 / 1) (#188)
by sebpaquet on Wed Jun 05, 2002 at 01:34:13 PM EST

A few interesting comments about the book can be found on bottomquark.
Ray Kurzweil has written a review of the book.
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some observations (3.00 / 1) (#191)
by notuorme on Sat Aug 31, 2002 at 09:44:34 AM EST

1. everything is unified, essentially borderless, transient, and sharing a common basis - the simple updates of the underlying rules. 2. everything is fixed in its evolution (even if unpredictable) essentially making it all a 'big computer' and eliminating the 'playing dice with the universe' of QM. 3. Everything is fundamentally the on/off of being and nothingness, implying universal awareness as the underlying stuff of the universe.

Wolfram publishes A New Kind of Science | 191 comments (166 topical, 25 editorial, 0 hidden)
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