Kip

What does everyone think of Wolfram's new opus?

While I agree with many of the speculations (such as the discrete, determined nature of spacetime, and the importance of neutralism in evolution), I wondered whether or the author was "offer of his rocker" on drawing some conclusions (many of which were simply incoherent).

Skepticwithachainsaw

I haven't read it (yet), so I can't really comment but the impression I have got from other people is that he makes alot of hot air over stuff thats really already been said before...

Demosthenes

I thought the book was interesting, but I agree with the author being off the rocker on some of the areas. He's making the error of generalizing too much from a few results in discrete mathematics. Also, he has this irritating habit of implying that everything in the book originated from him while many of the ideas had already been explored before.

Another thing that bothered me was that while the author discussed in depth about one thing, he would then briefly or miss out althogether talking about other topics that were implied by the subject. I realize that he can't possibily include everything, but when you're holding a book with over a thousand pages... I'd like to have seen at least something more to top the discussions off.

As pertaining to my comp sci and mathematics background, I was most interested in his principle of computational equivalence.

Lastly, I hated all of the loaded words in the book and the repetitive phrases. You would think that the author had invented science itself, but then isn't that what he's doing? Claiming to know better, the author chose to eschew using an editor, but his book only shows just how clueless the author was about art of editing.

Beyond that, the book's certainly a worthwhile addition to your library.

[ October 23, 2002: Message edited by: Demosthenes ]</p>

Steven S

This is generally what I've heard too. Wolfram's hubris is remarkable. But on the bright side I've also heard the book is a good introduction to cellula automata so I might pick up a copy of it someday.

Steven S

Friar Bellows

The idea of the universe as a giant cellular automaton is definitely not Wolfram's invention. Edward Fredkin beat him to it, and Wolfram apparently appears to been unaware of this fact despite being a long-time friend of Fredkin. In fact, there appears to be even earlier claims to this idea.

Take a look at this page for a short discussion of this, and a large collection of reviews of ANKOS (A New Kind of Science):

<a href="http://www.math.usf.edu/~eclark/ANKOS_reviews.html" target="_blank">Collection of Reviews of Wolfram's A New Kind of Science</a>

Personally, I borrowed the book from a friend, and read about 1/4 of it, skimming parts I found uninteresting. I agree with Demosthenes' appraisal of it.

Friar Bellows

OK, I can't help it, because I love satire. Here is an anonymous review of ANKOS from Amazon.com:

A New Kind of Review
by "a reader"

I can only imagine how fortunate you must feel to be reading my review. This review is the product of my lifetime of experience in meeting important people and thinking deep thoughts. This is a new kind of review, and will no doubt influence the way you think about the world around you and the way you think of yourself.

Bigger than infinity Although my review deserves thousands of pages to articulate, I am limiting many of my deeper thoughts to only single characters. I encourage readers of my review to dedicate the many years required to fully absorb the significance of what I am writing here. Fortunately, we live in exactly the time when my review can be widely disseminated by "internet" technology and stored on "digital media", allowing current and future scholars to delve more deeply into my original and insightful use of commas, numbers, and letters.

My place in history My review allows, for the first time, a complete and total understanding not only of this but *every single* book ever written. I call this "the principle of book equivalence." Future generations will decide the relative merits of this review compared with, for example, the works of Shakespeare. This effort will open new realms of scholarship.

More about me I first began writing reviews as a small child, where my talent was clearly apparent to those around me, including my mother. She preserved my early writings which, although simpler in structure, portend elements of my current style. I include one of them below (which I call review 30) to indicate the scholarly pedigree of the document now in your hands or on your screen or committed to your memory:

"The guy who wrote the book is also the publisher of the book. I guess he's the only person smart enough to understand what's in it. When I'm older I too will use a vanity press. Then I can write all the pages I want..."

It is staggering to contemplate that all the great works of literature can be derived from the letters I use in writing this review. I am pleased to have shared them with you, and hereby grant you the liberty to use up to twenty (20) of them consecutively without attribution. Any use of additional characters in print must acknowledge this review as source material since it contains, implicitly or explicitly, all future written documents.

CardinalMan

First, let me issue a disclaimer. I have not read Wolfram’s book very closely. However, I have browsed through it, skimming the parts that are relevant to the subjects I think about (computability theory and the foundations of mathematics), and I did attend a talk he gave last week about the book. Hence, my comments here are not grounded in a deep reading of “A New Kind of Science”.

I agree with many of the above comments (and the reviews above are hilarious). My perception is that Wolfram has very few, if any, fundamentally new or radical ideas, and that he certainly has not created “A New Kind of Science”. On the other hand, I find the book to be an interesting introduction and overview of ideas related to cellular automata, complexity in computations, and universal machines (those capable of simulating arbitrary computations).

It seems to me that Wolfram’s book boils down to three major assertions:
1) Even remarkably simple deterministic rules can produce incredibly complex results which can be indistinguishable from true randomness.
2) Beyond trivial computations that result in simple looping or nesting behaviors, all computation is equivalent (what he calls the “Principle of Computational Equivalence”).
3) Many computational procedures exhibit a kind of “Computational Irreducibility”, whereby the only way to determine their behavior is to explicitly run them.

The first point has been known in many fields for a long time (in biology, anybody who studies evolution or genetic algorithms can explain how simple competition for resources can create complex organisms, and in mathematics we see simple axioms bearing the fruit of rich and deep theorems). Wolfram seems to focus on cellular automata, where the fact that simple rules can lead to mind-boggling behavior has been known and studied for decades (and Wolfram gives no credit to these researches). Now it does seem to be true that Wolfram has found some dazzling complexity in computational procedures that are simpler than other known examples, but this seems to be an improvement over old ideas rather than a fundamentally new one.

Then Wolfram goes on to talk about his “Principle of Computational Equivalence”. Once again the origins of these ideas are quite old (dating to 1930’s), and although Wolfram mentions this in passing, he doesn’t seem to give credit where it is due. He spends a great deal of time discussing how various computational models (like cellular automata and Turing machines) can simulate and interpret one another, and how each model has “universal” machines which are able to simulate all machines in that model. These are wonderful ideas that have been known and appreciated for some time. Again, it seems that Wolfram has pushed these ideas forward somewhat by finding universal machines that are a good deal simpler than those known, but they do not seem to be qualitatively different. Furthermore, I think that he extrapolates much to far with his principle (see below).

As far as computational irreducibility is concerned, his ideas are closely related to Kolmogorov complexity, where one measures how complicated a certain object is by the length of the shortest computer program which produces it. One can show mathematically that a great many objects are computationally irreducible in the sense that no program which produces them can do much better than simply describe them in full detail. There are many books and papers devoted to the study of these ideas, and it seems Wolfram mentions none of them.

So what is new in Wolfram’s book? As far as I can tell, he has simply pushed some mathematical fields forward a small amount, and used this to extrapolate to grand, unoriginal, philosophical claims about the nature of the universe, science, and mathematics. Although I tend to agree with some of the ideas presented in the book about the nature of complexity, there are several places where Wolfram seems to be either flat-out wrong or just wildly speculating. For example, Wolfram quickly mentions a result in computability theory (the existence of intermediate Turing degrees) which seems to go against his “Principle of Computational Equivalence”. His explanation about why this potential failing is not important is incoherent to me.

As far as the foundations of mathematics is concerned, he makes a few conjectures:
1) There are many easy to state theorems whose shortest proof is remarkably long.
2) Nearly all axiomatic systems are equally complex.
3) Nearly all of the currently unsolved problems of mathematics will turn out to be undecidable.

The first claim is a provable fact, and (again) has been known since the 1930’s, although as far as I can tell he claims the conjecture to be his own. The second claim is in many ways false. There are a very large number of important axiomatic systems which do not exhibit the undecidability and universality present in things like number theory and set theory. However, if you restrict attention to all-encompassing theories, we find, lo and behold, that this has been known for some time. The third claim is merely conjecture, which may or may not be true. I know of at least one famous mathematical logician, who flaunts his impressive credentials as much as Wolfram, who conjectures the exact opposite. This logician believes that nearly all important and currently unsolved problems in mathematics (like the Riemann Hypothesis and P ?= NP) are solvable with our current axioms. At this point, we simply do not know.

In conclusion, I think that Wolfram has written a nice book that explains at a pretty elementary level with lots of beautiful pictures a certain branch of mathematics. Unfortunately, the book is filled with Wolfram’s self-praise, little credit to others, and mainly unoriginal ideas. Also, since few people know about the relevant mathematical fields and Wolfram has gone directly to the public, I fear that many people will think that much of this book represents original and groundbreaking work.

CardinalMan

echidna

<a href="http://iidb.org/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=57&t=000311" target="_blank">http://iidb.org/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=57&t=000311</a>
A challenging view of the universe

Shit, surprise myself sometimes, found it !

Rusting Car Bumper

First, whether or not Wolfram originated the idea has nothing to do with its validity.

Second, I think its way to early to judge it. The idea he is presenting is very rich and one isn't simply going to judge its validity by reading the book. I heard peole critisizing the book the week it came out!

Third, one reason for his approach is because he did essentially forward this idea before and because he wasn't thourough (and he wasn't) he feels he didn't get a fair hearing.

Fourth, he outright says that this is a fairly bold idea.

Now, me and a friend sat down with the book. He was already very famiiar with Wolfram's work because he is generally interested in cellular automata and has a degree in CS. I being trained in physics was generally intrested as well. We plowed through some of the math involved in some of it. One conclusion I reached was that its too rich an idea to reject outright. Many of the critics seem to realy have no deep understanding of cellular automata. It would easily take many months to get a grasp of it in order to actually say one has enough understanding in order to rejct it or give it creedence.

I think the jury is still out and will be out for a long while unless everyone shits on him because its too radical.

DC

CardinalMan

Of course. As I said above, I agree with many of the ideas in Wolfram’s book about the nature of complexity (its ability to arise from what seems like utter simplicity, and its resulting ubiquity). I certainly do not judge the ideas by the author.

However, imagine if I were to write a huge book about my new, radical, theory of physics that is virtually indistinguishable from quantum mechanics, except for the fact that I use different terminology and I draw a few more sweeping philosophical conclusions. Furthermore, I take this book directly to the public (who knows little about quantum mechanics) claiming that I am at the center of a paradigm shift in physics, and that nearly all of the ideas present originate from my own research. I think a little derision would be in order.

I agree that those who have not been exposed to these ideas already should not dismiss the work quickly or out of hand. However, if you’ve studied that basic ideas before, and agree with many of its conclusions (since many were mathematically provable facts long before the publication of the book), then what’s wrong with coming out and saying that the book has little originality?

I think that Wolfram does a nice job of explaining the ideas present in the book. His pictures and computer simulations allow newcomers to grasp the ideas present more quickly and without a strong mathematical background. If Wolfram claimed to write an expository book about important and central ideas related to the nature of complexity, I would have applauded him. Unfortunately, things have turned out differently.

I don’t believe that proving mathematical results that fail to be qualitatively different from old results, or stating philosophical conclusions that have been speculated about in the past constitutes boldness.

As I’ve said, I don’t reject most of the ideas. I do think that I have a fairly strong background in computability theory and the foundations of mathematics, and that’s where my comments were directed. Do you disagree with any of the comments in my original post? Do you think that Wolfram has some fundamentally new ideas in these areas? If so, can you be specific about them?

It’s not very radical to those who study these ideas for a living. If you’ve already served as a juror in a case where you’ve been convinced by the evidence, and then you’re brought to a retrial that has a small amount of new corroborating evidence, it doesn’t take long to reach a decision (and to become a little annoyed when the media jumps all over the second trial while remaining ignorant of the first).

CardinalMan