EDIT: I meant to add that it's very nice that the book is now free, in any case.
What I mean is that these simple rule programs can't be run any faster than the universe in which they are running. So you can't say "I predict this simple rule set will eventually draw a butterfly" (or whatever) - because you couldn't run it long enough for that to occur.
In a way, it's a simulation (or emulation) problem; just as you need a more powerful computer to run software to emulate a system in real time, provided that system is less powerful - you would need to do the same in order to run these simple programs. In essence, since the theory espoused in NKS (more or less - at least, that is what I got out of it - and maybe I am wrong) is that the universe at its base level (quarks? dunno) is composed and operates and creates based on these simple rules, in order to go faster than our universe (and catch up), you'd have to have a more powerful system than whatever the universe is running on (conjecture, I know - and Wolfram noted this as well IIRC).
So right now - just like if you were wanting to emulate a PS4 on a contemporary PC - the only way you can do it is non-realtime; you have to be satisfied at running the system at a slower rate. What is interesting about this - and this is pure speculation - let's say you are running "rule 30" on a computer, and unknown to you, it is actually computing a new universe (that is, simulating it) - to you, it is happening much more slowly than realtime - but to anyone "inside" that universe, they can't relatively know that they are running slower - their sense of "time" is "normal"...
I'd like to encourage you to read the book in full and maybe this new article as well. Yes - it's a real long slog. And maybe it is nothing more than a giant ego stroke on the part of Wolfram; I don't really know what to think about it anymore. But you might walk away (to get some aspirin for your headache?) with something to think about and ponder - even if it is completely wrong, or you think so, or whatever - simply reading it and understanding it might lead you to your own discoveries and ideas.
One way to summarize the thesis of book would be to say: Historically, we've analyzed natural phenomena and tried to fit equations to the data. But Nature may be doing something analagous to running simple programs instead of solving equations. What are the implications of this? Complexity and "randomness" comes about from the "programs", not from their initial inputs/conditions. And predicting behavior of programs is harder than predicting behavior of systems of equations, which sucks.
>but not any kind of science
I think many people who aren't familiar with the book are thinking that "a new kind of science" means "a new branch of science" like we have physics, chemistry, biology, and now this new "computery" science. But the book is actually about looking at nature with the new perspective of "programs", that previous generations of people didn't have a reference frame for. And some of things that we think are "complex" might actually be following simple rules (or can better be modeled as such).
I've seen a lot of criticism, most concerning being the lack of mathematical rigor in the work. Seems damning considering the author's background in math.
EDIT - to all the downvoters, I read like 40% of it but all of the criticism you can easily find about it is accurate. 10 years or so later it makes a really good doorstop, I have used it for that several times, it's super heavy with thick pages. I have used it as a source of knowledge exactly zero times and a doorstop probably 8 times, so it's utility to me is overall pretty high. I think you can get used copies for about $4, so it might be a good investment.
I did finish it (everything except the appendix/notes - though I did read a few of those, which are fascinating as well, and wholly attributed) - I do not consider my purchase a waste of money, either.
- I don't like Stephen Wolfram and his personal style offends me.
- This isn't new material because there were academic papers that covered some of this material scattered throughout the literature.
- Stephen should have been more generous in giving credit to previous work.
...If nothing else, get a copy to look at all the great pictures, and ignore the text if it bothers you.
>most concerning being the lack of mathematical rigor in the work
This book is about how very very simple programs can end up producing complex results. You can easily write the program for simulating the cellular automata in any programming language and check that you get the same picture as shown in the book. You don't have to accept anyone's philosophy of math and their opinions on the Axiom of Choice when it comes to uncountable infinities. It is completely formal. In fact, the best reason for getting the book is to encourage you to write tiny little programs to see the results for yourself.
As a book of recreational mathematics it's pretty fun. As a "New Kind Of Science" it's atrocious.
Investigating nature starting with the premise that the "laws" may be imperative procedures instead of pure functions doesn't seem orthodox (for 2002), so isn't that "new"?
Langton's Ant (1986) https://en.wikipedia.org/wiki/Langton%27s_ant
Avida (1993) https://en.wikipedia.org/wiki/Avida
Tierra (early 1990s) https://en.wikipedia.org/wiki/Tierra_(computer_simulation)
Fractal Geometry of Nature (1982) https://en.wikipedia.org/wiki/The_Fractal_Geometry_of_Nature
I dunno, some of these seem to be doing it much earlier than 2002.
And especially from a retrospective perspective, the importance of that can't be understated.
I'm not enough of a mathematician to be able to do this myself, but intuitively I expect that there must be some way to measure the chaoticness of a program-type mathematical system, the degree to which small perturbations in the input produce large changes in the output. We are familiar with this in practice in the programming world in the difference between languages like J or a fluffier language like Java. Within the domain of legal programs, perturbations in the original symbol stream are more likely to have larger effects on programs in J than in Java. My personal feeling, after watching people sort of screw around with CAs for the last many years (only recently unsubscribed from /r/cellular_automata) is that CA are simply too chaotic to be useful for any non-trivial purpose; the task of establishing correlation between a real physical outcome and a CA is too difficult, and then even if you do, the task of understanding the CA itself is still itself quite large! It just isn't a useful way of modeling the world. Or, if you prefer, the problem isn't that CAs are too simple to model things with, the problem is that in general they are too complex. Either a CA is degenerately simple or impossibly chaotic and there just isn't enough in between. The same characteristics that makes it fun to watch a CA explode from a very small seed into a complex diagram that is still somehow obviously structured in strangely complex ways makes it impossible to actually make them do anything you want to do.
Go look at the Turing machine implemented in Life. Look at the sheer size of the thing. It's a bit of a cheat because it is simulating something else that we already have models for, but... could you imagine trying to understand the behavior of Turing Machines through the lens of that Life model?
Another interesting thing to look at is the way people sometimes try to incorporate CAs into video games. It turns out they are very, very hard to tame into anything useful, without a lot of work spent constraining them down to something tractable. Or, in other words, by stripping out all their power just so they might do something slightly predictable.
Turing machines are a much better model of computation than CAs are of very many other real processes, and in practice, Turing machines are still virtually useless, useful only for the theoretical pleasingness of the UTM and the resulting mathematical theorems, but not something we use on a day-to-day basis. Lambda calculus is way more useful, and even more useful than that is just the adhoc models we tend to use day-by-day that may lack nice mathematical properties but actually resemble the machines we work with. CAs have an even larger gap between their sheer mathematical perversity on the one hand, and any useful application on the other.
In 2003 I analysed the statistical output of his ”minimal version of the efficient market hypothesis” and compared it to data in real financial markets and contrasted it with the output of other models for my thesis.
His was crap.
I'm the only sucker I know that bothered to do this.
(Incidentally it was really difficult to get in contact with a representative of his to get code for the actual model he'd only provided a sample output graph for in the book.)
The fact that many CAs are Turing-complete and given the meaning of that, it is theoretically possible to model anything with a CA. Yet CA models have never proven useful.
One possible explanation may be the timeless nature of mathematical explanations and the power of math to make predictions.
If I say F=ma (Newtonian mechanics), I can evaluate 'a' for any 'm' and 'F' trivially. I could also construct a CA -- maybe even one that modeled physics very well -- in which F=ma arose as a consequence of that CA's operation, but to make any prediction with this system I would have to actually compute the CA across all iterations until I reached my result. It wouldn't be useful because it would be too slow.
In other words predictive mathematical descriptions of nature are more useful because they find ways to factor out time.
This as well is a good argument against the book. The fact that there doesn't appear to be anything brought forth in other fields, or in the same field of work as the book doesn't bode well for it.
Then again, there have been many time in history where something was written or put down, which wasn't known or seen to be relevant, workable, or whatnot, until many decades or centuries had passed. I'm not saying this book is a case of that, only that it might be. We don't really know, and can't if or until it happens, of course.
...(skip down to the last paragraph).
I honestly tend to wonder if the people who are complaining about the book actually bothered to read it in its entirety, and understand the information and ideas being conveyed? So far, I'm not convinced they have, but I'm willing to change my mind if someone can point to a review or argument against it that holds up. The only one I've seen espoused by anyone (and was mentioned by a commenter here) is that the book doesn't actually do any "science" - but if you read the book, you would understand that this is an impossibility based on the premise of the work.
I've always wondered if there was a psychological component to it -- as in certain personality types get personally offended by Wolfram's prose. I'm certainly curious if there would be any correlation between liking/disliking the book and some sort of Meyers-Briggs type personality assessment. Maybe it is an INTJ vs. INTP type of thing?
I couldn't get past 10% of the book before I got sick of the "Look how great Mathematica is for describing these algorithms!"
I think a lot of the hate came because of the title.
Disclaimer: I'm neither a scientist, nor a mathematician.
Gary William Flake's "The Computational Beauty of Nature" is an accessible alternative with interesting ideas, pretty pictures, and no hyperbole:
I do remember it at times reading like a sales pitch for Mathematica though. :-)
It contains an interesting overview of some of the ideas and work done in cellular automata, made significantly worse by the authors seemingly pathological need to lay claim to work that was not his, and inflate the importance of work that was. It's entirely reasonable to decide you can't get past the tone and sheer tonnage of blather to dig for the good stuff hidden inside. As you note, it's also not very rigorous (and sometimes worse) but that's mostly forgivable in a lay text like this, and would be entirely addressed if it had a good set of citations.
It's interesting to contrast this with another book that came out around the same time, Stephen J. Gould's "The Structure of Evolutionary Theory". They are of similar size and scope, but Gould does a much better job of presenting some of his own ideas in the larger context, and giving both credit and useful pointers into that context.
As far as ANKS goes, I've always thought that there was probably a very nice 250 page book hidden inside it. It's just well hidden.
...then you could start to read the on-line version to see if Stephen Wolfram's writing style rubbed you the wrong way.
When this book came out, I purchased a copy, determined to read it; I was successful in reading it, minus the appendix and notes section (which is printed so small, that if expanded to the size of the font used in the book, would probably create at least one or more books of the same length - this thing is insanely dense - but at least it isn't a "House of Leaves").
I only ran into one issue - on the first copy of the book I purchased: So far into the book (I don't recall how much offhand) the text repeated or did something weird; basically I had purchased a copy of the book that was bound improperly or something. I kept that copy, and purchased another.
Anyhow - what I constantly see in reviews of this book (then and now) is the criticism that what Wolfram wrote wasn't original, or "new", and that it was "egotistical" of the author to publish it.
What I've never understood though, is that the Wolfram constantly asserts that what he is writing isn't anything original or new - that it all existed before. I mean, I recall reading this kind of language seemingly on every other page. But I don't think I've seen a critical review that has mentioned this?
At this point, 15 years later (has it really been that long?) - I'm not sure what to think of the work. Based on the first few comments here, it still seems to be something that raises the hackles of people. Maybe it's deserving of the criticism? Or maybe it's one of those texts that needs to age a bit more before we see it for what it is?
Whatever - I enjoyed reading it, as difficult a read it was, I still found it fascinating and curious.
(EDIT) The gist: "As the saying goes, there is much here that is new and true, but what is true is not new, and what is new is not true; and some of it is even old and false, or at least utterly unsupported."
I had no idea this review existed, but it captures many of my reactions to the book when I first tried to read it many years ago. I distinctly remember the lack of discussion of previous work, lack of specific citations to the academic literature, and the garbled way in which scientific fields I had some knowledge of were explained. The book seemed to take pains to make it appear as if the author were inventing something the likes of which the world had never seen before.
A "new kind of science", perhaps?
I slogged through about a third of the book and then skimmed the rest. I waited until there was a copy at the library because I knew it was getting poor reviews, and I was glad I had.
That said, I shared Wolfram's amazement at how amazingly complex behaviors emerged from simple sets of rules. And I too pondered how something like DNA combined with a set of simple rules could result in a fully functional human when those rules were repeatedly applied.
But I have yet to deduce any way in which I might reason from simple rules to a coordinated complex system, or to predict the system such rules would produce. In some ways it felt to me like applying Riemann sums to solve an integration and never being able to get past that algorithmic solution to the next step which is Calculus proper.
It is interesting to read from the author's perspective that after 35 years of thinking about it he hasn't come up with any way bridge that gap either.
It's worth noting that the more we learn about DNA, the more it seems that the rules governing gene regulation and expression are anything but simple. 
At one point, it was believed that the Human Genome Project would sequence our genome, and from there it would be relatively straightforward to "read" all the genes and figure out how to cure genetic diseases.
Now, twenty-ish years later, that view seems naive.
 https://en.wikipedia.org/wiki/Gene_expression#Regulation_of_... - for a very brief overview
If you keep following it down, and uncover the rules underneath the rules, then you reach the last irreducible set of rules. And then somehow that understanding will let you deduce something else or something. (that was were I fell off the train, trying to figure out the second part)
The problem is that emergent properties are difficult to predict from lower level analysis, and the complexity is such that it's expensive to rigorously simulate enough of the system to see what you care about seeing.
The incipit "I can only imagine how fortunate you must feel to be reading my review" is, AFAICT, NKS in a nutshell.
Apologies for the link quality.
Ego-trip indeed. There's little I find more gag inducing than someone discussing their own writing as if it's elevated cannon apart from themselves.
> But with every passing year I feel I understand more about what the book is really about — and why it’s important.
You don't say Mr. Wolfram
It's called "A New Kind of Review".
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.
The site you linked to missed the first subheading, which is "Why you are reading this review"