Like main book "The Mathematica book", this is also paper version of help which is included in the program. But, many people like take a book rather then reading from monitor. The main "The Mathematica book" together with this one, is a complete set for using the program.

I can say that this book is useful. It briefly describes all add-on packages of the program, following by several easy-to-understand examples.

Add-on packages much improve an already powerful program, so using them increase efficiency of every serious task. This book helps one to do this!

Certainly, this book talks about the most powerful feature of Mathematica. It talks about the part of the sotware, that makes it the best mathematics programm that has ever been made until our days. Without the contents of this book (Mathematica Packages) Mathematica becomes a common software like many others that exist today. It will surely help any person to use all the facilities of Mathematica. If you have ever wanted Mathematica to do something for you and people said that it was not possible, you should take a look in this book.

This is a nice collection of wolframs work on cellular automata (which first appeared as a number of papers in various physics journals). It is a nice coverage of cellular automata, but it would have been nice to give more credit to von Neuman for his pioneering work in cellular automata theory.

There is also an annoying habit for all of his work to concentrate on deterministic cellular automata, and the mathematics is constrained to this. Recent work has indicated that the origin of complexity in our universe is from random sources that are preserved.. not that the complexity all came from the initial conditions.

It is especially interesting to note in his book how the different rules of cellular automata play out to create varying degrees of complexity. It takes a very specific rule set indeed to allow for interesting complex behaviors to show up, as evinced by the long search Conway undertook to discover "life".

Hopefully Wolfram will comment on the recent research that indicates that complexity is introduced into our universe through nondeterministic phenomena. He also should have presented Fredkins ideas about reversible computation to more fully flush out the relationship between cellular automata, computability and reversibility.

the entire text of this book is included with mathematica, and if youre not going to buy the software, why buy the book? and if you are going to purchase the software, since it is included in the help file, why buy it? hmm. i suppose i lack the abstractive capacity to answer this question in any way supplemental to mr. wolfram's income. besides, there are problems with this book which, from the standpoint of an individual trying to learn the use of the software, may be summarized as incompleteness. do you want to plot a graph of the equation |x-y|+|x|+|y| <= 2? you will not find instructions on how to do it. for more complex functions, there is some, albeit sketchy, material to assist you; though, if you possess a sufficiently versatile comprehension of mathematics and programming, no doubt you'll puzzle out the necessary steps to produce graphic representations of whatever kind you may wish to plot. for the majority of students, who lack this kind of wisdom, i fear the information to make such graphs must be found in other books. i developed a definite resentment to mr wolfram when i attempted to locate the procedure for plotting the above equation, and, upon following the link to the information found a "buy the calculus whiz at 69.95 to find this out" blurb. stunning. buy this software, buy my reference book, and then, buy other books from me to find out how to use what my software and book--despite an advertised promise to enable, through these materials, the user with adequate information to empower his mathematical needs in toto--will not show you. i say, don't buy it. and, as an aside, don't buy his other book, "a new kind of science", either. that work could have been encapsulated in a monograph of some 30 pages; but then, you'd not have lined mr. wolfram's pockets to the tune of 50.00 dollars, would you? i have a suspicion mr wolfram is committed to said mr. wolfram's pockets, and his new science pretty much amounts to using all manner of shenanigans to stuff 'em. certainly, from the point of view of an irate purchaser of the software, this book, as with the manual "mathematica" is so much misspent dinero. caveat emptor. now i know why matlab is the preferred algebraic program among literate users.

I bought the 2nd edition of this book back in the early 90s when a student edition of the software was available to me inexpensively for the Mac. The book was very helpful in learning how to use the Mathematica program. There are examples galore and many graphical illustrations. As other reviewers have said, the whole book comes online with the software and you can easily search it, but I liked having an offline copy too. The later versions are just extensions of earlier ones.

It is easy to learn how to do simple examples from the book. Suppose you want to plot the expression |x-y| + |x| + |y|. On page ix, before the book really begins, there is an example of the syntax to make a plot: Plot3D[ Sin[x y], {x,0,Pi}, {y,0,Pi} ]. In chapter 1 (p. 49) you learn that the absolute value is given by the Abs[x] function.

So, you can type Plot3D[ Abs[x-y] + Abs[x] + Abs[y], {x,-2,2}, {y,-2,2}] to get a nice 3D plot of this expression, with x and y in the range -2 to 2. If you want to see a plot where the value of the expression is <= 2, you can restrict the Z range of the plot, as illustrated in chapter 1 (p. 157), like this:
Plot3D[ Abs[x-y] + Abs[x] + Abs[y], {x,-2,2}, {y,-2,2}, PlotRange->{0,2} ].

I have been a Mathematica user for many years, back when you could get it for just the MAC, and a big fan of Steven Wolfram.
If you are like me, you're just a bit curious to see what the 4,832th digit for Pi is, using N[Pi,4832]. Or what a Contour graph looks like, right! Well, this book will definately show you how to do it! This latest hardcover book, which includes reference for version 4.1 of Mathematica, is a add-on of the same(only smaller) book on version 3.0 of Mathematica. There are much more examples specific to version 4.x and also the book is a few hundred pages more than the v3 book. If you have the v3.0 book and dont use the v4.x software, there really is no need to get this book, unless you're really curious about what v4.x offers and like to lug around a 6 pound book! The graphics are very vivid, sharp and basically the same ones in v3.0. Due to some of the new graphing features in v4.x, there are samples of these as well. Overall, a great software reference to one of the best software packages ever made!

This review took almost one year. Unlike many previous referees (rank them by Amazon.com's "most helpful" feature) I read all 1197 pages including notes. Just to make sure I won't miss the odd novel insight hidden among a million trivial platitudes.

On page 27 Wolfram explains "probably the single most surprising discovery I have ever made:" a simple program can produce output that seems irregular and complex.

This has been known for six decades. Every computer science (CS) student knows the dovetailer, a very simple 2 line program that systematically lists and executes all possible programs for a universal computer such as a Turing machine (TM). It computes all computable patterns, including all those in Wolfram's book, embodies the well-known limits of computability, and is basis of uncountable CS exercises.

Wolfram does know (page 1119) Minsky's very simple universal TMs from the 1960s. Using extensive simulations, he finds a slightly simpler one. New science? Small addition to old science. On page 675 we find a particularly simple cellular automaton (CA) and Matthew Cook's universality proof(?). This might be the most interesting chapter. It reflects that today's PCs are more powerful systematic searchers for simple rules than those of 40 years ago. No new paradigm though.

Was Wolfram at least first to view programs as potential explanations of everything? Nope. That was Zuse. Wolfram mentions him in exactly one line (page 1026): "Konrad Zuse suggested that [the universe] could be a continuous CA." This is totally misleading. Zuse's 1967 paper suggested the universe is DISCRETELY computable, possibly on a DISCRETE CA just like Wolfram's. Wolfram's causal networks (CA's with variable toplogy, chapter 9) will run on any universal CA a la Ulam & von Neumann & Conway & Zuse. Page 715 explains Wolfram's "key unifying idea" of the "principle of computational equivalence:" all processes can be viewed as computations. Well, that's exactly what Zuse wrote 3 decades ago.

Chapter 9 (2nd law of thermodynamics) elaborates (without reference) on Zuse's old insight that entropy cannot really increase in deterministically computed systems, although it often SEEMS to increase. Wolfram extends Zuse's work by a tiny margin, using today's more powerful computers to perform experiments as suggested in Zuse's 1969 book. I find it embarassing how Wolfram tries to suggest it was him who shifted a paradigm, not the legendary Zuse.

Some reviews cite Wolfram's previous reputation as a physicist and software entrepreneur, giving him the benefit of the doubt instead of immediately dismissing him as just another plagiator. Zuse's reputation is in a different league though: He built world's very first general purpose computers (1935-1941), while Wolfram is just one of many creators of useful software (Mathematica). Remarkably, in his history of computing (page 1107) Wolfram appears to try to diminuish Zuse's contributions by only mentioning Aiken's later 1944 machine.

On page 465 ff (and 505 ff on multiway systems) Wolfram asks whether there is a simple program that computes the universe. Here he sounds like Schmidhuber in his 1997 paper "A Computer Scientist's View of Life, the Universe, and Everything." Schmidhuber applied the above-mentioned simple dovetailer to all computable universes. His widely known writings come out on top when you google for "computable universes" etc, so Wolfram must have known them too, for he read an "immense number of articles books and web sites" (page xii) and executed "more than a hundred thousand mouse miles" (page xiv). He endorses Schmidhuber's "no-CA-but-TM approach" (page 486, no reference) but not his suggestion of using Levin's asymptotically optimal program searcher (1973) to find our universe's code.

On page 469 we are told that the simplest program for the data is the most probable one. No mention of the very science based on this ancient principle: Solomonoff's inductive inference theory (1960-1978); recent optimality results by Merhav & Feder & Hutter. Following Schmidhuber's "algorithmic theories of everything" (2000), short world-explaining programs are necessarily more likely, provided the world is sampled from a limit-computable prior distribution. Compare Li & Vitanyi's excellent 1997 textbook on Kolmogorov complexity.

On page 628 ff we find a lot of words on human thinking and short programs. As if this was novel! Wolfram seems totally unaware of Hutter's optimal universal rational agents (2001) based on simple programs a la Solomonoff & Kolmogorov & Levin & Chaitin.

Wolfram suggests his simple programs will contribute to fine arts (page 11), neither mentioning existing, widely used, very short, fractal-based programs for computing realistic images of mountains and plants, nor the only existing art form explicitly based on simple programs: Schmidhuber's low-complexity art.

Wolfram talks a lot about reversible CAs but little about Edward Fredkin & Tom Toffoli who pioneered this field. He ignores Wheeler's "it from bit," Tegmark & Greenspan & Petrov & Marchal's papers, Moravec & Kurzweil's somewhat related books, and Greg Egan's fun SF on CA-based universes (Permutation City, 1995).

When the book came out some non-expert journalists hyped it without knowing its contents. Then cognoscenti had a look at it and recognized it as a rehash of old ideas, plus pretty pictures. And the reviews got worse and worse. As far as I can judge, positive reviews were written only by people without basic CS education and little knowledge of CS history. Some biologists and even a few physicists initially were impressed because to them it really seemed new. Maybe Wolfram's switch from physics to CS explains why he believes his thoughts are radical, not just reinventions of the wheel.

But he does know Goedel and Zuse and Turing. He must see that his own work is minor in comparison. Why does he desparately try to convince us otherwise? When I read Wolfram's first praise of the originality of his own ideas I just had to laugh. The tenth time was annoying. The hundredth time was boring. And that was my final feeling when I laid down this extremely repetitive book:exhaustion and boredom. In hindsight I know I could have saved my time. But at least I can warn others.

After I got the past the first few pages where Wolfram kept repeating himself about how this book described a new kind of science, and that he was going to describe the new kind of science in the book, I got into the examples which are quite exhaustive and meticulously researched. So far I think his observations are quite interesting. I haven't gotten to the heavy metaphysical insights yet, but given what I've seen so far, I am very much looking forward to reading them. Wolfram ties together results from several computer science (and other) fields and paints a picture of unified underlying concepts which may very well do as he predicts: change the way we understand the world (and educate the next generation about it) in a way which is as substantial and novel as Copernicus, Newton, Einstein etc. He proposes a worldview which is similar to Chaos, Complexity, Catastrophe, Fractals etc, but unified, rather than a tower of Babel.

Please excuse my review of a book I have not yet finished, but Amazon.com had the "be the first to review the book" button staring me in the face, so I had to do it since I like the book and who nose? Maybe I'll win a prize.

A New Kind of Plagiarism

Consider the following scenario: a mischievous person spends its free time for years copy pasting datum's about relativity theory. From many sources he compiles an enormous amount of information ALL taken from other people publications. Then, using in a literal sense Einstein's theory as he wrote it he uses it as the main theme (that he repeats over and over again) of a gigantic book full of all the information he gathered, in other words makes a compendium. He includes in this book the results of some computer games devised by others that he runed time and time again. Then he puts his name as author, does not include references and attributes everything to himself!. So he starts telling people, before publishing (and spends a huge amount of money on shameless self promotion for "his" upcoming book) that he is going to revolutionize science like never before anyone has managed to do. He announces to the world that his revolution will touch all cultural manifestations of mankind. He starts to be heralded as the "new Copernicus", the "super Newton", the "best mind in history", etc. Remember, his upcoming book, according to his own words will "change everything in philosophy, science, government and society in general, in fact, every aspect of mankind's culture". So the excitement grows to unprecedented heights (the publicity campaign is enormous) and the common folk grows impatient for the upcoming revelations. And, alas, the "greatest book in human history" arrives to the libraries one fine day. But wait, this book is just a compendium of things other people said, and worst, the guy is claiming to be the first to say this!. In fact, the main theme on the book is a shameless copy-paste of Einstein's theory of relativity!. So quite a lot of people discover the hoax and are appalled at the extent of the plagiarism, while the public in general is still being subjected to (paid) bogus reviews (the publication of the century!, one mercenary "reviewer" hollers). So a great confusion arises. Is this book a work of genius, that is going to revolutionize mankind's knowledge and way of life, or is it a gigantic hoax, a shameless attempt to steal many ideas from many people, a pathological self promotion by a chronic liar?. As always, some not really well informed good souls try to take a middle ground, but, how can someone seriously take a middle ground when someone says he just wrote the bible?. The whole ordeal seems out of a dramatic novel except that is happening right before our noses!. "A New Kind of Science", is, in fact, a recompilation of things that the proponents of Chaos Theory and Complexity Theory have said decades ago. There is not even the will to disguise this fact. The statements in the book are almost a copy-paste of what they said time and time again, even to the media!. I dare anyone to point out a single original idea in the whole monstrous plagiarism!. This kind of shameless theft of ideas is, indeed, unprecedented in human history. So, yes, in a way the book is unique, although only in the monstrosity of the plagiarism. Now then, many readers will think that such an easily verifiable fact as this one (that the book is just a compilation of other peoples ideas) will end once and for all the hype about the author, but, as one enlightened 20th century individual said "merchandising will be the philosophy of the 21 first century". In effect, given the enormous publicity campaign the book is still subjected to, it is quite possible that the "average Joe" for years to come (and, who knows, maybe for the rest of history) will think that the author delivered his promise!. The sad possibility is that the "new geniuses", at least for the popular mind, will be self promoted shameless pathological liars (there have been already many examples of this).
Let us hope that in this case (certainly the worst of all), intelligence will prevail and the book (and author!) will be given its rightful place!.

This is a book of ruminations about cellular automata. It is chiefly concerned with the way that the state of a system evolves when deterministic rules are applied to it. The simplest system is a single point in either state 0 or state 1. The transition rule could be that the state "0" changes to state "1", and state "1" changes to state "0". That rule can be expressed as follows.

{1->0, 0->1}

If the system's initial state is 1, then the transition rule (repeatedly applied) yields the following alternating pattern of states.

1
0
1
0
.
.

For hundreds of pages the author discusses the behavior of 1-dimensional automata built from 3-cell transition rules. The 2^3=8 different states of a 3-cell cluster can be written in binary notation from 000 up to 111. The cell in the middle can transition to either of two binary states, yielding a total of 2^8=256 rules. Most rules lead to periodically repeating behaviors, with short periods like the alternating pattern shown above.

An exception is rule 30 (30 in binary is 00011110; these bits the right-hand-side values for the 8 transitions).

rule 30:
{ 111->0, 110->0, 101->0, 100->1, 011->1, 010->1, 001->1, 000->0 }

When applied to an initial state of a single 1 surrounded by 0's, rule 30 generates the following pattern (developing downward from the top row). The array can be displayed as a bitmap of black and white pixels, producing a visualization of the evolving state of the horizontal rows.

..00000000100000000..
..00000001110000000..
..00000011001000000..
..00000110111100000..
..00001100100010000..
..00011011110111000..
..00110010000100100..
..01101111001111110..

What excites many people about such rules (and about replacement grammars in general) is that applying the rule to an input string produces new strings whose characteristics are hard to predict. Plus, the patterns in the resulting visualization look pretty cool and are suggestive of all sorts of things found in nature. It's very easy to write computer code that will generate the patterns based on input rules, so anybody can play the game.

Lots of people have implemented cellular automata and been fascinated that the behavior is so sensitive to the choice of input string and transition rules. Watching the patterns unfold is a bit like playing the slot machines. So many possibilities. So fun to watch. Addictive to play. Great to show your friends. A meme that keeps on meming. Search the Web for "one-dimensional cellular automata" and "applet" and you will find examples that you can run in your browser.

What bothers many readers about the book is that it is like an undergraduate honors project gone haywire. Page after page of printouts of these things. Thousands of them. And with endless streams of the impressions they made on the author. "My Daily Journal of Cellular Automata" would have been a fair title. Wolfram's inflated sense of their importance, and his own, is evident in the copyright statement:

Discoveries and ideas introduced in this book, whether presented at length or not, and the legal rights and goodwill associated with them, represent valuable property of Stephen Wolfram ..

Thus he lays claim to every cellular automaton and any application thereof. Pretty annoying, coming from someone arriving late to the automaton party.

He concludes of the book proper (pp. 844-845, just before his 350 additional pages of "notes") that

.. building on what I have discovered in this book .. there is nothing fundamentally special about us. .. For my discoveries imply that whether the underlying system is a human brain, a turbulent fluid, or a cellular automaton, the behavior it exhibits will correspond to a computation of equivalent sophistication. .. [W]hat my discoveries and the Principle of Computational Equivalence now show is that .. cellular automata can achieve exactly the same level of computational sophistication as anything else.

Wolfram discovery/epiphany appears to be that all algorithms can be computed by a simple model. An example of such a model, called the "Turing machine", is taught every semester to computer science students worldwide.

It excites many people that the physical world is inherently computable, allowing computational simulations to have predictive value. It is bizarre to read Wolfram represent that he is the author of this insight.

Of course it was not Wolfram but Konrad Zuse himself, inventor of the
first working programmable computer (1935-1941), who was the first to
suggest that the physical universe is being computed on a giant computer,
presumably a cellular automaton (CA). His first article on this topic
dates back to 1967 (in Elektronische Datenverarbeitung, pages 336-344,
vol 8). And Zuse's full-fledged book on CA-based universes came out
2 years later: Rechnender Raum, Schriften zur Datenverarbeitung,
Band 1, Friedrich Vieweg & Sohn, Braunschweig 1969.

Wolfram's book briefly mentions Zuse in the notes, but unfortunately
does not discuss his work in any satisfactory way. I guess an honest
title for his book would be something like: "More on Zuse's thesis."
An honest abstract would be something like: "In the 1960s Zuse proposed
that the universe and everything is the result of a dicrete computational
process running on a cellular automaton. Here I try to extend Zuse's
thesis as follows: 1).. 2).. 3).."

So far I have not found anything but minor extensions of Zuse's "new"
1967 science, and none of the expert reviewers (search for "Wolfram
reviews" on the web) has found anything real new either - since the
early 2002 marketing blitz the reviews have shown a tendency of becoming
both more competent and less favorable. The popular press interviews
focus on the "universe as a computer" idea - but neither there nor in
the book's main text Wolfram does anything to correct the wrong
impression it's all his idea, not Zuse's. But hey, the scientific
truth finding process will be stronger than any misleading
marketing efforts.

Nice pictures though. I give it two stars.