Reading the Preface and Chapter One, you may notice that Wolfram makes extensive use of the word
"I" and of the phrase "this book". In these sections, he also
takes the opportunity time and time again to
tell us just how long it has taken him to write "this book" and how much
effort it has taken him to write "this book".
Should we be impressed with the author for his labor?

The author also promises that his discoveries will revolutionize
understanding in Mathematics, Physics, Biology, Social Sciences, Computer
Science, Philosophy, Art, and Technology. Wolfram is very ambitious.

In Chapters 2-6, Wolfram shows many examples of his experiments with
cellular automata, mobile automata and other repeating algorithms and the
sophisticated patterns that these algorithms can generate. These patterns are
interesting and impressive and Wolfram presents this material in a very clear
and concise manner.

Although it is a great deal of material, a reader should go through all
of it to really appreciate the potential of a simple repeating algorithm. In
these chapters, Wolfram shows himself to be an excellent writer. The material
is understandable with only a basic understanding of mathematics or computing.

However,
work in this field has been done before. Cellular automatons have
certainly been studied in biology. He makes passing mention of other papers
but provides no explicit references. In the notes for Chapter 2, he does list
a number of his own papers related to the subject. But he does not state when
and where they were published, if at all! If he spent so many years, working
on "this book", why did he not at some point take the time to provide a clear
reference to the works of himself and of others in this field?

Frankly, I was left wondering what is Wolfram's original work and what
has been done before. I was also dismayed that there is no peer review in
evidence. I certainly hope that his "New Kind of Science" will include
references and peer review.

To be fair, Wolfram makes some mention other's work, albeit without
references, in the notes for Chapter 2. The author labels these as "close
approaches" to the discoveries that he himself has made. The motivation for
listing these close approaches may be for the opportunity to point out that how
and why others failed while Wolfram succeeded.

From Chapter 7 to the end of the book, Wolfram uses the outcomes of the
experiments of earlier chapters an an attempt to relate simple algorithms to
natural phenomena. But most of it is hand-waving.

He appears to make some headway with crystals and simple examples of plant
growth. He shows photographs of snowflakes, leaves and stems and compares them
somewhat favorably with the patterns produced by particular cellular
automations. There are, of course, no exact matches.

The cellular automation results certainly remind the reader of snowflakes
and plant stems but they are not mistakable for anything but cellular
automation results.

If this new kind of science has any promise, then the author has missed an
opportunity to demonstrate it by comparing say, a series of snowflakes to a
cellular automations which are indistinguishable from the respective snowflake.
Such an exercise would have required a great deal of computing power but it
would have been worth it for the resulting triumph.

Continuing with biological examples, Wolfram shows a number of photographs
of common seashell and animal shapes. Curiously, he does not attempt to
compare these to any cellular automaton or other results.

Over the course of discussion of real biological structures and
pigmentation patterns, Wolfram makes it clear he does thinks that natural
selection does not explain the observed patterns of biological systems. But he
does not actually state why he holds this opinion. He says that he thinks that
cellular automata algorithms are being chosen at random and natural selection
has nothing to do with it.

From the tone of Wolfram's discussion of the role of natural selection in
biology, he obviously is not well versed in either.

I suggest that a more reasonable suggestion would be that when a single
organism is growing, cellular automata algorithms determined by alleles are
used to perform tasks like the actual construction of shells or distribution of
pigmentation. But this does not mean that natural selection is not at work
driving the overall adaptive fitness of the species.

Use of certain cellular automata algorithms may offer a greater chance for
individual survival over other algorithms and mutation may alter genes thus
introducing new or modifing existing algorithms.

Wolfram moves on to a discussion of the role of cellular automata in
financial systems. But I will not comment on his financial discussion because,
unlike Wolfram, I do not talk about things that I do not understand.

In Chapter 9, Wolfram takes on fundamental physics. He starts by using
cellular automata to model a 2-dimensional ideal gas.

The actual point of these models is to demonstrate the behaviour of
cellular automata in the context of entropy and
The Second Law of Thermodynamics.
It is not clear to me what Wolfram is getting at. None of
these models involve heat, temperature or work. He keeps mentioning randomness
and changes in complexity instead of simply performing a calculation of the
changes in entropy of these systems.

On page 453, Wolfram claims that one of his cellular automation models
violates The Second Law of Thermodynamics. Of course, without a simple
calculation of change in entropy, it is not clear why it is in violation. He
provides no calculation showing a decrease in entropy over time. Then based on
the supposed violation by this model and some other irrelevant discussion of
order and randomness, he states on page 457 his Earth-shattering conclusion
that The Second Law of Thermodynamics is not valid.

There are no observed instances in nature of a violation of The Second Law
of Thermodynamics. Most reasonable people would say that behavior exhibited by
a model that is contrary to what is observed in nature indicates a flaw in the
model. But Wolfram is saying that the supposed violation exhibited by his
model is more important than observation.

Stephen Wolfram, if you are reading this, I have two words for you:

More seriously, I hate to quote `trhurler` but in this case it may be relevant,
"
The greatest conceit, and the greatest mistake, is to believe that your model IS what is modeled."
At this point, I did not judge the remainder of the book to be worth
reading. I skimmed the rest of it and picked up enough about his Principal of
Computational Equivalence to see that he is again rehashing other's ideas. The Universe is a computer.

In summary, if you have this book on order, see if you can cancel your
order. If you can return your copy unread, do so.

A New Kind of Science was published in 2002 by Wolfram Media, Inc.

Hardcover: 1192 pages.