This is a good book but not a great book. The author does a decent job of laying out all the basic concepts of modern thinking about information: classical concepts of entropy, the Second Law of Thermodynamics, Claude Shannon's revolutionary reformulation of the problem, and modern concepts of qubits. The writing is brightened by some brilliant metaphors and sparkling descriptions. However, it fell short of my expectations in several areas.
It made no mention of Maxwell's Demon, a paradox created by James Clark Maxwell around 1870. This thought experiment presented a means by which the Second Law of Thermodynamics could be subverted -- meaning that the Second Law isn't really a law! Now, everybody knew that this couldn't be, yet nobody could come up with a way to kill Maxwell's Demon until 1951, when he was finally done in with a quantum mechanical explanation based on the necessity of the Demon using information to perpetrate his crime against the Second Law. This was a crucial point in the development of our concepts of information -- it demonstrated that the Second Law is fundamentally a "conservation of information" law. Yet this book breathes nary a word of this profound development.
Another striking omission was the Uncertainty Principle, the realization that triggered the quantum mechanics revolution and provides the fundamental basis for recognizing information as a finite quantity. This major milestone in the development of concepts of information merits only a passing mention in this book.
Another gaping hole was the treatment of biology. There is a perfunctory discussion of genetic information content, but completely missing was any discussion of the biosphere capturing the negentropy (information) from the sun.
Lastly, I felt that the explanation of the relationship of entropy to information -- through such concepts as orderliness -- was weak. The author addresses this concept, but instead relies on looser terms such as "form", so the point isn't driven home as clearly as it could have been.
Then there are the digressions. The pages devoted to Democritus' atomic hypothesis are, I think, wasted; all readers know about atoms and the material doesn't affect any subsequent discussions. Similarly, the discussions of special relativity and general relativity, while intrinsically interesting, are not germane to the subject at hand and only serve to confuse the reader. And I think that the discussion of Bayes Theorem does nothing to advance the reader's understanding.
I think the book is best in its overall presentation of the paradoxes that quantum mechanics created regarding information. The discussion of Schroedinger's Cat (a classic paradox about information and reality) is good, and the detailed treatment of quantum interference is definitely the strongest point of the book. It's also a good point to emphasize, because it feeds into subsequent discussions.
Sadly, the discussion of the qubit doesn't illuminate the nature of this truly mysterious concept. I concede that this is a difficult concept to explain without the use of mathematics, but I think that a better job could have been done if the subject had been explained more slowly and thoroughly.
In the author's defense, I note that tackling all this without a single equation is quite a feat. He does refer to logarithms, but otherwise he keeps the math out of the picture, most likely at the insistence of his editors. Explaining information concepts without mathematics is like playing a sport with one hand tied behind your back -- it's theoretically possible but impossible to do well.
So, would I recommend this book? As always, it depends upon the audience. I would NOT recommend this book to anybody who is already familiar with the basics: Second Thermo, Uncertainty Principle, Shannon, and so forth. Its explanations of the modern concepts (black holes and information, qubits, information as a physical quantity) is inadequate to the needs of a prepared reader.
I would, however, recommend this book to the beginner who knows nothing about information theory. If you've heard about this stuff and are curious about the foundations, this is one of the better books to start with. However, if you want to understand the concept of the qubit or how it might be used to build computers, this book won't help.