This enterprising, enthusiastic, and energetic book undertakes to provide a foundational perspective on three phases of modern computing: theory, architecture, and scientific exploration. The author considers these to be exhaustive, and courageously surveys a substantial and growing field of publications that grapple with one or several of these aspects. He makes a strong case that there is no direct competitor--his scope is both wider and deeper than any other. But is it wiser? I applaud the vision and welcome the execution of this endeavor. At the same time, there are some shortcomings in assumed background and use of language that undermine the clarity of the pursuit.

After an introductory chapter, the book is divided into three sections, followed by a concluding chapter. Part 1, “The Mathematical Foundation,” comprises chapters 2 through 7; Part 2 covers “The Engineering Foundation” in chapters 8 through 12; and Part 3 consists of four chapters devoted to “The Experimental Foundation.” At the end of each of these 15 discourse chapters is a list of exercises, an important contribution that serves to strengthen the work’s position as a textbook. The exercises include summary essays, definitions, applications of concepts and techniques, explorations of online simulators, and problems (no solutions), some challenging.

The book intends to support three standard computer science (CS) courses: computability theory (chapters 2 through 5), computer architecture (chapters 8 and 9), and computer modeling and simulation (chapters 13 and 14). The capstone chapter in each section summarizes the exposition of that section in terms of flavors of computational validity: formal, physical, and experimental.

To appreciate the reading difficulty mentioned, consider the first two definitions, which follow a brief reference to propositional calculus, suggesting that the reader is already familiar with that.

Definition 1 (Interpretation) An interpretation of a formula φ is an assignment of meanings to any individual variable x of φ or predicative variable P(x) of φ for objects and predicates (or relations for predicates ranging over more than one variable) in the language of a system F.

Definition 2 (Model) A model Μ of a sentence φ (or a set of sentences Γ) is an interpretation in which φ (or every φ member of Γ) is true.

The definitions are separated by a short paragraph stating that the gap between the two is covered by the rules for logical connectives and the standard extension to quantifiers. A reader trained in logic will have no trouble following the abrupt development, but a newcomer may balk at the use of words such as predicative, objects, language, (formal) system, and true, used with no explicit introduction. Prepositions are supplied and overloaded strangely--witness by, in, of, and for, in particular.

We can ignore this problem at the cost of disregarding the book as a basic text. It may be that more regulated discursiveness will help in the other two areas as well. There seem to be very few textual flaws, but here are two: “principia” out of the blue on p. 14, and “formalism” instead of “logicism” on p. 19.

A nice addition to the second part is the characterization of very different machines by uniform measures: number of components, clock speed, operation speed, electrical power, and so on. While a good choice of machines is presented, it could be broadened by adding the ACE family pioneered by Turing and recognizing the universality of Colossus and even Babbage’s analytical engine.

Some of the most engaging experiences for the reader are the debates, where the author allows variant passionate interpretations full rein to contend. These appear in every setting, from theory to practice, and in every century if not decade.

In conclusion, the scope of the book is unparalleled, and the author succeeds in harnessing a vast variety of arguments, debates, and horizons. My objections to the first lines of the first chapter of the first section need not spoil any appreciation for the rest of the book.