Given the passion and thoroughness with which Gallistel and King tackle their subject, I am almost embarrassed to give this book such a low rating. The subject matter is, in itself, hugely interesting, and the authors' main thesis—which challenges the dominant connectionist orthodoxy—is a valuable contribution to the cognitive science literature. The thesis is also a simple one: "If the computational theory of mind, the core assumption of cognitive science, is correct, then brains must possess a mechanism for carrying information forward in time in a computationally accessible form" [p. 287]. The authors stress that neural plasticity, well accepted as a mechanism for learning, is unrealistically assumed to also be responsible for memory's "carrying information forward" and cannot possibly do the job it's claimed to do.
Sadly, for me at least, the authors' painstaking approach to establishing their case, complete with thorough analyses of Turing machines and detailed, protracted explanations of various toy implementations of a variety of tasks—from simple arithmetic to dead reckoning of location—made for often painfully dull reading. The book is not without its good passages, and it is at least equipped with chapter-ending summaries to refresh the memory of those rendered punch-drunk or finding themselves dragging their eyes over the material more than actually reading it. Chapter 16 serves as a nice closer to the book, and the reader pressed for time may do well to read it, the introduction, and the end-of-chapter summaries to more than adequately get the book's message.