One good thing about this book is that the author attempts to bend over backwards to be fair. He recognizes that psychic abilities and other "paranormal" phenomena are often regarded as beyond the pale and are thus treated poorly by mainstream science, and he argues that this is not an appropriate response. A second good thing are the mathematical and logical discussions for why we ought to be more open minded about real effects that are not yet explainable. But here's where the good parts end.
The discussion of the empirical evidence for psychic phenomena is so woefully lacking that this book just barely merits three stars, and most of that is credit for spelling and grammar. It is clear from the text, the notes, and the bibliography that the author is completely unaware of thousands of relevant experimental publications. Nor is he aware of dozens of meta-analyses, or of the substantial literature on the theoretical and philosophical implications of this domain. He misunderstands the meaning of "supernatural" and he repeats a line about parapsychology that comes straight out of the pseudoskeptic's playbook: "nothing resembling legitimate scientific discoveries ever came of parapsychology." Seriously? Leaving aside many empirical findings, just from a purely methodological perspective such a statement blithely overlooks development of double-blinded methodologies, use of statistical procedures in psychological experiments, the origins of the electroencephalograph, the origins of meta-analysis, and so on.
Well, he does mention one study published long ago, by "Harold Puthoff and Randall Targ of the Stanford Research Institute." He is then quick to add that SRI has no connection with Stanford University, perhaps because if it did then this might lend the work some credibility that is unwarranted. The problem with such a statement, which is representative of distressingly large sections of the book, is that it contains simple mistakes that could have been corrected in 10 seconds with a simple web search. Targ's first name is Russell, and SRI International was indeed part of Stanford University until it split off from the university in the 1970s.
One might argue that getting the details right as well as providing a more comprehensive coverage of the history and evidence may not have been the main focus of the book. And so my criticism is too harsh. However, arguing in favor of the possibility of paranormal phenomena on one hand, while overlooking or dismissing a wealth of relevant scientific data on the other, is at best a bizarre form of backhand compliment. At worst it is a demonstration of sloppy scholarship, and unworthy of a professor who does know his mathematics.