I think that James Tagg's aim was to compare the human brain with what is now and might ever be within the capabilities of an artificial intelligence, and to explore areas like creativity and free will where we may see a difference. And there are times that he does this very well. If you have the patience, you will find a lot to get you thinking in Tagg's meanderings through different aspects of the nature of thought and creativity, plus lots of insights into the developments of thinking computers (though not enough, I think on how AI has been developing using neural networks etc.). But the problem is that the book has no narrative arc - it is a series of almost independent chapters, which throw information at you, but don't tell a cohesive story. This is where the patience is required, but, as mentioned, you will certainly find plenty to make you pause and think, especially if you have accepted at face value the suggestion from IT experts that a conscious, more-intelligent-than-human supercomputer is inevitable.
Where I wasn't totally convinced was in a couple of chapters where Tagg tries to prove that there are some things humans can do that a Turing universal computer can't, because he reckons there are some things we can do that aren't computable. It's definitely true that there are some things that aren't computable. And I have to take Tagg's word for it that these include, for instance, Andrew Wiles' proof of Fermat's Last Theorem. But where it gets a bit doubtful is that he says that this also shows, for instance, that a computer could not write some of the music that humans could write, as you can turn Wiles' proof into a musical piece by substituting notes for characters. While this may technically be true a) I don't think any real musician (other than a poser) would want to compose that piece and b) there would still remain an infinite set of musical compositions a computer could produce, of which an infinite subset would be superb music. So does this really mean as Tagg argues that computers can't be creative as we can?
Even so, as we journey from the difference between communication with words and with full-on face-to-face human conversation, through microtubules in the brain and the nature of infinity to how creativity works, there is definitely a lot to make you think. I'm less certain about a topic I know a reasonable amount about, quantum theory, where Tagg makes the statement '[the uncertainty principle] does not prevent the universe knowing the information it needs to allow the particle to go about its business in an entirely deterministic fashion. There is a perfectly reliable an predictable wave function that governs the motion of every particle...' - unfortunately the wave equation is probabilistic, not deterministic, so I can't see how this is true.
One final concern is a certain sloppiness. In a single chapter, Tagg first confuses Babbage’s Difference Engine and Analytical Engine (he talks about the never-built Analytical Engine, but shows a picture of the Science Museum's completed Difference Engine). He describes the Antikythera mechanism, but that label is applied to a picture of a modern reconstruction. And Milton Sirotta, the nephew of mathematician Ed Kasner, who famously came up with the name ‘googol’ is turned into the more exotic Milton Sirocco. Oh, and there is hardly anything on the website the book keep referencing to find out more. (So I couldn't find out if his opening puzzle, supposedly solved there, was answered in a genuinely creative way, or using the uncreative stock answer.)
So it's an interesting mix of a book. It isn't brilliantly written and structured, and it's difficult to draw significant conclusions from it, but it does make you think, and that can't be a bad thing.
Review by Brian Clegg