I can sum up the theme of this long-winded 500-page book in one paragraph:
Human experience involves the interplay of two fundamentally opposed modes of reality, which we can refer to as rationality and mysticism, Apollonian and Dionysian (as Nietzsche would call it), scientific and religious (as Bertrand Russell says in
A History of Western Philosophy), or analytic and integrative. The structure of our brains reflects this fundamental opposition, with the left hemisphere corresponding to the first mode and the right hemisphere corresponding to the second mode. Over recorded history, and especially in the past century, the left hemispheric version of reality has taken on undue precedence.
Thinkers throughout the ages have commented on the basic opposition; McGilchrist's novel contribution is the claim that it maps to the asymmetries between the brain hemispheres. It's an interesting claim, and the early chapters where he describes the neuroscientific results are the most compelling — although even in these chapters, he seems to beg the question (in the traditional meaning of the phrase) of whether each hemisphere has its own worldview. Starting a few chapters in, he simply substitutes the terms "left hemisphere" and "right hemisphere," without further argument, in places where other philosophers would use one of the other pairs of terms. He piles on the "evidence" in a repetitive and not very original fashion. He doesn't really argue for his position so much as provide a mountain of facts that are merely consistent with it.
In the end, I was left to wonder what difference it makes whether he's right about how the distinction maps to the structure of the brain: as he carefully points out in the introduction to Part II, he's not claiming that the structure of the brain has changed over the course of recorded history, so how is his view different from a purely cultural explanation of our tilt toward scientism?
I think McGilchrist has an intriguing idea, but I found his presentation of it exhausting and unconvincing. The longer the book went on, the more it seemed like a mere plea for recognizing the importance of mysticism in opposing the sterility of a purely rational world.