I went ahead and downloaded the book to my Kindle. Sure glad I got it. 
I’ll share some quotes soon. Read the Prologue which was interesting last night. Of course that is about biology though, not the physics you asked about. One interesting tidbit is that we have less quantity of information in our DNA than a banana. But Ball explains that some of ours is coded in less rigid ways so that the same sequences can play more roles than in simpler organisms. One of the main changes in perspective is in seeing organisms as less mechanistic even though, as he and McGilchrist agree, the machine is sometimes a good tool for predicting effects even if it doesn’t help to understand the big picture. Another is in recognizing that development of the organism is not always built up from lower levels, that sometimes it is the region of cells affected which collaborate on a solution rather than carrying out immutable changes. This is not my area but Ball as a former editor of Nature magazine is writing with us in mind which I appreciate.
As for McGilchrist’s claims about physics, I believe they are the majority opinion now. Doesn’t change how you chart a mission to Mars. Newton’s science is capable of that. But as with the biology, looking at the unfolding of the cosmos in a strictly mechanical manner simply ran into a number of difficulties. But that was a hundred years sooner than with biology.
If we were AI (algorithmic invention) users we could just ask the program to assemble something about where things stand with physics. But I’d rather rely on the intelligence of people (preferably those with more preparation than I have in the subject).