Since I have never read Pirsig, let me just give a few excerpts from Nicholson's summary so that you get the main idea:
The Metaphysics of Quality is, in some limited sense, as follows. He had in his first book realized (and made the case) that Quality is an undefinable entity that is the precursor of subjects and objects; everyone knows what it is but no one can define it. He proceeds to understand that subjects and objects are only one dual pair of defined things into which the undefined Quality event gets split as it is “realized”—that is, made real through a necessarily incomplete attempt to define it. ...Nicholson then goes on to apply this metaphysics to the problem of "the unreasonable effectiveness of mathematics."
In his second book, however, he is led to a different split into what he calls “static” and “dynamic” aspects of reality as the best split possible, the most useful. He actually terms them static quality (or value) and Dynamic Quality, and with them he builds his Metaphysics of Quality, a metaphysical framework that provides a different, and, he demonstrates, better way of understanding the world we live in. Dynamic Quality is the undefined Quality that was described in his first book, but now he introduces static patterns of quality alongside it to reflect the “realization” of that undefined Quality which makes up our world. They act like a ratchet: the Dynamic Quality is the constant stimulus to move to something “better”, to ratchet up, but the static quality is the latch of the ratchet itself, the making tangible of the motion up into something concrete which will prevent falling down into something “worse”. Dynamic Quality is the creative urge, whereas static quality, or patterns of static quality, is what is created in response.
In building his Metaphysics of Quality, Pirsig classifies patterns of static quality into four discrete yet interrelated levels: Inorganic, Biological, Social, and Intellectual. He describes the relationship between these levels as being analogous to the relationship of computer hardware to computer software—the software is run on the hardware, but has nothing, really, to do with it. The program that you run on your computer and write your article with has nothing to do with the computer hardware itself. Furthermore, the content of your article has nothing to do with the program you write it in. In this way the levels of static quality are related to each other: Biological is built on Inorganic, Social is built on Biological, and Intellectual is built on Social, but each level is independent of the other.
Using this idea, Pirsig makes the case that Darwinian evolution is just Dynamic Quality at work by understanding “survival of the fittest” as meaning the movement of static quality (survival) towards Dynamic Quality (fittest). Then the four levels of static quality are levels of evolution.
The key word in Wigner’s thesis is “unreasonable”; he actually hit on the solution to the problem in the title of his article. Since Dynamic Quality cannot be defined, it is by definition (so to speak) unreasonable. But that is the reason that any explanation of Wigner’s observation requires an expanded metaphysics. In our tacitly assumed subject-object metaphysics, as Pirsig makes clear, anything “unreasonable” is discarded, and so the effectiveness of mathematics in describing the natural world is an insoluble quandary. Once an “unreasonable” entity, Quality is seen as the root or precursor to all subjects and objects, the quandary fades. ...As I understand this, it feels like simply an evolved, 20th century version of Platonism, with a dash of eastern religion added for flavor. And I'm entirely comfortable with that. The only thing I want to point out is how easily this Metaphysics of Quality fits into the idea of participation in the divine. Whereas the Platonist might say that concrete assertions in mathematics are reflections or shadows of a higher reality, Nicholson, drawing on Pirsig, is saying that mathematical ideas are "static patterns" emerging in response to Dynamic Quality. And whereas the Platonist might imagine this higher reality as unchanging while changeable things are merely shadows, Pirsig's philosophy flips that around and says that what is more real is changing, so that all of reality is cast in a Darwinian light.
The Metaphysics of Quality also easily solves another long-standing dilemma among mathematicians regarding the nature of their subject: the “is mathematics invented or discovered?” debate. The solution to this debate is reminiscent of the Metaphysics of Quality’s resolution of the “free will versus determinism” debate referred to above. Mathematics is invented insofar as it is a process of following Dynamic Quality—that is, insofar as it is “free”. It is discovered insofar as it is a process of fleshing out previously unknown consequences within the static patterns of quality that are mathematics as it stands. Most Ph.D. theses and much published mathematics are more of this latter type—original work, that is, new consequences of existing static patterns, but not in the sense of following only Dynamic Quality. In fact, one might say that any new development comes as a mixture of both types of originality; it lies on a continuum between purely static quality at one end and purely Dynamic Quality at the other. The most “creative” and “original” mathematics obviously sits toward the Dynamic Quality end of the spectrum.
Which leads me to the question: can we really escape the moral question about God's goodness? Whether God is the creator or simply the selector, whether he is the personal God of the Old Testament or the impersonal God of physics, it does seem like the process of discovery is tied up with this grand question: is it all worth it? In other words, if my intelligence is the result of a selection process that ultimately has no moral worth, why not rebel against it? Perhaps the answers we've been getting from science really are wrong on some fundamental level--not wrong in the sense that they have predictive power, but wrong in the sense that the universe is not worthy of our comprehension. Much like a young Christian who suddenly discovers he can't find it in himself to worship a God who banishes people to eternal torment in hell, maybe one day humanity will rebel against the very idea of knowledge, on the grounds that the universe is just too cruel or depressing to be worthy of our careful study.
Theodicy, it seems to me, is not merely a question for theists.