It is impossible to get a handle on what is going on in the first few chapters, and a lot of the dialogue is thus expository, drowning the reader in infodumps of tale after tale from Arbre’s colourful history. This is fine, except in that everything blends into a haze of names and events without anything to relate them to. Fortunately, the book gets much better.
Anathem uses a couple of old storytelling tricks. One: Erasmus, the protagonist, is always a bit out of place, an underachiever, very nearly (and then actually) an outcast. To someone looking in from outside Anathem’s segregated society, Erasmas is a perfect lens, an easy pair of eyes to peer through. Two: About one-third of the way through the story moves out of the monastic environs (the “concent”), and the tone of the novel switches from exposition to discovery. The reader and Erasmas possess the same knowledge at this point, and are perfectly in sync from then on.
The narrative is the usual (for Stephenson) genre-hopping skein, veering from philosophical discourses to arctic escapades. None of it is spectacular, but you can’t fault it for not being clever or gritty.
The “universals” of knowledge continue to pop up, now at higher levels of abstraction: The traveling salesman problem becomes the lazy peregrin, long since solved in Finite Time on Arbre on quantum computers (Saunt Grod’s machines). The adrakhonic theorem of right angled triangles (guess) rears its head in the plot proper.
The most surprising bits of theorizing are in fact on the nature of consciousness, which is one of the struts propping up Anathem’s central mystery. Stephenson spins a yarn about the brain using quantum effects to construct models of physical reality, which is a lot to swallow but does work if you don’t pay too much attention. (A lot of philosophy feels this way.) Another strut is the existence of the polycosmi, alternate realities forking at the resolution of each quantum event. It’s a bit too much to take in at once, but some elegant phase space (“Hemn space”) justifications make it palatable. (Readers of Penrose’s The Emperor’s New Mind will feel right at home here, inasmuch as it is possible to feel at home with the many-worlds interpretation of quantum mechanics.)
The mystery is pretty much resolved at this point; plot threads joining up slowly. Without dipping into spoiler material, it’s hard to see how this will end, though.