Some sf books are novels of power, where fully realized characters move through richly painted landscapes and evoke ideas of stunning originality. I love those books! Anathem is not that book. Other sf books are intricate puzzles for the mind, inviting you to enjoy identifying and solving neat intellectual puzzles. I love those books too! Luckily, Anathem is that kind of book. And when Neal Stephenson writes a puzzle book it's a bit deeper than your typical murder mystery. It leads one to ask the question "Why the heck is he writing this puzzle book?" and then (in further intellectual exercise) you can speculate up some interesting answers.
The biggest game in Anathem is Spot the Smeerp!  Except here instead of alien critters we're looking for Western philosophers. Throughout the background, world-building, dialog, encyclopedia excerpts, and appendices, Stephenson recapitulates for us the whole of Western classical philosophy, at least those bits that also include the natural sciences. But instead of discussing Occam's Razor, the characters here talk about Gardan’s Steelyard--Spot the Smeerp! 
How can he cram all this infodumping into an sf story? It's easy when your characters are (almost) all philosophers, and your hero is a young philosopher learning his way. The basic set-up of the world is that there are many Maths and Concents (cloisters of a sort) set up around the world, each divided into four parts. The fraas and suurs (smeerp versions of friars and nuns) in the Annual section open their doors to outsiders every year. In the Decade section, they only open their doors every ten years. I'm sure you can extrapolate to the Century and Millenium sections. The system (worked out in exquisite detail) has apparently been working pretty well for almost 3000 years now. They're perfectly capable of pulling up the drawbridges at any time and riding out the political and cultural storms outside their walls. They eschew any technology that may break down during Dark Age periods, trusting mostly large machines of stone and metal. They do not meddle in the affairs of others, dedicating themselves to collecting, preserving, and discovering knowledge. Needless to say, it is perfectly natural that 90% of their conversations revolve around science and philosophy. 
However, most stories can't thrive inside walls opened only once every 100 years or so. We need to get our ivory tower theoreticians out into the world. Along comes a handy crisis, upon which the Fate of the World (of course) rests. For some reason the philosophers can't go about openly, so instead we follow our young hero Erasmus as he drives, walks, and sails most of the way around the world, learning as he goes. Obviously he couldn't become the Hero he needs to be if he just caught a plane to the scene of the climactic action. However, rather against my expectations, he doesn't learn about the outside world and its richness and diversity and value--instead he learns more about the importance of abstract philosophy. In fact, it is only those philosophers who can Save the World!
So we have a fun book here (and don't let me fool you -- between the Spot the Smeerp game and the Bildungsroman,  it really is a fun book) that leads you through certain branches of philosophy. It will probably teach many of Stephenson's readers quite a bit about the traditions of Western thought. But why bother? And why do it now?
Well, Stephenson must think this is all very important; so important that only the people who know philosophy and live (mostly) pure lives of the mind will be his Heroes. Probably, like most sf readers, he feels the internal, intellectual life is very important and rewarding. OK, so when was he writing it? It came out in 2008, so he probably turned it in sometime in 2007, and he writes all his books in long hand with fountain pens, and it's well over 900 pages in print, it had to have taken a few years... Bush! It's all Dubya's fault!
Bush ran for office, rather famously, by being a "nice" guy and a "tough" guy instead of a smart guy. In fact, he embodied that strain of American culture that finds something rather suspicious about educated people. He was in favor of jocks with guns solving the world's problems. I think we can all see how well that's worked out. There are few jocks and no guns in Anathem--the closest you get are the coolly intellectual Shaolin (smeerp = Ringing Vale) monks. Frankly, Anathem is a paen to intellectualism and elitism--and I say Hurrah! 
The dark ages of 2001-2009 may explain certain certain resonances between Anathem and Incandescence, Greg Egan's latest novel.  In that book, we play Spot the Smeerp with physics experiments. (What does Foucault's Pendulum look like when conducted with rocks floating at the center of a tumbling asteroid orbiting a black hole?) It's only through sheer brain power (and, like Anathem, without digital computing) that an alien world can be saved. Why no digital computers? Perhaps to prove to ourselves that we don't need any stinkin' shiny AI/Robot/Computer/Logic-Named-Joe to make our science fiction--we can do it with only the power of our brains. 
Sure, these authors seem to say--sure, jocks with guns and SFX are fun to read about in Space Operas and Mil SF, but in the long run it's the smart guys who've learned the patterns of history and the system of the world  that are going to save us all.
 "Calling a Rabbit a Smeerp" being a traditional cheat in sf world-building.
 And if you have to look in the glossary, that's cheating!
 As opposed to say, gossip about the other fraas and suurs.
 No smeerp here, that just means a Coming of Age Story.
 With the caveat that he really should have included some philosophy from outside the Western tradition; as it is the book seems unbalanced due to its single minded focus on the West.
 Egan is Australian, but definitely aware of the political climate. See his story “Lost Continent” in Jonathan Strahan's Starry Rift anthology, which attacks Australia's own anti-immigrant movement.
 And sometimes banging those rocks together. Keep it up guys!
 Coincidentally, System of the World is the title of the 3rd book in Stephenson's Baroque Cycle trilogy.