From the Anathem wiki, I find a convenient copy of: "Our opponent is an alien starship packed with atomic bombs," I said. "We have a protractor".
Hmm. Now time has passed - we're into October - so it's about time to finish this off. TL:DR: it was worth reading again.
My principle objection to the book remains as before: that the in-math evocation of a life devoted to Thought is better, and more interesting, and more thought-provoking, than the second-half-of-the-book's Ninja Monks In Space. I would have liked to have read a second version of the book, slower paced - perhaps following my idea, below, of the aliens being further out - with no physical action, but everything done with thought.
When we turn to governance, always a fascinating issue, we discover what one might call the "Harry Potter Problem", which is that the apparently-ideal sub-world our hero lives in turns out to have dreadful governance. In HP world, for example, Azkaban is a dreadful "prison" which is really a worse-than-torture-chamber and the wizarding authorities make use of Dementors. In Anathem the mathic authorities turn out to be despotic and unchallengeable. And this weakness of the world doesn't get remarked upon: in order for the Deep Thought to remain Pure, the Deep Thinkers have to be in a sense children: non-self-governing. "Can you govern yourself?" is always the question.
As a token, I offer another plot hole: the idea that the alien spaceship would come so close. Why would you take your huge, vital, vulnerable, infinitely precious spaceship so close to a planet with nukes, when you could so easily not do so. Instead, you hang further out, and send a pile of smaller satellites to observe. Not only is the far safer, but it also uses far less manoeuvering energy - an important matter, since in the books the aliens start to run short of bombs.
The idea of the spaceship hanging further out brings up another unexplained matter, which is the connection or lack thereof between the in-this-universe travel of the ship, and the travel between universes. The travel is talked of as though it is long; one could perhaps "explain" this along the familiarish lines that "warp drive only works far from gravitational fields", so perhaps the ship needs to spend a century or so leaving the current solar system. But, all that goes unexplored.
2020 re-read
I re-read it, for the third read, in 2020. Again, I enjoyed it. I have more quibbles though.
At one point Our Heroes deduce that the Hedron is short of nukes. Their reasoning is totally spurious - the lack of a course change, which it hasn't made yet. Furthermore, it has a stonking great WorldBurner sitting on it all waiting to be turned into baby nukes.
At another point, Our Heroes deduce that the Hedron comes from different matter, because of the (by eye) colour of a red laser. This I think is again spurious - any subtle shifts would not be by-eye visible. Furthermore, what is the Hedron doing with a ready made giant illuminate-ground-targets laser, anyway? Also, much is made of the orbit, which just reaches 51 - or was it 56 - degrees, the latitude of the northernmost inviolate. But (a) the Hedron is out at 17k km, so doesn't need to be directly above; and (b) on any one pass, or sequence of passes, it won't go over any given set of three points anyway.
Orolo's departure from Bly's Butte is never really explained.
More seriously, the philosophy is objectionable. I should have realised this before but I've just re-read Popper (TOSAIE vol 1, The Spell of Plato) and the entire Hylean Theoric World is Plato's evil theory; but because it is put into the mouths of good people in the novel - indeed, it turns out to be true in the novel - it is presented as Good.
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