This second novel in Egan's "Orthogonal Trilogy" continues to follow the scientific and mathematical discoveries of creatures on a space ship hoping to find a way to save their home world. That plot and the interesting biology of the creatures may be of interest to some readers, but to really appreciate this novel one has to care about the fact that the laws of physics themselves are different in the universe that they inhabit. In particular, whereas the metric tensor of spacetime in our universe has one negative and three positive signatures, theirs is entirely positive.
Egan has done a spectacular job of considering the ways that life would be different in such a universe. For instance, it makes sense that plants would give off light and that the creatures would sleep in sand beds to shed heat while they sleep. Moreover, the discoveries he has his characters make are sensible, sufficiently similar to analogous discoveries in our own history that one can enjoy identifying them ("Oh, that's like when Einstein discovered special relativity!") and also sufficiently different to create an interesting comparison.
In this book, the primary mathematical content is in the algebra of 4dimensional space, which we would call the quaternions. In our (real) history, the quaternions were soon supplanted by the more general constructions of linear algebra, though they still have their proponents. In the universe of the Orthogonal Trilogy, however, the fully positive signature of the spacetime metric makes the quaternions seem even more useful and natural. So, this is a great place to see them in action.
As is often the case with trilogies, I feel that the second book does not stand as well on its own as the first book and is not as satisfying as the third. However, for me at least, the pay off from the entire series was definitely worth it. So, I encourage you to read all three: Clockwork Rocket, The Eternal Flame, and The Arrows of Time, in order.
