It doesn't take long for this book to get into the mathematics; We see it right on the first page! As in several of Egan's other books, a form of mathematical physics that builds on current theories of quantum gravity is the focal point. The so-called "quantum graph theory" is described in interesting and believable detail. Unlike some other mathematical fiction where the mathematics comes off sounding obviously fake, Egan is able to capture the essence and cadence of mathematical dialogue while saying things that, presumably, are equally fake. Here, for instance, the scientists brainstorm to try to figure out where they went wrong and eventually come up with an explanation that parallels the current attempts to explain the quantum measurement problem in terms of decoherence.

It is always difficult for me, personally, to read SF stories that take place so far in the future that the characters no longer really seem to be human. In this book, for example, bodies have become optional. The fact that I find it more difficult to identify with these characters however is counter-balanced by two wonderful consequences of this plot twist:

• Egan makes use of this to bring up some interesting questions surrounding the question of "identity" in philosophy. Suppose we could just leave our bodies like a person stepping out of a car, and have a new one built...to what extent do we then identify with our bodies? More mathematically, the title of the book is brought to bear on this old philosophical question. I must admit, I'd never heard of "Schild's Ladder" before, but it is apparently a constructive explanation of the notion of parallel transport of vectors on a manifold. The modern notion of "tangent vectors" in mathematics involves a "tangent bundle", which is to say a separate "tangent space" at each point on the manifold. Although this works well in general, it becomes difficult to say when the tangent vector at one point is the same vector that appears at another. So, the notion of "carrying" a vector around on a manifold becomes a subtle one of practical importance. Here, not only is this notion used to explain (by analogy) how we can tell from moment to moment whether we are the same person, but the mathematical fact that sometimes parallel transport of the same starting vector around different paths with the same endpoints will produce different resulting vectors!
• One character who has only temporarily taken on the form of a physical human body, is asked by some colleagues about what it was like where he grew up. His response is my favorite line in the book. He explains that he was raised in CP⁴ (which looks locally like a 4 dimensional complex vector space but has a very different global topology) and that he only sometimes visited 3 dimensional spaces to work on certain bizarre physics problems...but even then, he prefers working in symplectic manifolds where you can separate the positions and momenta!