This is like a religious story for radical transhumanists. As humans transcend biology, we will have many issues to face of humanity, mortality, and what identity means when you can redefine yourself in every way.
An upload, or Copy as it is here called, is a mental scan of a human being run on a computer network. You back up your brain in case of biological death, although you could start living an electronic life while your body is still going. Paul Durham copies himself to test some fundamentals about the nature of Copies. A later Paul Durham is selling an impossible immortality to Copies, and he enlists programmer Maria Deluca to help with some explorations of nonbiological life. Once you have abandoned the biology, is it you that wakes up inside that computer? Are we cheating death or just cheating ourselves?
The cosmological underpinnings seem unlikely at best, moving the away from traditional science fiction. Material-independent consciousness sustaining itself through ... what? The act of being consciousness maintains its own consistency? As we get into Part Two, the consistency becomes a greater issue as we can have literally competing models of reality. I enjoy both hard sci fi and speculative fiction that hurdles beyond the science, but bridging the two is hard to do well. At least when Heinlein does it, he commits to that leap into incoherence beyond science. We accept the impossible but not the improbable.
As a philosophical digression, "universe as cellular automaton" (as postulated in Part Two) could justify Berkeley and resolve the problem of evil. Cellular automata are not computable from their base states, or rather they are only computable and not predictable. The only way you see how the process works out is to run the process. This is how the Autoverse works. Assume for a moment that the universe exists in the mind of God and is a cellular automaton. God is trying to create the best of all possible universes, but to know which it is, he must think about the possibilities. Because universes are cellular automata, this involves mentally "running" every possible universe to see how it works out. Therefore, we exist in the mind of God, in the way a simulation exists on your computer; God is creating the best of all possible universes, and may in fact have done so, but we may not be part of that universe, simply self-conscious elements of a simulation; and all the possible universes that could exist in fact simultaneously do, to the extent that everything exists in the mind of God as fully as we exist. This would account for why problems exist in our universe given an omnipotent, omniscient, and omnibenevolent creator. But this takes us astray of our topic.
While Paul and Maria muddle about in cosmological questions, I find myself much more interested in Peer and Kate, copy stowaways in Permutation City. Part of that is because I sympathize with Peer completely; we share a contented acceptance that infuriates others, he is devotedly in love, and he has embraced his transhumanist Solipsist Nation ideals completely. More importantly, they are considering the meaning of all this on a very personal level, rather than expounding ill-defined metaphysics. Having surpassed human life, they exhibit very different senses of life. I am usually more interested in the personal import of ideas than the social import.
Thomas's side story is another sense of life entirely, providing a counterpoint that is explored but never discussed or integrated. His presence is jarring in a productive way.
This is not my strongest recommendation at a 3 rating, but the excellent parts outweigh the weaker ones. [Update: and the excellent parts are worth re-reading.] The perspectives from Peer and Maria are very good. Paul's philosophical exegeses are not as strong as they could be. Thomas's scenes might work better on film, but they still work. There are problems in the editing, such as "bail" versus "bale" and some typographical issues, but they are forgivable.
I am fully open to the notion that I am unduly attracted to a book that panders to my interests. I find the idea of uploading as desirable as others find it horrifying. Your mileage may vary. As a parting note, it is healthy for Americans to read Australian authors; I find the perspective similar enough to be instantly accessible while different enough to put a new light on things. The US is not always the center of the universe, in a way that we might dismiss in a European novel.
Amazon link (seems to be out of print)
Further thoughts at Kill Ten Rats