Leibniz thought that this actual world was singled out from all other possible worlds being being the fullest, the one with more compossible elements than any other. But why single out one possible world as actual at all? All of them are perfectly good logical possibilities, and from the inside one looks as real as another. (This is true even of the worlds where everyone has an unshakable conviction that they are not real.) You don't even need a separate universe for each one; all you need are events, sheer unordered chaos. Every internally consistent ordering of events into a space-time will look as good from the inside as every other; all the possible worlds exist at once, interpenetrating and intermingling, ``assembling themselves from the dust.'' This is what Egan's characters call ``the hypothesis of the dust,'' and proceed to exploit.
Accepting, for the sake of the novel, that consciousness is just a matter of a certain kind of computation, it can be perched atop an arbitrarily high tower of simulation. You can start with physical computers, implement a Turing-equivalent, indefinitely growing cellular automaton on it, and then implement a consciousness as a program running on a computer constructed in the cellular automaton. You do this so that when the physical computers are turned off, your consciousness (already copied into an abstract, programmatic form) is already firmly embedded in an ever-growing CA world, which is perfectly self-consistent and perfectly stable, and so, by the hypothesis of the dust, will continue regardless of whatever happens to the universe it was spawned from. This makes no sense, of course, since by that self-same hypothesis of the dust that universe already exists, whatever you do in this one; but human minds are not equipped to follow stories told sub specie aeternatis, and Egan is a good enough story-teller to carry the plot over this obstacle by sheer force. Then things begin to get strange.
It took me about half a day to argue myself out of the hypothesis of the dust. I'm still not completely certain it's altogether wrong. I am certain that I should have read this book when it came out, four years ago. Do so at once.