It’s not often that I get to enjoy a discussion of Cantorian set theory in a Science Fiction novel. I don’t remember much about this flavor of set theory since it’s not one of those things that comes up in day to day conversations. I do remember that it had to do with counting infinities.
The title of Brunner’s novel "The Infinitive of Go" has to do with a typically Brunner kind of science fiction idea, a transporter called a Poster. This device does not actually send anything through space, it just makes two areas of space appear to be the same so that things slip back and forth between these spaces. The problem arises when, using a Cantorian analysis, that there can be infinite areas of space that are identical across many possible universes. People start switching universes when the move through the poster because it the movement is not only to the area of space that is nearest in configuration, but also nearest in the set of all possibilities. This nearness, it turns out is based on the secret thoughts and desires of the person being transmitted.
This is a fun idea, which is full of interesting twists. The idea of an alien looking person, but still human, speaking English and claiming to be Catholic, but with a baboon’s face is a fun situation.
The Science Fiction adventure aspects of the plot more than make up for the very obscure bits of math used to generate the problems. Brunner treats Cantorian Rho space very lightly, never really trying to explain it. I would guess that most people would just accept the fact that there are infinite parallel universes and the poster device seems to be making some interesting choices as to who winds up where.
My only objection is that the characters are a little flat and the plot seems to be a Brunner standard. I have been reading Brunner exclusively for about a month and soon I will need to make a change, even if I have a dozen more Brunner novels to read in my box of unread books.