This is, in effect, a [Singularity](http://en.wikipedia.org/wiki/Technological_singularity) story, though a rather gentle, slightly comic one.
The AIs that gain self-awareness and seek to achieve independence and change the world, start out as part of an educational project called the Museum of the Mind. In this construct there are a number of simulations of figures from history (mostly fictional, like the victorian prostitute). School pupils, students, researchers and others can interrogate them about life in their time.
It’s interesting that Byrne has them start to gain self-awareness after their systems get infected with a religious program: a virus that tries to ‘convert’ them to Mormonism. I don’t know whether Byrne is trying to tell us that religion is necessary for self-awareness, or if it just seems like a useful trigger to give the programs some extra input and start them asking questions.
Anyway, one of the erams, as they are called (electronic recreation of a mindstate) is based on an early-20th-century socialist activist. Shocked at the apparent absence of socialism in the world he sees outside the computer networks, he organises his fellow erams, and sets out to change the world (and protect their very existence along the way). The title stands for “This Great Movement Of Ours”, which was once a common phrase in speeches by Labour activists, apparently.
It’s good fun, if lightweight. It was published in 1999; I wonder what’s happened to Eugene Byrne since then?