A fascinating tale set in a world where people are physically separated into six factions. To one faction, members of other factions are physically invisible, except at intervals when interactions between factions grow stronger, and they can start to see and interact with one another, only to fade away again. Non-living material can be made of up parts of all factions, so houses, etc. can be seen, felt and used by all. Ditto for writing implements (chalk) and there are scenes in this book where factions communicate with one another via ghostly hovering pieces of chalk that write.

In this world, people of each faction live in separate villages that trade with one another. As the tale begins, we learn of a town that has isolated itself from other factions because of a disease called the Dispersion. The disease causes parts of the body of a person to become disassociated with itself and become part of another faction, which is deadly. A girl from another village secretly visits it in order to get one of its scientific leaders to join efforts from other villages to study the Dispersion and figure out what is causing it and how to stop it.

As the group get together to study the Dispersion, with the help of volunteers who painfully contribute their own flesh for examination, radicals from the first town decide to take matters into their own hands over the Dispersion by attempting to get rid of the other towns by violent acts.

As matters come to a head, the girl, with the help of other versed in mathematics, make discoveries about how the factions interact with one another and how the Dispersion may fit into it and how it can be stopped. In a desperate attempt to prove her hypothesis, the girl deliberately infects herself with the Dispersion to try to cure herself.

While the beginning of the story may sound like some kind of strange, ghostly tale where invisible beings interact with one another, the story is grounded in the mathematics of multi-dimensional geometry (an area of interest to the author) and the characters start to make sense of how the interactions can occur geometrically and figure out how the Dispersion is another geometrical aspect of their world. The descriptions of various events (like invisible fires, floods and assassination attempts) also fit the world view where people can only see one-sixth of what is actually happening around them.

A fascinating tale of a world that is different from ours, yet feature the same kind of fractured politics, radical views and attempts to understand the world as it is.