ABSTRACT
Tolerance spaces are a mathematical tool useful for describing the brain. The intuitive idea of doing mathematics on a tolerance space is that we can move about within the tolerance without noticing any difference. Many of the things we can do with topological spaces we can also do with tolerance spaces, and for this reason we borrow both words and notation from topology. The main idea is to take into account the different parts of the brain, and we shall show how the notion of tolerance spaces can facilitate discussion. The chapter shows how tolerance spaces might be useful in discussing language. Ideas are sometimes distorted by putting them into words, and so this process imposes a tolerance on the set of ideas. Important place where homology theory will need to be used is to discuss the coupling and resonance of the differential equations in the hippocampus and cortex.
