One in a series of talks from the 2019 Models of Consciousness conference.
I present a mathematical definition of qualia from which a toy model of consciousness is derived, partly as an attempt to provide a mathematical formulation of the theory of qualia and concepts put forward by C.I. Lewis in 1929. This formulation is guided by the identification of basic principles that convey abstract aspects of the behavior of physical devices that “detect” qualia, such as brains of animals seem to do. The ensuing notion of space of qualia consists of a topological space Q equipped with additional algebraic structure that yields a notion of subjective time and makes Q a so-called stably Gelfand quantale. This leads to interesting conceptual consequences. For instance, “stable observers” emerge naturally and relate closely to the perception of space, which here, contrary to time, is not a primitive notion; and logical versions of quantum superposition and complementarity are obtained. Indeed a mathematical relation exists to quantum theory via operator algebras, due to which a space of qualia can also be regarded as an algebraic and topological model of quantum measurements.
Filmed at the Models of Consciousness conference, University of Oxford, September 2019.