“What is consciousness?” is a highly general question, a much more quantifiable sub-question is “what are the common mathematical properties of learning-capable systems?”. In this talk we will examine a number of architectures implementing learning systems, the features determining the topology of the computational spaces they implement, and how information is represented and manipulated within these spaces. Studying the topological commonalities among these spaces in conjunction with the properties of the systems implementing them gives a much more meaningful and quantitative approach to understanding the phenomena of consciousness. Additionally, this approach can greatly aid the development of novel, learning-capable systems as well as important principles for the design of their architectures.