Abstract
To arbitrate theories of consciousness, scientists need to understand mathematical structures of quality of consciousness, or qualia. The dominant view regards qualia as points in a dimensional space. This view implicitly assumes that qualia can be measured without any effect on them. This contrasts with intuitions and empirical findings to show that by means of internal attention qualia can change when they are measured. What is a proper mathematical structure for entities that are affected by the act of measurement? Here we propose the mathematical structure used in quantum theory, in which we consider qualia as "observables" (i.e., entities that can, in principle, be observed), sensory inputs and internal attention as "states" that specify the context that a measurement takes place, and "measurement outcomes" with probabilities that qualia observables take particular values. Based on this mathematical structure, the Quantum-like Qualia (QQ) hypothesis proposes that qualia observables interact with the world, as if through an interface of sensory inputs and internal attention. We argue that this qualia-interface-world scheme has the same mathematical structure as observables-states-environment in quantum theory. Moreover, within this structure, the concept of a "measurement instrument" in quantum theory can precisely model how measurements affect qualia observables and states. We argue that QQ naturally explains known properties of qualia and predicts that qualia are sometimes indeterminate. Such predictions can be empirically determined by the presence of order effects or violations of Bell inequalities. Confirmation of such predictions substantiates our overarching claim that the mathematical structure of QQ will offer novel insights into the nature of consciousness.
