Experience Spaces

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Experience spaces are mathematical spaces which represent conscious experience. Every element of an experience space corresponds to a state of consciousness which describes the totality of impressions, feelings, etc. that make up conscious experience. The mathematical structure of experience spaces represents the structure of conscious experience. Sometimes, experience spaces only describe certain aspects of conscious experience, such as visual or auditory experiences.


Experience spaces of IIT 3.x

In IIT 3.x, the following experience spaces are being used.[1]


An experience space is a set with

  • an \emph{intensity} function ;
  • a \emph{distance} function ;
  • a \emph{scalar multiplication} , denoted , satisfying

for all and .

According to IIT 3.x, every describes (or "is", according to the central identity) the complete experience of a system in a particular state. The intensity specifies the level of consciousness of the system. Though not made explicit in any IIT 3.x paper, one could understand the distance as representing similarity between experiences, as e.g. the case in quality spaces.

List of structural features of conscious experience that should be modelled

  • Similarity, e.g. using a metric
  • Intensity of experience (the level of consciousness, so to speak, as in IIT 3.x)
  • The compositional structure of conscious experience, including:
    • Inclusion: Whether aspects of experiences are included in other aspects
    • Composition: Whether an aspect of experience is composed of other aspects (the whole is equal to the sum, so to speak)
  • Precision[2]

Mathematical structure that has been proposed

Relation to qualia spaces and quality spaces



  1. Kleiner, Johannes, and Sean Tull. "The mathematical structure of integrated information theory." arXiv preprint arXiv:2002.07655 (2020).
  2. Cf. Lee, Andrew Y. "Modeling Mental Qualities."