501
edits
Changes
Jump to navigation
Jump to search
no edit summary
== Examples ==
=== Experience spaces of IIT 3.x ===In [[IIT 3.0x]] ===, the following experience spaces are being used.<ref>Kleiner, Johannes, and Sean Tull. "The mathematical structure of integrated information theory." arXiv preprint arXiv:2002.07655 (2020).</ref>
;Definition:
An experience space is a set <math>E</math> with
* an \emph{intensity} function <math>||. || \colon E \to \R^+$</math>;
* a \emph{distance} function <math>d \colon E \times E \to \mathbb{R}^+</math>;
* a \emph{scalar multiplication} <math>\R^+ \times E \to E</math>, denoted <math>(r,e) \mapsto r \cdot e</math>, satisfying
<math>
|| r || e ||= r \cdot || e || \qquad
r \cdot (s \cdot e) = (rs) \cdot e \qquad
1 \cdot e = e
</math>
for all <math>e \in E</math> and <math>r, s \in \R^+</math>.
According to IIT 3.x, every <math>e \in E</math> describes (or "is", according to the central identity) the complete experience of a system in a particular state. The intensity <math>|| e ||</math> 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]].
