A Mathematical Theory of Consciousness

Giulio Tononi's Integrated Information Theory

The Integrated Information Theory (IIT) of consciousness, proposed by Giulio Tononi quantifies our intuition that the whole is more than the sum of its parts. IIT quantifies the amount of information a system is generating above and beyond the information that is generated by parts of that system.

This kind of Integrated Information is difficult to generate. Most systems are either too connected or too segregated to generate information above and beyond their parts. For such systems, the reductionist approach is sufficient to explain and predict their behavior.

Our brain, however, is ideally suited to produce nonreducible, Integrated Information. The brain has the right balance of specialized functions, and global connections between such functions, to create massive amounts of Integrated Information.

Thus, IIT holds that our waking brain is quantifiably more than the sum of its parts, and that our vivid consciousness is expression of this remarkable fact. Check out the resources below to learn more! :)

Integrated Information Theory 3.0

This article contains the latest, up to date version of the integrated information theory.

Qualia: The Geometry of Integrated Information

This article explores how integrated information has an intrinsic geometry that can be used to account for difference and similarity relations among qualia.

Resources for Exploring Integrated Information

Here you can, among other things, set up your own network and explore how integrated information changes depending on the network.

Debate between Scott Aaronson and Giulio Tononi

From these discussions it appears Tononi's theory is still unconvincing for many, or at least incomplete as it stands. Some of it has to do with the mathematical calculation of integrated information, and some of it has to do with moe general skepticism regarding a mathematical theory of consciousness.

Anyone have any thoughts on this? I am deeply fascinated by this issue, but I don't have the mathematical or information-theoretical background to be able to assess the details.