Zenith Grant Awardee

Matilde Marcolli

California Institute of Technology

Project Title

Towards a Topological Model of Consciousness

Project Summary

The development of quantitative models of consciousness is motivated both by a better theoretical understanding of the brain, and by pressing medical and ethical questions such as detecting consciousness in people with damaged brains, in non-human animals, and possibly in artificial entities. Some mathematical models of consciousness have been proposed in recent years, based on a sufficient amount of informational complexity detecting a high level of interdependence over subsystems. These models, however, are computationally impractical and they may provide a necessary but not a sufficient condition for consciousness. This project aims at a different kind of model, based on topological methods for the investigation of brain structures. The fundamental idea that we want to formalize is that consciousness is a mechanism that constructs and transforms representations from neural codes topologically and that topology, the branch of mathematics that deals with intrinsic and stable properties of space, is the right language with which to attempt a mathematical formulation of qualia, intrinsic “subjective” experiences. The motivation behind this approach comes from recent results in neuroscience, showing that an increase in topological complexity is detectable in response to stimuli, and that the neural code stores information about the stimulus space topologically.

Technical Abstract

In recent years, new geometric and topological methods have come to play an increasingly important role in the mathematical modelling of neuroscience. The PI has recently been the main organizer of a month long focus program at the Fields Institute on these topics. The project presented in this proposal aims at investigating the possibility of applying these topological and geometric models for neuroscience to the construction of quantitative models of consciousness. There are existing proposals for mathematical measurements of consciousness, such as the theory of integrated information, but these suffer from a number of serious drawbacks. In particular, we would like to aim at a more fundamental model that would imply high values of informational complexity without being defined by it. The mathematical starting point is the notion of Gamma-spaces in homotopy theory, which parameterize consistent assignments of computational, metabolic or informational resources to subsystems of a system, and generate associated homotopy types. The generation and dynamical change of these homotopy types is proposed as a mechanism underlying conscious experiences. The proposed work will be a collaboration of the PI with Yuri Manin (for the mathematical part) and with Doris Tsao (for the neuroscience applications).