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Qualia: The Geometry of Integrated Information

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  • David Balduzzi
  • Giulio Tononi

Abstract

According to the integrated information theory, the quantity of consciousness is the amount of integrated information generated by a complex of elements, and the quality of experience is specified by the informational relationships it generates. This paper outlines a framework for characterizing the informational relationships generated by such systems. Qualia space (Q) is a space having an axis for each possible state (activity pattern) of a complex. Within Q, each submechanism specifies a point corresponding to a repertoire of system states. Arrows between repertoires in Q define informational relationships. Together, these arrows specify a quale—a shape that completely and univocally characterizes the quality of a conscious experience. Φ— the height of this shape—is the quantity of consciousness associated with the experience. Entanglement measures how irreducible informational relationships are to their component relationships, specifying concepts and modes. Several corollaries follow from these premises. The quale is determined by both the mechanism and state of the system. Thus, two different systems having identical activity patterns may generate different qualia. Conversely, the same quale may be generated by two systems that differ in both activity and connectivity. Both active and inactive elements specify a quale, but elements that are inactivated do not. Also, the activation of an element affects experience by changing the shape of the quale. The subdivision of experience into modalities and submodalities corresponds to subshapes in Q. In principle, different aspects of experience may be classified as different shapes in Q, and the similarity between experiences reduces to similarities between shapes. Finally, specific qualities, such as the “redness” of red, while generated by a local mechanism, cannot be reduced to it, but require considering the entire quale. Ultimately, the present framework may offer a principled way for translating qualitative properties of experience into mathematics.Author Summary: In prior work, we suggested that consciousness has to do with integrated information, which was defined as the amount of information generated by a system in a given state, above and beyond the information generated independently by its parts. In the present paper, we move from computing the quantity of integrated information to describing the structure or quality of the integrated information unfolded by interactions in the system. We take a geometric approach, introducing the notion of a quale as a shape that embodies the entire set of informational relationships generated by interactions in the system. The paper investigates how features of the quale relate to properties of the underlying system and also to basic features of experience, providing the beginnings of a mathematical dictionary relating neurophysiology to the geometry of the quale and the geometry to phenomenology.

Suggested Citation

  • David Balduzzi & Giulio Tononi, 2009. "Qualia: The Geometry of Integrated Information," PLOS Computational Biology, Public Library of Science, vol. 5(8), pages 1-24, August.
    • Handle: RePEc:plo:pcbi00:1000462
    DOI: 10.1371/journal.pcbi.1000462
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    References listed on IDEAS

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    1. R. Quian Quiroga & L. Reddy & G. Kreiman & C. Koch & I. Fried, 2005. "Invariant visual representation by single neurons in the human brain," Nature, Nature, vol. 435(7045), pages 1102-1107, June.
    2. Karl Friston, 2008. "Hierarchical Models in the Brain," PLOS Computational Biology, Public Library of Science, vol. 4(11), pages 1-24, November.
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    1. Werner, Gerhard, 2013. "Consciousness viewed in the framework of brain phase space dynamics, criticality, and the Renormalization Group," Chaos, Solitons & Fractals, Elsevier, vol. 55(C), pages 3-12.
    2. L. Ingber, 2011. "Computational algorithms derived from multiple scales of neocortical processing," Lester Ingber Papers 11ca, Lester Ingber.
    3. Takayuki Niizato & Kotaro Sakamoto & Yoh-ichi Mototake & Hisashi Murakami & Takenori Tomaru & Tomotaro Hoshika & Toshiki Fukushima, 2020. "Finding continuity and discontinuity in fish schools via integrated information theory," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-29, February.
    4. Masafumi Oizumi & Larissa Albantakis & Giulio Tononi, 2014. "From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0," PLOS Computational Biology, Public Library of Science, vol. 10(5), pages 1-25, May.
    5. Adam B Barrett & Anil K Seth, 2011. "Practical Measures of Integrated Information for Time-Series Data," PLOS Computational Biology, Public Library of Science, vol. 7(1), pages 1-18, January.
    6. Masafumi Oizumi & Shun-ichi Amari & Toru Yanagawa & Naotaka Fujii & Naotsugu Tsuchiya, 2016. "Measuring Integrated Information from the Decoding Perspective," PLOS Computational Biology, Public Library of Science, vol. 12(1), pages 1-18, January.
    7. L. Ingber, 2012. "Columnar EEG magnetic influences on molecular development of short-term memory," Lester Ingber Papers 12ce, Lester Ingber.
    8. David Engel & Thomas W Malone, 2018. "Integrated information as a metric for group interaction," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-19, October.

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