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Qualia: the geometry of integrated information.

Balduzzi D, Tononi G - PLoS Comput. Biol. (2009)

Bottom Line: Both active and inactive elements specify a quale, but elements that are inactivated do not.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychiatry, University of Wisconsin, Madison, WI, USA.

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. Phi -- 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.

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A quale.(A): Qualia space for a system of 4 elements is 16-dimensional (withan axis for each of the 24 possible states of thecomplex); the axes are flattened onto the page. Upon entering statex1 = 1000, thecomplex generates a quale or shape in Q-space. The quale isgenerated as follows. The maximum entropy potential repertoire (the“bottom” of the quale) is a point assigningequal probability to all states. Engaging a submechanism (in thiscase the pair of connectionsr = {c12,c21})“sharpens” the maximum entropy distribution intoan actual repertoire, which is another point in Q-space. The q-arrowlinking the two distributions (without and with r engaged)geometrically realizes the informational relationship specified bythe connections in r. The “length” (divergence)of the q-arrow expresses how much the connectionsharpens the distribution (the effective information it generates orrelative entropy between the two distributions); the direction inQ-space expresses the particular way in which theconnection sharpens the distribution. (B): Adding additionalconnections further sharpens the actual repertoire, specifying newpoints in Q-space and the corresponding q-arrows. The figure shows16 out of the 399 points in the quale; those generated bycombinations of the 4 submechanisms progressively engaged in theinsets. The insets around the quale show the repertoires generatedalong two q-edges (starting at the bottom left, going clockwise andanti-clockwise respectively) formed by q-arrows that engage the 4sets of connections in two different orders (pink arrows areconnections that are engaged; black arrows are connections that havealready been engaged in the q-edge). Cyan bars representprobabilities assigned to the 16 possible prior states. Together,the q-edges enclose a shape, the quale, which completely specifiesthe quality of the experience. Effective information (in bits) ofq-arrows in the q-edge is shown alongside.
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pcbi-1000462-g003: A quale.(A): Qualia space for a system of 4 elements is 16-dimensional (withan axis for each of the 24 possible states of thecomplex); the axes are flattened onto the page. Upon entering statex1 = 1000, thecomplex generates a quale or shape in Q-space. The quale isgenerated as follows. The maximum entropy potential repertoire (the“bottom” of the quale) is a point assigningequal probability to all states. Engaging a submechanism (in thiscase the pair of connectionsr = {c12,c21})“sharpens” the maximum entropy distribution intoan actual repertoire, which is another point in Q-space. The q-arrowlinking the two distributions (without and with r engaged)geometrically realizes the informational relationship specified bythe connections in r. The “length” (divergence)of the q-arrow expresses how much the connectionsharpens the distribution (the effective information it generates orrelative entropy between the two distributions); the direction inQ-space expresses the particular way in which theconnection sharpens the distribution. (B): Adding additionalconnections further sharpens the actual repertoire, specifying newpoints in Q-space and the corresponding q-arrows. The figure shows16 out of the 399 points in the quale; those generated bycombinations of the 4 submechanisms progressively engaged in theinsets. The insets around the quale show the repertoires generatedalong two q-edges (starting at the bottom left, going clockwise andanti-clockwise respectively) formed by q-arrows that engage the 4sets of connections in two different orders (pink arrows areconnections that are engaged; black arrows are connections that havealready been engaged in the q-edge). Cyan bars representprobabilities assigned to the 16 possible prior states. Together,the q-edges enclose a shape, the quale, which completely specifiesthe quality of the experience. Effective information (in bits) ofq-arrows in the q-edge is shown alongside.

Mentions: Qualia space Q is a 2n dimensional space (for asystem of n binary elements and 2n possible states), having anaxis per state and coordinates corresponding to the probability of eachstate; the space of probability distributions in Q is studied in informationgeometry [9]. Each submechanism m mapsto the point in Q given by actual repertoireX0(m,x1). Fig. 3A shows the mapping of the latticeL into Q for the system shown in Fig. 1B′. Since a16-dimensional repertoire cannot be drawn, we resort to a 2-dimensionalrepresentation of the 16 axes corresponding to the 16 possible states of thesystem of 4 elements.


Qualia: the geometry of integrated information.

Balduzzi D, Tononi G - PLoS Comput. Biol. (2009)

A quale.(A): Qualia space for a system of 4 elements is 16-dimensional (withan axis for each of the 24 possible states of thecomplex); the axes are flattened onto the page. Upon entering statex1 = 1000, thecomplex generates a quale or shape in Q-space. The quale isgenerated as follows. The maximum entropy potential repertoire (the“bottom” of the quale) is a point assigningequal probability to all states. Engaging a submechanism (in thiscase the pair of connectionsr = {c12,c21})“sharpens” the maximum entropy distribution intoan actual repertoire, which is another point in Q-space. The q-arrowlinking the two distributions (without and with r engaged)geometrically realizes the informational relationship specified bythe connections in r. The “length” (divergence)of the q-arrow expresses how much the connectionsharpens the distribution (the effective information it generates orrelative entropy between the two distributions); the direction inQ-space expresses the particular way in which theconnection sharpens the distribution. (B): Adding additionalconnections further sharpens the actual repertoire, specifying newpoints in Q-space and the corresponding q-arrows. The figure shows16 out of the 399 points in the quale; those generated bycombinations of the 4 submechanisms progressively engaged in theinsets. The insets around the quale show the repertoires generatedalong two q-edges (starting at the bottom left, going clockwise andanti-clockwise respectively) formed by q-arrows that engage the 4sets of connections in two different orders (pink arrows areconnections that are engaged; black arrows are connections that havealready been engaged in the q-edge). Cyan bars representprobabilities assigned to the 16 possible prior states. Together,the q-edges enclose a shape, the quale, which completely specifiesthe quality of the experience. Effective information (in bits) ofq-arrows in the q-edge is shown alongside.
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Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC2713405&req=5

pcbi-1000462-g003: A quale.(A): Qualia space for a system of 4 elements is 16-dimensional (withan axis for each of the 24 possible states of thecomplex); the axes are flattened onto the page. Upon entering statex1 = 1000, thecomplex generates a quale or shape in Q-space. The quale isgenerated as follows. The maximum entropy potential repertoire (the“bottom” of the quale) is a point assigningequal probability to all states. Engaging a submechanism (in thiscase the pair of connectionsr = {c12,c21})“sharpens” the maximum entropy distribution intoan actual repertoire, which is another point in Q-space. The q-arrowlinking the two distributions (without and with r engaged)geometrically realizes the informational relationship specified bythe connections in r. The “length” (divergence)of the q-arrow expresses how much the connectionsharpens the distribution (the effective information it generates orrelative entropy between the two distributions); the direction inQ-space expresses the particular way in which theconnection sharpens the distribution. (B): Adding additionalconnections further sharpens the actual repertoire, specifying newpoints in Q-space and the corresponding q-arrows. The figure shows16 out of the 399 points in the quale; those generated bycombinations of the 4 submechanisms progressively engaged in theinsets. The insets around the quale show the repertoires generatedalong two q-edges (starting at the bottom left, going clockwise andanti-clockwise respectively) formed by q-arrows that engage the 4sets of connections in two different orders (pink arrows areconnections that are engaged; black arrows are connections that havealready been engaged in the q-edge). Cyan bars representprobabilities assigned to the 16 possible prior states. Together,the q-edges enclose a shape, the quale, which completely specifiesthe quality of the experience. Effective information (in bits) ofq-arrows in the q-edge is shown alongside.
Mentions: Qualia space Q is a 2n dimensional space (for asystem of n binary elements and 2n possible states), having anaxis per state and coordinates corresponding to the probability of eachstate; the space of probability distributions in Q is studied in informationgeometry [9]. Each submechanism m mapsto the point in Q given by actual repertoireX0(m,x1). Fig. 3A shows the mapping of the latticeL into Q for the system shown in Fig. 1B′. Since a16-dimensional repertoire cannot be drawn, we resort to a 2-dimensionalrepresentation of the 16 axes corresponding to the 16 possible states of thesystem of 4 elements.

Bottom Line: Both active and inactive elements specify a quale, but elements that are inactivated do not.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychiatry, University of Wisconsin, Madison, WI, USA.

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. Phi -- 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.

Show MeSH
Related in: MedlinePlus