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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 (with                                an axis for each of the 24 possible states of the                                complex); the axes are flattened onto the page. Upon entering state                                    x1 = 1000, the                                complex generates a quale or shape in Q-space. The quale is                                generated as follows. The maximum entropy potential repertoire (the                                “bottom” of the quale) is a point assigning                                equal probability to all states. Engaging a submechanism (in this                                case the pair of connections                                    r = {c12,c21})                                “sharpens” the maximum entropy distribution into                                an actual repertoire, which is another point in Q-space. The q-arrow                                linking the two distributions (without and with r engaged)                                geometrically realizes the informational relationship specified by                                the connections in r. The “length” (divergence)                                of the q-arrow expresses how much the connection                                sharpens the distribution (the effective information it generates or                                relative entropy between the two distributions); the direction in                                Q-space expresses the particular way in which the                                connection sharpens the distribution. (B): Adding additional                                connections further sharpens the actual repertoire, specifying new                                points in Q-space and the corresponding q-arrows. The figure shows                                16 out of the 399 points in the quale; those generated by                                combinations of the 4 submechanisms progressively engaged in the                                insets. The insets around the quale show the repertoires generated                                along two q-edges (starting at the bottom left, going clockwise and                                anti-clockwise respectively) formed by q-arrows that engage the 4                                sets of connections in two different orders (pink arrows are                                connections that are engaged; black arrows are connections that have                                already been engaged in the q-edge). Cyan bars represent                                probabilities assigned to the 16 possible prior states. Together,                                the q-edges enclose a shape, the quale, which completely specifies                                the quality of the experience. Effective information (in bits) of                                q-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 (with an axis for each of the 24 possible states of the complex); the axes are flattened onto the page. Upon entering state x1 = 1000, the complex generates a quale or shape in Q-space. The quale is generated as follows. The maximum entropy potential repertoire (the “bottom” of the quale) is a point assigning equal probability to all states. Engaging a submechanism (in this case the pair of connections r = {c12,c21}) “sharpens” the maximum entropy distribution into an actual repertoire, which is another point in Q-space. The q-arrow linking the two distributions (without and with r engaged) geometrically realizes the informational relationship specified by the connections in r. The “length” (divergence) of the q-arrow expresses how much the connection sharpens the distribution (the effective information it generates or relative entropy between the two distributions); the direction in Q-space expresses the particular way in which the connection sharpens the distribution. (B): Adding additional connections further sharpens the actual repertoire, specifying new points in Q-space and the corresponding q-arrows. The figure shows 16 out of the 399 points in the quale; those generated by combinations of the 4 submechanisms progressively engaged in the insets. The insets around the quale show the repertoires generated along two q-edges (starting at the bottom left, going clockwise and anti-clockwise respectively) formed by q-arrows that engage the 4 sets of connections in two different orders (pink arrows are connections that are engaged; black arrows are connections that have already been engaged in the q-edge). Cyan bars represent probabilities assigned to the 16 possible prior states. Together, the q-edges enclose a shape, the quale, which completely specifies the quality of the experience. Effective information (in bits) of q-arrows in the q-edge is shown alongside.

Mentions: Qualia space Q is a 2n dimensional space (for a system of n binary elements and 2n possible states), having an axis per state and coordinates corresponding to the probability of each state; the space of probability distributions in Q is studied in information geometry [9]. Each submechanism m maps to the point in Q given by actual repertoire X0(m,x1). Fig. 3A shows the mapping of the lattice L into Q for the system shown in Fig. 1B′. Since a 16-dimensional repertoire cannot be drawn, we resort to a 2-dimensional representation of the 16 axes corresponding to the 16 possible states of the system 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 (with                                an axis for each of the 24 possible states of the                                complex); the axes are flattened onto the page. Upon entering state                                    x1 = 1000, the                                complex generates a quale or shape in Q-space. The quale is                                generated as follows. The maximum entropy potential repertoire (the                                “bottom” of the quale) is a point assigning                                equal probability to all states. Engaging a submechanism (in this                                case the pair of connections                                    r = {c12,c21})                                “sharpens” the maximum entropy distribution into                                an actual repertoire, which is another point in Q-space. The q-arrow                                linking the two distributions (without and with r engaged)                                geometrically realizes the informational relationship specified by                                the connections in r. The “length” (divergence)                                of the q-arrow expresses how much the connection                                sharpens the distribution (the effective information it generates or                                relative entropy between the two distributions); the direction in                                Q-space expresses the particular way in which the                                connection sharpens the distribution. (B): Adding additional                                connections further sharpens the actual repertoire, specifying new                                points in Q-space and the corresponding q-arrows. The figure shows                                16 out of the 399 points in the quale; those generated by                                combinations of the 4 submechanisms progressively engaged in the                                insets. The insets around the quale show the repertoires generated                                along two q-edges (starting at the bottom left, going clockwise and                                anti-clockwise respectively) formed by q-arrows that engage the 4                                sets of connections in two different orders (pink arrows are                                connections that are engaged; black arrows are connections that have                                already been engaged in the q-edge). Cyan bars represent                                probabilities assigned to the 16 possible prior states. Together,                                the q-edges enclose a shape, the quale, which completely specifies                                the quality of the experience. Effective information (in bits) of                                q-arrows in the q-edge is shown alongside.
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Related In: Results  -  Collection

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 (with an axis for each of the 24 possible states of the complex); the axes are flattened onto the page. Upon entering state x1 = 1000, the complex generates a quale or shape in Q-space. The quale is generated as follows. The maximum entropy potential repertoire (the “bottom” of the quale) is a point assigning equal probability to all states. Engaging a submechanism (in this case the pair of connections r = {c12,c21}) “sharpens” the maximum entropy distribution into an actual repertoire, which is another point in Q-space. The q-arrow linking the two distributions (without and with r engaged) geometrically realizes the informational relationship specified by the connections in r. The “length” (divergence) of the q-arrow expresses how much the connection sharpens the distribution (the effective information it generates or relative entropy between the two distributions); the direction in Q-space expresses the particular way in which the connection sharpens the distribution. (B): Adding additional connections further sharpens the actual repertoire, specifying new points in Q-space and the corresponding q-arrows. The figure shows 16 out of the 399 points in the quale; those generated by combinations of the 4 submechanisms progressively engaged in the insets. The insets around the quale show the repertoires generated along two q-edges (starting at the bottom left, going clockwise and anti-clockwise respectively) formed by q-arrows that engage the 4 sets of connections in two different orders (pink arrows are connections that are engaged; black arrows are connections that have already been engaged in the q-edge). Cyan bars represent probabilities assigned to the 16 possible prior states. Together, the q-edges enclose a shape, the quale, which completely specifies the quality of the experience. Effective information (in bits) of q-arrows in the q-edge is shown alongside.
Mentions: Qualia space Q is a 2n dimensional space (for a system of n binary elements and 2n possible states), having an axis per state and coordinates corresponding to the probability of each state; the space of probability distributions in Q is studied in information geometry [9]. Each submechanism m maps to the point in Q given by actual repertoire X0(m,x1). Fig. 3A shows the mapping of the lattice L into Q for the system shown in Fig. 1B′. Since a 16-dimensional repertoire cannot be drawn, we resort to a 2-dimensional representation of the 16 axes corresponding to the 16 possible states of the system 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