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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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Entanglement.(A): A silent AND-gate. (B): The quale generated by the                            system (maroon arrows). Notice that connections c13 and                                c23 generate more information in the full context (.33                            bits at the top of the quale) than in the  context (.08 at the                            bottom). The actual repertoires generated by submechanisms of the system                            are shown alongside in cyan. Repertoire                                X0({c13},x1) assigns probability                            2/3 to states where n1 was silent and 1/3 to states where it                            was not: the concept “n1 probably did not                            fire”. The actual repertoire of the whole,                                X0({c13,c23},x1),                            specifies “n1 and n2 did not                                both fire”, which cannot be recovered                            from the concepts generated by the two connections taken singly.                            Entanglement is computed by measuring the entropy of the actual                            repertoire of the whole relative to the product of the repertoires                            generated by the two connections singly, shown in gray. (C): A system of                            three elements, two of which implement the operation NOISY                            COPY: element n1 spikes with                            p = 0 if it receives silent input, and                            p = ½ if it receives a spike;                            this is the same operation performed by an AND-gate                            when one of its wires is treated as noise. (D): By construction, the                            informational relationships generated by connections c45 and                                c54 in the  context is the same as connections                                c13 and c23 in panel B. However, the qualia                            generated by the AND-gate and NOISY-COPY system differ because of how                            the informational relationships tangle at the top of the qualia; an                                AND-gate is not simply the combination of two                                NOISY COPY gates, as can be seen by comparing                            panels B and D. In the disentangled system, panel D, the actual                            repertoire of the whole coincides with a product of marginalizations of                            the actual repertoires of the individual connections.
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pcbi-1000462-g004: Entanglement.(A): A silent AND-gate. (B): The quale generated by the system (maroon arrows). Notice that connections c13 and c23 generate more information in the full context (.33 bits at the top of the quale) than in the context (.08 at the bottom). The actual repertoires generated by submechanisms of the system are shown alongside in cyan. Repertoire X0({c13},x1) assigns probability 2/3 to states where n1 was silent and 1/3 to states where it was not: the concept “n1 probably did not fire”. The actual repertoire of the whole, X0({c13,c23},x1), specifies “n1 and n2 did not both fire”, which cannot be recovered from the concepts generated by the two connections taken singly. Entanglement is computed by measuring the entropy of the actual repertoire of the whole relative to the product of the repertoires generated by the two connections singly, shown in gray. (C): A system of three elements, two of which implement the operation NOISY COPY: element n1 spikes with p = 0 if it receives silent input, and p = ½ if it receives a spike; this is the same operation performed by an AND-gate when one of its wires is treated as noise. (D): By construction, the informational relationships generated by connections c45 and c54 in the context is the same as connections c13 and c23 in panel B. However, the qualia generated by the AND-gate and NOISY-COPY system differ because of how the informational relationships tangle at the top of the qualia; an AND-gate is not simply the combination of two NOISY COPY gates, as can be seen by comparing panels B and D. In the disentangled system, panel D, the actual repertoire of the whole coincides with a product of marginalizations of the actual repertoires of the individual connections.

Mentions: Fig. 4A shows a tangled informational relationship generated by a silent AND-gate. The mechanism of the system, given by T = {c13,c23}, rules out the prior state [n1n2] = [11]. As shown in Fig. 4B, the q-arrow X0(maxH)→X0(T,x1) specified by T cannot be reduced to the q-arrows specified by {c12} and {c13} separately, since the actual repertoire X0(T,x1) does not reduce to the product of actual repertoires specified by submechanisms {c13} and {c23} separately. If the sub-q-arrows were not tangled the q-arrow X0(maxH)→X0(T,x1) would reduce to the diagonal of the parallelogram obtained by considering elements n1 and n2 separately. That is, unentangled q-arrows are orthogonal to each other; while entanglement “warps” the shape of the quale away from a simple parallelogram, see Section 4 of Text S1.


Qualia: the geometry of integrated information.

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

Entanglement.(A): A silent AND-gate. (B): The quale generated by the                            system (maroon arrows). Notice that connections c13 and                                c23 generate more information in the full context (.33                            bits at the top of the quale) than in the  context (.08 at the                            bottom). The actual repertoires generated by submechanisms of the system                            are shown alongside in cyan. Repertoire                                X0({c13},x1) assigns probability                            2/3 to states where n1 was silent and 1/3 to states where it                            was not: the concept “n1 probably did not                            fire”. The actual repertoire of the whole,                                X0({c13,c23},x1),                            specifies “n1 and n2 did not                                both fire”, which cannot be recovered                            from the concepts generated by the two connections taken singly.                            Entanglement is computed by measuring the entropy of the actual                            repertoire of the whole relative to the product of the repertoires                            generated by the two connections singly, shown in gray. (C): A system of                            three elements, two of which implement the operation NOISY                            COPY: element n1 spikes with                            p = 0 if it receives silent input, and                            p = ½ if it receives a spike;                            this is the same operation performed by an AND-gate                            when one of its wires is treated as noise. (D): By construction, the                            informational relationships generated by connections c45 and                                c54 in the  context is the same as connections                                c13 and c23 in panel B. However, the qualia                            generated by the AND-gate and NOISY-COPY system differ because of how                            the informational relationships tangle at the top of the qualia; an                                AND-gate is not simply the combination of two                                NOISY COPY gates, as can be seen by comparing                            panels B and D. In the disentangled system, panel D, the actual                            repertoire of the whole coincides with a product of marginalizations of                            the actual repertoires of the individual connections.
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Related In: Results  -  Collection

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

pcbi-1000462-g004: Entanglement.(A): A silent AND-gate. (B): The quale generated by the system (maroon arrows). Notice that connections c13 and c23 generate more information in the full context (.33 bits at the top of the quale) than in the context (.08 at the bottom). The actual repertoires generated by submechanisms of the system are shown alongside in cyan. Repertoire X0({c13},x1) assigns probability 2/3 to states where n1 was silent and 1/3 to states where it was not: the concept “n1 probably did not fire”. The actual repertoire of the whole, X0({c13,c23},x1), specifies “n1 and n2 did not both fire”, which cannot be recovered from the concepts generated by the two connections taken singly. Entanglement is computed by measuring the entropy of the actual repertoire of the whole relative to the product of the repertoires generated by the two connections singly, shown in gray. (C): A system of three elements, two of which implement the operation NOISY COPY: element n1 spikes with p = 0 if it receives silent input, and p = ½ if it receives a spike; this is the same operation performed by an AND-gate when one of its wires is treated as noise. (D): By construction, the informational relationships generated by connections c45 and c54 in the context is the same as connections c13 and c23 in panel B. However, the qualia generated by the AND-gate and NOISY-COPY system differ because of how the informational relationships tangle at the top of the qualia; an AND-gate is not simply the combination of two NOISY COPY gates, as can be seen by comparing panels B and D. In the disentangled system, panel D, the actual repertoire of the whole coincides with a product of marginalizations of the actual repertoires of the individual connections.
Mentions: Fig. 4A shows a tangled informational relationship generated by a silent AND-gate. The mechanism of the system, given by T = {c13,c23}, rules out the prior state [n1n2] = [11]. As shown in Fig. 4B, the q-arrow X0(maxH)→X0(T,x1) specified by T cannot be reduced to the q-arrows specified by {c12} and {c13} separately, since the actual repertoire X0(T,x1) does not reduce to the product of actual repertoires specified by submechanisms {c13} and {c23} separately. If the sub-q-arrows were not tangled the q-arrow X0(maxH)→X0(T,x1) would reduce to the diagonal of the parallelogram obtained by considering elements n1 and n2 separately. That is, unentangled q-arrows are orthogonal to each other; while entanglement “warps” the shape of the quale away from a simple parallelogram, see Section 4 of Text S1.

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