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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 thesystem (maroon arrows). Notice that connections c13 andc23 generate more information in the full context (.33bits at the top of the quale) than in the  context (.08 at thebottom). The actual repertoires generated by submechanisms of the systemare shown alongside in cyan. RepertoireX0({c13},x1) assigns probability2/3 to states where n1 was silent and 1/3 to states where itwas not: the concept “n1 probably did notfire”. The actual repertoire of the whole,X0({c13,c23},x1),specifies “n1 and n2 did notboth fire”, which cannot be recoveredfrom the concepts generated by the two connections taken singly.Entanglement is computed by measuring the entropy of the actualrepertoire of the whole relative to the product of the repertoiresgenerated by the two connections singly, shown in gray. (C): A system ofthree elements, two of which implement the operation NOISYCOPY: element n1 spikes withp = 0 if it receives silent input, andp = ½ if it receives a spike;this is the same operation performed by an AND-gatewhen one of its wires is treated as noise. (D): By construction, theinformational relationships generated by connections c45 andc54 in the  context is the same as connectionsc13 and c23 in panel B. However, the qualiagenerated by the AND-gate and NOISY-COPY system differ because of howthe informational relationships tangle at the top of the qualia; anAND-gate is not simply the combination of twoNOISY COPY gates, as can be seen by comparingpanels B and D. In the disentangled system, panel D, the actualrepertoire of the whole coincides with a product of marginalizations ofthe actual repertoires of the individual connections.
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pcbi-1000462-g004: Entanglement.(A): A silent AND-gate. (B): The quale generated by thesystem (maroon arrows). Notice that connections c13 andc23 generate more information in the full context (.33bits at the top of the quale) than in the context (.08 at thebottom). The actual repertoires generated by submechanisms of the systemare shown alongside in cyan. RepertoireX0({c13},x1) assigns probability2/3 to states where n1 was silent and 1/3 to states where itwas not: the concept “n1 probably did notfire”. The actual repertoire of the whole,X0({c13,c23},x1),specifies “n1 and n2 did notboth fire”, which cannot be recoveredfrom the concepts generated by the two connections taken singly.Entanglement is computed by measuring the entropy of the actualrepertoire of the whole relative to the product of the repertoiresgenerated by the two connections singly, shown in gray. (C): A system ofthree elements, two of which implement the operation NOISYCOPY: element n1 spikes withp = 0 if it receives silent input, andp = ½ if it receives a spike;this is the same operation performed by an AND-gatewhen one of its wires is treated as noise. (D): By construction, theinformational relationships generated by connections c45 andc54 in the context is the same as connectionsc13 and c23 in panel B. However, the qualiagenerated by the AND-gate and NOISY-COPY system differ because of howthe informational relationships tangle at the top of the qualia; anAND-gate is not simply the combination of twoNOISY COPY gates, as can be seen by comparingpanels B and D. In the disentangled system, panel D, the actualrepertoire of the whole coincides with a product of marginalizations ofthe actual repertoires of the individual connections.

Mentions: Fig. 4A shows a tangledinformational relationship generated by a silent AND-gate. Themechanism of the system, given byT = {c13,c23}, rulesout the prior state[n1n2] = [11].As shown in Fig. 4B, theq-arrow X0(maxH)→X0(T,x1) specified byT cannot be reduced to the q-arrows specified by {c12} and{c13} separately, since the actual repertoireX0(T,x1) does not reduce to the product of actualrepertoires specified by submechanisms {c13} and {c23}separately. If the sub-q-arrows were not tangled the q-arrowX0(maxH)→X0(T,x1) would reduce tothe diagonal of the parallelogram obtained by considering elements n1and n2 separately. That is, unentangled q-arrows are orthogonal toeach other; while entanglement “warps” the shape of thequale 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 thesystem (maroon arrows). Notice that connections c13 andc23 generate more information in the full context (.33bits at the top of the quale) than in the  context (.08 at thebottom). The actual repertoires generated by submechanisms of the systemare shown alongside in cyan. RepertoireX0({c13},x1) assigns probability2/3 to states where n1 was silent and 1/3 to states where itwas not: the concept “n1 probably did notfire”. The actual repertoire of the whole,X0({c13,c23},x1),specifies “n1 and n2 did notboth fire”, which cannot be recoveredfrom the concepts generated by the two connections taken singly.Entanglement is computed by measuring the entropy of the actualrepertoire of the whole relative to the product of the repertoiresgenerated by the two connections singly, shown in gray. (C): A system ofthree elements, two of which implement the operation NOISYCOPY: element n1 spikes withp = 0 if it receives silent input, andp = ½ if it receives a spike;this is the same operation performed by an AND-gatewhen one of its wires is treated as noise. (D): By construction, theinformational relationships generated by connections c45 andc54 in the  context is the same as connectionsc13 and c23 in panel B. However, the qualiagenerated by the AND-gate and NOISY-COPY system differ because of howthe informational relationships tangle at the top of the qualia; anAND-gate is not simply the combination of twoNOISY COPY gates, as can be seen by comparingpanels B and D. In the disentangled system, panel D, the actualrepertoire of the whole coincides with a product of marginalizations ofthe actual repertoires of the individual connections.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000462-g004: Entanglement.(A): A silent AND-gate. (B): The quale generated by thesystem (maroon arrows). Notice that connections c13 andc23 generate more information in the full context (.33bits at the top of the quale) than in the context (.08 at thebottom). The actual repertoires generated by submechanisms of the systemare shown alongside in cyan. RepertoireX0({c13},x1) assigns probability2/3 to states where n1 was silent and 1/3 to states where itwas not: the concept “n1 probably did notfire”. The actual repertoire of the whole,X0({c13,c23},x1),specifies “n1 and n2 did notboth fire”, which cannot be recoveredfrom the concepts generated by the two connections taken singly.Entanglement is computed by measuring the entropy of the actualrepertoire of the whole relative to the product of the repertoiresgenerated by the two connections singly, shown in gray. (C): A system ofthree elements, two of which implement the operation NOISYCOPY: element n1 spikes withp = 0 if it receives silent input, andp = ½ if it receives a spike;this is the same operation performed by an AND-gatewhen one of its wires is treated as noise. (D): By construction, theinformational relationships generated by connections c45 andc54 in the context is the same as connectionsc13 and c23 in panel B. However, the qualiagenerated by the AND-gate and NOISY-COPY system differ because of howthe informational relationships tangle at the top of the qualia; anAND-gate is not simply the combination of twoNOISY COPY gates, as can be seen by comparingpanels B and D. In the disentangled system, panel D, the actualrepertoire of the whole coincides with a product of marginalizations ofthe actual repertoires of the individual connections.
Mentions: Fig. 4A shows a tangledinformational relationship generated by a silent AND-gate. Themechanism of the system, given byT = {c13,c23}, rulesout the prior state[n1n2] = [11].As shown in Fig. 4B, theq-arrow X0(maxH)→X0(T,x1) specified byT cannot be reduced to the q-arrows specified by {c12} and{c13} separately, since the actual repertoireX0(T,x1) does not reduce to the product of actualrepertoires specified by submechanisms {c13} and {c23}separately. If the sub-q-arrows were not tangled the q-arrowX0(maxH)→X0(T,x1) would reduce tothe diagonal of the parallelogram obtained by considering elements n1and n2 separately. That is, unentangled q-arrows are orthogonal toeach other; while entanglement “warps” the shape of thequale 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
Related in: MedlinePlus