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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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Context-dependency of informational relationships.(A): The same set of connections engaged in two different contexts                                (red arrows) for the system in Fig. 3. At the bottom of the                                quale (in the  context) the connections generate 1.1 bits of                                information, whereas the up-set of the connections, in the full                                context, generates 1.8 bits of information. (B): A system of                                    AND-gates. The four cyan elements generate 1.5                                bits of information in the  context and 4 bits of information in                                the full context. (CDEF): The relationship between Φ and                                context-dependence. Each panel shows a system of 8                                AND-gates with two sets of connections chosen,                                shown in red and cyan (in panel E a connection is chosen twice).                                Each point in the graphs shows the average value of the difference:                                “r in full context – r in                                     context” = ei(X0(¬r,x1)→X0(T,x1))−ei(X0(maxH)→X0(r,x1)),                                averaged across network states where Φ is in the range                                [k,k+0.5), as k varies from 0 to 3.5 bits. The                                graphs show that, context as Φ increases, the information                                generated by a set of connections in the full context increases                                relative to the same connections in the .
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pcbi-1000462-g009: Context-dependency of informational relationships.(A): The same set of connections engaged in two different contexts (red arrows) for the system in Fig. 3. At the bottom of the quale (in the context) the connections generate 1.1 bits of information, whereas the up-set of the connections, in the full context, generates 1.8 bits of information. (B): A system of AND-gates. The four cyan elements generate 1.5 bits of information in the context and 4 bits of information in the full context. (CDEF): The relationship between Φ and context-dependence. Each panel shows a system of 8 AND-gates with two sets of connections chosen, shown in red and cyan (in panel E a connection is chosen twice). Each point in the graphs shows the average value of the difference: “r in full context – r in context” = ei(X0(¬r,x1)→X0(T,x1))−ei(X0(maxH)→X0(r,x1)), averaged across network states where Φ is in the range [k,k+0.5), as k varies from 0 to 3.5 bits. The graphs show that, context as Φ increases, the information generated by a set of connections in the full context increases relative to the same connections in the .

Mentions: Informational relationships are context-dependent, in the following sense. Recall from the Model section that a context is a point in the lattice L corresponding to a particular submechanism m. In Q, this point corresponds to the actual repertoire generated by that submechanism. As shown in Fig. 9A, the q-arrow generated by a connection (how it further sharpens the actual repertoire) can change in both magnitude and direction depending on the context. In Fig. 9A, when considered in isolation ( context), the connection r between elements 1 and 2 generates a q-arrow of 1.1 bits pointing in a certain direction. When considered in the full context provided by all other connections (¬r), the same connection r generates a longer q-arrow (1.8 bits) pointing in a different direction. Another example is shown in Fig. 9B, a system of 8 AND-gates. The four cyan elements generate 1.5 bits of information in the context and 4 bits of information in the full context, and the informational relationships point in different directions. Panels CDEF show results averaged across many different states of the same system, for different submechanisms. The results show that the information generated by a set of connections is higher in the full context than in the context when a system generates high Φ. Thus, within an integrated system, a submechanism produces different informational effects in different contexts, and usually it produces larger effects the richer the context. Note that this result is fully compatible with empirical work on functional connectivity [20] and related theoretical considerations [21],[22] on the role of neural context in cognition.


Qualia: the geometry of integrated information.

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

Context-dependency of informational relationships.(A): The same set of connections engaged in two different contexts                                (red arrows) for the system in Fig. 3. At the bottom of the                                quale (in the  context) the connections generate 1.1 bits of                                information, whereas the up-set of the connections, in the full                                context, generates 1.8 bits of information. (B): A system of                                    AND-gates. The four cyan elements generate 1.5                                bits of information in the  context and 4 bits of information in                                the full context. (CDEF): The relationship between Φ and                                context-dependence. Each panel shows a system of 8                                AND-gates with two sets of connections chosen,                                shown in red and cyan (in panel E a connection is chosen twice).                                Each point in the graphs shows the average value of the difference:                                “r in full context – r in                                     context” = ei(X0(¬r,x1)→X0(T,x1))−ei(X0(maxH)→X0(r,x1)),                                averaged across network states where Φ is in the range                                [k,k+0.5), as k varies from 0 to 3.5 bits. The                                graphs show that, context as Φ increases, the information                                generated by a set of connections in the full context increases                                relative to the same connections in the .
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2713405&req=5

pcbi-1000462-g009: Context-dependency of informational relationships.(A): The same set of connections engaged in two different contexts (red arrows) for the system in Fig. 3. At the bottom of the quale (in the context) the connections generate 1.1 bits of information, whereas the up-set of the connections, in the full context, generates 1.8 bits of information. (B): A system of AND-gates. The four cyan elements generate 1.5 bits of information in the context and 4 bits of information in the full context. (CDEF): The relationship between Φ and context-dependence. Each panel shows a system of 8 AND-gates with two sets of connections chosen, shown in red and cyan (in panel E a connection is chosen twice). Each point in the graphs shows the average value of the difference: “r in full context – r in context” = ei(X0(¬r,x1)→X0(T,x1))−ei(X0(maxH)→X0(r,x1)), averaged across network states where Φ is in the range [k,k+0.5), as k varies from 0 to 3.5 bits. The graphs show that, context as Φ increases, the information generated by a set of connections in the full context increases relative to the same connections in the .
Mentions: Informational relationships are context-dependent, in the following sense. Recall from the Model section that a context is a point in the lattice L corresponding to a particular submechanism m. In Q, this point corresponds to the actual repertoire generated by that submechanism. As shown in Fig. 9A, the q-arrow generated by a connection (how it further sharpens the actual repertoire) can change in both magnitude and direction depending on the context. In Fig. 9A, when considered in isolation ( context), the connection r between elements 1 and 2 generates a q-arrow of 1.1 bits pointing in a certain direction. When considered in the full context provided by all other connections (¬r), the same connection r generates a longer q-arrow (1.8 bits) pointing in a different direction. Another example is shown in Fig. 9B, a system of 8 AND-gates. The four cyan elements generate 1.5 bits of information in the context and 4 bits of information in the full context, and the informational relationships point in different directions. Panels CDEF show results averaged across many different states of the same system, for different submechanisms. The results show that the information generated by a set of connections is higher in the full context than in the context when a system generates high Φ. Thus, within an integrated system, a submechanism produces different informational effects in different contexts, and usually it produces larger effects the richer the context. Note that this result is fully compatible with empirical work on functional connectivity [20] and related theoretical considerations [21],[22] on the role of neural context in cognition.

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