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→New distance function
IIT 3.x makes use of a distance function on a space probability distributions. The theory uses this space of probability distributions in order to construct a space which it claims is identical to conscious experiences. Both the individual spaces as well as the prodcts are instantiations of what is called an ''experience space'' in Kleiner & Tull, which includes the said distance function.
Whereas in IIT 3.x the distance function is an adaptation of the first Wasserstein metric over probability distributions (also, known as Earth Mover's Distace; cf. Kleiner & Tull for details), IIT introduces a new distance measure, called '''Intrinsic Difference'''. It is similar to the KL-divergence, but extends to product spaces by use of the 'maximum' of the distances of the component spaces.
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;Def. Intrinsic Difference
: TBA
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For details and a conceptual justification of itthis new measures, cf. Barbosa et al., A measure for intrinsic information, 2020, ''Supplementary Material (!)''.
== More constrained partitions ==
