From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0
Φ (“big phi”) is quantified by measuring the distance C between the constellation of concepts of the whole set of elements C and that of the partitioned set , using an extended version of the earth mover's distance (EMD). The set is partitioned unidirectionally (see text for the motivation) until the partition is found that yields the least difference between the constellations (MIP, the minimum information i.e. minimum difference partition). In this case, the MIP corresponds to “noising” the connections from AB to C. This partition leaves 2 concepts intact (A and B, with zero distance to A and B from constellation C, indicated by the red stars), while the other concepts are destroyed by the partition (gray stars). The distance between the whole and partitioned constellations thus amounts to the sum of the EMD between the cause-effect repertoires of the destroyed concepts and the “null” concept , weighted by their values (see Text S2).