Granularity, scale and collectivity: when size does and does not matter.

Bridging levels of "granularity" and "scale" are frequently cited as key problems for biomedical informatics. However, detailed accounts of what is meant by these terms are sparse in the literature. We argue for distinguishing two notions: "size range," which deals with physical size, and "collectivity," which deals with aggregations of individuals into collections, which have emergent properties and effects. We further distinguish these notions from "specialisation," "degree of detail," "density," and "connectivity." We argue that the notion of "collectivity"--molecules in water, cells in tissues, people in crowds, stars in galaxies--has been neglected but is a key to representing biological notions, that it is a pervasive notion across size ranges--micro, macro, cosmological, etc.--and that it provides an account of a number of troublesome issues including the most important cases of when the biomedical notion of parthood is, or is not, best represented by a transitive relation. Although examples are taken from biomedicine, we believe these notions to have wider application.