A model of incomplete identification illustrating schooling behavior

We propose a model of interaction based upon incomplete identification consisting of alternate procedure of constructing a map from coarse-grained data by a contraction mapping and of applying the map to fine-grained data. In considering schooling of fish which is a typical emergent global behavior derived from local interactions, we argue that schooling paradoxically results from incomplete or indefinite identification of others. It suggests a system without boundary because any interaction is destined to be incomplete in this framework.