"Nicomachus gives three definitions of number. The first, "determinate multitude," is by genus and difference, and is ascribed by Iamblichus to Eudoxus. The second, "a group (i.e., organized complex) of units," [Iamblichus] ascribes to Thales and the Egyptians. The third stream of quantity composed of units Philoponus explains as another attempt to distinguish the particular kind of quantum treated in Arithmetic. The Unit was conceived either mystically as an Idea whose "essence" passes in some way into concrete individuals and even into the Ideas to organize them, or spatially and temporally as the boundary of individuals. The former conception gave rise to fantastic speculations on the cosmic meaning of number, examples of which Nicomachus has... given us; the latter gave rise to the s..."