The theory of computability in collective organization suggests: Individuals are discrete and Turing machine computable; Point-to-point organization between groups gives rise to new abstract group properties; and group properties are continuous. Take bitcoin as an example: Validation/block-producing nodes are discrete point-to-point computations. Validation is purely logical Turing machine computation, while block production involves intuitive selection beyond Turing machine computation; The emergent longest chain is a continuous group property.