between the management unit, the operation, and the environment must each have a higher capacity to transmit a given amount of information relevant to variety selection in a given time than the originating subsystem has to generate it in that time. Wherever the information carried on a channel capable of distinguishing a given variety crosses a boundary, it undergoes transduction (converting energy from one form to another); the variety of the transducer must be at least equivalent to the variety of the channel. The operation of the first three principles must be cyclically maintained without delays. Recursive system theorem This theorem states: In a recursive organizational structure any viable system contains, and is contained in, a viable system. Society itself can be seen as a system of recursion. In this case, recursion refers to systems that are nested within other systems. Axioms (Axioms are statements 'worthy of belief') These axioms are: The sum of horizontal variety disposed by n operational elements (systems one) equals the sum of the vertical variety disposed by the six vertical components of corporate cohesion. (The six are from Environment, System Three*, the System Ones, System Two, System Three and Algedonic alerts.) The variety disposed by System Three resulting from the operation of the First Axiom equals the variety disposed by System Four. The variety disposed by System Five equals the residual variety generated by the operation of the Second Axiom. The law of cohesion for multiple recursions of the viable system This law ('something invariant in nature') states: The System One variety accessible to System Three of recursion x equals the variety disposed by the sum of the metasystems of recursion y for every recursive pair. Measuring performance In Brain of the Firm (p. 163) Beer describes a triple vector to characterize activity in a System 1. The components are: Actuality: "What we are managing to do now, with existing resources, under existing constraints." Capability: "This is what we could be doing (still right now) with existing resources, under existing constraints, if we really worked at it." Potentiality: "This is what we ought to be doing by developing our resources and removing constraints, although still operating within the bounds of what is already known to be feasible." Beer adds "It would help a lot to fix these definitions clearly in the mind." System 4's job is essentially to realize potential. He then defines Productivity: is