Turtles All The Way Up: the Complexity and Hyperbolic Nature of Procedures

Abstract

There is a fundamental structure when considering the organization of work. The procedure to accomplish a task can be decomposed into a sequence of sub-steps, and likewise steps can be composed together to form more complex procedures and processes. The ability to do this arises because the unit of procedural work is fractal in nature and thus the same regardless of scale. This leads us to formally describe the step as the fundamental unit of procedure. We define the measure of complexity inherent in any such procedure, and propose a scientific notation for describing the magnitude and scale of this complexity. Finally we consider the relation between the complexity of a procedure and the complexity inherent in the design of a system. The paper ends with an analysis of the space that procedures occupy, showing it to be hyperbolic.