15 October 2009

System Topology

I rely on System Topology in the same that a network engineer for an information network would refer to a Network Topology. Only I am referring to the interconnected processes, and their relations amongst each other (as captured in the IDEF series of diagrams, or more recently, by Sowa's claim that a system is much more appropriately looked at as an interconnected graph of processes, rather than a group of data/object states, that only use process as a connective tissue).

A nice little definition (from Wolfram Mathworld) -
Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid. Similarly, the set of all possible positions of the hour hand of a clock is topologically equivalent to a circle (i.e., a one-dimensional closed curve with no intersections that can be embedded in two-dimensional space), the set of all possible positions of the hour and minute hands taken together is topologically equivalent to the surface of a torus (i.e., a two-dimensional a surface that can be embedded in three-dimensional space), and the set of all possible positions of the hour, minute, and second hands taken together are topologically equivalent to a three-dimensional object.

My intention is to use the term system topology to refer to the overall graph of interconnected processes within a system, which I submit is potentially dynamic and can be potentially changed as much as the value or nature of objects affected by those processes.

A decent book (compliments of Google Books, once again) introducing the mathematics of topology . . .




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