Scaling knowledge: how does knowledge accrue in systems?

This paper addresses the important and somewhat contentious matter of how knowledge accrues in a system. The matter has at its heart the establishment of a scaling function for knowledge (as distinct from the scaling used for information) which is related to the density of the knowledge structure at any point in the system. We commence with a discussion of whether it is possible at all to scale knowledge, dispensing with any concepts of knowledge as a simple finite resource and making a distinction between the establishment of a metric and the act of measurement itself. First, we draw on the Shannon–Weaver (H) measure to establish how knowledge can be seen as contributing to the partitioning of message sets under the H–measure. This establishes how knowledge contributes to the quantity of information held within a system when viewed as a meta–structure for that information. Second, we build on the idea of knowledge as an endemic property of a structure of interconnections between concepts. We observe that knowledge content can be dense both in structures that are highly interconnected deploying a modest number of concepts and in those where the interconnections are more sparse but where the number of concepts deployed is high. A scaling function exhibiting appropriate properties is then proposed. It can be seen that the scaling associated with knowledge as meta–information and the scaling deriving from the interconnectivity point of view are connected. This scaling function is particularly useful in three ways. Firstly, it outlines the properties of knowledge itself which can be used as criteria for future knowledge–based research. Its application in practice creates the ability to identify areas of knowledge concentration within a system. Finally, this identification of knowledge ‘hotspots’ can be used to direct the investment of resources for the management of knowledge and it provides an indication of the appropriate approach for the management of this knowledge.