Information: Α physical reality or a humanly tool? From the model order to the appropriate number of clusters

This paper is a presentation of two important types of information regarding natural signals and groups of relative things. The measure of the first information type is the order of the system that produces the signal, while the second one is the appropriate number of distinct clusters for the most effective classification of a certain group into narrower and more representative subgroups. Firstly a review is given concerning the two approaches, and then a certain method is proposed for the identification of the correct number of clusters to be used in K-Means clustering process. The two information measures, model order and number of clusters, can be considered as two equivalent views of an inherent natural element, an objective order behind any physical system.