What Is a Structural Measurement Process?∗

Numbers have emerged historically as by far the most popular form of representation. All our basic scientific paradigms are built on the foundation of these, numeric, or quantitative, concepts. Measurement, as conventionally understood, is the corresponding process for (numeric) representation of objects or events, i.e., it is a procedure or device that realizes the mapping from the set of objects to the set of numbers. Any (including a future) measurement device is constructed based on the underlying mathematical structure that is thought appropriate for the purpose. It has gradually become clear to us that the classical numeric mathematical structures, and hence the corresponding (including all present) measurement devices, impose on “real” events/objects a very rigid form of representation, which cannot be modified dynamically in order to capture their combinative, or compositional, structure. To remove this fundamental limitation, a new mathematical structure—evolving transformation system (ETS)—was proposed earlier. This mathematical structure specifies a radically new form of object representation that, in particular, allows one to capture (inductively) the compositional, or combinative, structure of objects or events. Thus, since the new structure also captures the concept of number, it offers one the possibility of capturing simultaneously both the qualitative (compositional) and the quantitative structure of events. In a broader scientific context, we briefly discuss the concept of a fundamentally new, biologically inspired, “measurement process”, the inductive measurement process, based on the ETS model. In simple terms, all existing measurement processes “produce” numbers as their outputs, while we are proposing a measurement process whose outputs capture the representation of the corresponding class of objects, which includes the class projenitor (a non-numeric entity) plus the class transformation system (the structural class operations). Such processes capture the structure of events/objects in an inductive manner, through a direct interaction with the environment. ∗This paper is a substantially expanded version of the conference paper [1].