Observement as Universal Measurement

TL;DR

This paper introduces 'observement', a generalized measurement framework that extends traditional measurement to non-numerical data like strings and graphs, enabling rigorous analysis across diverse data types.

Contribution

It formalizes a new measurement theory for non-numerical data, unifying various interpretive methods and revealing cross-disciplinary insights.

Findings

Non-numerical data can be rigorously measured using alternative mathematical models.

Existing widespread representations like strings and graphs are formalized within the observement framework.

The approach uncovers deep connections between different research fields through generalized measurement.

Abstract

Measurement theory is the cornerstone of science, but no equivalent theory underpins the huge volumes of non-numerical data now being generated. In this study, we show that replacing numbers with alternative mathematical models, such as strings and graphs, generalises traditional measurement to provide rigorous, formal systems (`observement') for recording and interpreting non-numerical data. Moreover, we show that these representations are already widely used and identify general classes of interpretive methodologies implicit in representations based on character strings and graphs (networks). This implies that a generalised concept of measurement has the potential to reveal new insights as well as deep connections between different fields of research.