Multidimensional representation of semantic relations between physical theories, fundamental constants and units of measurement with formal concept analysis

TL;DR

This paper introduces hierarchical graphs using formal concept analysis to visualize and analyze the complex semantic relationships between physical theories, fundamental constants, and measurement units, enhancing understanding of their interdependencies.

Contribution

It presents a novel application of formal concept analysis to model and visualize the semantic relations among physical theories, constants, and units, including the integration of a new fundamental constant.

Findings

Hierarchical graphs effectively illustrate interrelations of physical concepts.

Inclusion of Milgrom's critical acceleration expands the analysis.

Visualization aids in understanding dependencies and ontologies.

Abstract

We propose several hierarchical graphs that represent the semantic relations between physical theories, their fundamental constants and units of measurement. We begin with an alternative representation of Zelmanov's cube of fundamental constants as a concept lattice. We then propose the inclusion of a new fundamental constant: Milgrom's critical acceleration and discuss the implications of such analysis. We then look for the same fundamental constants in a graph that relates magnitudes and units of measurement in the International System of Units. This exercise shows the potential of visualizing hierarchical networks as a tool to better comprehend the interrelations and dependencies of physical magnitudes, units and theories. New regimes of application may be deduced, as well as an interesting reflection on our ontologies and corresponding theoretical objects.