Considerations about quantities, units, and dimensions for interoperability

There are no generally agreed principles on how digital systems should handle data about physical quantities. From the late 19
^th
century, scientific equations have been expressed in a unit-independent form that hides the existence of measurement scales (units), and are governed by the rules of quantity calculus. To clarify the meaning of such unit-independent equations, this paper looks at a particular representation for quantity terms and shows that expressions for dimensions arise as an inherent part of the calculations. We consider how to broaden the interoperable properties of traditional quantity equations to support other types of physical data. Three aspects associated with the data are important: 1) the kind of quantity; 2) the measurement scale and the associated class of equivalent scales; 3) the mathematical operations that can be meaningfully applied to data. By considering these aspects, digital systems will be able to handle a wider range of physical data. Software examples are provided.