How do we really compute with units?

Abstract

The methods that we teach students for computing with units of measurement are often not consistent with the practice of professionals. For professionals, the vast majority of computations with quantities of measure are performed within programs on electronic computers, for which an accounting for the units occurs only once, in the design of the program. Subsequent users of the program are given instructions to submit input quantities with a prescribed unit of measure, meaning submitting a dimensionless ratio of the quantity to a particular unit of measure. Likewise, users are also given instructions to interpret the numerical output as having prescribed units. Here we present a formal method for deriving both the computer code for the numerical computation, meaning the formula, and for deriving the instructions for submitting input and interpreting output. This formal method is analogous to the practice of labelling the axes of graphs with a ratio of a quantity to a unit, and treating the graph as an analogue computer for pure numbers.

Using an infrared thermometer for solar pyranometry

“…Now we solve for T s at alpha.wolfram.com. We can use the computational method in [5], and define T as the ratio of T s to K and submit this line of text: Big changes in T s result from the natural variability in the wind speed U . On the other hand, our calculations seem to tolerate errors, or lack of knowledge, of the precise value of s when compared with knowledge of U .…”