Part II. NUMERICAL REASONING
5. Quantities in the Real World
In this course, we seek to solve practical problems in natural resource management and ecology, but we focus on the use of quantitative tools in service of this objective. Before diving too deeply into problem-solving, we should ensure that we know what is meant by quantities, quantitative tools, and quantitative reasoning. We will also establish a few conventions for how quantities are represented in science and how quantitative information can be most effectively communicated.
5.1 Quantities in Natural Resources
If we can assess the presence or absence of something, count its number, measure some property that it has, or compare it to another object, it can be quantified. That quantified thing is then represented by a quantity that is itself now a property of the quantified thing. If that sounds confusing, read on to some of the examples below. A fully-defined quantity has five components:
Properties of quantities
- Name: what we call it.
- Procedural statement: how it is measured or computed.
- Number: numerical value(s) corresponding to magnitude or multitude.
- Units: how it is scaled.
- Symbol: a character that stands for the quantity in equations.
Defining a quantity might seem somewhat pedantic, but it has important implications for what we can and cannot do with it. This contrasts fundamentally with the abstract variables we encountered in high school math. In that setting, there is rarely any reason to question whether it is OK and meaningful to add 3x and 8y, we just do what we’re asked. But in the world of real quantities, if x stands for “milligrams of sodium chloride” and y stands for the number of eggs in a Northern Cardinal’s nest, it’s not so clear that we can perform that addition. Even if we do, it is not so clear what the result means.
In the introductory chapter, we pondered the Iowa DNR’s roadside pheasant survey and what it means for pheasant populations across the state. The pheasant count yields a single number each year, for example 23.9 individuals per 30 miles in 2015. We discovered what this quantity means and how it is measured in the Introduction, so we already have most of the ingredients of a fully-defined quantity. We only need a symbol. This is a pretty trivial step in simple problems, where the primary constraint is to make the symbol unambiguous and suggestive of the quantity it represents. Perhaps we should then choose PP for our symbol. If we were to prepare a document describing the DNR roadside pheasant survey, once we establish each of the five properties[1] of our quantity, we can thereafter use PP with confidence that the information conveyed by that symbol is clearly established: within the context of our document, PP would refer to the series of annual estimates of pheasant density according to the method established by the DNR. This formality thereby provides a shorthand name and eliminates any ambiguity in discussion of quantities. Note th