What is “Comparability”?

What is “comparability“? Basically it is a relationship between two things. If two things are “comparable“, in general parlance, then they are similar in some aspects. They share common features or functions. They are not “equal” necessarily, as there may be important differences between them. In fact, it may be that the interesting aspect of the comparison made between the two objects is in their difference, more than in their similarity. However, a test for equivalence is a very common comparison to make for things that are comparable.

Typically, the comparison will be made with respect to some common constraint, from a particular point of view, or within a particular context. Any two things can be compared, although the meaningfulness an dutility of the comparison is not always guaranteed. The most meaningful/useful comparisons will occur within a context where the two things are strongly similar.

For a simple example, consider comparing ants and humans. In order to do this meaningfully, a context for comparison must be established, and a set of common properties must be recognized. Comparing the “wing span” property of ants an dhumans would be a meaningless comparison, since humans have no wings, and most ants do not either. Comparing the anatomy of an example of each type of creature might form a context where the property “number of limbs” could generate a meaningful result.

Comparing the “strength” property of a human versus an ant may also be meainingless or at least misleading. The absolute strength of the human will be much higher than the absolute strength of the ant. However, comparing the “strength relative to weight” of each creature can tell us something much more interesting. The relative strength, where the weight of objects each creature can pick up is divided by the body mass (weight) of the creature.

Hence, while comparing absolute strength between ants and humans is meaningful, it is not terribly useful. Once the relative strength has been calculated, a meaningful and potentially useful comparison can be made, giving us an “apples to apples” comparison. By adjusting the strength property of each creature, we have created a comparison which is both meaningful and useful.

In this example, it is useful from the standpoint that the comparison is more understandable.

We have effected this improvement in the meaningfulness by establishing the context of comparison through the application of functions to the values of the creatures native properties. In other words, we have applied similar “conversion” functions in similar ways to the ant and human “strength” and “weight” properties to derive two new properties which are <em>more</em> comparable than each of the original values on their own.

The approach we took was to find where two things are analogous – where their similarties lie – and then to translate their analogous properties into meaningful and useful new values which can be compared.

The idea expressed by the term “comparability” implies that there will be similarities between the things compared. It also presupposes the expectation if not the a priori knowledge that there will be some differences, and that the differences between analogous properties can provide insight and knowledge.

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