Scientific journal articles today are all about formulas, and in The Book of Why Judea Pearl suggests that there is a clear reason why formulas have come to dominate the world of academic studies. In his book he writes, “to a mathematician, or a person who is adequately training in the mathematical way of thinking …. a formula reveals everything: it leaves nothing to doubt or ambiguity. When reading a scientific article, I often catch myself jumping from formula to formula, skipping the words altogether. To me, a formula is a baked idea. Words are ideas in the oven.”
Formulas are scary and hard to sort out. They use Greek letters and even in fields like education, political science, or hospitality management formulas make their way into academic study. Nevertheless, if you can understand what a formula is saying, then you can understand the model that the researcher is trying to demonstrate. If you can understand the numbers that come out of a formula, you can understand something about the relationship between the variables measured in the study.
Once you write a formula, you are defining the factors that you are going to use in an analysis. You are expressing your hypothesis in concrete terms, and establishing specific values that can be analyzed in the forms of percentages, totals, ratios, or statistical coefficients.
Words, on the other hand, can be fuzzy. We can debate all day long about specific words, their definitions, registers, and implications in ways that we cannot argue over a formula. The data that goes into a formula and information that comes out is less subjective than the language and words we use to describe the data and the conclusions we draw from the information.
I like the metaphor that Pearl uses, comparing formulas to baked ideas and words to ideas within an oven. Words allow us to work our way through what we know, to tease apart small factors and attempt to attach significance to each factor. A formula requires that we cut through the potentialities and possibilities to make specific definitions that can be proven false. Words help us work our way toward a specific idea and a formula either repudiates that idea or lets it live on to face another more specific and nuanced formula in the future, with our ideas becoming more crisp over time.