Two years ago I was diagnosed with cancer. According medical statistical data, given the particular cell type and the stage of the disease when it was discovered, I have better than a 70% chance of still being here three years from now—pretty good odds if I was betting on a sporting event, but they provide little comfort when the wager is pain and death.Indeed, I have a hard time grasping what a 70% chance actually means, how it is supposed to fit into my actual experience. As a tool to help me understand my situation, “70%” has very little traction; it is just a number.I know that it is better than “50%” and not nearly as good as “90%.” I know that for every 100 people in my position, 30 are doomed. But I don’t know 99 other people in my position, and no matter how hard I try, I can’t seem to partition hope and dread into the appropriate emotional ratio. Three years from now I won’t be seventy percent alive or thirty percent dead.
Our evolved cognitive machinery has only a limited capacity to deal with numerical information. We are good with countable frequencies because it was necessary to compare the size of the antelope herd in the valley to the north with the size of the herd in the valley to the south. We are reasonably good with simple fractions because it was necessary to know how to divide the antelope carcass into equitable portions for distribution—however, a recent study found that people do not mentally represent fractions in terms of their actual numeric quantities; instead, we tend to compare the relative difference between the countable integers that comprise the numerator and the denominator (the numerator is the herd in the valley to the north. . .). We are not so good with irrational numbers or with frequencies in the millions. In fact, our cognitive machinery is entirely unable to grasp large numbers as anything other than abstraction. Small countable integers such as fifteen have real-world meaning for us. Fifteen million is entirely outside of our first-person experience; it is an abstraction with no possible concrete experiential referent.
Statistical abstractions are likewise not part of our concrete experience. No one has ever seen an average or held a standard deviation. Percentages and proportions other than those that can be distilled to very simple fractions register only in terms of a sense of relative “bigness” or “smallness.” And too often these statistical concepts are applied to events that are themselves abstractions entirely absent of any concrete reality. The following news bite is emblematic:
There has been a 3.8% increase in private sector growth during the last quarter.
The private sector is an economic abstraction. And the notion that an economic entity can grow is pure metaphor. A 3.8% increase in the yearly metaphoric growth of an abstraction is a conceptual black hole. A 3.8% increase in the yearly (actual) growth of something entirely concrete, a tree for instance, is quite beyond any kind of experiential grasp. There is nothing in my concrete experience that I could point to that corresponds to a 3.8% increase in the amount of new tree being added this year. I can see the tree is growing. And if I was patient and attentive, I could probably tell the difference between a tree that is experiencing a 3.8% increase in its rate of growth and one that is experiencing a 10% increase if the two trees were growing side by side. And, again, if I was paying close attention, I could probably tell when a given tree is experiencing a substantial decrease in its rate of growth as compared to the year before. But 3.8% of an increase is just a number; and 3.8% of an increase in the growth of an economic abstraction is a mere rhetoric, if not outright propaganda.
I don't mean to deny the usefulness of statistical abstractions as conceptual tools. However, they are ultimately abstractions that have no actual referent in our concrete experience. And as abstract conceptual tools, they are functional only within a specific kind of conceptual framework.
It is this latter quality of statistics that concerns me the most: the fact that even though they are not properties of the universe itself, they are nonetheless being used as tools to shape our understanding of that universe, framing our experience in ways that trivialize or completely ignore core features of our humanity in the process.