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.