Mathematics has changed not only what I notice,
but also what I'm willing to ignore, at least
for a while. This is the power of abstraction.
When mathematicians study a problem, they often
set aside details that do not matter for the
question at hand. We may draw a triangle in blue
ink, tilt it to one side, or place it in the
corner of a page. These details are visible,
but they are not relevant to whether the sum
of the interior angles is 180 degrees in Euclidean
geometry. Ignoring them allows us to concentrate
on the structure beneath them. Abstraction can
help us to see what very different situations
have in common, but it also raises an important
question. Which details are irrelevant? and which
are essential? And that question becomes especially
important when we move from mathematical objects
to human beings. So, in the book X plus Y, mathematician
Eugenia Ching uses abstraction to reconsider
familiar ideas about gender and behavior. Rather
than labeling certain qualities as masculine
and others feminine, she proposes a different
dimension. Ingressive and congressive. Ingressive
behavior emphasizes the individual, asserting
oneself, competing, and pursuing individual achievement.
Congressive behavior emphasizes bringing people
together, collaborating, connecting, and strengthening
the community. Chang's point is not that one
category belongs to men and the other to women.
And once we set aside the gender labels, we can
examine the behaviors themselves and ask which
ones our institutions encourage and reward. That
change in abstraction helps us to ask better
questions. Rather than asking how many people
can succeed within a competitive system, could
become more congressive? Could success include
helping other people flourish? Could education
become less about demonstrating individual superiority
and more about building understanding together?
This has changed the way I think about fairness.
Fairness is not always achieved by treating everyone
the same, because people do not necessarily begin
in identical circumstances. But at the same time,
focusing on every difference can prevent us from
seeing our shared humanity. We need the wisdom
to know which differences matter in a particular
situation and which ones are distracting us from
the deeper structure. Mathematics does not automatically
answer these questions. An abstraction can clarify.
but it can also conceal. If we ignore the wrong
detail, we may create a model that is elegant,
but unjust. What mathematics gives me is a disciplined
way to ask, what am I choosing to notice? What
am I temporarily setting aside? What becomes
clearer because of that choice? Who might disappear
from view? Abstraction changes the way I see.
Fairness asks me to use that changed vision responsibly.