As a child, I learned that atoms are tiny, indivisible particles.
This was useful, but wrong.
In middle school, I learned atoms are made of smaller parts: electrons zipping around a nucleus of protons and neutrons, like planets around a sun.
This was still wrong, but less wrong.
In high school, I learned electrons don’t move in tidy orbits, but buzz in probabilistic clouds, because something mumble mumble quantum states.
This was even less wrong (and if I actually understood it, that’d be even better).
Each step of the way, I held in mind a slightly false view, a useful fib that served the needs of the moment. As a math teacher, the process reminds me of a Taylor series, each successive term offering a better approximation of a transcendental function. But this kind of advancement is perhaps better captured in this verse by architect/mathematician/poet Piet Hien:
The road to wisdom? —Well, it’s plain
and simple to express:
and err again
Sometimes I wonder: does the same go for moral progress? Do we get better and better and better, passing through various stages of wrongness on the road to moral truth?
We all know the MLK quote: “The arc of the moral universe is long, but it bends towards justice.” Isn’t there a whiff of calculus in the geometry of this image? Euphemia Lofton Haynes, the first African-American woman to earn a PhD in mathematics, made the connection explicit:
The concept of a limit is merely an expression [in] mathematical form of an ever receding goal of perfection for which man yearns and for which he strives, yet never attains. With each new approximation, he is merely closer…
I find the vision beautiful. I’m less sure about “true.”
It seems to me that history walks like one of those strange birds or lizards, zig-zagging back and forth. I can never tell which way it’s headed until it’s already gone there. And so, while the last few centuries have seen an unprecedented improvement of humanity’s material conditions, I’m wary of generalizing the pattern.
Still, even if a civilization does not progress this way, perhaps a single person can.
As William James argues in The Principles of Psychology (1890), humans are “gregarious animals,” always seeking the approval of others. Alas, this need for approval can lead us astray: “many a man truly great, many a woman truly fastidious… will take a deal of trouble to dazzle some insignificant cad whose personality they heartily despise.”
We struggle to tolerate censure, even the censure of idiots. Our social instrument is strung so tight, the least disturbance leaves us resonating for days.
But each of us also possesses a spiritual self: “a sort of innermost center within the circle, of sanctuary within the citadel.” These two selves present a sort of puzzle, a contradiction to reconcile. How can the gregarious animal escape its lust for status, stop dazzling the cads, and start cultivating its soul?
James presents a simple formula:
When for motives of honor and conscience I brave the condemnation of my own family, club, and ‘set’… I am always inwardly strengthened in my course… by the thought of other and better possible social judges than those whose verdict goes against me now… [T]he emotion that beckons me on is indisputably the pursuit of an ideal social self, of a self that is at least worthy of approving recognition by the highest possible judging companion…. This self is the true, the intimate, the ultimate, the permanent Me which I seek.
To rise above the petty judgments of our neighbors, we retreat into imagination. We envision better neighbors.
And then even better ones.
As our imaginary judges grow more just and discerning, our morality grows by corresponding steps.
“All progress in the social Self,” James says, “is the substitution of higher tribunals for lower.”
We grow by successive approximations.