On abstraction.

In a book of cheerful wisdom by math popularizer Lillian Lieber, I underlined these words:

A person who can be loyal to such abstract concepts as truth, justice, freedom, reason, rather than to an individual or a place, has the loyalty of a human being rather than that of a dog.

What exactly is Lieber saying? Loyalty to a cousin, a neighbor, a favorite teacher, a hometown… that’s somehow bad?

Not necessarily. She goes on:

Please do not think that we are using the word ‘dog’ in a disparaging sense, for they are very dear animals… But still they are animals and not human beings.

To rise above doglike instinct you must forget the specific sights, sounds, and smells your senses gather from the world. You must instead consecrate your life to Platonic abstractions. Let your mind govern your will.

Don’t arrange your life based on the familiarity of certain odors.

On abstraction.

But then, in a book of bittersweet wisdom by poet Bill Holm, I underlined these words:

Sacredness is unveiled through your own experience, and lives in you to the degree that you accept that experience… even, or perhaps particularly, if it comes into conflict with the abstract received wisdom that power always tries to convince you to live by.

Holm grew up on the Minnesota prairie, left for the glory and glamor of coastal universities, and then returned as a literary defender of the prairie life. As such, he is an anti-Lieber. Proudly doglike.

To Holm, what matters is your own experience, especially when it stands against the dicta and slippery platitudes of the powerful:

One of power’s unconscious functions is to rob you of your own experience by saying: we know better, whatever you may have seen or heard… we are principle, and if experience contradicts us, why then you must be guilty of something.

“Truth, justice, freedom, reason”—for Lieber, these are the highest ideals, but for Holm, they are words at once totally empty and impossibly heavy, words chanted by the powerful to drown out the quiet inner voice that tells you who you are.

So which is it? Are abstractions the essence of intellectual life, or the enemy of spiritual life?

I teach math. So I am, inescapably, a peddler of abstraction. I teach how to boil our irreducibly complex world down to simple numbers (i.e., abstractions). Then I teach how to perform calculations on these numbers (i.e., to wring new abstractions from old ones). Then I teach a language for comparing, combining, and undoing calculations, regardless of what numbers are actually being calculated upon—a language called algebra, which is an abstraction of an abstraction of an abstraction.

My work is in high demand. Consensus holds that every young person must learn this craft, must learn to perform certain mental operations with perfect indifference to the sights that flash and the sounds that buzz and the smells that waft around them. What I teach is something dogs can never learn.

Lieber would applaud my work. Holm, I am not so sure.

In the end, Lieber and Holm point to the same basic truth: Civilization depends on our power for abstraction. They differ in only one minor detail: how they feel about civilization.

Is it something the mind must embrace? Something the soul must resist? Or, terribly, both?