Fundamental Diversity


“That’s just what I complain of,” said Humpty Dumpty. “Your face is that same as everybody has—the two eyes, so—” (marking their places in the air with this thumb) “nose in the middle, mouth under. It’s always the same. Now if you had the two eyes on the same side of the nose, for instance—or the mouth at the top—that would be some help.” Alice Through the Looking-Glass, Chapter 6, Lewis Carroll.

“The sun has one kind of splendor, the moon another and the stars another; and star differs from star in splendor.” 1 Corinthians 15:41

When I was learning about our solar system in school some 40 years ago, I remember seeing artist conceptions of the planets and their moons. The planets, for the most part, were featureless globes, varying one from another only in  color and size. Of course, Jupiter had its red spot, and Saturn had its rings, but there was no telling Neptune from Uranus or Mercury from Mars. The moons all looked the same, drawn after the manner of the only moon with which we were familiar, pocked with craters, rocky, and desolate.

What a difference 40 years makes!

Now we know a good deal more about other planets and their moons. Pick up a modern textbook about our solar system, and you will see much greater variety in the depictions of other planets and moons, especially the moons.  You’ll see images of Io, orbiting so close to Jupiter that tidal forces keep it hot enough to melt rock. It is covered with volcanoes, some ejecting plumes of lava as much as 500 km above the surface. Or you might see Europa, nearly craterless, but covered with fissures and cracks hundreds of kilometers long. You might also see Titan, Saturn’s largest moon, covered with a thick, cloudy atmosphere composed mostly of nitrogen but with enough methane and ethane in it that scientists speculate that combustible rains might fall on its surface. The moons in our solar system are so varied, from tiny Deimos orbiting Mars to Ganymede orbiting Jupiter, that it hardly seems right to call them all by the same name: moon.

The fact is, moon is an abstraction for natural satellites orbiting a planet. The process of abstraction always ignores differences and emphasizes similarities. One feature that distinguishes humans from other animals is an amazing capacity for pattern recognition, for an ability to abstract similarities and treat the abstractions in ways that uncover still more similarities, which in turn are further abstracted. This process is fundamental to human understanding and knowledge. It can’t be sidestepped or avoided. It is how we understand.

It is also responsible for many of our failures to understand.

For example, racism (or sexism, or any form of bigotry) can be characterized by abstracting information about a group of people different from ourselves often based on limited (or even no) direct experience and extrapolating that information to the entire group. My uncle, for example, who died many years ago, was in the Philippines during World War 2. While on patrol one evening, he was beaten and robbed by a group of African American soldiers. From this experience he conceived a terrible hatred for all African Americans. But why African Americans? Why not soldiers? Well, he himself was a soldier and knew he would not do as these soldiers had done. Due no doubt to other cultural influences of which he may have been only dimly aware, he seized upon skin color as the one defining characteristic that separated this group of soldiers from other soldiers of his experience and allowed himself to hate an entire group of people based only on their skin color.

Racism is an easy target since it is now almost universally despised. What about this sentiment from a recent Facebook post I saw:

If a group of workers organize to demand fair compensation, conservatives call it “communism”.
If a group of executives organize to buy politicians and manipulate markets, they call it “capitalism”.

Notice how it tars all conservatives with the same brush and refuses to see any differentiation among them. They are all the same. They are all contemptible. Of course, I could have just as easily used an example disparaging liberals or Democrats. We are all too willing to impute to our opponents the most self-serving motivations while claiming that we and our friends are motivated by love and justice. We are individuals, but they are an anonymous collective.  We are real people; they are manifestations of the hive mind.

But I began with astronomy, and I want to return to the physical sciences to pose a question: What if electron differs from electron? What if quark differs from quark? What if the fundamental particles that we treat as abstractions (in part because we can detect them only indirectly or not at all) are as individual as different people? One consequence is that science can never explain everything, not even in principle. Science must abstract qualities like mass and charge from reality, treat them mathematically, and make predictions based on the mathematics. The process of abstraction ignores individual differences. It must; two things cannot be similar unless their differences are minimized. No matter how complete our knowledge of reality or how accurate our models, we can never capture everything in a system because the very act of creating a model requires that we ignore some of the information. In fact, we could say that reality is characterized by this fundamental diversity. No two real things are ever exactly alike; being exactly alike is a hallmark of the artificial, of the mass produced—though even here reality intrudes and causes slight variations in the things we make. The ideal of what is made is exact correspondence to an idea in the mind of the maker, and the idea is always an abstraction.

There are consequences for philosophy, too. Kierkegaard sharply criticized Hegel for trying to create a fully integrated system that would explain all of reality. He pointed out that every arena of knowledge has its own appropriate vocabulary, precepts, and arguments that both define and limit that arena. Extending any arena of knowledge to make it universal also makes it into a kind of madness. It’s not that the project can’t be done; it’s that insisting on completeness and consistency does violence to fundamental human experience. A misplaced faith in the power of reason leads to madness because reason fundamentally deals with abstractions, not with realities. So reason is good and essential to understanding, but it must not be allowed to insist on understanding everything and making everything fit into its systems. For everything can be made to fit, but only by a Procrustean solution—stretching some things and lopping off others.

This entry was posted in logic, mathematics, philosophy, race, racism, science. Bookmark the permalink.