(This is Part 12 of a continuing series. Go back to Pt 11.)
Perhaps you'd allow me to tell you an interesting little story about the Pythagoreans. The Pythagoreans were followers of the mathematician Pythagoras (580-500 BC), the discover of the famous Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the squares of the other two sides.
In addition to being a great mathematician, Pythagoras was a philosopher. He was so struck by the beauty of the positive integers and their relationships that he proposed that the entire universe originally arose from the the whole numbers: 0, 1, 2, 3...etc.
Pythagoras also played with the ratios between positive whole numbers such as 1/4 or 2/3. (Zero and the negative numbers, which we now take completely for granted, had not been discovered yet.)
One of the great discoveries of Pythagoras is that all the different notes of the musical scale can be represented as ratios of whole numbers on sections of a vibrating string. Thus 'C' one octave higher than the original 'C' is vibrating on a section of the string exactly 1/2 the length of the original note, and so on with similar fractions for each of the notes and harmonies in the octave.
As part of this philosophy, Pythagoras claimed that each planet made a sound of a particular pitch as it moved through the heavens. And so the phrase and the metaphysical concept "the music of the spheres" was born.
But now the plot thickens. It turns out that the Pythagoreans had a problem. It was a secret problem which they kept concealed from the public, but which troubled them greatly. You see, their theory was that the whole numbers and their ratios were everything, not just useful in mathematics but the foundation of the whole universe. In sum, the positive whole numbers were sacred.
However, using their own Pythagorean Theorem, they discovered a contradiction to their theory. They discoverd that a unit right triangle —a right triangle with two equal sides of length "1"—had a hypotenuse equal to the square root of 2.
What's the problem with that? The problem, as they themselves proved, was that this number, the square root of 2, could not be represented as the ratio of two whole numbers. Here was a number that was somehow beyond representation as a fraction between whole numbers. It's what mathematicians now call an irrational number.
Ultimately, the irrational numbers proved invaluable to mathematicians, including such examples as the irrational number pi and the mysterious number e,
In fact, e and other irrational numbers would prove to be the foundation not only for such critical mathematics as the exponential function and the logarithmic spiral—which describe so many functions in nature, from the growth of flowers to the decay of atoms—but would later prove central to the development of the most crucial functions in mathematics: the differential and integral calculus.
But this unexpected encounter with reality—in the form of a number that did not fit in with their prevailing theory—was so unsettling to the Pythagoreans that they suppressed it. They swore everyone in their group to secrecy.
Unfortunately, one of their members named Hippasus of Metapontum told some people outside the group about this first irrational number, the square root of 2. The Pythagoreans were so threatened and incensed by this contradiction to their prevailing theory that they killed him. Yes, they actually took Hippasus out on a lake and drowned him for revealing this unsettling contradiction.
Now let's step back for a moment. The Pythagoreans
killed someone—why? Because he "published" something which contradicted their theory about how reality is.
Is this unusual? Oh, no. Examples like it are littered all through human history, like patches in an endless quilt. Just a few short ones:
Jesus was crucified because he preached some radical ideas about life that contradicted the prevailing theories of life and its nature in the Roman Empire.
In one of history's greatest ironies, some centuries later during the Inquisition the very church that claimed to represent Jesus was itself torturing and burning people—in Jesus' name, who preached love—if they disagreed with the prevailing system about how things were.
Indeed, science was affected. When Galileo presented evidence that the earth was not the center of the universe but in fact moved around the sun, this idea was considered so radical and threatening that Galileo was forced, under threat of torture, to recant his discovery and declare it false. But of course it prevailed eventually anyway, because reality has a way of prevailing.
Indeed, the vast majority of the ideas that people have been suppressed or put to death for, such as new discoveries in math and science, or the politcal ideas of free speech and assembly and civil rights, or Jesus' new approach to life—and countless other examples could be given—wind up greatly benefitting the human race.
That's not an accident. Because it is reality itself that is sacred. Reality just as it is, in all its inconvenient aspects—its dualities, its blending of good and bad, right and wrong, beautiful and ugly, sacred and profane, its habit of exhibiting uncomfortable facts like irrational numbers or that we're not the center of the universe.
Our little 3-pound brain comes along and proclaims how things ought to be. They should conform to this or that theory. There should be no killing or war; there should be no death or disease, no thoughtlessness; what happened to me shouldn't have happened; my spouse/lover/associate/neighbor should respect me. On and on the theories go.
This is not to condone bad things when they happen. Rather, it simply means a recognition of reality as it is, that reality has all the aspects that it does. And how do we know that those are the right aspects for reality to have? Because it has them.
In other words, reality itself is the highest standard for how things should be. They should be exactly as they are right now. How do we know? Because that's how they are.
The surface of reality keeps changing, so we know that tomorrow, next week, next year certain things will be different. But reality won't be "better" then, because it's already perfect now. It moves from perfection to perfection.
Reality itself is the highest standard for good, because all things ultimately harmonize, all things ultimately fit together in one seamless fabric, all things—even the tiniest—contribute to the whole. Indeed, all things are the whole, are the one.
A tiny bit of this we can understand. And no doubt there are many dimensions of reality that we can never understand, not even potentially. Yet that's all right. We too are just as we are, perfect just as we are, perfect in all our complex and beautiful imperfection.
This may sound strange, but to me it's the very "imperfection" of reality that makes it so beautiful. It's somehow related to the essential humility of reality. We can understand reality just as well by looking at a flower or a bug crawling across the wall or the mixture of "good" and "bad" as we can by looking at a spiral galaxy.
Perhaps that's why Lao-Tzu said that if we want to understand reality we should look at water. Water always seeks out the lowest places. It takes the shape of any container it's put in. It's "humble," we might say, and yet that humility is also its mysterious majesty. So too with reality itself.
This is the end of Part 12. Go to Part 13.)
—jim sloman, 1.6.03 for 3.04.03
|
