Mathematics is a coded language through which we can assure the gods that we are not unaware of what is going on around us. Or it may be the most self-flattering, self-aggrandizing trivia game ever invented. The English philosopher Bertrand Russell seems to have seen these two points of view. He said that mathematics "possesses not only truth, but supreme beauty - a beauty cold and austere... yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." He also wrote that math "may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

We have found about a zillion ways of dressing up the equals sign. You can put x on one side and (-b ± Ö (b² - 4ac)) / 2a on the other. You can put E on the left and mc² on the right, or 1 on one side and 1 on the other. You can add (5 + 5 = 10), subtract (5 - 5 = 0), multiply (5 x 5 = 25), and divide (5 / 5 = 1). Do with numbers what you will, it all comes down to the equal sign. The rest is symmetry.

Did human beings always know that they had the same number of digits (!) on both their right and left hands? I prefer to think that one day, shortly after the dawn of Homo Sapiens, one individual came running back to the cave with that exciting discovery. "How obvious," we think. "E = mc² !" "How obvious," the gods think.

"There's a divinity that shapes our ends, rough-hew them how we will," said Hamlet. There is an order to the universe, and starting with the person who discovered the symmetries of the extremities, continuing through the present with formulators of theories about "string," galactic bubbles, DNA, dark matter, chaos, particles, and white holes, we human beings understand some percentage of that order. "Divinity," as Shakespeare wrote the word, with a lower-case d, could be interpreted to mean "divine-ness," not necessarily as "God." And what could be more divine that the fact that sunflowers, Norfolk Island pines, lizards and snowflakes use the same system we do?

The Taoists must have felt that human beings are part of that system. Their observations of nature guided their principles and their approach to life. But their focus was as much on the concept of opposition as on the idea of equality. The Taoists may or may not have been impressed that 5 = 5 or that 2 + 3 = 5. Symbolically speaking, they would likely have focused on the fact that the numbers in question were on opposite sides of the equal sign. Observing the sun and the moon, man and woman, night and day, they concluded that opposites are equal, and in balance.

The graphic inspiration behind the equal sign is not terribly well disguised: two separate elements of identical length in close juxtaposition - two things that are equal. The gods may have been satisfied when we realized that things that appear to be different can actually be the same. We can hope so, as we haven't progressed much beyond that theme.

Every specific proof depends on that symmetry. Every piece of art in some way responds to the concept of repetition and variation. Things are different, yet ultimately the same. Chaos, according to the Bible, is what preceded Creation. What follows is its opposite - order. Is chaos, then, equal to order? Yes, in that they are the two states in which we can imagine the existence of all things. Does order depend on awareness?

In any case, mathematics is our security blanket. As long as we have it, we can feel that our lives make sense - rough-hew them how we may.

The upper VM logo is created by John Langdon (langdojw@drexel.edu), the author of the Wordplay and many symmetrical ambigrams.

MathArtHOME