07/07/2000

"How do I love thee? Let me count the ways." Elizabeth Barrett Browning knew that the way to a person's heart was through mathematics.

Dudley Moore, meanwhile, made the number 10 synonymous with beauty and obsession; the numbers 36, 24, 36 are enough to make any man's eyes glaze over.

Is mathematics the language of love?

The physicist philosopher Eugene Wigner once wrote an article titled "On the Unreasonable Effectiveness of Mathematics in the Natural Sciences," exploring the amazing fact that mathematics gives a language for science capable of explicating the world around us. In this way, mathematics is truly a language for describing relationships. It is the language that describes the chemistry that may exist between two lovers, or the stars under which they are crossed. It provides the equations that illuminate the way two bodies might attract, repel or interact with one another.

However, while love, or any emotional relationship, is certainly natural, it is hardly (in spite of all the self-help therapy books now in print) a science. So what then does or can the language of mathematics have to say in this domain?

At the heart of mathematics is logic, a seemingly cold and rational subject, neatly personified by Mr. Spock of *Star Trek* fame, a creature so logical that any hint of emotion in him would be enough to send the crew of the USS Enterprise into a giggling fit.

The logical world is a world that proceeds by the axiomatic method. Starting with a set of self-consistent statements, truth upon truth is derived in an almost mechanical way. As long as the initial set of assumptions are not inconsistent, then a false statement is never generated. In the world of logic, nothing can be both true and false.

On the other hand, anyone who has ever been angry at a lover can tell you that this happens all the time in life. Contradictions abound, and few events absolutely necessitate others.

Life, love and romance are all about surprise: the surprise of an unexpected bouquet of flowers, a mysterious stranger met by chance at a party, the unannounced return of an old lover at your doorstep, the confusion of finding the unknown side of an old friend or acquaintance who becomes your partner. The freshness of a relationship kept new even after years.

Alive equals surprise.

The logical world, on the other hand, seems to be a world of no surprise, no serendipity, no romance. Axioms generate propositions, one deduction blindly follows another. The game is over almost as soon as it is begun. Where is the romance in that? No chance for the heart to overrule the head, contradiction to conquer cogitation, desperation and devotion to deliver you from derivation.

Or is there?

In the 1920s, a mathematician named Goedel proved that in any consistent logical system, there will always be statements whose truth or falsity can't be proved by the simple mechanical rules of logic. Even if these "undecidable" statements are appended to the list of axioms, as long as this enlarged system remains consistent, there will still be other statements whose proof or refutation lies outside the power of formal reasoning.

The unknowable and the unpredictable is embedded in even the most simple of things. Romantically speaking, I like to think of this as saying that if we have a guarantee of truth, and thus the possibility of honesty, then from this we must necessarily have surprise, even mystery - and maybe then, just maybe, with a little bit of luck, we must have love. Q.E.D.

* Daniel Rockmore is a professor of mathematics and computer science at Dartmouth College in Hanover, N.H.*