The Proof


Let us assume that A is a young man, college-educated, employed full-time with benefits by a corporation, in a field such as marketing research. For convenience, we will refer to A as “Abe.” This shortened version of the name Abraham carries no ethnic connotation, nor does it imply anything about his height, long legs, lean angularity, black hair, or marked facial features. We may note, however, that Abe is personable, easy-going, smart, and athletic. Abe likes dogs and cats, and he is good with children. He has a sense of humor. Most important for this exercise, Abe is single.

Let us further assume that B is a young woman whose age, education, white-collar job in emerging market development, taxable income, personality type, and so forth are nearly identical to those of Abe. For convenience, we will call her “Beth.” Again this arbitrary syllable, which could be short for Bethany or Elizabeth, implies nothing about her background, height, slender figure, muscle tone, lustrous hair, or remarkably mobile face. Like Abe, Beth is socially aware, relaxed in company, and intelligent. Beth does well with animals and children. She laughs easily. And, it is crucial to observe, Beth is single.

While Abe and Beth certainly did not grow up in the same neighborhood, or even live in the same city during their formative years, the general similarity of their socio-economic profile means that they have in common many experiences and assumptions. Both, for example, lived in a detached, single-family house for most or all of their childhood, and both spent a good portion of that childhood strapped in the back seat of a private automobile, being driven somewhere by a parent. Both expect to live a long and healthy life. Having known happiness, both anticipate a happy future.

In the matter of preferences and habits, it is uncanny how much Beth and Abe are alike. Both enjoy chocolate ice cream, for example. Both always put on the left shoe first. The list of such similarities could be extended. Yet we must bear in mind that the list does not represent shared experiences. The habits of Abe which recall those of Beth, and vice versa, do not result from imitation, to take one possible avenue of influence. Rather, the many ways in which Abe and Beth resemble each other should be ascribed to pure coincidence.

On meeting each other for the first time at a casual get-together sponsored by a local business enterprise, Beth and Abe are immediately struck by the convergence of their independent and until this moment mutually unknown existence. While each clings to a serving of an alcoholic beverage—a bottle of beer in the hand of Abe, and a glass of white wine in the hand of Beth—they continue to chat for over an hour, without feeling a need to refresh their drinks or check their messages.

We know that Abe and Beth currently inhabit a Midwestern city that is not particularly attractive to their demographic. Nothing like San Francisco or New York. The opportunities for dating are limited in this otherwise livable and friendly urban environment. Moreover, since moving here a year ago, neither Beth nor Abe has made much of an effort to get out and mingle. They take their jobs seriously, their work schedules are demanding, and they often find at the end of the day or the week that the amount of surplus energy available for leisure activity is small. It is a lucky chance, therefore, that they both decided to attend this social function, which to be honest did not sound all that appealing when they originally heard about it.

As the event winds down and the crowd thins, people leave in pairs or small groups, perhaps to catch a bite to eat in the vicinity. Peripherally aware that time is up, Beth and Abe face the challenge of objectifying their experience. Each came here alone, though both have a wide circle of friends with whom they occasionally socialize. And each has no pressing engagement to which he or she must hurry after this one has definitely died. Given the fortuitous nature of the encounter, nothing will be lost if they leave separately, perhaps never to see one another again.

On the other hand, Abe and Beth know from historical data in the field of marketing that chance can play a major role in determining the path of any one discrete chain of causation. How best can they analyze this problem, identify the variables, and predict the outcome?

It ought to be clear from the information presented up to this point that Beth and Abe, despite a difference in gender which is far from negligible, are as nearly equal as two persons who were not born identical twins can be. Reverting to a quasi-mathematical notation, let us therefore set down the proposition:

A = B

From this simple and culturally neutral proposition, two corollaries are immediately apparent. The first is a certain reciprocity in the relationship of A and B, which can also be expressed as a property of mirror-imaging. We can most easily see this by reversing the order of the elements:

B = A

The second corollary is no less true, but perhaps more interesting. Before we can state it, however, we ought to review a few facts. We do not know the intrinsic measure or absolute value of A or B, only that one is the same as the other. That value could be large or small, odd or even, positive or negative, a whole number or a fraction, or even an irrational number. Our inquiry does not extend to an estimate of this value, nor do we attach any significance to it. Likewise, we cannot fathom what A and B themselves think they are worth. What we can do is state the obvious:

A – B = 0

Reverse the order of the elements, and we obtain the equally true statement:

B – A = 0

In other words, the subtraction of one element from the other yields the empty set, or null. To restate this equation in a slightly more humanistic form, we can say that B minus A equals zero. Interestingly, if the evening proceeds in the direction it is currently trending, either Beth or Abe might think or say something along these lines, such as: “Without you I am nothing.”

Before we allow this train of thought to rush headlong to annihilation, let us look at another proposition, one that may lead to a more fruitful discussion, namely:

A + B = C

To repeat what was said earlier, we do not know what A or B represents in any measurable domain, such as intelligence quotient, grade point average, physical dimensions, SAT scores, number of “followers” as counted by mainstream social media, medical history (both appear to be in excellent health), or degree of personal satisfaction as mapped by the Streckfuss-Hamadi algorithm. But if we can imagine their quantitative or qualitative difference, we can just as well imagine their sum. Add B to A, or A to B, and the result is C.

What is this mysterious C? Where does it come from? It seems to spring from the void, trailing a whiff of ozone. What can we say about C that is not silly and tautological, but will contribute to a sound analysis of the problem that Abe and Beth must urgently solve?

Now, it is all too tempting to assign a value of 1 to A and B, so that the equation will read:

1 + 1 = 2

Unfortunately, this banal statement of singularity and duality tells us nothing we did not already know. In fact, it tends to obscure the real sense of newness that Beth and Abe instinctively feel.

When we consult ancient texts that address this issue, what we find suggests that the value of C is 1. In the biblical book of Genesis, for example, we read: “they shall be one flesh.” The fable advanced by Aristophanes in the Symposium of Plato, while facetious, makes much the same point, by saying that lovers are two halves of what was once a spherical whole. We may express this proposition thus. Since A = B, A + B = 2A or 2B. And since A + B = C, 2A = C = 2B. Divide each element by 2, and in Plato’s terms:

A = ½ C = B

Beth is frankly impressed that Abe remembers this stuff from college, while Abe is impressed as he watches Beth write equations with a wet finger on a tabletop. By now, the room is quiet. Everyone else has gone home or, as we earlier postulated, to one of several restaurants nearby that feature cuisines from around the world.

Beth took an introductory course in philosophy, but it was dry and dull. They learned about logic and linguistics, uncertainty and incompatibility, but they never got around to the issues she was interested in, the really juicy questions.

Abe can totally relate. He took a survey course in the great philosophers, but it was lots of names and dates and questions that no one cares about today.

Their eyes meet. By this time of night, each has usually eaten a sensible if hastily prepared meal at home, often while watching a televised news program. Freed from this routine, light-headed from low blood sugar and one six- or twelve-ounce drink containing alcohol, they are hungry. At precisely the same moment, both young people blurt precisely the same words.

“Would you like to have dinner with me?”

Robert Boucheron is an architect in Charlottesville, Virginia. His academic degrees are B. A. 1974, Harvard University, and M. Arch. 1978, Yale University. His stories, essays, poems and reviews appear in Bangalore Review, Bloodstone Review, Conclave, Digital Americana, Gravel, Grey Sparrow Journal, Lowestoft Chronicle, Milo Review, NewPages, North Dakota Quarterly, Origami Journal, Poydras Review, Sheepshead Review, Short Fiction, The Tishman Review.