Some have called the Golden Rule, the heart of the Charter for Compassion, the ethic of reciprocity. Treat others as you wish to be treated yourself. Reciprocity, according to the dictionary, means mutual, uniformly felt or done by each party towards the other or others; two-way. I’m not sure this is the best description of the Golden Rule: to me, it implies an expectation of — well — reciprocity. I will treat you well so that you treat me well. I won’t do you harm so that you won’t do me harm. The Golden Rule doesn’t make that promise, although it often turns out that way. It’s just one way of figuring out how to do the right thing, the moral thing, the just thing.

Thinking about that word reciprocity, though, led me to a related math term: reciprocal. A reciprocal is one of a pair of numbers that, when multiplied together, equal 1. The reciprocal of 4 is ¼: 4x¼=1. Remember?

I like that idea — that every number in the universe — even one too large and complex to grasp — has a reciprocal. If we multiply them together we always get ONE. Unity. Wholeness. Simplicity. Are all of our differences like that? Do they have a reciprocal that, when multiplied, makes us ONE? I’d like to think so. When we discover the reciprocal, when we multiply by a fraction, we can become whole.

I also like the idea that the reciprocal is the same number turned upside down. A totally different way of looking at things. And it will always be a big number and a small number. Both the big and the small are needed to make a whole.

Mathematical reciprocals have another interesting property: dividing by a number is the same as multiplying by the reciprocal of that number. For example 5 ÷ ¼ is the same as 5 x 4/1 (which is really 5 x 4, which you know equals 20.) When division is too hard, try multiplying.

In a recent interview, TV journalist and Texas native Bill Moyers talked about reciprocity:

Q: What role has your religious faith played in shaping your political views and your journalism?

Moyers: When I was growing up, I never heard anyone pray, “Give me this day my daily bread.” It was always, “Give us this day our daily bread.” That stuck. We’re all in this together. I take “We, the People” seriously because I don’t know how we build a civilization without reciprocity. There’s a moral contract in that Preamble.

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