The math on the back of the envelope

We have been told on reasonably high authority that true charity vaunteth not itself; it is not puffed up. You can puff yourself up with thank-you notes from a dozen organizations, or you can be truly charitable by concentrating your efforts where you believe they will do the most good.

Early in this century, the eminent economist Alfred Marshall offered this advice to his colleagues: When confronted with an economic problem, first translate into mathematics, then solve the problem, then translate back into English and burn the mathematics. I am a devotee of Marshall's and frequently follow his advice. But in this instance, I want to experiment with a slight deviation: Rather than burn the mathematics, I will make it available as a link.

I propose to establish the following proposition: If your charitable contributions are small relative to the size of the charities, and if you care only about the recipients (as opposed to caring, say, about how many accolades you receive), then you will bullet all your contributions on a single charity. That's basically a mathematical proposition, which I have translated into English in this column. If you want to see exactly what was gained or lost in translation (and if you remember enough of your freshman calculus to read the original), then click here.