We often refer to morality as being a force; for example, some charity is “a force for good” or some argument “has great moral force”. But which force is it?

Consider the possibility that it is gravity. In statements like “Sentencing guidelines should take into account the gravity of the offense”, the words “gravity” and “immorality” are used interchangeably. Gravitational language informs our moral discourse in other ways too: immoral people are described as “fallen”, sin is a “weight” upon the soul, and we worry about society undergoing moral “collapse”. So the argument from common usage (is best argument! is never wrong!) makes a strong case for an unexpected identity between morality and gravity similar to that between (for example) electricity and magnetism.

We can confirm this to the case by investigating inverse square laws. If morality is indeed an unusual form of gravitation, it will vary with the square of the distance between two objects.

Imagine a village of a hundred people somewhere in the Congo. Ninety-nine of these people are malnourished, half-dead of poverty and starvation, oozing from a hundred infected sores easily attributable to the lack of soap and clean water. One of those people is well-off, living in a lovely two-story house with three cars, two laptops, and a wide-screen plasma TV. He refuses to give any money whatsoever to his ninety-nine neighbors, claiming that they’re not his problem. At a distance of a ten meters – the distance of his house to the nearest of their hovels – this is monstrous and abominable.

Now imagine that same hundredth person living in New York City, some ten thousand kilometers away. It is no longer monstrous and abominable that he does not help the ninety-nine villagers left in the Congo. Indeed, it is entirely normal; any New Yorker who spared too much thought for the Congo would be thought a bit strange, a bit with-their-head-in-the-clouds, maybe told to stop worrying about nameless Congolese and to start caring more about their friends and family.

This is, of course, completely rational. New York City, at ten thousand kilometers, is one million times further away from the suffering villagers as the original well-off man’s ten meters. Since moral force decreases with the square of the distance, the moral force of the Congolese on the New Yorker is diminished by a factor of one million squared – that is, one trillion.

At that distance, all one billion Africans matter only 1/1000th as much as would a person at zero distance. There is, in fact, a person at zero distance from the average New Yorker – that New Yorker herself. So we find that our theory predicts that our obligations to the Congo are only one tenth of one percent as important as our obligations to ourselves.

We can confirm this experimentally. This article from 2005 lists private US overseas charitable contributions at $10.7 billion a year. The 2000 US Census gave a population of 281,421,906, meaning that the average American gave $38.02 in overseas charity. This is 0.107% of the average 2005 per capita income of $35,242, compared to a predicted .0100; that is, a margin of error of only about twenty four cents.

(This is why I love physics. You’d never get results that match up to predictions that precisely in the so-called “social sciences”.)

This methodology can be used to answer a seemingly very different problem that many of us face every day: just how far away from a beggar do you need to walk before you don’t have to feel bad about not giving her money?

Suppose the marginal value of an extra dollar to a beggar is ten times its value to a well-off person such as yourself. We start with the money in your pocket, about a meter away from your brain. If you pass right by the beggar then the money may be a meter away from the beggar as well. Distance to both people is equal, so here the moral force exerted by the beggar is ten times stronger than your own moral force: you are clearly obligated to give her the money.

As you double your distance from the beggar to two meters, the moral force of her need decreases by a factor of four; however, she still has a 2.5x greater claim to the money than you do. Even three meters is not sufficient; her claim will be 1.1x as strong as your own.

However, four meters ought to do it. At this distance, the importance of the beggar’s poverty has decreased by a factor of sixteen, while your own moral force has stayed constant. It’s now 1.6x better for you to keep the money for yourself – a comfortable margin of safety.

There has been some discussion on whether it is acceptable to just hang to the far outside of the sidewalk in order to avoid a beggar, or whether this is unethical and it necessary to cross to the entire opposite side of the street. We now have the tools necessary to solve this problem. If you are on a commercial throughway, downtown residential, or other sidewalk listed on this table as having a minimum width of 4m or greater, it is borderline acceptable (ignoring air resistance) simply to move to the other side of the walkway. However, on the smaller neighborhood residential sidewalks, industrial sidewalks and alleyways – not to mention anywhere the beggar is in the middle of the walkway – it is unfortunately necessary to cross all the way to the other side of the street.

Once again, the results of even a back-of-the-envelope calculation like this one mesh admirably with most people’s native intuitions. Just as even a young child who throws a ball will have a “gut feeling” about how long it will stay up in the air, so even people unaware that morality is a variant of gravitation can correctly apply these same “gut feelings” to moral dilemmas.

In summary, morality is a form of gravitation, albeit an unusual one. Calculations performed based on inverse square law assumptions correctly predict most people’s moral actions. Indeed, the majority of human moral behavior make no sense except under these assumptions, and without them our everyday moral reasoning would be ridiculous indeed.