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Newtonian Ethics

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.

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46 Responses to Newtonian Ethics

  1. Vanzetti says:

    There’s a “yo mom so fat” joke hidden here somewhere, but I can’t quite put my finger on it. Something about “yo mom’s moral gravity”…

    • B_For_Bandana says:

      Well, here moral force is related to significance, not mass. But maybe if Newtonian ethics is actually a low-speed special case of Einsteinian ethics, it might be possible to create an ethical wormhole by spinning a very valuable person at high speeds. This might create a wormhole that would allow us to go back in time and rescue the innocents we have needlessly lost.

      • 2ndnin says:

        Or perhaps the Einsteinian ethics is about rate at which we must make choices. In the normal world we generally make ethical choices at a ‘normal’ pace, choices made under either faster conditions (you have 30s to decide), or slower conditions (take a week, go think about it) would likely alter the moral balance because we have time to ponder and think more. Similarly exposure to the event, seeing the same homeless guy every day vs a different one would likely alter the moral choices again.

  2. anonymous says:

    Souldn’t the obligiations to oneself be infinite compared to the opligations to the Congo, because we have to divide by squared distance, that is 0?

    • Nick Barrowman says:

      I noted this mathematical singularity as well. But gravitational force is defined only for distances > 0. So moral gravitation would dictate the relative force of our obligations to others. If it were indeed a moral principle rather than a psychological observation.

    • Alejandro says:

      We are extended sources, not point sources. A finite part of me cares a great deal about another (overlapping or not) finite part of me, but not infinitely. We are comparable to planets, not black holes–the gravitational field inside the Earth is not infinite at any point.

    • Charlie says:

      It’s almost as if the cause of each argument, rather than flowing form correct mathematical procedure, flowed from some desired conclusion. But that’s silly. I mean, for that to make sense you’d need to be forcing the result to implausibly match some arbitrary external yardstick.

    • Scott Alexander says:

      Well, at those distances, quantum effects take over 😛

  3. Army1987 says:

    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?

    Electromagnetism. “This argument has great moral force” is something going on in the listener’s brain, and the brain doesn’t use the strong interaction, the weak interaction, or gravitation to a sizeable extent, and electromagnetism is what’s left.

    Gravitation is not responsible for people falling in love — electromagnetism is.

  4. Mary says:

    Which doesn’t explain why I skip beggars (whom I generally meet rarely and under circumstances where I suspect the money would go for drugs) and send money overseas.

  5. arrowpker20 says:

    This would explain why we never take parallel universes into moral consideration.

    • Vanzetti says:

      That, and also because they don’t exist. 🙂

    • Scott Alexander says:

      That’s actually kind of where this came from. Luke was talking about problems for ethics if the Universe was infinitely large, in which case there would be an infinite amount of both happiness and suffering and none of our actions would affect the total. Although there are a couple ways to deal with this, I suggested one of them might be a function where moral relevance decreases with distance.

      • komponisto says:

        Oh, so you meant it seriously and not as a satirical critique? That hadn’t occurred to me, and it would change my reaction.

  6. Deiseach says:

    This makes entirely too much sense. I must be reading it way too early in the morning 🙂

  7. roystgnr says:

    Is one-boxing also only rationally explicable by assuming that the second box is infinitely far away?

  8. jason says:

    This is fantastic!

    I wonder if it works the same with near future vs far future

  9. komponisto says:

    Not to my taste, I’m afraid.

    When I encounter these utilitarian arguments that imply (whether it is acknowledged or not) that I should drop everything and devote my efforts to famine relief, I feel like a lion who has suddenly “realized” that he “should” be a vegetarian.

    Utilitarianism is either wrong or a basilisk. Probably both.

    • orthonormal says:

      I take from utilitarian reasoning, not the conclusion that I should be totally altruistic (and indeed, I’m mostly selfish, and beyond that I care about my close friends more than I do about strangers), but rather that I should put careful effort into optimizing whatever portion of my activities are motivated by altruism.

      That is, I don’t feel the need to give away all my possessions to fight malaria in Africa, but with the (say) 10% of my money that I do feel like being charitable with, I’d better direct that to something at least as good as saving lives in the Third World with maximum effectiveness, instead of something warm and fuzzy but highly ineffective like most charities.

  10. Kaj Sotala says:

    “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. ”

    Given that this was about the impact of gravity on morality, I was disappointed that you didn’t instead say “it is no longer monstrous that the man on top floor of the skyscraper ignores the homeless people at ground level”. It would have been such a good comparison to the main in Congo.

  11. Alyssa Vance says:

    Please read this.

    Certainly, there should be charity in the world, and most charities are run horribly inefficiently. But everyone agrees there should also be businesses, and yet one can’t open a newspaper without hearing of the dangers of excessive greed. It seems wise to also warn of the dangers of excessive altruism.

  12. Joe says:

    If I intentionally resist the force of moral gravity by walking across the street, to avoid a beggar, should I feel guilty?

  13. Misha says:

    Most importantly: The smallest distance in morality is internal. You always have more and stronger moral feelings about people who are in your mind than people who are at a distance from you. This includes yourself, but also you feel more morally obligated to the CONCEPT of your brother than you do to your brother and, explains why many people feel the MOST moral obligation to god. This is why you can still feel bad when “betraying” someone you like (eg by getting a job with someone else), even if they’ve said it’s ok, because their permission is not the same as the copy of that person that lives in your head. When people give to charities overseas, it’s because those people have become more real within their minds than they previously were.

  14. Evan Guiney says:

    So what’s the correlate of mass here?
    The force of gravitation is proportional to the product of the masses; but moral force is proportional to my power or wealth, times the suffering or impotence of the object of my moral consideration.
    Given constant distance, I feel the most moral force if im wealthy and you’re suffering, and moral force is reduced either by decreases in my wealth, or lessening of your suffering.
    Since the gravitational theory of morality is obviously correct, clearly moral ‘mass’ is something other than power or suffering. But what???

  15. Atreic says:

    Oh, the internet needs many more posts that both make me laugh out loud and make me nervously worried about the world I live in. You’re a genius 🙂

  16. Alex says:

    This is very interesting, however, I would have expected a 1/r dependence since humans live on a two dimensional surface.

    Newton’s law of gravitation is the way it is because the gravitational field strength at a certain distance is inversely related to the surface area at that distance. This is where the r squared comes from (surface area is proportional to r squared). In a two dimensional universe, gravitational field strength would be related to perimeters rather than surface areas and we would observe a 1/r dependence.

    Of course experimental data trumps theory – I would be interested to see which model turns out to be more predictive given a larger data set.

  17. Army1987 says:

    We start with the money in your pocket, about a meter away from your brain.

    This suggests an easier way than going to the other side of the sidewalk/road: keep your wallet in your breast pocket.

    Also, this predicts that short people will be stingier than tall people, as their wallet is closer to their brain.

    • Scott Alexander says:

      This is why dwarves are always so greedy, not to mention why leprechauns put so much effort into protecting their gold.

  18. tobi says:

    Incredible article. I suspect it is beyond the intellectual ability to comprehend for most people. Yet it is so simple and obvious for us.

  19. Doug S. says:

    The interesting thing is that social distance doesn’t necessarily equal physical distance…

  20. Julia says:

    This is up there with Dead Child Currency.

  21. Creutzer says:

    In statements like “Sentencing guidelines should take into account the gravity of the offense”, the words “gravity” and “immorality” are used interchangeably.

    I have my doubts about the advisability of such a rhetorical move. Such etymology-based, language dependent (i.e. it doesn’t work in many languages) word-play is the hallmark of a lot of postmodern drivel. This, however, is much smarter, funnier, and more surprising!

  22. anon says:

    You might be interested in reading this article:

    It argues that there’s a cross cultural view that morality exists in a metaphorical vertical hierarchy, with animals at the bottom, deities at the top, and humans in the middle.

  23. Orem says:

    This is my standard summary of the influence that upright, bipedal posture left on our moral language: good people are straight, elevated, active, forward, and stable, while bad people are crooked, fallen, lazy, backward, and wavering.

    There’s a separate prejudice against things that travel low to the ground (slithering, crawling), but that’s because snakes, worms, insects, arachnids are unsanitary or harmful. Absent those indicators, humans don’t generally feel abhorrence, disgust, contempt toward other species being low down, crooked, lazy, and unsteady as evidenced by ground squirrels, starfish, manatees, sloths, and fainting goats.

  24. amuchmoreexotic says:

    This is a groundbreaking insight, but just as classical theories of gravity break down at quantum scales, so too does your classical gravito-morality model fail to explain why tiny structures like gametes and blastocysts can exert such powerful moral forces on people thousands of miles away.

    How can abortion protesters be compelled to travel internationally by the plight of early-stage fetuses typically massing a few grams?

    How can the Pope care so much for the fate of African spermatozoa? Even accounting for the greater mass of the total African sperm reservoir, he should still be much more concerned about Italian and European sperm.

    There must be some kind of spooky action at a distance involved. Oh for a unified theory which explains quantum mechanics and morality.