# A Conservation Law for Empathy?

Earlier this week I found myself in Rome in the morning with about 20 minutes to spare. Walking around the neighborhood I was staying in (Trastevere), I came across an elderly nun walking along one of the bigger, and more crowded, streets of Rome. As I waited for her to go through a narrow passage in the sea of people, a young woman pushing a stroller physically nudged her out of the way, using the stroller to deny the physical space in front of and adjacent to the older woman as she overtook her. The nun grimaced but seemed resigned to what happened. I saw this unfold despite having been out for only about ten minutes. In contrast, having walked US streets in San Francisco, Boston, and New York for over twenty years, I don’t recall seeing a similar situation happen even once. It follows that frequentist estimates of such occurrences in American cities and Rome suggest very different underlying distributions.

Not ten seconds passed when I saw yet another very elderly woman, walking at a pace that could not have exceeded a few yards per minute. She was being supported, with interlocked arms, by a much younger woman, possibly her granddaughter, with an apparent infinitude of patience. In the span of the twenty minutes that I walked around, virtually identical scenes unfolded three more times, all with that same infinitude. In contrast, in my over twenty years of walking American cities, I have observed similar scenarios only a handful of times (usually without the patience). Frequentist estimates again suggest very different underlying distributions.

(An important caveat: the age distribution of people in Rome is very different from the aforementioned American cities—far more elderly are visible in Rome. This cuts both ways.)

This prompts me to propose the following Law of Conservation of Empathy: On average (across cultures) the average (across individuals) amount of empathy that an individual displays toward other people is fixed; what changes is how that empathy is distributed across the people that an individual interacts with. To be clear, the capacity for empathy does vary across individuals, but the average capacity of individuals across cultures is largely fixed. I.e. $\text{Var}_{\text{societies}}\left[E_{\text{individuals}}[\text{empathy}]\right]$ is small, but $\text{Var}_{\text{individuals}}[\text{empathy}]$ is high for any given society. More importantly, the point I am making is that how this capacity for empathy is manifested toward people that an individual interacts with varies a great deal between cultures, despite the total amount of it being fixed on average. I.e. $E_{x,y\in \text{societies}}\left[D_{\text{KL}}\left[\text{Dist}_{\text{towards\ others}}^{(x)}[\text{empathy}]\parallel \text{Dist}_{\text{towards\ others}}^{(y)}[\text{empathy}]\right]\right]$ is high. Unrelatedly, I think $E_{x,y\in \text{individuals}}\left[D_{\text{KL}}\left[\text{Dist}_{\text{towards\ others}}^{(x)}[\text{empathy}]\parallel \text{Dist}_{\text{towards\ others}}^{(y)}[\text{empathy}]\right]\right]$ is probably small for most societies. (Sorry I just came back from NIPS.)

In cultures with strong local communities and tribalistic tendencies, most of the (statistically fixed total) capacity for empathy is directed toward family and close friends. If you’re close to someone, they will take good care of you. If you’re not, you’re sort of on your own. Cultures occupying this extreme end of the spectrum are mostly in the Middle East and Asia, are generally what one would think of as being very communal, and tend to exhibit somewhat discourteous behavior toward strangers.

In cultures with strong individualistic tendencies and pluralistic and multicultural outlooks, the capacity for empathy is more uniformly distributed across all persons that an individual interacts with. It doesn’t matter how close you are to someone, they will more or less treat you the same way they would treat a stranger, which is basically with common decency and courtesy, if a little cooly. Cultures occupying this extreme end of the spectrum are mostly in the United States and the English-speaking New World.

European countries generally fall in the middle, as do Latin American ones. In the US, the west coast tilts individualistic, the east coast communal.

This seems consistent with a persistent yet somewhat distressing observation I have made, and that is there appears to be no free lunch when it comes to social interactions. Either people are outwardly nice and fair, but always maintain a certain distance no matter how close you get, or they are a little curmudgeony, but are quite decent once you get to know them. If the empathy pie is truly fixed, then there’s no hope of creating this ideal society I’ve always dreamed of, where people are both outwardly nice and fair, and are capable of very close friendships. Too bad.

(I write the above somewhat in jest. There’s no real evidence backing any of what I’m saying, certainly not in the sense of any real “law” of human behavior.)

1. I disagree Mo (for once). I think the hospitality in the middle east is counter evidence. I was once upset and crying in Haifa, and had to stop because people were so upset and wouldn’t let me cry in peace. Cultures that are more distant (eg US) might be courteous, but they are not likely to intervene/help you out if you’re in need. I think there are trust and closeness issues that dictate some of these behaviors.

• Maybe it’s an Israeli thing? I don’t think what you’re describing would happen in the Arab world, not today anyway. I think strangers are far more likely to intervene/help in the US for example.

• Also, trust is far more prevalent in the West than in the Middle East in my experience. People are just not very trusting in war-torn countries. (Again perhaps Israel is an exception here, although I think the us-vs-them dynamic in Israel vs. the more civil war type of dynamic in Arab countries may also contribute to this.)

2. Seether says:|

Hi
You should be working on your paper!

3. Terry Fletcher says:|

There is an exhibit in the Exploratorium in San Francisco about an experiment conducted in different countries around the world. I believe it they had an actor playing a blind person trying to cross a busy street. From what I remember (and I could be wrong) the country in which strangers were most helpful was Brazil and the least helpful was Malaysia.

4. Reblogged this on In The Eye Of The Sky and commented:
Funny( especially the expected value of the KL divergence), interesting and mildly true.