Some believe that the Christmas card list, where we keep track of old favours and slights, is a sort of passive-aggressive vendetta. There is truth in this. Late in 1974, two sociologists, Phillip Kunz and Michael Woolcott, posted more than 500 Christmas cards to people they did not know. Some of them were “high status” cards, using expensive materials and signed “Dr and Mrs Phillip Kunz”. Others were from “Phillip and Joyce Kunz” or used cheaper stationery or both.

The Kunz family received, along with a complaint from the police, some rather touching replies: “Dear Joyce and Phil, Received your Christmas card and was good to hear from you. I will have to do some explaining to you. Your last name did not register at first . . . Please forgive me for being so stupid for not knowing your last name. We are fine and hope you are well. We miss your father. They were such grand friends.”

But what is most striking is that more than 100 strangers felt obliged to send a signed card in response. That is the power of reciprocity. (Response rates were particularly high if “Dr Kunz” had written on a fancy card to a working-class household. That is the power of status.)

If this is what Christmas cards are all about — mindless reciprocal obligation coupled with some social climbing — then I think we can all agree on two things: we could do without them; and we’ll never be rid of them. Thomas Schelling, a winner of the Nobel Memorial Prize for Economics, once advocated a bankruptcy procedure — wiping clean the list of people to whom we “owe” a Christmas card. If only.

But perhaps the Christmas card also serves other purposes. Consider the exchange, “How do you do?”, “How do you do?” This is phatic communication. It conveys no detailed information but it acknowledges others and implies that there is nothing much to report. “I’m OK, and you’re OK, and lines of communication are open if that changes.”

A Facebook “poke” could achieve the same thing at much lower cost. But perhaps the expense and the hassle is part of the point. If someone invites you for dinner and you say “thank you” as you leave, you may still wish to follow up with a thank-you note to show that you have enough invested in the relationship to take the trouble. If relationships weren’t hard work, they would not be relationships.

There’s a thing called the “social brain” hypothesis: it states that humans evolved large and energy-intensive brains not to do hard sums or design clever tools but because they needed them to navigate the complexities of dealing with other people. Back in 1992, Robin Dunbar — an anthropologist and psychologist now based at the University of Oxford — published a fascinating addendum to that idea. Dunbar had been looking at the social group size and the brain size of different primates, and found that primate species with larger neocortices had grooming relationships with larger social groups. Extrapolating to humans, he produced what has become known as Dunbar’s Number. If our brains are any guide, we’re built to handle a social network of about 150 people.

Dunbar’s Number is both more uncertain and more complex than popular presentations would have you believe. Dunbar himself argues that social networks are nested, following rough powers of three: five people to whom we might turn for substantial emotional or financial support in a moment of true crisis; 15 intimate friends; 50 friends; 150 rather casual friends, and so on.

Social networking tools let us reach more people, more quickly, and in some detail if we so choose. I can reach 90,000 followers on Twitter but — how can I put this tactfully? — they are not my friends. These new technologies are a great convenience but it is not clear that they are allowing us to expand the number of genuine friends that we have. A recent study by Bruno Gonçalves, Nicola Perra and Alessandro Vespignani examined 25 million conversations between Twitter users, and found that the network with whom people might actually have several reciprocal conversations was between 100 and 200 — Dunbar’s number again. As for close friends, women engage in two-way communication with around six people on Facebook; men with just four.

Much like primate grooming, a Christmas card requires effort, time and expense. An up-to-date Christmas list requires some thought about who matters to you, for reasons noble or ignoble. And a few years ago, two researchers carefully examined how big Christmas cards lists tended to be, once allowing for the fact that a single card could reach several members of a household. The researchers were Russell Hill and Robin Dunbar. And the number of people reached by a typical British Christmas card list? 154.