The mathematical formula that says how many friends you can have

a quarter century Ago, the british scientist Robin Dunbar suggested that the number of people with whom we relate in the usual way is approximately 150.

Some primatologists had noticed that there is a relationship between the number of individuals with the primates to relate socially and the size of their neocortex brain, which is considered, from an evolutionary point of view, the more modern part of the brain.

According to these observations, the ability to relate to more or fewer individuals would be limited by the volume of that part of the brain because that volume would affect the cognitive ability. Dunbar estimated the number of 150 from the relationship cited using data corresponding to 38 genera of primates. And since then that number, 150, has been named “number of Dunbar”.

it Also suggested that the size of the groups, real human just gets to be 150 individuals when the conditions in which it operates the group are very strict and its members have a strong incentive to stay together.

Only groups subjected to a pressure of survival intense, as villages of subsistence, nomadic tribes, and cantonments for military reach the number of 150. When you are not given these circumstances, the group would be smaller, while the ability to build relationships would still be in that rough boundary.


Researchers from the University Carlos III of Madrid and the Dunbar, of Oxford, have developed a theoretical model of social relations that were part of the basis of the capacity to interact with different people is limited and that different types of relationships require different degrees of involvement. (Ignacio Tamarit, José A. Cuesta, Robin I. M. Dunbar, and Angel Sanchez, 2018: Cognitive resource allocation to determine the organization of personal networks. PNAS).

The theory explains empirical observations according to which human relationships are typically deployed according to a structure in circles.

it is normal that we relate closely with very few people, between three and five; in this circle include the closest relatives and, sometimes, the intimate friendships.

The next circle is formed by ten other people, are good friends.

Something further away there is a group of about 30 to 35 people, which are those with who we are dealing with frequency . Surely it is no coincidence that the bands of hunter-gatherers in which were structured human populations during the greater part of the history of our species have, as much, about 50 individuals; perhaps those first three circles are reminiscent of those bands.

And finally, we have a hundred well-known with whom we interact regularly.

however, the model also gives an account of a social structure possible different , a configuration reverse to the above.

it Happens, for example, when the community to which he belongs an individual is small (less than 55 individuals); in that case, almost all of their relations are in the first circles, and the group has a great cohesion. This structure is the “inverse” of individuals who, by their personality, they have a tendency to relate with very few people. Or also when the individual belongs to the special communities, very few are effective, as are certain groups of immigrants.

What seems to be inferred from these studies is that we have a kind of knowledge capital more or less fixed, and that if we put that capital to relate with a few people, the relationship with them can be very intense. But if, by our personality, or by other circumstances, we have a tendency or need to interact with many people, then you will be able to devote to each one of them more than a small amount of capital-cognitive, relational. And is that although we have a large neocortex, and its volume is not infinite.

Juan Ignacio Pérez Iglesias is cCatedrático of Physiology in the University of the Basque Country / Euskal Herriko Unibertsitatea (UPV/EHU)

This article has been published originally in The Conversation.