Ask a room of professionals how many friends they have, and the answers tend to come quickly and in the hundreds. Ask how many of those people they would call at three in the morning, and the room goes quiet. Modern life is unusually good at producing connections. It is less good at producing friends. The distinction is not new. More than two thousand years ago, Aristotle drew it with a precision that still feels slightly uncomfortable to read.

In the Nicomachean Ethics, Aristotle describes three kinds of friendship. There are friendships of utility, in which each person is useful to the other: colleagues, contacts, the neighbour who waters your plants. There are friendships of pleasure, built on shared enjoyment: the tennis partner, the witty acquaintance, the companion for a night out. And there are friendships of character, in which each person loves the other for who they are and wishes them well for their own sake.

Aristotle is not snobbish about the first two. They are real friendships, and life would be poorer without them. But he notes that they are fragile by design. When the usefulness ends or the pleasure fades, so does the bond, and neither party is really to blame. Only the third kind endures, because it rests on something that does not depend on circumstance. It is also, he admits, rare, and it takes time. People cannot truly know each other, he says, until they have eaten a great deal of salt together.

Another self

What makes the third kind so valuable is also what makes it so hard to cultivate now. A friendship of character is, in a sense, useless. It does not advance a career or fill a social calendar efficiently. It asks for long, unstructured time together, much of it spent doing nothing in particular. Aristotle called the true friend another self, someone whose good becomes part of your own. That kind of intimacy cannot be scheduled into a lunch meeting. It accumulates slowly, often while no one is watching.

Lise Bergmann, a sociologist who studies adult friendship at the Norland Centre for Social Research, has found that most friendships fade not through conflict but through logistics. A change of job, a move across town, the arrival of children: each quietly removes the occasions that kept people together. Her advice is almost embarrassingly simple. Create a recurring reason to meet that has no purpose beyond the meeting itself, a weekly walk, a monthly dinner, and protect it as you would a deadline.

Adults don't lose friends because they stop loving them. They lose them because they stop having reasons to be in the same room.

Montaigne, mourning his friend Étienne de La Boétie, famously struggled to explain why they had loved each other, and concluded that there was no explanation beyond the simple fact of who each of them was: because it was him, and because it was me. That is the mark of the highest friendship Aristotle described. It has no answer to the question of what it is for. Nothing is produced. Nothing is gained, except the other person.

So perhaps the test of a friendship worth keeping is not how helpful it is, but how useless. Who would you still see if neither of you had anything to offer the other, no introductions, no favours, no entertainment beyond each other's company? The list will be short. That is fine. Aristotle thought a person could only have a few friends of this kind. The work is not to add more names, but to tend the ones already there.