The Mathematics of Friendship

This article explains the four variables that lead to lasting friendships & what role each variable plays.

\[\displaylines{Proximity \times (Frequency + Duration) \times \\ Intensity = Friendship}\]

Proximity

For a friendship to grow, it requires close proximity between parties. The author stresses the importance of a relaxed, “nonthreatening environment,” so that neither party feels the desire to withdraw.

In situations where proximity is impossible to achieve, the article suggests that technology can cross this gap to allow for continued communication.

Frequency

Frequency is the number of meetings you have with someone over time. The more frequent these meetings, the more “influence that person has over your thoughts and actions.”

The author cites this as the main way that someone can be positively influenced by a close mentor, or negatively influenced by a rebellious friend group.

Duration

On the other hand, duration measures the amount of time you spend with someone during one meeting. It has an “inverse relationship with frequency,” as less frequent meetings lead to meetings with longer durations and vice versa.

Having high frequency and duration in a relationship often leads to high intensity, which is commonly found in romantic relationships.

Intensity

The article defines relational intensity as the ability to “satisfy another person’s psychological and/or physical needs.”

This can be through body language that communicates engagement, and intimate conversations. The article stresses the importance of intensity, calling it “the glue that holds relationships together.”