Paper
Why connection disintegrates as a community grows
A community of fifty people fits in one head. You know who joined last week, who is looking for a co-founder, who would get on with whom and why. A community of two thousand is not the same job made bigger. It is a different job, and the reason is arithmetic rather than effort.
The curve below is that argument in one picture. It is an illustration rather than data: the chance that two people who should meet ever do climbs while a community is small enough to hold in one head, peaks somewhere around 150 people, and falls away after it. Everything that follows is the measured version of the same shape.
People add up. Pairs multiply.
People arrive one at a time. The connections between them do not. Somebody who joins a community of 150 does not add one relationship; they add a possible relationship with each of the 150 people already there. For a community of n people, the number of possible pairs is n(n−1)/2.
| People | Possible pairs | Pairs the next person adds |
|---|---|---|
| 50 | 1,225 | 50 |
| 100 | 4,950 | 100 |
| 150 | 11,175 | 150 |
| 250 | 31,125 | 250 |
| 500 | 124,750 | 500 |
| 1,000 | 499,500 | 1,000 |
| 2,000 | 1,999,000 | 2,000 |
Quadratic, not exponential.
Two things in that table are worth sitting with. The first is the last column: every new person adds as many possible pairs as you already have people, so the work of noticing who should meet whom grows each time somebody joins. The second is what happens when your community doubles. Going from 500 people to 1,000 doubles the people and multiplies the pairs by 4, from 124,750 to 499,500.
Say what this is, precisely. The growth is quadratic: pairs rise with the square of the community. It is not exponential, which would mean a fixed multiplier for every person who joins and would be far more dramatic than what actually happens. We are careful about the word because a paper that overstates its own arithmetic should not be trusted with anything else. Quadratic is quite enough. Nobody hires in proportion to the square of their network.
The chart plots the same equation up to two thousand people. Look at where the line leaves the floor. Everything below a few hundred people is squashed into the bottom of the plot, and that is exactly the range in which a community still feels manageable.
What one person can hold.
The other half of the problem is the person doing the noticing. In 1992 Robin Dunbar showed that group size in primates tracks the size of the neocortex, and extrapolated the relationship to humans[1]. The number that came out was about 150. He restated the prediction the following year as 147.8, with 95% confidence limits running from 100.2 to 231.1, which he called moderately wide[3].
Later work with Zhou, Sornette and Hill found that human groups cluster in a series of layers, each roughly three times the size of the one inside it: 5, 15, 50, 150, 500 and 1,500[2]. The innermost few are the people you would call in a crisis. The outer layer is closer to the number of faces you can put a name to.
Treat all of it as a cognitive estimate with a wide range, not a law. A re-analysis in 2021 found that modern statistical methods give intervals so wide — one of them ran from 4 to 520 — that the authors concluded no single number can be derived this way[4]. What survives the argument is the order of magnitude. One person holds a few hundred relationships, not a few thousand, and a community passes that line long before it feels like it has.
The drawing below is a community at whatever size you set it to. Watch the lines rather than the dots: one node is a single person, holding what a person can hold, while the web around them keeps filling in.
pairs
one person can hold ~150
What this means if you run a community.
None of this is a verdict on how well you do your job. The gap between what your community could be worth to its people and what any one person can keep track of is arithmetic, and it opens at a few hundred people whatever you do. Three things follow from it.
The valuable work is not making introductions. It is noticing which ones to make: which two people, out of tens or hundreds of thousands of possible pairs, should meet this month. Making an introduction takes two messages. The noticing is the part that does not fit into a week.
Anything that waits to be asked serves the confident few. A directory, a search box, a culture of posting in the channel when you need something: each hands the work back to your people, and the people who use them are the ones who were already well connected.
Whatever helps has to do the noticing continuously, for every person, rather than in a burst on the afternoon you have free. That is the only way the square gets covered. How that works in practice, one introduction at a time, is the next document.