Why are conversations limited to about four people?

Each person has a range of conversational contributions that they may feel comfortable with. A good university lecturer, radio show host, or stand-up comedian, for instance, might be able to sustain a maximum of 1.0 all alone for hours at a time. Someone with an inflated ego might not feel comfortable dipping below 0.5 for any length of time, whereas an introvert might range between 0.0 (pure listener) and a peak value they cannot sustain for long outside of a narrow range of topics.

So establishing the most efficient number of conversations, and their participants, becomes a form of the backpack problem. A conversation group can only achieve its highest efficiency of some people aim to fulfill different roles. Some participants are bulky and heavy, some are spongy and flexible, and others are small and light.

There's the baseline talker. This is likely the person with the highest sustainable coefficient. They drive the conversation. Then there are responders, who need to have a wide, tunable range of coefficient. They top off the conversation to 1.0 by adjusting their output to an appropriate value. There may be interjectors, who pipe up with a witty quip or relevant factoid every now and then, aiming for high return on low coefficient. There may also be swappers, who participate at a low level in multiple conversations, flipping to whichever one seems to have a lower coefficient, but less able to sustain higher coefficients than a responder. Sometimes there is even a gestural participant, who mainly contributes to the conversation with non-competing visuals rather than interruptable speech.

So having a single conversation with more than six people is easy. You kick out the baseline talker, get two responders to drive the conversation instead, and fill up the rest of the group with interjectors. This happens all the time in tabletop gaming groups, where the game itself adds a baseline coefficient, and the typical participant has a low maximum sustainable coefficient. Some people just don't want to talk much, and the game can create a structured conversation that pulls lower-coefficient players up enough to make the group reach 1.0 .

That in a picture with line graphs varying X, Y, people can't understand if the lines are different colours or the same colours (a third dimension)?

That people can't play 3D games because they can't understand that the image is depicting length, width and depth?

That people can't use windowing GUIs with overlapping windows, because they can't understand the Z-order of which window is "in front"?

It seems intuitive that people can cope with more than 2 variables and more than 2 "dimensions" spatially or otherwise.

What do you mean when you say they can't - what, specifically, can't people do?

There are bunch of possible reasons conversation size might be limited or optimal at certain numbers. They choose to focus on mentalizing -- your ability to maintain a mental model of another person. (I don't know if they have a strong claim for why they chose this.) One interesting observation that HN will love is that mentalizing is recursive. When I have a mental model of your mind, that model includes why I think your mental model of me is, and so on. If I say something to Fred while George and Harry listen in, I can reason about what Fred will think of what I say, what George will think of what Fred will think of what I say, and what Harry will think of what George will think of what I will think of what Harry will think of... ad infinitum.

By focusing on mentalizing, what matters more is the pairs of people in a conversation more than the number of people. It's about the relation between one person and their reaction to another. Pairs grow faster than linear as the number of participants increases. There are "n(n-1)/2" pairs in a conversation with "n" people.

Then they make a distinction between "inclusive" and "exclusive" pairs. An inclusive pair is one that includes you. So in a three-person conversation, there are three pairs: you-A, you-B, A-B. So two of those pairs are inclusive.

The number of pairs increases quadratically. The number of inclusive pairs increases linearly. At larger group sizes, most pairs of people don't include you.

They claim four is the magic number because that's the largest conversation size before the exclusive pairs outnumber the inclusive ones. With four people, there are three inclusive and four exclusive pairs. With five people, there are four inclusive and six exclusive.

It's a neat observation, but they note themselves that they are basically doing a post-hoc analysis. They started with four and then tried to find some math that makes it special, and eventually found two lines that cross at that point.

I do think there might be something to it. If you assume that the most valuable interactions are ones that involve you (versus deriving value from seeing what two people say to each other), then it stands to reason that you want to avoid conversations where most utterances aren't from you or to you.

But that also presumes (1) people don't derive much value from watching others talk to each other and (2) all participants are communicating to each other equally. Neither of those is true in practice.

I think a smarter way to look at it is that people strive to maximize the total value they get from all pair-wise communications. One way to do that is in a small even-handed conversation. But you can also get that by:

1. Giving a speech where you get to do almost all of the utterances. So even though there are many many pairs, most of those channels are silent, and most of the communication does involve you.

2. Watching a debate where even though your aren't participating, you get a lot of value from what the other two are saying to each other.

3. Less formal approximations of the above. All of us have probably experienced a conversation that grew to larger than four people because a minority of them had more dominant personalities so you end up with a couple of "performers" and some "audience" though people occasionally change sides.

Anyway, fun paper.

Do they, though? Maybe I participate in conversations differently, but trying to unravel how A interpreted B's comment is not something I would do.