There isn’t some set number of relationships you can have such that you’ve got to pick out the “important” ones.

Actually, there very much are.

Most people are familiar with Dunbar's number, which expresses the size of a total community. That's not the number of important relationships, but essentially the number of total relationships you can juggle.

In your life, should it be a reasonably long one, you'll experience about a half-million waking hours. If you get to know 10,000 people in your life, the total time you can dedicate to any one of them is about two days (48 hours).

In The Mythical Man Month, Fred Brooks notes the dynamics of team communications, which rapidly develop complexity after about 5-6 members. Programming teams, unless the work can be modularised to the extent teams have full independence generally lose effectiveness as they're scaled above this level.

The Politburo Standing Committee of the Communist Party of China -- effectively the inner cabal of government -- has ranged from 5-9 members, and is presently 7. (Each of them represents the interests of about 185 million Chinese.) Again, tight working groups simply do not scale past a large size.

I've been digging at various elements of this question for a few years, largely informally. But the clear point is that your relationship time is limited, that close relationships take time and investment, and that as attention is spread, the nature of those relationships tends to deteriorate.

(I'm not aware of specific literature on this offhand though I'm certain it exists.)

Thanks for writing that out that was pretty much where I was thinking :)

I think in a philosophical sense that is true. However, our wetware is just wired to keep about 100 fellow people close. More than that and relationships seem to become very superficial. Most people only maintain a very small number of close relationships. Those are the "important" ones. Importance is sort of decided naturally, though.

100 seems high. I have heard it's more like 12 to 15.

I think bitexploder is referring to the "Dunbar's number" which is 150.

https://en.wikipedia.org/wiki/Dunbar%27s_number

From the wiki: Dunbar's number is a suggested cognitive limit to the number of people with whom one can maintain stable social relationships. By using the average human brain size and extrapolating from the results of primates, he proposed that humans can comfortably maintain only 150 stable relationships.

That's not actually true.