ST PETER — Memorizing a seven-digit phone number: no big deal. Keeping up with an episode of Survivor or the subplots of Shakespeare: much more difficult.

Aye, there’s the rub.

It’s our social relationships that demand and require our brain power, which accounts for the rise of modern civilization, Oxford University professor Robin Dunbar said during the second day of Gustavus Adolphus College’s Nobel Conference.

In a conference about early humans, Dunbar asked a slightly different question: What can science say about why and how we’re human, not primate?

The answer, at least from a physiological perspective, is intimately tied to our social nature, Dunbar said.

In primates — and only primates, it appears — brains get larger as group size increases.

In birds, for example, bigger brains are found in species that pair-bond for life. Dunbar figures that’s because of the coordination demands placed on monogamous pairs.

“I don’t have to tell you that,” he said to laughs.

And in humans, there appears to be a group number that our brain is built for. It’s about 150, and it’s come to be called Dunbar’s Number.

Groups of approximately that number are found, for example, in the military at the company level, in the “clan” of tribal societies and in certain communal villages.

Put another way, it’s the number of people you’d willingly approach if you came upon them in an airport bar during a 3 a.m. layover, he said.

There are advantages to living in groups where everyone knows each other, Dunbar explained, including the power of peer pressure and the lack of a need for police.

And as these things typically are, Dunbar’s Number isn’t quite that simple.

Humans, it turns out, also form smaller groups of more intense relationships. Those groups, for some reason, are rough multiples of three; the smallest is five, followed by 15 and 50.

The more often we see people, the closer our relationship with them, he said, though there is the exception of those you see “very often, but you can’t bear.” No, not our family, he joked. Coworkers.

While it may be intuitive that social relationships require brain power, Dunbar explained a way to talk about social dynamics.

In the system called “orders of intentionality,” the first order is someone thinking about themself. The second order is thinking about someone else’s thoughts, and the third is, for example, thinking about what someone else thinks about what you think.

The limit for non-human animals is the second level, according to experiments designed so far.

In one vexing example, Dunbar said efforts to study dolphins failed after experimenters realized the mammals were picking up unintentional, nonverbal cues from researchers, not thinking about their state of mind.

Humans, if they can write the relationships out, can comprehend six or sometimes seven orders, but anything higher than that is exceedingly difficult, Dunbar said. (His limit is six).

Try this: Dunbar (1) hoped that his audience (2) could understand his thoughts (3) about how humans think (4) and about how they think other people think (5).

If you grasped that fifth-order thought without a headache, congratulations, you’re smarter than a chimp.