More friends should mean a more connected society. That’s the assumption underneath every “just get out there and meet people” piece of advice, and it’s the assumption a PNAS paper from late 2025 took apart with math. Why more social interactions lead to more polarization in societies, published online October 31, 2025 by Stefan Thurner, Markus Hofer, and Jan Korbel of the Medical University of Vienna and the Complexity Science Hub Vienna, built a computational model of a friendship network and found something that doesn’t sound like it should be true: past an average of roughly three to four close friends per person, a society doesn’t get more connected. It snaps — abruptly, mathematically — into two mutually hostile camps, each one internally uniform and near-unanimous in its opposition to the other. Not gradually more polarized. A phase transition, the same kind of sudden reorganization water goes through when it turns to ice. Georg Simmel, writing in Berlin in 1908, already had the mechanism for why this happens, and he called it something almost nobody remembers today: the web of group affiliations.

The Quick Verdict

Question	What we found
Who ran the study?	Stefan Thurner, Markus Hofer, and Jan Korbel — Medical University of Vienna and Complexity Science Hub Vienna
Where and when?	PNAS, published online October 31, 2025
What was measured?	A computational model of a friendship network, calibrated against decades of real survey data on self-reported close friendships
What was the threshold?	An average of about three to four close friends per person — cross it, and the network’s structure abruptly reorganizes
What was the twist?	More friends didn’t dilute conflict across a wider circle. It concentrated the population into two roughly equal, internally uniform, mutually hostile mega-clusters
What did Simmel already argue?	In Die Kreuzung sozialer Kreise (1908), individuality and social peace depend on belonging to many non-overlapping social circles — not one dense circle that swallows the rest

The Quick Version

A late-2025 PNAS model found that societies don’t get more cohesive as people accumulate close friends. Past an average of about three to four, the network collapses into two large, internally uniform, and openly hostile camps — a mathematical phase transition, not a gradual drift. Georg Simmel argued in 1908 that a person’s individuality and a society’s stability both depend on belonging to many crossing, non-overlapping circles. When those circles collapse into one, the buffer disappears and identity hardens into a binary. The model reproduces that collapse with equations. Simmel just watched it happen to Berlin.

What the Study Actually Found

Thurner’s team wasn’t asking whether polarization is real — that’s not in dispute. They were asking why a society gets more polarized as people become more socially connected, when every intuition says the opposite should happen. More friends, more exposure to different views, more cross-pollination — that’s the story social media told about itself for a decade.

The model says the story has a hidden threshold built into it. Below an average of about three to four close friends per person, the simulated population organizes into many small, overlapping, ideologically diverse clusters — the kind of society where your book club, your family, your coworkers, and your gym friends don’t line up neatly, and where disagreeing with someone at dinner doesn’t cost you your whole social world. Cross that average, and the structure doesn’t bend. It breaks — into two large clusters of roughly equal size, each one holding nearly identical opinions internally, with strictly negative, adversarial ties running between them. Korbel described the underlying dynamic to the Complexity Science Hub: “When people are more connected with each other, they encounter different opinions more frequently. This inevitably leads to more conflict and thus greater societal polarization.” Hofer put the shape of the finding more precisely: “This enabled us to show that increasing connectivity must lead to sudden polarization once a critical connectivity density is exceeded—just like a phase transition in physics, such as water turning to ice.”

That water-to-ice comparison isn’t decoration. Phase transitions are abrupt by definition — there’s no meaningfully polarized in-between state, just cohesion on one side of the threshold and fracture on the other. The mechanism has a specific engine: once someone has three or four friends instead of two, losing one over a disagreement costs much less. There are backups. Tolerance stops being load-bearing, because it’s no longer the thing holding the relationship together. Push that logic across a whole population and the cheapest way for each person’s circle to stabilize is to converge on people who already agree — which, multiplied across millions of people making the same low-cost calculation, produces exactly two attractors instead of many.

The historical data the model runs against is its own small gut-punch. Self-reported close friendships jumped from an average of about two to an average of four or five between 2008 and 2010, tracking the rise of smartphones and mass social media adoption — right as platforms were selling themselves as tools for more connection, not less. That jump in friend counts is a separate number from the model’s three-to-four threshold; it’s the historical shift that crossed the threshold, not the threshold itself. Pew Research has separately tracked ideological polarization as relatively flat before 2010, then rising sharply after. The model doesn’t claim social media caused polarization by exposing people to more disagreement. It claims something closer to the opposite: it caused polarization by giving people more friends, which made each friendship more disposable, which made the whole network cheaper to sort into two camps instead of many.

So, How Many Close Friends Is Too Many?

There’s no fixed number that applies to any one person — the threshold in the model describes a population average, not an individual ceiling. But the mechanism is specific: once your friend count is high enough that any single friendship becomes replaceable, tolerance for that friend’s disagreement stops being necessary to keep the relationship. That’s the tipping point the model identifies, not a friend-count you should personally avoid crossing.

Simmel Already Made This Argument, Without a Single Data Point

Georg Simmel isn’t a household name the way Marx or Weber are, even though he was working alongside both of them in Berlin at the turn of the twentieth century. His 1908 essay “Die Kreuzung sozialer Kreise” — translated into English decades later as “The Web of Group-Affiliations” — makes an argument that sounds almost too simple to be the foundation of modern social network theory. A person isn’t defined by membership in one group. A person is the specific, unrepeatable intersection of many groups: family, profession, neighborhood, religion, hobby, political affiliation, none of which map perfectly onto any of the others.

That non-overlap is doing the real work, and it’s easy to read past it. If your coworkers, your neighbors, your family, and your closest friends were all the same twenty people, you wouldn’t have four circles. You’d have one, and it would own you completely — your opinions, your loyalties, your sense of what’s normal, all supplied by a single, undivided source with no outside check on any of it. Simmel argued that modern individuality is only possible because circles don’t coincide like that. It’s also, he argued, what keeps a society from splitting into two armed camps. Cross-cutting membership means the person on the other side of your political disagreement is also your cousin, your bowling teammate, or your kid’s classmate’s parent. That overlap is friction, and friction is what a polarized binary can’t survive.

Simmel wrote this in 1908, watching industrializing Berlin fragment its old, dense, single-circle village structures into something more differentiated — more freedom, he thought, but also more fragility, because the whole arrangement depended on those circles staying numerous and staying crossed. He had no model of network topology, no phase-transition math, nothing resembling Thurner’s simulated population. What he had was an observation sharp enough to survive being translated into equations more than a century later: collapse the crossing, and you don’t get more connection. You get one circle standing in for all of them — and one circle, with nothing outside it to answer to, is exactly the shape a mega-cluster takes.

What Did Simmel Actually Argue in “The Web of Group-Affiliations”?

1. Individuality is intersectional, not singular. A person’s specific identity emerges from the unique combination of groups they belong to — not from deep membership in any one of them. Change the combination and you change the person.
2. Non-overlapping circles are the point. The less your family, your work, and your friendships map onto the exact same people, the more genuine independence you have from any single group’s total control over your views.
3. Crossing circles is what keeps conflict survivable. When your political opponents are also your neighbors or your relatives, disagreement stays embedded in relationships that have other things going on. Strip the overlap out and disagreement has nothing left to soften it.
4. Fewer, denser, more coinciding circles produce more fragile individuality — and more fragile societies. Simmel treated the multiplication of crossing circles as a hallmark of modern freedom. Their collapse back into one dominant, undivided group was, for him, a step backward, not forward.

This Site Has Covered Polarization and Connection Before — Here’s the Difference

Habermas’s account of communicative rationality, covered here after his death earlier this year, explains why conversations across a divide stop working once people quit trying to understand each other’s reasons and start performing for an audience. That’s a claim about what happens inside a single conversation. Simmel’s argument sits one level up — it’s about the network structure that determines who you’re even having conversations with in the first place. Habermas explains why the conversation breaks down. Simmel and the PNAS model explain why you stopped having it with anyone who’d disagree.

Rousseau’s account of amour propre — the self-worth that only exists relative to what others think of you — gets sharper against this backdrop. A social media feed sorted into a mega-cluster isn’t just an echo chamber for opinions. It’s a machine for supplying exactly the validation amour propre runs on, from an audience already guaranteed to agree. Simmel’s crossing circles used to interrupt that loop by exposing you to people who wouldn’t automatically approve.

Isaiah Berlin’s value pluralism makes a related case — that no single formula for the good life beats the honest plurality of formulas people actually live by. Simmel’s crossing circles are close to the social infrastructure that pluralism needs to survive contact with other people. A society with many overlapping-but-distinct circles has somewhere for real value pluralism to live. A society sorted into two mega-clusters doesn’t.

And this site’s piece on Aristotle’s three types of friendship argued that friendships of virtue — the deep, slow-built kind — are rarer and more durable than friendships of utility or pleasure. The PNAS model’s mechanism depends on friendships being at least somewhat fungible, disposable enough that losing one over a disagreement doesn’t cost much. Aristotle’s virtue-friendships were never meant to be disposable at all — a hint about what kind of friend-making resists the collapse.

Where This Doesn’t Hold Up

None of this makes Simmel a network scientist, and it doesn’t make Thurner’s team secret students of German sociology. Being honest about the gap matters more than making the comparison sound tidier than it is.

The PNAS model is exactly that — a model. It’s calibrated against real survey data on self-reported friendship counts, but the two-mega-cluster outcome is a property of the simulation, not something directly measured in an actual, present-day society split into exactly two camps of equal size. Real polarization is messier and more asymmetric than the clean binary a model can produce, and the paper’s own framing is about mechanism and plausibility, not a photograph of any one country’s political map. The finding has already drawn scholarly pushback in other PNAS exchanges arguing that connectivity alone doesn’t explain polarization without other ingredients, like actual opinion content — a reminder this is a live, contested research area, not settled science.

Simmel’s essay is a different species of claim, and flattening the two together would be dishonest. He wasn’t modeling anything. He was making an observation about industrializing Berlin, dressed in the language of early sociology, with no data set behind it beyond what he could see happening around him. He also wasn’t writing about friendship counts specifically — his “circles” are broader categories like religion, profession, and class, not a tally of close personal friends. The PNAS threshold of three to four is a precise number about a narrow variable. Simmel’s crossing circles are a looser, more qualitative claim. The overlap between them is real and worth taking seriously. It isn’t a one-to-one match.

A Practice Worth Trying

Neither Thurner’s team nor Simmel wrote this as a five-step plan, but the shared shape of what they found points somewhere specific.

1. Audit whether your circles actually cross. Do your closest friends, your family, your coworkers, and your online community overlap heavily, or barely at all? If the answer is “heavily,” you may be closer to one dense circle than several crossing ones — the arrangement Simmel warned thins out individuality and raises the temperature of disagreement.
2. Keep at least one relationship that costs something to maintain. The model’s mechanism runs on friendships being cheap to drop. A friendship you’d work to repair after a real disagreement is doing structural work a disposable one can’t — it’s friction the mega-cluster can’t absorb.
3. Don’t mistake more contacts for more connection. Adding people to your circle isn’t neutral. Past a point, it can concentrate your social world rather than widen it, especially if the new contacts mostly resemble the people you already know.
4. Notice when a group stops being one of several and starts being the only one. Simmel’s warning wasn’t about having strong group loyalty. It was about a single group becoming the sole source of your opinions, your validation, and your sense of who’s on your side. That’s the moment a circle stops crossing and starts closing.

The Crossing Was the Point

Thurner, Hofer, and Korbel weren’t testing Simmel. They built a computational model to answer a narrower, more mathematical question — why does more social connectivity produce more division instead of less — and found a specific, uncomfortable answer: past a threshold of about three to four close friends, tolerance stops being necessary to hold a friendship together, and a population sorts itself into two hostile, internally uniform camps almost overnight. Simmel wasn’t running simulations. He was watching Berlin’s old, dense village circles fragment into modern life, and he noticed that the fragmentation itself — many crossing, non-coinciding groups instead of one all-consuming one — was what made both individuality and social peace possible in the first place. He had no threshold, no equations, no phase transition. He had the crossing, and he understood, more than a century before anyone modeled it, that losing it was the actual danger. Not too few friends. Too few different rooms to have them in.

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This post discusses a September 2026 computational modeling study on social polarization alongside a classical sociological text. It isn’t a claim that anyone should have fewer friends, and neither the researchers nor Simmel argue that. If polarization within your own family or close relationships is causing significant distress, a therapist or family counselor can offer support a philosophy essay can’t.