Why cities almost never die, and companies always do
2026-08-20 · Scale
Double a city's population and you do not get twice of everything. Gas stations and cables grow by less than double, while wages, patents, crime — even how fast people walk — grow by more than double. That split, one half surging and one half saving, is the whole reason cities and companies meet different fates.
Last topic's animals were unanimous about one thing: everything slows down and cheapens with size. Heartbeats slow, per-gram metabolism drops, a single exponent runs the whole show. Cities tear that unanimity in two.
The "pipes" half — road length, water mains, cables, gas stations — behaves just like an animal and cheapens with size: double the city and you need only about 80% more of these. But the "people" half — wages, GDP, patents, restaurant variety, and also crime, disease, waste — runs the other way: double the city and these grow by more than double. The same city is decelerating in one half and accelerating in the other.
This is where the "Scale" phase lands. Topic 32 was self-similarity (one shape repeating across scales), Topic 33 was allometry (organisms must change proportion with size, and all of it sublinearly, slowing down). The one new word here is superlinear. Organisms have no superlinear half; cities do — and it is that half that makes a city behave less like an organ and more like a machine forever picking up speed. This topic chases a single question: why is that machine nearly impossible to stop, while a company's runs for barely a decade?
Start with the easy half. A city of ten million does not need twice as many gas stations as a city of five million.
In 2007, physicists Luís Bettencourt, Geoffrey West and colleagues laid out data on hundreds of cities across the US, Europe and China and measured how quantities scale with population. The result was unusually clean: everything infrastructural — total road length, cable length, number of gas stations, water pipes — grows as population to the power of about 0.85. An exponent below one means per-capita use falls as the city grows. Double the city (population ×2) and these need only about 1.8× as much (2 to the 0.85 ≈ 1.8).
The mechanism is the same supply network as last topic's animals → ref · Allometric Scaling: a distribution network that must reach every terminal (every household, every building) shares trunk lines and spreads cost as its reach grows, so unit cost drops. This is the hardest version of "economy of scale" — not a management slogan but a geometric law that spits out an exponent. Big cities are physically greener: a New Yorker's per-capita carbon and per-capita road are lower than a small town's.
Now the counterintuitive half. Across the same cities, wages, GDP, patent counts, restaurant variety, the fineness of specialization — these grow as population to the power of about 1.15. The exponent is above one.
Above one means per-capita output rises as the city grows. Double the city and economic output is not twice but about 2.2×; per-capita wages and patents gain roughly 15% out of thin air. This is why people crowd into big cities — not just for more jobs, but because the same person is on average worth more in a bigger one. This half is superlinear (exponent above one, output growing faster than size itself).
The mechanism is not pipes but connection. A city's value is not how many roads it has but how many times the people on them can run into one another. The bigger the city, the more other people, skills and ideas each person can reach — and that reachable count grows faster than population itself. Ideas meet ideas, buyers meet sellers, masters meet apprentices, and output pours out of the matches faster than heads are added.
This superlinearity has a merciless feature: the good and the bad use the same exponent. Wages scale at 1.15, patents at 1.15 — and so do crime, contagious disease, mental stress, at roughly the same 1.15. They are not three things but three exhausts of one thing: denser connection. A city's vitality and a city's pathology are two tailpipes on one engine; you cannot keep just one.
Whenever you hope to gain something "by getting bigger," first decide which slope your prize hangs on. Want to cut cost (infrastructure, logistics, compute)? Bigger helps — that's sublinear. Want output, innovation, matching (talent, ideas, deals)? Bigger helps too — but you will drag along the crime-like byproducts (friction, accident rates, disease, noise) magnified by the same exponent. Don't budget only the slope you want; list the same-exponent byproducts too, or the further you scale, the bigger the line you forgot.
Now settle the account of both slopes onto the question of how long things live.
Take companies first. In 2015, Madeleine Daepp, West and colleagues pulled 25,000 companies publicly traded in North America between 1950 and 2009 and ran survival analysis (the method medicine uses to compute patient survival). The result was strikingly clean: the half-life of a publicly traded company is about ten years — every decade or so, half of a cohort disappears (bankruptcy, acquisition, delisting). And the mortality rate does not change with age: a fifty-year-old firm's chance of vanishing next year is basically the same as a five-year-old's.
Statistically this is a constant hazard rate. It means the survival curve is an exponential decay — the same shape as radioactive decay and other memoryless random events. A company is not like a person, low mortality when young and rising with age; it is more like an atom that may decay at any moment, with seniority buying it no protection.
Cities are the opposite. You can barely name a handful of major cities that truly "died." Hiroshima was flattened by an atomic bomb and is a thriving metropolis decades later; the cities Europe's wars rolled over again and again are still there. Cities are extraordinarily hard to kill.
West's explanation lands exactly on the two slopes above. A company lives mostly on the sublinear curve: it behaves like an organ — chasing economies of scale, cutting redundancy, standardizing process. That makes it efficient young but also steadily rigid: layers of management, compliance and internal coordination rise with size and squeeze out the very exploration that let it take off. Most companies orbit a few products, and once the market shifts and that sigmoidal growth curve tops out, they have no second breath, and die. A city lives mostly on the superlinear curve: it rides not one product but the endless recombination of people; one industry fades and another grows out of the same crowd. So a city can reboot itself again and again, while a company mostly gets to grow only once.
Judge which curve your organization (company, team, product line, even your own career) sits on: does its edge come from doing one thing cheaper and more standardized (sublinear, economy of scale, destined to top out and decay), or from generating new combinations (superlinear, more alive when bigger)? The former should presuppose death and prepare the next curve early, never mistaking present efficiency for safety; the latter should protect diversity and internal connection, never standardizing it into a company for short-term efficiency. Treat "which curve are we on" as a question to re-answer periodically, not a one-time positioning.
Now the other side. Urban scaling is the most photogenic block of complexity science — a clean exponent, sweeping conclusions, a bestseller. Which is exactly why it draws so much rebuttal, and you must know it before you use it.
First, the exponent isn't that stable, and it depends on how you draw "the city." Where is a city's boundary — administrative limits, the metropolitan area, or the commuting zone? Change the definition and the same data yields a different slope. In 2015 Arcaute et al. and Cottineau et al. showed that recutting British and French cities by different definitions can weaken or even erase superlinearity. This is geography's notorious modifiable areal unit problem (MAUP): you draw the boundary first, and the boundary decides the exponent you measure. So 1.15 is not a rock; it drifts with the definition.
Second, 1.15 is a central tendency, not any single city's destiny. Around that line, individual cities scatter widely. For a specific city, how far it sits off the line (its "scale-adjusted metropolitan indicator," SAMI) is often more useful than the line itself — San Francisco's patents sit far above trend, while other cities of equal size sit far below. Using the slope of the whole line to predict one city is like using average height to guess one person's height.
Third, "cities don't die" is survivorship bias. Plenty of cities did die: Detroit fell from 1.8 million to under 700,000; the city of Rome shrank from about a million after the empire's collapse to a few tens of thousands and took over a thousand years to recover; the metropolises of the Maya and Angkor were abandoned outright. Urban resilience is conditional — it depends on the surrounding region and nation still functioning. Taking "Hiroshima rebuilt" as "cities don't die" counts only the ones that survived.
Fourth, calling company death a "law of physics" overreaches. A constant hazard rate is a statistical regularity, not a mechanism — it tells you the shape, not the why. And the data is publicly traded companies, itself a filter; "death" also lumps in acquisition (the company is gone, but the people and assets often continue, absorbed elsewhere), which is nothing like bankruptcy. Merging three very different endings into one "mortality curve" looks clean but erases exactly the distinction you most want.
Fifth, "superlinearity must produce a finite-time singularity, forcing you to innovate ever faster or collapse" is a model extrapolation. West argues that a city's growth, left undisturbed, races to infinity in finite time; since real resources are finite, it must keep "resetting the clock" with waves of ever-more-frequent innovation, or stagnate and collapse. It is a gripping argument, but it is a prediction from pushing the equations past their boundary, not an observed fact. The equations need not even hold near the singularity. Treating it as a description of the future requires far more than "the curve fits well now."
Before citing any urban-scaling number, answer three things: (1) which city boundary the line uses (administrative / metro / commuting) — change it and the exponent moves; (2) whether you care about the whole trend or one city's deviation from it — for a single object, the latter is what matters; (3) how much of "cities never die / companies always do" survives after stripping survivorship bias and "acquisition ≠ bankruptcy." If you can't answer all three, state only the direction ("social output is superlinear in size, infrastructure sublinear") — don't quote 1.15, and don't treat it as prophecy.
Possible, but the lever is not lowering the exponent — it's raising the intercept, or detaching one item from the shared connectivity. Cities of the same size differ several-fold in crime rate, and the difference is institutions, trust, distribution, not population. Scaling gives you "which band this city will roughly land in"; whether it lands high or low within the band is another, interveneable layer. The dangerous reading treats the exponent as destiny and uses it to excuse bad governance.
This is exactly what "conglomerate," "intrapreneurship" and "platform" try: growing a diverse, recombining internal ecology inside one firm. In principle it can nudge the firm toward the superlinear side. But beware: a city's diversity has no CEO optimizing it and no quarterly target pruning it, whereas corporate governance naturally tends to eliminate redundancy and unify direction — which is precisely converting superlinear back to sublinear. So "a city-like company" is an unstable state, sustainable only by constantly fighting one's own drive for efficiency.
It's real data: people walk faster on average in bigger cities, superlinearly, like wages and patents. It matters because it turns the abstract "connectivity" into a measurable physical quantity — "pace of life" is not literary flourish but something you can measure. The same mechanism both speeds the circulation of ideas and speeds a metabolism-like wear on people. It also hints that a city's pathology (stress, burnout) and its good (opportunity) really are two faces of one acceleration.
What's left hard is not the specific number but the qualitative split: "infrastructure sublinear, social output superlinear" holds robustly across many reasonable definitions, and the direction does not flip. What's soft is the decimal (1.12 or 1.20) and the singularity-type extrapolations. Separating "robust direction" from "precise value" is the first cut to make with any scaling law.