Growing in size makes systems more conservative, concludes a study published in PNAS by researchers from MIT Sloan and the Santa Fe Institute. They cross-referenced data from bacterial proteomes, federal agencies, corporations, universities and metropolitan areas, and found that across all those systems — whether cells, ministries or multinationals — doubling in size produces considerably less than double the number of distinct functions: the curve describing that relationship has exponents ranging from 0.35 to 0.57.
To formalise this dynamic, the team generalised the Yule-Simon stochastic model using two parameters: the first measures how strongly consolidated functions block the creation of new ones; the second, the extent to which a function gains weight simply by virtue of already having it. The result reveals a natural internal blocking mechanism inherent to structural dynamics. Dominant functions drain the probability of anything radically different emerging. Size crystallises the status quo.
The structural trap
This is the same pattern known in linguistics as Heaps' law: as a text progresses, the rate at which genuinely new words appear falls systematically. The accumulated structure of the text itself reduces the statistical probability of novelty. An organisational chart works exactly the same way.
Cities are the exception: the diversity of occupations follows not a power law but a logarithmic curve that flattens far more sharply. The reason is that large cities lack a command centre deciding which new functions to integrate. Their occupations emerge from the friction between millions of independent agents, without centralised design. Decentralised governance inscribes a different geometry directly into the data. And that geometry has a name in complex systems theory: it is the signature of systems operating far from equilibrium.
At the edge of chaos
Prigogine showed that dissipative structures — from cells to societies — do not evolve from stability but from controlled instability: it is in systems far from equilibrium that genuinely new complex order emerges. Christopher Langton and the Santa Fe Institute refined this intuition with the concept of the "edge of chaos": complex adaptive systems innovate and compute best in that zone of tension between rigid order and pure entropy. Systems that are too stable crystallise; those that are too chaotic collapse.
Complex innovation
The data from the PNAS study are a quantitative version of that same warning: innovation does not live in the comfort zone of mature systems, but at the edge where they begin to destabilise. What the study does not address is that the brain faces exactly the same constraint: consolidated neural connections actively compete against the formation of new pathways. The brain resolves this through an active destabilisation mechanism, without which no rewriting is possible. Cities and brains do not choose between order and plasticity. They manage both states simultaneously. Operating at that edge is the only known way out.
This article is republished from Futuribles. Here's the original article in Spanish and English.
