Scientists Find a 'Speed Limit' for Innovation

Innovation is a central currency of global power. Whether in the race for leadership in artificial intelligence, the development of clean energy technologies, or the search for medical breakthroughs, major players like China, the United States, and the European Union are investing billions in research and development to secure the next technological leap – and with it, economic and strategic advantage.

Yet, as a new study from the Complexity Science Hub (CSH), published in Physical Review Research, indicates, long-term innovation is only sustainable under specific structural conditions. First, the study finds that innovation can only endure over time if it is balanced with “exnovation” – the loss or forgetting of older possibilities.

"Second," says CSH researcher Eddie Lee, lead author of the study, "we discovered an interesting trade-off: while more connections between innovations speed up discovery, they also increase the risk of total system collapse.”

Lee and his colleague Ernesto Ortega-Díaz created a model showing that as different possible innovations become more interconnected – for instance, when advances in one field, like machine learning, directly accelerate developments in others, such as drug discovery or robotics – the system becomes more “truss-like.” In such structures, innovation moves faster, but the system is also more fragile: the unfolding set of possible directions makes innovation directions hard to sustain, leading to collapse. “The sweet spot for sustainable innovation turns out to be surprisingly narrow,” says Lee.

“This is like an evolutionary speed limit,” he continues. “Push innovation too hard on highly connected structures, and the whole system crashes. It's like trying to build a house of cards too quickly – the faster you go, the more likely everything tumbles down.”

The study also considers fundamental differences between how biological evolution and technological development navigate the "space of the possible" – the realm of all potential innovations.

"Think of evolution as climbing a tree – each species can only follow one specific path of mutations to get where it is," explains Lee. "But technology is more like a truss or scaffold, where many paths can lead to the same innovation. You could imagine a world where electric vehicles came before combustion engines, or where quantum computing preceded the transistor."

This structural difference, the researchers found, has profound consequences for system survival.

To understand the delicate balance between innovation (the creation of new possibilities) and exnovation (the loss of possibilities through obsolescence or extinction), Lee and his colleagues developed a mathematical model. In it, each node represents a potential innovation within a “space of the possible,” while agents – such as firms or species – move through this space, discovering new possibilities, going extinct, or influencing others. These dynamics are captured as two opposing fronts: an innovation front, which pushes into the “adjacent possible,” and an exnovation front, which removes outdated nodes.

The team identified three possible outcomes for any system: runaway growth, catastrophic collapse, or a delicate balanced state. Surprisingly, the researchers also identified a fourth regime – so-called “Byzantine” phases – where diversity persists at a high level, but change unfolds slowly.

“What struck us most was how small the stable region becomes as you add more connections,” notes Lee. “In highly connected systems, almost every path leads to extinction. It's a sobering reminder that more connectivity isn't always better.”

The research suggests that many persistent, diverse systems in nature and society may owe their survival to having fewer interconnections than we might expect. This “less is more” principle could inform everything from ecosystem management to innovation policy.

The findings have implications across multiple fields:

"We're used to thinking that more connections mean more resilience,” says Ortega-Díaz. "But our work shows the opposite can be true. Sometimes, keeping pathways separate is what allows diversity to flourish.”

The study "Innovation-exnovation dynamics on trees and trusses" by Edward D. Lee and Ernesto Ortega-Díaz was recently published in Physical Review Research (doi: 10.1103/ynwt-7g91).

It was funded by the Austrian Science Fund and the Austrian Federal Ministry for Climate Action, Environment, Energy, Mobility, Innovation and Technology.

The Complexity Science Hub (CSH) is Europe’s research center for the study of complex systems. We derive meaning from data from a range of disciplines – economics, medicine, ecology, and the social sciences – as a basis for actionable solutions for a better world. 

CSH members are Austrian Institute of Technology (AIT), BOKU University, Central European University (CEU), Graz University of Technology, Interdisciplinary Transformation University Austria (IT:U), Medical University of Vienna, TU Wien, University of Continuing Education Krems, Vetmeduni Vienna, Vienna University of Economics and Business, and Austrian Economic Chambers (WKO).