In the world of entrepreneurship and technology, the prevailing mantra seems to be “innovate or die.” We live in a constant race to create the new and the disruptive. But have we ever stopped to consider its counterpart—the process of forgetting, abandoning, and rendering the old obsolete? This process has a name: exnovation.
Innovation and exnovation are two sides of the same coin of change. While one expands the “space of the possible,” the other contracts it. This balance is similar to Schumpeter’s “creative destruction,” where new industries rise from the ashes of old ones. However, the relationship between these two forces—and, critically, how the structure of our knowledge networks affects this race—has been little studied.
A recent article published in Physical Review Research by Edward D. Lee and Ernesto Ortega-Díaz of the Complexity Science Hub proposes a fascinating model to understand this dynamic. Their findings serve as a crucial warning: the very strategy we use to accelerate innovation could be the one that leads us directly to collapse.
The map of innovation: From a tree to a lattice
To understand the race between creating and forgetting, we must first visualize how ideas connect. The researchers model the “space of the possible” (SOP)—the set of all existing technologies, mutations, or cultural practices—as a graph. The key to their work is that not all knowledge structures are equal. They propose two archetypes:
- The Tree-like Structure: Imagine the tree of evolution. To reach a specific species, one must follow a unique path of mutations. There are no shortcuts. This model represents a contingent development, where each step strictly depends on the previous one. It is a rigid and hierarchical structure.
- The Truss-like (or Lattice) Structure: Now, think about technological development. To invent the electric car, it is not essential to have first perfected the combustion engine. An innovation can arise by combining ideas from different previous domains. This is a convergent and flexible structure, where multiple paths can lead to the same outcome. It is a densely connected network.
The study uses a connectivity parameter (gamma, γ) to move between these two extremes: from a pure tree (γ=0) to a fully connected lattice (γ=1). This variable is fundamental because it represents how interconnected or isolated our teams, research lines, or business units are.
Simulating the race against obsolescence
The model simulates a population of “agents” (which could be companies, scientists, or species) occupying nodes on this innovation map. These agents face several forces:
- New Agents: Companies are founded, or individuals are born (influx rate).
- Death or Bankruptcy: Agents can disappear from the system (mortality rate).
- Innovation Front: Agents at the frontier of knowledge can “discover” new nodes, expanding the map into the “adjacent possible.” The ease of doing so is measured by an “innovativeness” factor.
- Exnovation Front: Simultaneously, a front of obsolescence advances from behind, eliminating nodes and the agents occupying them. It is the unstoppable, advancing wave of forgetting.
The system evolves as a race between these two fronts. Will the population manage to innovate fast enough to escape the pursuing wave of exnovation? The answer, surprisingly, depends on the structure of the map.
The key finding: Speed comes at a very high price
This is where the study delivers its most powerful and counterintuitive conclusion. One might think that greater connectivity (a lattice-like structure) is always better. After all, it allows for more combinations, facilitates the cross-pollination of ideas, and accelerates the speed at which the innovation front advances.
However, this advantage comes with a hidden and catastrophic cost: greater connectivity also dramatically accelerates the exnovation front, exponentially increasing the risk of a total system collapse.
The model predicts different phases for the system, depending on parameters like the mortality rate or the speed of exnovation:
- Runaway Phase: Innovation consistently outpaces exnovation. The system grows, sometimes infinitely.
- Steady-State Phase: An equilibrium is reached where innovation and exnovation keep pace. The system’s diversity remains stable.
- Collapse Phase: Exnovation is faster. The obsolescence front catches up to the innovation front, and the entire system disappears.
- Other Phases: The model also identifies more exotic regimes, such as bistable phases (where the system can either collapse or survive depending on initial conditions) or “low-density” phases (with high diversity but few agents, like a Byzantine empire full of knowledge but with little activity).
The crucial finding is that as connectivity (γ) or the number of branches (K) in the system increases, the “collapse” region on the phase map expands enormously. A highly interconnected system is fragile. Stability, according to the authors, appears to be a feature of systems with relatively independent lineages.
Implications for innovators, leaders, and strategists
The conclusions of this theoretical model have profound practical implications for anyone managing innovation:
- The R&D Director’s Dilemma: Should we foster total collaboration among all teams or keep them as semi-independent units? This study suggests that extreme collaboration, while potentially producing rapid breakthroughs, also synchronizes risk. A single failure or obsolete direction can propagate throughout the entire organization and destroy it.
- Modularity as Resilience: Long-term survival may depend on modularity. Having innovation pipelines that operate as “trees” or loosely connected branches, though seemingly less efficient, endows the system with incredible resilience. If one branch becomes obsolete and collapses, the others are not dragged down with it.
- There is a Cultural “Speed Limit”: The drive for hyper-connectivity and accelerated innovation may have a structural limit. Forcing connections in a system can push it beyond its point of stability, leading to an inevitable collapse.
Conclusion: Innovating with structural wisdom
The study by Lee and Ortega-Díaz forces us to refine our understanding of innovation. It is not just about the speed at which we create, but about the underlying structure upon which we build knowledge.
The paradox is clear: the very bridges we build between ideas to accelerate progress are the same ones that can allow the fire of obsolescence to ravage the entire system. Stability is fragile and, according to this model, is more often found in systems with lower connectivity and fewer branches, where the density of agents per idea is high.
For those on the vanguard, the message is not to stop innovating, but to do so with structural wisdom. Perhaps the key to “not dying” is not to run faster, but to build an innovation system that is resilient enough to withstand the inevitable march of exnovation.
Contact
Edward D. Lee
Complexity Science Hub
Metternichgasse 8, Vienna, Austria
Email: edlee@csh.ac.at
Reference (open access)
Lee, E. D., & Ortega-Díaz, E. (2025). Innovation-exnovation dynamics on trees and trusses. Physical Review Research, 7(3), 033102. https://doi.org/10.1103/ynwt-7g91
Editor and founder of “Innovar o Morir” (‘Innovate or Die’). Milthon holds a Master’s degree in Science and Innovation Management from the Polytechnic University of Valencia, with postgraduate diplomas in Business Innovation (UPV) and Market-Oriented Innovation Management (UPCH-Universitat Leipzig). He has practical experience in innovation management, having led the Fisheries Innovation Unit of the National Program for Innovation in Fisheries and Aquaculture (PNIPA) and worked as a consultant on open innovation diagnostics and technology watch. He firmly believes in the power of innovation and creativity as drivers of change and development.
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