In today’s world, innovation is heralded as the driving force behind economic prosperity, scientific progress, and technological supremacy. From the race to dominate artificial intelligence to ambitious breakthroughs in renewable energy and medicine, the magnitude of investments in research and development underscores how crucial continuous innovation is to global power structures. Yet beneath this urgent push for new discoveries lies a profound and overlooked vulnerability: the interconnectedness that fuels rapid innovation can also precipitate systemic collapse. A groundbreaking study from the Complexity Science Hub reveals this paradox through an innovative mathematical framework, reshaping how we understand sustainability in technological and biological evolution.
At the heart of the findings is a dynamic tension between two opposing forces: the creation of new possibilities, termed “innovation,” and the inevitable loss or forgetting of outdated possibilities, known as “exnovation.” The research emphasizes that for innovation to be sustainable over the long term, it cannot be a relentless upward trajectory alone. Instead, it must be tempered by selective forgetting, a pruning of obsolete ideas and paths. The study’s novel model captures this interplay as opposing wavefronts moving within a conceptual “space of the possible,” a vast landscape encompassing all potential innovations that might be discovered, realized, or discarded.
One of the most striking insights emerges when exploring how connectivity structures shape the innovation process. By conceptualizing innovations and their relationships as nodes and links in either tree-like or truss-like graphs, researchers illuminate a fundamental trade-off. In tree-like structures—hierarchical and branching—paths are relatively isolated, resembling the evolutionary trajectory of biological species that climb a single lineage of mutations. Conversely, truss-like structures exhibit dense interconnectivity, with multiple overlapping routes leading to the same innovation, a hallmark attributed to technological evolution where diverse pathways and interdisciplinary linkages are the norm.
The model shows that while greater connectivity accelerates the pace of discovery by facilitating the transfer of ideas across different fields, it simultaneously renders the innovation ecosystem exceedingly fragile. This fragility stems from the tightly interwoven dependencies that can cause cascading failures, akin to pulling one block from a complex, truss-like scaffold causing the entire structure to collapse. The researchers dub this phenomenon the “house of cards effect,” capturing the paradox that rapid progress in highly connected innovation networks risks triggering systemic breakdown.
Delving deeper into the model’s behavior, the team identifies several distinct regimes characterizing innovation dynamics. The first is runaway growth, where innovations proliferate unchecked, expanding the space of possibilities endlessly—a scenario that may seem ideal but is typically unstable. The second is catastrophic collapse, where the system succumbs to failure, losing vast segments of the innovation landscape. Between these extremes lies a narrow band of stability, a delicate balance where innovation and exnovation harmonize to sustain long-term diversity and vitality. Surprisingly, the model also uncovers “Byzantine” phases—regimes marked by persistent and diverse innovation, but evolving at a slow, steady pace rather than rapid expansion.
Importantly, as connectivity increases, this stable region shrinks dramatically. In highly connected networks, the paths to extinction multiply, making the system exceedingly susceptible to collapse. This counterintuitive conclusion challenges the commonly held belief that more connections inherently confer resilience. Instead, the data suggests an optimal, often narrowly confined, degree of connectivity fosters sustainable innovation, while exceeding this threshold invites systemic risk.
The implications of these findings reach far beyond abstract theory, resonating across sectors and disciplines. In the realm of technology, as systems grow increasingly complex and interconnected, the risk of rapid but unsustainable growth looms large. Ecosystems of innovation that spur dazzling advances in fields such as quantum computing, robotics, and bioengineering may simultaneously be prone to catastrophic failures if their underlying structures become overly integrated.
Economically, this research offers fresh perspectives on Joseph Schumpeter’s theory of “creative destruction.” Rather than viewing economic dynamism as an unmitigated force for progress, the model nuances this understanding by highlighting how the architecture of innovation networks—specifically their connectivity—determines whether diversity flourishes or flounders. Economies with fragmented or modular innovation systems may maintain a richer tapestry of ideas and technologies, whereas hyper-connected systems risk homogenization and collapse.
In biology, where evolutionary pathways are often compared to trees due to their largely unidirectional, lineage-based nature, the study draws fascinating parallels. The limited connectivity in biological evolution may in fact be a resilience mechanism, preventing the entire biosphere from collapsing due to overly interdependent traits. Similarly, fragmentation and selective isolation within ecosystems can promote survival and biodiversity by limiting the spread of perturbations or shocks.
The new mathematical model generalizes these insights through computational simulations, defining nodes as potential innovations and agents as entities—whether firms, species, or inventors—navigating the “space of the possible.” Innovation fronts expand the frontier by discovering new ideas, while exnovation fronts retract it by removing outdated or uncompetitive possibilities. These opposing forces generate complex dynamics that dictate the system’s fate, from explosive growth to slow, Byzantine stasis.
Lead author Edward D. Lee emphasizes the sobering reality that “more connections aren’t always better.” The allure of highly integrated innovation ecosystems must be balanced with awareness of their intrinsic risks. The study’s revelation that limiting pathways can sometimes enhance diversity flies in the face of traditional views that equate connectivity with robustness. Co-author Ernesto Ortega-Díaz explains, “It’s the separation of pathways and the maintenance of modularity that enables systems, whether biological or technological, to avoid collapse and sustain rich diversity.”
This work opens fertile avenues for policymakers, business leaders, and scientists alike. Innovation strategies may need recalibration to avoid pushing systems past their architectural limits. The recognition that sustainable diversity hinges on a delicate balance of connectivity could inspire new approaches to research funding, ecosystem management, and technological development. For instance, fostering multiple semi-independent innovation clusters rather than monolithic, fully integrated networks may prove more resilient in the face of uncertainty.
As technological ecosystems expand and intertwine ever more tightly across globalized networks, understanding the architecture of innovation becomes paramount. This comprehensive framework not only offers a conceptual lens for the ongoing innovation race but also warns of the potential fragility underlying rapid progress. It invites a paradigm shift: embracing measured connectivity and the disciplined forgetting of obsolescence as vital ingredients for the endurance of inventive systems.
By juxtaposing the evolutionary constraints of biology with the expansive potential of technology, the study enriches our conceptual toolkit, making clear that the future is not a limitless chain of ever-more discoveries but a finely balanced dance on the edge of possibility. The integrated “space of the possible” is not infinite in a practical sense—it expands, contracts, and can disintegrate, and only by understanding these dynamics can we hope to cultivate innovation that thrives sustainably for generations to come.
Subject of Research: People
Article Title: Innovation-exnovation dynamics on trees and trusses
News Publication Date: 31-Jul-2025
Web References:
https://doi.org/10.1103/ynwt-7g91
Complexity Science Hub
References:
Lee, E. D., & Ortega-Díaz, E. (2025). Innovation-exnovation dynamics on trees and trusses. Physical Review Research. https://doi.org/10.1103/ynwt-7g91
Image Credits: © Complexity Science Hub
Keywords: Modeling, Mathematical modeling, Physics, Complex analysis, Complex systems
