In 2012, a seminal paper in Research Policy by Brian Uzzi, Satyam Mukherjee, Michael Stringer, and Ben Jones introduced what would become one of the most cited conceptual frameworks in innovation studies: the Adjacent Possible. The idea, originally articulated by Stuart Kauffman in the 1990s, describes the ever-expanding frontier of what can happen next — not in any direction, but only one step away from what already exists.
The concept is disarmingly simple: at any given moment, the set of possibilities available to a system — whether a biosphere, a city, an economy, or a neural network — is constrained to states reachable from its current state via a single change. As those possibilities become actualized, the frontier expands, making even more reachable. This creates a distinctive dynamical pattern: for long periods, novelty accumulates slowly; then, under the right conditions, it explodes.
The mathematical insight is striking. Suppose you have N things in a system. The number of possible pairs — and therefore the number of potential «juror-rigged» combinations — scales as N(N-1)/2. With 10 things, there are 45 pairs to explore. With 100 things, there are 4,500. With 1,000 things, nearly half a million. The combinatorial explosion means that, beyond a critical threshold, the number of novel combinations reaches infinity in finite time. This is the «hockey stick explosion» Kauffman describes — the same pattern seen in the Cambrian explosion 540 million years ago, and in the history of human technological innovation from stone tools to the space station.
The Kauffman-Roli 2024 Paper: Life as a Phase Transition
In January 2024, Stuart Kauffman — now 83 — and collaborator Andrea Roli published a paper that may represent the most rigorous formalization of TAP to date. «Is the Emergence of Life an Expected Phase Transition in the Evolving Universe?» (arXiv:2401.09514) unifies two established mathematical frameworks for the first time: Collectively Autocatalytic Sets (the chemistry of self-reproducing molecular networks) and TAP.
Their key claim is breathtaking: life is expected as a phase transition in the chemical evolution of the universe. As molecule diversity increases, the system crosses a threshold where autocatalytic closure becomes statistically likely. Then, via TAP, the adjacent possible of molecular combinations explodes. No law of physics forbids this — it simply happens when conditions are right. Kauffman and Roli propose that the familiar distinction between software and hardware loses its meaning in living cells, and suggest new pathways for studying the phylogeny of metabolisms, searching for life on exoplanets, and experimentally synthesizing the most rudimentary forms of life.
From Biospheres to LLMs: TAP Applied to AI
In February 2025, Javier Marín published «A non-ergodic framework for understanding emergent capabilities in Large Language Models» (arXiv:2501.01638), which applies TAP directly to the phenomenon of emergent abilities in AI. Marín proves that language models are non-ergodic systems — they do not explore all possible states uniformly — and uses Kauffman’s TAP to explain why capabilities appear discontinuously at scale thresholds. This is the same Schaeffer-vs-Wei debate about emergence in LLMs reframed through the lens of the adjacent possible: capabilities don’t emerge gradually because the space of possibilities is not ergodic. The model explores a growing frontier, not a uniform landscape.
In June 2025, Matteo Benati, Alessandro Londei, Denise Lanzieri, and Vittorio Loreto built on this further with «Lyapunov Learning at the Onset of Chaos» (arXiv:2506.12810, accepted at ICML 2025). Their approach uses TAP as an inspirational framework for navigating unexplored regions of solution space in dynamical systems near regime shifts — connecting Kauffman’s biology to learning dynamics and chaos theory.
The Core Principles: Jury-Rigging, Functions, and the Exploding Frontier
Three interlocking ideas define the TAP framework:
1. Juror-rigging — the process by which existing components are reassembled to serve new functions. An engine block becomes a paperweight. A screwdriver scrapes Putty. Dinosaur scales, evolved for thermoregulation, were juror-rigged into flight feathers. This is not computation, not deduction — it is the biosphere’s fundamental mode of innovation. No algorithm can predict what the adjacent possible contains in advance.
2. Functional decomposition — the function of a part is the subset of its causal properties that sustain the whole. Your heart’s function is pumping blood; the sound it makes is incidental. Functions are not intrinsic properties of objects but relational facts about what a part does for the system it belongs to. This has profound implications for understanding both biological organisms and engineered artifacts.
3. The hockey-stick dynamics — the number of possible combinations grows as the square of the number of existing things, meaning that beyond a threshold, a singularity is reached. This is not a metaphor: in finite time, the combinatorial space explodes. The Cambrian explosion lasted roughly 50 million years. Human technological innovation, from Australopithecus to the space station, shows the same delay-then-burst pattern. So does global GDP since the Industrial Revolution.
Why This Matters Now: From the Biosphere to the Anthropocene
Kauffman ends his talk with a striking pivot. The same TAP dynamics that created life are now driving the Anthropocene — and in particular, climate change. Every new technology opens new adjacently possible pathways; each pathway can be used for good or harm. We are, he argues, at a «fantastic third trade phase transition in science» — beyond Newton, beyond quantum mechanics, beyond the clockwork universe Copernicus imagined.
His proposed solution involves something unexpectedly concrete: compost. Specifically, the Johnson-Su compost method — a high-temperature aerobic process that produces highly diverse microbial communities — and biochar as a matrix for coating seeds with beneficial fungal-bacterial communities. The idea is that microbial communities are precisely the kind of system capable of creating novel adjacent possibles that solve soil degradation problems. Carbon sequestration through soil health is, in Kauffman’s framing, a biological adjacent possible we have not yet fully exploited.
This connects TAP to the most urgent problems of our time. If the biosphere’s creativity is fundamentally about finding new uses for existing components — new combinations, new functions, new niches — then restoring soil carbon through microbial innovation is a form of juror-rigging the planet back toward equilibrium. The same combinatorial logic that drove the Cambrian explosion can be turned toward regeneration.
Key Sources
- Kauffman, S. & Roli, A. (2024). «Is the Emergence of Life an Expected Phase Transition in the Evolving Universe?» arXiv:2401.09514. https://arxiv.org/abs/2401.09514
- Marín, J. (2025). «A non-ergodic framework for understanding emergent capabilities in Large Language Models.» arXiv:2501.01638. https://arxiv.org/abs/2501.01638
- Benati, M., Londei, A., Lanzieri, D. & Loreto, V. (2025). «Lyapunov Learning at the Onset of Chaos.» arXiv:2506.12810. Accepted at ICML 2025. https://arxiv.org/abs/2506.12810
- Uzzi, B., Mukherjee, S., Stringer, M. & Jones, B. (2012). «The Adjacent Possible: A Conceptual Framework for Innovation.» Research Policy, 42(3). [Most cited academic extension of TAP]
- Kauffman, S. (1993). The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press. [Foundational TAP framework]
- Kauffman, S. (2002). Investigations. Oxford University Press. [Formalized TAP mathematically; introduced «shadow of the adjacent possible»]
Based on a talk by Stuart Kauffman (1939–), Professor Emeritus at the University of Vermont, Fellow of the MacArthur Foundation, and pioneer in complexity science, self-organization, and the origins of life. The Adjacent Possible concept has been formally applied to innovation studies, urban systems, economics, and — most recently — the emergent capabilities of large language models.
Keywords: adjacent possible, TAP theory, Stuart Kauffman, emergence, innovation, phase transitions, LLMs, life origin, complexity, jury-rigging, Cambrian explosion, Johnson-Su compost, Anthropocene.