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Extensions
Assembly theory’s authors propose that the framework applies anywhere construction history matters quantitatively — not only molecular biology but language, technology, music, cultural evolution, and cosmology. Some extensions are formally developed; many are proposed framings without much empirical or formal work behind them.
Language and cultural evolution
The claim is that languages, cultural artefacts, and technologies can be analysed via their assembly pathways — what enables what, how complexity accumulates through path-dependent histories. A word requires a phonological system; a sentence requires grammar; a novel requires literary convention. Each layer of construction depth builds on prior layers.
The formal apparatus has not been worked out for these domains as it has for molecules. The extension is a proposal, not a developed application.
Technology evolution
The “technosphere” framing. Computers, cities, and other complex technological objects require prior stack — earlier objects must exist before later objects can be constructed. The early universe could not have produced computers because not enough history had accumulated yet. A semiconductor fab requires metallurgy, optics, chemistry, clean-room engineering, each of which requires its own accumulated history.
This connects to evolutionary considerations about the path from cells to civilisations: the assembly index of a technological object measures how much prior construction history the object presupposes.
Music
Proposed as another domain where construction history matters quantitatively. Musical compositions operate in a combinatorial space of possible note-and-rhythm sequences; complex compositions presuppose prior musical conventions, instruments, notation, and performance traditions. The authors invoke music as an illustration of how complex objects in any combinatorial space follow assembly-theory-like patterns.
Specific empirical work applying the formal apparatus to music is limited.
Cosmological extensions
Walker and Cronin propose, particularly in the Aeon essay (2023) and Walker’s Life As No One Knows It (2024), that assembly theory has implications for cosmology. The future is the size of the universe; the universe expands in time as well as space; novelty becomes possible because the present is larger than the past.
The cosmological framing reaches further than the formal apparatus currently supports. The claim that the universe’s expansion in time — the growing space of possible constructions — is as fundamental as its expansion in space is speculative and contested. It connects to the time-as-object claims at their most ambitious scale.
TAP — Theory of the Adjacent Possible
The collaboration with Stuart Kauffman, Lee Smolin, and Marina Cortês: Cortês, Kauffman, Liddle, Smolin (2023) “The TAP equation: evaluating combinatorial innovation in biocosmology.”
TAP addresses the broader question of how novelty enters cosmological and biological history. The adjacent possible — the set of things that could come into existence given what already exists — grows as new things are created, opening paths that did not previously exist. TAP formalises this as an equation governing the rate of combinatorial innovation.
TAP is a separate framework, developed jointly by Kauffman and Smolin, that connects with assembly theory rather than being a sub-development of it. The connection is structural: both frameworks take construction history as fundamental and both propose that the space of possibilities grows with accumulated complexity. The collaboration extends assembly theory’s reach into cosmological territory and connects it to the broader complexity-science lineage at the Santa Fe Institute.
What is well-developed vs proposed
The mass-spectrometry molecular work is the most empirically established part of assembly theory — see the biosignature claim. The TAP collaboration is formally developed but is its own framework with its own lineage. Language, music, and cultural evolution applications are proposed framings rather than worked formal theories. The cosmological extensions are speculative, reaching beyond what the current formal apparatus and empirical record support.