{"path":"research/contingency-and-convergence-across-levels.md","content":"# Contingency and Convergence Across Levels — the assembly lens on whether minds converge, and the penguin corrected\n\n**Date**: 2026-09-06 · **Type**: founder challenge and founder-proposed lens, answered the same day ·\n**The challenge, verbatim**: *\"I'm dubious that humans' understanding of nouns differ so greatly in\nactual meaning. Apply an Assembly Theory lense to all this and let's ask ourselves at what levels we\ncould/would expect to see contingent-path-evolution of the accumulated complexity of [biology and\nculture and memeplexes and psychological drives/sub-agents within a person's mind etc] and how it\naffects whether and how concepts and perception and delineation of reality within a mind vs between\nminds converges or doesn't. I do remember Assembly Theory speaks about this contingent path evolution\nof complexity in some ways, no?\"* · **Companions**:\n[why-representations-converge-and-whether-minds-do.md](why-representations-converge-and-whether-minds-do.md)\n(the doc this corrects and extends), [assembly-theory-and-the-reuse-mechanism.md](assembly-theory-and-the-reuse-mechanism.md)\n(the corpus's assembly-theory home, whose caution about borrowed authority binds here),\n[convictions-across-scales.md](convictions-across-scales.md) (the genetic-code finding this generalises),\n[decomposing-value.md](decomposing-value.md) (the palette the descent bottoms out in).\n\n---\n\n## 0. In plain words\n\n**The doubt is right, and the earlier line overstated the finding.** Marti, Wu, Piantadosi and Kidd\nmeasured *similarity and feature judgements* — is a penguin more like a chicken or a whale, is a penguin\nheavy, is a seal graceful — and clustered people by their whole profile of answers. Their \"ten to thirty\nvariants\" are variants of that profile, and the one-in-eight figure is the chance that two people match\non the whole profile. The paper says what it shows: *\"some underlying differences\"*, and its authors\nadd that *\"no one confuses penguins with albatrosses.\"* So the **core** of a common noun — what it\nrefers to, which category it belongs to, the prototype — is shared, and the **periphery** — the graded\nfeatures, the associations, the weightings — varies, and varies more for politicians than for animals.\n\"Two random people share the same penguin one time in eight\" was my compression, not their claim;\nit is withdrawn on every surface that repeated it.\n\n**Yes, assembly theory speaks to this, and its word is *contingent*.** Its 2023 formulation defines\nfour nested spaces: everything combinatorially possible, everything physically possible, everything\nbuildable *given what history has already built and selection on that history*, and what is actually\nobserved. The third is called **assembly contingent**, and the paper's own sentence is that it is\n*\"the space of possible configurations of objects where … selection is possible, and the objects\nfound in the space are controlled by a path-dependency contingent on each object that has already\nbeen built.\"* A complex object, on this view, *is* its formation history. That is the lens the founder\nasked for, and applied to concepts it gives a two-axis answer that evolutionary biology reached\nempirically first:\n\n1. **Shared history.** Two systems that share a lineage share parts. Their agreement is **copy\n   number** — many instances of one object — and says nothing about the world. Humans in one\n   language community agree by descent; models trained on one web agree by descent.\n2. **Strength of constraint against size of space.** Independent lineages converge where the world\n   or the function forces the answer and the space of solutions is small; they diverge where the\n   space is huge and the constraint weak. Biology's replay experiments say exactly this: outcomes are\n   *\"surprisingly repeatable among closely related lineages, but disparate outcomes become more\n   likely as the footprint of history grows deeper\"*, repeatable at the level of genes, pathways and\n   performance, contingent at the level of exact mutations.\n\nEverything below is those two axes applied level by level. The short version: **perception and\naffect converge between minds because every human is a copy of one biological object; concrete\nconcepts converge because the world assembles most of them; abstract and political concepts diverge\nbecause most of their assembly is path — cultural, communal, individual — and the path is different\nin every lineage that built them.** A model averages across the lineages, so its vector for a\ncontested word is a point no lineage occupies; two models agree on that point because they copied the\nsame record.\n\n## 1. The correction, exactly\n\nWhat Marti et al. measured and what they claim, from the paper rather than the coverage:\n\n- Instruments: similarity triads and feature ratings, in two domains (common animals; U.S.\n  politicians), with repeated measurement so reliability could be modelled. They note the known\n  limitation themselves — similarity is *\"sensitive to the respects with which similarity is\n  computed\"* — and say that for their purpose it *\"is less important that features and similarities do\n  not completely characterize people's conceptual knowledge. Differences in features and similarities\n  still indicate that there are some underlying differences.\"*\n- Result: ten to thirty clusters per word in the population once measurement noise is modelled out;\n  the probability that two random participants land in the same cluster averages 14–70% for animals\n  and 13–33% for politicians; within-person reliability is high (the clusters are stable objects, not\n  noise); and people predict roughly two-thirds agreement whatever the actual rate.\n- The authors' own scope: the results *\"do not support the notion that every single use of a concept\n  is distinct or entirely idiosyncratic\"*; the variation *\"likely arises from experiential\n  differences\"*; and, to the press, *\"no one confuses penguins with albatrosses\"* — with Gelman's\n  gloss, *\"There's something that's shared. But maybe everything that gets attached to [words] is a\n  lot more idiosyncratic and varied than we thought.\"*\n\nSo the finding is about the **periphery** of a concept, and it is strongest exactly where the\nperiphery carries the meaning (politicians, and by extension the political vocabulary Rodriguez,\nSpirling & Stewart measure). What it establishes for this project is narrower and still useful:\npeople are unaware of peripheral divergence and assume agreement — the population's missing\nself-knowledge that a clarification layer supplies. What it does not establish is that people mean\ndifferent things by *penguin*.\n\n## 2. The lens: contingency, descent, and constraint\n\n**Assembly theory's version.** An object's assembly index is the minimum number of joining steps that\nbuild it, reusing anything already built; assembly proper is index weighted by copy number; and the\ntheory's central move is that *\"objects are not considered as point particles … but are defined by the\nhistories of their formation as an intrinsic property.\"* The four nested spaces — assembly universe,\nassembly possible, assembly contingent, assembly observed — locate contingency precisely: it is the\nrestriction that *\"only the knowledge or constraints built on a given path can be used in the\nfuture.\"* The authors anticipate the theory applying to *\"human languages and memes\"*, with the stated\ndifficulty that each application needs *\"an assembly space that has a clear physical meaning in terms\nof what operations can be caused to occur.\"* Two cautions carry from the corpus's own reading\n([assembly-theory-and-the-reuse-mechanism.md](assembly-theory-and-the-reuse-mechanism.md) § 6): the\nindex has been argued equivalent to a compression measure and the theory's authority is not\nborrowable, so nothing below says \"assembly theory shows\"; and for culture, copy number is a weaker\nsignature of selection than in chemistry, because memes spread by drift as well as by function.\n\n**Biology's version, which is older and has the data.** Homology is similarity by descent; convergence\n(homoplasy) is similarity by independent arrival under a shared constraint. Gould's *replay the tape*\nbet was on contingency; Conway Morris's was on convergence (*\"the evolutionary routes are many, but\nthe destinations are limited\"*). Blount, Lenski & Losos's 2018 review of the replay experiments and\nthe comparative record settles the shape rather than the winner: repeatable outcomes are common *when\nfounding populations are similar* and *when repeatability is defined broadly* (genes and pathways,\nnot exact mutations); convergence in nature is commoner than expected and commonest among close\nrelatives, because they *\"share more of their history\"*; and *\"evolution may be deterministic within a\nclade but contingent at deeper phylogenetic levels.\"* Lenski's twelve populations evolved in parallel\nin direction and performance and diverged in their genetic and physiological particulars — *\"broad,\ngeneral features … may be repeatable, but the details beneath them can vary due to historical\nhappenstances.\"*\n\n**The rule that both versions give.** Agreement between two systems is either **copy number** (they\nshare a lineage, or copied the same source) or **convergence** (independent lineages funnelled to the\nsame solution by a constraint stronger than the space is large). Only the second is evidence about the\nworld. And convergence has a grain: it appears at the level of function and coarse structure, and\ndissolves at the level of exact structure and contingent content.\n\nThat grain is the 2026 finding about models, stated by biologists in 2018: models converge on *which\nitems are neighbours* (function: predicting the same text) and not on distances or global shape\n(exact structure) — the Aristotelian and Plato's-Cave results in\n[why-representations-converge-and-whether-minds-do.md](why-representations-converge-and-whether-minds-do.md) § 1.\n\n## 3. The levels\n\nEach row is a lineage (or a shared constraint), what carries its memory, how it copies, what constrains\nit, what is contingent in it, and what that predicts for convergence *within* a mind, *between* minds,\nand between minds and models. Evidence cited is from the companion doc unless noted.\n\n| Level | Carrier · copying · constraint | What is contingent | Convergence predicted | Evidence |\n|---|---|---|---|---|\n| **0 Physics, chemistry** | no lineage; law | nothing relevant | universal | the sun is one object |\n| **1 Biology** (the phylogenetic lineage) | genome · reproduction · survival under physics | the particular solutions: trichromacy, the cochlea, the valence–arousal affect system, core knowledge | between human minds: **by descent** — every human is a copy of one high-assembly object, so perception and affect align; between species: convergent where function forces (eyes, wings), divergent in detail | hyperalignment; unsupervised brain-to-brain rotation at recall@1 0.83; Jackson's universal valence–activation axis under cultural variation |\n| **2 The shared world** (a constraint, not a lineage) | the correlational structure of the environment | little: sun, water, salt, mountain, number, kinship structure | convergent **across all lineages, human and model** — the only convergence that is evidence about reality | Youn's universal structure across 81 languages; Thompson: number, quantity and kinship align most; Hosseini: stimuli the world constrains are the ones models and brains agree on |\n| **3 Language and culture** (the glossogenetic lineage) | a community's usage · iterated learning plus communication · learnability, expressivity, the world | the carving: colexification, emotion concepts, idioms, *lagom*, which distinctions get words | within a community: **by descent**; between communities: alignment tracks phylogeny, geography and contact, i.e. descent and borrowing, not rediscovery — except where level 2 forces it | Kirby: only transmission plus communication yields structure; Thompson: cultural, historical and geographic proximity predict alignment; Jackson: emotion colexification tracks geography |\n| **4 Memeplexes and communities within a language** (ideologies, professions, subcultures) | a community's discourse · participation, media · coherence with the memeplex's other parts | which *object* is assembled under a shared word: the two *immigration*s, *black lives matter* ↔ *all lives matter* | **divergent between memeplexes, measurable**; the word is a level-3 part shared by descent, the concept a level-4 construction on top | Rodriguez, Spirling & Stewart; KhudaBukhsh et al.; Milbauer, Mathew & Evans; Mamakos et al. 2025 (moralised partisanship differs by audience) |\n| **5 Individual ontogeny** | one memory · copy number one, but the parts are copied from levels 1–4 · one person's experience | the **periphery**: heavy penguins, graceful seals, an \"interesting\" politician | **core shared** (parts from 1–3), **periphery contingent**; and the difference is invisible to its holders | Marti et al.: 10–30 profile variants, stable within a person, false-consensus about others |\n| **6 Sub-personal contexts and drives** (the founder's \"sub-agents\") | the momentary state · a concept re-assembled per use from stored parts · the current motivational context | the *weighting*: what *safety* is worth when afraid against when calm; wanting without liking | **within a mind, the parts are stable and the weighting is not** — the within-mind non-convergence, and the level the weighing descent's state-deficit and satisfier-belief screens target | Barsalou's situated conceptualisation and ad hoc categories; Berridge's wanting/liking dissociation; the three ingredients in [decomposing-value.md](decomposing-value.md) |\n| **7 Models** (a new lineage) | weights · training on one written record, one architecture family · the prediction objective | the training run's path: data mix, alignment tuning, seeds | between models: **copy number of the record's statistics**, not convergent evolution; independent lineages (different data) converge only coarsely; with minds: converge where levels 2–3 force it, diverge on everything contingent to bodies, memeplexes and individuals — the model holds the population's **mean** where a human holds one **mode** | vec2vec; Convergence Without Understanding (untrained models agree more than trained ones; post-decision divergence); Plato's Cave; Simple Transformations |\n\nThree readings of the table.\n\n- **Convergence between minds is real at levels 0–2 and mostly descent at level 3.** What people share\n  across cultures without sharing a lineage is what the world assembles for them. What they share\n  within a culture they share the way siblings share a nose.\n- **Divergence begins where the contingent fraction of a concept's assembly grows.** A concrete noun's\n  meaning is mostly level-2 construction, so its core converges and only its periphery drifts. A\n  political abstraction's meaning is mostly levels 3–6 construction, so under one word different\n  lineages build different objects. This is Gallie's *essentially contested concept* with a mechanism:\n  a shared exemplar (a low-index core, assembled by descent or by the world) and contested criteria of\n  application (a high-index periphery, assembled along different paths).\n- **Within one mind, the parts converge and the weighting does not.** Marti's within-person\n  reliability and the situated-conceptualisation literature are two halves of one fact: a person's\n  assembled concept is a stable object, re-weighted per context. That is why the descent's first\n  questions are state-deficit and satisfier-belief — they separate a level-6 weighting difference from\n  a level-4 or level-5 difference in the object.\n\n## 4. What the lens says that the earlier doc did not\n\n**\"Convergence\" in the Platonic hypothesis is mostly copy number.** Models trained on the same web are\none lineage. Their agreement is the agreement of copies, and the parts of it that survive calibration\n(neighbourhoods, input encoding) are the level-2 and level-3 parts the record itself carries. True\nconvergent evolution among models would need independent lineages — different data — arriving at the\nsame representation, and the 2026 measurements find that only coarsely, at the grain biology\npredicts.\n\n**A concept's contingent fraction predicts its divergence.** This is the assembly-theoretic version\nof Thompson's structure gradient (number and kinship align, natural kinds less, and by extension\nevaluative abstractions least): the more of a concept's construction happened after the world stopped\nconstraining it, the more its meaning is its path, and the more two lineages will differ under one\nword. It predicts, testably, that between-memeplex meaning distance (Rodriguez's method) rises with\nabstraction and evaluative load — which is why *immigration* and *equity* split and *penguin* does\nnot.\n\n**The average of paths is no path.** A model holds the mean of the level-4 and level-5 variants; a\nhuman holds one variant, built along one path. That is the precise sense in which the embedding of a\ncontested word is *\"nobody's meaning\"*: it is the centroid of objects that were assembled differently,\nand there is no lineage whose history produced the centroid. The companion doc said this as\nstatistics; the lens says why the statistic has no bearer.\n\n**The two-axis detector, applied to reasons.** Assembly theory's signature of selection is high index\n*and* high copy number. Read onto a claim graph: a premise recurring across *independent* sources and\nregisters (different lineages) is evidence of convergent selection — something the world or a shared\nhuman part forces; the same premise recurring within one memeplex is descent, an echo. The\nepistemic-selection instrument proposed in the assembly-theory doc (§ The code question) gains its\nmissing condition: copy number counts only across lineages that do not share the relevant history.\n\n## 5. What it changes for Deliberus — proposed, none of it ruled\n\n1. **Decomposition is disassembly, and the horizon is where contingency entered.** A descent through\n   a contested concept walks back down its construction path. At some depth the remaining parts are\n   shared — by the world (an empirical premise, resolvable) or by descent (a bodily need, an affect,\n   the level-1 palette the value descent bottoms out in). The horizon types may then read as the\n   *level at which the remaining contingency lives*: an empirical horizon is level 2 and closes;\n   structural and hinge horizons are level 3–4 (a cultural lineage's carving, not shared across\n   lineages); a fittingness horizon is level 5–6 (an individual's path or weighting). This is a\n   hypothesis about the residue taxonomy, checkable on the horizon map as it fills: the same descent\n   run by a pair from one memeplex should find shared parts *sooner* than a pair across memeplexes,\n   and the wager's honest test is the second pair.\n2. **The wager, restated.** Convergence at depth is predicted where the parts are shared by descent or\n   forced by the world, and not where a concept's meaning is its path. So the founding wager bets that\n   beneath contested concepts, once the path-steps are peeled, the remaining parts are shared human\n   parts — and its failure mode has a name and a predicted location: essentially contested concepts,\n   whose contested criteria do not peel, wherever the contingent space is large and the constraint\n   weak, which is exactly the evaluative and political vocabulary. Those are the permanent horizons;\n   the lens predicts they exist and says where.\n3. **Sameness includes the path.** Two claims in the same words assembled in different memeplexes are\n   different objects; the seven-key label set's *can't tell* and the concept layer's sense-split exist\n   for exactly this, and the assembly-theory doc's line that *\"the provenance row is not decoration\"*\n   is the same point from the other side. Merging across memeplexes by surface similarity is merging\n   objects with different histories.\n4. **Two models are two copies of one record.** The jury's independence lives only in the contingent\n   part of each model's path — its data mix and alignment tuning — which is where the reasoning-layer\n   divergence measured in 2026 sits.\n5. **The transfer test gains the biologists' first question.** *Mechanism identity* in the four-check\n   test ([convictions-across-scales.md](convictions-across-scales.md)) should ask whether a shared\n   structure is homology or convergence: homology transfers within the lineage and not across it;\n   convergence transfers wherever the same constraint holds. The genetic-code finding — shared by\n   common descent, not forced — was this question answered once; it is worth asking every time, and\n   the analogy daemon's checklist should carry it.\n6. **A measurement the graph can already make.** Per concept, the between-source share of usage\n   variation (attributed claims, embedding regression per group) against the concept's abstraction and\n   evaluative load. The lifecycle states *bifurcated* and *fragmented* are the phenotype; the\n   prediction is a rising curve. Proposed alongside the per-worldview instrument in the companion doc.\n\n**Applied to the concept layer** — why concept tracking exists, what the live layer measures, and the design turn *claims are cores, senses are peripheries*: [core-periphery-and-the-concept-layer.md](core-periphery-and-the-concept-layer.md).\n\n## 6. What was read\n\nSharma, Czégel, Lachmann, Kempes, Walker & Cronin, *Assembly theory explains and quantifies selection\nand evolution* (Nature 2023) — the four spaces and the contingency definition are quoted from the\npaper's text; Blount, Lenski & Losos, *Contingency and determinism in evolution: replaying life's\ntape* (Science 2018) — quoted from the abstract, the convergence section and the conclusions; Blount,\n*Replaying Evolution* (American Scientist 2017) for the Lenski-population detail; Marti et al.'s\nmethods, results and discussion; the corpus's own assembly-theory doc in full. Gould, Conway Morris,\nGallie, Barsalou and Berridge are cited from standing knowledge, not re-read today. The cultural\napplication of assembly theory exists only as commentary (an ideasthesia essay, Jan 2026), not as\nmeasurement — and the theory's own authors list *\"human languages and memes\"* as anticipated, not\ndone. Nothing in § 5 is ruled.\n\n## Sources\n\n- Sharma et al., *Assembly theory explains and quantifies selection and evolution*, Nature 622 (2023) — https://www.nature.com/articles/s41586-023-06600-9\n- Blount, Lenski & Losos, *Contingency and determinism in evolution: Replaying life's tape*, Science 362 (2018) — https://doi.org/10.1126/science.aam5979 · Blount, *Replaying Evolution*, American Scientist 2017 — https://www.americanscientist.org/article/replaying-evolution\n- Marti, Wu, Piantadosi & Kidd, *Latent Diversity in Human Concepts*, Open Mind 2023 — https://doi.org/10.1162/opmi_a_00072 · Scientific American coverage with Gelman's comment — https://www.scientificamerican.com/article/people-differ-widely-in-their-understanding-of-even-a-simple-concept-such-as-the-word-penguin1/\n- Thompson, Roberts & Lupyan 2020; Youn et al. 2016; Jackson et al. 2019; Rodriguez, Spirling & Stewart 2023; KhudaBukhsh et al. 2021; Milbauer, Mathew & Evans 2021; Mamakos, Charlesworth & Finkel, PNAS Nexus 2025 — full references in the companion doc\n- *From Molecules to Meaning*, ideasthesia.org, Jan 2026 (commentary on assembly theory and culture) — https://www.ideasthesia.org/from-molecules-to-meaning-can-assembly-theory-scale-to-cognitive-systems/\n"}