30 Lexicon
(ns meme-constructor.posts.lexicon
(:require [clojure.java.io :as io]
[clojure.edn :as edn]
[scicloj.kindly.v4.kind :as kind]
[meme-constructor.lexicon :as lex]))The book labels its main items with short codes. The entries below are grouped by the part that owns them, in the order Part I, Part II, Part III.
Part I, “A Constructor Theory of Computing and Design”, owns the general definitions (post I.0). Its formal items carry the letter C, from the computing system (C1) to selection as erasure (C9). Its propositions carry the letter S, from the information bound (S1′) to the reflexivity proposition (S4), and its experiments on Push3 and on the bit-string model the letter X. Part I also owns design and the adaptive process, both defined in post I.5: the knowledge, alternatives and fine-tuning conditions (D1–D3), and the unspecific-variation, competition and selection conditions (A1′, A2, A3). The variation condition (A1) of post 7 is listed beside the condition that replaces it.
Part II, “Memes as Abstract Constructors”, applies them. Its formal items carry the letter F, from constructor-theory basics (F1) to design and adaptive process (F13), and its experiments the letter E, some run in the toy models and some only planned. The letter G marks the assumptions of the growth proposition in post 4.
Part III, “A Constructor Theory of Adaptation”, reads design for living things (post III.0). Its formal items carry the letters AD, from design and adaptive process in biology (AD1) to symbiogenesis as merging constructors (AD10), and its experiments the letter Y, from the real-protein experiment (Y1) to the symbiogenesis experiment (Y9).
In the posts a code always follows the name of the item, as in “stasis experiment (E10)”, and each code in parentheses links to its entry here. Each entry says what the item is, why the book needs it and where it stands. The entries are generated from resources/lexicon.edn. The “also mentioned in” lines are computed when this page is rendered, by scanning the prose of every post of the three parts for links to the entry.
30.1 Part I: A Constructor Theory of Computing and Design
30.1.1 Formal items of Part I (C)
30.1.1.1 Computing system (C1)
A substrate whose state space contains information variables, among them an input medium and an output medium, and whose patterns act on the system itself. A pattern is an abstract constructor instantiated in those variables. The system’s own step relation is kept apart from external steps, which are writes to the input medium and programming. An output is an own step that changes the output medium. Part I needs the split to tell a universal constructor, programmable from outside, from a self-reaching system (C3). The host step relation of post 3 is one input step followed by one own step. In Push3 the patterns are programs, and their classes can be computed on finite test sets: 37,448 short programs fall into 41 classes, exactly so in a polynomial fragment (Proposition I.1.9). Speed is not a property of the class (Proposition I.1.12).
Introduced in: post I.1
Also mentioned in: post I.0, post I.2, post I.3, post 0, post 1
30.1.1.2 Non-programmability (C2)
A system is non-programmable if no input sequence fixes an output across the states it reaches by its own steps. The idea is Deutsch’s (2013, §3.15), “we cannot be programmed”; the formal version is ours. The naive reading, that no input yields a chosen output, is true of a stone, so the definition asks that no input determine the output. Proved: self-reachability (C3) without a bypass such as a reflex implies non-programmability, and with a bypass it holds exactly off the bypass inputs (Proposition I.2.4). Observed in Push3 (seed 1): a passive interpreter gives one output per input, a self-reaching generator 118 or 119. Weakness: a coin-flipper and a closed random generator also satisfy it, so on its own it separates little. It formalises Deutsch’s “we cannot be programmed”; his universal explainer is self-reachability (C3).
Introduced in: post I.2
30.1.1.3 Self-reachability (C3)
A system is self-reaching, a universal explainer, if every partial computable behaviour is held by some state reachable by its own steps. It is a universal computer if this holds once external steps, such as programming, are allowed too. It is persistent if every reachable state is itself self-reaching: no state the system can get into closes off the alternatives. Persistence is the structure of fallibilism (C10, post I.6), and it is the precise form of “ω-Reachable is independent of Existing”. Proved by construction, as a sketch that assumes Turing completeness, for a Push3 generator up to its memory bound. It separates a person from an idle laptop with a compiler (Proposition I.2.13). No condition on reachable sets, persistence included, separates a person from a laptop running an enumerator (Proposition I.2.14). Human versus mouse rests on Conjecture I.2.15. Status: a necessary condition for a person, not a definition.
Introduced in: post I.2
Also mentioned in: post I.0, post I.1, post I.6, post 0, post 1, post 2, post 3
30.1.1.4 Synthesis (C4)
The task that takes a specification and an empty program medium to the same specification and a program that meets it. Its product is the abstract constructor of the specification, so a synthesiser builds constructors. Over an acceptable language verification is undecidable (Rice), and only properties witnessed by finitely many input-output pairs can be confirmed by any procedure (Proposition I.3.4, Rice–Shapiro). That is the precise sense of “one has to run things”: it concerns confirmation, not method. A decoder is a verifier, so the proved half of the decoder dichotomy (F7) is a corollary (Corollary I.3.6). Both results need an acceptable language, one into which every program text can be translated; a universal one is not enough, as Friedberg numberings show. In an acceptable language examples never fix the class, so evidence is a criterion (Proposition I.3.8). In a closed language it can be the source, because the knowledge sits in the language (Proposition I.3.9; FlashFill). Observed (seed 1): Push generate-and-test accepted a program that fails on an unseen input. Universal self-synthesis does not define a person or an AGI: an enumerator has it.
Introduced in: post I.3
Also mentioned in: post I.0, post I.1, post I.5, post I.6, post 0, post 1, post 2
30.1.1.5 Adaptive synthesis task (C5)
A tuple of a task T, an information medium I, a variation constructor V, an elimination constructor E and a finite resource N, whose product is a population carrying a constructor for T. It has exactly two conditions: unspecific variation (A1′) and selection by the task (A3). Competition (A2) is a property some such tasks have, not a condition. Post 7’s adaptive process is an instance, with alternatives (D2) read relative to V. The task maps Popper’s schema of problem, conjecture and error elimination onto constructors. Results in post I.5: the information bound (S1′), about one bit of design per binary decision; the cumulative-selection proposition (S2), a known result; and the design conjecture, Conjecture I.5.12, that adaptationism is the best theory of design, supported by the failure of its rivals but not proved.
Introduced in: post I.5
Also mentioned in: post I.0, post I.3, post I.4, post I.6, post 0, post 6, post 7, post III.0, post III.1, post III.3, post III.5
30.1.1.6 Algorithmic variation (C6)
Chaitin’s (2012b) algorithmic mutation, given the role of a variation constructor. A mutation is a program M, drawn with probability \(2^{-|M|}\), and the distance between two variants is the length of the shortest program that turns one into the other, up to a constant, not the Hamming distance. Consequences stated in post I.4: selection must supply about the description length of a design, and a universal variator is never worse than a computable one by more than a constant factor \(2^{c_W}\). In practice \(c_W\) is large: the repository’s variator alone failed, and the mixed variator that worked was chosen after that failure. Algorithmic steps help only where the criterion rewards the intermediate forms, so the advantage belongs to variation and criterion together. The per-site measure of design in post 7 overestimates regular design: it credits a constant 64-digit target with about 213 bits, while selection supplied a median of 117 (Observation I.4.13). Limits: Push3 is not prefix-free, so all this holds only up to constants and encoding.
Introduced in: post I.4
Also mentioned in: post I.0, post I.5, post III.5
30.1.1.7 Locus of elimination (C7)
The substrate on which a discarded variant is destroyed. In biology it is the vehicle, since the organism dies. In culture it is transmission, since the idea is not passed on. In a brain and in science it is the representation itself, since the conjecture is dropped before anything is built. This turns Popper’s (1978) “let our theories die in our stead” into a statement about where elimination acts. It is the premise of the elimination-locus proposition (S3), which gives a smaller cost per round a higher ceiling on the growth of knowledge. Status: a definition. That eliminating a representation costs far less than killing a vehicle is an empirical claim, untested in the book.
Introduced in: post I.5
Also mentioned in: post 7
30.1.1.8 Reflexivity (C8)
An adaptive synthesis task (C5) is reflexive if the criterion of elimination is carried in the medium, copied by variation and eliminated like other patterns (Definition I.6.1). Otherwise it is a fixed-criterion process, as natural selection is. Popper’s epistemology is the reflexive case. Reflexivity is the second order of criterion and anchor (F8). Prior work makes variation reflexive (Pushpop, mutation operators that evolve), but not elimination. Results: the reflexivity proposition (S4). In the reflexive-criterion experiment (X5), with an external anchor a reflexive criterion beat a fixed one that tests half the blocks and lost to one that tests all. Without an anchor it did not collapse into “keep everything” but became unmoored and lost the content. One might think full self-reachability needs reflexivity. It does not, since reaching and keeping are both blind (Propositions I.2.14, I.6.5). What remains is what the keeping depends on (Conjecture I.6.6). Reflexive and persistent, a process is fallibilist (C10).
Introduced in: post I.6
30.1.1.9 Selection as erasure (C9)
Planned, not yet run.
A conjecture planned for post I.7. Elimination discards variants, and discarding is logically irreversible (Landauer 1961). So an adaptive process in a world with a reversible step function should need a growing sink for erased information, and its design content should be bounded by the sink’s capacity. This would tie the arrow of time, which constructor theory places in the tasks (Marletto 2016), to the growth of knowledge. Post I.1 showed that Push3 is not reversible and that a reversible fragment would need Bennett’s garbage stack. Status: only stated. Nothing is proved, the fragment is not built, and the test is the reversible-world experiment (X6). Posts I.1 to I.6 do not depend on it.
Introduced in: Planned for post I.7.
30.1.1.10 Fallibilism (C10)
A process is fallibilist if it is reflexive (C8) and persistently self-reaching (C3) in its patterns and its criteria: every state it reaches is itself self-reaching, so no state closes off the alternatives to anything it holds (Definition I.6.12). No idea is ever fixed as the right one, and every idea stays open to criticism, whether or not it happens to be exactly right. So fallibilism is a property of the process, not of the accuracy of a copy: exact copies occur, but none is treated as final. Alone it separates nothing, since an enumerator is persistent too (Proposition I.2.14). Without an external anchor it loses what it knows (Proposition I.6.2(b), X5). Even with one it has a price: anchored reflexive hosts kept about 5.75 of 6 hits where a fixed criterion that happened to be right kept all. Conjecture I.6.13: creativity is persistence plus anchored criticism.
Introduced in: post I.6
Also mentioned in: post I.0, post I.2, post I.5, post 0, post 1
30.1.1.11 Critics (C11)
Definition I.6.14 splits a criterion into two parts. A criterion is a label task: it reads a hypothesis, leaves it unchanged, and writes an aspect of it, such as “fails test 3”. A critic is a criterion followed by a decision that reads only the aspect: reject or keep, or a rank. An aspect that rejects nothing is a new problem in Popper’s sense. Conjecture I.6.15, Popper’s, says that criticism needs a representation: every critic acts on the hypothesis as written in an information medium, and where there is none, only execution criticises. Proposition I.6.16: a critic can refute, never certify, since under the Church–Turing principle no possible critic keeps exactly the programs that compute a total function (Rice–Shapiro, Proposition I.3.4). The critic whose input includes the world is the experiment, the external anchor. Creativity devises critics. The label task is close to a non-perturbing measurement (Deutsch & Marletto 2015, §5).
Introduced in: post I.6
30.1.2 Propositions of Part I (S)
30.1.2.1 Information bound (S1′)
Proposition I.5.3. Under the unspecific-variation condition (A1′), a run that ends in a set A had its eliminator supply at least the design content of A minus \(s\) bits, except with probability \(2^{-s}\). Design content is minus the log-probability of A under a blind reference that draws the decisions from a fixed code. Corollary: about one bit of design per binary keep-or-discard decision, akin to Kimura (1961) and Worden (1995) but per run and for any variator. A deterministic form, “at least \(-\log P_V(K)\) bits”, does not hold; the bound holds only in this probabilistic form, up to \(s\) bits, and of Chaitin’s time bounds it gives only order \(N\). The information-bound experiment (X4) fits it for strict climbers on one landscape. Limits: proved for one hill-climber, not for populations.
Introduced in: post I.5
Also mentioned in: post I.0, post I.4, post 7, post III.4, post III.5, post III.6
30.1.2.2 Cumulative-selection proposition (S2)
Proposition I.5.5, a known result stated for later use, for a strict hill-climber. If from every variant on fitness level \(i\) one variation step reaches a higher level with probability at least \(q_i\), the expected time to the target is at most the sum of the \(1/q_i\). A climber whose total chance of moving up is \(Q\) waits \(1/Q\) rounds. This is the fitness-level method (Wegener 2002). So cumulative selection is fast exactly when working variants are connected under the variation’s step relation, as in Maynard Smith’s word chain. Observed: on the needle landscape the bound of 24,290 rounds is nearly tight, and without block jumps it grows to about \(5 \times 10^{12}\). The collapse of Chaitin’s regimes on program-synthesis benchmarks (post I.4) is evidence for this reading. Limit: proved only for one strict climber.
Introduced in: post I.5
Also mentioned in: post I.0, post I.4, post III.4, post III.6
30.1.2.3 Elimination-locus proposition (S3)
Proposition I.5.7. If one round costs time \(c\) and the eliminator decides at most \(b\) bits per round, a design of content \(B\) takes, with high probability, at least time of order \(cB/b\). So a locus of elimination (C7) with a cheaper round has a proportionally higher ceiling on the growth of knowledge. That is all it says; the proof is one line from the information bound (S1′). Its content is the premise that eliminating a representation is far cheaper than building and killing a vehicle, which is empirical and untested.
Introduced in: post I.5
30.1.2.4 Reflexivity proposition (S4)
Proposition I.6.2, for one lineage with full-support variation. (a) A fixed criterion keeps a pattern forever exactly when it is maximal under that criterion. (b) With the criterion carried in the pattern, whether the candidate or the parent judges, every hit is lost in finite time with probability 1. (c) A self-judging criterion favours laxness: the empty test approves every candidate, including those that carry it. So whatever preserves knowledge in a reflexive system cannot lie inside one lineage. The candidate is selection among lineages by an external anchor. The reflexive-criterion experiment (X5) answered the worry in (c): self-approval is real but only speeds the loss by a factor of about 1.7; the loss itself is (b). Limits: one lineage, and part (b) needs full support on the criterion.
Introduced in: post I.6
Also mentioned in: post I.0
30.1.3 Experiments of Part I (X)
30.1.3.1 Chaitin reproduction (X1)
A re-run, in post I.4, of Chaitin’s three regimes with the Push3 repository’s code: 4,000 trials, seeds 1 to 3, a busy-beaver fitness bounded to 10,000 bits. Exhaustive search reached 4 bits after 246 programs and stopped improving. Cumulative evolution saturated the substrate in 2 of 3 runs, with a median of 12 accepted mutations. A designer that pays for a pool of 32 mutants per step reached 256 bits in 1 run of 3. Reproduced: evolution beats exhaustive search. Not reproduced: design beating evolution once the designer pays for its oracle. Chaitin never proved that separation. Cited, not re-run: on 31 program-synthesis benchmarks evolution and design agree in 91 of 93 runs. Limits: small budgets, and a computable fitness tests only the separation of regimes.
Introduced in: post I.4
30.1.3.2 Point-versus-algorithmic experiment (X2)
Does search cost follow a target’s raw length or its description length? In post I.4 the targets are \(L\) digits repeating a random block of \(p\) digits, found by point, algorithmic or mixed variation, with seeds 1 to 5 and 20,000 trials. Under point variation cost grew at least linearly in \(L\) at every regularity. Under mixed variation it grew sublinearly for periods 1 and 2, and at \(L = 64\) point variation needed at least 30 times as many trials for period 2. It failed at period 4, and random targets showed no gap. The repository’s variator alone failed, and the mixed one was chosen afterwards. Under the first score tried, which rewarded length, the refutation condition was met; the score was changed after that result. Verdict: fits the most regular targets only, and depends on score and variator. The lesson is that algorithmic steps help only where the criterion rewards the intermediate forms.
Introduced in: post I.4
30.1.3.3 Population-competition experiment (X3)
Does a population, which has competition (A2), beat Chaitin’s single hill-climber on isolated peaks? Post I.5 used the bit-string model of post 4 with 9 small points, a needle landscape with a neutral plateau and a moat landscape that rings each peak with worse variants. Strict and weak climbers were compared with populations of 30 and 100, with seeds 1 to 20 and 60,000 evaluations. The prediction failed. On the moat the medians of all four lay within about 15 %, with overlapping spreads. On the needle the populations needed 35 to 50 % of the strict climber’s evaluations, but the weak climber was faster still, so the gain came from neutral drift, not from competition. The moat is a weak test: the block redraw puts every peak one jump away, so no valley ever has to be crossed. The result fits the view that competition does not help to find a design; it does not show it.
Introduced in: post I.5
Also mentioned in: post I.0, post III.4
30.1.3.4 Information-bound experiment (X4)
Does the design content of a run stay below the selection information its eliminator supplied, as the information bound (S1′) says? Post I.5 ran climbers on the needle landscape for 100 to 10,000 rounds, from an empty start and from one carrying 5 of 9 points, with seeds 1 to 10. The code for decisions was chosen after a first code made the knowledge in a start come out as zero, and the numbers depend on it. Of 120 honest runs, 119 lay on or above the bound, and one fell short by 0.6 bits, which the proposition allows. Only the strict climbers test the bound: weak climbers count every neutral acceptance as a decision, supply far more bits than their design needs, and meet it trivially. A control whose variation reads the task, violating the unspecific-variation condition (A1′), broke the bound in all 15 runs at strength 0.3, by up to 62 bits. From the 5-point start the design content was 23 to 24 bits below the functional content, the knowledge already in the start. The prediction held, on the needle landscape only.
Introduced in: post I.5
30.1.3.5 Reflexive-criterion experiment (X5)
What happens when the criterion lies in the medium, with and without an external anchor? Post I.6 used 100 hosts with 42-bit strings, 64 loss-detecting criteria and parent weights by content, seeds 1 to 5. With the anchor, both reflexive regimes beat the fixed criterion: 5.72 and 5.76 hits against 5.34 of 6, while host selection alone reached 4.66. That comparison favours reflexivity, since the fixed criterion tests only 3 of 6 blocks while the reflexive test sets grow to about 4.7. A fixed criterion that tests all six reached 6.00, faster than both. So reflexivity buys finding tests it was not given, and it has a price. Without the anchor we predicted collapse into “keep everything”. That prediction failed. The trivial criterion was in force in 1.3 % and 3.2 % of hosts, the rate of neutral drift. The criterion became unmoored instead and the content was lost, to about 0.2 to 0.5 hits. Self-judgment sped the loss by about 1.7. Conjecture I.6.11 replaces the claim. It is a first check of the anchor half of the creativity conjecture (Conjecture I.6.13), not of its persistence half, because no test in the model can be wrong. Limits: a closed family of criteria and one landscape.
Introduced in: post I.6
30.1.3.6 Reversible-world experiment (X6)
Planned, not yet run.
The planned test of selection as erasure (C9), for post I.7. Build a reversible fragment of Push3 in which every instruction is paired with its inverse and erased values go to a garbage stack, after Bennett (1973). Run an adaptive process in it with and without a sink of growing capacity. The prediction is that without a growing sink no design accumulates, and that design content is bounded by the sink’s capacity. It would be refuted by design growing in a closed reversible world with a bounded sink. Post I.1 established only the precondition: Push3 as it stands is not reversible, since almost every instruction erases information. Nothing has been built or run, and no post reports a result.
Introduced in: Planned for post I.7.
30.1.4 Conditions for design (D)
30.1.4.1 Knowledge condition (D1)
The first condition of design (Definition I.5.0 in post I.5; first stated in post 7; cited in post III.1 as Definition III.1.1). The abstract constructor K for a task T is knowledge: it is resilient, so once instantiated it tends to cause itself to remain instantiated (Deutsch 2013; Marletto 2015 §3.1). It is what makes a design last and not merely occur. It is an achievement only where something could remove K: in a pool from which nothing is removed, a variant stays because nothing removes it (post 7). What keeps a design is a process that keeps reading the task. Long conservation of a site is its measurable sign under drift as null hypothesis (AD3). Post III.6 found that a single focus of attention gives it content even with unlimited storage, and post 5 that receivers who check their copies against the evidence keep most of the content without selection among hosts (Observation 5.10). Whether keeping a design under mutation needs competition (A2), or only selection that keeps reading the task, is the central open question of the book (post I.5).
Introduced in: post I.5
Also mentioned in: post I.0, post 0, post 7, post III.0, post III.1, post III.3, post III.4, post III.6
30.1.4.2 Alternatives condition (D2)
The second condition of design (Definition I.5.0 in post I.5): alternatives are possible within one step of a fixed step relation, such as a point mutation or one conjectural step. They lie in the same information medium and can be built from the same resources with the same sub-constructors. The relative reading is needed because under Deutsch’s “possible” almost any variant of anything is possible, and every structure would pass. A snowflake fails the condition: order, but no design. The choice of step relation matters: under algorithmic variation (C6) every variant is one step away, the condition always holds, and the fine-tuning condition (D3) does all the work. Spandrels, developmental constraint and self-organisation fail it as well (explanatory adaptationism and its critics (AD2)). Mutations occurring at a site show it on real data (AD3). Post III.5 found that it does not fit recombination or merging, whose reach depends on the rest of the population. A population-relative version is not stated.
Introduced in: post I.5
Also mentioned in: post I.0, post I.4, post 0, post 7, post III.0, post III.1, post III.3, post III.4, post III.5
30.1.4.3 Fine-tuning condition (D3)
The third condition of design (Definition I.5.0 in post I.5), taken from Marletto (2015, §3.1.1): the one-step variants perform the task T to a much lower accuracy. It is a degree, not a threshold: the larger the share of one-step variants that perform T much worse, the more fine-tuned K is, so design is graded. It separates design from mere information: a neutral site lies in an information variable but fails it. In biology its measure is Kimura’s constraint \(1 - k/\mu\), the share of mutations that selection removes. A site with constraint 0.56, such as the C-peptide of insulin, is weakly designed, without contradiction. The constraint is 1.0 on found small points in post 7’s toy and about 0.94 at the haem contacts of haemoglobin β (Y2). We first proposed to give it a threshold \(4N_e s > 1\). Post III.3 kept it free of any process: the threshold, a smooth rise centred near 2, belongs to the process and says which fine-tuning a population can hold (coarseness of the constructor (AD5)). Exaptation fails it for the new task.
Introduced in: post I.5
Also mentioned in: post I.0, post 0, post 5, post 7, post III.0, post III.1, post III.2, post III.3, post III.4
30.1.5 Conditions for an adaptive process (A, with A1 of post 7)
30.1.5.1 Variation condition (A1)
A first formulation of the variation requirement of an adaptive process, mentioned in post 7 and replaced by the unspecific-variation condition (A1′) of post I.5. New variants arise from existing ones, with inheritance, and non-specifically to the end product. This is Marletto’s (2015, §3.3) replacement for “random mutation”. Its wording invites a reading as uniform variation, which ideas do not have, so A1′ excludes only dependence on the task. A constructor that contained the product’s design would move the design, not explain it; post III.3 states that requirement as non-containment (coarseness of the constructor (AD5)). In the toy model, whole-block jumps and single-task flips meet both A1 and A1′. The conditions of an adaptive process are defined in Definition I.5.1 of post I.5: A1′ and selection (A3).
Introduced in: post 7
Also mentioned in: post I.5
30.1.5.2 Unspecific-variation condition (A1′)
The variation condition of the adaptive synthesis task (C5): the law of the variation constructor depends on the current population only, not on the task. Variation may be structured. It may recombine, duplicate, reuse modules and prefer short programs, because such a preference is the same for every task (Proposition I.4.6). It may not consult the task. It replaces the variation condition (A1) of post 7, which invited a reading as uniform variation. This is Popper’s sense of “blind”, and it meets the objection to Campbell that conjectures are built from existing knowledge. It is the one hypothesis the information bound (S1′) uses. In the information-bound experiment (X4) a control variator that reads the task broke the bound by up to 62 bits.
Introduced in: post I.5
Also mentioned in: post I.0, post I.4, post 0, post 6, post 7, post III.0, post III.1, post III.3, post III.4, post III.5, post III.6
30.1.5.3 Competition (A2)
A property that some adaptive processes have, not a condition of design (post I.5, with Definition I.5.1). The task has competition if the tasks by which the variants persist or get varied cannot all be performed together on the finite resource N. It is an impossibility, not an event: variants compete in principle and need never meet. One might think there is no design without competition. It does not hold: the competition experiment (E14) found and held design in a pool from which nothing was removed, when parents were drawn by the task. Nor did competition move to the budget of variation: in post III.6 the budget did no work of its own (Y7). Part III measures competition as a property of a mechanism that implements selection: its strength against drift through \(N_e\) (Y4; \(4N_e s\) measures selection against drift) and its unit, the genome without sex and the allele with it, readable from linkage disequilibrium (Y8). What stays open is whether keeping a design under mutation needs it, or only selection that keeps reading the task.
Introduced in: post I.5
Also mentioned in: post I.0, post 7, post III.0, post III.1, post III.3, post III.5
30.1.5.4 Selection condition (A3)
The second of the two conditions of an adaptive process, defined in post I.5 (Definition I.5.1). Which variants persist or get varied depends on how accurately they perform the task T, not merely on the fact that they persist. This keeps the definition clear of “what survives is what survives”. Drift fails it: a process, but not an adaptive one, and hitchhiking fails it for the carried trait (AD2). In post 7’s toy the uniform pool found no points and the pool weighted by \(F_\text{real}\) found them, so design needs the unspecific-variation condition (A1′) together with this one. Part III kept finding it doing the work: selection has to read the task somewhere, in attention or in the rule by which a unit takes over (Y7), and a merge helps only by importing selection from the partners’ niches (Y9).
Introduced in: post I.5
Also mentioned in: post I.0, post 0, post 7, post III.0, post III.1, post III.3, post III.6
30.2 Part II: Memes as Abstract Constructors
30.2.1 Formal items (F)
30.2.1.1 Constructor-theory basics (F1)
The vocabulary imported from constructor theory. None of it is ours. It covers substrate, attribute and task (Deutsch 2013). It covers the constructor and “possible”, which means performable to arbitrarily high accuracy, never exactly (Deutsch 2013 §1.1). It covers the information variable, the information medium and interoperability (Deutsch & Marletto 2015), the abstract constructor and knowledge (Deutsch 2013 §2.14–2.15), and Marletto’s (2015) self-reproducer architecture with recipe R, vehicle V, copier C and programmable constructor P. The series needs these because every later definition, from the meme to design, is stated as a task or a constructor. Status: imported definitions, restated with section references. Nothing is proved here and nothing failed.
Introduced in: post 1
30.2.1.2 Meme as equivalence class (F2)
A meme \(m\) is given by a repertoire \(T_m\), a set of tasks in a fixed task universe \(\mathcal{T}\): explaining, predicting, doing, justifying, passing on. A brain state \(b\) carries \(m\) iff \(T_m \subseteq T(b)\). So “carries m” groups physically different states by one functional property and is substrate independent. This answers the ontology problem of memetics without naming a neural code, and it puts memes in the same category as Deutsch’s and Marletto’s abstract genes. Carrying is strict about loss and blind to gain, and memes are relative to the chosen \(\mathcal{T}\). It is Part I’s abstract constructor \(K_\sigma\) (Definition I.1.6) with brain states in place of programs, and from finite tests the class is known only from above (Proposition I.1.9). Status: a definition (Definitions 1.6 and 1.7). Open: how to individuate a single meme when repertoires overlap and are holistic. The candidate “smallest repertoire that can be copied as a whole” depends on the receiver and need not be unique.
Introduced in: post 1
30.2.1.3 Copy task and ε (F3)
The copy task \(C_m\) takes evidence \(e_m\) and a receiver that does not carry \(m\) to a receiver that does. The receiver rebuilds the idea from the evidence: \(C_m\) is synthesis (C4) from examples, with a weaker specification than the one to be met. For the function of a culture meme, on the open level, the evidence is a criterion, not a source, and the copy needs the receiver’s creativity. On the closed level, the channel (an ape meme is nothing but this level), the receiver parses behaviour or sound into a fixed digital alphabet, the evidence can be the source (Proposition I.3.9), and the copy becomes arbitrarily accurate. The error splits into a loss \(\varepsilon^-\) (tasks of \(m\) not acquired) and a gain \(\varepsilon^+\) (new tasks outside \(m\)). A measure \(\mu\) on tasks turns them into a size \(|\varepsilon|\) and a fidelity \(\varphi\). The population models and the Price bridge build on this quantity. Proved (Proposition 1.11), for the function of culture memes: under underdetermination no reconstruction is guaranteed to be exact, open sources leave underdetermination for every finite evidence, and no exact copy of an infinite repertoire can be confirmed. The closed level is digital, and the claim does not apply to it. Single copies are exact all the same, so the claim that the copy error is never zero does not hold. What follows is the fallibilist stance (C10): no copy is ever treated as final. In the toy, most gain at small evidence is error, and being hard to vary is relative to the receiver’s conjecture space (Conjecture 1.19).
Introduced in: post 1
30.2.1.4 Nested sets (F4)
De la Guardia’s (2025a) chain Active ⊆ Existing ⊆ N-Reachable ⊆ ω-Reachable ⊆ Possible. Post 3 defines it from a step relation on host states, one input write followed by one own step of the host as a computing system (C1), and maps states to memes by behaviour. A step relation directly on memes would overcount. Possible means constructor-theoretic possibility and does not depend on the host. \(M(S)\), what the host’s hardware could carry, is a sixth set just below it. The inclusions are trivial. “Independent of Existing” is stated as persistence: no reachable state loses any of ω-Reachable. Strong connectivity of the reachable set is sufficient for it (Proposition 3.6). The prediction that N-Reachable saturates for closed hosts and grows faster than linearly for open ones does not hold in the toy: saturation follows a finite behaviour space, and superlinear growth needs combining steps (Proposition 3.9), which closed grammars also have.
Introduced in: post 3
30.2.1.5 Time and efficiency (F5)
Time-bounded reachability. A timer (Deutsch & Marletto 2025) gives “quickly” a physical meaning: a meme is in t-Reachable if the host comes to carry it before a timer of duration \(t\) shows done. The executable timer is the Push counter timer of post I.1; under a fixed schedule it counts the host’s search steps. t-Reachable is defined on states, because speed belongs to instances, not to classes (Proposition I.1.12). Observed: two hosts with the same step relation, the same N-Reachable and the same ω-Reachable differ about twentyfold in median time. So efficiency lies in the search strategy, not in N-Reachable. That t-Reachable fills ω-Reachable as \(t\) grows, or contains N-Reachable for \(t\) proportional to \(N\), holds only for a host told which path to take.
Introduced in: post 3
30.2.1.6 Open and closed hosts (F6)
The distinction between open and closed hosts. Post 2 takes it from post I.2 (Definition I.2.7), read on the host’s own steps: open means self-reaching (C3), closed otherwise. The obvious definition, “generated by a fixed repertoire”, separates nothing, because every host is a fixed program. Self-reachability separates a person from an idle laptop with a compiler, and from a mouse if Conjecture I.2.15 holds. It does not separate a person from a laptop running an enumerator, and no condition on reachable sets can (Proposition I.2.14), so open versus closed is not the line between persons and the rest. Open Problem 2.6 asks for a property of the dynamics that draws that line; candidates are receptivity from underdetermined evidence, what the keeping of ideas depends on (Conjecture I.6.6) and efficiency (F5).
Introduced in: post 2
30.2.1.7 Decoder dichotomy (F7)
The thesis that a non-creative decoder from brain state to meme exists exactly when the host is closed. It does not hold in either direction. What holds: meme identity is extensional, so a decoder is a verifier of the host’s own programs (Proposition I.3.5), and a digital, computable host whose reachable programs form an acceptable language has no full decoder, from outside or on its own steps (Proposition 2.7, Corollary I.3.6). Universality alone is not enough, as Friedberg numberings show. The limit of decoding runs along the questions: a parser decodes hosts whose memes are finite, total behaviour tables over a fixed behaviour alphabet, as ape memes are (Proposition 2.12), while a total, non-universal host can lack a decoder for “never does X” (Proposition 2.13). An idle laptop is closed and still has no full decoder. Running the program, that is asking, is the general semi-decoder (Corollary 2.10). That asking is also the most efficient route is Conjecture 2.11.
Introduced in: post 2
30.2.1.8 Criterion and anchor (F8)
A criterion keeps or discards variants of a meme by ranking them against the meme itself. The anchor is a property of a ranking used in keeping, whether by the criterion (which candidate a host keeps) or by transmission (which host is copied). It is internal if the ranking depends counterfactually on the meme or its hosts, as with closeness to the received version or the hosts’ psychology, and external if the ranking is the same for every meme and every set of hosts (Definition 4.2). Parent choice by psychology is transmission with an internal anchor; parent choice by \(F_\text{real}\), as in the reflexive-criterion experiment (X5), is transmission with an external one. Criticism by other ideas counts as external when those ideas were tested independently of the meme. This is the series’ proposal for where Deutsch’s line between rational and anti-rational memes lies: both use creativity, and they differ in the anchor. The anchor cannot be a property of the keep/discard map, because every copying criterion compares with \(m\). Under an internal anchor the content is blind to reality: every trajectory would be the same in any other world (Proposition 4.2). A criterion that is itself an idea and gets varied is reflexivity (C8), studied on post 4’s model in post I.6.
Introduced in: post 4
Also mentioned in: post I.6
30.2.1.9 Fitness and stasis (F9)
Fitness splits into \(F_\text{psy}\), how well a meme uses its hosts’ psychology, and \(F_\text{real}\), how well it survives criticism about what it is about. Rational selection ranks \(F_\text{real}\) first. In the toy population model, the anti-rational criterion with perfect levers keeps the content exactly static, since it keeps only exact copies. With imperfect levers the content drifts, blind to reality, and forgets where it started (Propositions 4.2 and 4.3): stasis is not stationarity. Under the rational criterion with an exact test, \(F_\text{real}\) never falls along a line of descent and, with uniform transmission, rises in expectation (Proposition 4.4, under assumptions G1–G4). Fidelity and growth are separate axes: the anti-rational criterion copies as faithfully as the rational one and does not grow (Observation 4.6). Transport is not neutral: parent choice weighted by psychology stalls growth although every single copy still obeys the rational criterion (Observation 4.9).
Introduced in: post 4
30.2.1.10 Convergence (F10)
The conjecture that isolated populations with the same external anchor converge in content, on the same small points. Populations with an internal anchor converge at most on features that psychology rewards. Convergence then reveals an anchor outside the lines of descent. In the toy, under an exact external test every host eventually carries every hidden point (from Proposition 4.4), and under internal anchors agreement is blind to reality (Proposition 5.4). The convergence experiment (E11) and a counterfactual reality fit it: content follows reality, levers follow psychology. The refutation condition was reformulated after the run, because empty point blocks also count as agreement. Real traditions are not tested.
Introduced in: post 5
30.2.1.11 Recipe–vehicle architecture (F11)
Marletto’s separation of recipe R from vehicle V, applied to the closed level of copying: strings over a fixed alphabet, such as ape memes, recitation, checklists, forks of source code, and the words and writing that carry culture memes. The function of a culture meme, rebuilt from reasons, is not a recipe. Writing separates them, oral traditions carry R redundantly inside V, and imitation reads R back from V. In a bit-string model with a separate recipe, a corrupted vehicle is rebuilt in one generation, which holds by construction. Under imitation every execution error enters the recipe (Proposition 6.3). Redundant renditions protect imitation against noise, but not against a systematic reinterpretation that hits all renditions alike. The repair thesis holds only in a weakened form: “not inherited” needs P to build V from R alone. If P learns from practice, vehicle errors are inherited and decay geometrically (Proposition 6.5), and no architecture in the model guards against a P that reads R differently.
Introduced in: post 6
30.2.1.12 Price bridge (F12)
The bridge between the possibility layer of the series and the dynamics of cultural evolution. The Price equation splits the change of mean \(F_\text{real}\) into a selection (covariance) term and a transmission term, and the transmission term is split further into \(\varepsilon^-\) and \(\varepsilon^+\) parts. In the toy the identity holds exactly, the criterion sets the sign of the transmission term, and transport by psychology adds a negative selection (covariance) term. The copy task fixes the causal parent assignment, and only under it is the transmission term copy error; this is what constructor theory adds to the Price algebra. Limits: the ε split is unique only for additive value, and hard-to-vary content is not additive. Two attribution orders differ by about 6 units. Of Boyd and Richerson’s forces, guided variation fits the transmission term only in a weak sense. Biased transmission is a selection term, not a special case.
Introduced in: post 6
30.2.1.13 Design and adaptive process (F13)
Post 7 reads design (D1–D3, Definition I.5.0), which mentions no process, and the adaptive process (the adaptive synthesis task C5 with A1′ and A3), both defined in post I.5, for memes. A good explanation meets the fine-tuning condition relative to a receiver’s conjectural steps, and design is graded: its measure per site is the constraint \(1 - k/\mu\) (Conjecture 7.6), so a cloud or the C-peptide (0.56) is weakly designed. That design lies in information (Proposition 7.2) is a sketch with a gap and needs two extra assumptions. The pattern of conservation separates rational from anti-rational memes in the toy, and the mind virus shows a third pattern, conservation only where psychology works. Conjecture 7.4, that working variants must be connected by single steps, was refuted in its planned form in post III.4 (Y3); what matters is the ridge (Conjecture III.4.10). In the competition experiment (E14) design was found and kept without competition. For memes the design conjecture (Conjecture I.5.12) predicts an adaptive process in the brain (Conjecture 7.14).
Introduced in: post 7
30.2.2 Experiments (E)
30.2.2.1 Open-versus-closed composition experiment (E6)
Planned, not yet run.
An experiment for the later series on hyperdimensional computing (HDC). A closed model binds only a fixed set of primitive vectors, to depth one. An open model binds arbitrary, newly created indices, to any depth. The measure is |N-Reachable| for N = 1, 2, 3, counted by distinguishable behaviour, against the number of learned concepts. Post 3 found in its toy that such counts do not separate open from closed: saturation follows a finite behaviour space and superlinear growth needs combining steps, which closed grammars also have. The experiment would test whether this carries over to HDC.
Introduced in: post 3
30.2.2.2 Concept-space search experiment (E7)
Planned, not yet run.
An experiment for the later HDC series on search in concept space. A query is a combination of concepts, for example by binding. The host looks for a stored or newly constructed situation that fits it. In a closed space the axes are fixed; in an open space newly formed concepts can serve as axes. The measures are the share of queries about never-experienced combinations for which a fitting situation is found, and the mean number of steps until a match. Post 3 found that efficiency lies in the search strategy, so the second measure is the one that may separate hosts.
Introduced in: post 3
30.2.2.3 Stasis experiment (E10)
The first population experiment. Does the anchor of the criterion decide between stasis and growth? 60 hosts, 400 generations, seeds 1 to 5, all starting from a tradition with \(F_\text{real} = 8\) of 20. Under the anti-rational criterion with perfect levers the mean stayed exactly at 8. With lever strength 0.9 it drifted down to about 4.3, and with no criterion to about 3.2. Under the rational criterion it rose to about 17.9. Tested against a counterfactual reality, the rational criterion’s content followed that reality. Further results: fidelity and growth are separate axes, the mind-virus criterion deletes content, and noisy tests or psychology-weighted transmission stall growth. The refutation condition was reformulated after the run: first “growth under the anti-rational criterion”, which reality-blind drift from an empty start met literally, now “content under the anti-rational criterion tracks reality”, which cannot occur in the model (Proposition 4.2).
Introduced in: post 4
Also mentioned in: post 0
30.2.2.4 Convergence experiment (E11)
Tests the convergence conjecture (F10). Six isolated populations each start from their own random founder, so there is no common descent; 60 hosts, 600 generations, seeds 1 to 6. Under the rational criterion the hit rate on the hidden small points reached 0.92 and agreement on point blocks 0.87, up from 3 % at the start, a toy version of multiple discovery. Under internal anchors the populations converged on the lever blocks but never on the hidden patterns. The mind-virus populations agreed perfectly on empty point blocks. That met the refutation condition as first worded, “converge in content”, so it was reformulated after the run as convergence on content fixed by reality. Against a counterfactual reality the populations found its points instead, with the same levers.
Introduced in: post 5
Also mentioned in: post 0
30.2.2.5 Error-detection experiment (E12)
Measures how much content error correction keeps without selection. A receiver compares its reconstruction, block by block, with what the source’s version does in the world and rebuilds any block that differs. There is no ranking criterion, no psychological lever and no selection among hosts. That the check catches deviations of a point is true by construction; the experiment measures what it keeps over time. 60 hosts, 300 generations, seeds 1 to 3: plain copying decayed from 20 to about 3.5, while with the check mean \(F_\text{real}\) never fell below 18.3 of 20 (Observation 5.10). Errors that slip past and drift to fixation are never repaired, and for clouds the check keeps function, not content. So content can be kept by error correction that reads the task, without competition; a controlled comparison with competition is not run.
Introduced in: post 5
Also mentioned in: post 0
30.2.2.6 Selfish-neural-meme experiment (E13)
Planned, not yet run.
Planned for the later hardware series, as an extension of the HDC experiment on inner niches and reach. Do self-reinforcing concepts inside one brain displace useful ones? Prediction: yes, when the criterion that keeps concepts has an internal anchor, and they are held in check when it has an external one, an experiment or ideas tested independently of the concept. Coupling retention to prediction error is no substitute: that is the genes’ fixed criterion, not a criticism of the idea. Refutation: no displacement even with an internal anchor. The programme post lists it as planned, next to the population experiments (E10–E12, E14). Nothing has been run. The closest result in the book is the competition-for-variation experiment (Y7) of post III.6, where attention that did not read the task found nothing (Proposition III.6.2).
Introduced in: post 0
30.2.2.7 Competition experiment (E14)
Does the toy find and keep the small points without competition (A2)? Competition was removed from persistence with a pool from which nothing is ever removed, and parents were drawn from it either uniformly or with weight \(e^{F_\text{real}}\). Controls kept a capacity of 60 hosts. Seeds 1 to 5, 600 generations. The weighted pool reached a hit rate of 0.86 to 0.90, about as high as weighted reproduction with a capacity limit. The uniform pool stayed near 0. So design was found and kept without competition, and not without selection by the task (A1′ with A3). Post I.5 uses this result to state that competition is not a condition of design. An HDC version of the experiment is still planned.
Introduced in: post 7
Also mentioned in: post I.5, post 0, post III.4, post III.6
30.2.3 Assumptions of the growth proposition (G)
30.2.3.1 Exact-test assumption (G1)
An assumption of Proposition 4.4, growth under an external anchor. The rational criterion tests without noise, σ = 0, so a kept candidate never has lower \(F_\text{real}\) than its parent. G1 carries part 1 of the proposition: along any line of descent \(F_\text{real}\) never decreases. Observation 4.6 shows what happens without it. With test noise σ = 1, a quarter of the value of one small point, the population still grows but copies less faithfully. With σ = 2 the gain is about 1, and with σ = 3 the tradition decays. An external anchor is not enough. The test has to resolve the differences that matter.
Introduced in: post 4
30.2.3.2 Transport assumption (G2)
An assumption of Proposition 4.4. The transport threshold τ lies at or below \(F_\text{psy}\) of the initial tradition. Below τ a variant is too hard to pass on at all. G2 makes the exact copy of a parent transportable and so acceptable, which lets the retry loop end. It also limits the maximum the population can reach to the variants with \(F_\text{psy}\) at least τ. G2 is not the same as uniform parent choice. The expectation claim of the proposition needs that as well, and with psychology-weighted transmission growth stalls although G2 holds (Observation 4.9).
Introduced in: post 4
30.2.3.3 Unbounded-attempts assumption (G3)
An assumption of Proposition 4.4, also used for strict stasis under the anti-rational criterion in post 4. A host retries its reconstruction until the criterion keeps a candidate. This ends with probability 1 whenever an exact copy is acceptable, because an exact copy has positive probability in every attempt. It lets the proofs ignore the fallback of taking the best-ranked candidate. In the simulations the budget is 50 attempts, and the fallback never fired in the reported runs. So the assumption matters for the proofs, not for the numbers.
Introduced in: post 4
30.2.3.4 Non-degeneracy assumption (G4)
An assumption of Proposition 4.4. The loss, gain and jump probabilities of the copy noise all lie strictly between 0 and 1. Then every variant has positive probability as a reconstruction, so from any host below the maximum a strictly better transportable variant can appear. This drives the strict increase in expectation and the arrival at the maximum in finite time. The same full support gives the ergodic drift of Proposition 4.3. Its weakness is that it guarantees reachability by full support alone and gives no time bound. Without whole-block jumps, which stand for conjecture, the small points would be practically unreachable.
Introduced in: post 4
30.3 Part III: A Constructor Theory of Adaptation
30.3.1 Formal items of Part III (AD)
30.3.1.1 Design and adaptive process in biology (AD1)
Section 2 of post III.1 places evolution by natural selection inside the adaptive synthesis task (C5) of post I.5. The task is staying instantiated in an environment, the medium is the genome, variation is mutation, recombination and duplication, elimination is differential death and reproduction, the resource is food, space, mates and the finite number of births, and the step is one mutation. Mutation meets the unspecific-variation condition (A1′): its law depends on the sequence, not on what the organism needs. Differential reproduction meets the selection condition (A3). A population of fixed size also has competition (A2), which post I.5 shows is not needed to find a design.
Introduced in: post III.1
Also mentioned in: post III.0
30.3.1.2 Explanatory adaptationism and its critics (AD2)
Following Godfrey-Smith (2001), post III.1 defends only explanatory adaptationism (Definition III.1.2): every design in a living thing came from a process meeting the unspecific-variation and selection conditions (A1′, A3). It is the design conjecture (Conjecture I.5.12, adaptationism is the best theory of design) restricted to biology, and unproved. It is the best theory because its critics offer no rival: spandrels and self-organisation explain traits that fail the alternatives condition (D2), developmental constraint shapes the step relation rather than choosing the fit variant, exaptation explains a trait not fine-tuned for its new task, drift and hitchhiking fail the selection condition (A3). Drift does not even keep a design: it is lost after a geometric waiting time of about \(1/(\mu L_c)\) generations.
Introduced in: post III.1
30.3.1.3 Drift as null hypothesis (AD3)
Definition III.2.1. Without selection a site has \(k = \mu\). The constraint \(1 - k/\mu\), with \(\mu\) estimated from synonymous sites, is the share of mutations selection removes, and so the degree of fine-tuning (D3) of the site. Design being kept shows as constraint. Design being made shows as a constraint that switches on at sites that gain a task and off at sites that lose one, not as an excess \(k > \mu\): after a single change of the task selection works on standing variation (Y5), and a lasting excess needs a task that keeps moving (Proposition III.3.12). In the real-protein experiment (Y1) the measure separated design within genes, and graded: the C-peptide of insulin, at 0.56, is weakly designed. Limits: it sees only design per site, misses design in a property of many sites such as a signal peptide’s hydrophobicity, and synonymous sites are not quite neutral.
Introduced in: post III.2
30.3.1.4 Design-carrying programs (AD4)
Conjecture 7.4 of post 7, read relative to the variator’s step relation (Conjecture III.4.1). A program carries design that an adaptive process can find only if its sites lie in information variables, its step is local, and its working variants are connected. Proposition III.4.3 shows that point mutation splits an RNA neutral network into up to \(2^k\) pair-class components, so connectedness depends on the step (whether this is new is to be checked against Grüner et al. 1996). The neutral-network experiment (Y3) refuted the reading that a target needs a large neutral network of its own: scattered targets were found as fast as networked ones. What counts is the ridge, every level of fitness below the design connecting to a higher one. Without graded fitness no process beats random search (Proposition III.4.8). The connectedness part was restated after the result as Conjecture III.4.10; its test, a networked target behind a moat, is not done.
Introduced in: post III.4
30.3.1.5 Coarseness of the constructor (AD5)
An adaptive process explains a design only if its constructor does not contain it (Definition III.3.1). The relative version suffices for a particular design. Marletto’s strong version, with constructors crude enough to need no explanation, is needed for the origin of life. Coarseness is measured by the scaled selection coefficient \(S = 4N_e s\), which measures selection against drift. For one site under weak mutation, the classical two-allele balance (Proposition III.3.3; Bulmer 1991) gives the constraint as \(1 - S/\sinh S\): 0.15 at \(S = 1\) and one half at \(S \approx 2.18\). The population-size threshold experiment (Y4) found a smooth rise centred near 2, as that formula predicts, and small populations losing weakly selected sites first. The threshold belongs to the process, not to the fine-tuning condition (D3): it says which designs a population can hold.
Introduced in: post III.3
30.3.1.6 Moving tasks (AD6)
When coevolution or niche construction moves the task, design becomes relative to \(T(t)\) (Definition III.3.10), and a design can stop being one without changing. The environment stays a constructor because it keeps its ability to vary and select, not its state. Proposition III.3.12, a sketch, says that an arms race keeps \(k > \mu\) as a steady state only if the task moves on a site faster than a neutral site mutates, \(\mu P < 1\). The toy fits it: \(k/\mu\) was 2.8 at \(\mu P = 0.25\) and 0.37 at \(\mu P = 2\), with a burst after each shift in both. It is the only sustained excess \(k > \mu\) in the book. Conjecture III.3.11, that designs persisting over many shifts are anchored in physics, such as the haem pocket, is untested.
Introduced in: post III.3
30.3.1.7 Adaptive process in the brain (AD7)
Conjecture 7.14 of post 7: a brain that produces hard-to-vary ideas implements unspecific variation (A1′) and selection by the task (A3) over ideas. The argument for it (ideas are designs, the genes do not contain them) rests entirely on the design conjecture (Conjecture I.5.12). In the toy of post III.6 selection must read the task somewhere, in what attention varies or in the rule that decides which idea stays; the budget of variation did no work (Y7, Proposition III.6.2). Units that persist and vary in place search cumulatively, so replication was not needed to find the toy’s points; copying only spread them.
Introduced in: post III.6
30.3.1.8 Conservation pattern in culture (AD8)
Planned, not yet run.
Planned for an optional post III.7 on culture, which is not written. It would take the pattern of conservation of post 7 (Conjecture 7.9, Observation 7.10) to real data. A rational criterion conserves where the content works, an anti-rational one conserves evenly, and a psychological one conserves only the levers. The proposed test uses variant readings in manuscript traditions, such as formulae against narrative parts, and only if a suitable collated data set exists. Nothing has been done, and no post of Part III depends on it.
Introduced in: Planned for post III.7.
Also mentioned in: post 7, post III.0
30.3.1.9 Sex as recombining variation (AD9)
Recombination is a variation constructor with two parents (Definition III.5.1). It meets the unspecific-variation condition (A1′) and is strongly structured, since it only combines parts already present. It weakens the connectedness part of design-carrying programs (AD4), but its reach depends on the rest of the population, which the alternatives condition (D2) does not cover. Without sex the waits for independent small points do not add up, only the sweeps do (Proposition III.5.2, the classical result of Crow & Kimura 1965 and Maynard Smith 1971), so sex helps only under Fisher’s condition, when new points arise while others still sweep. The sex-versus-asexual experiment (Y8) fits this and measures the unit of competition of the selection mechanism: without sex points compete as parts of whole genomes, with it as alleles. Sex also stopped Muller’s ratchet at \(N = 50\).
Introduced in: post III.5
30.3.1.10 Symbiogenesis as merging constructors (AD10)
A merge takes one variant from each of two lineages that evolved on separate resources and returns one unit carrying both modules (Definition III.5.8), after Margulis (Sagan 1967) and Watson (2006). It is a short program with a large effect. Proposition III.5.9 shows that, with modules in fixed blocks, a merge is a one-point crossover across lineages, so any gain lies in the selection the partners underwent. The symbiogenesis experiment (Y9) refuted the conjecture: the merge was slower than mutation alone when the joint task rewarded each module. It alone succeeded when only the complete pair paid, and a blind-merge control showed that the gain came from selection in the partners’ niches. Symbiogenesis is not a faster operator; it imports selection that happened elsewhere. The merged cell becomes the new unit of competition one level up (Definition III.5.12).
Introduced in: post III.5
Also mentioned in: post III.0
30.3.2 Experiments of Part III (Y)
30.3.2.1 Real-protein experiment (Y1)
The test of drift as null hypothesis (AD3) on real proteins in post III.2: preproinsulin (18 mammals), haemoglobin β (122 genera), histone H4 and fibrinopeptide A from UniProt, aligned with MAFFT, with haem contacts computed from PDB 2HHB. Prediction: insulin’s A and B chains conserved and the C-peptide near the fibrinopeptide rate, haem contacts more conserved than the surface, and H4 nearly invariant. Neither refutation condition occurred. The A and B chains change at 0.31 and 0.39 of the C-peptide rate, haem contacts at 0.12 of the surface rate, and H4 is identical in 109 of 118 genera. The C-peptide, predicted near neutral, is weakly designed: synonymous sites give it constraint 0.56 (Y2).
Introduced in: post III.2
Also mentioned in: post III.0
30.3.2.2 dN/dS experiment (Y2)
Partly run; the rest is planned.
Planned in two halves, run only in one. The conservation half was run in post III.2 on the coding DNA of insulin (18 sequences) and haemoglobin β (26), by Nei and Gojobori with the Jukes–Cantor correction. With \(\mu\) from the whole gene the constraint \(1 - dN/dS\) is about 0.87 for the insulin chains, 0.56 for the C-peptide, 0.94 for the haem contacts and 0.57 for the surface. No region has \(dN/dS > 1\), and the C-peptide is weakly designed, not neutral. The positive-selection half, at the antigen-binding sites of MHC class I after Hughes and Nei (1988), was not run. It needs allele data. Its refutation would be no site with \(dN/dS > 1\). So the \(k > \mu\) direction has no real-data test in the book.
Introduced in: post III.2
Also mentioned in: post III.0
30.3.2.3 Neutral-network experiment (Y3)
The test of design-carrying programs (AD4) in post III.4, in a small RNA folding model at \(L = 16\). A control map has the same phenotype frequencies but no neighbourhood structure, and a thinned map scatters the target’s network into isolated points. Prediction: networked targets are found, isolated ones are not, and the control gives no cumulative design. The control part held. On RNA a weak climber found rare targets up to 25 times faster than random search, and on the control nothing beat random search. The refutation condition occurred for the rest: thinned targets were found as fast as networked ones of the same frequency. The ridge of partly working structures mattered, not the target’s network. Without graded fitness no process can beat random search (Proposition III.4.8). The weak climber, with drift and no competition, was best.
Introduced in: post III.4
Also mentioned in: post 7, post III.0
30.3.2.4 Population-size threshold experiment (Y4)
The test of the coarseness of the constructor (AD5) in post III.3: a toy of 60 sites with a selection coefficient per site, Wright–Fisher populations of 10, 30 and 100, seeds 1 to 4. Prediction: the constraint \(1 - k/\mu\) jumps near \(4N_e s \approx 1\), and the curves fall together against \(4N_e s\) but not against \(s\). The refutation condition, no relation to \(N_e\), did not occur. The same fine-tuning was held by a large population and lost by a small one. But the rise is smooth, from noise at \(S \le 0.8\) to at least 0.93 at \(S \ge 8\), centred near 2, as Proposition III.3.3 predicts. A lag at \(N = 100\) was traced, with checks added after the run, to a high mutation supply rather than to linkage.
Introduced in: post III.3
Also mentioned in: post III.0
30.3.2.5 Positive-selection experiment (Y5)
The toy test of design being made in post III.2. Prediction: after the task changes, the affected sites show \(k > \mu\) briefly and then \(k < \mu\). The refutation condition occurred in both forms of the test. Under selection by rejection a new small point spread by drift, with \(k \le \mu\) in every window. With differential reproduction the sweep ran on standing variation, whose substitutions happened before the change, while still neutral. What a change of the task does produce is the constraint switching on at the new sites and off at the old ones, as in a pseudogene. Post III.3 later found a sustained excess only for a task that moves faster than a neutral site mutates, under moving tasks (AD6).
Introduced in: post III.2
Also mentioned in: post III.0, post III.3
30.3.2.6 Critiques experiment (Y6)
Post III.1 asks whether rates of change tell designs from non-designs in a bit-string toy with ten traits of known status: small points, a spandrel, drift blocks, a hitchhiker and a pleiotropic trait; 60 hosts, seeds 1 to 40. Three readings of Kimura’s constraint were fixed before the run. The first called the spandrel and the pleiotropic trait designs, so the refutation condition occurred. The other two failed on a true design, the spandrel’s source, which had not been foreseen. The finding: variation that couples two traits is symmetric, so no rate can say which carries the design. Replays of the step relation find the unit of variation; only an intervention that changes one trait alone decides. A procedure built on this after the run did no better than the intervention alone. The hitchhiker’s sweep would mislead; its rate does not.
Introduced in: post III.1
Also mentioned in: post 0, post III.0
30.3.2.7 Competition-for-variation experiment (Y7)
The test in post III.6 of whether competition moved to the budget of variation where storage is unlimited. One variation step per tick; attention decides where it goes: uniform, task-weighted, or a single focus. The budget was the same under every rule and did no work. Uniform attention stayed at chance, as it must (Proposition III.6.2). Task-weighted attention is weighted parent choice by construction, so it matches the weighted pool of the competition experiment (E14). New is the focus: one slot and one comparison per tick reach the same hit rate (0.88) and make staying an achievement. Selection must read the task somewhere, in what is varied or in what stays.
Introduced in: post III.6
Also mentioned in: post 7, post III.0
30.3.2.8 Sex-versus-asexual experiment (Y8)
The test of sex as recombining variation (AD9) in post III.5: six independent small points, Wright–Fisher populations of 50 to 12,800, asexual against uniform and one-point crossover, seeds 1 to 20. Asexual waits do not add up, only the sweeps do (Proposition III.5.2, after Crow & Kimura 1965), so the prediction, fixed before the sweep, was that the advantage grows with \(\lambda\tau\), the mutation supply during a sweep. The data fit it up to \(\lambda\tau \approx 1\). The advantage rose from 1.08 at \(\lambda\tau = 0.03\), within noise, to about 2.5, below the sketch at large \(\lambda\tau\). Without sex points were negatively correlated, competing as parts of rival genomes. With sex they were not. In a ratchet run at \(N = 50\) sex kept the least-loaded genome nearly intact; at \(N = 20\) it did not help.
Introduced in: post III.5
Also mentioned in: post III.0
30.3.2.9 Symbiogenesis experiment (Y9)
The test of symbiogenesis as merging constructors (AD10) in post III.5: two modules of three small points, 200 births per generation in every process, seeds 1 to 20. The merge process keeps two partner populations in their own niches and merges partners into a joint population. A blind-merge control uses unselected partners. Plan: a merge is faster once the modules can be selected one by one. With an additive joint task the merge was slower, a median of 627 generations against 508 asexual and 254 to 285 with crossover, so the refutation condition occurred. With a joint task that paid only for the complete pair, only the merge finished, in all 20 runs, and the blind merge never did. The gain came from selection in the niches, not from the operator.
Introduced in: post III.5
Also mentioned in: post III.0
source: book2/notebooks/meme_constructor/posts/lexicon.clj