9  Memes as Abstract Constructors: the programme

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Post 0 of Part II. Status: September 2026.

A meme is what a brain can do with an idea, read as an abstract constructor. Copying happens on two levels. The channel (sounds, words, writing, a fixed set of behaviours) is a closed alphabet that is fixed in the receiver at the time of copying, and because the alphabet is digital the copy on it is arbitrarily accurate. The function is rebuilt by the receiver’s own creativity from reasons, in the open mode, and no such copy is ever confirmed exact: it stays open to criticism even when it is exact. An ape meme is the case where a string on the closed level fixes the whole repertoire. A culture meme is carried by a closed channel, but its function lives on the open level. Whether a tradition stays still or grows is decided by the anchor of the criterion that keeps its variants.

The programme in one line
Meme
what a brain can do with an idea
its function is copied, in the open mode, by→
Receiver's creativity
rebuilds the function from reasons; on the closed level of the channel a digital alphabet makes the copy arbitrarily accurate
kept by→
A criterion with an anchor
decides stasis or growth
No copy of the function is treated as final, even an exact one.

This post states the problem, places the project, lists the theses with the post that treats each, and fixes the method. Part II applies Part I, “A Constructor Theory of Computing and Design”, to ideas in brains. A brain is a computing system (C1) in the sense of post I.1, copying a meme is synthesis (C4) from examples (post I.3), and design and the adaptive process are those of post I.5. Part II takes these as given and links to the post that proves them. Part I’s programme is post I.0.

9.1 The problem

Memetics describes ideas as replicators (Dawkins 1976; Blackmore 1999). The picture has three well-known weaknesses.

Three weaknesses of memetics
weakness
Ontology
Nobody can say what a meme physically is: a pattern of neurons, a behaviour, a text or an idea.
weakness
Fidelity
A listener does not copy an idea but reconstructs it, pulled towards cognitive "attractors" (Sperber 1996). Without high fidelity there is no cumulative selection.
weakness
Dynamics instead of possibility
Memetic models ask how often an idea occurs over time, not which transmissions are possible, what keeps an idea for centuries, or why knowledge grows in some societies and not in others.

9.2 Why constructor theory, and where the project sits

Constructor theory (Deutsch 2013) states which transformations are possible, which are impossible, and why. That is the question memetics lacks. Our model is Marletto’s Constructor Theory of Life (Marletto 2015), which explains accurate self-reproduction under laws without design by separating a digital recipe from the vehicle built from it. We conjecture that this picture carries over to the closed level of every meme, where a fixed alphabet makes the copy digital (Conjecture 0.6). The function of a culture meme has no recipe: an utterance is a recipe-like signal that the receiver reads as evidence and does not execute. Deutsch (2011, chs. 15–16) treats memes at length, but not in constructor-theoretic terms. A web search (September 2026) found no work that applies constructor theory to memetics. That is a search result, not proof that none exists.

Who What they provide What is missing for our question
Popper (1963), Deutsch (2011, 2013), De la Guardia (2025a) conjecture and criticism, fallibilism, constructor theory, nested reachable sets a formal treatment, and the application to memetics
Marletto (2015) a constructor theory of life: recipe, vehicle, copier, programmable constructor the transfer to culture
Dawkins (1976), Blackmore (1999) the replicator, a meme ontology in prose a precise ontology, and questions of possibility
Cavalli-Sforza & Feldman (1981), Boyd & Richerson (1985), Price (1970) a formal dynamics of cultural evolution ontology and architecture; the transmission term is a free parameter
Part I of this book computing systems, synthesis, persons, design and adaptive processes in constructor theory the application to brains and culture
Part II the possibility of cultural replication, with simulations the dynamics, which we borrow

Constructor theory says which copies are possible and with what architecture; the population models say how frequencies change once the transmission is given. The bridge is the copy error. Post 6 shows that the copy task fixes which parent each child is booked to in the Price equation, and only under that bookkeeping is the transmission term the copy error.

Where the two theories meet
Constructor theory
which copies are possible, with what architecture
the copy error→
Population models
how frequencies change, once transmission is given
Post 6: the copy task fixes which parent each child is booked to in the Price equation.

9.3 The theses

The map first, then each thesis with the post that treats it. The first thesis is the main one.

Map of the theses
Thesis
Claim
Post
What became of it
0.6 Two levels of copying
closed level (the channel): a string over a fixed alphabet, copied arbitrarily accurately because the alphabet is fixed; open level (the function): rebuilt from reasons, never confirmed exact
1
conjecture; the open half follows from Prop. 1.11
0.1 Meme as abstract constructor
a meme is a class of brain states, fixed by its tasks
1
made a definition
0.2 Copier asymmetry
a meme is part of its own copier's program
1
content-specific copiers conjectured (1.16); second half not modelled
0.3 Creativity is the copier
copying is synthesis from evidence
1
no exact copy guaranteed or confirmed (Prop. 1.11)
0.4 Anchor
the anchor of the criterion decides stasis or growth
4, 5
internal anchor: blind to reality (Prop. 4.2); growth in the toy
Open and closed
open = self-reaching on the host's own steps
2
not the line between persons and the rest
0.5 Decoding
the general way to read a mind is to ask it
2
core proved (Prop. 2.7); efficiency open (Conj. 2.11)
Design
culture makes graded designs by variation and selection
7
found and kept in the competition toy
Green: shown in the post. Amber: open. Red: the tempting reading does not hold.

Conjecture 0.6 (Two levels of copying). Copying a meme happens on two levels. The closed level is the channel: sounds, words, writing, a fixed repertoire of behaviours. It is a closed alphabet that is fixed in the receiver at the time of copying. It does not matter where the alphabet came from: innate, learned in early childhood or invented. That it is fixed is the assumption of this level, and the fixed alphabet is its central property. The receiver parses what it observes into the alphabet, with errors. Because the alphabet is digital, an error smaller than the distance between two symbols is absorbed, and the errors that remain are whole symbols, which watching more often or taking a majority makes as rare as one likes. So the copy on this level is arbitrarily accurate. A young gorilla watching nettles prepared copies the sequence of steps, not the movement: Byrne’s behaviour parsing (Byrne & Byrne 1993; Byrne & Russon 1998; Byrne 1999). The arbitrary accuracy, which comes from the fixed alphabet, is our conjecture. The limits of a closed alphabet are that it is expensive to pass on and can only express what the alphabet composes (Deutsch 2011, ch. 16). The open level is the function. It is not a string. The receiver rebuilds it from the closed-level evidence, in the open mode, from reasons and with its own creativity. Two heads share the signal alphabet but not the concepts: each builds its own. An utterance or a text is a recipe-like signal that the receiver reads as evidence and does not execute. No exact copy of the function can be guaranteed or confirmed. An ape meme is the case where a string on the closed level fixes the whole repertoire. A culture meme is carried by a closed channel, but its function lives on the open level. The two are not a partition of memes. The answer to Sperber reads his attractors as what makes copying faithful. On the closed level, we conjecture, they are the symbols of the fixed alphabet, the central property of that level, and copying is digital and arbitrarily accurate; its fidelity comes from the fixed alphabet and redundancy, not from a separate recipe. On the open level the attractor is hard-to-vary content and the receiver’s test throws out near-misses, and the copy is reconstruction that converges but is never confirmed exact. The open half is post 1, Proposition 1.11. The closed half is a conjecture. It predicts that variants in ape traditions come in whole elements, a step swapped, inserted or missing, with no gradual drift of one step into another, and that fidelity rises with the number of observations. It is refuted if, in an ape tradition, a step of the transmitted sequence drifts gradually into another over generations.

Two levels of copying
sounds, words, writing; fixes the whole repertoire of an ape meme
Closed level: the channel
  • a closed alphabet, fixed in the receiver at the time of copying; the receiver parses what it sees into it
  • digital: errors below symbol distance are absorbed, so the copy is arbitrarily accurate
  • fidelity from the fixed alphabet and redundancy, not from a separate recipe
what makes a culture meme
Open level: the function
  • the function is not a string; heads share the signal alphabet but not the concepts
  • rebuilt from reasons by the receiver's creativity; the utterance is evidence, not a recipe to execute
  • no copy is guaranteed or confirmed exact
Sperber's attractors explain fidelity: on the closed level the symbols of the fixed alphabet, on the open level hard-to-vary content.

Conjecture 0.1 (Meme as abstract constructor). A meme is a class of brain states, fixed by the set of tasks \(T_m\) that a brain in such a state can perform. A brain \(b\) carries \(m\) when \(T_m \subseteq T(b)\). Post 1 makes this a definition. It is Part I’s abstract constructor (Definition I.1.6) with brain states for programs, and from finite tests it is known only from above (the meme as equivalence class (F2)).

Conjecture 0.2 (Copier asymmetry). A gene is copied by a generic copier that does not depend on the content. A meme is part of the program of its own copier. Post 1 states the first half and conjectures that meme copiers are content-specific (Conjecture 1.16). The second half is not modelled.

Who copies what
generic copier
Gene
the copier does not depend on the content
part of its copier
Meme
the meme is part of the program of its own copier
Post 1 states the first half and conjectures that meme copiers are content-specific (Conjecture 1.16). The second half is not modelled.

Conjecture 0.3 (Creativity is the copier). The copy task \(C_m\) is synthesis from examples: the receiver must build a pattern that meets the evidence. For a receiver with an open conjecture space the evidence is a criterion, not a source, so the copy needs the receiver’s creativity. This is the open level of Conjecture 0.6. Post 1 proves that no exact copy can be guaranteed or confirmed, although exact copies happen (Proposition 1.11). So no copy is treated as final: fallibilism (C10), which Part I defines as a property of the process (post I.6). A closed conjecture space is the contrast case, the formal counterpart of the closed level: there a fixed procedure can compute the copy with no creativity (Proposition I.3.9). The copy error splits into what the copy loses, \(\varepsilon^-\), and what it gains, \(\varepsilon^+\) (Definition 1.9). The gain holds errors and improvements alike; in the toy it is mostly error.

What the evidence is, by receiver
evidence = criterion
Open receiver
  • every computable extension of the evidence is a conjecture it can form
  • the evidence rejects copies; creativity proposes them
evidence = source
Closed receiver
  • a fixed procedure computes the copy
  • no creativity needed (Prop. I.3.9)

Conjecture 0.4 (Anchor). Rational and anti-rational memes, in Deutsch’s (2011, ch. 15) sense, both use creativity and both correct errors. They differ in the anchor of the criterion that decides which variants are kept. An external anchor, such as reality, is counterfactually independent of the meme and its hosts; an internal one, such as authority or the meme itself, is not. Post 4 shows that under an internal anchor the content is blind to reality (Proposition 4.2), and in the stasis experiment (E10) an external anchor let the content grow and follow reality. Fidelity and growth are separate axes. Post 5 finds that isolated populations with an external anchor converge on the same small points, the convergence experiment (E11).

Two anchors of the criterion
e.g. reality
External anchor
  • counterfactually independent of the meme and its hosts
  • the content can grow and follow reality (stasis experiment, E10)
e.g. authority, the meme itself
Internal anchor
  • depends on the meme or its hosts
  • the content is blind to reality (Prop. 4.2)
Both kinds of meme use creativity and correct errors. Only the anchor differs.

Open and closed hosts. A host is open if it is self-reaching (C3): every computable behaviour lies among the states it reaches by its own steps (post I.2). This classes an idle laptop with a compiler as closed. It does not separate a person from a laptop running a program enumerator, and no condition on reachable sets can (Proposition I.2.14). So the open-closed line is not the line between persons and the rest.

Open and closed, on three hosts
closed
Idle laptop with a compiler
its own steps reach only its current state
open
Laptop running a program enumerator
its own steps reach every program
open (conjectured)
Person
no condition on reachable sets separates it from the enumerator (Prop. I.2.14)

Conjecture 0.5 (Decoding). For a host with an open conjecture space the only general way to find out which meme it carries is to ask it. Post 2 proves the core: a decoder is a verifier of the host’s own programs (Proposition I.3.5), so no host whose reachable programs form an acceptable language has a full decoder (Proposition 2.7), and running the program, asking, is the general semi-decoder. The limit of decoding runs along the questions (the decoder dichotomy (F7)). That asking is also the most efficient route is Conjecture 2.11.

Where decoding stops
does not hold
A decoder exists exactly for closed hosts
  • an idle laptop is closed and has no full decoder
  • a closed, non-universal host can lack one for a global question
holds
The limit runs along the questions
  • a decoder is a verifier of the host's own programs
  • running the program, asking, is the general semi-decoder

Design. Culture produces things that look designed: tools, rituals, theories. Design is defined in post I.5 without any process, by the knowledge, alternatives and fine-tuning conditions (D1–D3), and it is graded. The process that can produce it is the adaptive synthesis task (C5), which needs variation that does not read the task (A1′) and selection by the task (A3). Post 7 reads both for memes. In its competition experiment (E14) a pool from which nothing was removed found and kept design when parents were drawn by the task.

Design and the process that can make it
Variation
does not read the task (A1′)
then→
Selection
by the task (A3)
can yield→
Design
knowledge, alternatives, fine-tuning (D1–D3)
The adaptive synthesis task (C5). Design itself is defined without any process, and it is graded (post I.5).

9.4 Method

The formalisation is meant to find gaps. Every substantive claim is one of four kinds. Each post is a Clojure namespace, and every claim that can be computed is computed next to the prose.

Four kinds of claim
Definition
fixes a term
Proposition
with a proof, or a marked sketch
Conjecture
with a way to refute it
Observation
computed in the post, with its seed

A finding changes the idea itself. A thesis that does not survive is replaced by its improved version, or stays as one sentence where it would be tempting. Some parts of the models were adjusted after seeing results, and each post says so where it happens: the refutation conditions of the stasis and convergence experiments (E10, E11), the score of the point-versus-algorithmic experiment (X2), the code for decisions in the information-bound experiment (X4), the repaired procedure of the critiques experiment (Y6), and Conjecture III.4.10.

Tier Content Where
A: formal definitions and propositions: meme, copy task and ε, nested reachable sets, open and closed, decoding, criterion and anchor, convergence, recipe and vehicle, the Price bridge, design posts 1–7, with toy models
B: simulable a population model of copying under different criteria: the stasis, convergence, error-detection and competition experiments (E10–E12, E14); the selfish-neural-meme experiment (E13) is only planned, for a later hardware series posts 4–7
C: not yet formalisable speculation about experience Part VI, marked as speculative; nothing in Parts I–III depends on it

9.5 The posts

  1. The meme as an abstract constructor. A meme is what a brain can do with an idea. Copies on the closed level of the channel are digital and arbitrarily accurate; no copy of the function can be guaranteed or confirmed exact, so none is final.
  2. Open and closed, and why thoughts cannot be read off. A decoder is a verifier, and the general way to read a mind is to ask it.
  3. Five sets and time. What a host can reach and how fast it gets there are separate questions, and efficiency lives in the second.
  4. The anchor: stasis and growth. The anchor of the criterion decides whether error correction keeps a tradition still or lets it grow.
  5. Small points: convergence and error detection. Anchored populations converge on the same points, and error correction keeps content without selection.
  6. Recipe and vehicle, and the Price equation. What a separate recipe protects against on the closed level, and how the copy task fixes the Price bookkeeping.
  7. Design for memes. A good explanation is a graded design, and design needs variation and selection, not competition.

Reading order. The order of dependence is Part I, then Part II, then Part III. Read Part I first, or start here and read posts I.1 to I.3 before or next to post 1, and post I.5 before post 7. The lexicon lists every short code of the book with its name and links.

Order of dependence
Part I
computing and design; I.1–I.3 before post 1, I.5 before post 7
→
Part II
memes as abstract constructors
→
Part III

9.6 Open problems

  • Keeping a design. Does keeping a design under continuing variation need competition, or only selection that keeps reading the task? This is the central open question of the book (post I.5). Receivers that check their copies against the world keep most of the content with no selection among hosts (post 5, Observation 5.10).
  • Person versus enumerator: the problem of creativity. Post I.6 moved the question from what a system reaches to what its keeping depends on: fallibilism (C10) with criticism tied to an external anchor (Conjecture I.6.13). That is a conjecture about a process, and it is unproved.
  • Individuating a meme among overlapping, holistic repertoires (post 1).
  • The meme as part of its copier’s program, the second half of Conjecture 0.2, is not modelled.
  • Real traditions. Whether they show the anchor, the convergence and the pattern of conservation that the toys show (posts 4, 5 and 7).

9.7 References

  • Blackmore, S. (1999). The Meme Machine. Oxford University Press. (not re-checked)
  • Boyd, R. & Richerson, P. J. (1985). Culture and the Evolutionary Process. University of Chicago Press. (verified)
  • Byrne, R. W. (1999). Imitation without intentionality. Using string parsing to copy the organization of behaviour. Animal Cognition 2(2), 63–72. doi:10.1007/s100710050025. (verified)
  • Byrne, R. W. & Byrne, J. M. E. (1993). Complex leaf-gathering skills of mountain gorillas (Gorilla g. beringei): variability and standardization. American Journal of Primatology 31(4), 241–261. (verified)
  • Byrne, R. W. & Russon, A. E. (1998). Learning by imitation: a hierarchical approach. Behavioral and Brain Sciences 21(5), 667–721. (verified)
  • Cavalli-Sforza, L. L. & Feldman, M. W. (1981). Cultural Transmission and Evolution: A Quantitative Approach. Monographs in Population Biology 16. Princeton University Press. (verified)
  • Dawkins, R. (1976). The Selfish Gene. Oxford University Press. (not re-checked)
  • De la Guardia, C. (2025a). The five nested sets of the mind. Making Minds and Making Progress (Substack), 28 May 2025. https://carlosd.substack.com/p/sets (not re-checked)
  • Deutsch, D. (2011). The Beginning of Infinity. Allen Lane. (not re-checked)
  • Deutsch, D. (2013). Constructor theory. Synthese 190(18), 4331–4359. doi:10.1007/s11229-013-0279-z. (not re-checked)
  • Marletto, C. (2015). Constructor theory of life. J. R. Soc. Interface 12(104): 20141226. (not re-checked)
  • Popper, K. R. (1963). Conjectures and Refutations. Routledge. (not re-checked)
  • Price, G. R. (1970). Selection and covariance. Nature 227, 520–521. doi:10.1038/227520a0. (verified)
  • Sperber, D. (1996). Explaining Culture: A Naturalistic Approach. Blackwell. (not re-checked)
source: book2/notebooks/meme_constructor/posts/post_00_programme.clj