communicoupling · concept 5 of 26
How does a sound come to mean anything, when no one ever sat down and agreed what it should mean? Convention looks like it must have a first legislator. Lewis and Skyrms showed it needs none: a shared code self-organizes out of repeated, initially meaningless exchange, purely because coordination pays.
Think of the word everyone now uses as if it were carved in stone; the gesture your family alone understands; the market's flickering signals; a baby's first shared sound. We imagine meaning as a contract — a moment when parties agreed that this would stand for that. But a contract must be written in some prior language to be read at all. So the very first meanings could not have been agreed, because there was nothing yet to agree in.
Below is the smallest honest answer that works. A Sender who can see the world, a Receiver who can act on it, a shared stake in getting it right — and no code between them. Just repetition, and a memory that keeps what paid. Watch a language condense out of noise.
Sender · state → signal
one urn per state, over signals. Bright = the signal this state has learned to emit.
Receiver · signal → act
one urn per signal, over acts. Bright = the response this signal has learned to trigger.
Running success rate
the fraction of rounds where the Receiver's act matched the world's state, cumulative.
Which meanings formed?
Meaning without a legislator
The setup is deliberately impoverished. A Sender sees which state the world is in — one of a few situations, drawn at random — and emits a signal. The signal is a bare token: it carries no built-in meaning, and at the start the Sender is as likely to emit any one as any other. A Receiver sees only the signal, never the world, and must choose an act. If the act fits the state, both are rewarded; if not, nothing. That shared reward — a common interest in being understood — is the entire engine. No dictionary, no designer, no first legislator.
Learning is the crudest thing that could possibly work: Roth–Erev reinforcement, the mathematics of an urn. Picture, for each state, a jar of coloured balls, one colour per signal. To signal, the Sender draws a ball at random and emits its colour. The Receiver keeps a jar per signal, one colour per act, and draws from it to choose. When a round succeeds, you drop one extra ball of each winning colour back into the two jars that produced it. Success makes itself more likely next time; failure changes nothing. No agent understands anything. Yet the jars remember what paid — and over thousands of draws, that memory hardens the near-uniform noise into a set of one-hot columns: each state reliably emits its own signal, each signal reliably triggers its own act. A code, with no one to have written it.
What to try
Run it to convergence and read off the invented code. Leave states, signals and acts equal — the "perfect information" case — and press Run to convergence. The two matrices sharpen from grey static into a clean permutation: one bright cell per row. The success curve climbs off its chance baseline and presses toward 1.0. The Which meanings formed? panel names the vocabulary the agents just invented: signal B now means predator, and everyone acts on it.
Reseed, and watch a different code form. Press ⟳ Reseed and run again. Just as good a language emerges — but a different one. Last time B meant predator; this time it might mean food, or go unused while A and C carry the load. Which sound attaches to which situation is a frozen accident of who happened to draw what early on. That the code exists is near-inevitable; which code it is, is arbitrary.
Set signals below states, and meet a pooling equilibrium. Drag Signals down to 2 while states stay at 3. Now there are not enough words to go around. Two states are forced to share a signal, and the Receiver, hearing it, cannot tell which world it is in — it can only guess the more common one and eat the errors. This ambiguity is not a failure of learning; no amount of practice removes it. The channel is simply too narrow for the world. The success rate plateaus honestly below one.
The arbitrariness and the necessity
Reseeding stages, in miniature, Ferdinand de Saussure's arbitrariness of the sign: there is no natural bond between a signal and what it means. Nothing about the token B resembles a predator; it could have meant anything, and across runs it does. The particular word is contingent all the way down — a fossil of a random early draw that reinforcement then locked in place. This is why the same object wears unrelated names in different languages, and why no etymology ever bottoms out in a sound that had to be chosen.
And yet the existence of some shared vocabulary is very nearly guaranteed. Skyrms proved that for two states the simple reinforcement process converges to a perfect signaling system with probability one; with more states it can occasionally settle into partial pooling, but a working code of some kind is the overwhelming attractor of the dynamics. That is the deep asymmetry the instrument makes visible. Which convention arises is a coin-toss; that a convention arises is all but forced by the payoff structure. Meaning is arbitrary in its content and necessary in its form — a stable point that repeated coordinated play falls into, whether or not anyone is steering.
Where codes come from and go
Once you can see it, the mechanism is everywhere a group has a shared stake in being understood. The private jargon of a trade, the slang that marks who is inside a scene, the hand-signs of a crew on a loud floor, the conventions by which a price tells a stranger what a thing is worth — none were legislated. Each condensed the way the matrices do: out of repeated, initially arbitrary exchange, reinforced because coordinating paid. A market price is a signal in exactly this sense — a token that lets actors who share no plan act as if they did.
The same dynamics run the other way, too. Shift the payoffs — change what the group is trying to coordinate on, split the audience, let the world the signals track drift away — and a code that once meant something bleeds meaning back into noise. Words narrow, invert, or hollow into cliché; an in-group marker becomes generic the moment everyone adopts it and it stops distinguishing anyone. Convention is not a monument but a standing wave, held up only by the coordinated use that keeps paying to maintain it. The birth of a code and its erosion are one process filmed in opposite directions.
The mapping
| In the model | In social life |
|---|---|
| state | The situation to be communicated — what the world is doing that someone needs to know. |
| signal | The word, gesture, price or marker — a token that starts empty, meaning nothing at all. |
| act | The uptake: the response the hearer makes, the thing they do having taken the signal in. |
| coordination payoff | The shared interest that makes meaning worth forming — the reason it pays to be understood. |
| sharpening matrices | A convention crystallizing from use: near-uniform noise hardening into a one-hot code. |
| pooling | Ambiguity that survives because the code has too few signals for its world — unlearnable, structural. |
Where it tears
The engine here is a shared payoff: Sender and Receiver win or lose together, so honesty is simply the best policy. Where their interests diverge — the seller who gains from your believing the goods are better than they are — signaling becomes manipulation, and an honest code may never form. Then meaning has to be defended by cost or by punishment, not just by coordination. That is the separate world of costly signals and cheap talk, and this symmetric model cannot reach it.
Real language is compositional: a handful of parts recombine into unbounded meanings, and the meaning of the whole is built from the arrangement of its pieces. The model has none of that. It is a flat lookup table of independent signals, each learned on its own. What you are watching is the birth of reference — a token coming to stand for a thing — not the birth of syntax. Grammar is a further, harder story.
Because the Sender and Receiver are symmetric peers, the code that forms belongs to no one and serves them equally. Much real convention does not. Dominant parties routinely impose a vocabulary — whose language is official, whose category counts, whose price is quoted — and then call the result natural, spontaneous, the way things simply are. A model where everyone reinforces equally cannot see that asymmetry. "It self-organized" is sometimes true, and sometimes the alibi of whoever wrote the first word and made the rest of us pay to use it.