communicoupling
Two neighbourhoods begin as near twins — same housing stock, same incomes, same schools. Thirty years on, one thrives and one is boarded up, and every explanation on offer is something that happened along the way, nothing that was there at the start. Careers, marriages, reputations and firms show the same shape: enormous divergence downstream of no decision anywhere near big enough to account for it.
Magoroh Maruyama named the machinery in 1963. The first cybernetics studied deviation-counteracting loops — thermostats, homeostasis, systems that treat every difference as an error to be spent down. His second cybernetics studies their mirror image: deviation-amplifying mutual causal loops, in which an initial kick — however tiny, even pure noise — is magnified around the circuit until it crystallises into structure. The initial cause is trivial; the amplification is everything.
Below, two communities run the identical loop — investment raises reputation, reputation attracts investment — starting almost exactly level. One dial, the loop gain, decides whether their tiny difference is erased or compounded. Keep an eye on the gap's log-scale curve: the moment it runs straight, circumstance is earning compound interest.
Two cybernetics
Each community carries two stocks, investment I and reputation R, each feeding the other — a mutual causal circuit, I → R → I. Every deviation from the baseline also decays at a natural restoring rate, the first cybernetics' contribution, plus whatever counteracting effort c you buy. What remains is one number, the loop gain g, and the gap Δ between the communities obeys dΔ/dt ≈ (g − 1 − c)·Δ. Below the threshold the circuit is a thermostat, and even a generous head start gets spent down to nothing. Above it the circuit is an amplifier, and it waters whichever seed it is handed — in the fork, the identical loop drives one community up and its twin down, virtuous and vicious circle at once, from one mechanism with no opinion about who deserves to win.
The log-scale curve is the tell. On a linear axis, exponential growth stays invisible until it is overwhelming; on a log axis it is a straight line from the very first moment, slope g − 1 − c, and the fitted-rate readout recovers that slope live from the simulated run — compare it with the theory value printed beneath it. The tanh ceiling keeps the run honest: there are only so many tenants, clients and reputations to win, so advantage saturates, lock-in arrives, and the fitted rate collapses toward zero. The loop is as strong as ever. It has run out of world.
What to try
Set Δ₀ = 0.05, everything else at zero, and walk g from 0.8 to 1.0 to 1.2. The fitted rate reads −0.20, then 0.00, then +0.20, and the gap curve tilts from falling to frozen to rising. One dial, three worlds — and the border between them is a single number.
Press Noise alone: Δ₀ = 0, σ = 0.03. The communities start identical; luck leans one of them a hair's width, the loop seizes the lean, and lock-in follows. Restart a few times — the winner changes, sometimes both twins even land together, and nothing but noise decides which story you get.
Run The fork and raise c to 0.8 while the gap is small: it dies at −0.30/t. Now restart, Fast-forward past lock-in, and apply the same policy: it faces a ×13 structure, and the unwind takes nearly twice as long as the fork took to open.
Compound interest on circumstance
A first paper gets cited, which lands the grant, which staffs the lab, which writes the better second paper: two equally able researchers, one early citation apart, retire a career apart. A boarded shop window invites the second; two boarded windows tell every landlord what the street is worth. In a marriage, warmth invites warmth and grievance invites grievance — one circuit, opposite signs. In each case we hunt for a founding cause sized to the outcome, and the hunt fails, because above threshold the outcome carries no information about the size of its origin. The origin can be rounding error. In the noise-alone run it literally is.
"Virtuous" and "vicious" are the observer's verdicts on one mathematics; the loop knows only its gain. That is where Maruyama points intervention: at the gain, and early. Counteracting effort works arithmetic against an exponential, so its price compounds with every unit of delay — the time-to-lock-in readout is, in policy terms, the closing of the affordable window. Before lock-in you are correcting a rounding error; after it, you are dismantling a structure.
Neighbouring loops
Bateson's schismogenesis is this amplifier strung between two parties' behaviour — each side's response feeding the other's escalation — where here it runs between two stocks inside each community. Regime shifts add what this model lacks: hysteresis, basins that hold after the loop that carved them has died, so that dropping the gain no longer unwinds the gap. And categorical inequality is the gap grown old — divergence hardened into boundary, category and institution, long after anyone could point to the kick that began it.
The mapping
| In the model | In the world |
|---|---|
| loop gain g | How strongly advantage begets advantage — the interest rate on circumstance. |
| initial gap Δ₀ | The accident of where you started: inherited, unchosen, and above threshold never forgotten. |
| straight log-gap line | Compound interest on circumstance — steady multiplication drawn as a straight line. |
| the tanh ceiling | Saturation: finite tenants, clients and attention — the ceilings that finally stop the compounding. |
| counteracting c | Deliberate damping — policy, redistribution, repair — raising the threshold the gain must clear. |
| time to lock-in | The window in which intervention is still cheap. |
| noise σ | Sheer luck: shocks and accidents, sufficient on their own to seed a fork. |
Where it tears
The model holds g constant while the run lasts; real social circuits bend their own dials. A boom raises rents until the rents choke the boom; a monopoly invites the regulator; a winning streak breeds complacency. Deviation-amplification is usually a phase a system passes through — Maruyama himself treated amplifying and counteracting processes as stages of one history — and the constant-gain exponential is this model's cleanest fiction.
Virtuous and vicious name one mathematics from two seats. The gentrifying neighbourhood is a virtuous circle to the investor and a vicious one to the tenant priced out by it, in the same run of the same loop. The model prints a gap; only an observer with a stake can print a verdict, and the instrument stays silent on which community you should have been rooting for.
The instrument hands you the circuit pre-labelled: two stocks, one gain, nothing else. In a real neighbourhood, dozens of candidate loops tangle, gains go unmeasured, and any outcome can be retro-fitted with a flattering circle. Maruyama's diagram is the start of an empirical job — identifying which mutual causation actually carries the gain — and this simulation assumes that job is already done.
Which move breaks this loop?
| The move | Where it cuts |
|---|---|
| Scanning for latent change | Cuts before the threshold: a loop caught while g is still near one is a rounding error to correct, and the affordable window is open. |
| Genealogy | Traces the gap back to the turn where the circuit closed — the joint that closed the loop is the joint where it opens. |
| The premortem | Runs the loop to lock-in in imagination first, pricing the ×13 structure before the first round is joined. |