↩ ExploRational · A Catalogue of Divergent Rationality
explorational · a divergent move
The moment you adopt one explanation it becomes, in Chamberlin's phrase, an intellectual child you defend — and you start reading the evidence to protect it. How do you keep loyalty on the inquiry instead of on an answer? Hold a family of explanations at once, let each clue update all of them by Bayes, and refuse to marry one until the evidence — not your affection — has thinned the field.
In 1890 the geologist Thomas Chrowder Chamberlin published a short, strange paper called "The Method of Multiple Working Hypotheses." Its psychology is sharper than its geology. The instant the mind fixes on a single explanation, he wrote, "affection for his intellectual child springs into existence, and as the explanation grows into a definite theory his parental affections cluster about his offspring." From that moment the work inverts. You stop testing the theory and start defending it; ambiguous evidence is read in its favour; the contradiction becomes an anomaly to be explained away later. The single hypothesis does not win arguments — it recruits them.
Chamberlin's remedy is not neutrality, which no mind can sustain, but plurality. Bring a whole family of explanations to the table at once and raise them as equals. Loyalty, having nowhere singular to land, attaches instead to the question — and evidence recovers its power to discriminate, because you are no longer invested in what it says. But a family held forever is its own failure, the move's named risk: endless deferral, rigour's costume worn by paralysis. The discipline is a family that evidence is allowed to prune. The instrument below runs two minds side by side on one honest stream of clues — a family mind that keeps all its children until the evidence thins them, and a committed mind that adopts a favourite early and reads every later clue to protect it — so you can watch, in real Bayesian numbers, exactly what attachment costs.
the honest instrument
A recurring server outage has four candidate causes. One is truly to blame; the clues arrive one at a time, and each clue has a known likelihood under every cause. The family mind keeps a full posterior over all four and updates each by Bayes. The committed mind runs identically until it commits — then it collapses to its current leader and reads later clues to protect it, discounting whatever disconfirms, in proportion to an attachment dial. Both minds see the same clues, so any divergence is attributable to attachment alone. Press draw next clue, or auto-run, and watch.
A recurring outage · four candidate causes
Bayesian belief-tracker · clue 0 · likelihoods disclosed
posterior over every cause, by Bayes
runs with the family until it commits
the intellectual child
A single explanation is not a neutral place to start; it is a gravitational one. Once it exists it bends the search toward itself, because the cheapest operation the mind can perform is finding one more reason to believe what it already believes. Chamberlin watched colleagues spend careers this way and feel rigorous the entire time — because they were gathering data, running tests, reading closely. The rigour was real. It was simply pointed at defence rather than at truth. This is the mechanism psychologists later named biased assimilation: shown a mixed body of evidence, partisans on both sides rate the studies that support them as sound and the studies that oppose them as flawed, and walk away more confident and further apart than before.
The committed mind in the instrument is exactly this failure, made arithmetic. When it collapses to a leader, it does not stop reasoning — it keeps doing Bayes. But for its held belief it inflates every incoming likelihood toward the best case, so a clue that should have counted against the belief is read as consistent with it. At attachment 0 this distortion vanishes and the committed mind is the family mind. Turn attachment up and watch the same clue stream carry two minds to opposite conclusions: the family mind climbs toward the true cause, the committed mind toward the wrong one it happened to marry at clue two. Nothing separated them but the willingness to let evidence land.
what to try
Load the attached mind and auto-run. It commits at clue two to the wrong cause and, with attachment at 0.90, locks in confident wrongness — its probability on the truth flatlines near zero. Meanwhile the family mind, on the very same clues, crosses 0.90 confidence in the true cause by about clue five. Watch the family overtake you.
Now drag attachment down from 0.90 toward 0 and re-run. At 0.30 the committed mind partly recovers — evidence slowly overpowers the bias — and at 0 it converges exactly like the family. The gap between the two minds is entirely the attachment term; the evidence never changed.
Load the ditherer: high ambiguity, and the family set to never commit. Its probability on the truth rises, but the threshold is never reached and the clue counter climbs forever. Holding every child indefinitely is not rigour — it is the opposite waste, paying for evidence you will never let decide.
the family that evidence prunes
The move has two failure poles, and the instrument shows both. On one side is premature commitment — the committed mind, marrying a leader before the evidence has spoken and thereafter unable to hear it. On the other is endless deferral — the ditherer, so proud of holding every possibility open that it never lets any evidence count, forever drawing one more clue. Neither is Chamberlin's method. The method lives in the disciplined middle: a family of hypotheses held as genuine equals, each updated honestly by every clue, and narrowed only when the evidence itself has made one of them overwhelmingly likely.
That is what the commit threshold encodes. The family mind does not refuse to decide; it refuses to decide early. It commits when — and only when — the leading posterior crosses a bar you set, and by then the commitment is evidence-earned rather than affection-driven. Loyalty is not owed to a hypothesis at all. It is owed to the inquiry: to the standing willingness to let the field be thinned by what you observe rather than by what you hoped. A family you would never prune is not open-mindedness; it is a decision never to look.
model
Each of the K causes emits clues by a disclosed rule: cause Hᵢ produces its own signature clue with high probability and the other clues rarely, governed by the ambiguity dial — at ambiguity 0 each clue is a fingerprint, at ambiguity near 1 every cause emits every clue almost equally and no clue tells you anything. Formally P(clue j | Hᵢ) = (1−α)·[i=j] + α∕K, so every row is a proper distribution. One cause is truly to blame; the stream is sampled from its row by a seeded generator, which is all that reseed changes — same world, a different order of clues.
The family mind is plain Bayes: posterior(Hᵢ) ∝ prior(Hᵢ) · Πⱼ P(clueⱼ | Hᵢ), renormalised after every clue so the four probabilities sum to one. The committed mind is identical until it commits; then, for its held cause h only, it replaces the honest likelihood with a distorted one, Pₑ = (1−a)·P(clue | h) + a·max P(·| h) — reading each clue as if it were closer to h's best case. The attachment dial a runs this from honest (a=0) to fully blind (a=1, every clue treated as maximally confirming). That last term is a stylized knob, not a measurement of anyone's mind — its job is to make the dynamic of biased assimilation visible and manipulable. Everything you see — both posteriors, both probability-on-truth curves, the clue at which the family crosses your threshold — is recomputed live from these formulas on every draw. This illustrates a reasoning dynamic; it is not a real diagnosis of servers, symptoms, or anything else.
the move ↔ the instrument
| The move | The instrument |
|---|---|
| a hypothesis | a candidate cause held on the table as an equal, before any clue is weighed. |
| the posterior | evidence-earned confidence — belief after every clue has been scored against every cause. |
| premature commitment | the committed mind's collapse to a leader: the intellectual child that then filters what it sees. |
| biased assimilation | the attachment term — reading each later clue to protect a favourite rather than to test it. |
| the commit threshold | when a family may honestly narrow: the confidence bar the evidence must clear before you marry a cause. |
| endless deferral | the ditherer — never letting a clue land, paying for evidence that is never allowed to decide. |
how this opening fails
risk · endless deferral
The catalogue's named risk for this move, and the honest opposite of premature commitment. Multiplying hypotheses feels virtuous, so it is easy to keep multiplying past the point of use — to treat "I am still holding all options open" as a mark of sophistication when it has become a refusal to let evidence do its work. The ditherer preset is this failure in numbers: the family mind's belief in the truth genuinely rises, yet with no threshold it never narrows and the clue counter runs on forever. Openness that will never close is not the method; it is the master risk the catalogue warns of. The cure is a threshold set in advance — a standing agreement about what confidence would be enough.
risk · the model is a simplification
Real biased assimilation is subtler and more various than a single dial that inflates one likelihood toward its best case. Attachment in a living mind reaches into which evidence is sought, which is remembered, how sources are credited, and how the hypothesis itself is redefined to survive — none of which this one parameter captures. The disclosed likelihoods, too, are a convenient fiction: few real clues carry so clean a probability under each cause. What the instrument gets right is structural, not numerical — that honest Bayesian updating converges on the truth, that a discounted disconfirmation can hold a wrong belief in place indefinitely, and that on one shared stream the only thing separating the two minds is attachment. Read it as a disciplined illustration of a dynamic, never as a verdict about a real case.
Hold several explanations as equals until the evidence, not your affection, thins them.
can you use it?
RECOGNITION — Which is multiple working hypotheses? A: forming one explanation and testing it hard. B: adopting a family of explanations at once so evidence, not attachment, decides. C: brainstorming causes, then committing to the favorite.
B. The move holds several live at once to keep loyalty on the inquiry rather than any one answer. A is single-hypothesis; C collapses the family early.
THE NEAREST NEIGHBOR — Competing-hypotheses analysis also holds several explanations. What does multiple working hypotheses stop short of?
The scoring matrix. Multiple working hypotheses keeps the family alive; competing-hypotheses analysis adds the evidence-by-hypothesis grid and the test of diagnosticity. One prevents premature attachment; the other formally ranks.
PRODUCTION — Your app's sign-ups fell this week. State three genuinely different hypotheses you'd hold at once — not three versions of one — before you look at any data.
A version: a broken sign-up flow; a seasonal dip; a competitor's launch. Yours works if no two collapse into the same fix — if they do, you're protecting one hypothesis in disguise.