↩ ExploRational · A Catalogue of Divergent Rationality
explorational · a divergent move
Why does setting a quota of ideas before judging any of them reliably produce a better final idea? Because the first five options are memory and the tenth begins to be invention — and, by Simonton's equal-odds rule, quality tracks quantity. The gain is not that later ideas are better; it is that more draws reach further into the tail, and the best of many is what you keep.
Deferred judgment is a schedule, not a mood. Osborn's rule for a brainstorm is not "be positive" — it is a hard separation of two operations that fight when they share a room: generate now, evaluate later. The instant you let evaluation into the generating room, it starts pruning, and pruning caps the count. And the count is the game, because you do not keep the average idea — you keep the best one. The quality of what you keep is the quality of the best of N draws, and the best of N climbs, relentlessly, with N.
Dean Keith Simonton found the reason hiding in the careers of composers, scientists, and poets. Within a body of work, the hit-rate per attempt is roughly constant — this is his equal-odds rule. The years that produced the masterpieces were not the years of higher inspiration; they were the years of higher output. More attempts, same odds, so more hits — and, further out, more of the rare tail. Killing ideas early does not raise your odds on the survivors. It just shrinks N, and shrinking N is how a good final idea fails to get generated. The instrument below is that whole argument, made of real random draws you can perturb.
the signature instrument
Each idea is a draw of quality from a distribution. Set a quota, and the decision keeps the best of the batch. Everything to the right is computed live from those draws: the expected best-of-N rising along the true extreme-value curve, hits growing linearly with attempts at a constant rate, effective N collapsing when ideas are near-copies, and the tries it takes to reach the top 1%. Drag a control to rerun the model.
Brainstorm to quota
quality ~ Normal · keep the best of the batch · draws are real
Expected best idea kept, as the quota grows. More draws reach further into the tail.
Hits above threshold grow linearly — constant slope = hit-rate. Quality per idea is not rising.
Best-of-N kept · E[max]
this draw's best —
Effective N · diversity
of a nominal —
Equal-odds · hit-rate
E[hits] —
Tries to reach top 1%
1 / P(top 1%)
Kill-after-k · best kept
penalty vs full N —
Slope of hits line
hits per attempt — constant
generation is not evaluation
The move opens the options dimension by multiplying, and its discipline is temporal: it forbids evaluation until generation is done. This is not politeness toward bad ideas. It is a defence of N. Evaluation, allowed in early, is a killing function — it removes candidates before the batch is complete — and every candidate it removes is a draw that never happened. Since what you finally keep is the maximum of the batch, and the maximum can only rise as the batch grows, anything that shrinks the batch lowers the ceiling on the answer.
Early ideas tend to be weak because the obvious ideas come first. The first five options are memory: the solutions you already carried into the room. The tenth and the fortieth are where the search has been pushed past habit into combination — the same reason the instrument's best-of-N curve is steepest early and keeps climbing. Set the quota above where you would naturally stop, and you are simply buying draws in the region where the good ones live. The quota is not motivational. It is a promise to keep sampling after the point where evaluation wanted to close the room.
what to try
Drag quota N from small to large and watch best-of-N climb the extreme-value curve — fast at first, then with diminishing but never-vanishing returns. The tenth draw buys you more tail than the fifth; the fortieth still buys some. This is the entire case for a quota, drawn live.
Now pull diversity down toward zero — the "ten copies" regime. The hit count barely changes, but effective N collapses and best-of-N goes flat. A big idea-count buys nothing, because near-copies never reach a part of the tail the others didn't already cover. Count is not coverage.
Set kill after k to 3, the "judged too early" preset. The amber marker shows best-of-3 sitting well below best-of-N: the idea you would have kept had you not stopped. Separating generation from evaluation is the difference between those two heights.
quality tracks quantity
Look at the right-hand chart: hits versus attempts is a straight line. Its slope is the hit-rate, and the slope does not steepen as you generate more. Idea number forty is, in expectation, exactly as good as idea number two. Nothing about generating in bulk makes any single idea better. This is Simonton's equal-odds rule stated as a picture: within a body of work, hits are proportional to attempts because the odds per attempt hold roughly constant.
The better final idea comes from the maximum. When you take many independent draws from a distribution, the largest of them drifts outward into the tail — that is extreme-value statistics, and it is the left-hand curve. A top-1% idea sits at the 99th percentile, so a single attempt lands there about one time in a hundred; to reach it you need on the order of a hundred tries — the instrument shows the number from its own draws. The equal-odds rule and the extreme-value curve are the same fact seen twice: quality tracks quantity, not because quantity refines each idea, but because quantity is the only thing that reaches the rare draw you were hoping for. That is why the sampling must run to quota before judgment closes it.
model
Each idea is a random draw of quality from a Normal(0, σ) distribution, with σ the spread control. Generating a quota of N ideas means taking N such draws; the decision keeps best-of-N, the maximum of the batch. The smooth left-hand curve is E[max of n draws], estimated by Monte-Carlo averaging over many seeded batches — an estimated extreme-value curve for this distribution. The dots and the realized best marker come from one actual seeded batch, which is why reseed jiggles them while the expected curve barely moves: one draw is noisy, the expectation is stable.
The hit threshold defines a "hit" as any idea above it; the hit-rate is P(quality > threshold), and expected hits = N × hit-rate — exactly linear in N, which is the equal-odds line. Diversity sets a correlation ρ among the draws: at full diversity the ideas are independent, and as diversity falls each idea becomes ρ-correlated with a shared component — draws bunch toward one number. Effective N is then defined honestly as the number of independent draws that would reach the same expected maximum as your N correlated ones; the instrument computes it by inverting the independent curve. Correlation leaves the expected hit-count almost untouched (each idea is still marginally as likely to clear the bar) while it flattens the maximum — the precise statistical shape of "ten options, one idea." Read the tiles as a disciplined model of sampling, not a promise about your next hour of work.
the move ↔ the model
| The move | The model |
|---|---|
| an idea | a single draw from a quality distribution — unbudgeted, allowed to be poor. |
| the quota N | how many draws you take, and so how far you sample into the tail before stopping. |
| best-of-N | the maximum of the batch — the one idea you actually keep and act on. |
| equal-odds | a constant hit-rate per attempt, so hits rise in proportion to attempts, not faster. |
| killing early | capping N at k — a lower maximum, and the tail you never reached. |
| low diversity | correlated draws that are near-copies, shrinking effective N far below the count. |
how this opening fails
risk · duplicates in disguise
The catalogue's named risk for this move, and the instrument makes it literal. Drop diversity and the idea-count stays high while effective N — and best-of-N — collapse, because near-identical draws never reach a part of the tail their siblings didn't already cover. A brainstorm that produces forty rephrasings of one idea has met its quota and gained nothing: count is not coverage. The quota only works if the draws are genuinely different; a diversity constraint is not decoration on the move, it is the condition that makes the move do anything at all.
risk · a regularity, not a promise
Simonton's rule is a statistical regularity read across long careers and large outputs — it says nothing reassuring about whether your next ten ideas contain a gem. Any single batch is a roll of the dice, which is exactly why the reseed button matters: watch how far the realized best wanders around its expectation. The model is honest about sampling, not clairvoyant. And the Normal draw is a convenience; real idea quality is messier and often heavier-tailed, which changes the numbers, though not the structural lesson — that the best of many reaches a tail the best of few never touches.
Set a quota before you judge; the best of many reaches a tail the best of few never touches.
can you use it?
RECOGNITION — Which is quantity before judgment? A: generating three careful, well-judged options. B: setting a quota — say twenty options — and forbidding all evaluation until it's met. C: judging each idea as it arrives, keeping the good ones.
B. Generation and evaluation are separated on a schedule, because the first few ideas are memory and the later ones begin to be invention. A judges as it goes; C interleaves the two.
THE NEAREST NEIGHBOR — Enumerating the combinations also produces many options. What separates quantity before judgment from it?
Method of generation. Quantity before judgment sets a free-form quota and defers evaluation; enumerating the combinations walks a structured parameter grid. One is about volume and timing, the other about systematic coverage.
PRODUCTION — You need a name for a team ritual. Set a quota of twelve and write the first six now — no judging, no deleting, however bad.
A version: standup, huddle, the ten-minute, sync, the check-in, campfire... Yours works if you hit the quota without crossing anything out — the rule is deferral, and an idea you paused to reject is evaluation smuggled in.