↩ ExploRational · A Catalogue of Divergent Rationality
explorational · a divergent move
Total freedom produces your habits; an arbitrary rule produces your surprises. Why does forbidding yourself something — the letter e, the easy chord, the obvious opening — reliably force paths you would never have chosen?
In 1969 Georges Perec published La Disparition, a full-length novel without the letter e — the most common letter in French. The ordinary sentences were unavailable; something else had to be found. The same wager runs through the sonnet, the twelve-bar blues, and Eno & Schmidt's Oblique Strategies deck: volunteer for an arbitrary rule, and the work comes back stranger than freedom gave.
The mechanism is arithmetic. Habit is a probability distribution over continuations: given where you are, a few next moves are enormously likely — your fingers already know them — and left free, you sample your own most-likely next move. A strict rule masks the high-probability options; renormalize what survives and you must draw from moves you almost never make. Whatever the mask spares is, by construction, un-habitual. The instrument below builds a real habit and lets you forbid things to it.
the signature instrument
A 27-state Markov chain — a–z plus the word boundary — learns its counts at load from the corpus below. Free, it writes 60-letter lines and scores each one's familiarity: mean log₂ probability per letter under the habit itself. Impose a rule and it regenerates from the same seed under the mask; the original habit scores the result. The displayed values are computed live.
The habit machine
—
novelty — habit lost
—familiarity drop under the original habit, bits per letteroff-map moves
—change in the share of 3-letter moves your corpus never once madedead ends
—attempts with no legal continuation lefthover the chart — or drag the severity slider — to read any point
The sweep isolates the severity mask: forbid the k most common letters of the corpus, letter choice and structural rules held off, fresh lines at every k. Left of the shaded band the mask is loose and output stays close to habit; right of it the chain dead-ends — states arrive with no legal continuation and the attempt dies mid-line. The band marks the computed peak of novelty × completion: the rule that costs the habit most while sentences still exist. Novelty is measured over surviving lines only — at the far right there are barely survivors to measure.
| k | letters forbidden | novelty bits/letter | dead-end rate | window score |
|---|
habit is a distribution
The chain has read one small corpus the way you have lived one life. After t it expects h; after th it wants e so badly that a third of what it writes smells of the. Sampled freely it produces well-worn nonsense, every move from the top of its own distribution — and its familiarity score sits at the chain's own average, because the free output is the average. Typical is the condition this move attacks.
That is working without a form. Ask for any opening and you get your usual opening; the likeliest continuations are likeliest in proportion to how often you have already made them. A rule cannot make you imaginative. It can make your habits illegal.
what to try
Forbid e. Bite: about 12% — that much of this habit's next-move mass runs through one vowel. Familiarity falls about 0.17 bits per letter, and it compounds: each 60-letter line lands near a thousand times less probable under the old habit. The panels share a seed — each masked line tracks its free twin until the first forbidden draw, then forks. Zero dead ends: strict, and livable.
Forbid z instead. Bite: 0.3%. Both readouts move by a hundredth or two — noise. The rule costs nothing, so it buys nothing; the habit almost never went there anyway. "No doubled letter" is nearly as toothless here, a 2% bite. A constraint only generates where it intersects what you would actually have done.
Tighten until the form kills the sentence. At severity 11 or 12, near 9 in 10 attempts dead-end mid-line; at 13 or 14 nothing survives. Survivors are spectacularly novel; a form nothing can live inside produces nothing. Vowel–consonant alternation stands at the window's edge: an 18% bite, honest novelty, a third of attempts dead.
the enabling window
The sweep makes the studio wisdom computable. Severity zero: an empty mask, your average output. Each added prohibition costs the habit more — novelty climbs — until the mask swallows whole rows of the transition table. Then severity buys corpses: dead ends run to 100% and the novelty curve simply ends. The productive middle — the shaded band, the computed peak of novelty × completion — is where the rule forbids much of what you would have done and leaves something you can still do.
Working forms live there: the sonnet fixes meter, rhyme, and length and leaves the whole lexicon; the twelve-bar form fixes the skeleton and frees every note. The bite readout is the entry condition: severity is the share of your probable moves a rule forbids, not how impressive the rule sounds. Forbid z and you have a costume; forbid e and you have a form.
model
The corpus below is lowercased, punctuation collapsed to word boundaries, and every adjacent pair of the 27 tokens counted: that table of counts is the habit, and P(next | current) is its row-normalization. A rule zeroes forbidden columns and renormalizes the remainder; generation walks the masked chain from a word boundary, 60 steps, seeded. Familiarity is the finished line's mean log₂ P per transition under the original chain; novelty is its drop from the free baseline. Off-map moves is the share of emitted 3-letter sequences occurring nowhere in the corpus. A dead end is a state whose whole row the mask erased; metrics average over survivors, and the panels disclose the body count.
Limits. Survivorship: at high severity the novelty number describes the rare lines that finished — read the pair of curves together. And the definition: novelty here is improbability under your own prior habit. Novelty is measured against your habits; this is also the boundary of the claim. The mask relocates output away from habit and adds no imagination: the within-batch spread of the lines actually falls slightly, a chain with fewer options repeating its remaining ones harder. The constraint subtracts habit; what it seems to add was in you already.
the corpus — the whole of this habit's life experience
—
the move ↔ the machine
| The machine | The move |
|---|---|
| the trained chain | your habits of continuation — given where you are, what you tend to do next, with frequencies. |
| free sampling | working without a form: every draw comes from the top of your own distribution, and the output is your average. |
| the mask | the rule that forbids the easy next move — the lipogram's missing letter, the banned chord, the closed opening. |
| the renormalized choice | the invention the rule forces: the probability has to go somewhere, so it flows into moves you almost never make. |
| the log-probability drop | how far off your beaten path the output now sits — departure from habit, priced in bits per letter. |
| the dead end | the rule so tight nothing can live inside it: a state arrives with every continuation forbidden, and the line dies. |
how this opening fails
risk · novelty for its own sake
The catalogue's named risk, stated by the metric itself: familiarity drop measures departure from habit — only that. A line a thousand times less probable under your prior can be a discovery or drivel: departure and quality are different axes, and the chain sees only the first. Perec's constraint handed him rooms no French novelist had entered; he still had to furnish them. The rule does the subtracting. Judgment still does the selecting — this move opens options; a converging move must close them.
risk · the rule that doesn't intersect the habit
Forbidding z is theater: a 0.3% bite, deltas indistinguishable from noise, lines that track their free twins almost verbatim. So is any rule adopted for its aesthetics — the fast that skips a food you never ate. The bite readout is the honest test: the share of moves you would actually have made that are now illegal. Near zero, the discipline is a costume. The rule must cost you something to give you something.
The rule subtracts your habits; what survives the subtraction is the surprise.
can you use it?
RECOGNITION — Which situation calls for the move? A: every draft you produce looks like your last five. B: as discipline, you give up a food you never eat anyway. C: two finished options are on the table and you must pick one.
A. Free sampling returns your own average; a rule that bites makes those habits illegal. B is the near-miss: a zero-bite rule — the fast that costs nothing gives nothing.
THE NEAREST NEIGHBOR — Random entry also knocks you off the beaten path. What separates the constraint from it?
Subtraction. A generative constraint only forbids — probability flows into moves you already had but never made, and it works only where it intersects your habits. Random entry adds a foreign stimulus.
PRODUCTION — Every pitch deck you write opens with the market-size chart, and the last three pitches have blurred together. Design one constraint before looking.
Forbid the habit itself: no charts before slide five, or the product may never be named on the first three. Yours works if the rule has real bite — it outlaws something you would actually have done — while leaving decks you can still finish.