Changing alphabet

Two binary drawing alphabets split a six-column compound into revised three-column fragments.

Encounter

Supplied rule and learned state

Results and correctness

Consequence, rejection and limit

Changing alphabet

Two drawing learners build different alphabets from a shared surface. A recurring fragment becomes a unit; a longer unit can contain two smaller ones. A further drawing can split a compound or change what its cue completes. The next drawing then changes because recognition uses the revised inventory.

The particular problem is a repeated six-column mark. Recurrence treats it as one unit. A corrective drawing puts a boundary through it and changes three lower cells while keeping the upper cue. This forces a distinction between a compact description and a usable notation. In the supplied example, the recurrence-only control uses two units but reconstructs only 30 of 36 hidden cells. The corrective learner uses four units and reconstructs all 36.

This extends Language between, whose eight meanings and message identifiers were supplied. Here the pixels, task and learning rule are supplied, but there is no registered dictionary of units or meanings. The example's four drawing fragments are curriculum material; arbitrary participant drawings pass through the same learner.

Encounter

Open the page. Step through eight encounters or run the example. Inspect each learner's actual active units and their encounter numbers. Try a new combination, then load a revision and show that drawing. Try the new combination again. The control keeps the earlier completion until recurrence supplies enough contrary evidence.

Edit any cell by tap, click, drag or keyboard (arrow keys move, Space toggles). Draw a boundary with the controls beneath the surface. To correct a learner, freeze A's current attempt, edit its lower rows and show the further drawing. Upper-cue changes are new evidence, not paired revisions to that cue. Unknown columns cannot ground a paired correction. Either learner can draw from its recognized units for the other to observe. Reset empties both histories. The replay slider rebuilds all four states from encounter zero; drawing at an earlier position branches the history. Saving downloads a local JSON event record.

Supplied rule and learned state

Each drawing is twelve columns of six binary cells. At learning time A sees columns 1–9 and B sees 4–12. Their first four encounters differ. At test time both receive the upper three rows across the whole surface; neither receives the hidden lower rows. This change from local training windows to a shared test cue is explicit. The evaluator alone holds the full target.

Each learner enumerates contiguous spans of two through six columns in its observed window. A span becomes active after two distinct encounters; repeating it twice within one drawing counts once. Recognition greedily chooses the longest matching upper-row cue, then corrected status, then encounter count, then the earliest local ID. An unmatched column remains unknown. No nearest-neighbour or neural inference is hidden behind the drawing.

A compound is an active unit exactly decomposable into two shorter active units. All overlapping candidates are retained; this is a deliberately small exhaustive inventory, not an optimal segmentation model. Fifty-four active units per learner follow the eight-example curriculum. IDs depend on encounter order and mean nothing across learners.

A correction carries the earlier attempt and a further drawing. Explicit boundaries retire cue patterns that crossed the marked seam in that encounter. Within the separated spans, cue-preserving fragments revise incompatible completions and become active immediately. Corrections therefore have a stronger update rule than recurrence. Boundary bans persist for the rest of that history; changing one's mind about a boundary requires replaying without that encounter or reset. Repeated corrections can revise lower rows back and forth without duplicating unit identities. Recognition never receives the target's lower rows.

The recurrence-only controls receive the same pixels, windows and encounters but ignore correction roles and boundaries. They eventually learn the new completion through frequency; their first-correction failure is not a permanent incapacity. Generated drawings count as encounters, so repeated exchanges can reinforce mistaken units. The page leaves that possible.

Results and correctness

All six registered predictions hold in the supplied deterministic curriculum. The table reports counts and denominators. These are mechanism checks under a selected example, not six independent empirical discoveries.

Probe	Corrective A / B	Recurrence A / B
Novel arrangement before correction	36 / 36 hidden cells each; 4 tokens	36 / 36 each; 4 tokens
Novel revised arrangement after one correction	36 / 36 each; 4 tokens	33 / 36 each; 4 tokens
Repeated revised drawing after one correction	36 / 36 each; 4 tokens	30 / 36 each; 2 tokens
Novel revised arrangement, correction omitted	33 / 36 each; 4 tokens	33 / 36 each; 4 tokens

The tests additionally reconstruct all 24 permutations of the four original fragments, for both learners, without having seen those full drawings. The bounded standard is exact hidden-cell reconstruction: unknowns count as wrong. Coverage and exact-drawing success accompany cell counts. Tokens per drawing are reported separately; inventory size, bit coding, boundary messages and correction cost are excluded, so this is not a compression-rate result.

Consequence, rejection and limit

The consequence is local: revision of learned units can change what the learner draws in a new arrangement. The rejected alternative is to call a shorter description successful notation without naming what a reader must do with it. The limit is equally local: this task supplies pixels, contiguity, the upper/lower split, recurrence thresholds, a greedy recognizer and an explicit correction channel. A participant may invent marks or refuse the reconstruction task, but the engine cannot invent a new objective. No human reception, language understanding, robust freehand perception or emergence of goals is established.

The optional omission replay holds later recorded drawings fixed. It shows the downstream effect on the learner's state and current answer, not how another participant would have responded in a different conversation. A future study would need unseen participant drawings, independently judged uses, competing boundary hypotheses and a less stipulated correction channel.

Changing alphabet?

Encounter?

Supplied rule and learned state?

Results and correctness?

Consequence, rejection and limit?

Changing alphabet

Encounter

Supplied rule and learned state

Results and correctness

Consequence, rejection and limit