Language between

Two eight-position rings exchange words and replies while their clocks turn at different rates.

What can pass between two systems

The lifetime of a usable distinction

A small exchange that can fail

What the score leaves out

Paper in a different clock

Results and use

What the clocks account for

Language between

The first experiment asks whether two systems can keep a useful relation to one moving light when they perceive, speak and act at different rates. One system observes a position and sends a token. The other interprets it and acts. Its answer comes back, and the first system can correct it. The light keeps moving throughout the exchange.

Language can model a world through exchange between systems. This study asks what such a shared model needs from its participants, their sensing and the material carrying their marks. It also asks what changes when a medium responds on a much slower timescale. The signalling game tests specific conditions for an instructed action; a separate paper room explores material traces without assuming that responsive matter uses language.

Open the interactive or read the registered predictions. The interactive is a single HTML page that runs without a network connection once saved.

What can pass between two systems

A common vocabulary does not establish a common relation to things. The same word can acquire different connections to experience for different users. A sender and receiver might preserve every mark while using those marks differently. They might agree about what a message described and still act too late. They might agree because both lack the distinction that would expose their mistake.

Those possibilities require separate measurements. Shannon's 1948 paper, introduction and §8, separates reliable message reproduction from semantic questions and permits transducers with internal memory. Its engineering boundary is useful here. We can measure what reached B without claiming that B understood it. We can then ask what B did with it. Meaning has not been disproved by excluding it from a transport measure; that measure simply does not settle it.

The token game supplies a deliberately small use for its marks: selecting one of eight positions. Wittgenstein's Philosophical Investigations, §§2 and 7, gives an equally particular starting place in the builders' calls and activities. But §23 widens the field to commands, conjectures, stories, jokes, greetings and prayers. A language can describe a world, and it can also ask a question, make a promise or refuse an undertaking. Calling all these operations models risks concealing the differences that make them work. Success at this game's instructed action cannot represent the success of every language use.

Flusser's Communicology places communication, codes and technical imagination within mediated relations among humans and the world. Here that makes the channel part of the question. A disappearing flash, a stored message and a chemical trace permit different relations across time. The reader of an old page meets a writer who cannot now receive an answer. The encounter still draws on learned uses, later responses and a material history. “Between” can extend across an interval much longer than a conversation, without implying that every individual utterance receives feedback.

The lifetime of a usable distinction

Equal frame rates are neither necessary nor sufficient for this game. Two observers can act every five ticks and remain badly out of date if messages take eighty ticks to arrive. A receiver ten times slower than its sender can work well when the relevant world state lasts long enough. A stored message gives the slow receiver something to encounter after the original event has passed. Memory and prediction can also bridge different rates, although this first experiment tests storage and correction, not an anticipatory world model.

The operative question is how long a distinction remains useful compared with how long its passage takes. That passage includes waiting for a sample, transmission, waiting for a reading, interpretation and action. There is also a spatial question: what distinctions can either observer make, and can the action express them? Matching clocks cannot repair incompatible observations. Matching observations cannot make old information current.

“Frame of reference” therefore needs two meanings kept apart. Here it concerns an observer's timing, partition of space and available history. These are engineering choices in an integer-tick simulation. It does not mean a relativistic inertial frame, and the simulation tests no claim about light-speed limits, spacetime geometry or nervous-system frame rates. Its useful comparison is between durations and changes relevant to a task.

This extends Monday's Margin: a response is useful only within the room an undertaking gives it to be late. It also changes the question from Pictorial form. That census asked whether a picture retained enough information to determine its own next state. Here two observers can use a picture together even though neither predicts the next independent world change. We test coordinated action with renewed observations, rather than autonomous closure of a picture's dynamics.

A small exchange that can fail

The world has eight positions. At each world change, a seeded generator chooses a position independently and uniformly. A sees on its own clock, maps its observation to one of eight tokens and sends it. B reads on another clock, looks up a position in its dictionary and acts there. B then echoes its chosen position with a message identifier. A returns one bit saying whether that choice fitted A's original observation. The identifier ties the correction to the earlier episode, rather than to wherever the light happens to be now.

B's repair consists of eliminating rejected interpretations and retaining accepted ones. It receives the token and the returned bit. A receives its sensor reading. Neither receives the auditor's exact world state. This matters: giving a learner the true position through a hidden training channel would make the display of negotiation misleading. The feedback path is an actual part of the simulation, with timing of its own. The noise control corrupts only forward word tokens; return echoes and verdicts are delayed but noise-free.

Measure	What is counted	What it cannot establish
Transport fidelity	Uncorrupted token messages among delivered token messages	That receiver and sender use a token alike
Reference accuracy	Actions matching the actual position when A sampled	That the action fits the present
Present success	Actions matching the actual position when B acts	General understanding, agreement or consent
Uptake	Actions per opportunity for B to read	Whether a taken-up message is useful

The registered runs use twelve seeds, 24,000 ticks each, scoring from tick 6,000 inclusive. They vary dictionary alignment, repair, clock ratios, delay, channel persistence and sensor resolution. Multiplying all durations by seven tests whether only event order and duration ratios matter. The prediction file fixes thresholds before results; failed predictions remain failures under those thresholds.

Coarse sensing merges adjacent positions. Its feedback accepts either member of the observed pair. A may consequently approve an answer that misses the exact light. Stephen Wolfram's Observer Theory, particularly “The Operation of Observers,” treats observation as identifying many outside states with fewer internal states. The bridge here is precise: the observer's partition determines which errors it can notice. Our finite result cannot validate his broader claims about physics or the ruliad.

Transmitting a compact account of a world depends on much that its users have already learned: distinctions, instruments, habits of comparison and the circumstances in which a description applies. This experiment isolates one difficulty in that dependence. A mapping learned through corrective exchange can preserve only distinctions the correction makes available. Agreement with a teacher is not independent evidence that either has described everything relevant.

What the score leaves out

Laugier's “Voice as Form of Life and Life Form”, pp. 69–73, complicates the premise of negotiation. In her reading of Wittgenstein and Cavell, agreement is in language and use; an inventory of negotiated conventions cannot explain all that already lets people negotiate. Bodily scale, senses and voice matter alongside social practice. Someone can be spoken for, or excluded, while appearing to consent. A pair of converging dictionaries gives us none of those assurances.

The model therefore begins with much already shared: eight possible actions, message identity, a task and the authority of a correction. It does not discover why either party should care about the light. The participant can alter the supplied terms, but the finite experiment still measures an objective chosen by its author. Refusing that objective need not be a communication failure. A reception record must preserve what a person wanted to do, including something the score cannot reward.

Kristeva's “The Impudence of Uttering” supplies a further objection to equating language with accurate reference. Her account treats utterance as embodied signifying practice, shaped by drives, sound, historical language and medium. Rhythm or repetition can alter an encounter even when no new location is transmitted. This toy's clocks can help us notice duration, but they do not model her psychoanalytic account. Naming a delay “affect” or calling noise “the semiotic” would add an interpretation without adding a mechanism.

Turing's “Computing Machinery and Intelligence”, §§1–2, makes the conditions of an encounter explicit by restricting the imitation game to written exchanges and excluding voice and appearance. Our interface also selects what can count as an answer. Behavior under that restriction is evidence about that behavior. It establishes neither consciousness nor an inner absence of it. And computation need not be an exchange of language: a program can continue calculating between messages, or finish a batch calculation without an answering interlocutor. This project studies a computational feedback arrangement; it cannot estimate how much of all computation has that form.

Paper in a different clock

Paper has a changing physical state. The Library of Congress conservation account describes moisture-dependent acid hydrolysis, the shortening of cellulose chains, and degradation products that can accelerate further change. An inscription also depends on a substrate whose future condition affects its readability. Treating the page as an entirely passive surface would miss these material consequences.

The paper room offers a separate, uncalibrated reaction–diffusion study. A deposited reagent spreads and dissipates while changing a persistent pigment variable. Reflecting boundaries keep diffusion inside the grid. The participant encounters different durations of exposure and traces that outlast the reagent. Its numerical checks concern nonnegative concentration, conservation when reaction and decay are disabled, and persistence after reagent removal. No rate predicts the life of an actual sheet, and pigment here is an illustrative variable rather than a model of cellulose chemistry.

The paper room lets a participant vary physical change and the scale at which a trace becomes perceptible. Responsive chemistry establishes a material exchange with consequences. Calling it reading or language would require an additional account of how distinctions are used, corrected or sustained; the animation supplies no such proof.

Results and use

All eight registered predictions held across twelve seeds per condition. The table below reports the pooled counts and their different denominators. Several predictions are structural consequences of the chosen protocol, including perfect delivery with zero corruption and the fixed rotated dictionary’s failure. They are checks on the proposed mechanism, not eight independent discoveries about language.

Condition	Delivered	Uncorrupted	Actions	Reference hits	Present hits	Reading opportunities	Fidelity	Reference	Present	Uptake
P1	43200	43200	30852	30852	27203	30852	100.000%	100.000%	88.173%	100.000%
P2	43200	43200	30852	0	501	30852	100.000%	0.000%	1.624%	100.000%
P3	43200	43200	30852	30852	27203	30852	100.000%	100.000%	88.173%	100.000%
P4	43212	43212	43212	43212	5429	43212	100.000%	100.000%	12.564%	100.000%
P5	54000	54000	5412	5412	5217	5412	100.000%	100.000%	96.397%	100.000%
P6_ephemeral	30864	30864	756	756	756	5268	100.000%	100.000%	100.000%	14.351%
P6_durable	30864	30864	5268	5268	5241	5268	100.000%	100.000%	99.487%	100.000%
P7_four	43200	43200	30852	13002	12967	30852	100.000%	42.143%	42.030%	100.000%
P7_eight	43200	43200	30852	30852	30762	30852	100.000%	100.000%	99.708%	100.000%
P8_scaled	43200	43200	30852	30852	27203	30852	100.000%	100.000%	88.173%	100.000%

P1 uses a shared dictionary. P2 rotates it; P3 adds correction. P4 matches the clocks but lengthens delay. P5 slows the receiver in a slow world. P6 compares fleeting and durable marks. P7 compares four and eight sensory bins. P8 multiplies every duration in P3 by seven. The predictions specify each condition and its threshold.

A fleeting mark reached a reading opportunity only 14.351% of the time, against 100% for a durable latest-message buffer. The fleeting condition scored 100% success among its 756 actions; the durable condition scored 99.487% among 5,268 actions. This is why success among actions must be reported alongside uptake: refusing or missing most opportunities can make a conditional accuracy score look excellent.

The four-bin result of 42.030% is a finite sample, not a new theoretical ceiling. With a world change only every 1,000 ticks, each seed contributes relatively few independent world draws; many action counts repeat the same position. Under a uniform world the sensor's two-to-one partition makes 50% the natural long-run exact-position baseline for choosing one fixed member. These runs do not estimate that limit precisely.

Twelve substantive checks passed, including the policy's information boundary, association of delayed feedback, independent world and noise streams, exact clock scaling, and reflecting diffusion. The completed computation establishes these outcomes for this code and schedule. Human reception, the emergence of an unprovided convention, and the paper-as-language question remain untested.

The browser version needs no account, network or model service. The Time field computes 120 additional finite runs with seed 3 and a shorter window, separate from the registered experiment. Click a cell to enter its timing. In Exchange, open Instruments to rename tokens or change B’s meanings; click the world or use arrow keys to move the light. In Paper, drag or press Space over the canvas to deposit reagent, then remove it to see what remains.

The subject is one moving light communicated through eight tokens. The consequence under investigation is whether a received instruction still supports an action after sensing, delay and interpretation. The rejected alternative is a synchronized animation with a fixed shared dictionary: it would display harmony by construction. The limit is a finite game whose task, common space and correction rule are supplied in advance.

The game, metrics, learner, predictions, paper model and philosophical bridges were selected for this study; the task and its standards did not emerge from the exchange. No human reception has been recorded. Showing the piece without explanation, then recording what someone noticed before and after an explanation, remains an empirical task separate from software validation.

What the clocks account for

The delay results can also be calculated from the schedule without running the exchange engine. This accounting was added after the registered runs; it changes neither their thresholds nor their outcomes. Let A sample every a ticks, B act at t, and one-way delivery take d ticks. The latest arrived sample was taken at:

s = a × floor((t − d) / a)
age = t − s = d + ((t − d) mod a).

There is no message at tick zero. Count an action only if the latest message is unread, with a positive sampling time; a fleeting message must also remain within its lifetime. Let q be the fraction of these actions with no new world draw between s and t. Let m be the chance that the fixed dictionary and sensor recover the sampled position. Then:

E[present success] = q × m + (1 − q) / 8.

A shared fine dictionary gives m = 1, a nonzero fixed rotation gives m = 0, and four bins with one fixed representative per pair give m = 1/2. After an independent world draw, any previous choice has chance 1/8. The ordinary shared-dictionary schedule predicts 88.1904% present success, against 88.1726% observed. The delayed equal clocks predict 12.5%, against 12.5636%. The slow-reader schedule predicts 96.3137%, against 96.3969%. Four hand-specified schedule cases and 24 count comparisons checked the independent enumeration.

The coarse sensor predicts 49.8687% present success, against 42.0297% in the selected seeds. Its reference actions reuse only 18 source-world draws per seed. Weighting those independent draws gives an ideal ensemble standard deviation of 3.4021 percentage points for pooled reference accuracy, rather than the much smaller uncertainty an incorrect independent-action count would imply. The observed reference score is 2.309 such deviations below its 50% expectation. It is not a universal 42% ceiling.

With a fixed fine alphabet, zero noise and correctly associated feedback, repair eliminates at most seven wrong candidates per word, 56 across the dictionary. That bounds productive dictionary changes, not elapsed time. A word never encountered or feedback never received supplies no progress guarantee. The supplied task, common space and meaning of correction remain outside this calculation.

Language between?

What can pass between two systems?

The lifetime of a usable distinction?

A small exchange that can fail?

What the score leaves out?

Paper in a different clock?

Results and use?

What the clocks account for?

Language between

What can pass between two systems

The lifetime of a usable distinction

A small exchange that can fail

What the score leaves out

Paper in a different clock

Results and use

What the clocks account for