Abstract
Information-theoretic approaches to language often ask how much redundancy a linguistic system contains and whether that redundancy helps speakers, listeners, and learners. The question presupposes that analysts already know what the necessary information is, so that whatever exceeds it can be counted as surplus. This article argues that the presupposition inverts the actual problem of human communication. Living speech is puzzling because it contains astonishingly little rather than too much: symbolic articulation captures only a minute fraction of what participants perceive, feel, anticipate, and coordinate. Language works because it never works alone. Symbolisation operates within multisensorial embodiment, being-with, multiversal dwelling, and multimateriality, and wherever other persons are involved it operates interrecursively, with each participant's responses entering into the production of the other's next move. Starting from an artificial-language experiment on redundancy and grammatical generalisation, and from the noisy-channel model inherited from Claude Shannon, the article develops the concepts of criterion-relative redundancy, constitutive underspecification, compensatory verbosity, mesocosmic attribution, and recursive sufficiency. It argues that redundancy is a legitimate property of a specified code but not an elementary property of living communication, and that the central question for a theory of communication is how living beings coordinate when symbols carry so little of the worlds they share.
I. What even is “redundancy” in communication?
In a familiar kind of laboratory study, participants learn an artificial language presented as the language of an alien species. They see pictures of unfamiliar creatures and objects, hear novel words, and are later asked to name what they have seen. In one version of the language, a grammatical category such as noun class is marked once. In another, the same category is marked repeatedly, on the noun and again on an accompanying word such as a numeral, so that learners are reminded of the class every time an entity is mentioned. The experimental question is whether this repetition, described as redundancy, makes the language easier or harder to learn. In one such study the answer depended on age. Adults performed much the same whether or not the marking was repeated. Children performed worse with redundant marking when naming familiar items, but better when asked to extend the grammatical category to entities they had not encountered before, which is the moment at which language learning most clearly exceeds memorisation.
At first sight the question looks straightforward. If a distinction is marked several times, the learner receives more cues, and whether those cues help can be measured. Yet the concept of redundancy already carries a consequential assumption: that the analyst knows what the necessary information is and can therefore identify whatever exceeds it as surplus. A redundant marker is one that could have been omitted without loss, and the phrase without loss requires an account of what would count as losing something.
This article begins from a reversal of that starting point. In living communication, the basic difficulty is almost never that too much information has been encoded; the difficulty runs the other way. Symbolic articulation captures only a minuscule fraction of what participants perceive, feel, anticipate, and coordinate. A person could spend an entire day trying to describe a single moment of multisensorial bodily experience, the pressure of the floor, the temperature of the air, a faint tension in the jaw, the smell of the room, the angle of the light, the half-noticed rhythm of breathing, and still fail to exhaust it. Even an elaborate conversational utterance leaves unspecified almost everything about the situation in which it is used.
The puzzle worth explaining is therefore the reverse of the one that the concept of redundancy poses. The question is not why language contains information that could have been omitted but how such radically impoverished symbolic traces can suffice for living coordination at all.
The answer defended here is that language works because it does not work alone. Symbolisation is one of five mediations through which living beings coordinate: multisensorial embodiment, being-with, multiversal dwelling, multimateriality, and multisymbolization. These mediations are always co-present, with only their salience shifting. Human communication is therefore multimediated, and wherever other persons are involved it is interrecursive: each participant's responses enter into the production of the other's subsequent activity. Once these two facts are recognised, redundancy ceases to be an adequate foundational concept for understanding communication. It remains a useful technical notion within specified codes, while failing as a description of what speakers and listeners are doing when they talk.
II. What redundancy quietly assumes
The technical concept deserves to be granted its legitimate domain. Within a formally specified coding system, redundancy is perfectly meaningful. If the set of possible messages is fixed, if the probabilities of those messages are known, and if the criterion for successful transmission is defined in advance, one can calculate how much information a signal must carry and how much of what it actually carries is duplication or predictable pattern. Error-correcting codes rely on precisely this calculation. A check digit on a bank card, a parity bit in a stored file, and the repetition of a call sign over a crackling radio link all add redundancy deliberately, because the criterion of success is exact recovery of a prespecified string.
The difficulty begins when this operation is carried over into human communication as though the same prior specifications were already in place. To call something redundant requires an answer to a prior question: redundant relative to what? Consider cute little puppy, one of the phrases through which information-theoretic analyses of adjective use have been introduced (Dye et al. 2017). If puppy already means a young dog, little seems to add nothing that the noun has not supplied. Yet the additional words may do affective, rhythmic, interpersonal, and pragmatic work. They may convey tenderness, invite shared attention, slow the pace of an exchange, signal the speaker's stance toward the animal and toward the hearer, or help a young child pick out which creature is being talked about. The adjectives are redundant only relative to the task of identifying the referent's category.
Repetition shows the same pattern with greater clarity. Compare I know with I know, I know; yes with yes, yes; be careful with please, please be careful. In each pair the propositional content scarcely changes, while the living relation changes a great deal. I know, I know can mean that the hearer should stop, that the speaker is already overwhelmed, that the point has been conceded without being welcomed, or that affection is being offered in the form of mild exasperation. Please, please be careful, spoken to someone leaving for a dangerous journey, does something that be careful alone cannot do: it makes the speaker's fear available to the person addressed, and in doing so it places a small obligation on them to carry that fear with them.
These cases support a first conceptual clarification, which can be called criterion-relative redundancy. Something can be identified as redundant only once an analyst has stipulated what counts as successful communication. In most linguistic applications the stipulated criterion is propositional recoverability: an element is redundant if the proposition could have been recovered without it. That criterion is rarely stated because it seems obvious. Actual communication, however, carries many stakes at once: reassurance, intimidation, recognition, bonding, the management of attention, the coordination of joint action, the maintenance of politeness, the establishment of intimacy, the signalling of impatience, or simply keeping contact alive. An element that is redundant relative to propositional recovery may be the part of the utterance that carries the stake that matters most to the people involved.
Redundancy is therefore never a neutral description of an utterance. It encodes a prior decision about what the utterance is for, and that decision is made by the analyst rather than found in the exchange. None of this renders redundancy analysis worthless. A corpus study showing that speakers systematically include an optional word where the following structure would otherwise be unexpected reveals something real about how articulation is paced. What it reveals, however, concerns one dimension of a multimediated activity, measured against one criterion, and the finding should not be read as a discovery about what communication fundamentally is.
This yields the first major claim of the article: redundancy is a valid technical property of a specified code, but it is not an elementary property of living communication. It becomes available as a measure only after a great deal of the living situation has been set aside, and the setting aside is itself a theoretical act that needs to be made visible.
III. Shannon's abstraction and its illegitimate expansion
Claude Shannon's 1948 paper on the mathematical theory of communication is often caricatured by its critics, and the caricature weakens the critique. Shannon stated plainly that the semantic aspects of communication were irrelevant to the engineering problem he was addressing (Shannon 1948). His achievement was to model the transmission of signals through a channel of limited capacity under conditions of noise, and to show how coding could make transmission reliable at rates approaching that capacity. For telecommunications, and later for computation and data storage, the abstraction was extraordinarily powerful. Warren Weaver's introduction to the 1949 book edition moved in the other direction, distinguishing the technical problem of transmission from a semantic problem of meaning and an effectiveness problem concerning how received meaning affects conduct, while suggesting that the mathematical theory might illuminate all three (Weaver 1949). The expansion began early and was invited from within.
The difficulty arises when the architecture of source, encoder, channel, decoder, and destination migrates into linguistics, psychology, and social theory as an implicit ontology of communication. In that architecture a message exists before transmission, a signal carries it, noise threatens it, and success consists in the arrival at the destination of what left the source. The destination receives the message without participating in forming it.
Ordinary conversation has a different shape. When I speak with another person, I continually modify what I say according to how I perceive them receiving it, and their reception alters what I produce next. A puzzled expression prompts reformulation. A nod permits acceleration. An interruption redirects the trajectory of a sentence already under way. A hesitation may invite elaboration, or may signal that elaboration would be unwelcome. A joke changes the tone of what follows because the listener does not laugh. In each case the supposed receiver enters recursively into the production of the message itself, and does so while the message is still being formed.
This is interrecursivity: a relation between living counterparts in which each participant's activity responds to the other's responses, so that neither participant's next move is fixed by their own history alone. The difference from transmission is fundamental. In transmission, uncertainty concerns whether a message arrives intact. In interrecursive communication, uncertainty also arises because the participants continuously alter one another's subsequent activity, and what counts as the message is itself being jointly produced. Noise is only one source of uncertainty in such a situation, and often not the most important.
A qualification must be made at once. Mathematical models can represent aspects of interrecursive situations. Game theory, models of turn-taking, and computational accounts of pragmatic reasoning all formalise patterns in which one agent's action depends on expectations about another's. The argument here therefore makes no claim that interrecursivity is mathematically indescribable; its claim is that a mathematical representation of an interrecursive process should not be confused with the living process it represents. A model can capture regularities in how conversational partners respond to one another while leaving untouched the fact that each partner is actually responding, discerning, and changing course.
Shannon's framework works beautifully when participants can be treated, for the purposes of analysis, as nonrecursive endpoints: as devices that emit and absorb signals without the reception reshaping the emission. The extension to human communication fails when this simplification is forgotten and the endpoints are taken to be what persons are. Information transmission concerns the reliable movement of a signal. Interrecursive communication concerns the mutual, recursive coordination of living counterparts, and the reliable movement of signals is at most one of its conditions.
There is an empirical irony in the way such models are usually taught. A lecturer explaining the noisy-channel model to a room of students succeeds by constantly reading the audience: pausing where faces cloud over, repeating a point that did not land, answering questions, inviting the audience to guess before revealing an answer, reformulating, and adjusting pace to the energy of the room. The teaching of a transmission model works because the lecturer does not communicate like a transmission channel. Had the lecture been delivered at maximal information density, with every predictable element stripped out and no attention paid to reception, it would have transmitted its content with perfect efficiency to almost nobody.
IV. The radical underspecification of language
Take a small utterance: She is coming. The words do not specify how certain the speaker is, whether the arrival is welcome or feared, or whether the statement is a report, a warning, a promise, a reminder, a joke, or a threat. They do not say how the speaker knows, or whether coming means now, later today, next week, metaphorically, or only if some condition is met. They leave unspecified whether the speaker approves, and what relation holds among speaker, hearer, and the person referred to. A child whispering it to a sibling as a parent's footsteps sound on the stairs, a nurse saying it to a waiting family, a friend saying it with a raised eyebrow about an ex-partner who has accepted an invitation, and singers of a Bengali agamani song welcoming the goddess Uma on her annual return to her mother's house are using the same few words to do almost entirely different things. Yet in each of these situations the exchange can proceed without difficulty.
The reason is that interlocutors never receive words in isolation. What reaches them is a symbolic articulation embedded in a situation they already share, perceived by bodies already oriented toward one another, within a history of prior encounters and a material arrangement that makes some readings obvious and others absurd. Symbolic articulation always leaves enormous amounts of living reality unspecified, and this symbolic underdetermination is the normal condition of language rather than an occasional defect.
The point extends to the kind of operation a symbol performs. Living Value Theory distinguishes three symbolic modes. In coordination mode, a symbol participates directly in the situation it names, as a warning does. In reference-to-absence mode, it makes something not presently available matter to current coordination, as a report does. In re-presentation mode, it claims to make present again what is absent, lost, imagined, or never directly encountered, as ritual and art do. She is coming can operate in any of these modes. The whisper on the stairs is coordination; the nurse's statement refers to an absent person; the agamani song re-presents an arrival that no singer has witnessed in the ordinary sense. Ordinary language very often contains no lexical marker identifying which mode is active. Speakers discern it through situation, history, prosody, embodiment, and the ongoing responsiveness of their counterparts. If the mode had to be encoded, most utterances would need a prefix that no human language supplies.
Multisensorial embodiment provides the extreme case of underspecification. A single bodily moment includes temperature, muscular tension, pain or its absence, balance, proprioception, hunger, fatigue, posture, breathing, smell, visual orientation, affective tone, and a vast number of simultaneous processes that never become separately salient. Most of this proceeds at L1, as coordination that continues without becoming an object of attention. Some of it becomes salient at L2 as a felt disturbance, pull, or unease, a questionability that does not yet contain a question. Only a small part is ever articulated at L3. No finite description exhausts such a moment. Even a tremendously verbose description remains an impoverished symbolic trace: it selects, orders, and names, and in doing so leaves most of what it describes where it was.
This yields the article's central inversion. What requires explanation is not the presence of redundant language but the possibility of successful communication despite overwhelming symbolic insufficiency. Measured against what participants live through together, every utterance is drastically short of information. The question of whether a particular marker duplicates another concerns a small ripple on the surface of a very deep sparseness.
The condition can be named constitutive underspecification. Language works through context dependence rather than in spite of it, and the underspecification is constitutive because communication would become impossible without it. If every relevant aspect of experience had to be explicitly encoded before coordination could proceed, no one could finish a sentence, since the specification required by any sentence would itself require further specification without end. Speakers can say little because a great deal is already being held in common by other means, and the sparseness of the symbolic trace is the form in which that common holding shows up in language.
V. Multimediation carries the missing load
Consider the instruction Put it over there. As an abstract linguistic string it is spectacularly impoverished. It could refer to anything. There could be anywhere. No method of moving the thing is specified, no reason is given, and no deadline appears. Yet two people standing in a kitchen, one holding a hot pan and the other clearing space on a counter, may understand the instruction instantly and act on it within a second.
They can do so because they see the same object, stand within the same material arrangement, and are oriented bodily toward one another. One of them glances or points. Both know what task they are undertaking. They share a history of cooking together, or at least of kitchens, and each anticipates the other's next movement. The heat of the pan, its weight, the free patch of counter, and the direction of the speaker's gaze together settle what the words leave open. The symbolic burden can remain tiny because the other mediations are carrying almost everything.
Each mediation contributes distinctively. Multisensorial embodiment supplies orientation, affect, proprioception, gaze, gesture, timing, and the bodily recognition that someone is under strain or at ease. Being-with supplies histories of mutual knowledge, expectation, intimacy, deference, and recognition: the sense of what this person usually means, what they will tolerate, and what they have already understood. Multiversal dwelling supplies the conditions that no one made: gravity, which turns a hot pan held at arm's length into a matter of urgency; daylight or darkness; the carrying of sound through air and across distance, which determines whether a word needs to be raised or repeated; the time of day with its metabolic rhythms of hunger and fatigue. Multimateriality supplies the built and made world: the counter, the pan, the stove, the arrangement of a room whose layout already proposes where things go, and the material deposits of earlier activity that make one place the obvious place. Multisymbolization supplies, beyond the utterance itself, the sedimented forms that make some interpretations expectable: customs of household order, the conventions of a recipe, the institutional expectations that frame a professional kitchen differently from a domestic one.
Symbolisation, in the narrower sense of the utterance, selectively articulates within this already organised field. This yields perhaps the article's strongest proposition: symbolisation does not carry the entire informational load of human coordination, because most of the coordination is already being accomplished through other mediations. The words mark a small number of points at which the shared field needs adjustment, and they can do so economically because the rest of the field is not in question.
It would be too simple, however, to treat symbols as mere remainders, as whatever is left over once the other mediations have done their work. A single word can reorganise all the other mediations at once. Stop can freeze a body mid-movement; fire can empty a building; a name spoken across a room can turn an entire orientation of attention. Symbols have a distinctive capacity to redirect coordination across mediations and to make absent things matter to present action. What symbolisation never becomes, in living communication, is an autonomous channel containing everything required for coordination. Its power lies in how little it needs to specify, given everything else that is in play.
This account explains a phenomenon that looks paradoxical from within information theory, which may be called compensatory verbosity. When symbolisation is separated from the multimediated situation in which it would ordinarily operate, it must be expanded to do work that the other mediations previously did. Legal documents become elaborate because they are written to function among parties who may share neither a situation, a history, nor goodwill, and who may later read the text adversarially; everything a shared kitchen would have settled must be stated. Written instructions must specify what joint activity would leave tacit, which is why assembly manuals number their steps and still fail. Text messaging develops emoji, conventions of punctuation, lengthened vowels, and repeated letters partly because gaze, gesture, and prosody are absent, and something must carry the tone that a voice would have carried without effort. A full stop at the end of a short text can read as coldness precisely because the medium has stripped away the channels through which warmth would ordinarily travel.
The apparent informational richness of language, as it appears in written corpora, dictionaries, and laboratory stimuli, is therefore partly an artefact of isolating symbolisation from the multimediated processes that make it usable. Written language is language forced to compensate for the absence of the situation. When analysts take written text as the paradigm and then ask how much of it is redundant, they are measuring a form that has already been inflated to survive decontextualisation, and treating that inflation as the baseline of language itself.
VI. The alien language experiment is not alien enough
The artificial-language experiment can now be revisited in a different light. Participants are told that they are learning an alien language. They encounter novel words, novel grammatical markers, and pictures of unfamiliar creatures and objects. The experimental manipulation concerns symbolic novelty: the words and the markers are new, and the question is how the pattern of marking affects learning.
The underlying world, however, is far from radically novel, since the images remain recognisable at the scale of human perception and action. One figure has a face, limbs, and a posture that suggests it could move of its own accord; another has the look of an artefact or an inert thing. A participant brings to the task an enormous prior competence for distinguishing beings that move and respond from things that merely lie where they are placed. The alien grammar attaches unfamiliar markers to distinctions whose basis is already deeply familiar. Participants are therefore learning new symbolic allocations across an already intelligible world rather than learning an alien world.
The competence at work here can be called mesocosmic attribution: the attribution to an encountered entity of a position within the human-scale world of lived coordination. It includes recursive attribution, the discernment of whether a counterpart is nonrecursive like a stone, selfrecursive like a growing plant, or interrecursive like an animal that watches back, and it extends to further distinctions such as bounded and unbounded, individual and collective, living and dead. Classifying something as animate or inanimate is less the assignment of a linguistic feature than an attribution concerning what kind of entity one is facing and what kind of coordination it will permit. Such attributions are made long before, and far beneath, any grammar: an infant responds differently to a barking dog and a falling box. The grammatical category in the experiment can ride upon this far more basic multimediated recognition.
This alters the interpretation of the findings considerably. The question the experiment poses is whether linguistic redundancy helps people learn grammatical categories. The question it actually addresses is how repeated symbolic markings interact with mesocosmic distinctions that learners already possess. The children's improved generalisation to novel entities under redundant marking may reflect the repeated marker helping them bind a new sign to an attribution they were already making, without showing that redundancy helped them discover a category. Their poorer performance on familiar items under the same condition may reflect the burden of producing more symbolic material for distinctions that were already secure. Neither interpretation can be tested within the design, because the design holds the mesocosmic distinctions constant while treating them as background.
The experiment therefore quietly relies on exactly what its linguistic framing excludes. The visual entities, the participants' bodily perception, their familiar ontological categories, the setting of the laboratory with its instructions and its turn-taking with an experimenter, and the long history of their own language learning all perform enormous preparatory work. The symbolic system can be small precisely because so much of the task is already done. This is the pattern observed in the kitchen, a sparse symbolic trace operating within a richly organised field, except that here the field has been rendered invisible by the design and the credit has been assigned to the symbols.
A truly alien experiment would have to invent an unfamiliar ontology as well as an unfamiliar language. Its participants would encounter entities that resisted the distinctions between animate and inanimate, agent and object, individual and collective, inside and outside, bounded and unbounded, living and dead, tool and organism. Imagine an entity that sometimes moved of its own accord and sometimes only when pushed, whose parts separated and recombined, whose inside and outside could not be told apart by looking, and whose response to the participant's actions was intermittent and unpredictable. Participants would have to discover which distinctions the world itself afforded as well as which word applied. Such an experiment would investigate whether language can help constitute novel mesocosmic categories rather than merely map new signs onto familiar ones. It would be very difficult to run, and the difficulty is instructive, because it shows how far ordinary experimental designs depend on a world that is not in question.
The methodological point can be put sharply. The experiment novelises the symbols while keeping the world largely familiar, then disproportionately attributes successful learning to properties of the symbols. This is a specific instance of a wider tendency in which symbolic performance is measured as though symbols operated alone, and whatever the other mediations contribute is absorbed silently into the baseline. The finding about children remains interesting. Its interest lies in what it shows about the interaction between symbolic repetition and mesocosmic attribution in young learners, a question that the redundancy framing makes difficult to ask.
VII. Interrecursivity, timing, and recursive sufficiency
There is no context-independent optimal amount of linguistic information, because the appropriate amount depends on the counterpart. A child may require repetition that an expert experiences as tedious. A distracted listener requires slowing; a close friend may understand half a sentence and finish it; a stranger may require extensive explanation of what an intimate would take for granted. A noisy room changes what must be repeated, and a grieving listener changes what can be said at all. What counts as enough is recursively adjusted, moment by moment, in response to how the counterpart is taking what has already been said.
This can be called recursive sufficiency. The concept asks what degree and form of symbolic articulation is sufficient for this coordination, with this counterpart, at this moment. It improves on the notion of optimal redundancy because it places the criterion inside the living interaction rather than treating information density as a quantity to be optimised in general. Information-theoretic work on the pacing of speech has shown that speakers tend to spread information evenly, inserting optional material where what follows would otherwise be unexpected. A well-known study of recorded telephone conversations found that speakers are more likely to include the optional complementiser that after verbs rarely followed by a clause than after verbs that very often are, as if signalling in advance a structure the listener would not anticipate (Jaeger 2010). Recursive sufficiency accommodates this finding while locating it differently: the speaker adjusts to a counterpart, and what the corpus registers is the statistical shadow of countless such adjustments, each made to someone in particular.
Timing is crucial here, and information measures are largely blind to it. The same content delivered five times faster is not communicatively equivalent. Interlocutors need time to perceive, interpret, anticipate, reconsider, and respond, and the tempo of an exchange is itself a medium of coordination. Pauses, hesitations, repetitions, and reformulations are what interrecursive coordination looks like as it happens. What appears inefficient from the standpoint of signal transmission can be necessary for two living beings to keep pace with one another. Cross-linguistic research on turn-taking shows that the gaps between turns cluster within a few hundred milliseconds across very different languages, with systematic local variation (Stivers et al. 2009). Within that narrow band, a delay of half a second can register as reluctance, disagreement, or hurt. A silence can be louder than a sentence because the counterpart is waiting for it to be filled.
Interruption shows the same dependence on the living relation. Overlapping speech may signify aggression, enthusiasm, comprehension, intimacy, or a culturally normal style of turn-taking. In what Deborah Tannen called high-involvement conversational styles, overlap functions as a display of engagement, and a speaker who waits politely for a gap may be heard as distant (Tannen 1984). The same acoustic event, two voices at once, can be an attempt to seize the floor or a sign that the listener already knows where the sentence is going and is eager to arrive there together. Someone who habitually finishes other people's sentences may be experienced as unbearable by one partner and as deeply attentive by another. The acoustic phenomenon does not contain its social meaning, which participants discern recursively through the relationship and the situation, revising that discernment as the exchange continues.
Communication therefore cannot be reconstructed from formal signals alone. The formal signal is the residue of an interrecursive process in which each participant was continually recalibrating what the other needed, and a record of the signal preserves the output of that recalibration without preserving the recalibrating.
VIII. Prediction is not one thing
Information-theoretic accounts of language place great weight on prediction: redundancy is said to help listeners predict what is coming next, and speakers are said to manage the predictability of their own output. The word prediction, however, conceals radically different processes. Predicting where a falling object will land differs from anticipating how someone will finish a sentence. Anticipating a grammatical category differs from anticipating an opponent's punch. Treating these as instances of a single operation, the estimation of a probability distribution over future states, obscures the differences that matter most.
The differences become clearer when organised according to the three types of recursive counterparts. With a nonrecursive counterpart, anticipation can rest on stable regularities. A table stays where it is; a stone falls according to gravity; a thrown ball follows a trajectory that does not change because it has been observed. Here prediction is limited by complexity and by the precision of measurement, and more information does in principle yield better prediction. With a selfrecursive counterpart, such as a climbing plant finding its way toward light, present activity depends on the counterpart's own histories and adjustments, and anticipation must follow a process that is continually modifying itself, though not in response to being anticipated. With an interrecursive counterpart, each participant's anticipations enter into the activity of the other. I anticipate you, you anticipate my anticipation, and either of us may act precisely to defeat the other's expectation. The future here is jointly generated rather than merely unknown.
This is why interrecursivity is ontologically distinct from complexity. A complex situation contains many variables, and in principle a sufficiently informed observer could model it. An interrecursive situation contains counterparts who make up their own minds in response to one another, and whose responsiveness includes the capacity to respond to any model of themselves that becomes available to them. Formal accounts of pragmatic reasoning, such as the rational speech act framework, represent a listener reasoning about a speaker who reasons about a listener, and such models are typically truncated after a small number of levels (Frank and Goodman 2012). The truncation is a practical necessity, and it is also a sign that the recursion involved does not close in the way a physical regularity does.
Martial arts make the point with particular clarity, because anticipation is the very substance of the practice. A skilled fighter may anticipate an attack from posture, breathing, balance, a shift of weight, distance, and rhythm, without calculating anything. The opponent, meanwhile, is doing the same, and is also presenting misleading cues, feinting, and varying rhythm so that anticipation is punished. Much of the skill is embodied and acquired only through years of practice against responsive partners. It can be coached in words, and coaching matters, but no amount of verbal description can substitute for learning how to fight, in the same way that no verbal specification could teach an infant to walk. Put the right foot forward, shift the weight, resist the pull of gravity is a description a walker could recognise and a learner could not use.
The claim can now be stated precisely. Mathematical models may describe regularities in embodied anticipation, but the anticipatory competence itself is not constituted by the mathematical model. This guards against an unnecessary opposition to mathematics. What is at issue is whether modelling the patterns of interrecursive behaviour exhausts the ontology of what participants are doing, rather than whether such patterns exist, which they plainly do, some of them modelled with great success. A fighter who wins has not computed the model's output. A fighter who loses may have been predictable in exactly the way the model describes, and the opponent's success lay in discerning that predictability first, live, in the body, faster than any articulation could have supplied it.
IX. Institutions and interrecursive uncertainty
Institutions can be understood as technologies for reducing interrecursive uncertainty. They constrain what participants may do and when. A lecture regulates who speaks and for how long. A court imposes turn-taking, rules of evidence, and procedures for bringing testimony to a close. A job interview restricts the questions that may be asked and shapes the answers that can be given. A martial arts bout imposes rules on an antagonistic interaction, forbidding some techniques, scoring others, and stopping the contest when a threshold is crossed. In each case the institution makes human action more expectable among people who could not otherwise rely on one another's responses.
None of these institutions transforms interrecursive persons into nonrecursive devices. A lecture constrains what a student can do without determining the student's next question. A court structures testimony, yet no procedure can derive in advance every answer a witness will give, and cross-examination exists precisely because answers can surprise. A bout's rules narrow the space of moves without telling either fighter what the other will do within it. Institutionalisation is best understood as the partial stabilisation of interrecursive uncertainty rather than its elimination: a set of multisymbolic and multimaterial anchors that make some coordination among responsive persons expectable enough to continue.
This reinforces the distinction drawn in the previous section. If the problem institutions addressed were simply that social situations contain too many variables, better information would eventually make institutions unnecessary. Participants themselves recursively alter the situation in response to one another, and institutions exist because this alteration can be channelled but never abolished. The formality of a courtroom, the choreography of a lecture, and the ceremony of a bout all testify to the persistence of what they constrain. Even the most rigidly scripted institutional exchange remains an interrecursive encounter in which a participant may, at any moment, say something no one expected.
Conclusion: From information transfer to living coordination
The concept of redundancy seemed at first to identify something straightforward: duplicated information, markers that could be removed without loss. The analysis has shown that this judgement is downstream of a much larger abstraction. Before redundancy can be measured, an analyst must identify a message, specify what counts as its successful transmission, isolate symbolic form from its multimediated context, treat participants sufficiently like sender and receiver, and set aside much of the interrecursive process through which the utterance itself developed. Each of these moves is legitimate for a particular purpose. Taken together and forgotten, they convert a limited analytical description into what looks like a fundamental feature of human communication.
Once those moves are made visible, the major inversion can be restated. Human language is remarkably sparse rather than remarkably redundant. Its sparseness is possible because living beings coordinate through far more than language. The symbolic trace can remain radically incomplete because bodies, other persons, the unmade conditions of the world, the made world of objects and arrangements, and the sedimented deposits of earlier symbolisation are already carrying most of the work. Redundancy, where it appears, is a local and criterion-relative phenomenon within this sparseness, and its most interesting instances, from the doubled please to the repeated noun-class marker, turn out to be doing something other than duplicating information.
The consequences extend beyond linguistics. Theories that treat communication as the transfer of richly specified representations between isolated minds will systematically overvalue what can be written down and undervalue what must be lived through together. They will read written text as the paradigm of language, when writing is language forced to compensate for the absence of the situation. They will design experiments that novelise symbols while holding the world constant, and credit the symbols with what the world supplied. They will model conversation as the exchange of signals, when conversation is the mutual adjustment of counterparts who shape one another's next moves. And they will treat prediction as a single capacity, when predicting a falling stone and anticipating a partner or an opponent are different achievements with different ontologies.
The alternative can be stated in a single sentence: language does not transmit richly specified representations between isolated minds but contributes sparse symbolic traces to multimediated processes of living coordination. The traces matter, sometimes decisively, since a single word can redirect everything else that is happening. Their power, however, depends on everything they leave unsaid being held in common by other means.
Rather than asking how much information a signal contains, or how much of that information is redundant, a theory of communication must therefore ask how living beings manage to coordinate with one another when symbolisation captures only a minute fraction of the worlds they inhabit together.
Acknowledgements
I want to thank my Edinburgh University colleague Hannah Rohde, who first invited me to talk about anthropology to her students in cognitive sciences in November 2024. Trying to explain Living Value Theory to an audience of cognitive scientists turned out to be extremely fruitful, not least because it took me back to what I had been learning about language and the mind when I was a student. This particular article was inspired by a recent lecture by Hannah Rohde on redundancy.
Selected References
Dye, Melody, Petar Milin, Richard Futrell, and Michael Ramscar. 2017. "Cute Little Puppies and Nice Cold Beers: An Information Theoretic Analysis of Prenominal Adjectives." In Proceedings of the 39th Annual Conference of the Cognitive Science Society. Austin, TX: Cognitive Science Society.
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