Which Differences Count? Analogue and Digital as Two Logics of Symbolic Notation

Abstract

This article takes a closer look at what at first seems like an entirely obvious distinction, between analogue and digital symbolisation. I argue that they are two ways in which symbolic arrangements recruit material difference, and neither is a property of the world. Analogue symbolisation preserves selected continuous relations in a carrier, keeping its variation symbolically consequential. Digital symbolisation suppresses selected variation, so materially different states count as one symbol, a controlled material indifference. Writing already embodies this logic, computation mechanises it, and artificial intelligence externalises and accelerates it, decoupling symbolic operations from the temporalities of what they symbolise. Each answers one question: which differences count?

I. Introduction: Which Differences Count?

Two thermometers stand side by side on a shelf. One is a glass tube holding a thin column of liquid, the other a small plastic device with a display. Both are meant to say what temperature the room is, and for most purposes they say the same thing, but they do not arrive at it in the same way. In the glass thermometer a small change in temperature produces a small change in the position of the column, and every intermediate position the column can occupy is available to be read. In the digital thermometer a sensor responds continuously to the same change, yet the device ignores nearly all of that response until a threshold is crossed, whereupon one displayed number gives way to the next. Between any two thresholds an enormous number of physical differences occur, and none of them makes any difference to what the display shows.

Neither the contrast between continuous and discrete, nor that between older and newer technology, nor that between physical and computational locates the difference between the instruments, although each contrast holds in some respect. What distinguishes them is the way each symbolic arrangement decides which material differences matter.

Most accounts of the analogue and the digital begin too late, with electronics, computing, media technology, or information theory, and so treat the distinction as a fact about machines. This article begins earlier, from the account of symbolisation on which Living Value Theory is built. Every symbol has a material carrier, whether ink, light, sound, gesture, electrical potential, or a pattern of neural activity. Symbolic systems nevertheless differ radically in how they use variation in the carrier, and the argument here is that this difference in use, rather than any difference between the carriers themselves, is what the words analogue and digital pick out.

The Birth of the Notation (Ecks 2026) argued that a notation is no passive record. It selects what shall count as a variable and what shall be ignored, it makes its objects manipulable by rules internal to the system, and it makes its results stable and transmissible across persons and time, and in doing all three it is able to hold a phenomenon still. That argument concerned what notations make possible. The present article asks a question one level further down, namely what a symbolic system must do with material difference before notation of any kind can do those things. Notations differ not only in what they select but in how material difference itself is made symbolically relevant.

The thesis can be stated at once. Analogue and digital are two ways in which symbolic arrangements recruit material difference, and neither is an ontological property of the world. Analogue symbolisation preserves selected continuous relations between a material carrier and what it represents, so that variation in the carrier remains symbolically significant. Digital symbolisation suppresses selected material differences, so that materially different states count as the same discrete symbol. Both are achievements of multisymbolization operating through multimaterial carriers, and both are selective, since neither copies what it represents.

The argument proceeds through eight claims. First, analogue and digital are properties of symbolic arrangements and not of reality. Second, both depend on multimaterial carriers. Third, analogue representation preserves relational variation. Fourth, digital representation stabilises classes of equivalent states. Fifth, digitality confers extraordinary material and temporal portability on symbols. Sixth, writing, numbering, and notation contained digital logic long before any computer existed. Seventh, electronic digital computation mechanises a symbolic achievement thousands of years old. Eighth, artificial intelligence is a dramatic acceleration and externalisation of this digital and notational logic. Running through all eight is the single question that gives the article its title: which differences count, and by what rule?

II. Before Analogue and Digital: Notation as Selective Stabilisation

The earlier article established that a notation reproduces nothing. It fixes which dimensions of a phenomenon shall be representable and lets the rest drop out of view, and it acquires its power through exactly this omission, since only by ignoring almost everything can it render the remainder tractable. It then makes what it has selected manipulable by internal rules, and makes the results transmissible and stable (Ecks 2026). These three functions are the reason this article cannot treat analogue and digital representation as two ways of copying the world, one more faithful than the other. A thermometer, rather than reproducing the temperature of a room, registers one dimension of a state of affairs and discards the rest, and a digital thermometer does the same with a different procedure for managing what it discards. Both are selective coordinations, and the question to ask of each is what its selection is and how it is carried out.

Even an analogue instrument is demediated in the sense the earlier article gave the term. Reading the height of a column of liquid requires no recourse to how warm anything feels, and the scale on the glass is a symbol whose meaning lies in its relation to the other marks on the scale and not in lived association. Demediation is therefore common to both logics and cannot distinguish them. What distinguishes them is what happens to material variation once the vocabulary of lived association has been left behind.

A symbolic arrangement is accordingly already an operation of difference management. It decides what variation matters, what variation is irrelevant, which dimensions of a carrier are read, and which are discarded. In the terms of LVT this is the question that recursive discernment answers continually, and for the most part at L1, in bodily attunement: which aspects of an encountered entity are relevant to the coordination at hand. A body that attends to the slope of a path and ignores its colour has already decided which differences count, without any symbol being involved. Symbolic systems stabilise particular answers to the same question in forms that can be shared and carried across absence, and a notation is a deliberate and explicit stabilisation of this kind. The master question of this article is therefore the question of discernment as it appears once its answers have been deposited into material carriers.

The most careful philosophical treatment of the distinction is Nelson Goodman’s, and the present account is indebted to it. Goodman defined a symbol scheme as analogue when it is syntactically dense, so that between any two characters a third can always be found and every tiny variation in an inscription is potentially significant, and as digital when it is finitely differentiated, so that inscriptions can be sorted without ambiguity into disjoint characters (Goodman 1968). He saw that the distinction belongs to symbol schemes and not to media, and that a digital system has no special connection with digits. These insights are retained here. What LVT adds is a question that a formal definition of a scheme leaves open, namely what the scheme does with the material variation of its carrier, and what coordination depends on that treatment. Density and differentiation describe the result, and the material logic that produces the result, preserving variation or suppressing it, is what the remainder of the article analyses.

The earlier article also distinguished two kinds of symbol, narrative symbols that depict or recount and unfold in the order of the telling, and coordinative symbols that fix their elements into a structure governed by internal relations. The distinction between analogue and digital cuts across this one. A photograph is narrative in the earlier article’s sense, a trace of a single moment from a single vantage, and its tonal gradations correspond continuously to differences in the light that fell on the film, which is an analogue property. A page of mathematics is coordinative, and its characters are digital in the strictest sense. A slide rule or a plotted curve is coordinative and analogue, and a digitised photograph is narrative and digital. The two distinctions are independent, and a notation can contain analogue components, digital components, or both. Analogue and digital identify a more elementary property of symbolic construction than narration and notation do, namely how a symbol system treats the differences in its carrier, whether or not it goes on to organise its elements into a calculus.

III. Analogue Symbolisation: Preserving Difference

Analogue symbolisation can be defined as a symbolic coordination in which selected continuous differences in one domain correspond systematically to selected differences in another domain. The height of a mercury column corresponds to temperature, the angular position of a clock’s hands to the time of day, the displacement of a groove in vinyl to the pressure of sound at the moment of recording, a position among contour lines to altitude, and the deflection of a needle to an electrical magnitude. In each case the material of the symbol varies continuously, and the variation is read as corresponding to variation in what is symbolised.

What is preserved is some relational structure of difference, and a bare statement that continuity is preserved would say too little, since which structure is preserved depends on the arrangement. It may be magnitude, distance, ratio, order, orientation, temporal sequence, topological relation, or intensity. This is why analogue symbolisation need not be temporal. A ruler preserves ratios of length, a map preserves relations of nearness and direction, and a photograph preserves a pattern of tonal relations although it freezes a single moment. Two positions of a needle that lie close together on a dial stand for two states of affairs that lie close together, and if the dial is read slightly wrongly the error in what is read is correspondingly slight. The correspondence runs through the whole range of the carrier’s variation, and this continuity of correspondence is what makes the arrangement analogue.

Analogue symbolisation is distinct from resemblance, since a mercury column does not look like temperature and a vinyl groove does not sound like music, and what makes such arrangements analogue is structured covariance, a systematic correspondence between the variation of the carrier and the variation of what it stands for, with pictorial similarity forming no part of the definition. This keeps the account from collapsing analogue symbolisation into iconicity. Instruments of this kind also draw on regularities of the found world. The expansion of a liquid with warmth is a nonrecursive regularity that no one made and that does not alter because it has been put to use, and the calibration of a scale against it is an exercise in what LVT calls cosmic fit, established case by case against a cosmos that owes the instrument nothing. Such an instrument is a made anchor that takes its working from found ground.

An analogue instrument is also highly selective. The thermometer preserves one dimension of a body of air and ignores its molecular history, its smell, its colour, its chemical composition, and everything else in the room. Its closeness to reality is no greater than that of a digital arrangement, since it preserves only a selected pattern of variation, and the selection is as much the work of the arrangement as any digital threshold. The analogue is no less demediated than the digital, and it gives no privileged access to how things are.

In LVT terms analogue symbolisation recruits a continuously variable material property into symbolic work. The column of liquid, the groove, the needle, and the hand on the dial are multimaterial achievements, made things whose physical variation has been organised to stand in a standing correspondence with something else, and the arrangement is multisymbolic because that correspondence is held in place by convention and calibration as well as by physics. Material variation is deliberately kept meaningful, and the sentence on which the rest of the article depends can now be stated: analogue symbolisation works by making selected material variation symbolically consequential.

One consequence follows at once. Because variation in the carrier is symbolically consequential, whatever varies the carrier varies the symbol. A warped scale, a worn groove, a sticky needle, and a drifting calibration all change what is said, and the carrier can never be indifferent to its own history. The analogue symbol is bound to the material conditions of its production and reading in a way that the digital symbol, as the next section shows, is organised to avoid.

IV. Digital Symbolisation: Suppressing Difference

This section is the conceptual centre of the article, and it begins from a paradox. Every digital symbol is materially instantiated. There is no symbol without ink, light, electrical potential, magnetic orientation, sound, gesture, or neural activity, or some other carrier. Yet digital symbols behave as though their specific material form does not matter. A letter remains the same letter when it is written in a different hand, and a number remains the same number when it is carved in stone or displayed on a screen. How can a symbol be wholly dependent on a carrier and also indifferent to it?

The answer lies in symbolic equivalence classes. Digital symbolisation can be defined as a symbolic operation in which materially different states are treated as equivalent instances of a discrete symbolic identity. An A remains an A across fonts, sizes, handwriting, colours, printing technologies, and screens, and across a range of orientations within a tolerance that readers learn to apply. A binary one can be realised by quite different voltages in different devices. The symbolic identity survives material variation because the arrangement has been organised so that this variation does not count.

Digitality therefore depends on ignoring. This is the inversion that gives the account its force, since the common picture holds that digital representation is precise because it represents more, whereas it gains its power by refusing to count most differences. Analogue symbolisation preserves selected variation and digital symbolisation suppresses selected variation. The precision of a digital symbol is the precision of an identity, the guarantee that this symbol is one of a small set of distinct possibilities and no other, and it is bought by a corresponding imprecision about everything within the boundaries of each identity.

The mechanism is the threshold. Below some boundary, variation in the carrier is treated as irrelevant, and across the boundary a categorically different symbol appears. This is what gives digital symbols their discrete identity, and the material world need not contain discrete categories corresponding to them. A thermometer’s display steps from one number to the next while the temperature it senses has done nothing of the kind. Digitality is produced by the symbolic arrangement and imposed on the carrier. For this reason a threshold is always an L4 operation in the sense LVT gives the term, a stabilisation into portable form that compresses a continuous or multidimensional variation into a distinction between classes. It is indispensable, and it carries the risk that attends every binary, namely that the classification comes to be mistaken for the mesocosm, which is not intrinsically organised by the portable binaries through which classification divides it. A body does not change character at the temperature at which a clinic begins to call a fever a fever, and the practical value of the threshold lies in what it lets a clinic coordinate, which is a matter of mesocosmic fit.

Electronics makes the point vividly. A physical transistor contains no metaphysical zeros and ones. Voltages fluctuate continuously, and engineering establishes tolerance bands. A voltage within one band counts as a zero, a voltage within another counts as a one, and noise that remains inside a band is suppressed, because the next stage of the circuit responds only to which band the voltage lies in. The physical substrate stays continuous and messy. Digitality appears when a symbolic architecture treats ranges of material variation as equivalent, and it is maintained by constant engineering, since the bands must be kept wide enough, the circuits fast enough, and the noise small enough for the equivalence to hold.

The term proposed here for this achievement is controlled material indifference. A digital system becomes indifferent to selected material variation without becoming immaterial, and the indifference is a controlled one, produced and policed by standards, tolerances, training, and repair. Print standards, keyboard layouts, voltage specifications, and the schooling that teaches children to read all serve it. The formulation is considerably stronger than the equation of digital with discrete, since it identifies what discreteness is for and what it costs, and it explains why digital arrangements can be extremely robust within their tolerances and fail abruptly outside them.

The same formulation separates the logic of a symbolisation from the character of what is symbolised. The common contrast between continuous and discrete is usually applied to the represented domain, and it gets confused with the logic of the symbols. A digital notation can represent continuous change, as Newton’s notation of fluxions does (Ecks 2026). Its characters are discrete symbols with fixed identities, and its rules operate on them without any reference to the continuity of the motions they describe. An analogue arrangement can represent discrete quantities, as a bar chart does when the lengths of its bars correspond to counts. Which logic is in use depends on what the arrangement does with variation in its carrier, and is independent of whether the represented domain is continuous or discrete.

V. Writing before Computers: The Ancient History of Digital Logic

Alphabetic letters already embody digital logic. A child learning to read must learn that countless perceptual variations are irrelevant. The capital and the lowercase, the printed and the handwritten, the large and the small, the faint and the bold all count as the same letter, in spite of material differences that an observer unfamiliar with the script might find far more striking than the differences between one letter and another. The child must also learn which small differences do matter, since the mark that is a b in one orientation is a d in another, and a stroke added to an n may turn it into an h. Literacy is thus a training of perception to privilege symbolic identity over continuous perceptual variation, and what is trained is a controlled material indifference.

The capacity on which this training rests is zoetic in origin. Perceptual systems already sort continuous variation into categories in some domains. In speech perception, listeners hear acoustically continuous variation as belonging to one consonant or another, and they discriminate differences that cross a category boundary far better than differences of equal size within a category (Liberman et al. 1957). Multisensorial embodiment thus supplies a tendency to treat some differences as equivalent, and multisymbolization recruits that tendency and makes it durable, portable, and deliberate. Alphabetic writing carries the recruitment further by segmenting the stream of speech into a small number of recurrent units and assigning each a mark, so that a continuous flow of sound becomes a sequence of discrete identities that can be stored, copied, and recombined.

The discipline is also a connection between two mediations. The reader learns which visual differences matter, which mark another letter, and which remain variants of the same one, and this learning is a refinement of embodiment in the service of multisymbolization. Once it is well practised it passes into L1. A fluent reader does not experience the suppression of variation as suppression, and does not attend to letters at all, in the way that the grammar of a language one speaks fluently is no more salient than the ground underfoot. This is the trapdoor of ordinary symbolisation at work. The operation that makes the system possible is hidden from the people who use it, and the equivalence classes feel like the way things are and never like a rule that has been learned.

Numerals intensify the operation. A tally mark is the simplest digital system, in which every stroke counts as one however long, thick, or crooked it is. The numeral seven remains seven whether large or small, spoken or written, scratched in clay or displayed in pixels, and in positional notation the identity of a digit together with its place fixes a value, so that the operations of addition and multiplication can be carried out by rules applied to the characters, without reference to the quantities they stand for. Each step of this history greatly extends the portability of symbolic identity. A symbol that survives any change of size, hand, material, and medium can be carried through more places and kept for longer than any symbol whose meaning depends on its exact physical form.

Mathematical notation pushes the logic to its limit. The earlier article described mathematics as a purely coordinative symbolic system, whose symbols mean what they mean by their combinatorial relations to the other symbols and answer to nothing but the rules of the system until its conclusions are tested against the world (Ecks 2026). Discrete symbolic identity is what makes this possible. A symbol can take part in valid operations whatever its current material carrier, and in LVT terms this is an extreme degree of intersymbolic autonomy, in which the coherence of a system of symbols with itself is secured by the digital stability of its characters. The same autonomy has the consequence that coherence alone settles nothing about whether the system fits the cosmos or the mesocosm, which must be established separately.

The historical thesis follows. The digital revolution mechanised and accelerated a symbolic operation that humans had already developed through writing, numbering, classification, and notation, and it invented nothing of the operation itself. Computers belong in the deep history of notation, and the question what they do to material difference has the same answer as the question what an alphabet does. They treat ranges of materially distinct states as the same symbol, and they do it more reliably, at higher speed, and with machinery that carries out the rules without a reader.

VI. Analogue and Digital Are Not Rival Media

Most symbolic artefacts combine both logics. A graph arranges its data in analogue spatial relations, in which distance along an axis corresponds to magnitude, and it labels and numbers the axes digitally. A musical score gives note identities digitally, since a head that sits slightly off its line is still the note on that line. Its left-to-right layout preserves temporal order, and the hairpin signs that swell and taper above the staff preserve something of the continuous rise and fall of loudness they indicate. A map combines analogue geometry with digital place names and categorical symbols. An anatomical diagram combines analogue spatial relations with digital labels and codified conventions.

The anatomical case deserves a second look. The earlier article argued that anatomical images became powerful when they fixed bodily spatial relations into a coordinative form, idealised and labelled rather than copied from one cadaver, with conventions that must be learned before the image can be read (Ecks 2026). The distinction drawn here refines that account. The spatial form of the image works analogically, since relations of position, connection, and relative size on the page correspond to relations in the body, and a reader can check a vessel’s course against the next by looking. Its labels and standardised conventions work digitally, since a named vessel keeps its identity from one printing to the next and from one reader to the next however the line quality varies. The power of the image comes from the combination. The analogue relations carry structure that words can enumerate only slowly and partially, and the digital identities allow that structure to be named, cross-referenced, and corrected across copies and persons. The earlier article also noted that the anatomical image remained coupled to the appearance of its objects in a way that algebra does not. In the present terms this coupling reflects the retained analogue relations, which can be checked by perception, whereas the symbols of mathematical physics are digital identities whose operations owe nothing to how a structure looks.

There is accordingly no analogue medium or digital medium in an ontological sense, and the same artefact can perform different symbolic operations in different uses. A vinyl groove is read analogically by a stylus and may be scanned and read digitally by an optical device. A digitised photograph is a grid of discrete values when its pixels are counted and an analogue pattern of tonal relations when it is viewed at a normal distance. Goodman made the corresponding observation about pictures, that one and the same picture may function as a digital character in one situation and as an analogue picture in another (Goodman 1968). The article therefore speaks consistently of analogue operations and digital operations, and refrains from speaking of analogue and digital realities.

This restraint prevents two simplifications. One treats the digital as a replacement for the analogue, as if the two were successive stages of media history. The other treats them as opposed temperaments of representation, the one warm and continuous and the other cold and discrete. Both overlook that symbolic work is usually done by combinations, and that the question of which logic is operating at a given point in an artefact has to be asked of that point.

VII. Time, Sequence, and the Peculiar Freedom of Digital Notation

The earlier article said that a notation holds a phenomenon still, fixing its object into a form that can be read at once, operated on, and carried unchanged across persons and time (Ecks 2026). Analogue and digital arrangements accomplish this in different ways, and the difference is clearest in how each treats time.

Analogue symbolisation often preserves trajectory. A thermograph translates time into length along a strip of paper, so that a rising temperature appears as a rising line and its rate of change as the slope of the line, which the eye reads at once. A vinyl groove, an oscilloscope trace, an analogue clock, and a waveform on a chart recorder preserve sequence, duration, continuous change, and relative rate. Their symbols remain tied to the temporality or geometry of the relation they represent, because the variation that carries the meaning is the variation that unfolds. The curve of a body’s position against time, which the earlier article identified as what Newton’s notation allowed to be drawn and manipulated symbolically, is an analogue form in this sense, and it holds motion still by spatialising it.

Film shows both logics at once. It preserves tone and shape continuously within each frame, and it samples time discretely, at a rate chosen so that the discreteness does not count for viewers. The earlier article noted that the frame rates that solved the problem in practice were found empirically by the cinema trade and converge with what vision science describes as flicker fusion (Ecks 2026). A frame rate that works is a case of controlled material indifference, since it is a rate at which the viewer’s perception is indifferent to the gaps between samples.

Digital symbols can abstract from duration altogether. A digital expression such as 17°C, 14:53, or 3.6 billion years does not inherit the duration of what it represents. A billion years can be handled symbolically as quickly as a second, and a numeral that is displayed for a millisecond or inscribed for a millennium is the same numeral. Multisymbolization permits temporal compression in any case, since a name or a date allows a long process to be referred to in an instant, and digital notation radicalises the permission, because the identity of the symbol remains stable regardless of the duration of its material presentation or of the processes it stands for.

The strong formulation is therefore this. Digital notation allows symbolic operations to become partially independent of the temporal structure of the phenomena represented. The hardware remains temporal, and every operation takes time. But the time an operation takes bears no necessary relation to the duration of the process whose symbols are being operated on, and the symbols do not reproduce that duration.

This connects the argument to the temporal architecture of LVT. Each mediation has its own bandwidth of temporalities. Embodiment is bounded by metabolism and moves through the span of a heartbeat, a meal, a night’s sleep, and a lifetime. Being-with has the most open temporality of the three zoetic mediations, because its counterpart responds to one’s own responses. Dwelling ranges from the passing of a cloud to the turning of the seasons. Material infrastructures have temporalities of their own, set by wear, maintenance, and decay. The poietic mediations are in every aspect technologies of time. Multimateriality aims at durability, and holds forms steady across spans that no body could hold them. Multisymbolization rests on the premise that a symbol stays the same whenever it is taken up, so that its identity stands outside the time of any particular taking up, and mathematical symbolisation is its purest case. Together they decouple temporal reach from metabolic duration, and a being whose own span is short can coordinate with pasts it never lived.

Digital symbolic systems intensify this decoupling. They allow operations across temporal scales that no embodied process could literally traverse, from the nanoseconds of a circuit to the geological records of a climate archive, within a single sequence of manipulations. The past can be deposited in them, and indeed in great volume, but the future cannot, and projections run at high speed remain representations open to revision by what actually happens. These features become crucial for scientific notation and for the discussion of artificial intelligence below.

VIII. Perfect Copying, Error Correction, and Symbolic Persistence

The distinction between the two logics has consequences for what can be done with symbols technologically, and copying is the clearest. When symbolic meaning depends on preserving material variation, every copy introduces new variation. A photocopy of a photocopy, a tape dubbed from a tape, and an engraving taken from an engraving each add their own noise to the noise already present, and since all variation in the carrier is symbolically consequential, the noise accumulates in the symbol. The representation degrades, and it degrades gradually.

Digital arrangements behave differently because their meaning depends on identity and not on exact material state. A receiver of a digital symbol need not reproduce the physical original. It needs only to classify the state correctly, and having done so it can write a fresh instance of the symbol in a fresh carrier, with the noise of the old one left behind. Digital copying is accordingly a symbolic regeneration and no physical replication, and a digital copy is perfect only with respect to the identities that count. Every physical feature of the carrier that was not counted may differ without limit.

Error correction extends the same principle. In 1948 Claude Shannon showed that adding structured redundancy to a message allows a receiver to detect and correct errors, so that a noisy channel can carry a message reliably up to a limit set by the channel itself (Shannon 1948). The correction works by restoring symbolic identity, and it is another case of continuous material variation being rendered irrelevant, this time by design and in the middle of a transmission. Sampling theory shows the same logic from the other side. A signal that contains no frequencies above a given limit can be reconstructed exactly from samples taken at more than twice that limit (Shannon 1949), which means that the differences above the limit are the ones that do not count. The rate chosen for compact-disc audio, 44,100 samples a second, secures every frequency below about 22 kilohertz, a range that exceeds what human hearing generally uses. Here the answer to the question which differences count is written down as a mathematical condition.

The insight that follows reverses the usual story. Digital systems are powerful because symbolic equivalence allows imprecision to be corrected repeatedly, and the precision of their material carriers matters little. A circuit can be built from components of moderate quality and still carry a message without loss for as long as noise stays inside tolerance and the equivalence classes keep being restored.

Two costs belong beside this account. The first is that digital arrangements tend to fail abruptly where analogue arrangements fail gradually. A degraded analogue signal is noisier but still readable, whereas a digital signal is restored perfectly until noise exceeds the tolerance, whereupon it may be lost altogether, and the abruptness is the other face of the robustness. The second concerns persistence. In the terms of LVT, durability is the extent to which a formed state persists beyond the activity that produced it, and an inscription persists for as long as the material that carries it survives. A clay tablet persists by inertia, whereas the persistence of a digital file is that of a process. It survives for as long as it is recopied into new carriers, read by devices that still exist, and interpreted by people who still know the format. Poiesis does not remove recursion from the system but relocates it to maintenance and uptake, and digital persistence relocates it with particular intensity, since the symbolic identity lasts only because living people and working institutions go on regenerating it. A deposit of this kind can sit dormant for a long time, but it cannot be neglected for as long as an inscription in stone.

IX. From Notation to Computation

A notation already permits operations according to internal symbolic rules, and computation mechanises those operations. This follows directly from the earlier article’s argument that symbols become manipulable once they are fixed inside a coordinative system (Ecks 2026). The second of the three functions of notation, making its objects manipulable, was always performed by a person who read the symbols and applied the rules. A computer performs it without a reader, and does so at a speed and with a reliability that no reader could match. In this sense computation is notation in motion.

Digitality is ideal for this purpose, and the reasons are those already assembled. Discrete identities allow operations to be repeated exactly, errors to be detected, symbols to be stored and transmitted, damaged symbols to be reconstructed, one symbol to be substituted for another at high speed, and the course of an operation to branch according to which identity is present. A computer is therefore a multimaterial machine, engineered to sustain stable digital symbolic identities and to transform them according to formal rules, and no part of it is made of digital matter, since matter has no digital form. Everything that is digital about it lies in the controlled indifference of its circuits to variation within their tolerances.

The relation to demediation is direct. The earlier article described the pattern in which the more thoroughly symbolic operations can proceed by relations internal to the notation, the less they depend on continuous recoupling to lived experience, and it traced that pattern through the formal sciences. Computation pushes the pattern further by externalising rule-governed symbolic manipulation into technical systems. The extension carries a risk that the earlier article’s general law already anticipated. Intersymbolic autonomy secures the coherence of a system of symbols with itself, and coherence settles nothing about fit. A computation can be flawless and detached from the coordination it was built to serve, and the systematic form of this detachment is what LVT calls institutional drift.

The law also bears on where computation can be trusted. The earlier article argued that a coordinative notation fits only phenomena that hold still under symbolisation, which are nonrecursive, and that the recursive processes of the world can be notated only through the nonrecursive residues they leave behind (Ecks 2026). Digital computation inherits this constraint, with the difference that its power makes the constraint easier to forget. Where its object is nonrecursive, a computation can model a bridge, an orbit, or a reaction with extraordinary success. Where it is applied to selfrecursive or interrecursive domains, as in the scoring of a person, the ranking of a conversation, or the prediction of a market that responds to its predictions, what it manipulates is residue, a score on a day or a count at a moment, and the output tends to present itself as though it named the process directly. This is the disguised L4 in a digital form, and it is a case of type misfit, in which a logic suited to counterparts that do not answer back is applied to counterparts that do.

X. Artificial Intelligence: Digital Notation Run at Scale

The argument can now be brought to its most contemporary case, and it begins with a negative remark. Large language models are interesting for what has been done with symbolic operations over the accumulated archives of human writing, and their being digital explains very little, since electronic computers have been digital for decades.

The archives were already digital in the sense developed above. Alphabetic text consists of discrete identities that are indifferent to the hands, papers, typefaces, and centuries through which they were produced, and once such text is stored electronically, an entire literature becomes a homogeneous substrate of characters. A model trained on that substrate operates on symbolic identities that have been abstracted from the material and temporal contexts of their production. It can compare, recombine, transform, translate, summarise, and generate, at a rate and across a range that no human reader could approach. The operations are carried out on symbols that no longer bear the marks of the lives from which they came.

This yields the temporal decoupling discussed earlier, on a large scale. An archive accumulated over centuries can be processed in a matter of weeks, and a text of some length can be produced in seconds. Symbolic operations need not inherit the temporality of the embodied lives that produced the symbols, nor that of the lives that will read the results, and this is the larger consequence of digital notation. The decoupling is not symmetrical. Production proceeds at the speed of the machine, whereas uptake, which means reading, checking, interpreting, and acting, proceeds at the speed of beings who must eat and sleep. In the terms of LVT the burden of reopening a closure falls on the party with the least capacity to bear it, and a symbolic output produced in seconds may take a reader hours to evaluate. The mismatch between tempos is a familiar source of coordination failure, and here it is built into the design.

The proper formulation is that artificial intelligence is an unprecedented externalisation and acceleration of the coordinative powers of notation. The earlier article observed that Newton used a notation to let symbolic operations run ahead of observation, reaching conclusions that no one had seen and that the notation nonetheless licensed (Ecks 2026). Artificial intelligence extends the same principle into systems that can perform enormous volumes of intersymbolic operations outside any single human mind. What is externalised is the running of notation. The outputs of such a system are nonrecursive symbolic outputs, deposits that become effective only in uptake, so that the recursion they make possible lies in the reading, checking, and use by living people, and responsibility for what is done with them rests at the same point.

The earlier article’s guard concerning recursive processes applies here as well. A recursive process throws off nonrecursive residues, and a transcript is a coherent notation of a conversation that has closed. The corpus on which a language model is trained consists of such residues on an enormous scale, the settled words of countless exchanges, arguments, and instructions, left behind when the recursion that produced them had stopped. A model can therefore achieve remarkable intersymbolic fit with that corpus, and the fit, however excellent, says nothing by itself about mesocosmic fit with the coordination from which the residues came. Benchmarks that test a system against the symbolic knowledge of a profession measure the first and leave the second to be established by use.

The case also illustrates why this article speaks of operations rather than media. A language model takes in and gives out discrete tokens, and its arithmetic is performed on discrete numerical representations in digital hardware. The structure it learns, however, is organised as a geometry, in which nearness and direction in a space of many dimensions correspond to relations among the uses of words. That organisation resembles analogue symbolisation in conveying relations through graded covariance, although the continuity here is that of numerical values that are themselves held in digital form. The system is a hybrid in exactly the sense of the sixth section, with digital logic governing its carriers and its operations and covariance organising what it has learned, and calling it simply digital loses what is distinctive about it.

The multimaterial carrier, finally, never disappears. A language model depends on servers, chips, electricity, cooling systems, network infrastructure, and the human bodies that build, maintain, and repair them, as well as on mines, factories, and supply chains. The apparent immateriality of digital symbolisation rests on immense multimaterial support, and the case is a clear illustration of the trapdoor of ordinary symbolisation at its deepest. The poietic seems autonomous because the zoetic and material supports on which it depends have disappeared from attention, in the way that successful coordination generally does. Controlled material indifference is a way of making some of matter’s variation irrelevant to the symbols, and it requires matter in great quantity to keep the irrelevance in place, so that it brings no freedom from matter.

XI. Conclusion: Analogue and Digital as Ways of Governing Difference

Return to the two thermometers. The conventional distinction says that the analogue is continuous and the digital discrete. The reconstruction offered here says something different. Analogue symbolisation preserves selected continuous differences in a material carrier so that they remain symbolically consequential, and digital symbolisation suppresses selected material differences so that ranges of materially distinct states count as identical symbols. Both operations are selective, both are multimaterial, and both belong to multisymbolization, and neither describes reality in itself. A glass column and a plastic display are two answers to the question of which differences in a heated liquid or a heated resistor should be allowed to matter.

The common logic extends across writing, numbers, scientific notation, diagrams, recording, computers, digital communications, and artificial intelligence. They are all technologies for deciding which differences count, and the answer differs fundamentally between analogue and digital symbolic systems. Each answer has a price. A digital system gains portability, copyability, and mechanical manipulability by suppressing differences, and some of the suppressed differences may be the ones that mattered to the coordination it was built to serve. The decision about what may be ignored is answered, if at all, by mesocosmic fit and never by the symbolic system alone, whose own coherence is silent on the matter, and the test is whether what has been made irrelevant to the symbols is irrelevant to the lives and processes that depend on them. The threshold that sorts a patient, the score that sorts an applicant, and the category that sorts a population are all answers to the question of which differences count, and conceptual responsibility requires that the answer remain accountable to those whose differences have been ruled out.

The broader claim of LVT can now be stated. Symbolisation reorganises material relevance and never escapes materiality. Analogue notation does this by preserving selected variation, and digital notation does it by suppressing selected variation in order to stabilise identity. The history from writing to computation is therefore a history of increasingly powerful ways of making some material differences consequential and others irrelevant, and it shows no progression from material to immaterial representation.

The earlier article asked what notation makes possible. This one has asked the more basic question of what a symbolic system must do to material difference before notation becomes possible at all, and the answer is that it must decide, by some rule and in some material form, which differences count.

References

Goodman, Nelson. 1968. Languages of Art: An Approach to a Theory of Symbols. Indianapolis: Bobbs-Merrill.

Liberman, Alvin M., Katherine S. Harris, Howard S. Hoffman, and Belver C. Griffith. 1957. “The Discrimination of Speech Sounds within and across Phoneme Boundaries.” Journal of Experimental Psychology 54 (5): 358–68.

Shannon, Claude E. 1948. “A Mathematical Theory of Communication.” Bell System Technical Journal 27 (3): 379–423; 27 (4): 623–56.

Shannon, Claude E. 1949. “Communication in the Presence of Noise.” Proceedings of the IRE 37 (1): 10–21.