The quest for the relation between meaning and information

Right at the first page to The Mathematical Theory of Communication, Claude Shannon writes that “[the] semantic aspects of communication are irrelevant to the engineering problem [of communication]” (Shannon, 1963, p. 31). Shannon’s work, originally published as the product of his research at Bell Labs, is likely what Jacques Lacan had in mind when, in the second edition of his Seminar, he told the following story about how the ‘great adventure of the research concerning communication’ began:

The Bell Telephone Company needed to economise, that is to say, to pass the greatest possible number of communications down one single wire. In a country as vast as the United States, it is very important to save on a few wires, and to get the inanities which generally travel by this kind of transmission apparatus to pass down the smallest possible number of wires. That is where the quantification of communication started. So a start was made, as you can see, by dealing with something very far removed from what we here call speech. It had nothing to do with knowing whether what people tell each other makes any sense. Besides, what is said on the telephone, you must know from experience, never does. But one communicates, one recognises the modulation of a human voice, and as a result one has that appearance of understanding which comes with the fact that one recognises words one already knows. It is a matter of knowing what are the most economical conditions which enable one to transmit the words people recognise. No one cares about the meaning. Doesn’t this underline rather well the point which I am emphasising, which one always forgets, namely that language, this language which is the instrument of speech, is something material? (Lacan, 1978/1988, p. 82)

What is at stake in Shannon’s work, and what Lacan — as well as many others — saw as revolutionary was the possibility therefore opened to think the economy of an informational system that establishes itself independently of whatever meaning that information might or might not carry. Before we can talk about the semantic content of the material at play in communication, this very material already presents itself in specific forms that allow us, for the first time in history, to think of information as a concept completely distinguished from the concept of meaning. But if this is indeed the case, then how are we to re-think meaning in light of this new discovery?

Part One: From information to meaning in Shannon

For starters, we have to, first, clarify what exactly Shannon is after with this new concept of information. Given a set of symbols, each one with its given probability of being transmitted, the amount of information conveyed by a certain symbol will correspond to how much the transmission of this specific symbol actualizes out of the set of possibilities of transmission. In a coin toss, for example, the outcome determines a specific result out of a set of 2 possibilities with equal probability; in a card flip, the outcome determines a specific result out of a set of 52 possibilities with equal probability — therefore, a card flip carries more information than a coin toss¹. We can see that this definition relates to the intuitive distinction of how much information was available before vs. how much information is available now, but gives a statistical twist to it, showing that we can determine this how much by looking at how much the given content funnels out of the possible content to be given.

By pursuing this idea, Shannon was able to notice its relation to the thermodynamical concept of entropy, showing that the formula to determine how much information is transmitted per symbol in a process that transmits symbols out of a specific set of symbols with their given probabilities of being transmitted is the same as the entropy formula brought about by Ludwig Boltzmann in his H-Theorem (Shannon, 1963, pp. 48–51). As E. T. Jaynes (1967) would later demonstrate, the concepts of thermodynamical entropy and information entropy are not just similar or equivalent, but are the exact same concept: the maximum entropy of a system is the value of the best possible way of inferring the distribution of probabilities in a system given the information available. While in thermodynamics this formula is applied in the case of determining how many microstates can correspond to the given macrostate, in information theory the formula appears in its more abstract version, showing how much information we can infer to be transmitted out of each symbol in a system by establishing the most even distribution of probabilities given the known parameters.

The way of defining information entropy given above, however, makes necessary the clarification of the distinction between maximum entropy and conditional entropy. If we think of an indeterminate physical system of molecules, the macrostate in which the probabilities of each microstate would be the most evenly distributed would be in the form of a gas in its point of equilibrium, the configuration at which this system reaches its maximum entropy; in contrast, if we think of the same hypothetical system of molecules, a macrostate in which the probabilities are extremely unevenly distributed between the microstates would be, for instance, a crystal structure: in this case, there are few microscopic configurations that could give this macrostate, meaning that, in comparison with the previous gas state, the crystal structure has much lower entropy. This, in turn, means that, in the low-entropy structure, there are specific microstates that appear much more often than others that basically don’t appear at all — as it is certainly the case in a crystal, defined as a material whose constituents are arranged in a highly ordered microscopic structure, making it possible for us to describe these repetitive patterns in mathematical terms, for example.

Putting aside the material, then, the difference between maximum entropy and conditional entropy is precisely the difference between the entropy of the gas and the entropy of the crystal: while a set of symbols can be encoded in a way that distributes the probabilities of occurrence between the symbols in the most even way possible — the maximum entropy of the set — there are a number of other ways in which the same set can be encoded so as to make some specific symbols or orders of symbols way more frequent than others, which means that the set has an entropy conditional to its specific encoding. The difference between the maximum entropy and the conditional entropy is called redundancy, and it is precisely due to the fact that this difference is shown in elements and patterns that repeat themselves way more frequently than they would do so in a maximum-entropy encoding (Shannon, 1963, p. 56), such as in the case of the crystal when compared to the gas. Returning to the early examples of the coin toss and the card flip, a way to “encode” them so as to make their conditional entropy less than the maximum entropy would be, for instance, if the person tossing the coin or flipping the cards rigged the game (by making use of an altered coin or of card tricks, for example) so as to, for example, flip only red cards or make the coin almost always land in heads. A way more interesting example of redundancy, however, is language itself: grammar ensures that there are specific regularities in speech, making it so that people don’t just spit random sequences of sounds but, instead, emit sounds marked by specific patterns that make them subsumable to understandable rules.

With this, we come to the point of most interest for us: what becomes apparent here is the existence of a relation between entropy, redundancy, and meaning. As we have made clear above, it is impossible to convey meaning without redundancy: making something out a stream of information relies on the possibility of distinguishing patterns, instances of repetition, boundaries to said stream that show it to be orderly, not random. At the same time, however, meaning is not directly proportional to redundancy: a stream of information with full redundancy such as, for example, a sequence of symbols out of a set of 0s and 1s in which every symbol transmitted is a 1 and never a 0 is as meaningless as a random sequence — mere being and mere nothingness are equivalent. Even if it’s not possible to determine conditions of information sufficient to the rise of meaning, then, we can at least say that it is necessary for meaning that the information flow out of which we make it out has to present certain amounts of difference as well as certain amounts of repetition.

Par Two: Signifier and meaning in Lacan

In Lacan and the Concept of the ‘Real’ (2012), Tom Eyers coins the conceptual pair of the signifier-in-isolation and the signifier-in-relation in order to establish a systematic account of the way the French psychoanalyst employs his enigmatic and overly-debated concept of the Real. According to Eyers, while the signifier-in-relation refers to the way the value of the signifiers is determined by their differential relations to each other — Ferdinand de Saussure’s discovery — , the signifier-in-isolation refers to the signifier as a thing, to its material aspect, to the fact that the signifier is itself an object, not just a device of reference to other objects (Eyers, 2012, p. 5). Lacan renounces, then, the idea of the signifier and the signified as parallel opposites, proposing, instead, that meaning, or the idea of something that is signified by the signifier², is just and effect or a product of the way we give determination to the signifier through the differential relations they present between themselves: the word ‘tree’, for example, is not, as could be put from a Saussurian perspective, a signifier that references the concept of this well-determined type of object in the sensible world; instead, the interplay we establish between the signifiers in the activity of language produces the impression that there is some well-determined type of being that we have come to attach to the word given the regularity of its use (Lacan, 1966/2006, pp. 413–419). The realm of meaning, in Lacanian metapsychology, is the realm of the Imaginary, where we relate to the images that come as a result of this process of production of the impression of meaning. That being said, Lacan also explicitly cronfronts the thesis that, for psychoanalysis, what we usually call “reality” is just the fantastical product of an unbound process whereby language, thought of as a quasi-ideal and immaterial entity, is endlessly caught in a pure self-relation, like a dream without a dreamer (Lacan, 1973/1978, p. 53) — and the basis for this confrontation will be exactly the ideas wrapped up in Eyer’s concept of the signifier-in-isolation, pointing out how language inevitably has to deal with its Real aspects. When Lacan talks about the Bell Telephone Company in the previously cited passage, this is what he is referring to: language has a material aspect, it is itself an object, not an immaterial vehicle of meaning; signifiers are themselves stuff and, more than that, this materiality is the necessary condition to the rise of the signifier-in-relation. If we wish to establish an imaginary game of meaning, of giving and asking for reasons, we must first have what Eyers calls a matrix of “protosymbolic elements” that will then be put in differential relations between each other in order for meaning to arise (Eyers, 2012, pp. 20–21).

In his Seminar on “The Purloined Letter”, Lacan neatly demonstrates why this has to be the case with an exercise that is a brilliant working out, even if not explicitly acknowledged, from what Shannon notices about the structuring of sets of symbols in Markov chains. The mathematician first presents the idea by pointing out that we can represent a telegraph as a system that alternates between two estates: one in which the previously transmitted symbol is a space, be it a letter space or a word space (which are, materially, three and six time units of line open, respectively), and one in which the previously transmitted symbol is not a space, but a dash or a dot (which are, materially, one and three time units of line closure, respectively, followed by one time unit of line open). This way, all the possibilities of transmission are contemplated in the following graph (Shannon, 1963, p. 38):

We can see here that an initial relational restriction emerges out of the material aspects of the symbols: since spaces amount to leaving the line open, nothing further can be said to have been transmitted after a space unless it is a dot or a dash, the cases in which the line is again closed for determinate amounts of time — there is no possibility of a sequencing of spaces. This is still very simple, but this very idea gains further complexity when Shannon notes how we can gradually increase the conditions of a stochastic process of symbol transmission so as to eventually arrive in spoken language. Let’s see one of the examples: given the set of symbols {A, B, C, D, E}, Shannon determines a set of 16 “words” — not real words known to us or accepted in any real-world grammar, but merely arbitrary ways of putting these symbols together in this made-up pseudolanguage — such as “ADEB,” “BEED,” “CABED,” etc., each with an arbitrarily given probability of being transmitted (Shannon, 1963, p. 42). This leaves us with the following graph (Shannon, 1963, p. 46):

Although the probabilities are not specified in the graph, given that, in this example, Shannon attributes probabilities only to “words,” i.e., symbol sequences, we can easily imagine, as the mathematician himself points out, a more complex case of encoding in which, for example, the set of symbols is the entire latin alphabet and the probabilities of each symbol being produced by the stochastic process are conditioned on the previously transmitted symbols according to the probabilities of letters (and spaces) following each other as empirically attested in modern-day English; the result of this is the coming-up of a natural language without any reference to meaning whatsoever (Shannon, 1963, pp. 43–44). What is laid out by Shannon here is a new way of thinking, as Lacan would have put it, language as a purely material process, a process in which all the differential relations that will then be used to retroactively produce the impression of meaning are initially laid out.

Lacan himself, for his turn, presents Shannon’s idea of representing the material determinations of the activity of language in graphs in an initially rather simple way, talking about something as simple as a mere coin toss. His focus, however, is also somewhere else: possibly drawing from Roman Jakobson on how phonemes are first determined out of a set of simple “differential elements” (binary oppositions that, in the cases of oral speech, such as the ones studied by Jakobson, regard differences in the shape of the mouth) to then be themselves arbitrarily picked out in order to form signifiers (Jakobson, 1976/1978, pp. 69–87), Lacan will put emphasis on how arbitrary meaningless sequences can be reinterpreted as new patterns, therefore giving rise to restrictions previously absent in the stochastic process. To put it in a less abstract way, this is precisely what was already present in Shannon when he equates, for example, “three time units of line closure and one unit open” with “a dash”: only grouping together these initially random sequences in different units that will then be called something as “a dot,” “a dash” or “a space” can these patterns emerge. In Lacan’s example, starting from a random sequence of + and –, if we assign the name “1” to sequences with “symmetry of constancy” (that is, “+++” or “– — –”), the name “3” to sequences with “symmetry of alternation” (that is, “+–+” or “–+–”) and the name “2” for the remaining asymmetrical ones, we end up with the following graph (Lacan, 1966/2006, p. 35):

In it, we can see, for example, that there is no going from 1 to 3 without going through 2. Beyond this, however, Lacan notes that we can go even further, assigning names to certain sequences of these very 1, 2 and 3 sequences, mirroring that Jakobsonian idea of determining signifiers out of sets of phonemes themselves already determined by certain binary oppositions. In this second example, Lacan associates the greek letters α, β, γ and δ to arbitrary patterns of sequences of 1, 2, and 3 (the reconstructing of which here is not worth the time), resulting, again, in the exclusion of certain symbols from occurring in specific places, with the addition that this restriction gains a retroactive aspect: if we start from α with the prospect of arriving in γ as the fourth term, for example, δ cannot occupy neither the second nor the third terms through which we would arrive at the fourth one (Lacan, 1966/2006, pp. 36–38). Also, by pointing out the parallel with Jakobson’s ideas, we can see that this is the point at which the grammatical relations between signifiers are established.

All of this is to say that Lacan is able to demonstrate how, at the level of discourse, the differential relations between signifiers that are then retroactively seen as relations of meaning are in fact already established at the material level, completely independent of meaning — imposing determinate restrictions to discourse which cannot be justified by it, restrictions that stand as the meaningless conditions of meaning. Relating this to what we previously saw regarding entropy and redundancy, we can see here that these differential relations we talk about are really ways of encoding that, by virtue of their arbitrarity, establish uneven distributions of probabilities between the symbols that end up constituting precisely the necessary redundancy for language to spontaneously emerge as a rule-governed game whose rules extend far beyond what has already been given meaning: as Claude Lévi-Strauss has put it, “at the moment when the entire universe all at once began significant, it was none the better known for doing so” (Lévi-Strauss, 1950/1987, p. 60). The twist Lacan puts to that insight is to note that the “unknown” aspect of the significant universe is not contingently, but necessarily related to the “known” universe of meaning and, therefore, always present.

Part Three: From a (Post-)Kantian point of view

Along the Critique of Pure Plasticity seminar we were introduced to the idea that the concepts of information and entropy are not empirically determined, but deduced a priori from the categories of pure understanding as features necessarily always-already present in experience. Having this in mind, we can apply a Kantian twist to our Lacan to note how, in the Lacanian concept of the Real, what is at stake is something akin to the discussion that permeates all German Idealism about the self-referentiality of reason. In Kant, this initially takes the form of the transcendental dialectic, that is, the problems that arise once reason takes its own form as a different object, engendering its necessary illusions so dear to metaphysicians and superstitious men alike. These ideas, however, such as the idea of God or the Soul, nevertheless still play the role of guiding the subject in the realm of practical reason, that is, the realm of morality. The confrontation the Real poses to meaning, however different, plays a similar role: Lacan interprets the Freudian concept of Repetition as the necessary coming-back of the signifier chain to the formal meaningless interplay of signifiers that first poses the dimension of meaning in motion, an untenable beyond that makes so that Reason always reformulates itself (Lacan, 1973/1978, 53–64)³. Crucially, however, the Real is not painted in teleological colors, and its intervention in the symbolic game appears not as a guiding principle, but as an unsolvable problem that keeps posing itself in different ways, but always in the same form.

We can refine this analysis by pointing out to the fact that, from a post-kantian point of view, it is dogmatic to think that there is a first moment where the signifiers are first put as things only to then give birth to the game of meaning that succeeds their materiality logically; instead, we must flip the order and understand that the symbolic order establishes itself always in an already-repressed form — when a discourse is brought about, it dialectically also puts to itself its Real, implicit condition. Slavoj Žižek (ŽIŽEK & SO ON PODCAST, 2022) gives the example of the right-left distinction in politics: in it, the “Real” of this symbolic distinction is the definition of the very categories of right and left. If we accept the basis of the distinction, that is, that there are two opposing worldviews regarding politics, the implication is that any attempt of defining what is the right and what is the left already comes from either of these two fields — therefore, there can never be any external point of view that would determine what the right and the left really are. If we apply Eyer’s concepts, we see that, here, the terms “right” and “left” are the material condition for the rise of the right-left spectrum logic, the senseless coordinates that have to be established so that reality can be made sense of in virtue of it. Since the distinction necessarily has to be always presupposed, it can never be made sense of — the serpent can never eat its own tail.

This is, in fact, the problem first made explicit by Fichte in the project of reformulating Kant’s Transcendental Idealism that would then develop into Fichte’s own philosophy. In the effort, put forward in virtue of the spirit of Kant’s critical philosophy, of getting rid of dogmatic presuppositions, Fichte addresses directly the problem of already presupposing a range of formal elements, such as logic itself, in the reasoning necessary to engender a philosophy that is supposed to start purely from the fact of the existence of rational experience. The idealist notes that, even though there is simply no way of making philosophy without all these presuppositions in the form of the reasoning, since philosophy is supposed to be the science that justifies all the other sciences these very presupposed formal elements ought to be they themselves later justified explicitly as contents addressed in the developing of the system of the Science of Knowledge (Fichte, 1794/1982, pp. 93–94). This, however, creates an unbridgeable gap: the gap between saying and doing. For Fichte, the derivation of the presupposed formal elements does nothing except not to reveal to us that the system is false; this does not mean, however, that it is indeed not false, but only that it may be correct. The reason for this is that, as the philosopher rightly points out, no matter how much the human mind constructs an exposition of its own structure that appears to be, in fact, correct, there is no guarantee that such verisimilitude is not the work of chance: no matter how much we insist on verifying the agreement between knowledge and the way we present it, performing such verification is already constructing a new exposition, which may itself be wrong and turn two errors into a correct match. The analogy provided by Fichte is illustrative: if one was to verify the correctness of the result of a division by multiplying the result by the divisor, although obtaining a result different from the dividend would for certain show that the division was wrong, obtaining the same number would not, in fact, show that the division was right — it could be, for example, that the same mistake was made both in the division and in the multiplication, but this would not be known. A similar impasse occurs when Reason tries to chase its own tail and close its system in philosophy: the exposition is always ahead of the exposed, determining explicitly some content always implies an unfolding of the form of the discourse needed for such explicitation that has, obviously, to remain implicit during said explicitation (Fichte, 1794/1973, pp. 34–37).

We can go back to Lacan now to see that, by employing the concepts of the signifier-in-isolation and the signifier-in-relation, Tom Eyers makes explicit the importance of this same conflict to Lacanian thought: the construction of a system of meaning is always put in motion by placing, at the same time, a formal framework that has to be implicit and, therefore, detached from meaning, concerning only language as the material in which an interplay of signifiers — put in terms of information by Shannon — that later will be retroactively read as a conveying of meaning is initially put. What’s more, as we have now seen with Fichte, this disparity can only be seen when the discourse in question attempts to attribute meaning to itself, gives a try at self-referentiality, the moment at which the disparity between form and content in language is evidenced — exactly what we have seen with the example Žižek gives. This Žižekian interpretation, furthermore, can now be understood more clearly in relation to the way the philosopher gives a Hegelian spin to the traditional, vulgar reading of the relation between the Symbolic and the Real in Lacan to correctly point out that, for Lacan, we cannot speak of a pre-symbolic Real that is given as a foundational extra-rational basis for the Symbolic register — instead, the Real is put as formal aspect by the very Symbolic dimension it limits. This is, after all, precisely the insight with which Fichte has left us: the untenable formal dimension of discourse is always put by the unfolding of discourse itself and thus it remains the same not as content, but as form⁴. Finally, we can end this line of thought by suggesting, perhaps, that “the quest for the relation between information and meaning”, the title of this text, may be a question that cannot be answered directly precisely because it concerns this disparity inherent to language and, therefore, to Reason: there is no point at which form finally meets content, at which information transforms into meaning, except if we think of it in a dialectical way and appreciate this disparity as being precisely the aspect of Reason that makes possible for it to work.

Footnotes

¹ Specifically, a coin toss carries 1 bit of information, while a card flip carries 5,7 bits of information.

² An idea of great importance in Gottlob Frege’s distinction between sense and reference.

³ For an in-depth explanation of this dynamic, see Van de Vijver G, Bazan A and Detandt S (2017). It is to note, however, that the text lacks in its philosophical interpretation of the concept of Repetition, particularly regarding its post-kantian nature as we shall see briefly. Even so, the authors do a great job at mapping the concept in Freud and Lacan’s works.

⁴ This is the correct way of reading what Lacan is talking about when he says, interpreting the Freudian example of the Fort-Da (brought up by Freud in Beyond the Pleasure Principle to illustrate the psychoanalytical concept of Repetition), that “[t]he activity as a whole symbolizes repetition, but not at all that of some need that might demand the return of the mother, and which would be expressed quite simply in a cry. It is the repetition of the mother’s departure as cause of a Spaltung in the subject — overcome by the alternating game, fort-da, which is a here or there, and whose aim, in its alternation, is simply that of being the fort of a da, and the da of a fort. It is aimed at what, essentially, is not there, qua represented — for it is the game itself that is the Repräsentanz of the Vorstellung. What will become of the Vorstellung when, once again, this Repräsentanz of the mother — in her outline made up of the brush-strokes and gouaches of desire — will be lacking?” (Lacan, 1973/1978 pp. 62–63). We could, initially, understand the game that is the ‘Repräsentanz of Vorstellung’ in the classical/Cartesian sense of something that represents, symbolizes something real, as in the Aristotelian conception of language or in how Frege thinks of sense and reference; the question posed by Lacan at the end of the passage, however, clearly subverts this by indicating that when this Repräsentanz, the game, is missing, the Vorstellung will also be different. What occurs, what appears [Vorstellung], is something that, first, cannot already be represented — as in a conception that would take the real phenomenon being represented as, for example, merely the mother leaving — precisely because it is formal; second, what occurs, which is not represented, is itself altered based on the representation that operates upon it. This instance of the encounter with the Real, of the failure/rupture in the symbolic/imaginary system of reality, this gap, transforms as we repeat it, with representations and language games; it truly becomes something new.

References

Eyers, T. (2012). Lacan and the Concept of the ‘Real’. Palgrave Macmillan.

Fichte, J. G. (1973). Sobre o conceito de doutrina da ciência [On the concept of the Science of Knowledge]. In V. Civita (Ed.), J. G. Fichte, F. W. J. Schelling: Escritos filosóficos [Philosophical writings] (R. R. Torres Filho, Trans.; Vol. 26, pp. 15–38) Abril Cultural. (Original book published in 1794)

Fichte, J. G. (1982). The Science of Knowledge: with the First and Second Introductions (P. Heath, J. Lachs, Trans.) Cambridge University Press (Original book published in 1794)

Jakobson, R. (1978). Six Lectures on Sound and Meaning (J. Mepham, Trans.) The MIT Press. (Original book published in 1976)

Jaynes, E. T. (1957). Information Theory and Statistical Mechanics. The Physical Review, 106(4), 620–630. https://doi.org/10.1103/PhysRev.106.620

Lacan, J. (2006). Seminar on “The Purloined Letter”. In B. Fink (Trans.), Écrits: The first complete edition in English (pp. 6–48). W. W. Norton. (Original work published 1966)

Lacan, J. (2006). The Instance of the Letter in the Unconscious, or Reason Since Freud. In B. Fink (Trans.), Écrits: The first complete edition in English (pp. 412–441). W. W. Norton. (Original work published 1966)

Lacan, J. (1998). The Seminar of Jacques Lacan Book II: The Ego in Freud’s Theory and in the Technique of Psychoanalysis 1954–1955 (J-A. Miller, Ed.; S. Tomaselli, Trans.) W. W. Norton. (Original book published in 1978)

Lacan, J. (1978). The Seminar of Jacques Lacan Book XI: The Four Fundamental Concepts of Psychoanalysis (J-A. Miller, Ed.; A. Sheridan, Trans.) W. W. Norton. (Original book published in 1973)

Lévi-Strauss, C. (1987). Introduction to the Work of Marcel Mauss (F. Baker, Trans.) Routledge & Kegan Paul. (Original book published in 1950)

Shannon, C. (1963). The Mathematical Theory of Communication. University of Illinois. Van de Vijver G., Bazan A. and Detandt S. (2017). The Mark, the Thing, and the Object: On What Commands Repetition in Freud and Lacan. Frontiers in Psychology, 8, 2244. https://doi.org/10.3389/fpsyg.2017.02244

ŽIŽEK & SO ON PODCAST. (2022, July 17). Žižek on the Lacanian Real [Video]. YouTube. https://www.youtube.com/watch?v=InZUkhk4heg

Artist: Marcel Duchamp