Visualization of Jacques Lacan’s Registers of the Psychoanalytic Field, and Discovery of Metaphor and of Metonymy. Analytical Case Study of Edgar Allan Poe’s “The Purloined Letter”

Visualization of Jacques Lacan’s Registers of the Psychoanalytic Field, and Discovery of Metaphor and of Metonymy. Analytical Case Study of Edgar Allan Poe’s “The Purloined Letter”

Fionn Murtagh, Giuseppe Iurato
Email: fmurtagh@acm.org
Abstract

We start with a description of Lacan’s work that we then take into our analytics methodology. In a first investigation, a Lacan-motivated template of the Poe story is fitted to the data. A segmentation of the storyline is used in order to map out the diachrony. Based on this, it will be shown how synchronous aspects, potentially related to Lacanian registers, can be sought. This demonstrates the effectiveness of an approach based on a model template of the storyline narrative. In a second and more comprehensive investigation, we develop an approach for revealing, that is, uncovering, Lacanian register relationships. Objectives of this work include the wide and general application of our methodology. This methodology is strongly based on the “letting the data speak” Correspondence Analysis analytics platform of Jean-Paul Benzécri, that is also the geometric data analysis, both qualitative and quantitative analytics, developed by Pierre Bourdieu.

Keywords: Text mining, narrative, Lacan registers, real, imaginary, symbolic, Correspondence Analysis.

1 General Objectives and Outline

Narrative analysis is at issue here, using what has been a highly profiled text in literary studies. Our approach is unsupervised, relative to supervised learning. It involves visualization of our data, using semantic content, in such a way that there is revealing of relationships in the data. This can be taken further, if so desired, in the direction of statistical modelling and supervised machine learning. Our desire though is to deal with dynamic and fluid expression, and flow and evolution in our data content. Therefore our analysis methodology is motivated very much by the visualization and the verbalization of our data (Blasius and Greenacre, 2014). We can even state (see subsection 2.5) that our methodology is data analysis integrated with information synthesis.

A prime objective in this work is the introducing of innovative potential, as both language studies and psychoanalysis still tend to reject quantifying approaches to text and psyche respectively. However, this is more due to historical differentiation within the sciences than to ultimate scientific justification. Lacan’s further development of psychoanalysis and the symbolic is affected by Lévi-Strauss’ structuralist reasoning, thus necessitating systematic approaches of visualizing these very structures. Structuralism and geometric data analysis share a common epistemology as both are genuinely relational or topological in their ways of conceptualizing entities. As a matter of fact, the first-ever presentation of correspondence analysis by Jean-Paul Benzécri dealt with textual data and the visualization of the structures that are hidden in texts. Thus, the main orientation of this paper is both innovative in a methodological sense and orthodox in an epistemological sense. In doing so, and due to the traceability of the methodic steps, it might invite scholars from language studies and psychoanalysis to apply similar strategies to their own research fields. (Cf. Acknowledgements.)

Our methodology is also highly cross-disciplinary. We aim to demonstrate how an important set of perspectives, developed by Lacan, are generally and broadly applicable, to literary theory. But an even greater objective is to apply Lacan’s work to practical investigative problem-solving, including psychoanalytical investigative work. Such is our ultimate aim and ambition.

In section 2, comprehensive background discussion is provided on Lacan’s revealing and relevant methodology.

An initial study that is exploratory is carried out in section 3. Geometric data analysis is our methodology, based on the work of eminent social scientist, Pierre Bourdieu, who followed in his work, eminent data scientist, Jean-Paul Benzécri, whose earliest work embraced mathematics and linguistics.

In section 4, we show how Lacanian registers can be visualized in the context of narrative flow. The culmination of such visualization is in subsection 4.5.

Then in section 5 we seek analytical perspectives that will be revealing in regard to discovering metaphor and metonymy. Synonyms in a semantic framework are of potential relevance. Word associations are analysed through clusters determined from the semantic mapping.

In the Conclusions, section 6, a link is provided to the Poe story following our preprocessing of it with each successive sentence on a new line. Furthermore a good part of the R software used in this work is provided.

2 Introduction to Lacan’s Registers and Analytical Framework

2.1 Jacques Lacan’s Language and Unconscious: Observing and Tracking the Imaginary and the Symbolic, Dynamically Engaged with the Real

Lacan’s reading of Poe’s story is closely based (although not explicitly indicated by Lacan) on Marie Bonaparte’s reading of the same Poe’s story, according to which the letter Dupin finds hanging in a letterholder between the “cheeks” of the fireplace represents the “rephallization” of the mother (i.e., the queen, with the letter as the phallus lacking to the queen). This has been just the main remark due to Derrida in the 1980s (Derrida 1980). See also Todd (1990, Part V, Ch. VIII, pp. 166-171).

Jacques Lacan’s seminar on this story by Edgar Allan Poe (Lacan, 1956) includes interpretation that is “sufficient for us to discern […] so perfect a verisimilitude that it may be said that truth here reveals its fictive arrangement”. A dialogue in the tale by Poe “presents the real complexity of what is ordinarily simplified, with the most confused results, in the notion of communication”. Complexity results from: “… communication is not transmissible in symbolic form. It may be maintained only in the relation with the object.” What is integral to this: “Language delivers its judgement to whoever knows how to hear it”.

Then: “What Freud teaches us in the text we are commenting on is that the subject must pass through the channels of the symbolic, but what is illustrated here is more gripping still: it is not only the subject, but the subjects, grasped in their intersubjectivity, […] who […] model their very being on the moment of the signifying chain which traverses them.”

The context, that we are dealing with, is simple if we just look at events from afar. Consider the following, in Lacan’s seminar. The signifier related to this purloined letter: “It remains for it now only to answer that very question, of what remains of a signifier when it has no more signification.” This is our interest too, even if: “what the ‘purloined letter’ nay, the ‘letter in sufferance,’ means is that a letter always arrives at its destination” . We now turn to the following work, Ragland (2015), in order to point out motivation and justification for what follows in this article, i.e., the general and potentially very beneficial and rewarding application.

Ragland (2015) presents a comprehensive account of Lacan’s work. Let us summarize the important perspectives for us in this work. All citations in the following part of this subsection are from Ragland (2015). At issue is how Lacan provides a “conceptualization of mind structure” (p. 107), and that (p. 112) “Lacan gives us a means to go beyond biological or cultural materialisms.” Therefore (p. 137) “Lacan was concerned with structure […] – not with the content of the unconscious.”

Language is both representation and also an instrument: “Language itself merely represents desire at one remove” (p. 3). “language promotes jouissance, not just communication, or information” (p. 2). Thus (p. 62), “speech (or writing) carry desire […] ‘discourse’ is not grammar”. In this perspective, then (p. 5), “for Lacan […] language is imposed from the outside. It is not innate or hardwired into the brain.”

Fundamental to Lacan is that language’s way of being an infrastructure for desire, is manifested visually and by shape, as summarized in the following terms (p. 51). “We have left behind the linear logic of linguistics and phenomenology and walked into the universe of multiform, contradictory logic that Lacan calls a way of ‘topologizing’.” For Lacan, one’s mind is related to one’s body, and the topology of the body are in particular what comprise holes, input and output, and the body surface (cf. p. 21). Important then for the mind is when body parts, and objects later, are perceived as missing, or are gaps. We have (p. 106): “the surface of the body marked by holes and rims (mouth, ear, nose, etc.)”

“For psychoanalysis, topology […] is not a metaphor, but confirms the presence of the real … Topology is an active showing of the real of structure.” (p. 120). “Topology […] is not a metaphor. Not an allegory. It does not represent the subject. […] Topology presents ‘the foundations of the subject’s position.’ The subject combines itself in the Borromean unit” (pp. 124–125). There follows how important the subject’s gaze, and “visual structure” are here.

For Lacan, “language is duplicitous”, and it expresses “affective knowledge”, and justification for this is how language is not a set, fixed (grammatical or taxonomic) structure, but is dynamical, and fluid (p. 114): “language is duplicitous, not only because it is an agent of repression, but also because it does not succeed in repressing the material of identifications that aim the drives towards lures, towards the goal of repeating the familiar.” “By bringing the drives into language as an affective knowledge – a montage of the real and the imaginary, the symbolic and imaginary, the real and symbolic – conflict or torsion can be proposed as a property of language whose referent is the concrete nature of the drives.” (pp. 115–116).

“In consideration of the predilection among intellectuals to think of language in purely abstract logical terms, it is vital that we become aware that there is a dynamics of language.” (pp. 116–117). Ultimately, at issue (p. 127) is how we have “language as signifying something other than what it says.”

Regarding “geometric” written in the following manner, it is stated that: “thought and body are geo-metric” (p. 12), “topological structure is a knowledge of being, not an academic knowledge” (p. 4), and (p. 108) “topology is not […] a knowledge to be taught by concepts or fundamental texts: ‘It is a practice of the hole and its edge’ ”

“As a mathematical knowledge of the real, topology itself draws ‘pictures’ of how body, language, and world co-exist, intertwined in contradictory ways, that can be explained logically all the same.” (p. 45). At issue is “Lacan’s theory of a topological ‘structuring’ of the unconscious” (p. 46). “Lacan’s topological forms […] introduces the real into language, as a set of affective, albeit emotionally ungraspable, meanings.” (p. 112).

Metaphor and metonymy are quite central issues here: “each of Lacan’s discourse structures has […] the double, substitutive structure of metaphor” (p. 57), and “interpretation works as a metaphor which allows substitution of one thing for another”(p. 5), with this perspective (p. 88): “the dialectical link between metaphor and metonymy as poetic tropes that make the brain function”, “He described condensation as metaphors (substitutes) linked to the object that causes desire […] by the concrete metonymous displacements and contiguities of desire.”

For Lacan, “structure is Borromean. By Borromean he means the knotting together of the symbolic, imaginary, and real dimensions bound together by the symptom/sinthome.” (p. 24). There are: “the three different dimensions of knowledge – the real, the symbolic, the imaginary” (p. 2).

So there is the following, with a major role in our work that will follow: “the signifying chain is not […] grammar, language, or writing, but, rather, a chain of dimensions — Real, Symbolic, Imaginary” (p. 63). Thus “the real of the (partial) drives […] what is repressed in the real returns, anyway, into the symbolic order of language and social conventions.” (p. 106). “The drive […] designates the prevalence of an ‘organic’ dimension of symbolic and imaginary traits that coalesce with the real of the flesh as a mapping in language” (p. 106).

While fully separate from what will follow in our analyses of Poe’s “The purloined letter”, it is nice to note, in the paragraph to follow, how Lacan also used the term “letter”!

“Ancient cave paintings were a writing before writing, a way to make a meaningness Lacan called the letter.” (p. 12). This expresses a role for this term, letter: “every truth has the structure of the fiction and that truth and fiction are linked by the letter. The function of the letter is topological. … it indicates the place where language and the unconscious are linked.” (p. 12). Here, there is: “a ‘letter’ or visual representation” (p. 127). “Lacan described the lettre as a place where being (l’être) resides between the unconscious and language, calling the lettre a localized signifier that one can recognize as language converging with the unconscious.” (p. 136).

2.2 Psychoanalytical Use of Edgar Allan Poe Story

Edgar Allan Poe’s “The Purloined Letter” (Poe, 1845a, 1845b, 1845c) is a story that is investigative and elaborative. It is not just explanatory, reducing the case study in this story to facts and assertions that are ordered. Rather, it is also elucidatory, and positioning in a larger, broader, contextual picture. Also this allows to identify better where truth lies by means of simple psychoanalytic tools. Positioning is done through contextualization. We hypothesize that any and all such elucidation, and contextual positioning, is potentially relevant for various domains such as theatre and drama, legends and mythology, and mutatis mutandis, for poetry and music.

Therefore, Poe’s story is not simply the investigation of illegal behaviour. There are parallels and analogies drawn with schoolboys playing with marbles and strangely enough with mathematical reasoning. These strange connections are just possible in the unconscious realm. A lot of foremost thinkers have discovered, or at least viewed, very interesting mappings of Poe’s story into the most interesting contexts. See Department of English at FJU (2010) for discussion with graphical portrayal of Michel Foucault, Jacques Lacan, Jacques Derrida and others.

Description follows of the psychoanalytical approach developed by Lacan, encompassing analysis of synchrony and of diachrony. Diachrony can be based on the inducing of a segmentation of the narrative or storyline into a sequence of main scenes or acts. The synchronous elements decompose any act by means of the three Lacanian registers or orders of the so-called psychoanalytic field in which every human event performs at the unconscious level. The three Lacanian registers, comprising the psychoanalytic field, are the real, the imaginary and the symbolic. Lacanian psychoanalysis seeks to outline the co-participation of these three registers in each event and subject of the story, but with a synchronic predominance of one over the others, which will then be the one that is diachronically identifiable. However this is only under the surface of symbolic, the only register that represents the other remaining two (Recalcati 2012–16, Vol. II, pp. 549–550).

Our study has the following objective. Firstly we seek to reveal or to determine Lacan’s registers in a highly realistic case study.

Our mapping of Lacan’s registers in the Poe story leads to visualization, to represent visually these registers, in the context of their roles. Specifically seeking metaphor and metonymy is at issue in a later section.

2.3 Source of Data and Preparation

In this subsection, and throughout this paper, we detail the data processing carried out, firstly for reproducibility of this study, and secondly for all aspects relating to generalization of this work, and application to other textually expressed content.

The Edgar Allan Poe text of “The Purloined Letter” was taken from Poe (1845a). Accented characters required correction, following the 1845 editions in Poe (1845a, 1845b, 1845c). A program was run on this text that determined sentence boundary (using a full stop), and also took into account blank lines that indicated paragraph boundary. Some cases of repeated dashes, repeated dots, exclamation marks and question marks were modified manually in the input text. The processing allows the specification of standard contractions that are not to be taken as sentence boundaries. (The following were at issue in regard to being ended with a full stop or period but this did not connote the end of a sentence: no, No, C, G, St.) A CSV (comma separated values) formatted file was created, with the sentence sequence number, the paragraph sequence number, and the sentence content. This led to 321 sentences and 123 paragraphs. For each paragraph, the speaker was also noted: the Narrator, Dupin and the Prefect. In section 2.4, some further background description on the Poe story will be provided.

2.4 Dramatis Personae

The characters in this short story are as follows: (1) C. Auguste Dupin (young private detective); (2) Monsieur “G – –”, or G. or Prefect (police chief); (3) the narrator (Dupin’s friend and roommate); (4) the Minister “D – –”, or “the D – –”, or the minister (the villain); (5 and 6) the personage [in the royal boudoir], or other unnamed royal person (often considered as Queen, King); and (7) “S –”, sender of the letter (only one occurrence of this name).

Examples follow of the first and the last sentences.

  • First: “At Paris, just after dark one gusty evening in the autumn of 18 – , I was enjoying the twofold luxury of meditation and a meerschaum, in company with my friend, C. Auguste Dupin, in his little back library, or book-closet, au troisième, No. 33 Rue Dunôt, Faubourg St. Germain.”

  • Last: “They are to be found in Crébillon’s ’Atrée”

2.5 Brief Background on the Geometric Data Analysis Methodology

Our approach is influenced by how the leading social scientist, Pierre Bourdieu, used the most effective inductive analytics developed by Jean-Paul Benzécri. See Le Roux and Rouanet (2004), Grenfell and Lebaron (2014), Lebaron and Roux (2015). This family of geometric data analysis methodologies, centrally based on Correspondence Analysis encompassing hierarchical clustering, and statistical modelling, not only organises the analysis methodology and domain of application, but even integrates them. The second in a set of principles for data analytics, listed in Benzécri (1973, page 6), included the following: “The model should follow the data, and not the reverse. … What we need is a rigorous method that extracts structures from data.” Closely coupled to this is that (Benzécri, 1983) “data synthesis” could be considered as equally if not more important relative to “data analysis”. Analysis and synthesis of data and information obviously go hand in hand.

The work of Andreas Schmitz, dealing with Angst and fear (Schmitz, 2015, Schmitz and Bayer, 2014), links together Freud and Bourdieu, for example, in regard to “libido within habitus-field theory”. Among the conclusions in Schmitz (2015) are how we have:

  1. “Libido constitutive for the foundational concepts of habitus and fields”.

  2. Janus-faced character of libido: interest and Angst as constitutive moments of (i) Habitus and practice, (ii) Social space and social fields, and (iii) Symbolic domination.

In Schmitz and Bayer (2014), also presented in Schmitz (2015), the limits are noted of statistical linear modelling for relating personality factors in social space. Moving beyond that methodology, there is categorical interest and personality types, accompanying the socio-structural information for the geometric construction of social space. The aim is to demonstrate in general, whether psychological characteristics will correspond with the structure of social space in a discontinuous way. (This summarizes perspectives in Schmitz and Bayer, 2014, p. 11. The following is from p. 14.) Habitus defines the nexus between structure and subject, whereby the correspondence of social position and “psychic” disposition are understood as class-specific, and thus discontinuous. Psychiatric indicators are used in a discontinuous way (as befits such categorical variables). From a psychoanalytic viewpoint, the habitus roughly corresponds to Freudian super-ego agency, hence it belongs to the Lacanian symbolic register. So, studying the latter, we might infer features of habitus, hence answer to the above issue regarding links between psychological characteristics and social structure. We shall focus on the linguistic.

3 First Exploratory Study: Analysis Using Simple Diachronic Model

Below, in this paper, most of the set of words in the Poe text are used. This is so as to take account of emotion and sentiment, expressed language-wise through adjectives and adverbs, and so on. Also below, text-based, i.e. data-based, story or narrative flows are considered.

In this first study, a somewhat simplified diachronic model of the Poe story is used. That is, a model of the evolution or flow of the story is used. This is strongly based on a Lacanian interpretation. Also in this first study, from the text of the Poe story, nouns are used. This is in order to have a relatively quick, first view of the relationship between key terms.

We consider now, the Lacanian motivation, and indeed justification, for this work.

Lacan’s psychoanalytic field is structured into three dimensions or orders, termed the Lacan registers, which may be considered as components of this field, closely linked to each other (Borromean knot). These are the symbolic register, the imaginary register and the real order. The Lacan psychoanalytic field relies on the unconscious realm.

The symbolic register is that field component in which signifiers act, operate and combine according to laws and rules of structural linguistics, above all the negation. The main law of this field component is the so-called Name-of-the-Father, which triggers the formation of the signifier’s chain. This register is the most prominent one in acting on the individual, through the intervention of imaginary register.

The imaginary register is that field component which springs out of the unconscious apprehension of one’s own bodily image of the child (mirror stage) on the basis of the primary dual relationship of identification with one’s own mother. It is the basis for the growth, by alterity, of the Ego agency and the narcissistic pushes, when mother, through Name-of-the-Father law, casts the child into the symbolic register, naming her or him.

The real order is that field component which is defined only in relation to symbolic and imaginary registers, where there is all that impossible, unbearable or inexpressible content expelled or rejected by these latter two registers. The symbolic and imaginary registers, together with the real order, are in relationship to each other, mostly in opposition.

A simple example of the action of the three registers is as follows. This is a good example of Imaginary-Symbolic interconnection. This is the case of Venice with its renowned carnival. Indeed, this carneval was instituted around 1090 and as early as that date, many tide phenomena flooded Venice. I.e., the unconscious-Imaginary impregnating Venice meant the coming about of this institution of the Symbolic to quite popular malcontents due to social status differences (just featuring the Symbolic), levelling these for instance with masks which made possible the anonymity, the indistinctness, that are most typical of such unconscious relationship as the mother-child relationship of the Imaginary. All the artistic creativity typical of Venice carnival is due, we can claim, to the irruption of the Imaginary (tide and flooding) in the Symbolic. This agrees with the well-known interest of Lacan toward surrealism! In this case, we might claim further that the fear of death due to the flooding of sea water, just belonging to the Real, is such that we have a practical example of Borromean interconnection We observe the Real-Imaginary-Symbolic relatationship.

Lacan registers Persona
Act 1
Real Queen aware of the letter’s content
(just belonging to Real register).
Inconceivable content of the letter,
besides, unknown.
Imaginary Queen worried about letter and its
content. This was then hidden.
The Queen belongs to this register
as she has hidden the letter; this is a
behaviour just belonging to
Imaginary register.
Symbolic Minister seizes letter using
apparent substitution with own
letter. The King, as main signifier
giving rise to the symbolic chain to
which he is inscribed.
Act 2
Real Police also unsuccessful.
Police were on Queen’s request.
Hence unaware.
[Required solution: link between
real (the Queen, the only persona to
know letter’s content) and symbolic
(Police interviews because of it
being inscribed in a symbolic
order).]
Imaginary This Imaginary register, in which
operates Minister (as a robber),
then seen as a poet (belonging to
imaginary register, the one related
to mere creativity and art), thanks
to which prefect didn’t catch him.
Indeed, Poe says too that prefect
(belonging to symbolic, i.e., the
blind person who does not see the
letter) would have caught him if he
had had a mathematician’s
behaviour (symbolic – see next Act
3), as Minister was both a poet
(imaginary) and a mathematician
(symbolic).
Symbolic Dupin, having his aim disguised,
sees probable letter; returns;
seizes letter using apparent
substitution with own letter.
Prefect and Police intervention
because of their nature and
behaviour which make them
belonging to symbolic register.
Act 3
Real Minister unaware, could be
threatened also by this affair.
Letter with its content now known
to Dupin and which might be
revealed.
Imaginary Dupin replacement letter had
sinister sentence. Dupin’s revenge
in regard to Minister, left to be
presaged or described or guessed
by the Crebillon sentence written
by Dupin.
Symbolic Here: the letter, the signifier, in its
circuit.
[It was/is real; the imaginary was
associated with it;
symbolic related to apparently
similar letters, and
also being related to various
associated contexts.]
Minister seen not as a poet (Act 2)
but as a mathematician with
accordingly a behaviour belonging
to symbolic register.
Table 1: Very summarized rendition of the Poe story. Summary of participant roles, relative to Lacanian registers.

The main message of this Lacan seminar is to stress the predominace of symbolic order in constituting human being as such, illustrating this by means of a Poe story in which Lacan emphasizes how a simple signifier (the letter, which reifes or materializes, according to Lacan, the death agency) and its pathway, determines the whole scenes, in particular, it determines the succession of the three personages involved there, with their role, each of whom occupies that position just determined by the letter (signifier) and its movements, which is never where it is as it is the symbol (in that, signifier) of an absence. On its turn, the seminar also stands out the imaginary’s impregnations owned by symbolic chain, which mark the unavoidable insistence of the death drive by means of the compulsion to repeat mechanism.

Lacan underscores the precedence of signifier (letter) on signified (letter’s content), which is besides unknown. What is important is that there is contained in this letter, whatever is its effective content which, nevertheless, cannot be revealed (real order) because it is a letter addressed to the queen who is inscribed into a precise symbolic register that, as such, surely warrants, in the symbolic chain in which it is inserted, the symbolic imposing, a priori, of the (unknown) signified just vehiculated by the (known) signifier. This latter will mould the disposition of the other various signifiers (personages) along a chain which will give rise to symbolic order. So, it will be the various personages of the scenes to be placed along a well-determined chain (of signifiers) of the symbolic order, and only this chain will be given, signified, to every subject (personage) so involved: the queen and the king are placed near real register because of the not revealable content of the letter (which is ineffable just because it belongs to the real register); the minister is mainly placed in the imaginary register (because of his feminine curiosity, intricacy and narcissistic push which led him to become even a thief), as well as Dupin, but with touches also with real register, which constantly provides the right fear to the intrepid actions which they perform; while police and prefect are located in the symbolic register because they represent the law and are in search of what belongs to symbolic, i.e., the letter, but without results because fully immersed in it, without the right amount of imaginary needs to see. Thus, signified (meaning) springs out only once the chain of signifiers (words) is established into the symbolic order. So, the symbolic order with the predominance of signifier on signified, moulds, in a well-determined chain, the various personages and their intersubjectivity: there cannot exist a single, isolated subjectivity but rather an inter-subjectivity provided by the reciprocal opposition between the elements existing in the chain along which they are placed, inserted just by symbolic order. Hence, it is the symbolic order of signifiers that give a precise disposition to the personages in action in the scenes, giving them too an intersubjectivity which exists only within this chain that determines them.

The consequences of the (besides unknown) content of the letter belong to the real register. The chain of signifiers that it emits, belongs to the symbolic register, while it is the imaginary which glues together the rings of such a chain, the register that can spring out only thanks the intervention of a woman (indeed, only the queen knows the real content of the letter) during the relation child-mother.

In Table 1, there is a useful, very summarized, rendition of the Edgar Allan Poe story. It is structured as what we label here as the succession of Acts 1, 2, 3. One register will dominate others synchronically, i.e. at any given time-point. The symbolic register will win out, in that there is a fairly natural progression from the real, to the imaginary, thereby resulting in the symbolic. The real register is occupied by what the symbolic ejects from reality, and that cannot by formalized by language.

In this first study, the Poe story consists of 321 sentences, and a corpus of 1741 words. These words are of length at least 1, all punctuation has been removed, and upper case has been set to lower case. Then we require a word to be present at least 5 times, and used in at least 5 sentences. Next, words in a stopword list were removed. These are (definite, indefinite) articles and common parts of verbs, and such words (using the tm, text mining, package in the R software package). Single letter words were also deleted (e.g. “s” resulting from “it’s”, or “d” resulting from “didn’t”, when the apostrophe here was replaced by a blank). Then just nouns alone were selected. There were 48 nouns at this stage. Some of the 321 sentences became empty. There were 213 non-empty sentences, as noted, crossed by 48 nouns. In the 213 sentences, there were 424 occurrences of these words.

The sentence set, characterized by words used, endowed with the chi squared metric is mapped, using Correspondence Analysis, into a Euclidean metric-endowed factor space. In order just to retain the most salient information from this semantic, factor space, we use the topmost 5 axes or factors. These 5 axes account for 17.75% of the inertia of the sentences cloud, or identically of the nouns cloud. Figure 1 displays the hierarchical clustering of the sentences, that are in their 5-dimensional semantic or factor space embedding. The complete link agglomerative clustering criterion permits adherence to the sequential order of the sentences (Murtagh, Ganz and McKie, 2009; Bécue-Bertaut et al., 2014, Legendre and Legendre, 2012).

Figure 1: Hierarchical clustering of sentence by sentence, based on the story’s sequential structure. There are 213 sentences here, being the terminal (or leaf) nodes, ordered from left to right. Each sentence contains some occurrences from the corpus of 48 nouns that are used. The vertical axis, for such a dendrogram, records the cluster criterion agglomeration values and levels.

To follow our template of three acts, we take the three largest clusters. In the dendrogram in Figure 1 we therefore have the partition, containing three clusters, close to the root node. These clusters relate to sentences 1 to 53, sentences 54 to 151, and sentences 152 to 213. These are to be now our acts 1, 2, 3, following the template set out descriptively in Table 1. The number of sentences in each of these acts is, respectively, 53, 98, 62. Next for analysis, we create a table crossing 3 acts by the noun set of 48 nouns.

The complete factor space mapping is just in 2 dimensions. We may just note the visualization benefits that follow the relating of nouns to what we term the acts, rather than the individual sentences. Figure 2 displays the words that have the highest contribution to the inertia of this plane. To see the relationship between the words that are close to the origin, thus essential to the whole of the narrative line, to all acts, Figure 3 displays the region of the plane that is close to the origin. We see “letter” and other words.

Figure 2: Correspondence Analysis, top contributing 20 words. Words with high contribution, somewhat overlapping in this display, with projections on the positive factor 1 are: case, microscope, school, reward, boy, furniture; and book, poet. Also displayed are the three acts, 1, 2, 3.
Figure 3: From Figure 2, here are shown the words that are near the origin.

We can try to investigate the internal structure of our “template” acts. Figure 4 displays the hierarchy (using the appropriate agglomerative criterion of Ward’s minimum variance) constructed in the 5-axis or 5-factor embedding of this data. From left to right here, the three clusters resulting from the dendrogram cutting, or slicing into a partition, as displayed, correspond mapping-wise to act 2, act 3, act 1. Cf. what is displayed in Figure 2.

Figure 4: Hierarchical clustering of the word set, from the 2-axes, correspondence factor space, semantic mapping of this data. Here the hierarchy structure is visually displayed.

With the perspective of Lacan’s registers we could look at a set of three clusters in each of these acts. Let us look at the leftmost cluster here. We can read off the following three clusters: first cluster, “reward, boy, case, school, furniture, microscope”; second cluster, “secret, course, thing”; third cluster, “chair, individual, book”. This has just been reading off three fairly clearly determined clusters. Of course we can see that the second cluster and the third cluster are merged fairly early on in this agglomerations.

Rather than attempting to relate these clusters with Lacan’s registers, let us instead just draw the following conclusion. In this first study, it has been shown how a template of segmentation can be easily considered. So the diachrony can be investigated. In our opinion, the retained words consisting of nouns are a good way to focus our study, and also while we succeeded well in imposing our template of the segmentation of the Poe story into three acts. However while they certainly lead to interesting perspectives, for general-purpose use of this methodology, it would be preferable to allow for a somewhat more open perspective on the data. This we do next, analysis of diachrony and of synchrony, both newly investigated.

4 Visualizing Lacanian Registers in the Narrative Flow

4.1 Lacanian Framework

Fundamental aspects of Lacanian methodology encompass the following (Richardson, 1985).

  • Metonymy, e.g. the name of the cause is used for denoting the effect or the object; it is associated with, and expressed by, diachronicity. Diachronicity horizontally combines patterns into metonymy. Finally, metonymy is to be associated with (Freudian) unconscious displacement, shifting and moving, under the pushes or drives of desire, the various signifiers, without an end but rather aimed always at seeking the lost object (lacking for the human) which escapes every signification.

    Metaphor, e.g. a word or term is replaced with another similar or analogous term; through selection, metaphor is enabled by synchronicity. Synchronicity vertically selects patterns into metaphor. Finally, metaphor corresponds to (Freudian) unconscious condensation, which disguises and upsets meanings, until reaching the deepest unconscious levels.

    Metonymy and metaphor are the two main (Freudian) pathways of semantic action.

  • Signifiers will constitute the symbolic register. These signifiers combine like the basic structural elements of a language. The signifiers of the symbolic register undergo the rules of metonymy and metaphor.

    For Lacan, the signifier dominates the signified, and not vice versa (as for Ferdinand de Saussure), through certain structural rules (similar to the linguistic ones) in which the former (signifiers) link together to give rise to signifier chains. Signifier chains are diachronic combination of signifiers synchronically selected, in which the signifiers follow each other oppositionally, like the words of a phrase.

    Indeed, (synchronic) selection includes the case where a signifier excludes another one but remains in relationship with that other signifier, at least negatively, according to Aristotelian logic. These signifier chains will acquire then a conscious meaning following usual grammatical rules.

  • The Imaginary is a register complementary to the Symbolic one. Generally, it is the realm of images and of the sensible representations (mostly, the visual ones) which mark our own lived experience. Imaginary fantasies and representations (thing representations) belong to the imaginary register as well, which will prepare the ground for the subsequent word representation.

  • The Real is not reality as this is usually meant, that is to say, the world of everyday experience, which is already characterized by images and symbolic language, but it rather deals with the primary, rough experience of what is still not symbolized or imagined, with the impossible, that is to say, what is impossible to inscribe in every symbolic system, or however represented in any possible imaging form.

4.2 Narrative Flows

All discourses, happenings, history, etc. are narratives, with one or more, and often many, narrative flows. In the narrative, there are various chronologies that may be investigated as sub-narratives. These include the sequence resulting from: (i) sections, (ii) speaker or agent, (iii) time or date or location, (iv) statistical segmentation into sections. The latter may be through syntax and style based clustering since tool words (function words) predominate. To the above can be added: (v) sentences, (vi) paragraphs. All this, is the result of the diachronic nature of the discourse, which, therefore, is explainable through Lacanian theory. In particular, Lacan points out that, in the symbolic register, the diachronic selection axis of discourse is closely related with synchronic combination of signifiers which gives rise to the diachronic meaning, or signified, of the discourse. These combination and selection processes, taking place in the symbolic register, are greatly influenced by the real register and, especially, by the imaginary register. These latter both push on the former.

We seek the most enlightening or the most illustrative of these narrative flows. By enlightening, we intend: seeking or determining specific outcomes. By illustrative, we intend: detecting or observing dialectical movement, or Aristotelian logic, or unconscious mind processes.

We are most interested in (i) metaphor, being an indicator of unconscious mind processes, for its synchronic nature, and (ii) metonymy, i.e. a term indicating diachronic employment (or use), that can be, therefore, transfer and handover.

Following the mapping of the text story into a semantic space, in regard to combinations of signifiers according to Lacan, for (i) metaphor, due to its synchronic nature, we use clustering. While, for (ii) metonymy, due to its diachronic nature, we use sequence constrained, i.e. chronologically constrained clustering. In (i) our aim is close association, expressed by highly compact clusters, while in (ii), we may consider varied chronological flows.

Our semantic analysis starting point is the set of all interrelations between narrative flow segments, belonging to the diachronic selection axis, and the words selected and retained, belonging to synchronic combination axis. We have that: “One terms the distribution of a word the set of its possible environments” (Benzécri, 1982).

4.3 Text Narrative Analysis: Initial Processing Stages

The Poe story, in our text formatting, consists of 321 sentences, arranged as 123 paragraphs. As noted above, paragraph here is defined as text segments that are separated by blank lines. That includes vocal expressions, perhaps with some additional explanatory text, and also it may be noted that a few of the vocal expressions can be quite short. Nonetheless it is clearly the case that the paragraphs form useful text, and narrative, segments.

Next we also considered a segmentation into 8 sections, based on a reading of the Poe story. The introduction part of the story had 19 paragraphs. The initial outlining of the essential story, relating to the purloined letter, told by the Prefect with dialogue elements from the narrator and from Dupin, constituted section 2, with 26 paragraphs. Section 3, with 28 paragraphs recounted the Prefect’s search of the Minister’s hotel room. Section 4, with 14 paragraphs, takes place one month later, detailing the revelation that Dupin could provide the letter to the Prefect. Then section 5, with 6 paragraphs, starts off the background explanation by Dupin to the narrator. Section 6, with 16 paragraphs, continues in great detail as Dupin provides explanation to the narrator. Section 7, with 8 paragraphs, is the core of the storyline, where Dupin explains how he found the letter, how this was verified by him, and how he took hold of it in the following morning, putting what is referred to as a facsimile in its place. Finally section 8, with 6 paragraphs, is the explanation of, and justification for, the replacement of the letter by a facsimile.

Because of the consolidated and integrated description, with motivation and explanation, Dupin’s explanation of all of this, in sections 5, 6, 7, 8, may be additionally considered in our analysis. We have just noted the paragraphs that correspond to these sections. Section 5 begins with sentence 172 (in the set of 321 sentences). So the Dupin explanatory sub-narrative, in dialogue with the narrator, embraces sentences 172 to 321, that is, paragraphs 88 to 123. So the Dupin sub-narrative here comprises 151 sentences, that are in 36 paragraphs.

Our next step in data preprocessing is to select the word corpus that will be used. This starts with removal of all punctuation, numeric characters, and the setting of upper case to lower case.

It is reasonable here to remove tool words, also referred to as function words. In Murtagh (2005, chapter 5), and in Murtagh and Ganz (2015), the case is made for these function words in mapping emotional narrative or stylistics (e.g. to determine authorship), but these are not of direct and immediate relevance here. Instead, as outlined in section 2.1, metaphor and metonymy are the forensic indicators, or perhaps even the forensic highlights, for us.

Sufficient usage of the word in the storyline is important. While very clearly the case that one-off (isolated, unique) use of a word can be very revealing, nonetheless we leave such an investigation to an alternative comparative study of storyline texts. Sufficiently frequent word usage both supports comparability between the text units we are studying, and also permits the focus of the analysis to be on inter-relationships, and not on uniqueness of word usage. Therefore we require the following for our word corpus: that a word be used at least 3 times in the overall storyline, and that this word be used in at least 3 of the text units (sentence, paragraph, section) that we are dealing with.

For the 321 sentences, we start with 1742 words. There are, in total, 7089 occurrences of these words. Then, having removed stop words, and requiring that a word appear in 3 sentences and be used at least 3 times, we find that our 321 sentences are characterized by 276 words. There are 1546 occurrences, in total, of the corpus of 276 words.

For the paragraphs, proceeding along the same lines, the 123-paragraph set is characterized by the 276 word set, and there are, as for the sentence set, 1546 occurrences, in total, of the corpus of 276 words.

For the sections, once again proceeding along the same lines, the 8-section set is characterized by the 276 word set, and, again clearly, there are 1546 occurrences, in total, of the corpus of 276 words.

This data preprocessing and selection is carried out for the following objectives.

Firstly, we will have one or more levels of text (hence, storyline) unit aggregation so that the principal factor space axes account for most of the information content. (Were it the case of having rare words in the analysis, then axes would be formed in the factor space to account for them.) We recall that for text units, characterized by terms, the factor space dimensionality will be min( , ). This first point relates to the use of paragraphs and sections. (Let us note that in Bécue-Bertaut et al. (2014), where the flow and evolution of narrative is the aim, our aim is a little different here, because the text units that encompass the most basic text units, the sentences, can be themselves interpretable. Cf., e.g. vocal expression on a theme being all in one paragraph.)

Secondly, our selection of words directly impacts the interpretation of the data.

4.4 A Preliminary Visualization of the Narrative Structure

We have here the successive sentences characterized by their constituent words, from the retained corpus. We firstly map the cloud of sentences, 321 sentence cloud in a 276-dimensional word set space, into a Correspondence Analysis factor space. Since the word set has been reduced from the original set of 1742 words, some sentences become empty. Non-empty sentences account for 310 of these 321 sentences. In Figure 5 we required words to be at least 5 characters long. This led to a corpus of 205 words, with 293 sentences not becoming empty.

Figure 5: Contiguity-constrained, where contiguity is the chronology or timeline, hierarchical clustering of the 321 sentences. These sentences are characterized by their word set (1087 occurrences of 205 words). This hierarchy is constructed in the factor space, of dimension 5, that is endowed with the Euclidean metric. Due to the reduced word entailing that some sentences become empty, the number of sentences in the correspondence factor analysis was 293 (from the 321). Here the dendrogram structure is displayed.

In Figure 5, sentences 11 and 12 are merged very early in the sequence of agglomerations, and these sentences are found to be quite exceptional. They are as follows: Narrator: “Nothing more in the assassination way I hope?”, Prefect: “Oh, no; nothing of that nature.” The two large clusters that are merged at the 3rd last agglomeration level have the last sentence of the first large cluster, and the first sentence of the second large cluster as follows. Sentence 182: “But he perpetually errs by being too deep or too shallow for the matter in hand; and many a school-boy is a better reasoner than he.” Sentence 193: “I knew one about eight years of age, whose success at guessing in the game of ‘even and odd’ attracted universal admiration.” This is early in what has been taken as the Dupin explanatory section of the narrative. The second very large cluster constitutes the major part of this Dupin explanatory part of the storyline.

In Bécue-Bertaut et al. (2014), it is described how the text units, taking account of the chronological order, can be statistically assessed (using a permutation-based statistical significance testing) at each agglomeration, for the agglomeration to be based on a pair of homogeneous clusters. This allows derivation of a partition of the set of text units. Since the chronological, hence contiguity, constraint applies, this partition is a statistically defined segmentation of the text units. In this particular work, we prefer to use paragraphs and sections, as described above, in view of their interpretability.

4.5 Visualization of Lacanian Registers from Semantic Analysis of Chronology Using Storyline Segments

In this section, we are most concerned with diachrony, or the evolution of the narrative. For this, we find a correspondence – what we may refer to as homology, in the sense of Bourdieu-related geometric data analysis – between a pattern that we uncover in the data, and Lacan’s registers, viz. the Real, the Imaginary and the Symbolic. In the storyline here, we find an evolution, or narrative trajectory, between these registers. Lacan’s registers are of value to us as an interpretive viewpoint. It has been noted above in section 4.1, how both synchrony and diachrony of the semantics of the storyline narrative are of importance here. As noted also, we can determine statistically a segmentation of the narrative. This is achieved through first mapping the narrative into the semantic factor space, taking account of all interrelationships of narrative text units and the words and terms that are associated with these text units. For interpretation, we prefer, see section 4.3, to use what we have selected as natural segments in the narrative text.

The cumulative percentages of inertia associated with factors 1 to 7 are as follows: 20.2, 38.1, 54.2, 68.8, 81.5, 92.9, 100. The principal factor plane is displayed in Figures 6, 7. The chronological trajectory is to be seen in the first of these figures. The second figure has a triangular pattern, that is a display of the narrative, with reference to the chronology of the narrative. Usually with such a triangular pattern, we look especially towards the apexes in order to understand it. Figure 7 shows the most important words.

Figure 6: Principal factor plane of the 8 story segments crossed by the 1546 occurrences from the selected 276-word corpus. Arrows link the successive segments, numbered 1 to 8.
Figure 7: Displayed here are the 40 words that most contribute to the inertia of these factors, factors 1 and 2. In the upper right (beyond equal, poet), terms are: mathematician, world, value, truths, see, mathematical, intellect, fail, error, ingenuity, identification, hidden, given, concealment, reason, hand.

From this display, taking the figures 6, 7 (not overlaid in the same figure, to make the displays clearer), we can conclude in this way: segments 1, 2, 3, 4 are gathering facts and impressions from the Real; segment 5 advances into the Imaginary; segment 6 expresses this in a Symbolic way; and that allows a consolidated, integrated, “overall picture”, core of segments 7, 8.

In Figures 8 and 9, factors 3 and 4 are displayed. If this viewpoint expressed above is acceptable, namely that segments 5 and 6 comprise the move towards the Imaginary, then towards the Symbolic, then we can draw this perspective: that the effect of these two segments in the overall narrative is to take such segments as segments 3 and 4, operating in the Real, then work through the Imaginary and Symbolic discussion, and arrive then, as a consequence, at the final, terminal and more conclusive segments, segments 7 and 8. In a way, we are drawing the conclusion, from this particular storyline, as to how the Imaginary and the Symbolic serve to be taken into (and become part of) the Real, or how the Symbolic emerges from the Real and the Imaginary.

Figure 8: Plane of factors 3, 4, displaying the 8 story segments, with arrows linking the successive segments, numbered 1 to 8.
Figure 9: The 40 words that most contribute to the inertia of these factors, factors 3 and 4. The word dname is a rewritten form of “D–”, i.e. Minister D. In the text, there is discussed: the Real, left here; the Imaginary, upper right; and the Symbolic, lower right.

Moving on now to the third and fourth factor plane, Figure 9, there is a more interesting and selective perspective, given our interest in having an informative visualization of Lacanian registers. We propose the following perspective on this figure, Figure 9. Take the words on the left, negative half axis of factor 3, as pertaining to a Real register. Therefore, mostly, they betoken the unknown or the unknowable. Next, take many of the words displayed in the upper right quadrant as associated with the Imaginary. This includes “furniture”, “houses”, “microscope” and so on. This is how we can imagine problem-solving. Thirdly, and finally, take many of the words in the lower right quadrant as betokening the Symbolic. What we have here is money, payment. In other words, in a practical setting here, the problem solving is associated with the symbolic value of money.

We conclude that Lacan’s registers have been of major benefit in providing semantic-related understanding of the essential pattern that we determined in the narrative chronology. Such homology of semantic structure, i.e. morphology of narrative, is to be sought in any domain, such as the Poe story here, that can be modelled through Lacan’s registers.

5 Textual Data Mining as a Basis for Discovery Metaphor and Metonymy

5.1 Contextual, Semantic Clustering

In order to provide a basis for metaphor and metonymy finding, we will use the dominant words in clusters that we determine. For general data mining, a particular selection of words is used.

In summary, from section 3, we start with the 1741 words derived from the 321 sentences in the Poe story. Firstly, in order to exclude anomalous words, because of their exceptionality, we require that a word is used in at least 5 sentences, and that the word is used at least 5 times. This will also remove the small number of French words used in the Poe story. Secondly we exclude English stopwords. That resulted in 127 words being retained. In this general data mining framework, thirdly, we decided to retain only nouns. That resulted in 48 words being retained. Some sentences become empty through removal of their words. This left us with 213 non-empty sentences, i.e. 213 sentences crossed by 48 words. In addition, to focus our data mining, we used the three acts in the Poe story, as defined in section 3. That aggregated the sentences comprising these three successive parts of the story. So we use two data sets, 213 sentences crossed by 48 words, and 3 acts crossed by 48 words.

Carrying out a hierarchical clustering on the full Correspondence Analysis ensures that the Euclidean metric endowed space is fully appropriate to have clustering carried out, using the minimal variance agglomerative criterion (i.e. minimal change in inertia, or variance since all masses are unity). The full factor space dimensionality is used so that there is no loss of information through reduction in dimensionality. Such is not always the best approach because it could be argued that the principal factors represent the essential interpretational information.

From the 213 sentences ×48 retained set of nouns, the minimum variance (or Ward criterion) hierarchical clustering gave a partition into 10 clusters, using the greatest change in variance. For the 3 acts 48 retained set of nouns, the same criterion gave a partition into 3 clusters.

For the first of these, there are the following non-singleton clusters: cluster 1, boy, school; cluster 5, individual, microscope, doubt; cluster 7, letter, prefect, dupin, minister, document; cluster 8, paper, power, secret; cluster 9, poet, mathematician; and cluster 10, design, reason. Very close semantic similarities are clear here. We may consider poet being a metaphor for mathematician, and vice versa. While letter is strongly related to paper, document, it is also metaphorically related to power and secret.

For the acts crossed by words data, there are the following clusters: cluster 1, table, fact, document, possession, dupin; cluster 2, conversation, length, hotel, good, paper; and cluster 3, book, individual, boy, case, furniture. We interpret this output as overly concentrated, that it can be considered in relation to Lacanian registers, but that it is of less directly interpretable value compared to the previous output, described in the previous paragraph.

Another approach to addressing the discovery of metaphor, and related interpretable outcomes, is to carry out the clustering – hierarchic clustering, followed here by partitioning – on the sentences, and then to investigate the words that are statistically significant for the clusters that are found. Hypothesis testing is carried out using the v-test (Husson et al., 2011). For the acts crossed by words data, there is not great statistical significance. For the sentences crossed by words data, a most interesting set of three clusters, in the greatest change in variance partition, is obtained. Cluster 3 (with arbitrary numerical labelling of clustering) has the words reason and design. Cluster 2 has the words poet and mathematician. Finally, cluster 1 has all of these words: reason and design, and poet and mathematician. Very interestingly, we find here that poet and mathematician are metaphorically related through their involvement in reason and in design. We consider that this also provides for metonymy.

We may with to look for pointers towards the triad that defines a metaphor (e.g., poet, mathematician, and reason; poet, mathematician, and design). Consider how Ricoeur (1977, p. 276) conceptualized this: “We arrive at metaphor in the midst of examples where it is said, for instance, that a certain picture that possesses the colour grey expresses sadness. In other words, metaphor concerns an inverted operation of reference plus an operation of transference. Close attention must be paid, therefore, to this series – reversed reference, exemplification, (literal) possession of a predicate, expression as metaphorical possession of non-verbal predicates (e.g. a sad colour).” Thus in brief, we may consider here that x = picture, y = grey, z = sadness, and we have the proximity of x and y that we may view as comprising the apexes of the base of an isosceles triangle. A triangle that is isosceles with small base is the defining property of an ultrametric topology (i.e. representing a tree or hierarchical relationship). Such an ultrametric relationship expresses unconscious reason, cf. Murtagh (2012a, 2012b, 2014).

From looking at the close semantic (i.e., based on the semantic factor space embedding) association of cluster members, we have pointers to what could play the role of metaphor, being locally and temporally, contextualized synonyms. This is together with what could, over a time line, play the role of metonymy.

A final issue addressed now is in regard to metonymy. Aspects of the imaginary and symbolic are potentially of relevance, including the poet and mathematician referred to in the purloined letter case, and symbolic rationalisation from the school boy with his marbles. Essentially, relationships are to be determined and discovered in the semantic factor space. They may be then further assessed relative to the original data. As an illustration of this, consider a selection of words retained, crossed by what we are referring to as acts in the Poe story, Table 2.

Act letter dupin minister police power prefect question reason reward search secret
1 8 13 5 2 5 8 3 2 0 1 1
2 13 15 6 3 0 13 4 1 7 5 3
3 11 4 9 1 1 8 0 4 0 3 1
Table 2: The acts are the successive major segments of the Poe story. From the 48 words retained here, the frequency of occurrence data is shown for a selection of 11 words.

5.2 Further Exploration of Statistically Significant Word Associations

For close associations of words leading to either metaphor or metonymy, we adopt the following principles. Firstly, we seek such associations from the data, and we do not impose an a priori statistically-based probabilistic model or other prespecified criterion. Secondly we want to have such associations contextualized. The latter is for the seeking of associations to be in semantically-defined clusters.

We also investigated the chronology based on the following: the sequence of sentences; the sequence of paragraphs, i.e. text segments, that were mostly either a continuous speech segment, or relating to an individual; a set of eight sections covering the entire story that was manually segmented, approximately in line with the timeline; and four statistical segmentations of the storyline based on combinatorial probabilistic significance levels. Successive segmentation of the storyline was, respectively, with the following numbers of segments: 321, 123, 8, 46, 26, 13, 11. It was found that these sequences were weakly correlated with the factors. As supplementary elements on the factor space planar projection, they were very close to the origin. We conclude that there is not much that carries chronological meaning in this story. That is on the global or overall level. Word associations or sequences (that could play a role in metaphor or in metonymy formation) are a different issue.

Based on the Correspondence Analysis factor space mapping, endowed with the Euclidean distance, the clustering of sentences and also of words was investigated. Although distinct in regard to the basis for the clustering, while of course using the minimum variance – hence inertia in the Euclidean-endowed factor space – agglomerative criterion, the outcomes implicitly share the 5-dimensional (used just by default as a small set of factors) input.

It has already been noted how factor 1 counterposes the specifics of investigation to the ancillary small sub-narratives, relating to mathematical thinking analogies (upper right quadrant) and to the marble-playing schoolchild motivation and decision-making analogies (lower right quadrant).

The 5-class partition obtained allows us to look closely at some of the clusters. These clusters are of cardinalities, for the words: 10, 218, 5, 19, 24, and for the sentences: 8, 258, 6, 21, 17. They are in sequence of their mean value projections, from left to right on the first axis.

Let us look at low level partitions in the dendrogram in order to select small cardinality, very compact clusters. Following Husson et al. (2011, p. 151) we can use the v-test of association of the category presence values relative to the mean value of that variable. This allows for a null hypothesis test of “the average … for [the] category … is equal to the general average”, “in other words, [the] variable does not characterise [the] category … and can therefore calculate a p-value”. A p-value not far from zero indicated rejection of that null hypothesis. That is to say, a p-value near zero indicates that the variable emphatically does characterise the category.

When we look at an 11-class partition we find classes 1 and 2 consisting of:

Class 1:
            p.value of H0 using v.test
puff        1.188185e-13
abernethy   1.097031e-03

Class 2:
            p.value for v.test
probed      1.693836e-06
looked      1.758749e-03

Class 5 with the following words, with p-values of the v-test less than 0.05 (therefore rejecting the null hypothesis here at the 95% significance level): letter, man, ordinary, gname, reward, asked (Here gname is the Prefect. There is for example the following in the Poe text: “Monsieur G – – , the Prefect of the Parisian police.”). In this 11-cluster partition, class 10 is mainly about the mathematical analogies, and class 11 is about the schoolboy analogies.

In order to find some small clusters, leading to useful relationships that are semantically very close due to cluster compactness, we looked at various sized partitions derived from the hierarchical clustering dendrogram. From a 50-cluster partition, we find the following.

Cluster 40 consisted of the words “mathematician”, “poet”.

Cluster 43 consisted of the words “example”, “analysis”, “algebra”.

Cluster 47 consisted of the words “reason”, “mathematical”.

Cluster 48 consisted of the words “truths”, “general”.

Cluster 50 consisted of the words “truths”, “mathematical”.

Cluster 15, including “letter” had these words: “possession”, “letter”, “premises”, “still”, “since”, “observed”, “said”, “main”, “far”, “power”.

Cluster 1 consisted of “puff”, “abernathy”.

Cluster 20 consisted of the words “document”, “especially”, “things”, “point”, “importance”.

Cluster 27 consisted of the words “personage”, “document”, “royal”, “thorough”, “necessity”, “question”, “make”.

Our overall objectives here are to determine potentially interesting word associations, that could then be taken as, or found to be, some triadic metaphor (synchronic) relationship, or metonymy, a diachronic relationship. Richardson (1985) has discussion of time dimension of consciousness, related to diachrony. (This relates to the Vietnam War, and is different from our work here.)

Synchrony is indicative of the contemporary presence of all three Lacanian registers in every human act. Word-wise and textually, this may be inferred only by means of metaphors. But consciousness may reflect or echo the message of only one out of these three, which therefore provides explanation in a sequential manner, parallel to the arrow of time which characterizes human consciousness. In Iurato et al. (2016), at issue is the origin of human consciousness. This is linked to time development, that gives rise to diachrony, and we refer to this for further examples of this type.

In very general analogy to the observational science of astronomy, we do not seek to statistically test the properties of what is found, but rather to obtain relevant, candidate relationships, that, as candidate relationships, will then be assessed further in other contexts. Such, we may wish to state, could be considered for the words “poet” and “mathematician” in this case.

6 Conclusions

In this work, we introduce for the first time quantitative text analysis in humanities, and in psychoanalysis in particular, that casts a bridge between human and what are termed natural or exact sciences

Through the semantic mapping of the storyline, we have a visualization approach for displaying how patterns found can be related to Lacanian registers.

This semantic mapping is into the Euclidean metric endowed factor space. All relationships between the units of analysis, e.g. sentences, paragraphs, text segments, and their attributes, here retained word sets, i.e. corpora, are accounted for in the mapping into the factor space, so in that sense, i.e. taking account of all interrelationships, this is a semantic mapping. The endowing of the dual spaces of text units and their attributes with the Euclidean metric in the factor space is from the initial text unit and attribute spaces that are endowed with the chi squared metric.

We have then considered approaches to the clustering of semantic and contextualized data. Beyond the semantics as such, the main contextualization at issue here is relating to chronology. We considered different chronological units, including successive sentences, successive speaker-related paragraphs, story segments that can be helpful for summarizing one’s understanding, and for focusing one’s interpretation.

In the sense of unsupervised classification and exploratory data analysis, our approach is both “The model should follow the data, and not the reverse!” (Benzécri quotation) and “Let the data speak for themselves” (Tukey quotation).

Our text analysis has pointed out the intertwining among three Lacanian registers. The storyline segments, in the semantic analysis, identify a quasi-cyclic circuit starting from the Real and the Imaginary registers to the Symbolic one.

In all the planar projection plots related to this semantic analysis of chronology by means of storyline segments, we note that Imaginary clusters are almost always placed in the centre of each diagram (clearly in Figure 8), besides to be the intermediate, hinge step between the Real (the realm of angst and fear according to Schmitz, 2015, Schmitz and Bayer, 2014) and the Symbolic (socio-symbolic domination of Schmitz). So the Symbolic roughly corresponds to Schmitz’s Habitus-field intermezzo, coherently with the fact that Lacanian Symbolic corresponds to Freud’s Super-Ego agency, the place in which there takes place the crucial passage from thing representation to word representation. Furthermore, we also note the prevalence of Real register in the first steps of semantic storyline, moving to Imaginary toward Symbolic, the prevalence of unconscious realm underlying conscious meaning of language.

To aid in reproducibility of our research findings, a copy of the Poe story, as a CSV (comma separated value) format with sentences on successive lines, and much of the R code used in the analytics at issue here, have been provided at this address: http://www.narrativization.com

In conclusion, our Correspondence Analysis of Poe’s story has been useful in identifying certain formal structures resembling the action of Lacan’s registers in giving rise to language.

Acknowledgements

To add acknowledgement for paragraph 2 of the Introduction section.

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