Shakespearean tragedies show clear antagonisms and the resolutions are rational which means they obey the Aristotelian unity-ofaction principle. Any tragic play must rely upon its own movement. Therefore, it is complete and there should not be extra characters written only for the sake of resolution, so called "Deus-ex-Machina". In this work, Deus-ex-Machina characters are automatically detected using machine learning methods. We rst train unsupervised Doc2Vec network by using all plays of Shakespeare. Then, we collected all the lines uttered by each character in a separate document and extracted the document vectors. Thus, each character is represented with a vector in the semantic space of Shakespeare. We measure the semantic similarity between characters using the cosine di erence, the angle between normalized vectors of each character document and we observe characters form a cluster. According to this work, it is possible to detect Deus-ex-Machina characters. Examples of strong unity-of-action principle plays could be demonstrated as well as distinct characters. Dis/similar characters between the plays could also be shown.
The Shakespearean dramas are the most outstanding examples of theatrical
pieces. Most of the plays show clear antagonisms and the resolutions are very
rational which means the inter-character relations are consistent within the plays.
This is so called the "unity-of-action" principle. Any tragic play must rely upon
its own movement. There was no more need for a Deus-ex-Machina for the stage
of Shakespeare, though there are exceptions. The term is an invention of Greeks,
indicating a weakness according to Aristotle [
The above analyses is directly related to the recent state of the eld. The
literary criticism recently meets computerized analysis, [
In this paper, we would rstly like to overview our mathematical approach to have a document vector and then show o the experiments we carried out on Shakespearean characters as representing each character in a n-dimensional space. The last section is left to discussions on the characters and the relationship between the plays. 1.1
The eld of digital humanities (DH) mostly with the quantitative analyses of
literary and cultural studies [
The method proposed is an unsupervised neural learning algorithm. By this
way, each document can be represented by a document vector. The xed length
representation of each document helps to nd semantic relations between
documents. Similar documents are represented in a similar location in latent space.
The cosine similarity between vectors is used as a measure of similarity.
The document vector extraction is an unsupervised neural operation that
recursively predicts the next word [
For example, the context of given three words, "the", "cat" and "sat", the next word "on" is predicted. In this framework, every document is mapped to a unique vector, represented by a column in matrix D and every word is also mapped to a unique vector, represented by a column in matrix W. In the experiments, we use concatenation as the method to combine the vectors.
As an unsupervised process, there needs texts to train such algorithms. After training, at inference stage, the input texts can be mapped to a N-dimensional latent space. Semantically similar documents would have similar features, such as orientation or location. Consistency is important between training and inference texts, when constructing such latent space. The cosine similarity of any two N dimensional vector x and y computes L2normalized dot product, kxk kyk The Euclidean (L2) normalization projects the vectors onto the unit sphere, the angle between normalized vectors is the similarity measure k(x; y). (1) 3
Training dataset is the collection of Shakespeare dramas. Lines of each play treated as a document and trained for 40 epochs. A vocabulary is created out of all the plays. The number of documents is 37, it is low, the texts are long on average, around 20K. Vector length is 50. We use Gensim-Doc2Vec package.
At the inference stage, lines uttered by each character treated as a document and have a xed length vector representation in pretrained semantic space of Shakespeare. 4
In this section, the characters that have 40 lines or above are chosen for consistency analyses. The rst subsection is on detection of Deus-ex-Machina characters in each play. The distinct characters are identi ed in order to analyze the strength of a play, the unity-of-action principle. The second subsection left to similar characters between the plays. 4.1
Shakespearean comedies as well as tragedies are so strong in terms of dramatic structures. All can be thought of as Aristotelian. According to Aristotle, a play consists of complications, crisis and resolution. In the beginning of a play, the problems occur on protagonists. The crisis is the peak point which all problems need for a solution. According to Aristotle, the resolution should emerge from the plot itself. If the resolution comes as an outside force, for instance a Greek god appears at the end and kills the antagonists and saves the protagonists, this is so called Deus-ex-Machina. This is a weakness according to Aristotle. The play should be complete among the chain of events.
By thinking unity-of-action principle, we can assume that all characters in
a play should be related, their speeches should be coherent. In the previous
section, we construct a semantic space in an unsupervised manner by using
Shakespeare's all plays. In this semantic space, similar characters have similar
orientations. The position of the vector of a character has a semantic meaning.
In this semantic space, all characters of a play lie inside a cluster of a play, while
the Deus-ex-Machina characters would be distinct. Since Shakespeare's plays are
in dialog form, as the characters talk to each other, the semantic cluster of a play
forms. Following the conjuncture idea on literature by Moretti, [
In order to verify above conjecture, the cosine di erence between all characters is measured in pairs. By this way, similarities of all characters could be graphed in Figure 2 as a lower triangle. Each row and each column corresponds to a character, x and y in similarity function k(x; y), respectively. The document vector projections would be maximized, if there are semantic similarities between characters. Then, strongly similar characters, the characters that have similarity close to 1, are represented with reddish colors, while dissimilar characters are blueish.
In Figure 2, there graphed six plays by Shakespeare. Bottom row is Macbeth, Othello and The Tempest, respectively. These are very good examples of unityof-action principle. Three plays by Shakespeare demonstrate strong semantic similarity between characters. Each character's dialogues are at least 0.5 related to the others. Some of the characters are apparently more similar, for example, two main protagonists Macbeth and Lady Macbeth, in addition to Lady Macbeth and Banquo. Similarly, Othello and Iago are also intensely related, as well as Iago and Casio. These character pairs have importance for the play from a dramatic perspective. Strong semantic similarity is a good indicator.
The top row is Measure for Measure, Merchant of Venice and Richard III.
These plays have a distinct character, who has nearly no semantic similarity with
the rest of the characters. Mariana in Measure for Measure, Duke in Merchant
of Venice and Richmond in Richard III demonstrates a di erence from the rest.
In Richard III, Richmond clearly presents himself as a Deus-ex-Machina, as
drop to resolve the play. Mariana in Measure for Measure also has a similar
function in the play. The Duke in Merchant of Venice is literally a
Deus-exMachina [
In order to identify inter-play relations of characters, we measured and graphed semantic similarities among four plays, Macbeth, Richard III, Merchant of Venice, Othello, respectively. It is very apparent that within-play consistency is much denser than inter-play consistency. Each reddish triangle is a play, while the blue rectangles are inter-play relationships.
If we examine the dominant colors of rectangles that show inter-play relations, Macbeth and Merchant of Venice are least related plays, the dominant color is blue. On the other hand, Merchant of Venice and Othello, as having topics on revenge, have warmer colors. Besides, Macbeth and Richard III also have warmer colors, as their topics are mostly on taking the throne. The similarities between the plays can be observed from the dominant colors.
There are other observations on Figure 3. Some of the characters are almost similar to each character in di erent plays. Lady Macdu of Macbeth, Iago of Othello are examples of such characters, this is probably due to their compatible nature. In addition to that, Macbeth is dissimilar to all the characters in the rest of the other plays. Another interesting observation is the Duke in Merchant of Venice. Although the Duke is dissimilar to everyone within the play, it has similarities with other characters in other plays.
All in all, inter-play relations are demonstrated to a certain extent. It is very crucial to detect similar characters between dramas, for the purpose of play writing. Characters like Iago are compatible with everyone, while Duke-like characters can be found in other texts. Character similarities are observable by the analysis we proposed. 5
Thus far, we cover the analyses on the characters in each play and between the
plays. These two analyses can be useful from the perspective of play writing
as well as arti cial literature. It is kind of hard to have an evaluation metric
for any kind of generative model, however literary criticism helps to identify
basic characteristics of a play. Drama has a well-de ned form that shaped the
beginning with Aristotle. In a previous work, we had identi ed a way of showing
antagonisms, [
Richmond in Richard III and The Duke in Merchant of Venice are given as a successful identi cation of distinct characters. Algorithms almost always successfully detect these distinct characters, though exceptions. The weakness of such a method is based on the assumption of the characters. Instead of judging a character based on the lines, we treat the characters as a whole. All lines by a character are token and represented in a latent space. This holistic view of a character fails when dealing with multi-function characters like the Duke in Measure and Measure. In addition to these detection, the strongly similar characters are another observation. The most important characters of a play always show a strong similarity. We also observed that some of the characters are compatible with every other character. Lady Macdu and Iago are examples. Other types of characters are dissimilar to every other character in other plays, such as Macbeth. These observations are very important for the insight into the plays.
It is important to develop further evaluation metrics for drama. The
generative models have a promising future in terms of dialogs, [
Acknowledgments This work was supported by grant 12B03P4 of Bogazici University. The author would like to thank Muhittin Mungan for suggesting this Master of Science topic as his advisor and Meltem Gurle Mungan for her kind opinion. The author would also like to thank Prof. Berrin Yan koglu for reviewing article and actor Gunes Yak n for talks together on Shakespeare.