Modelling the Semantic Landscape of Angels in Augustine of Hippo

1.1 Computationally Assisted Text Analysis

In recent years, the employment of mathematical modelling via computational methods has risen not only in the humanities in general but also among classicists and New Testament scholars.^[1] The variety of applications is almost as diverse as the different research questions, for which reason it becomes almost impossible to speak of computational methods per se, and each study has its own research question and its own aim.^[2] Within the humanities and theological disciplines when working computationally, i.e. analysing texts assisted by mathematical models, we need to be fully open about the parameters set in order for “non-computational,” colleagues to follow along. Our aim in this contribution is thus to analyse the angelology in Augustine with a method called word-embedding while prioritising a detailed description of the steps involved in conducting such an analysis. In accordance with the aim of this special issue of Mathematical Modelling Early Christian Literature, our contribution here will evaluate the strengths and weaknesses of this approach, specifically, the use of word-embedding. The computational methods are not a means in themselves, but assisting tools in analysing and unfolding insights of research questions, in this case, Augustine’s angelology, and nevertheless, we wish to prioritise space in the contribution for showcasing and outlining the methodology, as well as the “unstated” or hidden assumptions that lie behind the methodology in order to continue bridging a perceived gap between “digital” and “traditional” research methods.

Computational text analytical methods arise from the possibilities offered from “data mining” and “knowledge discovery in databases” which won terrain in the 1990s.^[3] The Italian literary scholar Franco Moretti provocatively encouraged that, “we know how to read texts, now let’s learn not to read them.”^[4] One of Moretti’s students, Matthew Jockers, followed the lines of Moretti, but advocated also for employing a “blended method.”^[5] In recent years, manifold examples of computationally integrative research have been employed.^[6]

One of the most recognised forms of computational methods is the stylometric approach of determining authorship or structural questions.^[7] The methodological setup of stylometry is usually to take a debate embedded in a research tradition and reassess the question moving from a qualitative analysis to a quantitative stylometric “bottom-up”-analysis, where, for example, minor features of conjunctions, pronouns, word-sequences reveal “hidden” structures and can offer quantitative results.^[8] Some computational approaches in recent years take a similar methodological setup, of reassessing a discussion embedded in the literature, for example, in discussing the structure of the Danish mediaeval work of Saxo Grammaticus (ca. 1180-1210), Gesta Danorum.^[9] In this study, the methodological aim is to “combine automated techniques … in order to reassess Gesta Danorum’s composition debate.” Moreover, it is stated in the study that their approach “is more akin to qualitative text analysis as it is practised in the humanities and social sciences, but it utilises the transparency and formal rigour of mathematics and computation.”^[10] The foundational idea here is similar to the methodological approach we stress in this contribution, namely, that a) the need to embed methods in a research context and b) the combination and cross-fertilisation of computational and traditional, close-reading methods.^[11]

2.1 Text as Data and Its Preparation

2.2 Word Embedding

After structuring and transforming the text into numerical data, the data are ready to be modelled. At this stage, a wide range of modelling are available for extracting patterns and information from the text, which depends on the research question at hand. Since we in this investigation focus on angelic terms in a large text corpus, we have selected the method of word embedding, which is suitable for this purpose. As mentioned earlier, word embedding vectorises text with a CBOW method, but unlike methods such as BOW and TF-IDF, CBOW does so through a “training” process involving machine learning principles.^[22]

Word embedding involves “training” an artificial neural network on a large corpus of text. This training requires the algorithm to iterate over the text repeatedly, learning to predict the likelihood of a word based on its context. Through this process, it develops weights that determine the parameters of the resulting semantic vector space. The model is designed to assign similar vectors to words that appear in similar contexts, effectively capturing contextual or distributional semantics and relationships between words. Consequently, even if certain words are not common across documents, their vectors still hold dense and meaningful values derived from the contexts in which these words occur. The data size has been Augustine’s complete works which amounts to approximately 5 million tokens.^[23]

Using word embedding focuses on the context, i.e. the internal context in a corpus. Words within the corpus are given weights, and thereby meaning, through their co-occurrences. Each word is assigned a value not just based on its frequency but also on its contextual meaning, derived from the words surrounding it during vectorisation. The representations and the semantic space they span is a simple implementation of a view on language called distributional semantics. Within distributional semantics, the meaning of a word is dependent on its distributional position in the semantic vector space, or in other words, that the meaning of a word is “characterised by the company it keeps.”^[24] The “embedding” refers to the process of representing words as dense vectors in a semantic vector space, in other words, words are embedded in the contextual corpus.^[25]

The computational word embedding analysis is unsupervised since there are no predetermined labels. The information and patterns are calculated solely within the corpus. The resulting semantic vector space contains information on every word across the entire corpus, and in order for Augustine scholars to survey, for example, angelology, we need to extract portions of the semantic vector space. The process is thus in two steps: the first with a computational unsupervised step, and the second a supervised step, where informed Augustine scholars query labelled seed-terms. While such a mix of unsupervised word embedding and supervised input, it is not strictly a semi-supervised method; however, our approach reveals a mix of unsupervised and supervised methods.^[26]

The output of a word embedding analysis is a pattern of the so-called co-occurrence structure, i.e. how words co-occur based on their contextual embeddings, where distance/proximity is measured between vectors with cosine similarity.^[27] When we query angelologic terms, we receive structural information concerning these terms. The results come in a list of words with first-level and second-level associations, which is visualised in semantic networks that gives a picture of the semantic “landscape” around the queried terms. The output of a word-embedding analysis needs to be evaluated, and further, it needs to be interpreted and integrated into the broader analysis.^[28]

A first-level association is a term that is primarily associated with the seed term. An example from angelus’ network in our study could be nuntius, which is a first-level association to angelus. This means that the vector of nuntius has a low cosine distance, and therefore high similarity to the seed term, angelus, in the semantic vector space. A second-level association is a term that has the same relationship, not directly to the seed term, but directly related to one of the first-level associations. In the semantic kernel of angelus, interpreter is therefore not linked directly to the seed term angelus but to the first-level association nuntius. If we had nuntius as our seed term, then the second-level association interpreter would appear as first level.^[29]

3.1 Angelus

To investigate the angelology of Augustine, we begin by creating an individual semantic kernel with angelus as seed term. To create a comprehensive yet manageable network, we have chosen a network with six first-level associations and four second-level associations. More or less words could be included in the visualisation, since all vectors have been stored in the trained model. The result of this first word-embedding analysis with angelus as seed term is a list of 28 words, of which 6 are first-level associations, and 21 second-level associations. The network is visualised in Figure 1.

Figure 1

Semantic network with “angelus” as seed term, and 6 first-level associations and 4 second-level associations.

The nodes and edges represent the distance and proximity between the terms, and the colouring of the clusters is based on an extra layer of community detection between the terms, which is built with the Louvain best partition method.^[32] The semantic network of angelus reveals three clusters.

The largest and most dense is the red cluster, which contains terms such as aequalis, ANGELICAM, angelica, angelicus, angelica, AEQUO, caelestis, immortalitas, resurgentium, sublimo, ineffabilis, rationalis, a cluster that can be interpreted as a topic of become equal with angels and obtaining their heavenly status and immortal being.^[33] In his writings, Augustine describes angels as having spiritual bodies (Gn.litt. 6,19; 6,24), which is rendered in the associative terms of caelestis, immortalitas, and sublimo, but what is more striking is the strong presence of the aequalitas theme. It is important to note that while such a topic is present in the In Iohannis Evangelium Tractatus, where Augustine writes about the aequalitas which human beings hope for (Io.eu.tr. 100,6), our network is a representation of all occurrences of these words in Augustine’s works, and at the same time, a passage from a particular text can, with our knowledge of Augustine, be linked as an illustrative passage that can be interpreted and contextualised with the computationally produced semantic network.^[34] The topic of aequalitas is, however, needed to be compared with how Augustine views angels as static creatures. Many interpreters have shown how Augustine describes angels as having received a choice at their creation, and unlike human beings, angels are not able to make progress or regress in the salvific scheme. Angels remain the same status from creation, they are eternal and unchangeable beings. This insight needs to be included in the result so that the dynamic of aequalitas is not mistaken to concern angels, but rather concerning a perspective toward humans becoming like angels, and not vice versa.^[35]

The second cluster is the yellow cluster. This contains fewer terms and is more sparse. It has the seed-term ANGELUS, followed by NUNTIUS, nuntio, edico, interpreter, latina. This is thus a cluster that can be interpreted along the lines of the communicative aspects of the angels. In his writings, Augustine notes that benevolent spiritual beings are called “angelus/angeli” from Greek, ἄγγελος, and nuntius/nuntii in Latin due to their role as conveyer and speaker of the divine message (Io.ev.tr. 24,7; trin 2,13).^[36]

Finally, we have the purple cluster, which is slightly more connected than the yellow, nuntius-cluster. The purple cluster has COLAPHIZO, satanas, extollar, stimulus, and extolleretur. This colaphizo-cluster represents the darker side of angelology, with evil cosmic and moral adversaries, satan, and colaphizo. This last cluster seems to be a topic developed due to that Augustine frequently relies on 2 Cor 12:7: “datus est mihi stimulus carnis meae, angelus satanae, qui me colaphizet,” which Augustine cites, e.g. in Enarrationes in Psalmos (130,7) and De gratia Christi et peccato originali (12,xi).^[37] However, it is important to note that a dualistic interpretation of this finding would be misfitting for Augustine.^[38] The spiritual struggle consists of the “temptation, and behind every temptation is the demonic inducement to join the proud,” a struggle which is primarily against self-centeredness and pride.^[39] The battle is not fought in dualistic terms, but with Christ’s sacrifice as the model.^[40]

From this network with only one seed-word, we are able to discern three aspects of Augustine’s angelology: the angels as messengers (nuntius), the angels as related to evil (satanas) and moral internal combat (stimulus, colaphizo), and finally, the heavenly, rational aspect of angels which aequalitas is desired by human beings. The network is a representation of all occurrences of these words in Augustine’s works, and at the same time, a passage from a particular text can, with our knowledge of Augustine, be linked as an illustrative passage that can be interpreted and contextualised with the computationally produced semantic network.

The prominence of “nuntius” may communicate with Ellen Muehlberger’s analysis, which shows how Augustine reinterpreted the Old Testament by removing divine actors and replacing them with angels as messengers, thereby resolving theological issues concerning the materiality and visibility of God.^[41] Elizabeth Klein has shown further, how Augustine interprets divine apparitions that are described in the Old Testament, that “angels act in persona Dei, representing God,” and compares with the roles of the prophets. This will corroborate why our finding has “nuntius” as a prominent co-occurring word to angelus.^[42]

Concerning the topic of “aequalitas,” it is important to note that this topic is present in the In Iohannis Evangelium Tractatus, where Augustine writes about the aequalitas which human beings hope for (Io.eu.tr. 100,6).^[43] The topic of aequalitas is, however, needed to be compared with how Augustine views angels as static creatures. Many interpreters have shown how Augustine describes angels as having received a choice at their creation, and unlike human beings, angels are not able to make progress or regress in the salvific scheme. Angels remain the same status from creation, they are eternal and unchangeable beings. This insight needs to be included in the result so that the dynamic of aequalitas is not mistaken to concern angels, but rather concerning a perspective toward humans becoming like angels, and not vice versa.^[44]

In the following, we will investigate two new networks that enable us to dive deeper into the interconnections of angelus by investigating homo and daemon in connection to angelus.

3.2 Angelus, Homo, Daemon, and Their Relation

In this next part of the analysis, we will focus on two new networks, where we query, first, angelus together with daemon, and, second, angelus together with homo. In the first, we analyse angelus and daemon, and the results are shown in Figure 2.

Figure 2

Angelus-Daemon 6-4.

The network forms two discernable clusters, one with angelus and its three subclusters as we saw in the previous analysis, and one with daemon. The terms that are contained in the daemon-cluster are as follows: DIUINATIO, DAEMO, DAEMONI, DIVINATIO, seligo, DIUUS, falsor, dius, appuleius, ars, poetaris, ludicrum, sacrificor, magicaris, adorator, numen, MAGICUS, magice, vates, sacrum, ludus.

The first observation is that the daemon-cluster is more dense than the angelus-cluster. Moreover, concerning the relation to terms in the angelus-cluster, the term satanas is not directly linked to daemon (it is neither linked to diabolus, which we tested, but not visualised). This makes an interesting case, namely that daemon/daemones in Augustine’s work is limited to the treatment of daemones in esp. De divinatione daemonum, which concerns the magical ability of daemones to predict (divinatio) future events. We observe in this context also ludus, ars, ludicrum, and poetaris as terms that fall under this topic. Moreover, Augustine’s discussions of daemones in De civitate dei chaps 8–10 concerning communication with false daemones are also reflected in the terms falsor, adorator.^[45] Again, if we test the connection with malus, noceo, and other “negative” terms, daemon still forms a separate, dense cluster as in Figure 2. Finally, the position of nuntius is remarkably right between daemon and angelus, which reflects how Augustine discusses the role of daemones in the Greco-Roman world as messengers between gods and humans (Figure 3).^[46]

Figure 3

Homo and angelus 6-4.

In the following investigation, we queried angelus together with homo. This network has the same parameters, 6 first-level associations and 4 second-level associations. Here, we can also see two-coloured clusters, the purple coloured is around homo, and the yellow is around angelus. Even though the Louvain best-partition-layer (cf. note 32) has coloured the groups and thus detects two separate groups, it is nevertheless remarkable how homo and angelus are much closer in the semantic network than the relation between angelus and daemon in Figure 2.

The homo-cluster contains creator, condio, ADAM, CREO, FACIO, MEDIATOR, UTIQUE, DEUS, opero, salvator, and reconciliator. We notice the bridging terms of creator and condio between angelus and homo, both are created beings. This reflects several aspects of Augustine’s discourse on creation, e.g. how the angels were witness to creation and how angels understand the relation between incarnation and creation.^[47]

We notice how the proximity of aequalitas and related terms, and most remarkable, that aequalis and rational, which were in the outskirts of the network of angelus, are now clustering closer with the homo-cluster. This adherence of rational and aequalis in the homo-cluster nuances the topic of aequalitas: Initially, it is not only concerning angelus/angeli, and, further, it does not only describe a topic common to both humans and angels, but rather it is telling of the anthropological focus of Augustine, where aequalitas concerns how humans as rational beings in the end will be transformed to an angel-like state. This transformation is supported by Augustine’s reading of Luke 20,36 concerning becoming angel-like; however, it is not a corporeal likeness, but a spiritual likeness where humans share the love and true worship with angels toward God.^[48]