Mathematically Modeling Early Christian Literature: Theories, Methods, and Future Directions

1 Computation, Statistics, and Mathematics

Does mathematics have any relevance to biblical studies? What types of reasoning are involved in computing early Christian texts? In this topical issue, a group of scholars from the humanities and from various technically oriented fields come together to theorize how to advance early Christian scholarship using computationally assisted methods. Computational approaches to early Christian texts have been deployed intermittently throughout the twentieth century by scholars such as Percival Neale Harrison,^[1] Robert Morgenhalter,^[2] Andrew Queen Morton,^[3] and Anthony Kenny.^[4] In recent decades, following the advent of more advanced computational tools, scholars such as David L. Mealand,^[5] James Libby,^[6] Sophie Robert-Hayek,^[7] Jermo van Nes,^[8] and Jacques Savoy^[9] deployed computational methods in early Christian studies with greater sophistication than has previously been possible. Despite these important forerunners, the use of computationally assisted methods remains rather new in early Christian scholarship. For this reason, the purpose of this topical issue is to theorize how scholars in biblical studies and related fields can conduct computationally assisted research in a principled manner.

For most scholars in biblical studies and related fields, engaging in computational research involves grappling with a new lexicon. Three key terms, which are used throughout this topical issue, are particularly important and are closely related. First, we define the term computation as the use of digital tools to acquire quantitative information about a corpus and to visualize that information through images such as charts or tables. Second, we define the term statistics as the analysis and interpretation of quantitative data. Third, we define the term mathematics as reasoning within logical frameworks, which are specified by well-established theorems and axioms. More than computing and statistics, the branch of study known as mathematics is about building arguments. In other words, in mathematics, the emphasis is less on the answers and more on the logical processes the analyst employs to obtain a given result.

So, then, why does computing in a Bible context matter? Different scholars may give different answers to this question. Saving time and scaling up are among the reasons given, both of which are perfectly valid to me. In terms of saving time, using digital tools to find and count things for you spares mental energy, which could be spent on other things instead. In terms of scaling up, it is arguably an advantage to be able to look at a collection of ancient texts on a macro-level and make large-scale comparisons to another collection of texts, since more perspectives are always better than fewer. Temporarily forgoing close readings does not have to be scary, because you can always shift your perspective again and scale back down. But more important than saving time or scaling up is the opportunity to think using a different type of epistemology. Computing gives us a chance to deploy mathematical reasoning based on empirical observations. But what does it mean to think mathematically?

2 Mathematical Reasoning and Early Christian Studies

Talking about mathematics in a biblical studies context makes people cringe. I have heard from one very smart person that they are allergic to math, from another that they are too old to learn it, and from another that no Bible scholar wants to talk about it. At the same time, I have met some (but, emphatically, not many) scholars in technically oriented fields who act like mathematical gatekeepers, deciders of who can do true science, and, for them, humanitarians typically do not make the cut. These experiences remind me of a scene involving Alice in Through the Looking Glass, wherein the Red and White Queens talk about math in all the wrong ways:

“Can you do addition?” the White Queen said. “What’s one and one and one and one and one and one and one and one and one and one?” “I don’t know,” said Alice. “I lost count.” “She can’t do addition,” the Red Queen interrupted.^[10]

Many people are put off by mathematics because it is presented in an autocratic, black and white fashion. It is wrongly understood to be about finding the right answers to obscure questions. People think they either “get it” or they do not “get it,” creating an unfortunate split between “math people” and “not math people.” Mathematics, however, is not about answering trick questions. Fundamentally, it is about logical rigor, deep questioning, and the use of our creative faculties to explore the boundaries of knowledge.

Computing early Christian literature requires an approach to mathematics that is more productive than what Alice experienced with the Red and White Queens. I prefer the approach taken by mathematician Eugenia Cheng, who describes mathematics as a journey with logic:

Maths might seem like it’s about getting the right answers, but it’s really about the process of discovering, the process of exploration, the journey toward mathematical truth, and how to recognise when we’ve found it.^[11]

The framework of mathematics is logic, and the reason I am drawn to it is that I don’t want to trust other people what information counts as true…Maths doesn’t work by evidence: it works by logic. Logic is how we decide that something counts as “right” in maths. That doesn’t mean it is right; it means it is right according to the framework of maths, which is logic.^[12]

Since the Industrial Revolution, there has been a major divide between the sciences and the humanities, and mathematics came to be affiliated with the hard sciences or fields that fueled capitalistic growth.^[13] I wish more biblical scholars would reclaim mathematics as a humanistic method, even if it means going to places we think we do not belong or working in fields where some say we are unwelcome. The essence of mathematics is not the right answers to complex equations, but rather the process of deepening our understanding of why we think something is right. For this reason, I think mathematics is already more of a friend of biblical studies than many people realize.

The opportunity to re-read familiar texts with mathematical reasoning is the crowning achievement of digital biblical studies. To be sure, getting to the point where one can engage in actual text-analysis with digital methods takes extensive work – possibly years of preprocessing machine-readable files, data acquisition, and learning how to use computational tools. This topical issue is about what happens once all of that is done. Digital biblical studies is not about turning our minds over to the computer and letting artificial intelligence think for us. The authors in this issue, equipped with different kinds of digital infrastructures, view computation as an essential gadget in the exegetical tool kit and deploy various forms of mathematical reasoning to interpret ancient texts. In what follows, I briefly summarize the types of mathematical reasoning that recur in this topical issue.

1. Inductive reasoning and falsifiability: Computing early Christian texts involves inductive reasoning based on information collected from big datasets. By inductive reasoning, I mean the articulation of general hypotheses or theories derived from specific observations. In other words, given a set of quantitative outcomes, we look beyond our specific results and articulate how our data might be relevant in different yet analogous settings. In these cases, further studies are always needed to test and refine our hypotheses. However, since the authors make their datasets and code publicly available, other scholars can reproduce our studies and thereby re-examine the veracity of our results.

2. Redundancy and hypothesis testing: Computing early Christian texts involves forming hypotheses and testing whether it is possible to disprove them. The spirit behind hypothesis testing is to self-verify that one has obtained good results. Hypothesis tests are attempts to disprove one’s own ideas, to attack one’s own arguments to see how well they hold up, the result of which either strengthens one’s confidence in their ideas or exposes flaws in one’s logic. In addition to hypothesis testing, a common practice throughout this topical issue is methodological triangulation. In other words, instead of relying on a single data analysis technique, each of which has its own biases and limitations, the authors tend to revisit the same question with multiple methods to assess the validity of their findings. To give a less-than-perfect analogy, airplanes are designed with redundant systems to reduce the risk of malfunction. Of course, an airplane can fly with only one engine – but it is better to have two.

3. Abstraction and structural comparisons: Computing early Christian texts involves investigating the underlying mathematical structures in a text and making comparisons to other phenomena that have similar structures. Through the process of abstraction, the mathematical essence of something is extracted and compared to another thing that has the same essence. To state the obvious, no two things are completely identical, meaning ancient texts have many differences from anything else that can be observed in the real world. The point of abstraction, however, is to temporarily forget the differences and find out what is the same, all for the purpose of deepening our knowledge about something important to us.

4. Interdisciplinary connections and inferring causes from effects: Computing early Christian texts involves exploring what kinds of interpretive and interdisciplinary prospects become possible through quantitative analysis. Interdisciplinarity is a core value in biblical studies and related fields, but many of the fields that biblical scholars like to dabble in routinely deploy quantitative approaches and draw conclusions from high-quality statistical work. By contrast, it is a common procedure among biblical scholars to borrow concepts from fields such as sociology, psychology, or anthropology and read passage x in light of theory y, without engaging in the kind of statistical work from which such theories emerged in the first place. Of course, there is value in such approaches, but the authors in this topical issue share the conviction that computation can take biblical scholarship deeper into social science fields, since many interpretive paradigms require statistical data before they can be operationalized. Deep engagement with the social sciences enables the authors of this issue to theorize backwards from their data to the ancient world and thereby formulate hypotheses around what intermediate realities may be responsible for quantitative outcomes.

Two primary questions motivate the authors in this topical issue: how and what next? Our starting point for the question of how is that corpus linguistics software and web applications are becoming increasingly available and user-friendly. Of course, we regard these technological advancements as a good thing, but we also believe it is essential to establish solid theoretical and methodological underpinnings before we use these infrastructures as tools for humanities research. The question of what next stems from our recognition that computational approaches are deployed only by a minority of biblical scholars. Not a single author in this issue claims to be a crime scene detective who has definitive answers based on irrefutable evidence. For every result reported or exegetical insight made in the essays to follow, there are multiple avenues for future scholars to build upon and refine our conclusions. The spirit behind this topical issue, then, is that our work is very future-oriented.

3 Summary of Contributions

The topical issue begins with an article by Alessandra Luce and Paul Robertson entitled “Comparing and Assessing Statistical Distance Metrics within the Christian Apostle Paul’s Letters.” The article is placed first in the topical issue because Luce and Robertson survey a range of data analysis techniques (e.g., Euclidean distance, cosine similarity, Manhattan distance) and evaluate the literary settings in which each technique is most effective. Working with an eye towards comparing the use of literary features in Paul’s letters with the use of the same features in ancient philosophical, rhetorical, and apocalyptic literature, Luce and Robertson show empirically how one’s selection of data analysis technique directly impacts one’s results. The authors argue for the importance of methodological triangulation and caution against reliance on a single statistical method to cull insights about ancient texts.

Dane Rich is the author of the next article, “Something to Do with Paying Attention: A Review of Transformer-based Deep Neural Networks for Text Classification in Digital Humanities and New Testament Studies.” In this review article, Rich argues that transformer-based deep neural networks have great potential to advance New Testament scholarship, particularly in the areas of authorship attribution, text dating, and genre classification. After providing an overview of the state of the art of digital methods in biblical scholarship, Rich specifies ways neural networks can advance New Testament studies in the three research domains listed above. Rich also discusses the limitations and potential problems involved in applying modern digital approaches to the New Testament, with a particular focus on the issues of data scarcity, validity, and ethics.

Following the two methodologically focused articles described above, the topical issue continues with an article by Erich Benjamin Pracht and Thomas McCauley. In their study, “Paul’s Style and the Problem of the Pastoral Letters: Assessing Statistical Models of Description and Inference,” Pracht and McCauley review previous quantitative research in New Testament studies regarding the question of the authenticity of the Pastoral Letters, three short letters whose Pauline authorship has been debated for nearly two centuries. The authors find that the field lacks clarity on how to use Paul’s undisputed letters as a standard of measurement. Pracht and McCauley describe the statistical behavior of various stylistic features within Paul’s letters by applying three discrete probability models – the binomial, the Poisson, and the negative binomial distributions – before turning to the Pastorals to see if the same features are governed by the same distributions. The authors conclude that the Pastoral Letters are not as stylistically distinct from the undisputed letters as has previously been claimed in New Testament studies.

Next, we find an article by Harri Söderholm, Nina Nikki, Zdeňka Špiclová, and Jimi Vesala, “Seek First the Kingdom of Cooperation: Testing the Applicability of Morality-as-Cooperation Theory to the Sermon on the Mount.” The authors use the Sermon on the Mount in Matthew 5–7 as a test case to assess whether the Morality-as-Cooperation theory (MAC), which posits a range of moral domains as collective solutions to societal challenges, is a valid interpretive paradigm for early Christian texts. Data collection was carried out by five participants, each of whom coded small segments of the Sermon on the Mount according to their interpretation of whether any of the seven domains of the MAC theory are present in each segment. The authors then analyzed the data computationally using Pointwise Mutual Information and other statistical metrics. The major finding of this article is that the seven components of the MAC theory are indeed present throughout the Sermon on the Mount, with reciprocity and deference being the most prominent.

The topical issue continues with “Modelling the Semantic Landscape of Angels in Augustine of Hippo,” a research article by Eva Vrangbæk and Christian Vrangbæk. Using a digitized corpus of Augustine’s extensive literary output, the authors trained an artificial neural network to assign weights to various Latin terms in Augustine’s angelology. In so doing, the authors apply the computational method known as word embedding, which transforms all lexemes in Augustine’s corpus into vectors and measures distances within these data structures using cosine similarity. Ultimately, Vrangbæk and Vrangbæk are looking for which terms in Augustine’s corpus tend to co-occur with other Latin terms, which for them is indicative of a given search term’s contextual meaning. The authors evaluate the usefulness of applying word embeddings to Augustine’s corpus and find that, even though lemmatization and preprocessing may result in some inaccuracies, the method enables them to discover that the term angelus in Augustine carries heavy anthropological connotations.

The topical issue concludes with “Was the Resurrection a Conspiracy? A New Mathematical Approach,” a theologically and philosophically oriented research article by Nathan Rockwood. In his article, Rockwood builds and applies a mathematical model to the question of whether early testimonies to the resurrection could have been a fabrication carried out by the followers of Jesus. In this study, Rockwood assesses the probability of things such as how likely it is that all early witnesses to the resurrection could fabricate a story and collectively maintain their false testimony without any leaks. Ultimately, Rockwood concludes that – from the perspective of the earliest followers of Jesus – testimonies to his resurrection were sincere, meaning it is extremely unlikely that these testimonies could have been a deliberate fabrication.

Arguably, the defining feature of this topical issue is that it pushes interdisciplinarity beyond what is typical for biblical scholars. In fact, some of the authors represent disciplines such as theoretical mathematics, software engineering, and computer science, all of which are traditionally viewed as very far from early Christian studies. Nevertheless, all authors are united by the fundamental conviction that computing early Christian texts forces us to think about why we think what we think. Tradition and consensus influence all of us, but data-driven methods give us a new way to subject our knowledge claims to deep questioning. Each of us enjoy moving between different worlds and perspectives: qualitative and quantitative, micro and macro, close readings and distant readings. I submit that the articles in this topical issue show that the boundaries between these seemingly opposite approaches are quite fluid.