• 1. Introduction
• 2. Defining digital humanities
• 2.1 Challenge
• 2.2 Approach
• 3. Models
• 4. Modeling uncertainty
• 4.1 Uncertainty in computer science
• 4.2 Uncertainty in digital humanities
• 5. Conclusion
• Bibliographic References
• List of Figures with Captions

1. Introduction

As the saying goes, »nothing can be said to be certain, except death and taxes.« Uncertainty is an unavoidable aspect of life and thus we have an intuitive understanding of uncertainty, but coming up with a strict definition of uncertainty is hard. Uncertainty is generally considered to be related to a lack of information (or ignorance) or imperfect information. Ignorance is used here in a non-pejorative sense; Smithson remarks that ignorance is usually treated »as either the absence or the distortion of »true« knowledge, and uncertainty as some form of incompleteness in information or knowledge.«[1] He notes that to »some extent these commonsense conceptions are reasonable, but they may have deflected attention away from ignorance by defining it indirectly as nonknowledge.«[2]

Predictions, such as about the weather, are generally uncertain, as we only have limited information about the future. But uncertainty does not only concern the future; the following statements could all be said to express uncertainty:

1. I know Bob is married, but I don’t know the name of his spouse.

2. I know Bob is married, but I don’t remember whether his wife’s name was Alice or Alicia (or was it Alison?).

3. Jack told me that Bob’s wife is called Alice, but John said it was Alicia.

4. Bob is about 30.

5. Bob is 30 or 31.

6. Bob is between 30 and 35 years old.

7. Bob is a player.

Upon closer inspection, the uncertainty in these statements not only relates to different pieces of information, but it also takes different forms. For example, in statement 1, the name of Bob’s wife is completely unknown, whereas in 2 it is one from a set of names; statement 4 could be called vague, whereas in 5 a set, and in 6 a range of possible ages is given. In addition, not all options may be equally likely; in statement 2, for example, the speaker may consider Alice or Alicia more likely than Alison. In statement 3, uncertainty stems from conflicting information; whether the speaker considers one of the two options more likely may also depend on whether Jack or John is considered (or believed to be) more trustworthy. Finally, in statement 7, uncertainty about the meaning of the statement is caused by the lack of context and by the semantic ambiguity of the word »player.«

These examples are not intended to be exhaustive but rather to illustrate that uncertainty can have different causes, take different forms, and is related to other phenomena such as imprecision, vagueness, and ambiguity; it may also involve issues of belief and trust. These different types of uncertainty may thus have different consequences and may need to be addressed in different ways. Some cases of uncertainty may be resolved, or the uncertainty may at least be reduced; for example, we may be able to ask Bob about the name of his wife, or new information may allow us to narrow the range of ages in statement 6. Predictions about the future, on the other hand, will remain uncertain until the prediction can be compared to the actual outcome. Yet other cases of uncertainty are effectively unresolvable because the required information is inaccessible (such as other people’s thoughts, lost documents, or perfectly precise measurements) or nonexistent (e.g., when considering counterfactual questions such as »If John Wooden were alive and coaching in the NCAA today, would he be as successful?«), or because the criteria for deciding an issue are unknown or subjective. In fact, one may argue that in the general case, uncertainty can never fully be resolved, as we will never have perfect knowledge when we are dealing with the real world; Parsons notes that »any intelligent system, human or otherwise, is constrained to have finite knowledge by virtue of its finite storage capacity, so it will always be possible to find some fact that is unknown by a particular system.«[3]

Fig. 1: Smithson’s taxonomy of ignorance. [Piotrowski 2019, redrawn after Smithson 1989, p. 9.]

Fig. 2: Smets’s taxonomy of imperfection. [Piotrowski 2019, drawn after Smets 1997.]

Various taxonomies have been proposed that aim to systematize uncertainty and related concepts, for example by Smithson (see Figure 1), who considers it a sub-type of a broader concept of ignorance,[4] or by Smets, who uses imperfection as the general concept (see Figure 2).[5] Parsons discusses further taxonomies that have been proposed,[6] eventually coming to the conclusion that »while it is far from clear that the taxonomies that they provide are of fundamental importance, they do help to outline what uncertainty is.«[7]

As uncertainty is so pervasive, it obviously also affects research and scholarship; Pollack writes: »The uncertainty arises in many ways, and the nature of the uncertainty may change through time, but the scientific endeavor is never free of uncertainty.«[8] Humans are generally quite good at dealing with uncertainty in everyday life, for example with respect to the weather or to public transit. However, these estimations of uncertainty heavily depend on individual knowledge and previous experience, and are generally hard to communicate. For example, what should an out-of-town visitor make of a statement like »usually the train’s on time, but sometimes it’s delayed quite a bit in the morning, but I think you’re gonna be fine«?

As scholarly research strives for intersubjectivity, it requires transparency with respect to uncertainty; appealing to »common sense,« experience, or intuition is clearly insufficient. Mathematics and the natural sciences have developed intricate formal methods for dealing with (particular types of) uncertainty, which is probably one reason why »people who are not scientists often equate science with certainty, rather than uncertainty.«[9]

In the humanities, uncertainty is usually described verbally; one domain that describes (again, particular types of) uncertainty in a relatively systematic fashion is that of critical scholarly editions: critical apparatuses record illegible passages, uncertain readings, uncertain identifications of persons and places, and other cases of uncertainty pertaining to the edited sources. In addition, research in the humanities does not only need to deal with uncertain, vague, incomplete, or missing information, but also with an irreducible variety of positions (points of view, values, criteria, perspectives, approaches, readings, etc.), resulting in what Paul Ricœur calls »le conflit des interprétations.«[10]

Now, what about digital humanities? If digital humanities is the intersection (or at the intersection?) of computer science and the humanities, as is often said, what does this mean for the handling of uncertainty? For example, Burdick et al. argue that computing »relies on principles that are […] at odds with humanistic methods,«[11] and assert that »ambiguity and implicit assumptions are crucial to the humanities.«[12] »What is at stake,« they conclude, »is the humanities’ unique commitment to wrestle with uncertainty, ambiguity, and complexity«.[13] We believe that one cannot really answer this question without defining what one means by »digital humanities«. In the next section we will therefore first present our definition of digital humanities. As we will see, the concept of models is central to our definition; we will thus, in the subsequent section, outline our notion of models. In the following section, we will give a brief overview of the modeling of uncertainty in computer science and in digital humanities. In the final section we will conclude our discussion by outlining what we belief to be the specific challenges for digital humanities and what should be the next steps to advance the state of the art.

2. Defining digital humanities

3. Models

The construction of models is an everyday task; we construct models all the time. In his influential 1971 paper »Counterintuitive behavior of social systems,«[27] Forrester points out:

»Each of us uses models constantly. Every person in private life and in business instinctively uses models for decision making. The mental images in one’s head about one’s surroundings are models. One’s head does not contain real families, businesses, cities, governments, or countries. One uses selected concepts and relationships to represent real systems. A mental image is a model. All decisions are taken on the basis of models. All laws are passed on the basis of models. All executive actions are taken on the basis of models.«

Fig. 3: Original – model mapping. [Piotrowski 2019, redrawn after Stachowiak 1973, p. 157.]

The construction of models in the humanities is thus not per se new: all research, whatever the domain, is based on models. As in the case of uncertainty, we have an intuitive understanding of the term model, but it is surprisingly hard to come up with a good definition. We use the term in the sense of Stachowiak’s Allgemeine Modelltheorie.[28] The basic assumption is that arbitrary objects can be described as individuals characterized by a finite number of attributes.[29] Attributes can be characteristics and properties of individuals, relations between individuals, properties of properties, properties of relations, etc.[30] Modeling is then a mapping of attributes from the original (which can itself be a model) to the model, as illustrated in Figure 3. According to Stachowiak, models are characterized by three fundamental properties:[31]

Mapping property (Abbildungsmerkmal) Models are always models of something, namely mappings from, representations of natural or artificial originals, which can themselves be models.

Reduction property (Verkürzungsmerkmal) Models generally do not capture all attributes of the original they represent, but only those that the model creators and / or model users deem relevant.

Pragmatic property (pragmatisches Merkmal) Models are not per se uniquely assigned to their originals. They fulfill their replacement function

1. for particular subjects that use the model,

2. within particular time intervals, and

3. restricted to particular mental or actual operations.

With respect to the mapping of attributes, three interesting cases shall be briefly mentioned: preterition, abundance, and contrasting. Preterite attributes are attributes that are not mapped from the original to the model; abundant attributes are attributes that do not exist in the original. Contrasting refers to the exaggeration of certain attributes in the model, typically to highlight certain aspects of the original.

Now, if all disciplines create models, the choice is not »whether to build models; it’s whether to build explicit ones.«[32] In contrast to much of the natural and engineering sciences, which tend to use—explicit and formal—mathematical models, models in the humanities are traditionally often only partially explicit and tend to be expressed informally using natural language.[33] The word formal means nothing more than »logically coherent + unambiguous + explicit.«[34] While there are different degrees of formalization, it should be clear that in the context of digital humanities we are ultimately interested in a degree of formalization that allows models to be processed and manipulated by computers, i.e., computational models. Traditional—informal—models in the humanities do not lend themselves to computational implementation as directly as mathematical models. Furthermore, research questions in the humanities are primarily qualitative rather than quantitative, which, too, has held back the full adoption of the computer as a modeling tool rather than just as a writing tool and a »knowledge jukebox.«[35]

4. Modeling uncertainty

If we accept that »being uncertain is the natural state of things,«[36] it follows that we need to consider uncertainty when constructing models. Furthermore, if we define digital humanities as the construction of formal models in the humanities, we thus also need to reflect upon how to formally (i.e., in a logically coherent, unambiguous, and explicit fashion) represent uncertainty as it occurs in the humanities. The formal representation of uncertainty in digital humanities should have two main objectives:

1. to make uncertainty explicit, and

2. to allow reasoning under and about uncertainty.

The following brief example may serve to illustrate these two objectives. Consider a database of historical persons—a common computational model. In some cases, there will be uncertainty with respect to the dates of birth and death of these persons. The uncertainty may take different forms; for example, only one of the dates may be known with some certainty. But it may also happen that both dates are unknown and the existence of a particular person is only inferred from some evidence indicating that they were alive at some point, for example by a document such as a contract.

Suppose the (database) model represented birth and death by a single date each (e.g., of the SQL DATE type): dates would all be represented in the same way, whether certain or uncertain, exact or approximate. Even if the procedure for mapping uncertain dates to a date in the model were documented somewhere, the uncertainty would not be represented formally and thus be inaccessible to the computer. The computer may thus respond to a query with an exact date such as 1291-08-01, but there would be no information about the certainty (nor the precision) of this date. The computer would also be able to carry out operations such as date arithmetic without any problems—but one date may in fact represent a range and the other just a guess. Taken at face value, this may lead to an »illusion of factuality,« which is obviously problematic, in particular if this information were to be used as a basis for further work, as the uncertainty would propagate.

If, however, the database used unstructured text fields to represent the dates, users could enter something like »between 1291 and 1295,«»late 13th century«, »probably 1291«, etc., or even describe how an approximate date was inferred, and thus preserve the uncertainty. The obvious downside is that such informal representations cannot be processed by the computer: neither could we perform queries or arithmetic on the dates (reasoning under uncertainty), as searching for »1291« will not find »late 13th century« and vice versa, nor could we perform operations on the uncertainty itself, such as a query for all dates of birth that are known to be exact to at least one year (reasoning about uncertainty).

5. Conclusion

In this article we have tried to show the challenge of uncertainty for the construction of computational models in the humanities—digital humanities. It is clear that we cannot ignore uncertainty, and we cannot eliminate it either: we need to model it, and we thus need computational models of uncertainty.

Computational models of uncertainty already exist in various research disciplines and are being used in commercial and industrial applications. There is ongoing fundamental research on uncertainty and its representation in mathematics, philosophy, and computer science. Some of these approaches may also be suitable frameworks for computational modeling of uncertainty in the humanities—what is lacking, however, is the »bridge« that could relate the uncertainty encountered in humanities research to these formal modeling frameworks. What is missing in particular, is a systematic account of uncertainty in humanities research, which would aim to document causes for uncertainty, as well as its behavior, i.e., questions such as: Could this type of uncertainty be (in principle) resolved? What information would be required to resolve it? What happens when new information becomes available? How is it taken into account? And so on.

We would like to stress that the goal is not to come up with an answer to the ontological question of the »true nature« of uncertainty, but rather to find ways of modeling this omnipresent but still elusive phenomenon. We would also like to stress that it is unlikely that anyone will ever come up with a »grand theory of uncertainty« allowing for a single universal model—we recall Stachowiak’s pragmatic property of models. What may very well be possible, though, are more general modeling frameworks that provide researchers with the building materials required for constructing models of particular types of uncertainty in a particular domain.

As we have noted above, there are numerous approaches for the formal modeling of uncertainty, which differ in many respects. Smets notes: »Newcomers to the area of uncertainty modeling are often overwhelmed by the multitude of models. One frequent reaction is to adopt one of the models, and use it in every context. Another reaction is to accept all the models and to apply them more or less randomly. Both attitudes are inappropriate.«[72] We are not sure whether the (digital) humanities have even reached this point; in any case, there is no catalog of uncertainty modeling frameworks from which humanities scholars could pick a framework according to a set of criteria. Neither are there best practices in the humanities that could guide the selection; whether an approach that was successfully used in one digital humanities project can be transferred to another is not much easier to answer than the question of whether the methods used for dealing with uncertain environmental measurement data could be adapted to the domain of medieval manuscripts.

Intuitively, the kinds of uncertainty encountered in the humanities tend to differ in some respects from many more »traditional« applications, such as in engineering, meteorology, or demography; for example,

• humanities data is often more like expert knowledge than measurements;

• the amount of available data tends to be relatively small and often concerns singular, non-repeatable events;

• the reasoning is rather evidential than predictive;

• intercausal, counterfactual, and deductive reasoning may be of more importance;

• phenomena similar to those known as selectively reported data and missing data in statistics may be more frequent;[73]

• uncertainty is rather qualitative than quantitative, or at least hard to quantify;

• belief is likely to play an important role with respect to conflicts of interpretation.

This is obviously just a very superficial assessment. All of these phenomena may occur in other fields as well—knowledge representation in classical AI comes to mind—, and there are certainly cases in the humanities that do not exhibit them. What we are trying to say is that uncertainty in humanities research likely has »typical« characteristics, just like uncertainty in, say, gambling and structural engineering is caused and influenced by different factors and thus exhibits particular characteristics; the two fields are also driven by different concerns, so some modeling approaches will be more pertinent than others.[74]

As Bradley notes, »[w]hen dealing with uncertainty, it often seems like the right approach is to try to quantify that uncertainty,« but, he stresses, »there are limits to what we can (and should) quantify.«[75] This certainly applies to many types of uncertainty in the humanities; mathematical and logical approaches to uncertainty are important as potential modeling and reasoning frameworks to target, but there is still the open problem of how (if at all) to quantify this uncertainty—which is not incidentally the main issue in the approach suggested by the TEI Guidelines (see above).

From this we conclude that we need theoretical digital humanities and theory formation to study questions such as what types of uncertainty do we find in the humanities? What are the specifics? What can be generalized? Building on our insights we can then evaluate approaches from mathematics, logic, and computer science and develop methods and recommendations for applied digital humanities. In other words: It is the task of the theoretical digital humanities to develop, in close dialog with the humanities disciplines, modeling frameworks and methods that can specifically address these challenges. Theoretical digital humanities is crucial for laying the theoretical groundwork for the development of models and methods appropriate for the humanities—instead of using »second-hand« methods originally developed for completely different purposes. This is, we believe, what Meister refers to when he characterizes digital humanities as »a methodology that cuts across disciplines, systematically as well as conceptually«.[76]

And this way, digital humanities can in fact play an important role for the transformation of the humanities within the larger digital transformation of society as a whole, and mean more than just »contemporary humanities«.