Complexity science refers to the theoretical research perspectives and the formal modelling tools designed to study complex systems. A complex system consists of separate entities interacting following a set of (often simple) rules that collectively give rise to unexpected patterns featuring vastly different properties than the entities that produced them. In recent years a number of case studies have shown that such approaches have great potential for furthering our understanding of the past phenomena explored in Roman Studies. We argue complexity science and formal modelling have great potential for Roman Studies by offering four key advantages: (1) the ability to deal with emergent properties in complex Roman systems; (2) the means to formally specify theories about past Roman phenomena; (3) the power to test aspects of these theories as hypotheses using formal modelling approaches; and (4) the capacity to do all of this in a transparent, reproducible, and cumulative scientific framework. We present a ten-point manifesto that articulates arguments for the more common use in Roman Studies of perspectives, concepts and tools from the broader field of complexity science, which are complementary to empirical inductive approaches. There will be a need for constant constructive collaboration between Romanists with diverse fields of expertise in order to usefully embed complexity science and formal modelling in Roman Studies.
The spread of religions in the Roman world offers great examples of how complexity science can help us better understand important aspects of the Roman past. Mithraism, early Christianity, Jupiter Dolichenus: the processes behind the rise of these religions were extremely complicated, and the success of their dissemination was the result of many factors, from the individual decisions made by believers and non-believers up to state policies and attitudes towards religions. But what were the key factors, how important were the choices of individuals, and why were some religions extremely successful while others were not? Was it the inherent nature of a particular set of beliefs? Or maybe the coincidence between the decisions made by emperors such as Galerius and Constantine about early Christianity and the state of the society at that moment? Perhaps success was due to a genuine improvement the religions brought to people’s lives? Or their integration with the organisational structure of the Roman state? Whatever the combination of reasons, archaeological and historical empirical evidence can only take us so far in establishing and testing theories about the main causes of these complex processes. By complementing and testing hypotheses based on empirical sources, complexity science can help us understand aspects of the successful spread of religions. It offers a research perspective and tools to treat such complex phenomena as emerging through the interactions of large numbers of people in specific historical and institutional contexts: phenomena whose properties and functioning are very different from those of the individuals that gave rise to them.
Roman Studies abounds with examples of such phenomena: institutions and the Roman state, communities and social networks, demography and urbanisation, cultural transmission and technological innovation, trade, agriculture and the impacts of climate change. In each example, the behaviours of multiple individuals and their context collectively gave rise to properties that cannot be understood as merely the sum of individual practices. As such, these phenomena represent complex systems that are most appropriately studied via the perspective and tools of complexity science.
The study of complex systems has primarily been undertaken in contemporary settings, in disciplines such as physics, ecology, medicine, and economics. Yet, in recent years archaeologists have increasingly employed such approaches for the study of the past, while the concepts of ‘emergence’ and ‘complexity’ have been considered central to archaeology’s
Complexity science has great potential as a research perspective for Roman Studies, and we argue that the formal computational tools associated with it should complement our existing toolbox. Before presenting a manifesto that sets out our arguments, we provide a brief introduction to complexity science and the advantages of working with formal methods to explore theories about past complex systems in a scientific framework. The manifesto is followed by an overview of the research themes in Roman Studies for which a complexity science perspective offers particular potential. In this reference overview, we provide brief introductions to key concepts and methods and discuss how their application can provide important contributions in a range of research contexts within the broader field of Roman Studies.
Complexity science is a branch of science concerned with studying complex systems. Contrary to the conventional reading of the word ‘complex’ in archaeology (as in, ‘complex societies’), a ‘complex system’ does not imply ‘complicated’, ‘hierarchical’ or even ‘large’. A complex system is a system in which multiple entities (e.g., traders, brain cells, or birds, etc.) may interact with each other and with their environment following often simple rules (e.g., ‘change religion if the majority of your social contacts do so’, ‘buy low, sell high’, ‘align your flight with nearby birds’). These simple interactions give rise to unexpected global, population-level patterns that have vastly different properties than the entities that produced them (e.g., Christianity as a world religion, stock exchange fluctuations, birds flocking). Thus, the meaning of ‘complex’ is best expressed in the saying ‘the whole is greater than the sum of its parts’. This property of complex systems – the disparity between the characteristics of the entities that make up the system and the global outcomes of their behaviour (believers >< Christianity as a world religion, traders >< stock markets, birds >< flocking) – is called ‘emergence’. Emergence is a key concept in complexity science because it dictates the development and selection of appropriate methods to study complex systems (good introductions to the field of complexity science include
The research perspective of complexity science cannot be separated from its formal computational tools and scientific process: formal representation of theories, computational simulation modelling, falsification of hypotheses, and ability to replicate results. We will explain this strong link between tools and perspective by highlighting the four advantages of applying them:
Dealing with emergent properties,
Specifying formal theories,
Hypothesis testing,
Transparent, reproducible and cumulative research.
The human brain is particularly bad at forecasting the behaviour of complex systems with emergent properties: it might be easy enough for us to imagine the outcome of an interaction between a believer in a religion and a non-believer, but to predict the successful spread and establishment of a world religion emerging from such interactions of millions of individuals is beyond the abilities of any human. Computers, on the other hand, are very adept at keeping track of simple calculations repeated over and over again. These simple operations can be used as formal representations of behaviours and interactions of millions of individuals. Similarly, in other kinds of studies repeated calculations done by computers are required to identify patterning in empirical datasets of thousands or millions of data points and determining their correlations with modelled distributions: the human brain is much less reliable at such millions of repetitive tasks and would take infinitely longer to process these large volumes of data. Thus, complexity science perspectives cannot be meaningfully applied to research problems without the use of formal mathematical and computational modelling methods. This notion applies to both data modelling and theory modelling.
The application of formal, computation tools in research, in general, has benefits beyond the ability to understand the emergent properties of complex systems. Crucially, it enforces formalism in the definition of hypotheses and analysis of data. This formalism ensures that there is only one possible reading of the propositions put forward by the researchers, therefore minimising the risk of ideas being misinterpreted or misused. For example, when a scholar theorises that the spread of Christianity was structured by the social networks connecting people throughout the Roman Empire, there are numerous ways in which these notions (social network structures, spread mechanism, interaction) could be interpreted. Thus, for this theory to be representable in computational tools using mathematics and computer code, all its components need to be unambiguously defined: what precise structure of social networks is theorised, what is the probability of a pair of Roman citizens connected in a social network to influence each other’s beliefs? Formalism also enforces so-called ‘hygiene of thinking’, that is, limiting the scope for under-determination of scientific models. It is possible in verbal arguments and natural language to gloss over troublesome details such as specifying the ability for two people living two thousand years ago to influence each other’s beliefs (do they live near each other? Are they part of social groups that regularly interact?). Formalism prevents this from happening – without specifying all elements of one’s theory with concrete values or their ranges this theory cannot be formally represented, and thus the ability of the theory to explain the data patterns as argued by the theory’s proponent cannot be demonstrated. One may worry that such unambiguously defined models (hypotheses) cannot be meaningfully formulated given the high level of uncertainty that is inherent to any study of past societies. Or that precise social processes that took place 2000 years ago could not possibly be made concrete and formal. However, this is what a model does – it is an abstract proposition of how the world might have worked, and whether it did, in fact, work this way and is therefore correct can only be verified if it is formally presented and tested against the available evidence (data). Only by testing multiple models of social processes 2000 years ago can we see which ones are consistent with the only direct remaining evidence of said social processes – the data. Providing only under-defined theories prevents us from ever getting closer to explaining past phenomena. Avoiding unambiguous formalism does not remove the uncertainty; it compounds it.
Formal representations enable testing alternative hypotheses against available evidence and determining their plausibility, at least in relation to other models. The probability that a given formal model correctly represents a past phenomenon can be established and compared to the probability of any other formal model developed to explain that phenomenon. Low-probability models and the hypotheses they represent can be rejected if they do not agree with the available evidence (archaeological and historical data), thus limiting the number of possible explanations for a studied phenomenon. This is a probability-driven process, meaning that with each new iteration of comparing an implementation of a model to data (including different datasets) we gain more certainty regarding the plausibility of the hypothesis. Note that the outcome of this process is establishing that some models are less probable explanations of a complex past phenomenon than other models, and not necessarily to completely discard models. If different models representing a theory fail to match multiple independent data sets, but those of other theories do, we have established beyond reasonable doubt that the former theory does not portray the past as well as the latter theory. For example, the plausibility of each competing theory for the successful and rapid spread of Christianity, and their agreement with data, can be established. If a formal model that emphasizes the structuring role of social networks on the spread of Christianity better represents the rate and scale of adoption of the religion than a formal model emphasizing the role of government intervention through edicts, then future research efforts for credible explanations of this past phenomenon can focus more on the role of social networks than that of government intervention. Similarly, more complex formal models may one day be able to demonstrate how different degrees of social integration in different provinces combined with the specific timing of an imperial edict created the perfect conditions for early Christianity to flourish in some regions but not in others. Such complex models can be realised in a cumulative fashion by first trying and testing simpler ones.
Formal models enable a research process of proposing, testing, rejecting or improving theories of past phenomena. The results of formal modelling in a complexity science framework are cumulative, in that each new model is built on the basis of previously tested models, incrementally bringing us closer to a more detailed and more robust theory of a past phenomenon. For example, early Christianity was no doubt an extremely complicated phenomenon, and its successful spread can never have been the result of one single factor such as the structure of social networks. However, by first establishing the plausibility of one formal model representing the structuring of social networks, more complex models can be built by adding other factors to this first model. Such a research process is cumulative but also necessarily more transparent and reproducible than non-formal approaches. Every step is clearly spelt out so that any researcher can repeat it and check whether the claims stand up to scrutiny. Although it is not possible to completely remove the social and personal biases in any research, the
Complexity science has proven a highly constructive addition to virtually every other discipline (
The study of complex systems is integral to Roman Studies.
It is appropriate to conceptualise and study the Roman state, its territory and inhabitants, and their interactions with states and peoples within and across their borders at any time during its history as a complex system.
It is also appropriate to conceptualise and study phenomena that are aspects of the Roman complex system as complex systems in their own right: society, politics, economy, religion, institutions, communities, military, micro-regions and others.
Complexity science is a constructive and necessary contribution to existing research perspectives in Roman Studies, providing theoretical approaches and methods for studying key concepts in complex phenomena, such as emergence, self-organisation or self-organised criticality.
Constructively applying complexity science requires breaking through disciplinary silos to look for similar patterns, processes and models across different scientific domains to gain a more holistic view of the system in question and to avoid reinventing the wheel.
To understand the behaviour of complex systems and to propose falsifiable theories of Roman complex systems one needs to use the formal tools developed to represent and study such systems.
A multiscalar approach is integral to studying complex Roman systems, to understand how local interactions of Roman individuals resulted in regional patterns and the dynamics of the whole system.
The plausibility and internal coherence of any hypothesis explaining a data pattern or emergent phenomenon should be formally demonstrated.
Formalism and transparency should be employed in hypothesis formation, testing and reporting as well as in data analysis and management. All research output should be reproducible.
Traditional archaeological and historical methods, fieldwork, geochemical analysis, close reading, epigraphy, numismatics etc. are not in any way less crucial or informative than complexity science approaches. It is only by taking full advantage of all scientific techniques available to us – especially the confrontation of empirical data and modelling approaches – that we can make progress in understanding the Roman past.
So far this manifesto has focused strongly on introducing complexity science and formal modelling – approaches so far rarely applied in Roman Studies and therefore requiring a more in-depth introduction. How exactly can they help further our understanding of the Roman world? Which Roman phenomena can be usefully studied using complexity science and formal modelling? What specific formal techniques and models are particularly appropriate for addressing research questions in Roman Studies?
In this final part of the paper, we provide an overview of the main research themes in Roman Studies to which formal modelling approaches within a complexity science framework can be usefully applied. Because complexity science and formal modelling are umbrella terms covering very different concepts and techniques, this part of the paper presents a series of short sections each focused on a particular concept or technique. Each of these has the same structure: a brief definition of the topic is followed by a specific applied example from Roman Studies and a discussion of the potential for future application to Roman Studies research themes. This part of the paper is meant as a reference point for Romanists to explore how complexity science and formal modelling can be usefully and critically applied in their own research.
The concepts and techniques covered in this overview are strongly interrelated (Figure
A map of complexity science themes and approaches to Roman Studies: key concepts (orange), key methods (blue), spatial methods (pink) and urban phenomena (green).
Lead authors: Iza Romanowska and Tom Brughmans
Lead author: Dries Daems
Lead author: Dries Daems
Lead author: Xavier Rubio-Campillo
While lacking the flexibility of natural-language based models, formal models provide advantages such as non-ambiguity (i.e. clear definition of every concept) and completeness (i.e. full description of those interactions within the system deemed most relevant) that promote the insightful exploration of research questions. These benefits also facilitate the testing of working hypotheses against existing evidence through quantitative analysis as formal models can generate a prediction on the behaviour of a system under a given set of initial conditions. The comparison between predicted values and evidence allows the researcher to assess the plausibility of an idea and discard weak explanations.
Lead author: Iza Romanowska
Lead author: Iza Romanowska
Lead author: Tom Brughmans
Lead author: Paul Kelly
Lead author: Stephen A. Collins-Elliott
Lead author: Simon Carrignon
Lead author: Maria del Carmen Moreno Escobar
Lead author: Manuela Ritondale
Lead author: Katherine A. Crawford
Lead authors: Eleftheria Paliou and Tymon de Haas
Lead author: Eleftheria Paliou
Lead authors: Francesca Fulminante and John W. Hanson
Lead authors: John W. Hanson and Matthew J. Mandich
Lead authors: John W. Hanson and Matthew J. Mandich
A complexity science theoretical framework implemented through formal modelling tools has great potential for leading to new insights on a wide range of topics in Roman Studies. In this paper, we have introduced complexity science and formal modelling and provided arguments as to why they should be adopted as tools of the trade in Roman Studies. An elaborate encyclopaedia-style overview of the different concepts and computational techniques included in the approach shows how it can make contributions to our understanding of many Roman phenomena and will offer inspiration and bibliographical pointers to any Romanist interested in using these approaches in their own research.
The constructive integration of complexity science in Roman Studies requires the adoption of an open scientific process. It should be clear that this manifesto does not claim all past phenomena can or should be studied through formal scientific approaches. However, we do argue that for those aspects of past phenomena that can be studied using these formal approaches, Romanists should
We believe complexity science has great potential for enhancing Roman Studies, but achieving this potential will require close collaboration between scholars with different expertise. If the final aim of this manifesto is to make important and substantial gains in our understanding of the Roman world, particularly computer literate advocates of the approach, such as the authors of this paper, simply cannot and should not achieve this in isolation. Instead, formal modelling and complexity science should be considered a field of expertise in Roman Studies in its own right (alongside archaeobotany, epigraphy and ceramology to give but a few examples). Scholars with this expertise should collaborate with those with other expertise to identify what research questions and phenomena can be appropriately studied through critical data analysis and formal modelling. Moreover, they should provide the resources and guidelines to make it possible for other Romanists not aiming to work within this framework to independently enable future formal modelling of their theories and using their datasets. The authors of this manifesto are committed to this cause and firmly believe in the need for constant constructive collaboration to usefully embed complexity science and formal modelling in Roman Studies.
This manifesto was originally inspired by a TRAC session at RAC/TRAC 2018 held at the University of Edinburgh titled ‘Formal Approaches to Complexity in Roman Archaeology’. We thank the conference organisers for supporting this full-day session and all presenters for their contributions, while a special note of thanks also goes to Luis Bettencourt for acting as a discussant. TB was supported by The Leverhulme Trust (project MERCURY), JWH was supported by the James S McDonnell Foundation through his participation in the Social Reactors Project, DD was supported by a fellowship from FWO-Research Foundation Flanders, IR and SC were supported by the ERC funded EPNet Project (ERC-2013-ADG 340828).
The authors have no competing interests to declare.