Lord of the Rings, Disney’s Mulan and the stuff I do: it’s all the same

Yes, there are similarities between my work and things that people actually want to spend time listening to. But you really have to look hard for them. I’ve given a lot of presentations over the last few years and noticed that one of the best ways of getting a difficult idea across is to use a movie analogy. I also learned I was very bad at preparing my presentation in time to think up movie analogies. So here’s a blog post to make up for it, inspired by a new paper I wrote that just came out in Journal of Archaeological Method and Theory. My work is a bit like Lord of the Rings and Mulan.

But not in the way you hope it is. There is nothing near as exciting in my research as the cavalry charges in both those movies, and I definitely never experienced a ‘montage’ moment that provided me in a ridiculously short timespan with the crazy skills needed to destroy the baddie.

What my work has in common with both Mulan and Lord of the Rings are fire signals. This video shows the memorable scene from Return of the King when the fire beacons in Gondor are lit, triggering the lighting of a chain of other beacons. The message is clear and reaches its target quickly: Gondor looks to Rohan for help.

The opening scene of Disney’s Mulan is similar: when the bad guys attack, beacons are lit all along the great wall of China to warn the Chinese people of the coming threat.

These scenes are not completely unthinkable fantasy scenarios, but are inspired by early communication systems that actually existed in the past. In times before telephones and telegraphs, signalling systems using fire, smoke, sound or light could have been used to spread messages over very long distances.

Archaeologists studying the Iron Age of Spain believe such a communication system might have existed in some regions. And it is easy to understand why. The settlement pattern in much of Spain during the Iron Age was dominated by large fortified urban settlements on hills, hence they are sometimes referred to as hillforts. These large urban settlements were surrounded by smaller rural settlements. The surrounding landscape could be visually controlled from many of these hillforts, and the hillforts were visually prominent features that could be seen from far away.

Now what scene of Lord of the Rings does this remind me of? That’s right: the Eye of Sauron perched on top of the massive tower of Barad Dur, scanning the surrounding landscape for his enemies, and to his followers acting as a visible reminder of who’s boss.

Many archaeologists believe these large urban settlements were located on hills on purpose, and not just because a hill was easier to defend but because of the views it offered: visually controlling the landscape, being visually prominent from its surroundings and acting as a good link in a fire signalling network.

And this is where networks come in! If archaeologists argue that settlements might have been located with visibility in mind for the three reasons mentioned here, then we should approach these statements as hypotheses that need testing. And we can do that in three ways using network science:

1) visualise the network of inter-visible settlements using our knowledge of the settlement pattern;
2) explore its structure to see whether it would function well as a communication network, or whether some settlements are more visually prominent;
3) simulate a process where places are settled so that a well-functioning communication network and/or a few more visually prominent settlements is established, and compare this simulated settlement pattern with the observed one.

This is what I do. The first approach uses network data representation and network layout algorithms to show a network of inter-visible settlements, and explore this pattern in a new way by extracting it from its geographical context and focusing just on its structure for a change. The second approach then uses exploratory network analysis techniques that tell us something more about individual nodes in the network and about the network as a whole (e.g. identify most visually prominent settlements, identify chains of inter-visible settlements). The third approach is in my eyes the most interesting one because it is totally new: using simulation models we generate millions of networks according to the process we hypothese might have taken place and we compare the simulated networks with the oberved ones using the same exploratory network analysis techniques as in the second approach.

This new approach to simulating our hypotheses about visibility networks is called exponential random graph modelling for visibility networks. A pair of papers just came out in which we introduce this method and apply it to Iron Age and Roman Southern Spain. The results are really interesting: there is no evidence for a well-functioning communication network, but there is definitely reason to believe that the pattern of visually prominent settlements that visually control surrounding rural settlements was purposefully established in the Iron Age. The importance of visibility as a factor determining settlement location then gradually decreases throughout Roman times.

Our recently published paper in Journal of Archaeological Method and Theory tells you the full story. The method is explained in detail in our paper in Journal of Archaeological Science. Both are available through my Academia.edu page or my bibliography on this blog. Enjoy!

The networks they are a-changin’: introducing ERGM for visibility networks

In my madness series of posts published a few months ago I mentioned I was looking for a method to study processes of emerging intervisibilty patterns. I can finally reveal this fancy new approach to you 🙂 Here it is: introducing exponential random graph modelling (ERGM) for visibility networks. In previous posts I showed that when archaeologists formulate assumptions about how lines of sight affected past human behaviour, these assumptions imply a sequence of events rather than a static state. Therefore, a method is needed that allows one to test these assumed processes. Just analysing the structure of static visibility networks is not enough, we need a method that can tackle changing networks. ERGM does the trick! I just published a paper in Journal of Archaeological Science with Simon Keay and Graeme Earl that sets out the archaeological use of the method in detail. You can download the full paper on ScienceDirect, my Academia page or via my bibliography page. But in this blog post I prefer to explain the method with LEGOs 🙂

 

Social network analysts often use an archaeological analogy to explain the concept of an ERGM (e.g., Lusher and Robins 2013, p. 18). Past material remains are like static snapshots of dynamic processes in the past. Archaeologists explore the structure of these material residues to understand past dynamic processes. Such snapshots made up of archaeological traces are like static fragmentary cross-sections of a social process taken at a given moment. If one were to observe multiple cross-sections in sequence, changes in the structure of these fragmentary snapshots would become clear. This is exactly what an ERGM aims to do: to explore hypothetical processes that could give rise to observed network structure through the dynamic emergence of small network fragments or subnetworks (called configurations). These configurations can be considered the building blocks of networks; indeed, LEGO blocks offer a good analogy for explaining ERGMs. To give an example, a network’s topology can be compared to a LEGO castle boxed set, where a list of particular building blocks can be used to re-assemble a castle. But a LEGO castle boxed set does not assemble itself through a random process. Instead, a step by step guide needs to be followed, detailing how each block should be placed on top of the other in what order. By doing this we make certain assumptions about building blocks and their relationship to each other. We assume that in order to achieve structural integrity in our LEGO castle, a certain configuration of blocks needs to appear, and in order to make it look like a castle other configurations will preferentially appear creating ramparts, turrets, etc. ERGMs are similar: they are models that represent our assumptions of how certain network configurations affect each other, of how the presence of some ties will bring about the creation or the demise of others. This is where the real strength of ERGMs lies: the formulation and testing of assumptions about what a connection between a pair of nodes means and how it affects the evolution of the network, explicitly addressing the dynamic nature of our archaeological assumptions.

More formally, exponential random graph models are a family of statistical models originally developed for social networks (Anderson et al. 1999; Wasserman and Pattison 1996) that aim to scrutinize the dependence assumptions underpinning hypotheses of network formation by comparing the frequency of particular configurations in observed networks with their frequency in stochastic models.

The figure below is a simplified representation of the creation process of an ERGM. (1a) an empirically observed network is considered; (1b) in a simulation we assume that every arc between every pair of nodes can be either present or absent; (2) dependence assumptions are formulated about how ties emerge relative to each other (e.g. the importance of inter-visibility for communication); (3) configurations or network building blocks are selected that best represent the dependence assumptions (e.g. reciprocity and 2-path); (4) different types of models are created (e.g. a model without dependence assumptions (Bernoulli random graph model) and one with the previously selected configurations) and the frequency of all configurations in the graphs simulated by these models is determined; (5) the number of configurations in the graphs simulated by the models are compared with those in the observed network and interpreted.

My madness series of posts and the recently published paper introduce a case study that illustrates this method. Iron Age sites in southern Spain are often located on hilltops, terraces or at the edges of plateaux, and at some of these sites there is evidence of defensive architecture. These combinations of features may indicate that settlement locations were purposefully selected for their defendable nature and the ability to visually control the surrounding landscape, or even for their inter-visibility with other urban settlements. Yet to state that these patterns might have been intentionally created, implies a sequential creation of lines of sight aimed at allowing for inter-visibility and visual control. An ERGM was created that simulates these hypotheses. The results suggest that the intentional establishment of a signalling network is unlikely, but that the purposeful creation of visually controlling settlements is better supported.

A more elaborate archaeological discussion of this case study will be published very soon in Journal of Archaeological Method and Theory, so stay tuned 🙂 Don’t hesitate to try out ERGMs for your own hypotheses, and get in touch if you are interested in this. I am really curious to see other archaeological applications of this method.

References mentioned:

Anderson, C. J., Wasserman, S., & Crouch, B. (1999). A p* primer: logit models for social networks. Social Networks, 21(1), 37–66. doi:10.1016/S0378-8733(98)00012-4

Lusher, D., Koskinen, J., & Robins, G. (2013). Exponential Random Graph Models for Social Networks. Cambridge: Cambridge university press.

Lusher, D., & Robins, G. (2013). Formation of social network structure. In D. Lusher, J. Koskinen, & G. Robins (Eds.), Exponential Random Graph Models for Social Networks (pp. 16–28). Cambridge: Cambridge University Press.

Wasserman, S., & Pattison, P. (1996). Logit models and logistic regressions for social networks: I. An introduction to Markov graphs and p*. Psychometrika, 61(3), 401–425.

Madness part 2: processes of emerging inter-visibility

The second post in the madness series, describing the run-up to my PhD submission! Last time I wrote about why visibility networks might be an interesting method in archaeology. There was a hidden agenda in that post however: I am not just interested in visualising a visibility network, that has been done before by many archaeologists. My main interest is in understanding the decisions that went into the establishment of lines of sight. That is, the processes that led to the visibility network I study. This might sound rather ambitious, since many factors influenced the selection of the settlement locations I study in my PhD, and visibility networks are merely one factor derived from our limited knowledge of past settlement patterns. However, I argue it is necessary to understand such processes. Mainly because when archaeologists formulate assumptions about how lines of sight affected past human behaviour, these assumptions imply a sequence of events rather than a static state. Therefore, a method is needed that allows one to test the assumed processes, and I have some ideas on how to go about this 🙂

Visibility network between Iron Age and Roman settlements in Southern Spain

Network representations of archaeological data are often used as static snapshots conflating an ever-changing dynamic past. By performing an exploratory network analysis we get an idea of their structure during a given period of time. Such an approach can be considered a type of exploratory data analysis. However, archaeologists use these data networks as representations of past phenomena. It is these past phenomena that archaeologists are ultimately interested in understanding, and most of past phenomena were not static but involved change through time. It is entirely plausible that at an earlier or later stage in time a given network would have had a different structure.

A commonly used technique for archaeologists to overcome this problem is to formulate theoretical assumptions about how the emergence or disappearance of a relationship between pairs of nodes in their data networks affected the change of past networks over time (from here-on referred to as dependence assumptions). Such dependence assumptions are frequently accompanied by (explicitly formulated or implied) expectations of the kinds of network patterns they give rise to. In other words, archaeologists frequently make theoretical statements about dynamic processes that cause change in past phenomena, and how these are represented in networks of archaeological data. Nevertheless, we rarely evaluate whether processes guided by our dependence assumptions can actually give rise to the networks we study, nor do we consider the effect multiple dependence assumptions can have on each other in such processes. Instead, archaeological network analysts have relied on the identification of the expected patterns in an observed network’s static structure when discussing the social processes that caused a network to change from one state to another.

The study of visibility networks in archaeology serves as a particularly good example of this problem. Archaeologists have used visibility networks as a method for studying the role particular visibility network patterns could have in structuring past human behaviour, for example through communication networks using fire or smoke signalling, or the visual control settlements exercise over surrounding settlements. Formulating dependence assumptions for visibility networks implies a sequence of events where new lines of sight will be established as a reaction to pre-existing lines of sight. For example, if we observe that a settlement is positioned in a visually prominent location from where many other settlements can be seen then we might formulate the hypothesis that this location was intentionally selected to enhance communication with or visual control over neighbouring settlements. A further example: if an effective signalling network was considered during settlement location selection then settlement locations inter-visible with other settlements would have been preferred. However, archaeological network analysts have so far studied these processes exclusively through an analysis of static network representations. By pointing out the patterns of interest, an exploratory network analysis can only take us so far to evaluate our dependence assumptions, leaving hypotheses surrounding the intentional creation of visibility patterns untested. A good example of this is Tilley’s (1994) study of a network of inter-visibility between barrows on Cranborne Chase, in which an observed network pattern is interpreted as the intentionally established outcome of an untested process: “One explanation for this pattern might be that sites that were particularly important in the prehistoric landscape and highly visible ‘attracted’ other barrows through time, and sites built later elsewhere were deliberately sited so as to be intervisible with one or more other barrows. In this manner the construction of barrows on Cranborne Chase gradually created a series of visual pathways and nodal points in the landscape” (Tilley 1994, 159).

Very few visibility studies have explored hypotheses about such processes explicitly (see Swanson 2003 for a notable exception). In my case study, however, the decisions to establish certain patterns of visibility among urban settlements are the focus of attention. Most crucially, I will try to evaluate to what degree this changed through time. The approach taken here is experimental. It will initially focus exclusively on the patterns of inter-visibility between settlements, exploring their observed structure as a static snapshot, and then addressing the following hypothetical question: if the visibility patterning that we have observed was the only reason for selecting the locations of sites, what then would be the process that is most likely to have led to the observed patterning? This question will be evaluated through a statistical approach that models the creation of visibility patterns in abstract space (i.e. by simulating the creation of points and lines without taking the landscape’s topography into account as a constraint). Finally, the results of this exploratory network analysis and statistical simulation approach will be re-contextualised within a wider archaeological discussion to shed light on aspects of the changing interactions between urban settlements in the study area through time, as reflected through visibility patterns.

Next time I will introduce the archaeology of this study area and show you some actual results 🙂

As always, I very much welcome your comments. They are very valuable to me in these last stages of my PhD.

References:
Swanson, S. (2003). Documenting prehistoric communication networks: A case study in the Paquimé polity. American antiquity, 68(4), 753–767.

Digital Classicist video online

The Digital Classicist people edited the video of the talk I gave a week ago (they do work fast). It’s available on their blog and on my bibliography page. Enjoy 🙂