I have written elsewhere about how texts are underspecified relative to maps, e.g., in my presentation at From Pole to Pole. The 26th International Cartographic Conference (ICC) in Dresden in 2013. Underspecification in this context means that the text opens up for a number of different spatial interpretations. The definition I use is:

Underspecification: a verbal text describing a spatial phenomenon in a way that can be understood as two or more significantly different phenomena by a competent reader, thus, an ambiguity stemming from a lack of information.

Most of my work on underspecification has been based on input from the source text only, without the use of contextual information such as pre-existing maps or knowledge about the area being described. Restricting context in this way is problematic, and no clear lines can be drawn; however, the method worked in the sense that it gave a deeper understanding of how geographical texts work.

In this blog post I will follow up on a paper I gave at the 41st Computer Applications and Quantitative Methods in Archaeology (CAA) Conference in Perth in 2013. The abstract and the slides are online. I will examine what happens when place names are connected to pre-existing maps but a limited number of the places are not identified. How can we use the underspecified textual information to model the locations of the unknown places on the map? How can we present users with scholars sound visualisations where the interpretations we do are clearly shown? How can we use geometrical models to separate between different types of interpretative practices? This blog post offers no final framework, it is rather a tentative sketch of a possible way of development.

Levels of testability

All maps are creative products. Maps also refer to something outside themselves and many maps can be tested against some sort of evidence. Topographical maps, to take one example, are based on and testable against a physical landscape. This is closely linked to what was called truthfulness in my previous blog post The head of the cartographer, where I claimed there that such testing can only be done by humans. Map surveying can be seen as hypothesis testing and modification. A base map based on airplane or satellite images is a hypothesis that the surveyor tests against the landscape, making an improved hypothesis, eventually developed into map data used to create printed and digital maps.

However, not all maps refer to landscapes which are available for such testing. In figure 1 some map types are ordered  by their levels of testability. In some types of mapping of cultural heritage information, the testability is comparable to that of topographical maps. In other cases, no hypothesis testing against a landscape is possible. Examples of the former is mapping of existing social practices, such as contemporary tourism. Examples of the latter include fictitious works such as Tolkien’s books about Middle Earth. On a scale between these two extremes we find many pre-historic and historic situations.

In an underspecified textual historical source many places mentioned in the text can be identified on historical or modern maps. While such maps cannot be tested against the historical landscape, they can be tested against our contemporary landscape, which includes archaeological evidence. In cases where such testing against a landscape is impossible we can still use pre-existing maps which are based on agreed upon representations, as in the case of the landscapes created by Tolkien.

Unknown places

I have shown elsewhere, e.g., in the ICC paper mentioned above, that underspecification is significant even in textual descriptions which seems to be very detailed. A large number of choices must be made in order to create text based maps. Most of these choices are made in one go when a pre-existing map is chosen. But some underspecification still remains, e.g., when it comes to unidentified places. How can we best handle such remaining uncertainty?

In the remaining of this blog post I will discuss places on the surface of the earth only, that is, I will read textual sources as references to geographical places. All places mentioned in texts will have a room where they can possibly be located; the area in which they must be found has an outer bound. The largest possible room is the face of the earth. In most historical sources contextual information can be used to limit the rooms significantly. In travel narratives one can make assumptions based on maximal possible travel speed and means of transport. Places may also be typified and described in a way which limits possibilities. For instance, an island must be in water, and if the size of the island is given we can infer a lower limit for the size of the water body the island is found in.

In the following I will focus on a different type of criteria, namely, relations between places as they are expressed in texts. The method I will describe is in line with what has been proposed for time by Holmen and Ore. Figures 2–4 are taken from their work. It shows how  time uncertainty can be reduced by adding data to a time calculus system.

Figure 2 shows the situation where we know that a church was planned in 1660, and stood finished in 1690. The building of the church could have started early in 1660 and be finished the same year. The building could also have started and finished in 1690. Thus, based on the available data both the beginning and the end of the building of the church could be anytime from 1660 to 1690.

In figure 3 we see the result of adding information about the time it took to construct the church: at least six years. The church could not be finished earlier than 1666 (if the building stared in 1660 and took minimum time) whereas it could not be started later than 1684 in order to be finished by 1690. Thus, by adding this piece of information the uncertainty in the system has been reduced.

Figure 4 shows the result of adding yet another piece of information: a coin from the reign of James II was found in the foundation. As he was crowned in 1685, we know that the building process could not have been finished earlier than that year. Thus, the possible points in time when the building of the church was finalised is now the five years from 1685 to 1690. The uncertainty is reduced further.

Such a method cannot be transferred directly to spatial uncertainty. Space is fundamentally different from time (if anybody disagrees I will be happy to discuss it, please post a comment). Yet, the basic idea in the work on spatial information is taken from the Holmen-Ore calculus. Texts often express explicitly relationships between places, e.g., claiming that “place B is some 2 miles east of place A.” Such a claim does not express a precise relationship between the places; mile is not exact in most historical sources, and east usually does not mean straight east (90°). Yet, if we know where A is we have an indication for B as well, as shown in figure 5.

If we then have another place, C 2 miles south east of B, we do not have a fixed point to start from. In order to express the added information, every possible locations of B must be taken as possible starting points for the new relationship. Four examples are shown in red in figure 6.

What if we connect the visualisation of uncertain textual data to a map, as was suggested above? In many cases most of the places in historical sources can be identified. More than 90% identification is common for early modern and modern sources from Scandinavia. Such identification is time consuming, but in some cases the job is already done, e.g., in place name registers published in printed editions of source documents. Let us take a modern map from an area in Northern Norway as an example. The map is shown in figure 7 with three relational claims drawn onto it. The three claims refer to the same place as it is located relative to three other places. The possible area, which is the intersection between the three rooms of possibilities, is smaller than any single one of them. Thus, each new statement added to the map reduced uncertainty, in line with what we saw for time above.

This method shows the uncertainty based on the parameters used to establish the rooms of possibilities. It clarifies in the geometrical model what is known and what is not known due to underspecification. This enables us to separate problems caused by errors and inconsistencies in the source text from situations where one is unable to make definite conclusions due to underspecification.

This is a method to visualise the unknown. It can be used to present different maps as different hypothesis, that is, as different interpretations of textual material. It points towards a clearer specification of the unknown. One remaining problems is how to express clearly the levels of confidence connected to such visualisations of data. Another is to find ways to make graphical presentations of uncertainty which are understandable to map readers. Both problems will have to be delayed to a future blog.

2014-09-26 Øyvind Eide

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