I have been thinking a lot recently about using maps as effective tools for visual communication of data. Chen et al. (2014) wrote that visualization of data should be about getting your message across in a time-efficient manner, which Kent (2005) stated depends upon producing aesthetically pleasing results. All maps (being one form of data visualization) are imperfect models of the world (as all models are imperfect) and we must take care to make sure that our maps communicate the messages we wish to express effectively.
Without wishing to get unduly political, I want to work through these ideas using the example of this summer’s “Brexit” vote. Data on the referendum results can be found here and data on UK boundary lines here. There are many (infinite?) different potential ways of visualising this data spatially, but I am going to explain the messages I see in a few examples here.
First up, we have a simple rendering of the results using the district divisions by which the data was originally counted and parcelled up, in which the saturation of the yellows (remain) and blues (leave) show the percentage lead each vote had in districts which each side “won”:
Yellow and blue have been used as that seems to be the convention settled on by most of our media. This map shows which areas felt particularly strongly one way or the other about the question asked and works well in that regard. However, it also gives a somewhat misleading message, as some of the high value districts are of relatively low population density. As an alternative then, we can keep the same division into “leaver” and “remainer” districts, but instead use the shading to show population density:
This map loses the nuance of showing how strong the vote was in either direction, but gains something by showing which districts have more people living in them. Most notable is the stark difference between the districts in eastern England around The Wash, which are of low population density (for the UK!), but which felt very strongly that the UK should leave the EU.
We can also look at the result in much more stark terms. The recent High Court decision has increased the likelihood of their being a Parliamentary vote on invoking Article 50, so I wanted to see which way the various constiuencies fell in terms of “leave” or “remain”. This is not simple, however, as the results were reported using districts, which often do not match constiuencies. As such, I reapportioned the vote from districts between consituencies on the basis of spatial area (e.g. if a constiuency covered half a district, it would receive half the votes). This is imperfect, as population density is not uniform across any district, but was the best I could do with the data to hand. The results show that, if Parliament does get to vote on Article 50 and MPs vote as their constituents voted, then “Leave” will comfortably win (Northern Ireland has not been included, but does not have enough MPs to make a difference either way):
All of these maps work reasonably well at expressing one element of the data, but I wanted to come up with a visualization that produced a more complex picture of the results yet without abandoning geographic space (i.e. I did not want to use a cartogram):
This final map reworks the results into hexagonal spatial bins, using the same method as when I reworked the results into constiuencies (i.e. assignment by spatial area overlap). Here, the blue / yellow shading has returned to showing the strength of the result, but we can now also see data on population at the same time through the thickness / blackness of the lines around the hexagons. I feel that this map does a pretty good job of showing the distribution of the vote (spatially, strength-wise, and population-wise) whilst still allowing people to locate themselves reasonably well geographically (which would not be the case with a cartogram). Hexagons have been preferred over squares largely to their visual appeal and due to the fact that humans have a tendency to see false straight lines in data binned into square-based grids.
Whatever you think of the referendum result, I hope that my worked example has helped to explain how making a map is not always a simple task. Careful thought about audience, message, and data structure needs to go into any visualisation if effective communication is to be achieved. I hope that my final map succeeds in that task!
Chen, M., L. Floridi, and R. Borgo. 2014. What is visualization really for? The Philosophy of Information Quality. Springer Synthese Library Volume 358, 75-93
Kent, A.J. 2005. Aesthetics: a lost cause in cartographic theory? Cartographic Journal42(2), 182-188
All maps contain Ordance Survey data (C) Crown copyright and database right 2016
Ever since I was an undergraduate (and attempted to write a “mental geography” of Roman Britain for my dissertation), I have been interested in Claudius Ptolemy’s Geography. Ptolemy was an Alexandrian Greek and his Geography dates to the mid second century AD: it contains coordinates from which it is possible to make maps of the entire known world at that time, including data representing the earliest surviving reasonably accurate survey of the British Isles. For the purposes of the EngLaId Atlas, that I am currently working on, I decided to see if I could plot Ptolemy’s Britain (or Albion as he called it) over the modern OS map.
To do so, I copied out the coordinates for Ptolemy’s places (representing points along coastlines, islands, and major settlements) from Rivet & Smith 1979. I suspect that there may be one or two typos in their lists (as a couple of the points in the final maps are not quite in the same place as they are on Rivet & Smith’s map), but I am not too worried about that for now. The task was then to convert Ptolemy’s coordinates so that they could be plotted onto the OS National Grid.
The first job was to correct for Ptolemy’s underestimate of the circumference of the planet (it was this underestimate that caused Columbus to be so confident about being able to reach the Indies by sailing west, thus accidentally discovering the Americas): to do so, all of the coordinates were first multiplied by 0.798. I then needed to recentre the coordinates so that they related to modern latitude / longitude: I used London / Londinium as a fixed point in both Ptolemy and the modern world, on the assumption that the provincial capital of Britannia ought to be relatively precisely located in Ptolemy’s data. This involved adding 8.41 degrees to each latitude measure and subtracting 16.06 degrees from each longitude measure.
I then created a shapefile in ArcGIS from the coordinate list using the WGS84 projection settings and then reprojected the map into OSGB 1936, ArcGIS’s representation of the OS National Grid. The points were then filtered out into islands, settlements, and coastline vertices. I had given the coastline points an “order” field (based upon the order of coordinates in Ptolemy) and used the Points to Line tool in ArcGIS to convert them to a line. I then converted the line to a polygon using Feature to Polygon. Finally, a few extra vertices were added to the coastline polygon using the editing tools in order to ensure that the settlement points were all on dry land. Here is the result:
Several things jump out. The most noticeable (and long commented on) is Ptolemy’s rotation of Scotland. Why he did this has been the subject of much debate, possibly being due to him believing that a N-S Scotland would extend too far north or possibly being due to a lack of reliable data on travel times through those non-Imperial lands. The latter is rather key to understanding the Geography: whereas latitude was fairly straightforward to calculate in the past, without chronometers longitude was much more difficult and relied largely upon calculations made using travel time itineraries. We can see the results of this in the way that most of the settlements in England / Wales are reasonably precise in their latitude (N-S) but much more imprecise in their longitude (E-W): York forms a good example. Overall, considering the time when it was constructed, Ptolemy’s Geography contains an impressive representation of Britain (south of Scotland).
I then experimented with a couple of transformations to see if I could improve the plotting onto the National Grid. First, I tried rotating the data so that the north of England more closely aligned with the modern map (actually an affine transformation using London, York and Chester as fixed points, so the geometry is slightly deformed, especially for Scotland):
The result is not really all that great, as the south of England then becomes much less closely aligned with the modern map. I also tried a rubbersheet transformation, using London as a fixed point and moving Ptolemy’s York onto modern York:
This turns the map into a really quite close approximation of the modern English / Welsh coastline, with the exceptions of the immense length of the south west and the rather stunted East Anglia. However, as it disturbs the geometrical relationship between Ptolemy’s coordinates, I decided in the end that my first model was probably the best: after all, I could keep adding points to the transformation until everything mapped perfectly onto the modern geography, but what would be the point of that? I would just be recreating the OS map.
This was just a short experiment for the purposes of debate and making a nice map. It seems likely that I may have done something spatially naive in plotting the data using the WGS84 settings, but the end results are rather pleasing in any event.
Rivet, A.L.F. & C. Smith. 1979 The Place-names of Roman Britain. London: Batsford.
The maps contain Ordnance Survey data (OpenData). (C) Crown Copyright and Database Right 2016.
This is another post about field systems, following up on my previous work on the subject (I)(II)(III). As stated in my last post on the subject, I now have a dataset of 40 field systems that I have digitised (based upon NMP data) and subjected to various analyses. Some initial results will be discussed below.
They range in enclosed area from around 2ha to over 1,100ha and cover time periods from the Bronze Age to the Roman period (with a single small section of early medieval reuse in one case). When plotted by time period, the earlier field systems are largely in the south of the country, whereas the Iron Age / Roman ones feature a more comprehensive national spread (the blue “PR” dots represent unspecified prehistoric or possibly Roman field systems):
When classified into rough categories of “coaxial” (meaning essentially rectilinear and perpendicular in character) and “aggregate” (meaning more amorphous), both types of field system occur across the country:
All of these field systems have been subjected to analysis of their morphology, topology (to a limited extent) and landscape character. Probably unsurprisingly, but usefully, field systems with less orientation “peaks” tend towards perpendicularity (y-axis is the difference in degrees between the centres of the first and second peaks on the orientation graphs, the x-axis is the number of peaks on the orientation graphs [5 peaks = 5+ peaks]):
Interestingly, the degree of “coaxialty” of each field system appears to have very little to do with how “open” the landscapes are, which suggests that the layout of field systems (particularly in the Bronze Age) did tend towards “terrain blindness” (x-axis is how “coaxial” each field system was from 0 [not at all] to 1 [very]; y-axis is how visually open the enclosed area of each field system is from 0 [very restricted intervisibility] to 1 [high degree of intervisibility]):
One pattern that has emerged is a degree of bias in orientation towards a particular pair of approximate compass bearings around 100-120˚ and 10-30˚ (this graph shows the direction [and strength] of the two strongest orientation peaks from every field system):
As the graph makes clear, this is not the case across the board, but it is common enough to suggest that there is something going on here. The orientation data was also plotted against the orientation of the aspect of the local terrain, to see if the latter could affect the former (red lines show aspect, black lines field system banks/ditches):
As should hopefully be apparent, the aspect of the ground surface can influence the orientation of field systems (especially in the case of FS_id 25, which runs along the side of a fairly steep hill), but not in many cases.
Nationally, these data have been collated by 100x100km OS grid square, alongside orientation data for ridge and furrow, and for unstudied field systems via automated extraction of boundaries. Both of the latter datasets were based purely on the more modern CAD-based NMP projects and processed using automated methods, so the results are based upon more data than my set of field systems, but data that has been less rigorously filtered (numbers record the number of line segments analysed in each square):
The ridge and furrow data shows a particularly interesting pattern here, with a very common bias towards perpendicular orientations just west of north and just north of east for areas north of the Humber. Hall has noticed this pattern before in Yorkshire, suggesting that it probably is the result of a planned reorganisation of the landscape on a large scale at some time before the C13th (2014:53), but my analysis suggests that this may have occurred over a very substantial area of northern England.
So, what we have here is people in prehistory and the Roman period constructing field systems that were sometimes very regular (“coaxial”) in character and sometimes less so, with the ground surface sometimes having an effect on the orientation and regularity of the field systems, but with field systems also often being laid out in a way that ignored the affordances provided by the ground surface. Often, these field systems were laid out on an orientation that pointed approximately towards a compass bearing of 100-120˚ (and at 180˚ to that, as these lines have no direction) and, to a lesser extent, towards approximately perpendicular alignments. When so-called “open field” systems were created from the later early medieval period, these also show an orientation bias (a different one), particularly north of the Humber.
I suppose that the natural inclination of archaeologists working in their respective time periods would be to find a more ritual explanation for the earlier phenomenon and a more pragmatic explanation for the later phenomenon. This in itself is problematic and one of the reasons why working across traditional time period boundaries (as we are) has the potential to produce new interpretations and understandings. For myself, I am not sure what I think (yet)…
Hall, D. 2014. The Open Fields of England. Oxford: OUP.
Following on from my previous work on field system orientation (I)(II), I have now finished data gathering for a set of 40 field systems across England, mostly within our case study areas, using data provided by Historic England’s National Mapping Programme. These cover almost 6,000 hectares and represent in part all of our time periods of interest (albeit there is only one early medieval example and even that is reuse of part of a larger prehistoric system). They should provide a decent set of evidence within which we can search for spatial and temporal patterns in prehistoric and Roman field system morphology.
I have gathered a whole series of metrics on these field systems (including dating evidence, length of boundaries, count of boundaries, etc.), which will be drawn upon in our later analyses, but I have started by thinking through orientation further. The set of graphs in the image below show the approximate orientation of field boundaries within each of our 40 field systems. The graphs require a little explanation. They each vary from 0 to 179˚ on the OS National Grid: this means that any axis through the centre of the graph represents 90˚ not180˚. The black line shows the total length of boundary lines for each degree (relative to the bearing of greatest total length). Each line has been smoothed in order to bring out trends rather than showing the full complexity of the field system.
As such, symmetry along any axis on the graph can be seen as representing a stronger degree of “coaxiality”, as 180˚ on the graph represents 90˚ on the ground. Tighter peaks (so long as there are only two and they fall opposite each other) also represent a stronger degree of “coaxiality”. This provides us with a simple visual aid for assessing how “coaxial” or “rectilinear” a field system is and how each compares to other field systems. In this case, by “coaxial” I mean field systems where the boundaries tend to be orientated along two alignments perpendicular to one another.
The variation seen remains to be analysed, to see if there are patterns across time and space, but some tentative initial conclusions can be drawn:
Many field systems show strong perpendicular symmetry. This is often also the case with those that did not appear particularly “coaxial” in plan form.
Some field systems show no favouritism towards particular alignments, although even these often avoid certain alignments.
Currently, there appears to be a bias across the dataset as a whole towards a particular coaxial alignment approximately targeted on NNE/ESE, although this needs further investigation to see if this represents a strong bias in one particular time period or spatial area.
However, we have yet to explore this dataset in its fullest detail, so further work is needed. I will try to report on any interesting patterns seen here in the future.
I have recently been pondering the definition of regions, in the sense of carving England (or any country) up into contiguous zones of particular archaeological character. I would suppose that as a method of archaeological enquiry, this probably goes back at least as far as Fox’s division of Britain into “lowland” and “upland” zones along a dividing line running approximately from Dorset to Yorkshire. As a modern practice, I would suggest that recent interest in defining regions probably arises, at least in part, from the influential work of Roberts and Wrathmell (2000).
The reason why I have especially been thinking about this subject of late is due to the way in which two projects contemporary to our own have gone about structuring their reporting of their results. Their final report currently in press (Rippon et al. 2015), the Fields of Britannia (FoB) project divided the country (in this case being England and Wales) up into a series of regions (made up of groups of bio-geographical “pays”). Similarly, the Roman Rural Settlement Project (RRSP) has also divided the country up into their own set of regions based upon the archaeological character of the excavated evidence found within each. Both of these projects based their regions around conglomerations of Natural England’s “Natural Areas“.
If we compare these various regions on a map against the “Settlement Provinces” defined by Roberts and Wrathmell (R&W), we can see that there are broad similarities but also substantial local differences between the various regions (and provinces) defined. Herein lies the major problem with projects defining their own regions for analysis and reporting: it makes cross-comparison between different projects’ results difficult. For example, the Chilterns and the Berkshire Downs both fall within the south east regions of R&W and FoB, but within RRSP’s central zone: as such, can their respective “central” zones truly be compared? The simplest solution to this would be defining regions based upon modern political boundaries or, say, 100x100km grid squares. However, such an approach would result in regions that are archaeologically and bio-geographically irrelevant, which is very far from ideal (and so not recommended here!).
More fundamentally perhaps, I am also not convinced that archaeological remains (and thus, by implication, past human culture) truly lacks variety across such continuous areas of space and changes according to such sharp boundaries. I am sure that all of the researchers involved would agree with me on that and there is no doubt that defining regions helps in formulating ideas / arguments and in reporting results. However, I just wonder if there is a better way to structure our space? Some degree of structure is necessary, or all would be chaos and incomprehensible, but could alternative structures be preferrable?
As an experiment, I constructed a regional model for England, but one that did not result in continuous regions, but rather fractured zones spread across the whole country. This model was based upon a mixed classification of elevation and terrain ruggedness and resulted in three new zones: a coastal zone (which largely seems to accord with former wetland areas), a lowland zone, and a highland zone (which seems to capture every important range of hills in England). These zones can exist in pockets within one another: they are not contiguous. Although not (by design at least) archaeologically relevant, these zones certainly have a degree of bio-geographic meaning. Furthermore, they would be reproducible by other scholars, assuming I publicised their construction method. As a Warwickshire man, I am particularly taken with the result that my county almost looks like a “natural” division of the country!
If we compare these three “HiLo” zones (named for Oxford’s infamous Jamaican inn) against the regions of the other projects we can again see some similarities between the borders of my zones and those of the other projects, but again with substantial local differences. Obviously, if we were to use my HiLo regions for reporting on our project, we would just end up compounding the problem of difficulty of comparison, but the experiment remains of interest.
I then tested each set of regions against a series of other datasets: elevation, terrain ruggedness, broad soil types, soil wetness, etc. The graphs above show just the elevation results, but the broad conclusions were similar for all comparisons. Essentially, the FoB and RRSP regions look far more distinct than the R&W provinces. This is hardly surprising as they are of smaller spatial extent: the smaller a sample area, the more distinct from the general “population”/pattern a variable ought to tend to be. This is clearly the case here. However, the HiLo model sits somewhere in between. It only has three zones, but they appear far more clearly differentiated than the R&W provinces. As such, we can conclude that they have greater geographic differentiation, due to their non-contiguous nature, despite being of similarly large extent.
As a final test, I then compared each set of regions against our archaeological data, using our coarsest level of thesaurus categories. I did this for each broad time period, but the results shown above are for all EngLaID time periods combined (unspecified prehistoric, Bronze Age, Iron Age, Roman, early medieval). The conclusions, interestingly but perhaps not surprisingly, are very similar to those seen when comparing against the “natural” factors described just above. FoB and RRSP regions look fairly distinct, R&W rather homogeneous (albeit with less dense data in the north west), and HiLo regions are more distinct than R&W but less so than the others. Again, the size of regions remains key (due to the MAUP).
Since undertaking these comparative experiments, I have been reading a recent report by Historic England’s Andrew Lowerre (2015). In the second half of the report, Lowerre uses a mixture of environmental variables alongside Roberts and Wrathmell’s data to define regions using automated clustering techniques. The regions that he produced (across a series of different models), much like my HiLo model, are non-contiguous and possess fuzzy borders. As such, to me at least, they seem much more representative of the data than regions defined manually. I wonder if this type of automated region creation is the way forward if we wish to define regions for our analysis and reporting?
Regions are undoubtedly a useful and intuitive way to divide up space that makes analysis and reporting of results within the context of a project relatively simple and straightforward, both in terms of how a team thinks about their data and in terms of how an audience may digest the same. However, the cross-comparison issue is distinctly problematic when one begins to think beyond the bounds of the results of a single project. We could potentially define a set of regions based on the natural environment that all projects should attempt to use, but we as archaeologists often seem to be naturally inclined to always do our own thing, so I am not sure that would be fruitful. Plus the set of regions defined might not be relevant across multiple time periods.
As such, I do wonder if we ought to avoid the idea of archaeological character regions altogether and just talk about variation in data across space. So long as that data is quantifiable and mappable as continuous fields, then cross-comparison becomes simple: map overlay is after all the most obvious application and strength of GIS, with whole suites of tools and methods dedicated to it.
This post is not intended as a criticism of the methods of other projects, which have undoubtedly proved fruitful and interesting in each case. I just wanted to express why I feel we (as EngLaID) ought to avoid regions in our reporting, especially as a project looking across traditional period boundaries. Others might disagree, but I do feel the cross-comparison issue of bespoke regions is a thorny problem, particularly for those interested in broad syntheses across time and space.