Fuzzy time (and the PAS)

We’ve been thinking recently about why and how we might apply the concept of temporal fuzziness (uncertainty) to our data, particularly because it is a research interest of mine (see Green 2011 for more details).

The reason why dealing with temporal fuzziness is important is well illustrated by the following graph, based upon the work of Frédéric Trément.  The graph shows how a dating of this villa site based purely upon the well-dated finewares would disguise the fact that the villa was very active into the fifth and sixth centuries, which actually account for the greatest amount of coarseware pottery.  If you ignore the coarsewares because of their poor dating, thus, you produce a false narrative of the history of activity on the site.

Comparison of fineware and coarseware dates from the villa site at Sivier, France (redrawn from Trément 2000 - Fig 9.16)
Comparison of fineware and coarseware dates from the villa site at Sivier, France (redrawn from Trément 2000 – Fig 9.16)

One way in which we can include less closely dated material in our analyses is to take account of temporal fuzziness.  In essence, this means defining a set of sub-periods and then calculating the probability (as a percentage in this simplest instance) of each object in the dataset falling within each sub-period.  This is essentially an adaptation of aoristic analysis, created for the study of crime patterns by Ratcliffe (his 2002 paper covers a more robust method than his previous work) and experimented with by various archaeologists.  Where appropriate, we can then sum these probabilities for each time-slice, to produce a model of changing deposition over time.

The most obvious dataset of ours to apply this fuzzy temporal analysis to is the PAS (Portable Antiquities Scheme) data.  This is because most PAS records represent a single object which has had start and end dates defined for it by the PAS team.  Some records need start and end dates adding (based upon the start and end periods, or in the absence of those, the broad periods) and some records need their start and end dates correcting (typically where they have been mistakenly reversed or where dates BC have not been given negative numbers), but all of this is possible to automate using Python scripts.  Once this data standardization has been completed, it is then possible to define a set of sub-periods and calculate the probability of each object falling within each sub-period (again, using a Python script).

PAS: summed probability by century
PAS: summed probability by century

The graph above shows the summed probabilities of PAS data when calculated and collated by centuries.  We can see here the general temporal profile of the PAS for our period, involving low levels of Bronze Age finds, increasing activity during the Iron Age, especially after the introduction of coinage, a massive increase through the Roman period, and then a return to lower levels of activity through the early medieval period.

PAS: summed probability by century: only objects of greater than 90% probability
PAS: summed probability by century: only objects of greater than 90% probability

The graph above then shows how the summed probabilities look if we only include objects with a greater than 90% chance of falling within each century.  Obviously, this example is a little fatuous, as it is not really very easy to date objects that precisely prior to the introduction of coinage, but it does make the point that only including very precisely dated material produces a biased temporal pattern.

PAS: summed probability by century: count of objects of greater than 0% probability
PAS: summed probability by century: count of objects of greater than 0% probability

At the opposite extreme, the graph above shows the count of objects within each century that have a greater than 0% probability of falling within said century.  Thus, in this graph, if an object spans three centuries, it is counted equally in all three.  Naturally, this method then produces another biased temporal pattern, this time over-representing activity in each century.

As such, the first graph, which takes account of the probability of every object is, in my opinion, the most honest representation of the temporal pattern.  However, as hinted above, century brackets are not really ideal, as objects can only very rarely be dated that precisely before coinage came into use.

PAS: mean probability by century
PAS: mean probability by century

This graph shows the mean probability (from 0.0 [0%] to 1.0 [100%], albeit the graph doesn’t scale that far) for all of the objects within each century bracket.  It shows that (on average) Middle Bronze Age and most Iron Age material is coarsely dated, that Later Bronze Age and Late Pre-Roman Iron Age material is better dated, that Roman material (particularly 4th century) is finely dated, and that most early medieval material falls somewhere between the prehistoric and Roman data in terms of its precision of dating.  The very low probabilities in the 5th century partially reflect the post-Roman transition, but are likely to be largely caused by the huge bulk of essentially 4th century Roman material that has been given an end date of 410 or 411.

The conclusion I draw from this graph is that we need to vary the width of our sub-periods over time to reflect the changing level of precision of dating within each period.  This ought to produce the most useful representations of temporal pattern, and is as equally simple to calculate as fixed century blocks.

PAS: alternative sub-period groupings
PAS: alternative sub-period groupings

This final graph, then, shows the summed probabilities for three different possible sets of sub-periods.  The y-axis is the summed probability and the x-axis is time from -1500 (1500 BC) to +1065 (AD 1065).

The orange line shows the same century brackets as before, which clearly is the worst model, as it reduces prehistory to a low-level trace yet also removes significant change in the Roman period (notably the sharp drops around AD 200 seen in both other lines).

The blue line shows a set of conventional sub-periods.  This shows a much more interesting temporal pattern than the century brackets.

The red line shows an alternative set of sub-periods, designed to break away from conventional dates assignments and to take more account of the changing rate of dating precision over time.  This is probably my preferred model, but there is no reason to make hard and fast choices, we can continue to experiment with multiple sets of sub-periods for now.

In the context of our project, this is very much preliminary work, intended to test out some of the possibilities of working with fuzzy temporality using our datasets.  I have also begun experimenting with building the EMC (the Early Medieval Corpus of Coin Finds maintained at the Fitzwilliam Museum, University of Cambridge) into this dataset.  There is also potential for doing something similar with the HER data that we have gathered, albeit implementation is more complex due to the variable structure of that data.  Once we have our methodology nailed down, it will become possible to construct graphs like the final one above for different types of object or for different regions of England.  We could also create a series of maps showing changing probabilities over time, perhaps combined into animations.

Whether this proves fruitful, only time will tell, but I do believe that this type of analysis has great potential for helping to explore continuity and change in EngLaId data.

Chris Green


Green, C.T. 2011. Winding Dali’s clock: the construction of a fuzzy temporal-GIS for archaeology.  BAR International Series 2234.  Oxford: Archaeopress.

Ratcliffe, J.H. 2002. “Aoristic signatures and the spatio-temporal analysis of high volume crime patterns.” Journal of Quantitative Criminology 18(1), pp. 23-43.

Trément, F. 2000. “Prospection et chronologie: de la quantification du temps au modèle de peuplement. Méthodes appliquées au secteur des étangs de Saint-Blaise (Bouches-du-Rhône, France).” In Francovich, R. and Patterson, H. (eds.) Extracting meaning from ploughsoil assemblages. Oxford: Oxbow, pp. 77-91.

Author: Chris Green

Postdoctoral Researcher (GIS)

3 thoughts on “Fuzzy time (and the PAS)”

Leave a Response

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s