Fuzzy time II (14C and PAS)

Following on from a previous post (see which and also Green 2011 for more details on the methods discussed here), I have been experimenting more with the application of fuzzy probability modelling of our data. We decided to expand out the previous experiments, which had only been done using PAS data, to take in radiometric dates. Although our search was rather cursory, just taking in the CBA Index maintained by the ADS (and periodically updated by English Heritage) and a search of published dates from within the OxCal database (kindly conducted for us by Christopher Bronk Ramsey at RLAHA), we were able to create a database of over 5,000 radiocarbon (14C) dates that fell within (or partially overlapped) our time period of interest (for this exercise, being 1500BC to AD1050).

I rewrote my fuzzy probability calculation scripts to enable them to use the full detail of the radiocarbon probabilities output by OxCal and then ran them on a series of timeslices across this new dataset. Initially, I used the sub-periods defined in the previous experiment, but it became quickly apparent that the sub-periods chosen for the Late Iron Age and Roman period were too narrow to produce high enough probabilities of dates falling within them to be of interest. So I defined a different set of sub-periods, which resulted in a higher average probability for dates through the LIA-Roman period:

  1. 1500 to 1151BC
  2. 1150 to 801BC
  3. 800 to 401BC
  4. 400 to 151BC
  5. 150BC to AD49
  6. AD50 to 199
  7. AD200 to 410
  8. AD411 to 649
  9. AD650 to 849
  10. AD850 to 1050

The results were collated in ArcGIS and could then be mapped for each time-slice as follows:

1 raw dates 400 to 151 bc
Example of 14C date probabilities for 400 to 151BC

However, there is a problem with reading these maps due to the relatively clustered nature of the distribution which results in a lot of overlapping points. This results in some low probability dates obscuring higher probability dates within the same local area. To get around this, I collated the results using hexagonal bins, with the maximum probability of any date within a given bin being used to define the probability for that bin (maximum rather than summed values were used as 14C dates are not really discrete objects in the same way as finds and so multiple dates do not necessarily represent greater density of activity in the past):

2 collated dates 400 to 151 bc
Example of 14C dates collated by hexbin (max value) for 400 to 151BC

I then reran the probability calculations for PAS and other dated finds in our database using the new sub-periods and summed the results by hexagonal bin (summing was used rather than the maximum here as finds very much are discrete objects and, as such, more finds does imply more past activity, with certain caveats [modern archaeological / metal detecting practice being the most obvious one]):

3 finds dates 400 to 151 bc
Example of finds dates collated by hexbin (summed value) for 400 to 151BC

I then combined the two sets of results, using the maximum value across both datasets. As such, if the weighted finds probability within a cell was greater than 1.0, then it was preferred, but if less than 1.0 and less than the 14C probability within the cell, then the 14C probability was preferred. Although the finds dominate the results, the 14C does fill in some gaps and increase probabilities in some areas, especially in prehistory:

4 all dates 400 to 151 bc
Example of 14C and finds dates collated by hexbin (max value) for 400 to 151BC

The results for each time-slice can be viewed in the following animation (click to enlarge):

Animation of combined finds and 14C date probabilities through time

What can we read into this? Well, firstly, it should be noted that this is just an experimental model and shouldn’t read too much into it. There is a possible element of duplication in some of the finds data, as some PAS records are present in both our PAS dataset and our HER dataset (dependent upon local HER practice). Secondly, the 14C dates only add something quite subtle to the finds dates, as we have far more finds dates than 14C dates in our possession, but the subtle addition is, I feel, an important one.

However, subject to these caveats and the further element of uncertainty introduced by the affordance factors at play in the background (see previous posts: PAS; monuments), there are certain tentative archaeological conclusions that we could draw. The picture I see in the animation is one of relatively widespread activity in earlier prehistory, which intensified in the south and east in the Late Iron Age and especially through the Roman period, with late Roman and especially early medieval activity being particularly focused on the central / southern / eastern area of England (essentially Cyril Fox’s lowland Britain). Whether this remains the case as we build in more sources of evidence, remains to be seen.

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.

Author: Chris Green

Postdoctoral Researcher (GIS)

5 thoughts on “Fuzzy time II (14C and PAS)”

  1. This is an interesting exercise, but there is going to be an inevitable and significant bias caused by differences in the number and intensity of investigations from which the data is derived. Upland areas have not only lower numbers of investigations but greater amounts of pasture and hence less PAS-reported finds. The Pennine ridge is an obvious example in the displayed data but the effect is everywhere. If these biases could be removed the result is likely to be quite different. Without dealing with the geographical biases assessing the spatial variation of data isn’t going to be reliable.

    1. Oh yes, I don’t doubt that for a second. That was part of the reason for attempting to build the 14C dates in, so it wasn’t so biased by where people metal detect. But it does need something else too, probably things found most commonly through aerial survey (e.g. enclosures, barrows, hillforts, that sort of thing), although inevitably these will be more imprecisely dated. That’s probably the next iteration of my model I suppose!

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