ABSTRACT
The conference at Yarnton was very closely focussed on specific chronological issues in the Iron Age of the Levant. These issues are of critical importance to the understanding of the interrelationship of the polities of the region and would be of academic interest in any other region under archaeological investigation. However, in this case the arguments are given even more prominence because of the implications for our interpretation of the nature of King Solomon’s political impact. The main debate is most clearly seen in the differing interpretations put forward for Tel Reh ov (Chapters 13-17, this volume) but also bring in almost all of the other research presented in this volume. From the exchanges published in the journal Science on this topic (Bruins, van der Plicht, and Mazar 2003; Finkelstein and Piasetzky 2003; Bruins and van der Plicht 2003), it can be seen that the chronological arguments amount to about a hundred years at most. From the historical point of view such a period of time is very significant, being of the order of three generations, but from the point of view of radiocarbon dating, where a single calibrated date rarely gives a range (95% probability) of less than 100-200 years, this is too short a time interval to resolve easily. Largely for this reason, radiocarbon has often been ignored when confronting issues of this kind. However, where other forms of scholarship fail to produce a consensus it clearly makes sense to
try to use scientific dating techniques to inform the argument. We do, however, still have the problem that we are at the limit of what the method can achieve and so we have to use all of the tools at our disposal to pool the information from various sources. The Problem
Given that any single measurement is usually unable to resolve issues at the level of one hundred years or less it is necessary to use many measurements made on samples from different periods to try to uncover the underlying chronology. In doing so we are essentially using two main datasets: the radiocarbon measurements on known-age, dendro-chronologically dated wood which make up the radiocarbon calibration curve (Reimer et al. 2004; Stuiver et al. 1998), and the measurements on the material from the contexts of interest. We are then using these datasets to try to determine both the true dates of the samples we have measured and also the dates of key changes in a particular site, or region, which we assume to be related in some way to the samples measured. Thus we typically have tens to hundreds of measurements on our samples being used to estimate a slightly larger number of unknown dates with some prior information about their relationship-a multivariate statistical problem of a very high order. In order to cope with this problem, it is normally broken down into two stages. The first stage is calibration of each of the individual dates onto the calendar timescale-this is a relatively simple operation and gives a probability density function (PDF) for the true age of each sample Li(ti). In the nomenclature generally used in such analyses, this PDF is referred to as the ‘likelihood’ that a particular calendar date is associated with the radiocarbon measurement or ‘observation’ made on the sample. An example calibration is shown in Figure 5.1. This process is common to almost all radiocarbon calibration programs and is almost universally applied. From this ‘likelihood’ distribution it is possible to derive a range of most likely dates that encompass 95% of the area of the PDF. These are the ranges normally calculated as part of the calibration. It should be emphasised that in converting a radiocarbon date to a calendar date we often end up with multimodal distributions that are very far from being Normal. It is also the case that radiocarbon dates from a representative selection of dated material (e.g. a whole sequence of tree rings) are not evenly distributed in radiocarbon age. It is therefore very difficult to interpret distributions of raw uncalibrated dates in a robust way since doing so essentially ignores the complexity of the calibration dataset. After this calibration stage we then have many individual probability distributions and we have to use these to infer information about the chronology of a site or region, and this is where the difficulties often arise. Up to this stage we can treat each of the age determinations as being essentially independent. At some level this is an approximation since they are all based on the same calibration dataset and they may share some measurement uncertainty from the radiocarbon laboratory. However, such effects are usually of minor significance since the uncertainties in the measurements on unknown samples are usually much larger than those of the calibration curve, the numbers of measurements are usually lower. Also important is the fact that within the laboratory the uncertainty quoted on the unknown sample usually only has a very small systematic component from shared measurements on standards. This is not to say that samples cannot have systematic biases due to environmental effects and/or chemical pre-treatment deficiencies. This is an important issue to which we will return later. The problem we have, then, is how to synthesise the observations made on the individual dated samples with our understanding of the chronology we wish to study.
