Hi Chris,

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Dr Ramsey combined radiocarbon and archaeological evidence within a Bayesian paradigm to produce an absolute chronology for early Egypt. I thought to bracket the OK between two of his dates that would provide us with a time frame into which Dynasties 4 - 8 (about 450 years) needed to fit: Dyn. 3 Netjerikhet c.2658 BC and Dyn. 11 Ipi-ha-ishutef c.2070 BC, about 588 years. 588 - 450 = 138 years into which Netjerikhet to Snefru (about 78 years) and beginning of FIP to Dyn. 11 (about 35 years) needs to fit. 78 + 35 = 113 years which is close enough to 138 years.

Neither on the basis of radiocarbon dating, nor on the basis of statistical modeling, it is impossible to speak with confidence about such accurate dates as you use in the calculation.
I can explain using estimates for Djoser's reign as an example.

1. Dr Ramsey et al. estimated dates for Djoser's reign in their 2010 article (2013 article refers to earlier periods).
The authors used 9 samples (including one combined) of which 2 turned out to be outliers; thus a total of 7 radiocarbon ages were taken into account in the model.
Here they are: 4084±32 BP, 4177±28 BP, 4108±30 BP, 4135±30 BP, 4145±32 BP, 4168±27 BP, 4123±32 BP (combined).
Average radiocarbon age for this dataset is: 4134±32 BP.

2. When calibrating the radiocarbon age of 4134±32 BP in the Calib program, we get the following calibrated date ranges (with their probabilities in the last column):



and graph:



Resulting 1-sigma range (2861-2632 BC) is highlighted by me in green; 2-sigma range (2872-2588 BC) is highlighted in red.
For estimation, one can use both 2-sigma range and 1-sigma range.

3. As one can see, radiocarbon dating itself gives a wide range of dates, each of which has the same probability and therefore any of them can be considered suitable. Using radiocarbon dating, the resulting wide range of dates cannot be reduced, therefore, statistical modeling with the introduction of independent temporal information is used.
The introduction of independent temporal information into the model is nothing more than the direct definition of the sequence of kings' reigns and the durations of their reigns. That is, for Khufu, for example, the duration of the reign is set (see Appendix to 2010 article by Ramsey et al.) as 23±var years (the var is calculated during modeling).

Obviously, after the introduction of historical information, the reliability of the obtained model completely depends (if data on radiocarbon ages are not enough, how are they not enough for the Old Kingdom in discussed article) on the reliability of determining the durations of the kings' reigns by historians (as known, historians reconstruct durations on the basis of royal lists, which are incomplete and often contradict each other).

4. Using the durations of reigns by the Shaw's chronology, the authors get a model in which the beginning of Djoser's reign is estimated by range of 2696-2623 BC and falls into the "younger" part of the wide calibrated range:



Estimates for the beginning of Djoser's reign is highlighted in violet. This range is even exceded lower ("younger") border for 1-sigma calibrated range.

5. If historians are significantly mistaken in any of their estimates for the durations of reigns (I assume that the duration of the 9-10 dynasties is underestimated by 200 years), then in p.4 (above), we need to introduce other temporal information and the result could be completely different.
For example, nothing prevents us from introducing a duration of 9-10 dynasties of 250 years (according to Breasted based on Manetho's data) and then the expectations for the beginning of Djoser's reign will shift to the upper ("older") border of the calibrated range:



The "older" dates shown correspond to radiocarbon data as good as the "younger" dates in the previous picture.

I think that’s what Dr Dee meant when he wrote "the absolute dates for the Old Kingdom, as far as I am concerned, could still be moved by 1-2 centuries".

In general, only the creation of the master dendrochronology for Egypt based on wooden samples from Egypt will allow us to determine more or less exact dates.

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It seems Ian Shaw’s OK dates are reasonably accurate to within +-50 years

The results by Dr Ramsey and co-authors correspond to the Shaw's chronology well because the durations of the reigns according to Shaw were used in the modeling.

Alex.



Edited 6 time(s). Last edit at 03/15/2020 09:13AM by keeperzz.