In my previous post on the Chronological Gradient, I suggested that it could be explained by an area of contamination off the ‘top right’ of the sample, on the Holland backing cloth, which had carried over to the Shroud material itself. However, a more detailed examination of the measurements and the statistics derived from them suggests that we might need to look elsewhere.
The paper published in Nature was, to my mind, a little coy in its remarks about the anomalous nature of the Shroud radiocarbon results compared to those of the control samples. “The spread of the measurements for Sample 1 is somewhat greater than would be expected from the errors quoted.”
More simply, the probability that three measurements of the same material could turn out so diverse was a mere 5% in the case of the Shroud, but 30%, 50% and 90% in the case of the control samples. There being a nineteen-to-one chance that the Shroud measurements came from different materials, or at least from differently composed sections of a single textile, it is a worthwhile – indeed a necessary – exercise to try to find out why.
The percentages quoted above derive directly from what are known as chi-squared values, which are given as: 6.4 (Shroud), 2.4, 1.3 and 0.1 (Controls). Again, it is readily apparent that the Shroud is very much the odd one out.
Each of these chi-squared values is actually the sum of three values (one from each laboratory), which derive from the means and deviations found in each case. The sums are:
1.9 + 4.1 + 0.3 = 6.3 (Shroud)
0.0 + 1.1 + 1.3 = 2.4 (Control)
0.4 + 0.2 + 0.7 = 1.3 (Control)
0.1 + 0.0 + 0.0 = 0.1 (Control)
In each case above, the first value is from Arizona, the second from Oxford and the third from Zurich. Among all twelve values, Oxford’s Shroud value (4.1) is clearly the odd one out, so it is in Oxford’s sample that we should look for the reason for the anomaly, not in Arizona’s or Zurich’s.
Numerous commenters have noted the apparent chronological gradient across the Shroud sample, from Arizona (youngest), to Oxford (oldest). They have generally supposed that this is due to something making the Shroud appear too young, such as interpolated threads from the 16th century or a burst of neutrons enriching the radiocarbon content. In my previous post on the subject I suggested contamination on the Holland cloth. However, there is nothing anomalous in the values derived by Zurich or Arizona (the ‘young’ end). To resolve the anomaly, we really ought to look for something making the Shroud appear older, at the Oxford end.
From the data recently released by the British Museum, the Oxford dates (‘Before Present’) for each of its sub-samples are:
Shroud: 795, 730, 745, Weighted Average: 749, Weighted Error (σ): 31,
65% probability range (average plus and minus error): 780 – 718
Nubian Mummy: 980, 915, 925, Weighted Average: 938, Weighted Error (σ): 29,
65% probability range (average plus and minus error): 967 – 908
Egyptian Mummy: 1955, 1975, 1990, Weighted Average: 1977, Weighted Error (σ): 33,
65% probability range (average plus and minus error): 2010 – 1944
Cope of St Louis: 785, 710, 790, Weighted Average: 756, Weighted Error (σ): 26,
65% probability range (average plus and minus error): 781 – 730
The value of σ is to a certain extent related to the number of tests carried out. Although the Oxford team cut all their samples in to three subsamples, each subsample, when reduced to graphite, ended up in one or two tiny targets on the test carousel. The Nubian Mummy and Cope of St Louis ended up on six targets altogether, the Shroud on five, and the Egyptian Mummy on four.
Although none of the samples is outside the 95% probability range (2σ), both the Shroud and the Nubian Mummy gave values higher than the 65% range, and the Cope of St Louis gave one lower. The slight Shroud outlier is not even the most extreme (1.5σ, while the Cope of St Louis’ early date is 1.8σ away from the mean), and it is interesting that the most ancient specimen, the Egyptian mummy, was the most consistently dated. That, however, is an artefact of the dating process: the smaller the remaining percentage of radiocarbon, the easier it is to distinguish from the 100% of a modern material. The STuRP proposal to radiocarbon date the Shroud says: “Accuracies, σ, of ±120 yr for “time-of-Christ” era and ±250 yr for the AD 1300s can be easily obtained.”
All this suggests that although the Oxford date for the Shroud appears anomalous, it should not be rejected on statistical grounds, and practical reasons should be sought to account for it.
Various possibilities suggest themselves:
1) The Oxford cleaning regime was slightly different from the other laboratories.
Oxford used petroleum ether, which the other labs didn’t. However this did not affect its analysis of the control samples, so it does not seem to be a relevant factor exclusive to the Shroud sample.
2) The Oxford values were all rounded up to the nearest 5.
But even if all the Oxford results are reduced by 5, the anomaly persists.
3) “Final errors less than 40 years have been arbitrarily increased to 40 or 45 years.”
Adjusting the errors makes very little difference.
4) The oldest Oxford date is an outlier and should be ignored.
Unfortunately, if the date (795) is omitted altogether, then although the probability of the Oxford sample being integral with the rest is increased, it is only to 15%, which although now sufficiently large for statisticians not to reject the hypothesis that it is integral, is hardly inspiring.
5) The Shroud was contaminated with a substance that reduced the radiocarbon proportion.
This is possible and not unreasonable, although the petroleum ether treatment was specifically used “to remove lipids and candlewax”. Candidates for the substance include mineral oil, (known as asphalt or gargates in the Middle Ages), although it is difficult to produce a credible scenario for its use on the Shroud. Fish oil could be another possibility, perhaps used as a paint medium, but to be honest this is not much easier to explain.
Further information is clearly required for a satisfactory solution to the problem.