The three laboratories chosen to radiocarbon date the Shroud were given samples which they cut into subsamples for dating. Oxford used three subsamples, Arizona used four and Zurich five. As we know the order in which the samples were originally placed on the cloth – Oxford nearest the end, then Zurich, then Arizona – an approximate gradient, from oldest to youngest, can be observed.
The correlation value (R2) of 0.48 is not statistically convincing, but the fact that the Oxford and Arizona values so little overlap, even including their quoted errors, gives us grounds for supposing the gradient to be real. This being so, it makes some sense to suppose that the values within each laboratory fall along the same gradient. In the absence of information about how the subsamples were cut, it could be assumed that the oldest values are nearest to the end of the cloth, in all three laboratories’ results.
The correlation (R2 = 0.62) is now more convincing, but the situation can be further improved by making a model and refining the assumption above in the light of better information. The model is that the three samples derive from a rectangle 42mm long, divided into lengths of 15mm, 15mm and 12mm, to correspond with the c.50mg, c.50mg and c.40mg masses of the three pieces given to the laboratories, and the assumption is that the subsamples were achieved by slicing each piece at rightangles to the long axis of the strip. In fact we know this isn’t what happened, but it will lead us to a more realistic assessment later on. Each date can now be given the longitudinal measurement of the centre of the subsample it represents.
Although considerably less obvious, it is not impossible that there is also a gradient across, as well as along the sample strip. Obviously the order of each laboratory’s sample cannot be rearranged along the cloth, but as we do not know exactly how they were subdivided, there is no a priori reason why we should suppose they were sliced transversely rather than longitudinally, or in a combination, which seems to have been the case with both Zurich and Arizona, at least. The Oxford sample, for example could have been cut in any of the following ways – and this itself assumes that the pieces were of equal area, which they may not have been.
In their remarkable analysis of nearly 400 000 possible configurations of the positions of all twelve subsamples, Marco Riani and Anthony Atkinson1 confirmed that the probability of the gradient being genuine was statistically significant, and incidentally found, as was later confirmed, that a small strip of the ‘reserve’ portion given to Arizona to make up its weight to 50mg was not used at all. However, they did not identify the single particular configuration – if there was one – which best represents the gradient, suggested by the twelve laboratory dates.
Nevertheless, in a powerpoint presentation of the paper2, authored, in order, by Riani, Atkinson, Giulio Fanti and Fabio Crosilla, the results were interpreted like this:
And in the Italian version of his latest paper3, Paolo di Lazzaro interprets them like this:
This suggests that the configuration which best fits the smoothest interpretation of the chronological gradient is this:
However both these interpretations are flawed.
1) As about one third of the Arizona piece was retained by the laboratory – which in an earlier paper4 I identified as the upper third – the Arizona results must be confined to the lower two thirds of their sample.
2) A montage of unknown provenance5, but appearing to derive from the ETH laboratory in Zurich, and whose illustrations are far from clear, nevertheless suggests that their sample was first cut horizontally, and then the upper piece was divided into three and the lower into two.
In his report on the results, Willy Wölfli explains that his sample was cut into two approximately equal parts, the first to be tested being cut into three and the second being cut into two.
3) Dates given in Years BP exactly reflect the radiocarbon proportion of the sample they refer to. When calibrated, they result in a range of calendar dates, sometimes two or three ranges. Giulio Fanti’s dates are therefore necessarily selective.
The interpretation below is also selective, of course, but I think represents a more accurate depiction of the configuration suggested by all the data. In the centre of each subsample is a dot which represents the ‘average’ position at which the radiocarbon result can be considered to be from if a point source is required.
Using these dots, isochrones can be derived, based on the assumption of a regular gradient between each one. For convenience, they are simplified to the nearest ten.
Although this diagram should not be taken too literally, some interesting ideas can be derived from it. For a start, the isochrones are much closer together in the Arizona sample than they are in the Oxford sample, with Zurich intermediate, as it is in position. In fact this is true regardless of the position of each subsample: the range of dates found by Arizona (701-591 = 110) is greater than that found by Zurich (733-635 = 98) which is in turn greater than that found by Oxford (795-730 = 60).
This in turn suggests that the source of the ‘disturbing factor’ appears to be somewhere off the top right of the diagram, acting to make the cloth appear younger, and not off the bottom left, acting to make it appear older. It is impossible to be precise, but the illustration below gives an idea of the possibility.
Some kind of contamination of the Holland cloth, possibly deliberately applied to stain it to match the Shroud, which spread onto the Shroud but which was not fully removed by the cleaning process, could have been responsible for this interpretation of the results. On the other hand Bob Rucker, who thinks that the gradient was a feature of neutron enrichment emanating from the body at the moment of Resurrection6, points out that the correlation between the points is just as valid if the entire diagram is inverted about its long axis (although obviously the Arizona section would have to be displaced, it would make little difference to the result). It that case the centre of the disturbing factor would be off the bottom right hand corner, and towards the middle of the body image.
In a personal communication, Bob has pointed out that he made the assumption that the bottom of the Shroud was folded under the feet of the body of Jesus, so that the sides ended up more or less on its midline. In a graph showing the dates his hypothesis predicts along the midline, Rucker’s gradients range from about 70 yr/cm to 100 yr/cm over the distance from the toes to the ankles, which compares quite reasonably with the 40 yr/cm to 90 yr/cm suggested by the radiocarbon dates over the length of the sample strip.
At first sight then, the radiocarbon dates appear to support the neutron enrichment hypothesis. However, like the endlessly repeated illustration of the Roman flagrum, which was specifically engineered to fit the scourge-marks on the Shroud, it must be remembered that the neutron enrichment model has been similarly engineered to fit the radiocarbon dates. In the absence of independent corroborative evidence, neither the flagrum nor the neutron enrichment hypothesis can be connected to historical occurrence.
Footnotes
1. Riani, Marco, et al., (2013). ‘Regression Analysis with Partially Labelled Regressors: Carbon Dating of the Shroud of Turin’, Statistics and Computing, Vol 23, Issue 4
2. Riani, Marco, et al., (2017). A Robust Statistical Analysis of the 1988 Turin Shroud Radiocarbon Dating Results, powerpoint presentation at the Pasco International Conference on the Shroud of Turin, published at https: academia.edu by Robert A Rucker with the title ‘Video on Statistics by Riani, Atkinson and Fanti, S52
3. Di Lazzaro, Paolo, (2020). Revisione Propositiva dei Risultati di Radio-Datazione della Sindone di Torino, ENEA
4. Farey, Hugh, (2019). Reconstructing the Radiocarbon Corner, at medievalshroud.com.
5. This diagram appears at archiv.ethlife.ethz.ch/e/articles/sciencelife/turin.html, but it is only an unexplained illustration to that article.
6. All the data from Bob Rucker is from Rucker, Robert, (2018). The Carbon Dating Problem for the Shroud of Turin, Part 3: The Neutron Absorption Hypothesis, at shroudresearch.net/research.html