Radiocarbon dating has revolutionized the study of archaeological specimens, but it remains something of an art. Fluctuations in the 14C content of the atmosphere over time make calibration against other dating techniques necessary, and the spectre of contamination with recent organic matter always hovers.
There is probably no single instance in which these inherent ambiguities in the technique's precision have been more widely publicized than its application to the Shroud of Turin in 1988. That investigation, described the following year (P. E. Damon et al. Nature 337, 611–615; 1989) famously revealed the shroud's linen to be of medieval origin, most probably early fourteenth century, suggesting that this celebrated relic of the Catholic Church is a fake and not the true burial shroud of Jesus.
Whatever the science might say, there is now a groundswell of dissent that is finding a voice in prominent media outlets. One objection is that the dating was distorted either by recent fungal growth on the material or by smoke or scorching from a fire in 1532 that is known to have damaged the shroud, burning holes that were later patched.
These issues were in fact addressed at the time of the initial report by one of the investigators, the late Teddy Hall of Oxford University (Archaeometry 31, 92–95; 1989). Hall pointed out that if the linen was truly 2,000 years old, it would have to be contaminated with as much as 40 percent of modern carbon to give the date measured. Moreover, the data did not vary between samples washed to different degrees. And tests on other samples of cloth gave unchanged dates for various degrees of scorching.
Another view is that the small sample removed from the shroud for dating came from a section that had been repaired in the Middle Ages with an almost invisible weave. The claim is not entirely ad hoc – circumstantial and technical arguments can be advanced in its favour (R. N. Rogers, Thermochim. Acta 425, 189–194; 2005). It's certainly regrettable that only one small part of the shroud was studied.
Other critics challenge the radiocarbon study with historical evidence. Hall echoed the standard view that the shroud first appears in the records in 1353. But it is now claimed that an identical shroud is depicted in a late twelfth-century manuscript from Hungary, and that an alleged burial shroud imprinted with the image of Christ can be traced at least to the sixth century.
It's fair to say that, despite the seemingly definitive tests in 1988, the status of the Shroud of Turin is murkier than ever. Not least, the nature of the image and how it was fixed on the cloth remain deeply puzzling. All of this calls for further testing, but that's unlikely to be permitted any time soon. Of course, the two attributes central to the shroud's alleged religious significance — that it wrapped the body of Jesus, and is of supernatural origin — are precisely those neither science nor history can ever prove.
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Ball, P. Shrouded in mystery. Nature Mater 7, 349 (2008). https://doi.org/10.1038/nmat2170