The Shroud of Turin · Chapter 19 of 21

The radiocarbon paradox: the 1988 test and its critics

What radiocarbon dating measures and what it assumes, how the 1988 protocol was designed and how it was carried out, the three laboratory results and the apparent heterogeneity, the reweaving and contamination questions, the later re-analyses, and what the test does and does not establish about the age of the linen

On 13 October 1988, the British Museum held a press conference at which the results of the radiocarbon test on the Shroud of Turin were announced. Three laboratories, in Oxford, Arizona and Zurich, had measured the age of a small sample of linen from the cloth, and their results pointed to a date in the Middle Ages. The announcement was reported around the world. It was one of the most publicised scientific results of its time, and it was presented as a settled answer to a question that had been argued since the nineteenth century. The result has since been disputed, re-examined and defended, and the dispute has become a case study in how a scientific test can be sound in its methods and still leave questions open. This chapter sets out what radiocarbon dating measures, what it assumes, how the 1988 protocol was designed, how the samples were taken, what the results were, the problems that have been raised with them, and the later work that has followed.

What radiocarbon dating measures

Radiocarbon dating measures the decay of an unstable form of carbon, carbon-14, which forms in the upper atmosphere and enters living organisms through the food chain. While an organism is alive it takes up carbon-14 in the same proportion as the atmosphere. After death, the uptake stops, and the carbon-14 in the tissue decays with a half-life of about 5,730 years. By measuring the remaining proportion of carbon-14 relative to the stable carbon-12, a laboratory can estimate how long ago the organism died.¹

The method requires calibration, because the proportion of carbon-14 in the atmosphere has varied over time. The variation is measured from tree rings, corals and other archives whose ages are known independently. Calibration converts a radiocarbon age, reported in years Before Present, into a calendar range, with a stated probability. The calibration curve is continuously refined, and the calibrated range for a given measurement depends on the version of the curve used.

A radiocarbon date is therefore not a single year. It is a range with a probability, and it depends on the sample, the measurement, the calibration and the assumptions. The reader should keep that in mind when a single year is quoted in the press.

What the method assumes

Radiocarbon dating rests on several assumptions. The first is that the sample is homogeneous, so that the material tested came from a single period. The second is that the sample has not gained or lost carbon since the death of the organism, or since the time the date refers to. The third is that the sample is free of contamination, or that the contamination can be removed. Each assumption can be violated, and each violation can shift the date.

The linen of the Shroud raises particular difficulties with these assumptions. The cloth is a textile, and textiles can be repaired, patched, rewoven and treated with substances that add carbon. Linen can absorb carbon from smoke, from handling, from storage and from the air. Any of those processes could make a sample appear younger or older than the linen itself. The assumptions therefore have to be tested for the particular object, and not taken for granted.

The Shroud and its history of handling

The Shroud has been handled, displayed, kept in reliquaries and damaged by fire. The fire of 1532 in the chapel of Chambéry, where the cloth was kept, is documented, and the cloth was folded and repaired afterward. The repairs and the handling mean that the linen is not a single undisturbed piece of cloth from one period. The reader who wants to understand the radiocarbon result must understand the history of the handling, because the history determines which parts of the cloth are likely to contain material of a different age.

The repairs are visible on the cloth. Some areas show patches and reweaving, and the threads of the repairs are of a different appearance from the original weave. The repairs were made to close the damage from the fire and to reinforce the cloth. The 1988 sample was taken from a corner, and the question of whether that corner was part of the original cloth or a repair is one of the central issues of the dispute.

The 1988 protocol

The Shroud was made available for dating in 1988 after a long debate in the Church and among the scientific community. The protocol that was agreed was designed to address the concerns about homogeneity and contamination. It called for multiple samples taken from different, non-adjacent locations on the cloth, for the samples to be prepared and labelled so that the laboratories did not know which sample came from the Shroud, and for oversight by an independent committee. The protocol was intended to provide a robust test, and to show that the result was not the product of a single sample or a single laboratory.

In practice, the protocol was modified. The sampling was carried out in a single location, a corner of the main cloth, rather than at several places. The samples were cut from the corner, which was adjacent to an area that had been sampled in 1973 by textile experts. The sample from the corner was divided into subsamples, which were sent to the three laboratories. The departure from the plan was significant, because the single location meant that the samples could not test whether the cloth was homogeneous across its length.²

The sampling

The sample was cut by a textile expert, and it was taken from the corner of the cloth. The cutting was done in the presence of observers, and the material was divided and packed for transport. The subsamples were sent to Oxford, Arizona and Zurich, where they were prepared and measured. The laboratories were given samples with codes, and they were not told which sample was the Shroud, in line with the blind design of the protocol.

The sampling raises several questions. A single corner may not represent the cloth as a whole. The corner may have been part of a repair, or it may have been exposed to handling or to a source of contamination. The location of the sample relative to the earlier 1973 sampling is also significant, because the earlier cut could have left material that contaminated the new one. The questions were raised after the results were announced, and they are central to the later analysis.

The three results

The results were published in Nature in February 1989. The Oxford laboratory returned an age of 750 years Before Present, plus or minus 30. The Arizona laboratory returned 646 years plus or minus 31. The Zurich laboratory returned 676 years plus or minus 24. After calibration, the three results pointed to a range in the late thirteenth and fourteenth centuries, and the calibrated ages were presented as consistent with each other.³

The results were presented with confidence, and the press took them as a definitive dating of the cloth. The authors of the Nature paper were more careful, and they noted that the dating depended on the sample and the assumptions. The results were also presented as consistent, and the consistency was taken to show that the sample was homogeneous and that the laboratories were accurate.

The apparent heterogeneity

The three results were not as consistent as they appeared. The Oxford result was older than the Arizona result by more than the measurement errors would predict. The authors of the original paper computed a statistic to test whether the three subsamples came from a homogeneous piece of linen, and the statistic was higher than the threshold that conventionally raises questions about homogeneity. The result was described in the paper, and it was discussed in later critiques.

The heterogeneity question is important for the interpretation. If the subsamples came from a homogeneous piece of linen, their dates should agree within their measurement errors. If they came from linen of different ages, their dates would disagree, as they did. The disagreement suggests that the sample was not uniform, and that the corner included material from more than one period, or from contamination. The argument has been made in many forms, and it is the basis of the most serious criticism of the 1988 result.

The contamination argument

The contamination argument holds that the sample was affected by carbon from a source other than the original linen, and that the contamination made the sample appear younger than the linen. The argument points to the handling of the cloth, to the smoke from the fire of 1532, to the treatments applied to the cloth over the centuries, and to the possibility that carbon-bearing compounds from the sampling process itself affected the material. Each of these sources could add carbon, and a small addition could shift the result significantly.

The argument has been tested by cleaning the samples, by comparing the results of different cleaning methods, and by examining the samples for the chemical signatures of contaminants. The results have been mixed. Some cleaning methods removed contaminants, and others did not remove them completely. The question of how much contamination remained in the 1988 samples cannot be answered with certainty, because the samples were consumed in the measurement.

The reweaving argument

The reweaving argument holds that the corner sample came from a repair, and that the repair was made with linen of a different age. A medieval repair in an old cloth would give a date that reflects the repair, not the original. The argument is that the sample represents the repair, and that the rest of the cloth may be older.

The argument has an evidential basis. The repairs on the cloth are visible, and some of them are in the areas that were sampled. The reweaving changed the structure of the cloth in places, and the threads of the repairs may be of a different material. The argument is strong if the sample came from a repair, and it is weaker if the sample came from the original cloth. Benford and Marino argued in 2002 that a patch of later linen mixed with original linen could produce the 1988 date, though critics dispute their calculation.⁶ The question of which is correct is one of the most debated points in the literature.

The Arizona data

The Arizona laboratory’s results, which were the lowest of the three, have been examined in detail by later researchers. The subsamples in the Arizona run showed a pattern that some have read as evidence of heterogeneity, and the pattern was discussed in a later analysis published in the peer-reviewed literature. The analysis drew on records of the measurements, and it asked whether the Arizona results had been properly reported. The reader should note that the analysis was based on the laboratory records, and that its conclusions depend on the completeness of those records.

The Arizona results have also been compared with the other laboratories, and with the results of later work. The comparison shows that the three laboratories did not agree as well as the original paper suggested, and that the difference could reflect the sample, the procedures or the measurement. The reader should weigh the comparison with care, because the sources of the difference are not fully established.

The Freer-Waters and Jull analysis

In 2010 Rachel Freer-Waters and A. J. Timothy Jull published a photomicrographic examination of a sample split from the 1988 Arizona sample. They found no evidence that contradicts the sample coming from the main part of the cloth, no evidence of coatings or dyes, and only minor contaminants. A 2026 report by the same authors, which some sources describe as a direct textile examination of two Arizona fragments, could not be confirmed, and its findings are not relied on here.⁴

The Rogers analysis

Raymond Rogers, a chemist who had taken part in the STURP investigation, examined the surviving material from the 1988 sample. In a paper published in 2005, he argued that the dated sample came from a rewoven area of the cloth, and that the area was coated with a yellow-brown plant gum containing dye lakes, so that the sample was not representative of the cloth. He also stated that the sample could not be older than about 1290. The argument has been disputed, and a 2014 critique questioned the provenance of his samples. The reader should note that Rogers’ analysis is one of the more specific claims in the literature, and that its strength depends on the chemistry of the sample.⁵

What the date would mean

If the 1988 date is correct for the linen, the Shroud would be a medieval object, and the Gospel burial would have to be a tradition attached to a later cloth. If the date is wrong for the original linen, because the sample was a repair or was contaminated, the date does not settle the age of the cloth, and the question remains open. The implications of the result therefore depend on whether the sample represents the cloth.

The date would also bear on the image. A medieval date for the linen would have to be squared with the image, the blood, the chemistry and the other evidence, and each of those lines of evidence has its own interpretation. The date is one piece of evidence, and it cannot decide the question alone. The series asks its readers to see the date in that context.

What the test can and cannot establish

The 1988 test can establish that the sample taken from the corner of the cloth had a radiocarbon age consistent with a date in the late thirteenth and fourteenth centuries. It can establish that the three laboratories measured the sample and reported their results. It cannot establish that the whole cloth has that age, that the sample was free of contamination or repair, or that the cloth is the burial linen of the Gospels. Those claims require evidence beyond the single measurement.

Later tests and new samples

Since 1988, the question of the Shroud’s date has been raised in other studies, including proposals for new samples and new methods. The proposals include the testing of samples from other areas of the cloth, the use of new cleaning methods, and the application of other dating techniques. None has yet produced a result that settles the question, and the field remains divided. The series treats further testing as desirable, and it asks that any future test follow a protocol agreed in advance, with the sampling, the cleaning and the controls stated.

What the paradox teaches

The radiocarbon paradox is the apparent conflict between a sound measurement and an uncertain interpretation. The measurement is sound in the sense that the laboratories used reliable methods. The interpretation is uncertain because the sample may not represent the cloth. The paradox teaches that a precise result is not the same as a secure conclusion, and that the design of a test, including its sampling, must be judged as carefully as its measurements.

The laboratory procedures

The three laboratories used different procedures to prepare the linen for measurement. The preparation involves removing contaminants, converting the cellulose of the linen to carbon dioxide or graphite, and measuring the carbon-14 content with an accelerator or a counter. Each step can add or remove carbon, and each step has its own controls. The procedures used in 1988 were standard for their time, but they differed in detail, and the differences matter when the results are compared.

The cleaning step is the most debated. Laboratories have used acid and alkali washes to remove carbonates, humic acids and other contaminants, and they have used heat or chemical treatments to remove contaminants that are bound more tightly. The strength of the cleaning determines how much of the sample is retained, and how much of any contaminant remains. The 1988 laboratories used cleaning procedures that were considered adequate for most archaeological textiles, and the question is whether they were adequate for the Shroud, given its history of handling and repair.

The accelerator mass spectrometry used by the Oxford and Arizona laboratories counts carbon-14 atoms directly, and it needs far less material than the older counting method. The Zurich laboratory used a combination of methods. The use of accelerator measurements was a significant advance, and it made it possible to test a small sample. The small size of the sample also meant that the material available for later testing was limited, and the protocol had to balance the need for measurement with the need to preserve the cloth.

Calibration and the curve

The calibration of the 1988 results was carried out with the calibration curve available at the time. The curve has since been revised several times, and the revisions have shifted the calibrated ranges for radiocarbon dates from many periods. The 1988 calibration therefore gives a range that is not the same as the range that would be obtained with the current curve, and the reader should note that the calibrated dates quoted in the press may have been produced with an earlier version.

The calibration curve has also been an object of study in its own right. The variations in atmospheric carbon-14 are caused by changes in the sun and the earth’s magnetic field, and the curve shows wiggles over periods of decades and centuries. Some periods show plateaus, where the curve is flat, and a measurement from a plateau gives a wide calibrated range. The thirteenth and fourteenth centuries have such features, and the calibration of the Shroud date therefore covers a broad span of years. The reader should note that the breadth of the range is a property of the curve, not an error in the measurement.

Radiocarbon dating in practice

Radiocarbon dating has been applied to many textiles, manuscripts and works of art. The method is routine for organic materials of the last several thousand years, and it has produced reliable dates for many objects. The practice shows that the method is sound, and it also shows the cases in which the method has been challenged. Textiles that have been repaired or handled are among the most difficult, and the protocols for them are more demanding than the protocols for simple organic remains.

The dating of the Dead Sea Scrolls is a useful comparison. Scrolls were dated by radiocarbon in the 1990s, and the results were checked by several laboratories and by palaeographic study. The scrolls were not repaired in the same way as the Shroud, but the case shows how a radiocarbon result can be combined with other evidence to reach a conclusion. The Shroud case has not been combined with the same range of independent evidence, and that is one reason for the continuing dispute.

The sampling and the ethics of destruction

Radiocarbon dating is destructive. The sample is consumed in the measurement, and a cloth that has been sampled cannot be restored to its original state. The 1988 sampling therefore involved a decision about the cost to the object, and the custodians and the scientists had to weigh the benefit of a date against the loss of material. The decision was taken with the agreement of the Church and under the protocol, and it was accepted by many as a reasonable balance.

The ethics of sampling are not only a matter of preservation. The sample also represents a choice about which part of the object is tested, and that choice shapes the result. A sample taken from a repair tells a different story from one taken from the original weave, and the choice must be justified in advance. The series asks that future sampling decisions be made in the open, and that the reasoning be published before the samples are taken.

The reception of the result

The 1988 result was received in several ways. Some scientists and some members of the public took it as a definitive refutation of the authenticity of the Shroud. Some religious writers rejected it, and argued that the sample was unrepresentative or that the test had been flawed. Others accepted the result as a sound measurement, and argued that the question of origin was still open because the sample might not represent the whole cloth. The range of responses shows how a scientific result can be used in arguments that go beyond its evidence.

The reception also showed the strength of the public interest in the Shroud. The press coverage was intense, and the result was quickly summarised in popular form. The summaries often omitted the qualifications of the original paper, and they sometimes presented the result as a final answer. The series aims to correct that tendency, and to present the result with its qualifications.

The Church and the test

The Roman Catholic Church, which holds the Shroud in the cathedral of Turin, permitted the test under the conditions of the protocol. The Church’s position was that the test was a matter for scientific investigation, and that it did not settle the religious significance of the cloth. The Church has since maintained a careful position, neither affirming nor denying the authenticity of the Shroud, and presenting it as an object of devotion and of study.

The Church’s position is one example of the way in which a scientific test can be placed in a wider context. The test answers a question about the material, and the religious question is answered by other means. The series keeps the two questions apart, as it does throughout.

What a new test would need

A new radiocarbon test would need to be designed with the lessons of 1988 in mind. It would need a sampling plan that covers several areas of the cloth, including areas known to be original and areas known to be repaired. It would need a cleaning protocol agreed in advance, with controls for each step. It would need blind measurement, with the samples coded so that the laboratories do not know their origin. It would need an independent committee to oversee the process, and it would need the full data to be published, including the laboratory records.

A new test would also need to be linked to the other evidence. The date would be interpreted alongside the image, the chemistry and the history of the cloth, and the interpretation would be stated with its assumptions. A test designed in this way would be more likely to settle the question than the 1988 test was, and it would be easier to interpret if the result was not in agreement with the original.

The statistics of agreement

The question of whether three laboratory results agree is a statistical one, and it depends on the measurement errors and on the method used to combine them. A simple test compares each pair of results and asks whether their difference is larger than the combined error would allow. A more demanding test asks whether all three are consistent with a single underlying age. The original paper used the more demanding approach, and it found that the agreement was adequate for the protocol, though the margin was not large.

The statistics can be read in different ways. One reading is that the results agree sufficiently, and that the differences are within the normal variation of the method. Another is that the results agree only at the margin, and that the margin is too narrow to support confidence that the sample was uniform. The disagreement between these readings is not about the arithmetic, which is not in dispute, but about the threshold for accepting agreement and about the number of samples needed to establish homogeneity. A test with three subsamples from one corner cannot establish homogeneity across the whole cloth, however the arithmetic is done.

Custody and oversight

The 1988 test was carried out under an arrangement of custody and oversight. The custodians of the cloth, the Church, agreed to the test, and an independent committee was set up to oversee the work. The committee’s role was to ensure that the protocol was followed, that the samples were handled properly and that the results were reported openly. The oversight was an important safeguard, and it gave the result a credibility that a test without oversight would not have had.

The oversight also had limits. The committee did not control the sampling in every detail, and the departure from the protocol in the choice of the single corner was a decision that was taken in the field. The reader should note that oversight is not the same as control, and that a committee can ensure the process is followed without ensuring that the protocol itself is adequate.

Closing the account of 1988

The 1988 radiocarbon test is a precise measurement of a sample whose relation to the whole cloth is uncertain. The laboratories did their work carefully, and their results are reported in the literature. The protocol departed from its plan in the choice of sample, and that departure has shaped the debate ever since. The result is a date that many accept as the date of the linen sampled, and that many question as the date of the cloth. The two positions are not necessarily in conflict, because the sample may or may not represent the cloth, and the test cannot by itself settle which.

The series holds that the radiocarbon result is important, and that it should be taken seriously. It also holds that the result is a single piece of evidence, and that its interpretation depends on the sampling, the cleaning, the calibration and the history of the cloth. A reader who keeps those points in view will be able to judge the result on its merits, and to see what further work would be needed to resolve it.

What the radiocarbon test contributes to the series

The radiocarbon test is the most direct scientific test of the cloth’s age, and it is therefore central to the question of whether the Shroud is the burial linen of the Gospels. Its result is important, and its interpretation is open. The next chapter turns to the question that the test cannot answer on its own: how the image was formed, and what that formation implies about the process and the maker.

Reading the 1988 result on its own terms

The 1988 result should be read first on its own terms, before it is set against the claims of either side. On its own terms, it is a set of three measurements of a single corner of the cloth, with stated errors, calibrated against the curve of the period, and reported with a test of their mutual consistency. Each of those features can be checked against the published data. A reader who wants to know what the test shows should begin there, and only then ask what the test was taken to show by those who used it.

Other sources of error

Beyond the sampling and the contamination, several other sources of error can affect a radiocarbon result. The measurement itself has a statistical uncertainty, which is reported with the result. The background of the instrument, the blank samples used to check it, and the standards used for calibration all carry their own errors. The laboratory must control each of these, and the controls must be reported. A reader who sees a result without its controls cannot judge its reliability.

Some errors arise from the material itself. Linen can contain plant matter other than the flax fibre, such as seed residues, dust or traces of other plants used in its processing. These materials can differ in age from the fibre, and if they are not removed they can shift the date. The cleaning procedures are designed to remove them, but they cannot remove everything, and the residual error depends on the cloth. The Shroud, having been handled and displayed for centuries, may carry a larger burden of such material than a well-kept museum textile.

A closing note on the paradox

The radiocarbon paradox is not a paradox in the strict sense. The measurements are internally consistent, the methods are sound, and the calibration is standard. The difficulty lies in the relation between the sample and the cloth, and in the question of whether the test answered the question it was designed to answer. The paradox is therefore a problem of inference, and it can be resolved only by better sampling and by independent evidence. The series does not claim that the paradox is resolved, and it presents the issues in the form in which they have been debated. Where a claim about the date rests on the 1988 result, the reader is asked to check whether it also addresses the sampling, the contamination and the reweaving, since a claim that does not address them has not yet met the objections. The same standard applies to claims in favour of the cloth and to those against it, and it applies with equal force here. Each claim should be read against the original paper, not against a summary of it.

References

1. Libby, W. F. (1955). Radiocarbon Dating. 2nd edition, with a chapter by Frederick Johnson. Chicago: University of Chicago Press.
2. Protocol and sampling of the 1988 radiocarbon test, as described in the literature on the dating. See the original reports and the discussion in the companion book. Publication details to be confirmed before publication.
3. Damon, P. E., Donahue, D. J., Gore, B. H., et al. (1989). Radiocarbon dating of the Shroud of Turin. Nature, 337, 611–615. doi:10.1038/337611a0
4. Freer-Waters, R. A., & Jull, A. J. T. (2010). Investigating a dated piece of the Shroud of Turin. Radiocarbon. Volume and pages to be confirmed before publication.
5. Benford, M. S., & Marino, J. G. (2002). Textile evidence supports skewed radiocarbon date of Shroud of Turin. Available as a PDF on shroud.com; journal not confirmed.
6. Rogers, R. N. (2005). Studies on the radiocarbon sample from the Shroud of Turin. Thermochimica Acta, 425, 189–194. doi:10.1016/j.tca.2004.09.029