# A critical review of the radiocarbon dating of the Shroud of Turin

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A critical review of the radiocarbon dating of the Shroud of Turin

Proceedings of the International Workshop on the Scientific approach to the Acheiropoietos Images, ENEA Frascati, Italy, 4‐6 May 2010 A critical review of the radiocarbon dating of the Shroud of Turin. ANOVA - a useful method to evaluate sets of high precision AMS radiocarbon measurements Remi Van Haelst w w Kerkstraat 68 Bus 4 2060 Antwerp Belgium. [email protected] ro ei ch .a w Abstract A review of the radiocarbon literature illustrates limitations the AMS method shows when dating bones and all kind of living plants like flax, mainly composed out of cellulose. A number of old and recent radiocarbon dating results, made on linen and wood, are compared. Keywords: AMS Statistics, Chi² test, IEM-EEM, ANOVA. 1. INTRODUCTION fo .in Until 1977, radiocarbon measurements were made by counting the number of 14C decays over a long period. The development of AMS with real 14C isotope counting was a revolution. One became able to almost os 2. AMS MEASUREMENTS t ie po In 1989, Nature [1] published the report on the radiocarbon dating of the Shroud of Turin, by the laboratories of Oxford, Arizona and Zurich. Claimed was of mediaeval date for the Shroud with a least 95% confidence. I then published a small booklet [2], with a complete statistical analysis, including Chi², IEM-EEM and a small ANOVA [3] tests; showing that the claimed 95 % confidence was not supported by a statistical test. Today ANOVA is accepted by NIST [4]. When I conducted some heating experiments on inducing 14C enrichment, I received an official dating report from the Oxford radiocarbon laboratory. I was surprised to read the following caveat: ”One should bear in mind that these measurements have been made on organic material and that this cannot be regarded as a guarantee of the article date of manufacture. It should be noted that the undetected presence of any contaminant may affect any radiocarbon result.” A caveat in contrast with the more stringent requirements imposed for industrial laboratories. In that context, a precision in part per million is mandatory. completely separate nitrogen and carbon isotopes. In 1986, a Zurich AMS test run with 14 standard samples, showed a counting error of 0.3% and an overall error of ~ 1 %. The conclusion of that study was: “One should improve the count rate and reduce contamination by at least a factor 2” [5]. So, the need to improve the precision of AMS measurements has been known for some time. Scott, analyzing the 1990 International Collaborative Programme [6] concluded: ”It seems reasonable to consider that a laboratory performs adequately if it has no systematic bias and assesses its internal and external variability adequately. IEM & EEM should not significantly different from 1. In total, only 15 out of 58 laboratories did meet these 3 basic criteria”. Today in its website, the AMS laboratory of the University of Arizona at Tucson [7] claims an error as low as 0.2%, a high level of precision in RC year terms. They note that when results are in doubt, measurements are repeated and the AMS equipment tuned or even shut-down for repair. This level of precision and accuracy has changed over time. In 1990-1992, Arizona obtained ~ 85% correct measurements. By 2000, they improved to about 92% but this still means nearly one failure out of ten measurements. May one wonder about the failure rate in 1988? It should also be noted the need for a statistical analysis of the 14C count, due to some unpredictable spontaneous reactions: 14 N + n = 14C + p & 14C => 14N + b + 160 keV Proceedings of the International Workshop on the Scientific approach to the Acheiropoietos Images, ENEA Frascati, Italy, 4‐6 May 2010 795 + 65 = 860; 860/8267 = 0.104015; exp(0.104015) = 1.1096; 9500/1.1096 = 8561.5 14C count 795 65 = 730; 730/8267 = 0.088292; exp(0.088292) = 1.0923; 9500/1.0923 = 8697.2 14 C count Mean date = 8629 +/- 68. From this it is apparent that relatively small changes in 14C count can translate into large changes in reported radiocarbon dates. 3. COMPARISON OF A SET OF DATES, REPORTED BY POLACH AND THE DATES REPORTED FOR THE SHROUD ro ei ch .a w w w Analysing char and root fractions from grain and pollen samples, NIST researchers [8] noted significant differences in the 14C content of different fractions taken from the same sample. Analysis of SRM 1649a NIST reference material showed an elemental 14C char/soot ratio of 2.75. The biomass is about 38% and contains a mixture of about 13% aromatic components. Because such a high biomass carbon fraction is very important, there must be a significant missing carbon component in this material. Most important, it was noted that cellulose (such as the linen of the Shroud) is an excellent candidate for easy contamination! Recent “molecular analysis” of individual amino acids from crude collagen and gelatine fractions from the Dent Mammoth [8], shows 14C counts between 4000 and 2500 (8000 ~ 11000 BP). In Radiocarbon n° 40 (1996), the same author noted: “In the nearby future modern 14C techniques will eventually lead to the application of a real isotopic mass balance, using actual true 14C counting”. As recommended by Polach [9], 14C count values are more appropriate in analysis than using “RC ages” which are log-normally distributed. An example of this effect is as follows. A RC age of 795 ± 65 years represents an uncertainty range of 65/795 or ± 8.2%. The equivalent 14C data produces a count of 8629 ± 68 which represents an error of 68/8267 = 0.82%. t ie po Likewise, To illustrate how best to evaluate radiocarbon data, Wilson and Ward [9] used data for three independent measures of a single piece of wood, given by Polach [9]. From this we can conclude that there is no evidence to reject the null hypothesis the three samples observations are consistent. Using these three samples with a calculated χ2 value is a useful way to compare the Nature [1] data reported in Table 2 for the Shroud. Here we apply the same methodology as above to evaluate the hypothesis that the measurements are consistent. As showed previously, one should correct Table 2 as follows (see the full analysis on www.shroud.com, paper by Van Haelst): Thus, in both the published and corrected cases, there is no reason to accept the null hypothesis that the observations are consistent and provide 95% confidence. However, for the Shroud measurements the radiocarbon researchers rejected this conclusion. One laboratory even questioned the statistical method used by the British Museum. According to Prof. Ramsey, Director of Oxford RC Laboratory, the measurements for the Shroud obtained in 1988 were within the acceptable error range of the AMS facilities fo .in os Comparison between the Polach samples and data given in Nature. =============================================== Polach Nature Table 2 Nature following Table 1 Sample a 4330 ± 190 Arizona 646 ± 31 Arizona: 646 ± 17 Sample b 4560 ± 210 Oxford 750 ± 30 Oxford: 749 ± 31 Sample c 4940 ± 300 Zurich 676 ± 24 Zurich: 676 ±24 Mean: 4525 ± 128 Mean 689 ±16 Mean 672 ± 13 Chi² : 2.99 < 5.99 Chi² 6.35 > 5.99 Chi² 8.56 > 5.99 p = 0.24 p = 0.042 p = 0.012 of that time. He noted that he did not wish to spend his time recalculating data statistics [10]. Dr. Hedges (Oxford) and Prof. Jull (Arizona) agreed that there is indeed a “small” statistical problem, the Oxford dates being different from the two other laboratories [10, 11]. Unfortunately, none of them answered the question: “How did you obtain the claimed 95% confidence?” Another recent example of a possible erroneous radiocarbon result is the dating of the “Seamless Cloth” Proceedings of the International Workshop on the Scientific approach to the Acheiropoietos Images, ENEA Frascati, Italy, 4‐6 May 2010 [12], the type of garment mentioned in the Gospel of John (19:23). The cloth kept in Argenteuil, thought to be the Seamless Cloth, was twice radiocarbon dated by Seamless Cloth dating results: Gif A 40100: 1450 ± 40 Error weighted Mean: 1407 ± 23 Gif-sur-Yvette and later in a totally blind evaluation by ETH Zurich. See below for the dating results. Gif A 40101: 1510 ± 40 χ2 : 21.2917 > 5.66 ETH 30402: 1260 ± 40 p-value =0.0000 ro ei ch .a w w w Also the analytic details related to the Acid-AlkaliThus, the hypothesis that the measurements are Acid cleaning are noticeable: homogeneous and the means equal is rejected and the dating results are shown to be not conclusive. Carbon Oxygen Aluminium Sulphur Calcium Iron Before 56 43 3 9 31 2 After 54 29 15 14 10 0 (height of the peaks in mm on the graphs.) A loss in Carbon, Oxygen, Calcium and Iron. A gain in Aluminium and Sulphur. A loss of about 1/3 in weight, probably indicating some heavy contamination. runs are indeed too large. By chance alone, the F statistic should be ~ 1.00. Errors are assumed to be due to chance or to experimental uncertainty. 4. ANOVA t ie po In 1986, the British Museum applied an Analysis of Variance on the 12 individual measurements supplied by the laboratories, to determine the td value for 2 - 9 degrees of freedom [1]. They found that the errors based on the scatter should be multiplied by a factor 2.56 to more appropriately represent the variability in the data. In the English version of a small booklet published in 1989 [2] I already employed ANOVA. Analysing the 12 mean data in Table 2 of the Nature paper [1], I concluded: “The calculated F value 4.7 is larger than 4.2, the critical F value for 2-9 degrees of freedom.” With results like these, one should not draw any conclusions but ask for more and better measurements. Further, other researchers have also used ANOVA to analyse Table 2 and came to the same conclusion [13]. The accuracy of the ANOVA method can be impacted by differing numbers of measurements per group, large deviations from the normal distribution and inequalities in the variances of each of the groups being evaluated. Being sure these factors are accounted for, ANOVA provides a useful means of evaluating comparative measurements. Using 14C count means much tedious calculation work, but is readily made manageable by using an Excel worksheet or by using any of the modern commercially-available statistical packages. In this study the laboratory data given in Table 1 will be analysed by ANOVA, taking into account the observation fo .in os It is clear from these two examples that there are apparent difficulties in reliably dating old fabric using standard radiocarbon dating precleaning techniques. Today in AMS single run, one measures with repetition between 6 ~ 20 pure carbon targets prepared from the same sample, together with a number of standard and blank samples. The pure carbon is mixed with a graphite carrier. These pellets (targets) are placed on a turning wheel, to be measured one after another using sophisticated AMS equipment. Measured are also a number of standard samples and blanks. The targets are bombarded with high energy beams. Separation of 12C, 13C and 14C isotopes is almost complete while care is taken to avoid crater formation in the targets. Note that 14C is counted, while the other isotopes are “frequency current” measurements. In Arizona the laboratory uses “coulomb/second” measurements. The measured ratio 14C/13C is about 18 times the natural ratio [7]. In practice, AMS measurements still are of variable precision. Therefore one needs corrections, taking in account a possible instrumental “drift”. Each laboratory uses a specific method to correct variable counts, taking into account the correction factors for the measured ratio 14C/13C and 14C count and as a result, for this reason, “raw” count data cannot be used in statistical analysis. Several runs such as this are made to create a set of measurements with their standard errors. For instance, for the 1988 Shroud dating, Arizona made eight independent runs [10]. Each single AMS measurement is the combination of at least 6 observations per run. Applying a classic analysis of variance (ANOVA) taking in account only the counted 14C particles, allows to determine whether the measurement differences noted are due to chance or to the fact that the differences between the Proceedings of the International Workshop on the Scientific approach to the Acheiropoietos Images, ENEA Frascati, Italy, 4‐6 May 2010 measured under the same conditions, in the same AMS machine. To simplify calculations, we assume that the exact number of 14C counts for each standard sample totals 30000 with the measurements normally distributed ± 0.3% around the mean for each run. In our example, the total number of 14C count is equal to 10,030 + 10,000 + 9,970 = 30,000. With the above assumptions we observe that: that each single date is the results of multiple measurements. The errors based on quoted errors and in percent are used. 5. MODELLING Let suppose there are three runs, each counting 10 standard samples (targets) with a number of blanks, Run B 984 990 994 996 999 1001 1004 1006 1010 1016 Run C 981 987 991 993 996 998 1001 1003 1007 1013 ro ei ch .a w w w Run A 987 993 997 999 1002 1004 1007 1009 1013 1019 We then use one-way ANOVA to evaluate the null hypothesis that the mean value of each of the runs is equal. Average 1003 1000 997 Df 2 27 29 MS 90 87.98 Variance 718 718 718 S.D. 8.93 8.93 8.93 F 1.02297 P-value 0.3730 Conclusion: the hypothesis that the mean value of each of the runs is the same is accepted. A practical example In the past, I received a breakout of the original measurements provided by the University of Arizona’s Tucson radiocarbon dating facility to the British fo .in SS 180 2375.44 2555.44 Sum 10030 10000 9970 os ANOVA Source of Variation Between Runs Residual error Total t ie po ANOVA: Single Factor SUMMARY Groups Count Run A 10 Run B 10 Run C 10 Museum as a part of the 1988 radiocarbon dating experiment [10]. These data (originally reported laboratory measurements) are: Proceedings of the International Workshop on the Scientific approach to the Acheiropoietos Images, ENEA Frascati, Italy, 4‐6 May 2010 1988 Radiocarbon dating experiment: original measurements with quoted error of measurement at 1 σ level. Shroud of Turin samples Laboratory Measurement (RCYBP) 606 574 753 632 676 540 701 701 +/+/+/+/+/+/+/+/- 41 45 51 49 59 57 47 47 Zurich 733 722 635 639 679 +/+/+/+/+/- 61 65 57 45 51 Oxford 795 730 745 +/- 65 +/- 45 +/- 55 Arizona Error ro ei ch .a w w w 574-+45 632-+49 676-+59 701-+47 Combined: (Van Haelst Acts CIELT Rome 1993 p 216) 591± 30 690 ± 35 606 ± 41 701 ± 47 646 ± 17 (Nature: 647 ± 31) [1] Run A 8539 8589 8618 8642 8664 Run B 8592 8642 8672 8696 8718 Run C 8591 8641 8671 8695 8717 Normally Distributed Run D 8617 8668 8698 8722 8744 distribution of observations that make up each of the runs and test the hypothesis that the runs means are the same. Let us assume the following characteristics: counting error = 0.3%, with eight runs each using 10 targets as shown in the following example: fo Unfortunately, the Nature paper never mentioned the combination of the eight observations into four observations and, as a result, the statistical analysis reported was somewhat misleading. Because no information was provided by the laboratories, I was obliged to recalculate the number of 14 C atoms detected. I used this calculation to simulate a .in os Original data: Session A 606 ± 41 Session B 753 ± 51 Session C 540 ± 57 Session D 701 ± 47 Mean 646 ± 17 t ie po The Arizona data were combined into four measurements and those measurements are the dates reported in the Nature paper [1]: Run E 8664 8714 8745 8769 8791 Run F 8691 8742 8773 8797 8818 Run G 8725 8776 8806 8831 8852 Run H 8750 8802 8832 8857 8878 Proceedings of the International Workshop on the Scientific approach to the Acheiropoietos Images, ENEA Frascati, Italy, 4‐6 May 2010 8684 8706 8730 8759 8809 8738 8760 8784 8814 8864 8737 8759 8783 8813 8863 w w Count 10 10 10 10 10 10 10 10 8811 8833 8857 8888 8938 Sum 86740 87280 87270 87540 88010 88290 88630 88890 ANOVA Source of Variation Between Runs Residual error SS 389,588.8 488,692.6 Total 878,281.3 Average 8674 8728 8727 8754 8801 8829 8863 8889 8874 8895 8920 8950 9001 Df 7 72 MS 55,655.54 6,787.40 8900 8921 8946 8976 9028 Variance 6619.368 6702.043 6700.507 6742.032 6814.622 6858.051 6910.973 6951.580 F 8.1998 P-value 0.0000 79 os We reject the hypothesis that the means of each of these runs is equal and accept the hypothesis that one 8840 8861 8885 8916 8967 t ie po ro ei ch .a w ANOVA: Single Factor SUMMARY Groups Run A Run B Run C Run D Run E Run F Run G Run H 8764 8786 8810 8840 8891 or more of the means is statistically different. Ratio: Count A/((Total – A)/7) = 8899/((70273 – 8899)/7) = 1.015 The same calculations for B, C, D, E, F, G and H. All counts about 2σ away from the mean may be possible outliers. Sum: 8899 8863 8829 8801 8754 8727 8727 8673 = 70273/8= 8784 Ratio 1.015 1.01 1.006 1.002 0.996 0.993 0.993 0.986 = 8.001/8 = 1.00125 fo .in Detection of possible outliers using the method given by Burr [7] The dates 8899 (= 540 yr) and 8673 (= 753 yr) are borderline results. Interestingly, Christen, [15] analysing the Shroud data as given in [1] and using Bayesian statistics, came to the same conclusion: the dates 591 (Arizona) and 795 (Oxford) are possible outliers. It should be noted that by simply discarding one outlier the Shroud data are more consistent. Applying the IEM-EEM criteria, as proposed by Scott, leads to the same conclusion [6]. For Oxford and Arizona the External Error Multipliers are 1.45 and 1.5 Proceedings of the International Workshop on the Scientific approach to the Acheiropoietos Images, ENEA Frascati, Italy, 4‐6 May 2010 ANOVA Analysis of the Shroud RC data, reconverted to 14C count, based on the quoted errors. Targets DF Ox 18 2-15 Ar 24 3-20 Zu 30 4-25 Mean 72 11-60 Between 13900/2 = 6950 57492/3 = 19164 49603/4 = 12401 247390/11 = 22490 Residual F ratio 46459/15 = 3097 6950/3097 24563/20 =1227 19164/1227 73815/25 = 2953 12401/2953 160312/60 = 2672 22490/2672 = = = = 97.5% 2.2 < 5 = 15.6 > 4 = 4.2 > 3.5 = 8.4 > 2.3 OK FAILS ???? FAILS 5. Suter et al. Nuclear Instruments and Methods. 223. (1986). 6. CONCLUSION ro ei ch .a 4. Perry’s Chemical Engineering Handbook (Fourth Edition). The practical example of the F-test given on pages 2.72-74 was used to test the Excel programme. w w w Enlarging the errors for Zurich and Arizona, in order to obtain the critical F values, is not sufficient to obtain the critical F value for the combined 12 data. 6. Scott et al. Antiquity Volume 64 (June 1990) & International Collaborative Programme ‘Trondheim Radiocarbon Conference. 7. Burr et al. Nuclear Instruments and Methods B 259 149-153 (2007). 8. Lloyd, Currie: “The Remarkable Metrological History of Radiocarbon Dating”. (Part II in NIST volume 109 N° 2 2004) & (Radiocarbon 40 1998). See also Czechoslovak Journal of Physics 53, cited by Lloyd. t ie po 9. Wilson and Ward. “Archaeometry” 30 (1978) 10. Private correspondence with Dr Ramsey and Dr. Hedges (Oxford) and Prof. Jull (Arizona). 11. R. Hedges in “Approfondimenti pro Sindone” 1 (1997). os The radiocarbon dating of cellulose-based textiles need to be approached very carefully since textiles appear to present experimental limitations which can result in non-homogeneous measurements. Concerning the Shroud dating, the Arizona F value is out of range and should not be used in further calculations and certainly not in drawing conclusions supporting a 95% confidence. The Zurich F value is a borderline case. In theory, the combination of 12 data is meaningless. As stated by Burr, et. al. [7], one should verify the tuning the equipment and the effectiveness of the AAA cleaning methods before drawing any conclusions. The different data for –δ13C: Oxford: 0.027, Arizona 0.025, Zurich 0.0251, given in Table 1 of Nature [1] indicate a further need to examine the homogeneity and the chemical composition of the twelve sub-samples. 12. Acts “Costa” “Argenteuil” Edition de Guibert Paris (2005). NOTES AND REFERENCES 1. Damon et al., Nature, 337, 611-615 (1989). 2. R. Van Haelst “Radiocarbon dating the Shroud of Turin.” Privately released. (1989). 3. NIST Technical note. B Taylor &C. Kuyatt (1994) 13. B. Walsh ”The 1988 Shroud of Turin Radiocarbon Tests Reconsidered” Proceedings of the 1999 Shroud of Turin Conference, Richmond, VA, B. Walsh Ed., Glen Allen VA: Magisterium Press (1999) pp. 326– 342. fo I like to thank: the Referees for their competent remarks and constructive suggestions; Bryan Walsh for his precious help and technical assistance and Diana Fulbright for inviting me to present this paper to the IWSAI Conference Frascati 2010. .in ACKNOWLEDGMENTS 14. J.A. Christen. “Applied Statistics 43 pp 489-503 (1994). Technical Literature: 9 “Technical Repertory Mathematics & Mechanical” (Dutch Edition Elsevier) Wilcoxon test (page 1.8 f 2.8), “Kruskal-Wallis” & “Bonferoni Pairwise Ttest Comparison”. 9 McCall “Linear Contrasts” Quality Control” July 1960.