Casabianca, T., et al., 2019, "Radiocarbon Dating of the Turin Shroud: New Evidence from Raw Data," Archaeometry, 22 March

© Stephen E. Jones[1]

This is my long-promised post on this article (including a possible reconciliation of the carbon contamination and/or medieval repair theories with my hacker theory)! I have worked through most of it, commenting on its key points. Much of it is highly technical statistics and although I have studied statistics units in my

[Above (enlarge)[2]: The online heading of the article.]

university degrees, that was many years ago and I am no statistician! The article's words are bold to distinguish them from mine. Emphases are mine unless otherwise indicated.

Abstract In 1988, three laboratories performed a radiocarbon analysis of the Turin Shroud. The results, which were centralized by the British Museum and published in Nature in 1989, provided ‘conclusive evidence’ of the medieval origin of the artefact. However, the raw data were never released by the institutions. In 2017, in response to a legal request, all raw data kept by the British Museum were made accessible. A statistical analysis of the Nature article and the raw data strongly suggests that homogeneity is lacking in the data and that the procedure should be reconsidered.[3]

The claim in the 1989 Nature article was:

"The results provide conclusive evidence that the linen of the Shroud of Turin is mediaeval ... AD 1260-1390, with at least 95% confidence"[4].

But as we saw in 17Feb19, the "with at least 95% confidence" was a lie (see below) by the author of the article, Dr Michael Tite[5], then of the British Museum. It was a lie because as Tite must have known, as discovered by Remi van Haelst, a Belgian industrial chemist and expert in statistical analysis, that Arizona laboratory had provided the British Museum with eight radiocarbon dates of the Shroud, some of which when calibrated and converted to calendar years, were more recent than 1355, when the Shroud first appeared in undisputed history at Lirey, France:

"Arizona did not provide FOUR but EIGHT data ... The error-values between brackets are estimated ... Mathematically, the calculations following Wilson-Ward, with EIGHT and FOUR data will give the same result. So why were this data reduced from EIGHT to FOUR???? Because with the quoted errors the Arizona data overspans an era of 540-95 = 445 to 753+93 = 846 ... Converted into calendar date 1270-1430 ... [which] ... conflicts with the historical deadline of 1355, when started the veneration of the Shroud in Lirey ... Dr. Leese [Morwen Leese the British Museum's statistician and a signatory to the 1989 Nature article] wrote a letter to Arizona (dated July 28 1988), asking to REDUCE the EIGHT data to FOUR, by considering the TWO runs made the same day, like ONE run. So the data presented in table 1 are not INDIVIDUAL measurements, but the mean of TWO measurements. Which are in fact the average of between 10-20 measurements. Arizona agreed. because they knew that their mean result 646±31 was in fact conflicting with the historical deadline of 1350" (van Haelst's emphasis)[6].

Below is my more compact spreadsheet copy of van Haelst's table in his Shroud News article:

[Above (enlarge): Arizona laboratory's original eight dates, uncalibrated, which were fraudulently statistically manipulated by the British Museum's statistician Dr. Morwen Leese ( presumably as directed by Tite and with Arizona's approval) to become four dates in the 1989 Nature article (see above). Note that the midpoint of 574±45 is 1950-574 = 1376, which 21 years after 1355. So that was combined and averaged with 606±41 to make it 591±30, the midpoint of which is 1950-591 = 1359, still 4 years past 1355! And 540±57, the midpoint of which is 1950-540 = 1410, 55 years after 1355, was combined and averaged with 676±59 to make it also 606±41, the midpoint of which is 1950-606 = 1344, now only 11 years before 1355!]

This was scientific fraud by Leese, presumably directed by Tite and agreed to by Arizona, "making results appear ... more definitive than they really are":

"The term `scientific fraud' is often assumed to mean the wholesale invention of data. But this is almost certainly the rarest kind of fabrication. Those who falsify scientific data probably start and succeed with the much lesser crime of improving upon existing results. Minor and seemingly trivial instances of data manipulation-such as making results appear just a little crisper or more definitive than they really are, or selecting just the `best' data for publication and ignoring those that don't fit the case-are probably far from unusual in science. But there is only a difference in degree between `cooking' the data and inventing a whole experiment out of thin air"[7].

What makes this "with at least 95% confidence" claim a lie is that in a "chi-square distribution table ... for 2 degrees of freedom, the critical value for a 0.05 [i.e. 95%] probability is 5.99"[8]. But according to Table 2 of the 1989 Nature article (see extract below) the Chi-square

[Above (enlarge). Extract from Table 2 of the 1989 Nature article. As can be seen, sample 1 (the Shroud) contrasts markedly with the Chi-square values of the linen control samples 2 (0.1), 3 (1.3) and 4 (2.4), so already there was a serious, but unexplained problem. According to my hacker theory, the solution to that problem is that unlike the radiocarbon dates of the control samples which were real, the dates of the Shroud samples were computer-generated by Arizona laboratory physicist Timothy W. Linick's program.]

value ("Χ² value (2 d.f.)") of sample 1 (the Shroud) was 6.4, which means it was already beyond the 0.5 or 95% critical value. Moreover, according to Van Haelst, the chi-square value of the Shroud samples when there were eight, not four Arizona dating runs is actually 7.13[9], which makes the "with at least 95% confidence" claim even more a lie!

INTRODUCTION The Turin Shroud (TS) is a piece of linen cloth approximately 4.4m long and 1.1m wide, considered by some to be the burial cloth of Jesus of Nazareth. The first certain historical record dates to the second half of the 14th century AD. In 1987, after a decade of negotiations, three laboratories (Arizona, Oxford and Zürich) were chosen by the Vatican authorities to perform a 14C test using accelerator mass spectrometry techniques (AMS). On 21 April 1988, a sample was taken from one corner of the cloth, and pieces of the sample were delivered to the laboratories, along with three additional control samples. The results were centralized at the British Museum, where the statistical analysis was performed. In their Nature article, Damon et al. (1989) stated that there was ‘conclusive evidence’ that the linen of the TS was medieval (AD 1260–1390 with at least 95% confidence).[10]

I realise that "... considered by some to be the burial cloth of Jesus of Nazareth" is the best that can be written about the Shroud in a secular science journal, but the truth is that the evidence is overwhelming that the Shroud is authentic, that is, the very burial sheet of Jesus! What Yves Delage (1854–1920), the agnostic Professor of Zoology at the Sorbonne pointed out in 1902 to the `free-thinkers' on the French Academy of Sciences, is still true today, ~117 years later:

"If, instead of Christ, there were a question of some person like a Sargon, an Achilles or one of the Pharaohs, no one would have thought of making any objection"[11].

That is, if it was anyone other than Jesus, the evidence would be readily accepted that the Shroud was His!

And see above on the lie that the "medieval (AD 1260–1390" radiocarbon date of the Shroud was "... with at least 95% confidence"!

Currently, non-specialists consider this general conclusion straightforward disproof of the hypothesis that the TS is an antique linen cloth (Ball 2017). However, since 2005, a growing number of studies have provided elements and arguments contradicting the medieval hypothesis (Rogers 2005; Poulle 2009; Fanti and Malfi 2014; Bevilacqua et al. 2014; Boi 2017; Casabianca 2017). In 2013, a new statistical study based on a regression analysis seriously called into question the reliability of the conclusions of the 1988 dating (Riani et al. 2013). Recently, we obtained the raw data and, for the first time, measured their convergence with the radiocarbon dates published in Nature.[12]

I don't have all these articles, and even if I did, there is no space here to consider them. Besides it would be a diversion from the central point of this article. It is noteworthy that it took "a legal request" (see above) that is, a Freedom of Information request (see below) to the three laboratories and the British Museum and only the latter complied. This raises the question: what are the laboratories hiding? This secretiveness falls far short of the standard of scientific honesty that all scientists should adhere to, stated by the late Professor of Physics at Caltech, Richard P. Feynman (1918–1988), that "... the idea is to try to give all of the information to help others to judge the value of your contribution":

"It's a kind of scientific integrity, a principle of scientific thought that corresponds to a kind of utter honesty - a kind of leaning over backwards. For example, if you're doing an experiment, you should report everything that you think might make it invalid-not only what you think is right about it: other causes that could possibly explain your results; and things you thought of that you've eliminated by some other experiment, And how they worked-to make sure the other fellow can tell they have been eliminated. Details that could throw doubt on your interpretation must be given, if you know them. You must do the best you can-if you know anything at all wrong, or possibly wrong-to explain it. If you make a theory, for example, and advertise it, or put it out, then you must also put down all the facts that disagree with it, as well as those that agree with it ... the idea is to try to give all of the information to help others to judge the value of your contribution; not just the information that leads to judgment in one particular direction or another ... I'm talking about a specific, extra type of integrity that is not lying, but bending over backwards to show how you're maybe wrong, that you ought to have when acting as a scientist"[13].

The basic idea of this paper is to conduct a robust statistical analysis using the raw data and to compare these results with those obtained using the official data. We use statistical tests to determine whether the measurements intra and inter laboratories can be combined to obtain a calendar range. Based on the statistical results, we question the level of confidence of 95% attributed to the AD 1260–1390 calendar age range.

This is no little thing. It has been a major part of Tite's, the laboratories' and anti-authenticists' propaganda that the Shroud's 1260-1390 radiocarbon date was "with at least 95% confidence":

"During the second week of October 1988 press personnel of the English-speaking world were notified that the results would be announced on Thursday, 13 October in the British Museum's Press Room ... Accordingly, early that Thursday afternoon I joined this gathering in a ... room of the British Museum. At one end of the room had been set a low platform which three men mounted ... They were ... Dr Michael Tite, with the Oxford radiocarbon-dating laboratory's Professor Edward Hall and Hall's chief technician, Dr Robert Hedges ... their only `prop' was a blackboard behind them on which someone had rather crudely scrawled: `1260-1390!' ... as Dr Tite explained, these numbers represented radiocarbon dating's calculation, to a ninety-five per cent degree of probability, of the upper and lower dates of when the Shroud's flax had been harvested. Representing an average of the laboratories' findings, which had proved in excellent agreement with each other [another lie see 20Dec14], they indicated that the Shroud's raw flax had most likely been made into linen on or about the year AD 1325, give or take sixty-five years either way"[14].

But they were wrong on that major point, and it cannot have been a mistake. Tite and the laboratory leaders were and are experts in the application of statistics to radiocarbon dating and Tite had a statistician, Morwen Leese, working for him. Besides, it has been brought to their attention by Van Haelst and others many times that the "with at least 95% confidence" claim is false, but they have ignored it, even though they must know that the criticism was true. The very least that the living signatories to the 1989 Nature article, including Tite, Timothy Jull of Arizona and Christopher Ramsey of Oxford should have done, and should do now is to publicly write to Nature advising that the "with at least 95% confidence" claim was false. It will be interesting to see what they will do now after their lie has been exposed in this Archaeometry article!

DATA AND METHODOLOGY Since 1989, scholars interested in the TS have often requested the raw data from the laboratories, without success (Pourrat 1991). This denial of access led to controversy and hindered the assessment of the analysis performed by the British Museum (Marinelli 2012; Rinaldi 2012). In 2017, several Freedom of Information Act (FOIA) requests to the institutions involved in the TS radiocarbon dating were made. The British Museum replied favourably and made all its files, ‘not dated or arranged in any order’, available. On 18 July 2017, the British Museum electronically sent a file of 211 pages and in September 2017, one of the authors (T.C.) visited the British Museum and scanned more than 500 new pages[15].

Again, that the laboratories have since 1989 (i.e. for 30 years) refused to provide Shroud scholars with the raw data of the 1988 radiocarbon dating:

"... the Belgian researcher, Remi Van Haelst, who has consistently and persistently claimed that the results were incorrectly calculated. He has been campaigning for years to be given the raw data from the three laboratories so that others may examine their accuracy, but so far has been rebuffed by all of them. He gave a detailed resume of his years of work on the statistical data, profusely illustrated by graphs, indiscernible in the auditorium, but supporting his constant claim that inconvenient data were ignored by the laboratories, their calculations were wrong and that there is no conclusive evidence to suggest that the Shroud is medieval"[16].

can only be because they have something to hide! If the laboratories truly believed that, "The results provide conclusive evidence that the linen of the Shroud of Turin is mediaeval ... AD 1260-1390, with at least 95% confidence," they would be eager to share the raw data which is that "conclusive evidence." Instead the laboratories' `body language' betrays that they don't truly believe it! Theirs is the very antithesis of Feynman's, "you must ... give all of the information to help others to judge the value of your contribution" (see above).

We learned that Zürich performed 4 × 10 measurements for each of their five TS subsamples. Oxford performed five measurements, and while the detailed measurements were not sent to the British Museum, a mean was provided for two measurements, resulting in only three radiocarbon dates. The Arizona report shows that 40 measurements (5 × 8) were made. Several scholars already disclosed the eight Arizona radiocarbon dates (Van Haelst 2002), but these dates have never been confirmed. We are now certain that the eight disclosed dates (designated Arizona raw 2) were correct. However, previously, Arizona modified the errors of two of its eight dates (designated Arizona raw 1). In contrast to Zürich and Oxford, Arizona included in its report eight computer printouts along with the counts of the detected radiocarbon atoms (designated Arizona counts).[17].

Zurich's "4 × 10 measurements" is presumably what Prof. Harry E. Gove (1922-2009) described of Arizona's dating, and if so, presumably applied to all three laboratories:

"The first sample run was OX1 [an oxalic acid standard]. Then followed one of the controls. Each run consisted of a 10 second measurement of the carbon-13 current and a 50 second measurement of the carbon-14 counts. This is repeated nine more times and an average carbon-14/carbon-13 ratio calculated. All this was under computer control and the calculations produced by the computer were displayed on a cathode ray screen. The age of the control sample could have been calculated on a small pocket calculator but was not-everyone was waiting for the next sample-the Shroud of Turin! At 9:50 am 6 May 1988, Arizona time, the first of the ten measurements appeared on the screen. We all waited breathlessly. The ratio was compared with the OX sample and the radiocarbon time scale calibration was applied by Doug Donahue. His face became instantly drawn and pale. At the end of that one minute we knew the age of the Turin Shroud! The next nine numbers confirmed the first. It had taken me eleven years to arrange for a measurement that took only ten minutes to accomplish! Based on these 10 one minute runs, with the calibration correction applied, the year the flax had been harvested that formed its linen threads was 1350 AD-the shroud was only 640 years old! It was certainly not Christ's burial cloth but dated from the time its historic record began"[18].

So not only did Tite with Arizona laboratory commit scientific fraud (i.e. "improving upon existing results ... making results appear just a little ... more definitive than they really are" - see above) by stating

[Right (enlarge): Extract from Table 1 in the 1989 Nature article, showing the dates of each sub-sample at each laboratory of Sample 1, the Shroud[19]. The dates are years before 1950[20]. Thus the midpoint of Arizona's first date was actually 1950-591=1359, i.e. four years after 1355, when the Shroud first appeared in undisputed history at Lirey, France!]

in Table 1 of the 1989 Nature article [right] that Arizona dated four Shroud sub-samples ("individual measurements"), when it was actually eight (see above); Tite with Oxford also committed scientific fraud by stating that Oxford dated three Shroud sub-samples, when it was actually five! Only Zurich was honest in correctly stating that it dated its "five TS subsamples"!

The Nature and raw radiocarbon dates (Table 1) show that relevant differences exist among the estimates provided by the three laboratories: the Arizona minimum Nature estimate is 591, whereas the Oxford minimum is 730; the Arizona maximum is 701, whereas the Oxford maximum is 795. Most importantly, discrepancies exist even within the laboratories. For example, Arizona’s estimates range from 540 to 701, whereas Oxford’s estimates reach a value of 795.[21].

Below (enlarge) is my Excel copy of Casabianca, et al.'s Table 1[22]. I

made the point in my posts of 17Feb19, 18Nov15, 11Feb15 and 13Jun14, that the wide variations in the dates of the Shroud samples across the three laboratories' (and even within each laboratory!) is evidence that they are not real dates but were computer-generated by a hacker's (Timothy W. Linick's) computer program.

The computed error in the radiocarbon dates by Arizona presents differences (the error ranges from 30 to 41 in Nature and from 37 to 57 in the raw dates), whereas Oxford appears to have produced consistent estimates (homogenous radiocarbon estimates between Nature and the raw dates), but the computed errors in the raw radiocarbon dates are lower than the published errors (the most relevant is 730 ± 30 in the raw data against 730 ± 45 in Nature). Regarding Zürich, the problem is related to both the estimates and computed errors: the estimates are incongruent between the raw and Nature dates (a clear difference in the fifth observation, which is equal to 595 in the raw data and 679 in Nature).[23].

According to my hacker theory, the "extremely mathematically gifted" Timothy W. Linick[24] wrote a program which (with the possible exception of Arizona's very first run which returned the psychologically crushing calibrated date of "1350" - see above), thereafter would automatically intercept the output of the AMS system at each of the three laboratories, en route to the control console computer's screen and replace the Shroud's first (or early because of irremovable contamination) century date with random dates within limits which, after calibration, displayed dates clustering around 1325 ± 65. Then finally the hacker's program would order its own deletion when that laboratory's dating of the Shroud would have been completed (e.g. after 6 months from the program's activation), leaving no trace of its previous existence [see 08Jun14, 13Jun14, 05Jul14, 13Dec14, 30Jan15, 31Mar15, 22Feb16]. Whether Linick's program also generated bogus error ranges, or the laboratories calculated these from the bogus dates, my theory is compatible with either. However, recently I have been thinking that Linick may have preset the random number limits lowest (most recent) for Arizona, intermediate for Zurich and highest (oldest) for Oxford, although why he would do that is unclear. Or it may well be that Jesus, the Man on the Shroud, who as Yahweh come in the flesh (Jn 8:24,28,58; 13:19; 18:5-6; Mt 14:23-27; Mk 6:47-50; Jn 6:16-20) [the Greek ego eimi literally is "I AM" (Ex 3:14. Dt 32:39; Isa 41:4; 46:4 LXX)][25], directs the outcome of random numbers (Pr 16:33), created problems in the random number outputs of Linick's program that statisticians would later find invalidated them!

From a statistical perspective, these differences do not create a problem if they are irrelevant, but the data published in Damon et al. (1989) are affected by several problems (Brunati 1996; Van Haelst 1997, 2002; Riani et al. 2013). The Arizona counts table (Table 2) represents the eight sessions (A1, A2, A3, …) included in the report sent by Arizona to the British Museum. Two sessions were performed daily using the same standards (A1 and A2, A3 and A4, A5 and A6, and A7 and A8). Due to a technical incident encountered in the two first measurements of A2, the Arizona printout of A2 only includes four values, one of which (17 584) is the equivalent of two measurements. For the purpose of the analysis, we chose to keep five values for each session and we attributed the mean value (17 584/2 = 8792, in italics in Table 2) to the two problematic measurements.[26].

See below (enlarge) my Excel spreadsheet copy of Casabianca, et al.'s Table 2[27]. The first thing I noticed in transcribing this data was the

great variability in these "counts of the detected radiocarbon atoms." Reading across from Arizona's sessions A1 to A8, the maximum C14 atom count was 11409 in session A6 and the minimum was 5128 in session A7. That is a difference of 6281 or 122.48%! This could be explained by the subsamples being unequal in physical size, a larger subsample containing more carbon-14 atoms than a smaller one but why would a laboratory do that? The obvious thing to do would be to cut each subsample into as near equal in size as possible. And according to Gove who was there, that is what Arizona did: "divide the total area ... into four pieces each about 0.5 square centimetres or 1/4" x 1/4" in area":

"Around 5 pm, Paul Damon called and suggested he come to the Doubletree [Hotel in Tucson, Arizona] and have a beer and a chat with us ... He said when he and [Douglas] Donahue had returned from Turin on the Saturday after the sample had been removed from the shroud, they had decided to divide the total area of about 2 square centimetres (0.3 square inches) they had received in Turin into four pieces each about 0.5 square centimetres or 1/4" x 1/4" in area and to store them in different places"[28].

Presumably the eight columns A1-A8 are of the four equal subsamples each further subdivided in half. But note that it cannot be this second subdivision of Arizona's four subsamples into eight that was unequal because while column A1's numbers are mostly higher than A2's, the first number (which equated to "1350" - see above - and which I claim may have been the only date `hardwired' in Linick's program), is lower than any of the numbers in A2. The same applies to the A7-A8 pair. While A7's numbers are mostly higher than A8, the lowest count, 5281, is in A7!

As I have posted before [11Feb15, 18Nov15, 24Oct16 & 17Feb19], this is (or seemed) inexplicable if the Shroud sample dates were real, given that the three laboratories' Shroud `postage stamp' size samples[29] were all sub-divided from the same ~8 cm x ~1.2 cm sample, cut from the Shroud[30] (see below). And the three laboratories were effectively

[Above (enlarge): Drawing of the approximately 8 cm x 1.2 cm sample cut from the Shroud and subdivided into sub-samples from right to left: "A" (Arizona), "Z" (Zurich), "O" (Oxford), and "A1" (Arizona additional), with a photograph of the sample superimposed over the bottom right hand side[31]. Was there a significant difference in carbon contamination (including from a medieval repair) across the three laboratories' samples, especially Arizona's two samples A1 and A which were from opposite ends of the Shroud sample?]

clones[32], using the same AMS dating method on near-identical machines.

But looking at the great variability of Arizona's C14 atom counts across its subsamples A1-A8 (above), it has just now occurred to me that the carbon contamination and/or medieval repair theories and my hacker theory may not be incompatible. What if Linick's program did not substitute the C14 atom counts coming from the Shroud, but in a mathematically sophisticated way inflated them to 13th-14th century dates? If so, then the variability of the C14 atom counts could reflect actual carbon-14 variability across the Shroud sample, due to contamination and/or younger repair threads (see above that Arizona's subsample was in two parts A1 and A from opposite ends of the Shroud sample). But the 13th-14th century dates of the Shroud samples would be due to Linick's program inflating that carbon-14 variability to 13th-14th century date levels!

And again note that in favour of my theory is that `odd man out' very first run C14 atom count of 8226 (above) which equated to "1350" (see above).

The methodology adopted in this study is classical. A central argument proposed by critics of the TS radiocarbon dating results is that the computation of the p-value using the method in Ward and Wilson (1978) contains an error (Brunati 1996; Van Haelst 1997). The Ward and Wilson method is used to test whether the radiocarbon determinations can be combined (Ward and Wilson 1978, 23). Following Van Haelst (1997), we present the results of the chi-square tests using the Ward and Wilson method to detect statistically significant inconsistencies in the raw radiocarbon dates and we perform ANOVA, parametric and non-parametric tests to determine possible significant differences between means in the raw data to eventually validate the results. To test the eventual existence of an interaction effect between the types of data (raw vs. Nature) and the laboratory that produced the data (Arizona, Oxford or Zürich), we perform a two-way ANOVA. Hereafter, a 5% level of significance is assumed for all procedures.[33].

The conclusion of "Van Haelst (1997)" (according to my `reading between his lines') was that the statistical analysis of the radiocarbon dating of the Shroud was both fraudulent and corrupt:

"CONCLUSION:
Facts :
The Arizona error was arbitrary enlarged from 17 to 31. The Wilson & Ward mean 689±16 was replaced by the UNWEIGHTED mean 691±31. The multiplying t-factor for 95% confidence was enlarged from 1.96 to 2.6. The claimed `at least 95 % confidence' for the medieval dating of the Shroud is NOT supported by statistical analysis. One may wonder, why these OBVIOUS facts, were not spotted by the `team of peers' who judge all papers before publication in Nature. Even stranger is the FACT, that Prof. Bray of the `Istuto di Metrologia' of Turin, confirmed that the results of the 3 labs were mutually compatible, and that, on the evidence submitted, none of the means WERE questionable. Prof. Bray declared not to be at liberty to answer any questions. His answer was : `On the evidence submitted, no averaged results APPEAR questionable. The scatter for sample 1 is about equal to the limit.' The only possible explanation is, that NOT all evidence was submitted to Prof. Bray. Prof. Bray refused to comment on the `combination from EIGHT to FOUR Arizona dates. I asked the editor of Nature, to compare my calculations with the results given by Damon et al. Following Dr. Laura Garwin (Physical Science Editor) : `You are asking me questions that are beyond my ability to answer. The Damon et al paper was refereed by qualified referees and no dissatisfaction was raised with the assignment or errors.' I also asked the advice of Prof. Bene (University of Geneve). `I would like to congratulate you for the quality of your work. You established definitive evidence, that the measurements made on the linen of the Shroud are NOT homogeneous and that they should be rejected.' Prof. Jouvenoux (University of Marseille-Aix): `Van Haelst was probably the first to question the radiocarbon dating of the Shroud in a scientific way'" (Van Haelst's emphasis )[34].

and that therefore the 1989 Nature article should never have been published and should be retracted!

Finally, due to the current importance of radiocarbon procedures, we present results obtained with the software OxCal version 4.3 (OxCal 2018), which was used here to statistically analyse specific versions of the radiocarbon dates. OxCal is an open-access diagnostic tool based on a Markov chain Monte Carlo developed by Christopher Ramsey (Oxford) in the mid-1990s and is currently used by many radiocarbon specialists (Ramsey and Lee 2013). The individual agreement, model agreement and overall agreement indexes should generally all be over 60% in the case of a homogeneous result. Several individual measurements below the 60% level combined with model and overall agreement indexes below 60% indicate the presence of at least one problem in the data, probably due to a flawed measurement or contamination.[35].

Spoiler Alert! [Left [36].] Here where I can't think of anything to comment on in the above, is a good time to reveal that because Casabianca, et al's paper accepts the radiocarbon dates as real, albeit flawed, they are not going to find that the 1989 Nature article was wrong in its claim that "the linen of the Shroud of Turin is mediaeval," only that it wrong in its claim that it is "AD 1260-1390, with at least 95% confidence" (which itself is significant because Tite and his statistician Dr Morwen Leese must have known that the latter claim was false and therefore they knowingly lied in claiming it - see above). Later in their paper Casabianca, et al admit that:

"Our statistical results do not imply that the medieval hypothesis of the age of the tested sample should be ruled out"[37].

What does not merely "imply" but proves beyond reasonable doubt "that the medieval hypothesis of the age of the tested sample should be ruled out" is the overwhelming evidence that the Shroud is authentic. See my brief presentation of that evidence in my "Open letter to Professor Christopher Ramsey" of 4 October 2018. I sent a copy of that open letter to Prof. Ramsey both as an email and snail mail, but he never responded. I don't mind him ignoring me but I do mind him ignoring the evidence for the Shroud's existence all the way back to Edessa in AD 544!

"A picture that is worth a thousand words" in that open letter to Prof. Ramsey was the c. 1070 depiction by John Skylitzes (c.1040s–c.1101) of the transfer of the Image of Edessa from Edessa to Constantinople in

[Above (enlarge): "Surrender of the Mandylion [the `Image of Edessa] to the Byzantines"[38].]

944 [see "944b"], and behind the face-only Image of Edessa is the full-length Shroud (see above)!

RESULTS The ANOVA on Nature radiocarbon dates (Table S2) shows that at least two groups’ means are significantly different from each other, providing evidence that the differences among the laboratories are not irrelevant, especially for the Arizona/Oxford Nature dates (Table S3). The Ward and Wilson test is also above the critical value (8,60>5.99). The OxCal 4.3 software confirms these results with an overall agreement index of 41.8%, strongly below the usual threshold of 60%. On 12 radiocarbon dates, three have a low individual agreement index (Table 3 for the Ward and Wilson tests and the OxCal analysis)[39].

A note at the end of the article explains that Table S2 and S3 are part of the "Additional supporting information" that is not in the article itself. "ANOVA" or "Analysis of variance" "... in its simplest form ... provides a statistical test of whether two or more population means are equal"[40].

There are two questions here: 1) Why is there any significant variability at all in the Shroud samples between the three laboratories and indeed within a laboratory? And 2) Why does the first-century Shroud (according to the overwhelming weight of the evidence) have, not just a 13th-14th century radiocarbon date, but a `bull's eye' 1325 ±65 radiocarbon date?

The carbon 14 variability in the Shroud samples cannot have been a problem with the AMS systems at the laboratories because the 1989 Nature article admitted that the agreement in the control samples across the three laboratories was "exceptionally good" yet the "spread of the measurements" of the Shroud samples was "greater than would be expected":

"An initial inspection of Table 2 shows that the agreement among the three laboratories for [control] samples 2, 3 and 4 is exceptionally good. The spread of the measurements for sample 1 [the Shroud] is somewhat greater than would be expected from the errors quoted"[41].

The answer to both questions is provided by my recently realised proposed reconciliation of the carbon contamination and/or medieval repair theories with my hacker theory. First, there was carbon contamination variability across the Shroud sample that the laboratories' cleaning could not remove, as pointed out by textile expert (later Professor) John Tyrer:

"In 1532 the Shroud was being kept inside a silver casket stored in the Sainte Chapelle, Chambery, when a fire nearly destroyed the building. The intense heat melted a corner of the casket, scorching the folded linen within, and producing the now familiar scorch marks on the Shroud. Since silver melts only at 960 degrees centigrade, the heat inside the casket must have been intense. In these circumstances moisture in the Shroud would turn to steam, probably at superheat, trapped in the folds and layers of the Shroud. Any contaminants on the cloth would be dissolved by the steam and forced not only into the weave and yarn, but also into the flax fibres' very lumen and molecular structure ... Under the circumstances, contaminants would have become part of the chemistry of the flax fibres themselves and would be impossible to remove satisfactorily by surface actants and ultrasonic cleaning. More drastic treatments to destroy the contaminants would inevitably damage the flax fibres themselves"[42].

But that irremovable residue of the previous total carbon contamination would have to be not only about 60% of the Shroud sample [see 01Nov13, 24May14, 22Aug14, 08Dec14 ...], but exactly the right amount to shift the first century Shroud's carbon date thirteen centuries into the future to the `bull's eye' date, 1325 ±65!

Second, according to my "Revised Hacker Theory" [see further 02Sep19 & 14Feb20.], Timothy W. Linick's hacker program was designed to build on (not substitute for) the existing level of carbon 14 in each Shroud sample, and inflate it so that when combined and averaged (with fraudulent help by Tite and Leese - see above ), it was 1325 ±65, the midpoint of which was a mere 30 years before the Shroud first appeared in undisputed history in 1355!

With that I will conclude this post. The remainder is highly technical statistics and I do not claim to understand it sufficiently to comment on it.

Notes
1. This post is copyright. I grant permission to quote from any part of it (but not the whole post), provided it includes a reference citing my name, its subject heading, its date, and a hyperlink back to this page. [return]
2. Casabianca, T., et al., 2019, "Radiocarbon Dating of the Turin Shroud: New Evidence from Raw Data," Archaeometry, 22 March, pp.1-9, 1. [return]
3. Ibid. [return]
4. Damon, P.E., et al., 1989, "Radiocarbon Dating of the Shroud of Turin," Nature, Vol. 337, 16 February, pp.611-615, 611. [return]
5. Morgan, R., 1990, "Interview With Dr. Michael Tite by Orazio Petrosillo and Emanuela Marinelli, 8 September 1989, during the Paris Symposium," Shroud News, No 59, June, pp.3-9, 7. [return]
6. Van Haelst, R., 1991, "Radiocarbon data indeed manipulated," Shroud News, No 68, December, p.5. [return]
7. Broad, W. & Wade, N., 1982, "Betrayers of the Truth: Fraud and Deceit in the Halls of Science," Simon and Schuster: New York NY, p.20. [return]
8. Banas, T., "How to Chi-Square Test," Sciencing, April 24, 2017 . [return]
9. Van Haelst, 1991, p.7. [return]
10. Casabianca, et al., 2019, p.1. [return]
11. Walsh, J.E., 1963, "The Shroud," Random House: New York NY, pp.106-107. [return]
12. Casabianca, et al., 2019, p.2. [return]
13. Feynman, R.P., 1985, "Surely You're Joking, Mr Feynman!," Unwin Paperbacks: London, Reprinted, 1990, pp.340-343. [return]
14. Wilson, I., 1998, "The Blood and the Shroud: New Evidence that the World's Most Sacred Relic is Real," Simon & Schuster: New York NY, pp.6-7. [return]
15. Casabianca, et al., 2019, p.2. [return]
16. Morgan, R., 1993, "The Rome Symposium - Part 2," Shroud News, No 78, August, pp.4-16, 5. [return]
17. Casabianca, et al., 2019, p.2. [return]
18. Gove, H.E., 1996, "Relic, Icon or Hoax?: Carbon Dating the Turin Shroud," Institute of Physics Publishing: Bristol UK, pp.264. [return]
19. Damon, et al., 1989, p.612. [return]
20. Damon, et al., 1989, p.611. [return]
21. Casabianca, et al., 2019, p.2. [return]
22. Casabianca, et al., 2019, p.3. [return]
23. Casabianca, et al., 2019, p.2. [return]
24. Jull, A.J.T. & Suess, H.E., 1989, "Timothy W. Linick," Radiocarbon, Vol 31, No 2. https://goo.gl/ZDcXAW. [return]
25. Rhodes, R., 1992, "Christ Before the Manger: The Life and Times of the Preincarnate Christ," Baker: Grand Rapids MI, pp.14-15, etc; Bowman, R.M., Jr. & Komoszewski, J.E., 2007, "Putting Jesus In His Place: The Case for the Deity of Christ," Kregel: Grand Rapids MI, pp.160-161, etc. [return]
26. Casabianca, et al., 2019, pp.2-3. [return]
27. Casabianca, et al., 2019, pp.2-3. [return]
28. Gove, 1996, p.259. [return]
29. Scavone, D.C., 1989, "The Shroud of Turin: Opposing Viewpoints," Greenhaven Press: San Diego CA, pp.104; Wilson, I. & Schwortz, B., 2000, "The Turin Shroud: The Illustrated Evidence," Michael O'Mara Books: London, p.94; Tribbe, F.C., 2006, "Portrait of Jesus: The Illustrated Story of the Shroud of Turin," Paragon House Publishers: St. Paul MN, Second edition, p.170. [return]
30. Wilson, I., 1991, "Holy Faces, Secret Places: The Quest for Jesus' True Likeness," Doubleday: London, p.6; Wilson, 1998, pp.6,191; Wilson, I., 2010, "The Shroud: The 2000-Year-Old Mystery Solved," Bantam Press: London, pp.82A, 87, 95. [return]
31. Wilson, 1998, p.189. [return]
32. Wilson, 1991, p.178; Wilson, 2010, p.281. [return]
33. Casabianca, et al., 2019, pp.3-4. [return]
34. Van Haelst, R., 1997, "Radiocarbon Dating The Shroud: A Critical Statistical Analysis," Shroud.com. [return]
35. Casabianca, et al., 2019, p.4. [return]
36. Extract from Thompson, C., 2018, "Spoiler Alert!," Eagle Nation News, May 14. [return]
37. Casabianca, et al., 2019, p.7. [return]
38. "Chronography of John Skylitzes, cod. Vitr. 26-2, folio 131a, Madrid National Library, in "File:Surrender of the Mandylion to the Byzantines.jpg," Wikimedia Commons, 20 December 2012. [return]
39. Casabianca, et al., 2019, p.4. [return]
40. "Analysis of variance," Wikipedia, 1 June 2019, [return]
41. Damon, et al., 1989, p.611. [return]
42. Tyrer, J., 1988, "So How Could the Carbon Dating Be Wrong?," British Society for the Turin Shroud Newsletter, No. 20, October, pp.10-12. [return]

Posted: 29 May 2019. Updated: 14 April 2021.