In a recent podcast with Mike Creavey,1 Bob Rucker reiterated his hypothesis that the Shroud was irradiated with neutrons, which explains how the radiocarbon dating could be wrong. His explanation, as ever, was clear and apparently compelling, and, most importantly, easily capable of being falsified – as indeed, I have no doubt, it will be in due time. However, it also includes what to my mind are certain statistical misapplications, and it is these to which this post is addressed.
We’ll start with this, which appears at about 23:35 into the video:
There is much to probe here, so bear with me.
1). The ‘Nature’ paper gives the following data for the ages of the three laboratories’ samples as:
Oxford: 750±30, Zurich: 676±24, Arizona: 646±31, which numbers are in ‘years Before Present,’ or ‘BP.’ They are derived from a simple mathematical formula for converting fractions of C14 into a number of years before 1950, to provide rough rule-of-thumb dates AD. As a simple way of illustrating a late medieval date for a lay audience which might not recognise 700BP, subtracting the BP dates from 1950 is understandable, but as a basis for any further interpretation, it is wholly inadequate. The BP dates must be calibrated against dendrochronological data in order to provide accurate AD dates, which, had that been done, would have produced a rather different graph.
Subtracting the BP dates from 1950 (Rucker) gives: Oxford: 1200AD, Zurich: 1274AD, Arizona: 1304AD.
Calibrating them properly (Oxcal)2 gives: Oxford: 1258AD, Zurich: 1297AD, Arizona: 1306AD.
[In fact, the vagaries of the calibration curve give two dates each for Zurich and Arizona, but since the two higher dates are later than the Shroud’s known appearance at Lirey, they have been discarded]
Here is the amended graph (green additions mine):
It’s not clear to me that Rucker really understands this, but it does show that neither the spread (48 years rather than 104) nor the gradient (17 years per centimetre rather than 36) of these points is as severe as he says.
2). Next, we note that the x-coordinates of the samples on the graph above have no error bars at all, as if every measurement was taken at an exact distance along the sample strip, and as if that distance were known. Neither of these is true. The x-axis is based on another rule-of-thumb estimation in Riani, Atkinson, et al.’s paper on their own analysis of the radiocarbon statistics,3 beginning with the assumption that the sample strip looked like this:
Most of these distances were never measured at all, and those which were, the overall original length and width, were not measured well to millimetre precision. The diagram above allows for a 5mm trim along the top edge, which certainly occurred, although it was never measured, but not a similar trim along the left edge, which also occurred and was also never measured. The final strip from which the samples were cut was about 7.5cm x 1.5cm, but any further precision is guesswork. We will return to this below.
To be fair, these distances hardly affect Rucker’s model above, so let’s move on to the “line of best fit.” The first thing any scientist has to do with a scattergram of results is to decide whether the “line of best fit” is best described as a straight line or a curve or something else. This can be a rather subjective judgement, especially if there are only a few points, as here, and if there is no a priori reason for deciding one or the other. He must also consider whether the equation thus derived can be extrapolated beyond the extent of the known data. In this case, while Rucker’s decisions can be used to show that the data support the neutron radiation hypothesis, they cannot be used to suggest it.
To my mind, the data are not best related by a straight line, something demonstrated quite well by another of Rucker’s graphs, at about 29:10 in the video (the blue ovals are mine):
Here we can see no significant difference between the Zurich and Tucson dates, but quite a large difference between those two and Oxford. This was noticed by eminent STuRP scientist Lawrence Schwalbe and colleague Bryan Walsh in two papers published in 2020 and 2021.4 They speculated that the Oxford cleaning regime may have removed a contaminant which the other two labs didn’t, and noted that a 20-year adjustment (of Oxford upwards or the other two downwards), would have made all three results statistically similar.
Consequently to assume a straight line correlation is not justified, and the equation derived from it is meaningless. In fact Rucker is well aware of this. Although he cheerfully explains that at the same gradient, a sample from further along would date far into the future, his own model shows that a sample from further still would return almost to where it started, and in fact, his own calculations do not relate to the equation at all. Here is his own graph (black), compared to his earlier prediction (red, by me), at about 27:30 in the video:
3). Another of Rucker’s diagrams also merits reinterpretation. Below left I reproduce Rucker’s possible configuration of the twelve subsamples into which the Radiocarbon labs cut their pieces, and his version of the dates AD suggested by the ‘Nature’ paper. However, since the configuration was chosen to fit the chronological gradient, it’s not surprising that there is a correlation. In fact, there is some evidence to suggest that that his configuration is incorrect.
In the case of Arizona, a piece of the radiocarbon sample was retained, and later photographed by Barrie Schwortz.5 Given that we believe the Arizona sample was the last along the sample strip, it can sensibly be placed in its correct position. In the case of Zurich, a schematic illustration suggests a particular configuration of the five dated samples.6 Here is Rucker’s idea, next to a more evidence-based one. Note that in indeterminate cases, it is not possible to be more specific.
4). Returning to Rucker’s most misleading approximations, the idea that calendar dates can be achieved by subtracting BP dates from 1950, here is the difference between the two:6
From this, it can be seen that a BP date of, say, 800 indicates an actual date of about 1250AD, and not 1150AD as calculated by subtracting it from 1950. It is therefore apparent that, far from being widely spread out, the radiocarbon dates are actually quite tightly grouped:
5). All this leads me to wonder about Rucker’s methodology in programming his MCNP. The plan was to find a neutron emission which would increase the apparent date of the Shroud from about 30AD to a gradient of about 750BP to 646BP. However, neither MCNP nor radiocarbon dating actually measure dates. They measure proportions of radiocarbon. To find the increase in radiocarbon, all the relevant dates must be converted to numerical proportions. The medieval BP dates can easily be converted to proportions of radiocarbon by the simple formula which produced them in the first place: 0.91327 to 0.92482. The first century date, however, is more difficult. First, 30AD must be converted to years BP, and second, the years BP must be converted to a proportion of radiocarbon.
Using OxCal: 30AD »» 2000BP »» 0.78511. This is correct.
Using 1950-30, Rucker’s preferred method: 30AD »» 1920BP »» 0.79274. This is wrong.
If Rucker used the lower calculation, then he would have added a smaller neutron emission than would actually have been necessary to achieve his result. In itself that’s not very important: there are plenty of spare neutrons available in a human body. But it would have affected the Sudarium of Oviedo. This required enough neutrons to make a 30AD cloth appear to be from 700AD.
Using OxCal, 700AD »» 1250BP »» 0.85967. This is correct.
Using 1950-30, 700AD »» 1250BP »» 0.85967. This is also correct. By coincidence, 700AD is one of those places where the calibration line and the 1950-BP line coincide. This means that, using the same radiation values as were used for the Shroud, Rucker could not have “corrected” the Sudarium to its radiocarbon date. It would have come out at about 50 years too young.
6). It has to be said that regardless of differences in details of the tomb, position of the body and sudarium, sample selection and radiocarbon results, the MCPN calculator could probably have been used to produce a possible level of neutron emission to adjust the medieval date to fit a first century preconception whatever the parameters, so the various comments made above can have no effect on its overall probability. However, I do feel that Rucker’s presentation has the side-effect of putting the findings of the radiocarbon laboratories in a worse light than they deserve, and hope that this post will help to establish a more balanced interpretation.
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1). ‘Shroud of Turin NEW RESEARCH!’ (youtube.com/watch?v=vSAU2ushM1M), 9 January 2026
2). The calibration curve is derived from ‘OxCal,’ the online program designed and maintained by Christopher Ramsey, one of the participants of the Shroud dating exercise and a signatory of the celebrated ‘Nature’ paper.
3). Marco Riani, Anthony Atkinson et al., ‘A Robust Statistical Analysis of the 1988 Turin Shroud Radiocarbon Dating Results,’Statistics and Computing, 2012
4). – Bryan Walsh and Larry Schwalbe, ‘An instructive Inter-laboratory comparison: The 1988 Radiocarbon Dating of the Shroud of Turin,’ Journal of Archaeological Science: Reports, 2020
– Larry Schwalbe and Bryan Walsh, ‘On Cleaning Methods and the Raw Radiocarbon Data from the Shroud of Turin,’International Journal of Archaeology, 2021
5). Barrie Schwortz, ‘Report on the STERA, Inc. – University of Arizona Radiocarbon Dating Laboratory,’ at shroud.com/pdfs/arizona.pdf
6). This diagram is repeated all over the internet, but I can’t find where it originated.
The decimal points are marked with commas rather than dots, which is a European continental style, but it is not further attributable. The images of the ‘first division’ are simply the original sample cut in two, the images of the ‘second division of the top half’ bear no relation to it, and the ‘second division of the bottom half’ is missing altogether. Still, it comes from somewhere!
In Rucker’s video, the figures at 21:18 and 23:23 in the video were altered, for some unknown reason, by the process of making the video. In the video at 21:18, the location of the values produced by the statistical analysis were scrambled. In the video at 23:23, the range on the y-axis was increased, which had the effect of shifting its intersection with the x-axis from the bottom of the figure up toward the middle of the figure.
The dates in these figures are the uncorrected carbon dates, i.e. without correcting the dates for the changing C-14 concentration in the atmosphere. These values are listed in units of AD rather than BP (years Before Present where present =1950) because people are much more familiar with AD than BP. The measured values in Damon are in units of BP, so Rucker calculated these AD values from Damon’s BP values using the equation AD = 1950 – BP. This equation does not include accounting for the changing C-14 in the atmosphere. Rucker fully realizes this. In normal practice, this correction for the changing C-14 in the atmosphere is done after the statistical analysis is completed.
In Farey’s second figure, he converts (prematurely, since this is not after the statistical analysis was completed, see above) Rucker’s uncorrected carbon dates to corrected carbon dates, and plots the results using large green circles, but without indicating the uncertainties for each value, as Rucker did. If Farey had included the uncertainties, it would be clear that the measured dates depend on the location, which should not be the case if the Shroud was entirely made at one time in the middle ages. The main point of this plot is to show that the measured dates depend on the location, which indicates that something strange is going on. The main point is not to show that the slope is of a particular value, so Farey’s calculation of a slope of 17.22 years/cm compared to Rucker’s value of 35.87 years/cm is of secondary importance. The difference between the two values is the result of Farey comparing his corrected carbon dates to Rucker’s uncorrected carbon dates.
The measurements of the width of the samples are good enough to use in such a plot. But Rucker’s plot is not based on their measured widths. The x-values in Rucker’s plot is based on his calculation of the sample widths from the sample weights assuming a constant height. Considering how the subsamples were cut from each of the samples, it should be clear that some of the subsamples would have been to the right of the sample’s central point and thus a little higher than the average value, and some of the subsamples would have been to the left of the sample’s central point and thus a little lower than the average value. Since the higher values will tend to compensate for the lower values, calculating the average value of the subsamples and plotting it at the mid horizontal point of the sample is a legitimate thing to do. This type of plot has been made by multiple Shroud researchers, including in papers published in peer reviewed journals, with the conclusion that the measured carbon date is dependent on the distance from the short end of the cloth, with some of the slopes even higher than Rucker’s value of about 36 years/cm. Farey’s estimation of about 7.5cm x 1.5cm for the size of the sample would still indicate that the carbon date is a function of the distance from the short end of the cloth. Farey agree with this when he said, “these distances hardly affect Rucker’s model above.”
In Farey’s second figure, Rucker has not unreasonably extrapolated the data because the x-axis only goes from 4.0 to 8.0 cm and the data is between 5.0 and 7.7 cm. The data shown in black dots in Farey’s fifth figure are not an extrapolation of the data in Farey’s second figure, but are values calculated in the MCNP nuclear analysis computer codes based on: 1) the assumption of neutrons homogeneously emitted from the body, 2) the physics properties of neutron scattering and absorption in the materials in the tomb, and 3) the model of the body, cloth, and limestone used in the MCNP calculations as described in Rucker’s paper 13 on his website on Shroud Research Network. When Farey says “while Rucker’s decisions can be used to show that the data support the neutron radiation hypothesis, they cannot be used to suggest it”. When Rucker first read Ref. 1, which was in about 1993, the relative mean dates from the three laboratories suggested the neutron absorption hypothesis to him, contradicting the above statement.
On Farey’s fourth figure, if he averages the multiple values into a single value for each laboratory, it would suggest a reasonably straight sloped line as shown in Farey’s first figure. Farey says, “Here we can see no significant difference between the Zurich and Tucson dates”, but the slope becomes obvious when the top two points for Oxford, Zurich, and Tuson are compared, and when the bottom two points for Zurich and Tucson are compared. The way in which the subsamples were cut from the samples produced a middle value, between the upper two data points and the lower two points, for Zurich, but no middle value for Tucson. The way in which the subsamples were cut from the samples also did not produce two lower points for Oxford. Regarding Farey’s reference to Schwalbe and Walsh’s speculation in two (Rucker remembers only one) of their papers that this slope in the carbon dates could have been the result of inadequate cleaning, it should be kept in mind that they also speculated that this slope in the carbon dates, which they concluded was true, could have been due to something that had altered the ratio of C-14 to C-12 in the samples as a function of location. Their speculation that the slope in the data was caused by a problem in the laboratory’s cleaning process is contrary to the laboratory’s good dating results for the three control standards. Their speculation that something had “altered the ratio of C-14 to C-12 in the samples as a function of location” is explained by Rucker’s MCNP nuclear analysis computer calculations. These calculations have shown that emission of about 2 x 1018 neutrons homogeneously from the body is consistent with, i.e. can explain, the four types of evidence from the 1988 carbon dating of the Shroud: 1) The mean or average date of about 1260 to 1390 AD, 2) the uncorrected carbon dates as they change according to their distance from the short end of the cloth at a rate of about 36 years/cm (91 years/inch), 3) the distribution of the carbon dates for the 12 subsamples, and 4) the carbon date (about 700 AD) for the Sudarium of Oviedo which is believed to be the face cloth of Jesus in John 20:7. The medieval Shroud hypothesis can only explain the first of these four evidences whereas the neutron absorption hypothesis explains all four of these evidences. Thus, the neutron absorption hypothesis is superior to the medieval Shroud hypothesis because it is much more consistent with the evidence.
Farey said, “Consequently to assume a straight line correlation is not justified, and the equation derived from it is meaningless. In fact Rucker is well aware of this.” Rucker says this is totally false. Farey’s rejection of the carbon date being dependent on its distance from the short end of the cloth is entirely unfounded.
Regarding Farey’s fifth figure, he said regarding Rucker that “his own calculations do not relate to the equation at all. Here is his own graph (black), compared to his earlier prediction (red, by me)”. In this sentence, “the equation” refers to “Y = 35.87x + 1030.67” in Farey’s figures 1 and 2, and “compared to his earlier prediction (red, by me)” refers to the red line in Farey’s fifth figure. The red line should only have a length of about 4 cm as in Farey’s figures 1 and 2. This is the length over which the carbon dating values apply but Farey extrapolated it to a length of about 200 cm, which is certainly not justified. But then Farey makes an even more significant mistake in believing that the equation (Y = 35.87x + 1030.67) for the red line, which applies to only about a 4.0 cm length near the feet, when extrapolated is a prediction of the distribution of the carbon dates over the entire length of the body. This is 100% false! The black dots that form the black line in Farey’s fifth figure are the carbon dates that result from Rucker’s MCNP nuclear analysis computer calculations. The black line should only be compared to the red line over about 4.0 cm near the feet, consisting of the left-most three black dots. The comparison between these three black dots and the red line is very good over this short range at the feet. The left-most three black dots indicate a slope that is a little steeper than the red line. This is because the black dots were MCNP calculated values at the centerline of the body, whereas the red line is the result of the experimental carbon dating measurements from the corner of the Shroud, which would have been a distance from the centerline of the body. This indicates an excellent agreement between the 1988 experiments and Rucker’s MCNP calculations.
The sixth figure shows Rucker’s MCNP results for the 12 subsamples relative to the measured values. Starting at 37:59 in Rucker’s video, using a standard chi-squared analysis to compare the predicted carbon dates for the 12 subsamples to the measured carbon dates, Rucker shows that his MCNP results for the neutron absorption hypothesis have a chi-squared value that is 4.5 times lower than occurs for Farey’s medieval Shroud hypothesis (chi-squared = 7.30 for Rucker vs 32.69 for Farey). This indicates that Rucker’s neutron absorption hypothesis is much closer to the measured carbon dates for the 12 subsamples than the medieval Shroud hypothesis, so that if science alone is considered, the neutron absorption hypothesis should be accepted as a better hypothesis than the medieval Shroud hypothesis.
When doing forensic science on a non-repeatable event, the normal practice for the researcher is to make assumptions that lead to the best agreement with reality. For example, if a researcher is trying to determine a hypothesis for how the planets in our solar system were formed, he chooses assumptions that result in the best agreement between his hypothesis and the planet’s current characteristics. Rucker is doing the same thing in his research on the Shroud of Turin. In his MCNP calculations for the 12 subsamples, the most significant things that we do not know are: 1) how the three samples were cut into the 12 subsamples, and 2) where the group of 12 subsamples was at the instant of Jesus’ resurrection. The MCNP results shown in Farey’s sixth figure is only the first iteration of Rucker’s MCNP calculations. These MCNP calculations took about two weeks of continuous run time on his quad-core desk top computer. In future iterations with MCNP, he plans to make a better evidence-based decision how the 3 samples were probably cut into the 12 subsamples and will search in other locations where the 12 subsamples could have been located at the instant of Jesus’ resurrection. The optimum assumptions for these two unknowns will probably result in MCNP calculated carbon dates that are much closer to the measured carbon dates for the 12 subsamples. This will increase the advantage of the neutron absorption hypothesis over the medieval Shroud hypothesis. When these optimum assumptions are determined, they will then become part of the neutron absorption hypothesis, which is part of the Vertically Collimated Radiation Burst (VCRB) Hypothesis when image formation is also included.
Regarding Farey’s figures seven and eight, he said “Returning to Rucker’s most misleading approximations, the idea that calendar dates can be achieved by subtracting BP dates from 1950 …” Rucker claims he has never believed this, claimed this, or used this. This only arises because Farey misunderstands what Rucker has said. To repeat it, the equation AD = 1950 – BP does not account for the changing C-14 concentration in the atmosphere. It does not produce what is called a “calendar date”, defined at the date AD after taking into account the changing C-14 concentration in the atmosphere. But this equation can be used to convert an uncorrected carbon date in BP units to an uncorrected carbon date in AD units. In doing this, Rucker is only changing units for the convenience of his readers and listeners, but he is not taking into account the changing C-14 concentration in the atmosphere.
After Farey’s eighth figure, he said that Rucker’s plan, i.e. goal, “was to find a neutron emission which would increase the apparent date of the Shroud”. Rucker denies this saying that his goal was to find a hypothesis that best explains all the data related to the 1988 carbon dating of the Shroud. This includes the mean value, the slope of the carbon dates, the distribution of the carbon dates for the 12 subsamples, and the mean carbon date for Jesus’ face cloth. This “best hypothesis” is the neutron absorption hypothesis. Farey said that MCNP does not measure carbon dates. This is true because MCNP does not measure anything. MCNP calculates the distribution of neutron densities, i.e. neutron flux, which can then be used to calculate the carbon dates at any location. Again, Farey said that Rucker used the equation AD = 1950 – BP to calculate the calendar dates, i.e. corrected carbon date, and again Rucker denies this.
He would have written and talked about it.
has Rob Rucker ever managed to create a reproduction of the shroud using radiation? I feel that this would be important