The dating of the samples at 1:20 is something I had never seen before, and if the dates are accurate I wonder why they are chronological.
Hi GT/CS. Your inquiry is particularly interesting to me, as I find myself using exactly the same data which, about 50 pages back, led me to believe in the 'invisible reweave' hypothesis, but which I now think fails conclusively to do so.
However, the position is not a clear cut as some commentators here declare, and, as I have said many times before, the observations of anomalies are often accurate and valid. It is their interpretation which fails.
Benford and Marino noticed two statistical anomalies, namely that the three dates provided by the three labs were very different, and that they were in chronological order across the samples. The 'Nature' paper announcing the carbon dating age (
http://www.shroud.com/nature.htm) acknowledged the first, showing in Table 2 that there was only a 5% chance of obtaining such a variable set of results from three similar samples. Nevertheless, since there was no question (at that time) that the samples were, in fact, different, the matter was allowed to stand. It will be discussed further in a minute. The second anomaly, that the three samples were in chronological order, can be dismissed on the grounds that there are only six ways of listing three numbers, and two of them are in order (backwards or forwards), and something that happens with a probability of 1/3 is hardly anomalous at at all.
In fact, course, there were not three dates achieved, but twelve (4 from Tucson, 3 from Oxford and 3 from 5 from Zurich). although the order of each laboratory's total sample was known, the order within each lab was not. If they had each sliced their sample vertically, the possible number of ways in which the dates could be ordered would be 17280. If this was indeed the way the samples were cut up, and the dates for each were known, and they were chronological, the case for contamination would be irrefutable. However, how the samples were cut up was not known (vertical, horizontal or a mixture), and which dates referred to which sample was not known, so that there are some 400 000 possible configurations of the 12 numbers in two dimensions. Nevertheless, with the information available, Riani and Atkinson set to work on regression statistics and did indeed demonstrate a significant likelihood of chronological progression along the dating sample. They did not speculate on the cause of this chronological progression, nor what it might mean in terms of the date of the shroud, nor the proportion of contamination required to change one date into another.
So far, so good for the 'invisible weavers,' and the speculations of the three Textile Analysis companies to whom Benford and Marino sent photographs. Although these companies' analyses are described as 'blinded' by Benford and Marino, we are not told what they were actually asked, or what they actually replied in response.
The bottom line, for me, comes with the proportion of contaminant required to change a 1st century date into a 14th century one, and here, I think, Benford and Marino are guilty of serious misrepresentation. This is a serious charge, so I will quote their words (from
http://www.shroud.com/pdfs/marben.pdf).
"According to Ronald Hatfield, a scientist at Beta Analytic, the world's largest radiocarbon dating service, a merging of threads from AD 1500 into a 2,000 year old piece of linen would augment the C-14 content, such that a 60/40 ratio of new material to old, determined by mass, would result in a C-14 age of approximately AD 2010." This is demonstrably untrue, as Harry Gove pointed out. His criticism was replied to in
http://www.shroud.com/pdfs/textevid.pdf. Firstly "16th century" and "1st century" were defined as the years AD 1500 and AD 75 respectively, which seems odd if the shroud were supposed to date from before the death of Christ. Each date was then converted to a "measured conventional BP equivalent" of 360 BP and 1940 BP respectively, and then to a "fraction modern value," which I take to be the proportion of C-14 remaining in a sample of that date. The final proportions are 67/33. What I find staggering is the comment "the percent variability between these percentages and the original claim of 60/40 is within an accepted margin of 10%." If this is meant to mean that proportions of 51/49 and 69/31 are acceptable variations on 60/40, then I consider the whole argument downright dishonest.
This is all important. Even by their own calculations, almost 70% needs to be contaminant even to give the oldest of the radiocarbon ratings. To get the youngest it needs to be nearly 90%. The diagram shown by Benford and Marino (Figure 3 at
http://www.shroud.com/pdfs/marben.pdf) wholly misrepresents this, as surely they knew at the time.
Finally, two photographs can be usefully compared, and even lined up side by side. The first is the Zurich sample (apparently intact), which is Figure 6 of
http://www.shroud.com/pdfs/marben.pdf; and the second is about half of the bigger Tucson sample, which was retained, Figure 2 (bottom) at
http://www.shroud.com/pdfs/arizona.pdf. With a bit of rotating they line up quite well, and the supposed new threads can be examined closely in the Tucson sample. I can only say they look OK to me...