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158 Radiocarbon “Distraction”

Figure 4.5 Possible spatial conﬁguration of the dates (dark circle) of the

subsamples deriving from the piece of the Shroud taken for the radiocarbon

test and dated by the three labs: Oxford (O), Zurich (Z), and Tucson in

Arizona (A1 and A2). The fragment R on the left is the so-called Reserve—

the part retained in case further material was necessary. The part indicated

with T is the nonsigniﬁcant edge of the fabric. The dashed lines indicate

the subsamples’ placement. A contamination is evident that in 6 sq. cm

(0.093 sq. in.) of fabric causes a bias of 204 years.

single sample of the Shroud displayed in Fig. 4.5, in which a trend

of the date can be noted that depends on the physical position of

each fabric sample.

First of all, this result shows, without any elaborate statistical

evaluation needed, that the uncertainty assigned by the Nature

paper, at a 95% conﬁdence level, equal to ±65 years, is not correct,

because in 12 samples there is a variation of 204 years, which is far

more than the 130 years considered in the report.

Beyond this, the variability of the resulting dates shows that

the few centimeters of fabric, taken from the Shroud, cannot be

representative of the whole, longer than 4 m (13 ft.), cloth. In fact,

the fourth fundamental hypothesis states that the sample taken has

to be representative of the entire fabric. If in just a few centimeters a

variation of more than two centuries is observed, it is clear that the

hypothetical dating of each piece of such a big cloth would furnish

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A Result Nonresult 159

far more diﬀerent dates, and so the few-centimeter piece taken from

a corner of the cloth is not representative of the whole Shroud. To

do something better it would be necessary to date samples coming

from diﬀerent areas of the sheet, but obviously it is not possible to

riddle the Shroud with holes. Here is one reason that explains why a

second radiocarbon dating test of the relic has not been performed

yet.

Starting from these observations, a group of professors of

statistics at Parma (M. Riani), London (A. Atkinsons), and Udine

(F. Crosilla), in cooperation with the ﬁrst author, demonstrated that

the 1988 radiocarbon dating result referring to the Shroud is not

reliable.

These results have been ﬁrst published in the Italian Society of

Statistics review [121], in which, among others, conclusions are:

The statements of Damon et al. (1988) that <<the quoted errors

reﬂect all sources of error>> and that <<the results provide

conclusive evidence that the linen of the Shroud of Turin is

mediaeval>> need to be reconsidered in the light of the evidence

produced by our use of robust statistical technique. In other words,

the 12 measurements produced by the 3 labs cannot be considered

as repeated measurements of a single unknown quantity, therefore

an environmental contamination in the analyzed piece of fabric that

acted in a non-uniform linear way, adding a non-negligible bias, can

be hypothesized.

Conclusions are very important:

If the bias highlighted by the radiocarbon dating of the three

labs was directly transferred all along the Shroud, it could be

hypothesized, for a length of about 4 meters, a variation of twenty

millenniums in the future, starting from a date of the edge dating

back to the ﬁrst millennium A.D.

This conclusion aﬃrms therefore that the result of the 1988

radiocarbon dating is unreliable and scientiﬁcally meaningless.

Analogous results have been later published by the same authors

in a prestigious international statistics review [120]: After a “robust

statistical analysis” of 387,072 diﬀerent possible conﬁgurations of

the distribution of the 12 subsamples of the strip taken from the

Shroud, conclusions are that the data relative to the carbon dating

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160 Radiocarbon “Distraction”

“show surprising heterogeneity” and the resulting trend could be

due to an environmental bias.

The bias producing this date variation is not deﬁned yet, but it

seems obvious that if this bias is not uniform along the Sheet, dates

are heterogeneous. For example, let us think about pouring some oil

drops on a big sheet folded in several layers, and let us suppose that

the oil could vary the radiocarbon percentage of the threads: the oil

will stain the paper surface heterogeneously. If some samples are

then taken in order to make a radiocarbon dating test, it is easy to

think how much the resulting dates will be heterogeneous.

In agreement with the previous work, and in support of the reli-

ability of robust statistical analysis carried out on 12 subsamples, it

turned out that some conﬁgurations are not statistically signiﬁcant.

These conﬁgurations correspond to the hypothesis of considering

both fragment A1 and fragment A2 given to the lab in Arizona

(Fig. 4.3).

According to this statistical analysis therefore it is unlikely that

sample A2 has been dated. Well, the Tucson lab director Timothy

Jull conﬁrmed to Prof. Fanti that actually only sample A1 had been

used for the radiocarbon dating, thus indirectly verifying also the

reliability of the robust statistical analysis performed on the Shroud

samples.

Concluding the presentation of the results regarding this

controversial radiocarbon test performed in 1988, it can be stated

that:

(1) Results obtained are not statistically reliable because of

incorrect data evaluation.

(2) Environmental bias that could have altered the results even of

thousands of years has not been taken into consideration.

(3) Historical events, especially in the ﬁrst millennium, that could

have inﬂuenced the Shroud, as far as environmental conditions

are concerned, are not known. For example, the thymol

exposition has perhaps inﬂuenced the chemical conditions

of the fabric cellulose; who can exclude that during the

earliest centuries the relic had been conserved in an aggressive

environment like that with thymol of 1988, with the purpose of

better conserving the Holy Linen?

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A Result Nonresult 161

(4) The little piece of fabric taken from a corner of the Shroud is

not representative of the whole sheet in terms of dating.

(5) Not all the fundamental hypotheses of the radiocarbon dating

method are veriﬁed; condition number 3 stating that there

must be no environmental contamination is not veriﬁable.

(6) Condition number 4 regarding the sample representativeness

is not veriﬁed.

(7) The deviation of the obtained result can also be caused by an

environmental eﬀect linked to the body image formation. The

body image formation process is not yet clear, but it would

seem related to an intense burst of energy.

(8) Since the process described in point 7 is not yet known to

science, one needs to wait for clarifying the phenomenon

itself before repeating a further radiocarbon dating test on the

Shroud.

(9) The radiocarbon average date obtained by the 1988 test, of

1325 A.D., can be temporarily acceptable, provided that an

uncertainty of some millenniums will be assigned instead of

the ±65 years declared in the report published in Nature.

(10) It is necessary to proceed with alternative dating methods, and

this is will be the subject of Chapters 6 and 7.

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