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244 The Mechanical Multiparametric Dating Method

Table 7.4 Estimates of the Shroud age

provided by the ﬁve dating diagrams

Characteristic Years

σ

R

577

E

f

14

E

c

456

η

D%

−510

η

I %

564

Fibers of the Shroud, coming from the back of the sheet (in

correspondence of the gluteal area) and picked up during the 1978

Shroud of Turin Research Project (STURP) analyses (Section 2.3),

after petrographic microscope identiﬁcation by the ﬁrst author

(Section 5.3), have been tensile-tested by the second author.

Each dating diagram was used for evaluating a dating range of the

relic. For example, once the value of the breaking strength σ

R

of the

Shroud on the regression line of the corresponding dating diagram

(namely σ

R

vs. time) was set, we calculated its abscissa, which is

the dating of the sample. From the relative band we obtained the

uncertainty. What we just described for the breaking strength has

been done for each of the ﬁve mechanical properties in a bijective

relationship with time (condition 9).

The obtained results are shown in Table 7.4 and Fig. 7.19, which

also shows the ﬁnal result, namely the dating of the Shroud, with its

relative uncertainty at a conﬁdence level of 95%, according to the

ISO-GUM-BPIM guide [26].

A useful parameter able to assess the reliability of the used

mechanical method is the dispersion of the results derived from

the ﬁve mechanical datings. The more the resulting values are

diﬀerent from each other, the more we can suppose that various

environmental factors might have negatively aﬀected the results,

providing values aﬀected by not negligible bias. For instance, in

some deteriorated ﬁbers the dispersion of the results turned out to

be excessive, with diﬀerences between the dates resulting from the

same sample to be even around 2000 years.

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Results 245

Figure 7.19 Dates of the Shroud resulting from the analyses of the ﬁve

diﬀerent mechanical parameters and combined result corresponding to A.D.

400 ± 400 years at a conﬁdence level of 95%.

For the Shroud all the dates, except the one given by the direct

loss factor, are compatible

64

with each other. This means that we

obtained results containing dates around A.D. 400.

The diﬀering result (represented by the dating from the direct

loss factor) can be explained as follows. Both the slippages between

the microﬁbrils and the plasticity of the ﬁber, not stabilized by

suitable pre-tensions that have not always been possible during

the tests, might have aﬀected the result. Therefore in the case of the

Shroud the relatively low dispersion of the results indicates that the

ﬁnal date is little aﬀected by environmental bias and thus reliable.

We thought that the simple arithmetic mean of the ﬁve dating

results, which gives for the Shroud the value A.D. 220, would be a

less correct procedure. To combine into a single value the ﬁve values

coming from the dating diagrams, we preferred a relationship

65

in

which a greater weight is assigned to the mechanical properties

less susceptible to plastic slippages. Hence the ﬁnal dating value of

the relic is evaluated as a weighted mean between the ﬁve results

obtained from the dating diagrams.

64

See footnote 10 on p. 138.

65

The assumed equation is

Y =

2Y

σ

R

+ Y

E

f

+ 3Y

E

c

+ Y

η

D%

+ 3Y

η

I %

10

in which the chosen weights favor the contribution of E

c

with respect to E

f

and of

η

I

compared to η

D

. As regard the breaking strength’s weight coeﬃcient we assumed

the value 2, intermediate between the minimum and maximum chosen values.

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246 The Mechanical Multiparametric Dating Method

We observe that if we had used a weighted mean with Pearson’s

coeﬃcients as weights, we would not have given greater weight to

the mechanical parameters less dependent on plasticity, which is

instead the criterion assumed to deﬁne the way of combining the

ﬁve obtained dates together.

For the Shroud the MMPDM gives the date of A.D. 372.

The computation of the uncertainty, associated with the value

corresponding to the combination of the ﬁve dates, gives a value of

±400 years at a conﬁdence level of 95%. Therefore, the dating of the

relic is A.D. 372 ± 400 years (95%), but it can be rounded to A.D. 400

± 400 years (95%). Hence the ﬁnal result is compatible with the era

in which Jesus of Nazareth lived in Palestine.

We also observe that this result is compatible (Section 9.1)

with those provided by the chemical dating methods described in

Chapter 6 and by the numismatic analysis described in Chapter 3,

but it is not compatible with the 1988 radiocarbon dating result

discussed in Chapter 4.