May 22, 2015 16:56 PSP Book - 9in x 6in Fanti-Malﬁ

190 Inquiries into Alternative Chemical Dating

Figure 6.1 Dr. Orit Shamir, director of the Israel Antiquities of Jerusalem,

while she exposes some samples of antique fabrics to the ﬁrst author for the

choice of some fragments.

presence instead of a known exponential decay, like that of the

14

C

method, we would obtain a negative exponential-type curve.

But when the variation law, namely the function Y = f(x),is

unknown, being still the object of the research, by measuring the

Y property on a enough large number of samples of diﬀerent ages,

what we obtain is a set of points placed in a Cartesian diagram,

having the years on the x axis and the values of the Y property on the

y axis (Fig. 6.3). Due to various experimental reasons, also related to

May 22, 2015 16:56 PSP Book - 9in x 6in Fanti-Malﬁ

Requirements of a New Dating Method 191

Figure 6.2 Some recent and ancient ﬂax samples with a known dating

method used for the calibration of alternative dating methods.

the repeatability

10

of the tests, the points reported in a Cartesian

diagram are not “well ordered one by one.”

What seems at ﬁrst sight in a diagram to correspond to a linear

or exponential trend must ﬁnd experimental concreteness:

• by deﬁning in mathematical language, according to a

criterion, the actual variation law, that is, determine the

function Y = f(x);and

• by considering on the basis of objective—and not

subjective—features the degree of its actual “description”

10

Repeatability is the degree of concordance among the results of subsequent

measurements of the same value carried out in such a way as to respect

all the following conditions: same measurement method, same observer, same

measurement instrument, same place, same conditions of use, and repetition

within a short period of time. Such a characteristic is usually expressed in terms

of the results’ dispersion. If one of the above-mentioned conditions is not respected

(e.g., the one concerning the same observer), we must talk of reproducibility and

not of repeatability.

May 22, 2015 16:56 PSP Book - 9in x 6in Fanti-Malﬁ

192 Inquiries into Alternative Chemical Dating

Table 6.1 List of ﬂax samples used in the chemical vibrational spec-

troscopy tests (Raman and FTIR/ATR) (1)

Picture Name Description Dating Origin Collection Notes

A

New herring-

bone fabric

3–1

2000

A.D.

Liotex

Italy

Private

Bleached

with NaOH

AR

New herring-

bone fabric

3–1

2000

A.D.

Liotex

Italy

Private

Similar to A for

repeatability

B

New fabric

with rough

texture

2000

A.D.

Graziano

Italy

Private Not blenched

AII Book paper

1800

A.D.

Italy Private

Washed with

water

BII Book paper

1746

A.D.

Italy Private

Washed with

water

with reference to the trend manifested by the points which

are being measured.

As a matter of fact, we can draw inﬁnite straight lines or

exponential curves ﬁtting the points reported in the diagram.

11

Thus we have to deﬁne the criterion with which we choose

the “better” curve describing the trend of the Y property with

time through a number of measured points. To characterize this

aspect from a quantitative point of view, we have to refer to a

suitable mathematical parameter capable of objectively evaluating

the “goodness” of the choice that we have made. In other words,

this mathematical parameter must permit us to state if a determined

linear interpolating curve actually describes the data trend better

11

In technical terms this operation is known as data interpolation.

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Requirements of a New Dating Method 193

Table 6.2 List of ﬂax samples used in the chemical vibrational spectroscopy

tests (Raman and FTIR/ATR) (2)

Picture Name Description Dating Origin Collection Notes

DII

Medieval

fabric 1–1

800–

1200

A.D.

Pit 38

Qarantal

Jericho

Israel

Israel

Antiquities

Authority

Washed

with water

D

Medieval

fabric 1–1

544-

605

A.D.

Coptic

Fayyum

Egypt

M. Alonso

14

C dated

FII

Mummy

fabric 1–1

55-74

A.D.

Masada

Israel

Antiquities

Authority

Washed

with water

E

Mummy

fabric 1–1

300–

500

B.C.

Egypt

Egyptian

Museum

Turin

Dated by

historical

information

HII

Mummy

fabric 1–1

1000–

720

B.C.

Egypt

Egyptian

Museum

Turin

Dated by

historical

information

than others curves like, for instance, a quadratic, cubic, polynomial,

or logarithmic one. So, to achieve this goal, we can use the math-

ematical method called least squares ﬁtting based on the research

of the so-called optimum curve able to minimize the deviations

between the measured values and those that would be obtained if

the mathematical model had perfectly described the relationship

we were looking for. A valid method to judge the validity of the

result obtained is based on the calculation of the so-called Pearson

correlation coeﬃcient.

12

12

The Pearson correlation coeﬃcient is the measurement of the deviations between

the mathematical model that has been hypothesized (straight line, exponential

curve, etc.) and the pairs of values relating to a property under study and the

corresponding historical date. Correlation coeﬃcients inferior to 0.60 correspond

to values that are too scattered in the interpolating curve determined with the least

May 22, 2015 16:56 PSP Book - 9in x 6in Fanti-Malﬁ

194 Inquiries into Alternative Chemical Dating

Table 6.3 List of ﬂax samples used in the chemical vibrational spectroscopy

tests (Raman and FTIR/ATR) (3)

Picture Name Description Dating Origin Collection Notes

K

Mummy

fabric 1–1

2600–

2200

B.C.

Egypt

Egyptian

Museum

Turin

Dated by

historical

information

MII

Mummy

fabric 1–1

2500–

2200

B.C.

Thebes

Egypt

Egyptian

Museum

Turin

Dated by

historical

information

LII

Mummy

fabric 1–1

3500–

3000

B.C.

Egypt

Egyptian

Museum

Turin

Dated by

historical

information

With respect to condition 1, we studied diﬀerent ﬂax fabrics’

properties, and in reference to condition 2 we deﬁned various

relationships between the properties chosen and the age of the

fabrics. For example, it is known that ﬂax turns yellow with time (see

Section 1.2), and therefore its color has been considered as one of

the possible properties to be correlated to the time in order to obtain

the relationship needed to satisfy condition 2. However, it was found

that condition 3 could not be veriﬁed because the coloring of the ﬂax

also depends on other factors, mostly environmental (temperature,

humidity, and exposure to light), which can produce a bias that

cannot be neglected and it is actually too inﬂuential to provide a

dating method reliable enough.

In the case of the chemical composition of the cellulose, which

can be measured through the FTIR/ATR and Raman spectroscopic

methods, and in the case of the mechanical properties, it was

squares ﬁtting method; values superior to 0.90 correspond instead to an excellent

correlation, where 1.00 is the best value. For example, we will obtain the best value

1.00 by calculating the Pearson correlation coeﬃcient of the points belonging to

the same straight line. As a guarantee of their reliability, in these studies Pearson

correlation coeﬃcients superior to 0.90 have been found.