Journal of Modern Mathematics Frontier Volume 2 Issue 3, September 2013
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A Stochastic Process to Explain the Turin Shroud Body Image Formation Giovanni Fazio* Istituto Nazionale di Fisica Nucleare, Sezione di Catania, 95123 Catania, Italy Dipartimento di Fisica e di Scienze della Terra dell’Università di Messina, 98166 Messina, Italy *
gfazio@unime.it
Abstract In this paper, a natural mechanism capable to explain the Shroud body image formation has been studied. The physical and chemical characteristics of the above image agree with a stochastic process triggered by a little quantity of energy that has yielded a latent image. This mechanism is the sole that can explain both the reversed color characteristic and the 3D reconstruction without distortion of the above image. Therefore, the other mechanisms (deterministic processes) must be rejected.
Chapelle of Chambery. Here, in 1532, a fire caused the above cited scorched and burned areas. Successively, in 1983, Humbert II of Savoy gave the Linen to the Roman Catholic Church. Actually, the Archbishop of Turin is the Pontifical Custodian of the Shroud. It is underlined that this cloth is very important because many people believe that it is the burial one of Jesus of Nazareth even nowadays. On the other hand, for others, it is a forgery of the Middle Ages.
Keywords Linen of Turin; Mechanism of the Body Image Formation; Stochastic Process
Introduction The Shroud of Turin is an ancient cloth where the front- and back-image of a tortured, scourged and crucified man appears (Jumper et al., 1984). The body image is an uneven superficial discoloration due to the oxidation and dehydration of the linen cellulose structure with formation of conjugated carbonyls (chromopheres) that have colored the fibrils (Heller and Adler, 1981). In details, this linen cloth (~ 4.36 m length x ~1.10 m width), preserved in the Turin Cathedral, shows a male with wounds on the forehead, nape, wrist, feet and chest and scourge marks are present everywhere but especially over the legs and torso area. Moreover, burned and scorched areas and holes due to the combustion of linen at high temperature in a limited oxygen environment (1532 Chambery fire) and water marks, due to its extinguishing, appear (Figure 1). The last tracks have an evident contour made of dusts and impurity. This ancient cloth has a history confirmed from the middle of the 14th Century when it was in possession of the Count Geoffrey de Charney in Lirey, France. In synthesis, in 1432 it was ceded to the Duke Ludwig I of Savoy who from 1502 placed it in the Sainte
FIG. 1 FRONTAL IMAGE ON THE SHROUD OF TURIN
In this paper, the formation mechanism of the body image has been investigated, because the knowledge of such a mechanism is the main goal of the research on the Linen of Turin. In 1898, Secondo Pia, for the first time, photographed the Shroud showing the reversed color of the obtained image. Consequently, many formation mechanisms have been suggested. For example, in order to prove
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that the image was an artifact, painting, printing, rubbing or a chemically structure modification (scorch, chemically-induced modification) have been proposed. On the other hand, to demonstrate that the Linen of Turin was a Shroud, the Vignon vapor graphic theory or the Pellicori-German latent image model were proposed. However, all these hypotheses, together with the other not quoted in this paper, have not been able to explain the body image formation. In the XXI Century, other formation mechanisms appeared in literature by:
attempts made to obtain a fake that was in the possibility of a medieval artist (Garlaschelli, 2010),
different experiments with UV radiation (Baldacchini et al. , 2008; Di Lazzaro et al., 2010) or corona discharge (Fanti, 2010 and 2011).
been yellowed (all with the same value of optical density) from the ones that must maintain the background color. Consequently, it appears clearly in terms of the insurmountable difficulty to demonstrate that the image on the Linen of Turin is a fake product in the Europe of the Middle Ages. Moreover, these attempts (using pigments and thermic treatment) do not take into account that the blood image formation has preceded the body image formation. Indeed, the presence of blood stains predisposed on the fabric before the above experiments should be damaged (Jackson et al., 1984).
The hypothesis of fake is reasonable. Indeed, the Shroud appeared in about the middle of the 14th Century when in Europe an infinity of objects related to the Nazarene was present. However, all the attempts made to demonstrate that the above Linen is a forgery have been rejected because they failed to explain the physical and chemical characteristics of the body image. Also the mechanisms of Shroud body image formation by UV radiation or corona discharge must be discarded because a human body cannot emit the above radiation or generate an electrostatic field. These are utopias and the experimental sciences have not the instruments to study the above hypotheses. Analysis The difficulty to understand the Shroud body image formation is due to the distribution of the fibrils (10-15 µm each) that yielded the above image. These fibrils, with the same value of optical density, are present only in the areas where the body image lies and are mixed with the background one with a lower value of optical density (Pellicori and Evans, 1981). It is underlined that the last fibrils can hold a soft variation in the optical density values typical of the fabrics exposed to light and/or heat. Moreover, the more yellowed ones penetrate in the fabric in depth of 20-30 µm while the others, that have the background color, involve the whole thickness (~365 µm) of the linen (Weaver, 1980; Mottern et al., 1980). In other words, the body image floats on the fabric. Therefore, the variation of image intensity (e. g., the forehead is darker than the neck) is related to the density of the yellowed fibrils. Consequently, the hypothesized mechanisms must distinguish the fibrils that have
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FIG. 2 3D RECONSTRUCTION OF THE SHROUD FRONTAL IMAGE
On the Shroud, as affirmed, in the region where the body image lies, there are fibrils with background color together with fibrils that have a greater optical density value. These last yellowed fibrils, that have yielded the image are, numerically, distributed with a maximum value in the areas with cloth-body distance z = 0 (contact regions) and then decrease, as a linear regression, when the z value increases. Consequently, the Image intensity versus the cloth-body distance z is a linear function (Jackson et al., 1984; Fazio, 1996) that can be written as linear regression: I(z)= Ib + I0 (1-z/R0) (1) where Ib is the image intensity of background color, Ib + I0 the intensity in the contact areas and R0 the cloth-
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body distance value which gives I(R0)= Ib. For the frontal image, the R0 parameter is 3.7 cm (Jackson et al., 1984). This result displays that in the image region there is codified information of the cloth-body distance as appeared in the 3D reconstruction of the frontal image (Fig. 2).
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contact regions and zero when the cloth-body distance is R0. For this last value of z, the fibrils have only the background color.
Obviously, as well the absorbed energy for unit of surface of the fabric that yielded the above distribution has an analogous trend. In the regions of cloth-body, contact is the maximum (as occurrence of the above intensity of image) and then decreases, as linear regression, when the z value increases (Fazio and Mandaglio, 2011). Therefore, for the energy, the function can be written as: E(z)= Eb + E0 (1-z/R0) (2) where Eb is the average energy value per unit area received by electromagnetic radiation, Eb + E0 is the energy per unit area in the contact regions and R0 the cloth - body distance which gives E(R0) = Eb. In the formula (2) the contribution is due to the electromagnetic radiation (Eb) and the interaction between human body and linen cloth (E0 (1-z/R0)). Nowadays, there are several scientists that still believe in the radiative mechanisms for the formation of the above image without taking into account these deterministic hypotheses are not able to discriminate the fibrils yellowed from the ones maintaining the background color. These scientists, in their experiments can penetrate the linen for a depth of 2030 Âľm, as it is for the Shroud body image. This thickness can be obtained because it is possible for a deterministic process. On the contrary, the choice of the fibrils that must be yellowed to yield the image is impossible for the above mechanism. Therefore, it is necessary to introduce a stochastic process. The stochastic ones are mechanisms known for the following characteristics: a) they are triggered by a little quantity of energy, b) they have not a threshold to appear, c)
the effects have time of latency of the order of many years,
d) they are absent just when the energy is zero. These processes appear when the probability to have an event is proportional to the received energy and when the above events are produced with the same intensity. In this case the above probability can be written as: p = k(1-z/R0) (3) where k is a constant; p value is maximum in the
FIG.3 NEGATIVE PHOTOGRAPH OF THE FRONTAL IMAGE ON THE SHROUD OF TURIN
The distribution of the yellowed fibrils, that is undoubtedly stochastic, certifies that a weak energy has been transferred from the body to the linen triggering the above process. Consequently, the image has been yielded in a few decades. Therefore, there is no miracle or forgery. In other words, before the formation of the Shroud body image, all the fibrils had the background color. Successively, regarding the human body-cloth interaction (e.g., after a few decades), many fibrils (in line with the correlation between image intensity and cloth-body distance) increased the optical density yielding the above image. The result of the stochastic mechanism is a density of the yellowed fibrils (the one that has yielded the body image) that must be represented by a linear function type: d = d0 (1-z/R0) (4) where d0 is the density value in the contact regions and R0 is the same parameter that appears in the formulas (1), (2) and (3). In this way, there is nothing unusual about the reversed color of the Shroud image (Figure 3) and 3D reconstruction (Figure 2) characteristics. This is the result of the action of the stochastic process that has yielded a correlation between image intensity and cloth-body distance. The physical and chemical characteristics of body image are connected with the above distribution of the
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yellowed fibrils.
Turin Shroud image”, Journal of Imaging Science of
Now, there is the question to locate the source of energy: it is believed that the triggering of this process might be due to the emission of thermic energy (Fazio and Mandaglio, 2011), possible for an human body, and the low-temperature chemical processes between reducing sugars and amine with the aim to yield the conjugated carbonyls that color the fibrils (Rogers and Arnoldi, 2003). Unfortunately, for a stochastic process, it is impossible to distinguish among different sources of energy that are able to trigger the above mechanism. However, the result is very interesting because it can explain the Shroud body image formation, that is, it is a latent image yielded by a natural phenomenon.
Technology, vol. 54, pp. 040302-1-6, 2010.
Conclusions In this article, a stochastic process has been hypothesized for the comprehension of the body image formation, then the physical and chemical characteristics of the Shroud image explained by the above mechanism have been demonstrated. Moreover, the coexistence of the blood image with the body image has been resolved. Indeed, while the blood stains match with a wounded human body enveloped in the Linen of Turin, the body image is not in line with this hypothesis that a man can leave tracks containing codified information on the cloth-body distance. The stochastic process is the sole that overcomes this apparent discrepancy and explains the coexistence of the blood stains with the body image. All the other deterministic processes show great difficulty in the attempts to explain the Shroud body image. Therefore, they must be discarded. ACKNOWLEDGMENT
The author would like to express appreciation to her wife Antonella for the support and encouragement and to the Prof. Patrizia De Leo for the improvement in the English language. REFERENCES
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