To Revisit a Stochastic Process

To twice slay the slain,
[…] Is but labour in vain,
Unproductive of gain,
                                                         
—"Monkeyana" from Punch, May 1861

Blogging is different than mid-nineteenth century satire. It is at once more interesting and less poetic.

Barrie Schwortz, in his latest update, highlighted a relatively new, fascinating paper, The Mysterious Coexistence of Bloodstains and Body Image on the Shroud of Turin Explained by a Stochastic Process by G. Fazio, Y. Clement and G. Mandaglio. The article was published in the Mediterranean Archaeology and Archaeometry International Journal (Vol.14, No. 2) in June of 2014. Barrie noted that he has added the above link to appropriate lists of papers on his site.

If you missed it before (or you want to twice slay the slain) there are some interesting comments from when I blogged about this paper this past June in Paper Chase: A Natural Stochastic Process May Explain the Coexistence of Bloodstains and an Image on the Shroud of Turin. Read all 15 comments.

Within a day of the posting, Yannick Clément felt compelled to write, at some length, Clarification of the Stochastic Process Paper. It is important to read this along with the paper.

Thibault Heimburger was one of the people who had commented. That evoked this from Colin Berry (see Photomicrographs and Stochastic Imaging):

Thibault Heimburger is correct – Shroud photomicrographs lend no support to the notion of a ‘stochastic’ imaging mechanism.

And there is more. You can enter ‘stochastic’ in the blogs search field.

Threads photograph is inlined from Colin’s blog HERE. Colin captions the image: “The difference between those areas within the blue and red rectangles may possibly have theoretical significance as regards the mechanism of imaging (stochastic v deterministic, if you’ll pardon the jargon). Why? Read on…”

Photomicrographs and Stochastic Imaging

imageColin Berry in his blog tells us that Thibault Heimburger is correct – Shroud photomicrographs lend no support to the notion of a ‘stochastic’ imaging mechanism.  Colin writes:

So where does Thibault Heimburger MD, Paris-based French physician and member of the Shroud Science Group enter this story? Some might be surprised to find his views being favourably received on this site, given there is so much on which we differ, notably the contact scorch hypothesis (one that TH rejects). But that does not mean he’s wrong – or right- on everything, far from it, as my follow-up to a recent comment on his on shroudstory.com will now show.

TH appeared on the recent thread, the latter flagging up the presence of a Fazio et al  paper recently published in Mediterranean Archaeology and ArchaeometryHe queried the claim (or supposition?) that yellowed  fibres were randomly distributed across Shroud image-bearing regions, stating that they could appear together in bundles  . . . . Were that correct, it would deal a devastating blow to any theory that required the coloured fibres to be randomly distributed (though occasional clumping is not totally ruled out, albeit being of low expected frequency).

You are going to want to read Colin’s posting. Now we just need to hear from Thibault.

imageNote about the image:  The above image is ME-29, a 64x photomicrograph of a part of the nose area by Mark Evans. CLICK HERE or on the picture to enlarge it to 1088 by 770. Because I am hot-linking to the image as it is stored in Colin’s blog, it appears as a properly proportioned rectangle. For some reason it has been distorted into a 320 by 320 square in Colin’s blog (not that this seems to make any difference for the purpose at hand).  According to the shroud.com gallery of images, the original size is 2940 by 1984.

Clarification of the Stochastic Process Paper

imageYannick Clément wants to clarify some points about the paper, THE MYSTERIOUS COEXISTENCE OF BLOODSTAINS AND BODY IMAGE ON THE SHROUD OF TURIN EXPLAINED BY A STOCHASTIC PROCESS discussed HERE. What follows is an email he sent last evening. Following that is a summary that he also sent:


Thank you for your post on the blog that inform people of the publishing of the MAA paper I wrote with Fazio and Mandaglio! Well done!

Concerning what I said to you Friday about the fact that, even though the title of our paper can suggest otherwise, we are not willing to discard the hypothesis proposed by Rogers for the image formation on the Shroud in the form he wrote it, it’s important to understand that we still think an alternative scenario involving the release of a smaller quantity of postmortem gases than what he thought, which would have started a stochastic event of coloration on the top-surface of the Shroud, is more probable and we also think the possibility is quite high that this kind of stochastic event could have been started by some other forms of weak energy released by the corpse of the Shroud man, other than the postmortem gases proposed by Rogers (especially the heavy amines). That’s why our main conclusion mention this: “In our opinion, the bloodstains formation was followed shortly thereafter by a transfer of a little quantity of energy that was released by the dead body in direction of both parts of the cloth (ventral and dorsal parts), which triggered a stochastic process that produced, after some time (e.g. a few decades), a yellowing of some fibrils on the cloth’s surface.”

This precision is important to understand…

And on a more general note, I just want to point out that the main conclusion of our paper is the fact that, on a theoretical level, the discontinuous distribution of colored fibers in the Shroud’s image area can only be explained by a chemical process of oxidation and/or dehydration that must have involved only a very small amount of energy during a mild and natural event that most probably happened at normal temperature.

And, for us, such a weak amount of energy could only have produced two possible results:

1- A stochastic event of coloration that could have come from various possible natural sources (i.e. thermal diffusion from the corpse, postmortem gases released by the corpse or by some biological products (like urea and/or lactic acid) left on the skin and hair because of the abundant sweat of the Shroud man, a release of singlet oxygen atoms from the corpse, etc.), which would have lead to the formation of a latent image on the top-surface of the cloth that would have only be clearly visible years or even decades later. (note: this is the scenario that, me, Fazio and Mandaglio are favoring the most to explain the Shroud’s image).

2- An event of coloration coming from the release of postmortem gases by the corpse that would have produced Maillard reactions in the layer of impurities resting on the top-most fibers of the cloth, just like it was described by Rogers (i.e. a non-stochastic event that would involved a yellowing reaction of the layer of impurities EACH TIME these impurities would have come in contact with the amines released by the corpse), which would also have lead to the formation of a latent image on the top-surface of the cloth that would have only be clearly visible years or even decades.

Here, it’s important to note that, theoretically speaking, it’s much easier for the scenario #1 (stochastic event) to explain the discontinuous distribution of colored fibers in the image area than it would be for the scenario #2 and Rogers was fully aware of this when he wrote in his book about the Shroud: “However, identification of a probable chemical process does not explain one of the perplexing observations on the Shroud, the discontinuous distribution of the color on the top-most parts of the weave.” But as I wrote myself in my paper entitled “Raymond N. Rogers’ observations and conclusions concerning the body image that is visible on the Shroud of Turin” (http://shroudnm.com/docs/2013-01-10-Yannick-Clément-Reflections-on-Ray-Rogers-Shroud-Work.pdf), such a statement by Rogers doesn’t mean that the discontinuous distribution of colored fibers observed in the image area cannot be compatible with a natural mechanism for image formation that would involve a chemical process like the Maillard reaction he proposed before his death in 2004. To me, this quote from Rogers only means that, in order to explain properly this discontinuous distribution of the colored fibers, at least one more factor other than a chemical process like a Maillard reaction must have been active during the image formation process. For example, this additional factor could have been the presence of an uneven and very thin layer of impurities on the top-most fibers of the cloth (which would have render only a portion of those top-most fibers suitable to get easily colored) and/or a much smaller amount of energy involved in image formation process than what Rogers thought (note: this last possibility would place Rogers’ hypothesis in scenario #1 instead of #2, because it would mean that a much smaller amount of postmortem gases were involved in the image formation event, which would have lead to a stochastic result of colored fibers).

It should be noted that the possibility of a chromophore of the image residing only in an UNEVEN (this word is crucial) layer of carbohydrate impurities that could have produce a thicker coating of impurities on bundles of fibers that are adjacent to bundles of fibers that are coated with much less impurities as well as bundles of fibers that maybe are completely free of any impurities (which is a possibility that, unfortunately, we did not mentioned in our paper) can be seen as a possible answer for the good questioning that was emitted by Thibault Heimburger on your blog (when he said: “the colored fibers are not randomly colored.In a colored thread, there are BUNDLES of colored fibers adjacent to bundles of uncolored fibers.”). I think the possibility that an UNEVEN layer of carbohydrate impurities could be the only chromophore of the image give the two scenarios I mentioned more credit in the light of Thibault’s observation… Note also that this possibility of a chromophore residing only in an uneven layer of impurities can fit with Rogers’ hypothesis (scenario #2) as well as with a stochastic event of coloration (scenario #1) if such an event affected only the layer of impurities described by Rogers (which is truly possible, especially when we take into account THE FACT that such a layer of carbohydrate impurities is much easier to yellow than the structure of the linen fiber itself, including the PCW).

In the end, after we (i.e. me, Fazio and Mandaglio) took into account the fact that, on a theoretical level, the discontinuous distribution of colored fibers in the Shroud’s image area can only be explained by a chemical process of oxidation and/or dehydration that must have involved only a very small amount of energy (e.g. scenarios #1 or #2), we were able to state categorically that all the image formation hypotheses involving an important amount of energy (like the ones proposed by Fanti, Di Lazzaro, Jackson, Moran, Rinaudo, etc., and even the one that will be proposed in St-Louis by Villareal, which involved a release of alpha particles) must be discarded because they cannot rationally explain the discontinuous distribution of colored fibers in the Shroud’ image area. This lead me to conclude that this kind of discontinuous distribution of colored fibers is certainly the aspect of the image that can be seen as the most important “deal breaker” for all these image formation hypotheses. Effectively, in all these cases, the amount of energy would have been too high to produce a stochastic event of coloration or to only colored the top-most fibers of the cloth that were coated with enough carbohydrate impurities, without affecting also the structure of the fibers underneath those impurities, as well as the other top-most fibers surrounding those heavily coated fibers.

I really think you should post this present email on your blog in order for people to understand more easily the heart of our MAA paper (as well as offering an interesting response to Thibault’s questioning). Thank you in advance for doing this…

[ . . . ]

Yan J

P.S.: Concerning the possibility that, on the top-surface of the Shroud, there is an UNEVEN layer of carbohydrate impurities, which would have been the only thing colored during the image formation, I remind the readers of your blog to read carefully the footnote #163 of my paper “Raymond N. Rogers’ observations and conclusions concerning the body image that is visible on the Shroud of Turin” (http://shroudnm.com/docs/2013-01-10-Yannick-Clément-Reflections-on-Ray-Rogers-Shroud-Work.pdf), which reads: “In his paper entitled An Alternate Hypothesis for the Image Color (2001), Rogers reported an evaporation-concentration experiment he made with a cotton nap and a dye solution and described the result like this: “The photomicrograph shows that the main concentration of dye on the top surface appears on the fibrils of the nap that are pointing straight up and on the top-most surfaces of the threads.” This is a clear indication that when an evaporation –concentration phenomenon is active inside a cloth, it normally produces an uneven layer of impurities that concentrate mostly on the top surface of the cloth, thus giving us a possible explanation for the discontinuous distribution of colored fibers in the image area of the Shroud (as well as the extremely superficial aspect of the image). Effectively, starting from this result obtained by Rogers, we can presume that, after the active phase of the image formation process (which was most probably mild), only a portion of the coated fibers located on the top surface of the cloth (i.e. the ones that were coated by a thicker layer of impurities) were able to get colored enough to help produce the body image that we see on the Shroud, because the amount of impurities, in their case, would have been sufficient to produce such a result. Notice also that Rogers reports the same kind of evaporation -concentration experiment with dye in his book “A Chemist’s Perspective on the Shroud of Turin”, while mentioning that the degree of dye concentration can be variable even between two adjoining fibers (see quote #114), which confirms very well this personal interpretation of the previous quote coming from his paper entitled An Alternate Hypothesis for the Image Color (2001).”

SUMMARY

There is a true possibility that the answer to the Shroud’s image formation can be found in BOTH a stochastic event that involved only a very small amount of energy released by the corpse (i.e. a natural event that happened most probably at normal temperature) AND the presence of a UNEVEN layer of carbohydrate impurities that coated the top-most fibers of the cloth and which would have been the only thing that was affected by that stochastic event, which was so mild that it provoke the oxidation and/or dehydration of only a portion of the most coated fibers on the top-most part of the cloth (while not affecting at all the structure of the linen fiber itself, as well as not affecting in a visible way the other top-most fibers, even if some of those fibers were directly adjacent to those that became yellowed), thus leading to the formation of a latent image that became fully visible only years or even decades later.

Paper Chase: A Natural Stochastic Process May Explain the Coexistence of Bloodstains and an Image on the Shroud of Turin

clip_image001The paper, THE MYSTERIOUS COEXISTENCE OF BLOODSTAINS AND BODY IMAGE ON THE SHROUD OF TURIN EXPLAINED BY A STOCHASTIC PROCESS by Giovanni Fazio, Yannick Clement and Giuseppe Mandaglio and published in Mediterranean Archaeology and Archaeometry is now available online:

The presence of bloodstains certifies that a wounded human body has been enveloped in the Shroud of Turin and that most parts of this corpse came in direct contact with the cloth during the burial procedure. On the contrary, the ventral body image, by correlation between image intensity and cloth-body distance, shows codified information regarding the distance from which the cloth was versus the body at the time of the image formation. At first sight, this last statement seems to be impossible for a human corpse. Therefore, the coexistence of the bloodstains and the body imprints on both sides of the Shroud could be seen as unnatural, especially when we consider that a deterministic process as the UV radiation or the action of an electrostatic field (corona discharge), as well as manmade chemical and thermal treatment. These processes do not explain all the known characteristics of the body images (ventral and dorsal) because they do not distinguish the fibrils that must be yellowed from the ones that must retain the background colour. In this paper we prove that a natural stochastic process can offer a rational and scientific explanation that can account for all the known properties of these bloodstains and body images. However, another possible explanation that must be taken into account is a natural process involving the production of oxygen that yields a latent image.

Mediterranean Archaeology and Archaeometry is an open access journal published by the University of the Aegean.