It began by asking a simple question. Suppose one dusted a 3D figure completely with white flour (now this blogger’s preferred imprinting medium, admittedly requiring an oven to ‘develop’ the image to a visible brown colour). Suppose one imprinted the two sides separately. Would there be a ‘frontal’ image and a ‘dorsal’ image, as per the Turin Shroud, with no imprinting of the sides, or would one see unsightly imprinting of the sides as well, through having used a printing mode dependent on physical contact. ?
Using my “Galaxy Warrior” again as template, I first smeared it all over, front, back and sides, with vegetable oil, then dusted liberally with white flour, then knocked off the excess. It was checked carefully to see that no parts had been missed, adding extra flour where necessary and again knocking off the excess. It was now ready for imprinting.
The frontal side was imprinted onto wet linen first, using what I call the LOTTO mode (Linen On Top, Then Overlay). The dorsal side was then imprinted onto the same piece of linen, reproducing in miniature the distinctive, some might say iconic Turin Shroud head-to-head configuration using the LUWU configuration ( Linen Underneath With Underlay). The flour imprints were of course somewhat faint and indistinct at this stage, but on close inspection there did not seem to be imaging off the coated sides of the template. So far, so good. It’s presumably the vertically-applied pressure onto the template (LUWU) or the overlying linen that allows one to imprint off the frontal and dorsal surfaces without imprinting the sides as well (which would make for a unsightly end result).
The imprinted linen was then suspended vertically in a fan oven supplying hot air by forced convection – the only source of thermal energy (i.e. no conduction, no radiation). Some 10 minutes later there were the expected reddish-brown imprints, presumably the result of Maillard reactions between reducing sugars and protein in the flour. Again, on quick inspection, there was no obvious wrap-around distortion. Was that surprising? Some might think so, given the manner of imprinting, and indeed a photograph taken at the stage when linen was pressed onto the template in LOTTO mode shows considerable ‘wrap-around’ suggesting that the images would be too ‘expanded’, and suffering consequently from accompanying lateral distortion. Was the image expansion maybe there, but too small to be easily detected, and if so, why? These seem important questions needing to be asked, so I make no apology for using a convenient 3D template, the ‘Galaxy Warrior, what was described today in comments as a “curious toy”. If nothing else, it’s more economical on pricey linen than using my hand as template (see previous postings).
Here’s the double imprint. It seems OK at first sight, viewed alongside the template. There’s certainly no grotesque distortion, indeed scarcely any.
Note that the buttocks have been imprinted on the dorsal surface, unlike the previous session. Why? There was insufficient underlay (the second U of LUWU) last time. This time. several layers of woollen pullovers with plenty of ‘give’ under pressure were placed under the template. Problem solved.
Here’s a close-up of the dorsal imprint (left). Any lateral disortion due to wrap around effect?
If it’s there, it’s not immediately obvious. Neither was it apparent when the template was placed down directly on top of the imprint:
Enough of the eye-balling. Let’s do some measurements to compare dimensions of the template and the imprint.
Let’s do one more check from the frontal image – those thighs:
Again, the match is almost perfect. How come? What am I doing NOT wrong?
Let’s take a look at the dorsal side too, bearing in mind that the imprinting method was different (LUWU not LOTTO).
Is there not something wrong here? Should there not be a larger width for the imprint, compared with the corresponding two points on the template? Or are we taking too simplistic a view of the ‘wrap-around’ effect, assuming that it always results in expansion of image relative to template? Let’s put pencil to paper and do some calculations.
Here we imagine, purely as an intermediate starting point, that we are seeing a portion of the anatomy in cross-section, represented as a circle (yes, a simplification) and that it is pressed down into a yielding linen underlay, represented as a thick blue line. What’s more the depth of penetration is 1/3rd of its circumference, which means there is an angle of 120 degrees (1/3rd of 360) subtended at the centre of the circle.
Now, the maximum width of the anatomical feature that is perceived by the eye or a camera is the diameter, shown in red. How does the length of the imprint compare with that diameter, after the linen has been straightened out?
Let’s take the coward’s way out initially and use coloured cotton, red and blue, to compare those two relative lengths.One sees that that circumference, or rather 1/3rd circumference, is longer than the diameter, due to that ‘wrap-around’ effect, but only SLIGHTLY LONGER, at least for the partial embedding of the circle/cylinder/sphere (whatever) in the linen and underlay. What if the half the circumference of the circle had been embedded, or any other fraction? Can one derive a mathematical expression that compares the width of the image (“buried circumference”) with that of the template (“diameter”)?
The circumference of a circle is 2πr, so 1/3 of the circumference is 2πr/3. That is now to be compared with the diameter D, which is 2r. So let’s derive an expression for the partial (buried) circumference that finally gives the width of imprint:
Partial circumference (shown in non-wavy blue above) as a percentage of the diameter (real width of template) is (2πr/3 x 1/2r) x 100%, or more simply, 100π/3 = 104.6%. So yes, the length of blue cotton was just slightly greater than red. So for partial embedding of the template in linen, as shown in the diagram, there is in fact scarcely any elongation of imprinted image relative to template, explaining no doubt my finding the same by experiment.
In fact, one can calculate the angle subtended at the centre of the circle where image width exactly matches that of template. It is 114.5 degrees, slightly less than the arbitrary 120 degrees used in the diagram. So it’s already obvious, or should be, that the wrap around effect only creates artefactual enlargement of contact imprint with respect to template when the subtended angle at the centre is greater than 114.5 degrees and/or the buried circumference is appreciable greater than a third (approx).
What is the effect of ‘burying’ one half of the circumference, were that physically possible in the template/linen situation, such that the subtended angle above increases from 120 to 180 degrees? The buried circumference now becomes one half of 2πr, i.e πr, while the diameter stays the same at 2r. So the corresponding percentage of partial circumference relative to diameter can be calculated as (πr/2r) x 100%. Now that is a big and indeed somewhat alarming number, i.e. 157%. So there’s a huge shift in the ratio of apparent to real width in going from 1/3 to 1/2 of ‘buried’ circumference. But that’s not a basis for taking the worst case scenario where half is buried, and assuming that to be the routine norm for a template pressed into linen (LUWU) or linen pressed onto a template (LOTTO) and declaring that ALL contact images must suffer from distortion due to wrap-around effect. Indeed, if the template were buried with appreciably less than a third of the circumference, then the image width would be LESS than actual: partial embedding, provided it is not too much, can actually IMPROVE the look of the imprint, making it a better match with actual width than would be the case if there were no wrap-around effect.
Finally, added as an afterthought (Wed 13 Jan) let’s generalize on the maths. Instead of choosing particular numerical values for the buried fraction of the circumference (e.g. one 1/3 above). let’s represent the fraction by the symbol F. Let’s then introduce the ratio R, which is (width of imprint/width of template).
It’s then a simple matter to show that R= 2πrF/2r, or simply πF. In other words, R is a simple linear function of F, with π as the proportionality constant. This can be seen by plotting R (vertical axis) against F (horizontal).
As already stated, the most ‘virtuous’ zone of the graph when it comes down to the fidelity of contact imprinting is where the fraction of total circumference that is buried is close to a third, as indicated above by the orange lines.
(ed, 14th Jan: I have removed the section that was here in the original posting, having had second thoughts about the the theory, and having realized there’s a simple experiment that can be done to make the intended point. It’s been tacked onto the end of this posting as a series of 10 photos. See Late Addition, in large red font).
So what’s the more realistic scenario? Half the circumference buried, with gross image enlargement and distortion, or a more modest third? Let’s continue the debate in Comments should anyone be interested in what they have read so far.
Afterthought: here’s a simple experiment anyone can do with a bottle and with thick padding (I used several layers of woolen pullover). Actually, it’s two experiments, one in LUWU mode the other with LOTTO (the mechanics are different in the two instances, but arguably lead to the same conclusion).
See if you can get more than a third or so of the bottle’s circumference to make contact with the padding in the two situations: (a) by laying the bottle on top and pressing down hard, i.e. LUWU mode or (b) by draping the padding on top of the bottle, with or without pressure applied from above.
Late addition: here’s an extra experiment that’s just been done to see how much image elongation is generated when one imprints off a perfect cylinder (a cider bottle!) applying downward pressure with one’s slightly cupped hand to capture surface relief, being careful to imprint off no more than half the facing circumference. White discs were attached to the bottle to provide the surface relief, which were then painted with vegetable oil, flour coated (sprinkled vertically), imprinted onto wet linen, followed by oven-roasting. In other words the bottle test conformed as closely as possible to the imprinting procedure developed here and unique to this site.
So, to repeat the question: how serious is the ‘elongation’ effect when imprinting off a curved surface onto linen? (I’ll attach numbers later to the template v image widths you see above).
Is not the term ‘lateral distortion’ somewhat misleading? The shape of those discs – circular – did not distort on imprinting. How could it, given the linen stayed tangential to each disc at all points of contact? If the truth be told, it’s not the imprint that is distorted, excluding the elongation relative to the cross-sectional width of the bottle, i.e. diameter. It is the “appearance” of the template to the eye or camera that is distorted, inasmuch as those discs appear progressively slimmer and more oval-like as one moves away from the centre.
In fact, the problem with contact imprints, potential or realized, is not lateral distortion, but lateral non-distortion, in as much as repeated motifs, if present, maintain their shapes to the periphery INSTEAD of becoming distorted from the viewer’s perspective on the original template. In fact, the eye depends on a number of cues for detecting that something is round rather than flat. the obvious one is light and shade, generated by oblique illumination, whether from daylight or artificial light. But there are those other subtle clue that come from shape changes, or rather APPARENT shape changes linked to curved surfaces.
What about the Shroud? What visual cues if any are we given to 3D-ness or otherwise? Answer. NONE, absolutely none that I can see. Firstly, the image is famously ‘non-directional’, i.e. lacking patterns of light and shade that give a clue as to direction of incident light (meaning there was no incident light, and effectively ruling out a brush-painted portrait – unless the artist was deliberately trying to imitate the look of an imprint, but making too good a job of it, given the negative image).
What a pity then that we don’t have a recurring motif, like my little discs, or links on a chain, spanning the entire width of the body that could allow us to detect a maintenance of shape consistent with imprinting . Or at any rate, we don’t with the image as we see it now. But what if it’s been altered or otherwise been tampered with? What about that peculiar ‘coiled rope’ at waist level that one sees on the Lirey badge, and better on discoverer Arthur Forgeais’ line drawing? It’s not a lot to go on, admittedly, but it’s time maybe to take another long hard look at that ‘coiled rope’to see if there’s evidence of an initial image that was later seen as maybe too imprint-like*, and amended accordingly (while acknowledging that it’s easier to add to a roasted flour imprint than to take away). Of course, one could always add something else on top, like blood, to mask what was underneath, turning a coiled rope into Wilson’s somewhat stylized “blood belt”. Or there again, considering this blogger’s aversion to 99% of conspiracy theories, he might decide not to go down that road…
*This needs a little word of explanation, or at any rate qualification. The TS image may have been designed to look like an imprint of a crucified man, and then executed as such, i.e. by imprinting off a template, whether human or inanimate.
But there was a fine line to be trod: while looking at first sight to the medieval eye like an imprint, correction, double imprint on up-and-over linen (as might have been left by a real man 1300 years earlier) it must not on any account have looked like an obvious ‘modern’ imprint (modern being mid-14th century). Indeed, there had to be a certain ‘ghostly’ quality about it, with fuzzy and indistinct features, indeed, more ambitiously, an enigmatic negative image that may or may not have been immediately recognized as signalling an imprint rather than an artist’s portrait.
The genius of the TS was to create an image that was not immediately capable of being mentally pigeon-holed into this or that artistic genre, one designed to mystify. The rest as they say is history – with many layers of ‘mystification’ added in later centuries by those who have fallen under its spell. Never underestimate the creativity and resourcefulness of the human mind, once encouraged, determined and no doubt rewarded to achieve a certain pre-set goal, especially if that is defined as curing the sick, averting ill-health or saving wayward souls.
Update: 23rd Feb 2016
Suppose, just suppose, that the TS image we see on the linen had suffered a degree of ‘lateral distortion’, or at any rate, lateral expansion, as a result of imprinting off a 3D subject. What would the “real” subject look like if one could somehow correct for that effect?
What you see below is a very crude attempt to make that correction. I have taken the Durante face from Shroud Scope, printed it out to get a photo that is approx. 1/3rd the circumference of a wine bottle, then stuck it to the side of the bottle, then re-photographed with the camera ‘square on’.
Here’s the very first result, with factors still to be controlled, especially colour, but which give an idea of the likely degree of distortion generated by a contact-imprinting model.
Ouch. The colour difference is a huge distraction, and the bottle-mounted image has been cropped too severely. Here’s the same after after tweaking: