# Fermi-Bayes and the Shroud of Turin

 How Fermi could estimate things! Like the well-known Olympic ten rings, And the one-hundred states, And weeks with ten dates, And birds that all fly with one… wings. ― David Morin, “Introduction to Classical Mechanics”, 2008 Imagine it’s true.  Then imagine it’s not. How likely in each are the facts that you’ve got? The odds of the facts times the odds for the thought say how sure or unsure you ought be of what’s what. ― myself, 2012

Not long ago, Mark Shea proudly trumpeted the upcoming informal non-peer-reviewed publication of new analyses performed on the Shroud of Turin by a man with a long history of arguing that the Shroud is the burial shroud of Jesus of Nazareth.  I like Mark and often read his blog.  I get the impression that, unlike most conservative Catholic bloggers, Mark isn’t a raving bigot, and that when he spews calumny about people, he does so only because of his religious persuasion and not because of his personal inclination.  And when he endorses poppycock, he appears to do so as an ordinary, untrained human thinker rather than due to any special perverse motivation.  I thought it would be interesting to examine the publicly available evidence about the Shroud of Turin using a Fermi estimate of Bayesian reasoning.

The claim is that the Shroud of Turin is the burial shroud of Jesus of Nazareth.  I’ll start with an “ignorance prior”, a subjective a priori estimate of the probability of the claim. The claim could be true or it could be false. Those are two options and the claim is one of them, so I’ll call the prior probability 50%, which is 1:1 odds. That’s my starting estimate before looking at any evidence. And it’s a Fermi estimate, so don’t whine about the imprecision.  Imprecisely making use of what little evidence happens to be available is how Fermi estimates are done.  There’s a lot of evidence regarding the Shroud of Turin, actually, but detailed analysis of it depends on expertise in dozens of fields, none of which I will ever have.  That’s virtually the same as the evidence being unavailable to me.

The counter-claim (“No, it isn’t.”) is exceptionally broad, as the possibilities are literally endless. It could be, as Mark mentioned, a deliberate medieval forgery. It could also be a genuinely miraculous burial shroud, but of someone besides Jesus. It could be a normal burial shroud to which forgery was added. It could be a freak occurrence of natural and accidental effects that happened to a real but ordinary burial shroud.  It could be an artistic work that was not intended to be a forgery but for which the provenance was forgotten. It’s too hard to work with all of these at once, so I’ll pick the same one Mark picked on. That means it will fit better with some evidence than the alternatives and less well with other evidence. The Fermi estimate method relies on the tendency of errors to cancel out, so that the result, though terribly imprecise, is usually a good guide to the truth.

My first thought was to take as evidence whatever has enough scientific/historical/social consensus behind it to have made it onto the Wikipedia page for the Shroud of Turin. I wouldn’t be surprised if that’s where criticism of my estimate will primarily come from, as advocates and debunkers will have their own special cache of evidence that they’ve collected and believe in but that isn’t generally known or accepted enough to be on the Wikipedia page.  For all the pieces of evidence below, I’ve listed my sense of the likelihood for both hypotheses and the odds ratio between them in the order {pro-genuineness:pro-forgery}.  If you disagree, then change my numbers to your preferred numbers and see what effect it has on the overall product of odds ratios.

Image

• The image is a negative and has a 3D effect.
• Images produces by bodies pressed against something are positive images and have no 3D effect. So the argument goes that it’s a miraculous effect.  This is used in response to many objections about the Shroud, but to avoid double-counting, I’ll only mention it here.  Miracles aren’t everyday things, so I’ll toss out a very generous rough estimate for now that one image out of every thousand is miraculous. Probability estimate: 0.1%.
• On the other hand, you could easily make a 3D effect if you were painting a forgery, and you certainly would if you intended the forgery to look lifelike.  And if the paint were washed off in an acid wash to make the cloth look old, that would leave a negative image. Probability estimate: 30%.
• Likelihood ratio for this piece of evidence: 1:300.
• The image is of the front of a man with straight posture and hands hiding the crotch.
• There are no side impressions, so if it’s the linen that was wrapped around Jesus, it’s surprising that it fit the top like a nice portrait but didn’t drape down his sides.  Probability estimate: 20%.
• A painting would definitely focus on the frontal portrait. Probability estimate: 75%.
• Likelihood ratio for this piece of evidence: ~1:3.
• In the image, the man obscures his crotch with folded hands.
• It would be difficult to keep a limp body in that position while rigor mortis was setting in.  Probability estimate: 10%.
• Carefully arranged genital modesty is exactly as expected from medieval sensibilities.  Probability estimate: 70%.
• Likelihood ratio for this piece of evidence: 1:7.
• The image is 5’7″ to 6’2″ tall.
• That would be tall for Jesus’ time period, which would be unexpected since nobody mentioned his height.  Probability estimate: 25%.
• It would normal or tall for a medieval artisan. Probability estimate 70%.
• Likelihood ratio for this piece of evidence: ~1:3.
• One wrist has a large splotch. The other is not visible.
• That’s exactly what we’d expect if it’s one of Jesus’ wounds.  Probability estimate 90%.
• Many artists would have put the wound mark on the hand, however, rather than the wrist.  Probability estimate: 10%.
• Likelihood ratio for this piece of evidence: 9:1.
• One ankle has a large splotch. The other does not.
• Why only one wounded ankle?  That’s quite unexpected given the Gospel accounts.  Probability estimate: 10%.
• This feature is still unexpected as an artisan’s rendering, but an inaccurate painting is less surprising.  Probability estimate: 15%.
• Likelihood ratio for this piece of evidence: 2:3.
• The left flank has a large splotch, presumably from a wound.
• That’s exactly what we’d expect from the Gospel accounts.  Probability estimate: 95%.
• That’s also exactly what we’d expect from a forged image based on the Gospel accounts, though inaccuracies may happen. Probability estimate: 90%.
• Likelihood ratio for this piece of evidence: 19:18.
• The forearms have streaked stains.
• We would expect Jesus’ skin would have been washed and so bleeding only from the wounds when it was entombed.  Probability estimate: 15%.
• Artists do generally add extra rivulets of blood for effect to images of Christ during his Passion.  Probability estimate: 50%.
• Likelihood ratio for this piece of evidence: ~1:3.
• The forehead has streaked stains.
• That’s exactly what we’d expect from the Gospel accounts.  Probability estimate: 95%.
• That’s also exactly what we’d expect from a forged image based on the Gospel accounts, though inaccuracies may happen. Likelihood estimate: 90%.
• Likelihood ratio for this piece of evidence: 19:18.
• There are lots of other splotches and stains all over the cloth.
• If the cloth is genuine, it probably had a very rough history.  Probability estimate: 90%.
• If the cloth is a forgery, it would have been made to look like it had a rough history, and then it would have a real rough history afterwards.  Probability estimate: 90%.
• Likelihood ratio for this piece of evidence: 1:1.
• The image darkness undulates.
• A miracle of wavy quality is a bizarre supposition.  Probability estimate: 5%.
• A wavy quality is not especially surprising as an artifact of an artistic technique.  Probability estimate: 10%.
• Likelihood ratio for this piece of evidence: 1:2.
• Forensic experts disagree on how anatomically realistic the image is, with some insisting it’s artwork and some insisting it’s compatible with a real figure.
• If it were from a human figure, there’d be virtually no doubt about the proportions.  Probability estimate: 10%.
• An artist would be pretty likely to get it subtly wrong, though. Probability estimate: 70%.
• Likelihood ratio for this piece of evidence: 1:7.
• If it’s a painting, the method of medieval painting has been well-known for hundreds of years. Replicas were made by Luigi Garlaschelli using medieval acid-wash techniques, Nicholas Allen using medieval photographic techniques, Jacques di Costanzo using medieval bas-relief, and many others. The quality is disputed.
• If the Shroud is a miracle, it is a surprising coincidence that the techniques for forging it just happen to become available when records of the Shroud first appeared.  Probability estimate: 2%.
• If the Shroud is a medieval artifact, then of course medieval techniques can make it.  Probability estimate: 90%.
• Likelihood ratio for this piece of evidence: 1:45.
• X-ray fluorescence and infrared thermography showed no paint pigments.
• This is exactly what would be expected from a miraculous image, provided no one tried touching it up with paint later.  Probability estimate: 95%.
• This would be quite surprising if the shroud is a forgery and limits the number of available techniques that could have been used.  Probability estimate:  5%.
• Likelihood ratio for this piece of evidence:  19:1.
• There may be images of coins on the eyelids from 29 AD. This is disputed.
• If the Shroud is from Jesus’ burial, it supposedly showing the Greek custom of putting coins on eyelids is slightly surprising but not shocking. Probability estimate: 50%.
• Coins can be painted just as easily as really placed, but it would be surprising if a forger knew what the old coins looked like. Probability estimate: 5%.
• As this piece of evidence lacks consensus that it’s even real, I’m cutting its evidential weight in half.  Likelihood ratio for this piece of evidence: 10:1.

Provenance

• There are no clear records of where it was before 1390 AD. The first clear mention is from the 1350’s.
• Since possession of Jesus’ burial Shrould would have been a majorly big deal, the lack of mention for over a thousand years is utterly shocking if the shroud is genuine.  Probability estimate: 0.1%.
• On the other hand, it’s exactly what would be expected if it’s a forgery, unless it’s a forgery and a genuine Shroud also existed. Probability estimate: 98%.
• Likelihood ratio for this piece of evidence: 1:980.
• Records first pin down its location (Lirey, France) in 1390 when the bishop with charge of it wrote that it was a forgery and the artist had confessed.
• If the Shroud is genuine, it’s a shocking coincidence that the very first unambiguous account of its provenance is the relevant Church authority declaring to his superior that he had researched the matter and found it to be a fake.  Probability estimate: 1%.
• If the Shroud is a forgery, the fact that the bishop thought so and that someone confessed to forging it are unsurprising, although it’s possible the bishop may have acted without adequate justification.  Probability estimate 80%.
• Likelihood ratio for this piece of evidence:  1:80.
• Clear provenance is established since then.
• If it’s genuine, why should provenance suddenly clear up as soon as the bishop declares it’s a recent fake? That’s another surprising coincidence.  Probability estimate: 10%.
• If the bishop was right, then provenance records suddenly being available makes perfect sense. Probability estimate: 85%.
• Likelihood ratio for this piece of evidence: ~1:8.

Fabric and material

• Three independent carbon datings of the material gave a 95% confidence interval that it was made in 1260-1390 AD. The cloth patch from which the datings were done was uncharred and showed no weaving flaws on either side. Statisticians say the radiocarbon dates could be off by about two centuries.
• The 95% confidence interval being 1230+ years off is vanishingly unlikely.  Far more likely would be some unknown systematic error.  Probability estimate 0.25%.
• The confident interval exactly matches the historical records.  Probability estimate 95%.
• Likelihood ratio for this piece of evidence: 1:380.
• Art historian WSA Dale, assuming it was art, dated it to the 11th century.
• If it’s genuine, the fact that it looks like medieval art is slightly surprising.  Probability estimate: 30%.
• If it’s a forgery, it makes sense that the forger would try to make it look old, but have a culturally influenced notion of what old images look like.  Probability estimate: 60%.
• Likelihood ratio for this piece of evidence: 1:2.
• The herringbone twill weaving method of the shroud does not match the simple two-way weave of the only confirmed 1st century burial shroud from near Jerusalem.
• If the Shroud is genuine, a match between it and the confirmed shroud is more plausible than a mismatch.  Probability estimate: 30%.
• If it’s a fake, we wouldn’t expect a match.  Probability estimate: 90%.
• Likelihood ratio for this piece of evidence:  1:3.
• A seam in the cloth uses a 3:1 twill weaving, and so does a confirmed 1st-century Syrian cloth.
• That at least some of the weaving techniques are confirmed to have been used in the right area and era is definitely expected if the Shroud is genuine.  Probability estimate: 95%.
• That at least some of the weaving techniques are confirmed to have been used in the right area and era is still likely if the Shroud is a fake, but there’s a greater possibility of no matching techniques.  Probability estimate:  90%.
• Likelihood ratio for this piece of evidence: 19:18.
• Pollen grains on the shroud mostly match pollen grains from Jerusalem, but different areas of the cloth have different pollen.
• Wow, that’s really impressive. It’s exactly what we’d expect if the shroud had spent time unprotected near Jerusalem, though it’s slightly surprising that those pollen grains stayed lodged in the Shroud over the course of thousands of years, but scarcely any others did.  Probability estimate: 99.8%.
• If it’s a forgery, achieving the same effect would need smudges from pilgrims or, as is usually proposed by critics, deliberate contamination, which would explain the different pollens in different areas of the cloth.  Probability estimate: 1%.
• Likelihood ratio for this piece of evidence: 100:1.
• Travertine aragonite limestone dirt on the shroud matches limestone from ancient Jerusalem tombs.
• This is not particularly surprising if the Shroud is genuine.  Probability estimate: 85%.
• Bah, travertine’s everywhere, especially in artisanal workshops. But if the Shroud is a forgery, it would be somewhat more likely that some of the dirt would be something special not found in Jerusalem tombs. Probability estimate: 15%.
• Likelihood ratio for this piece of evidence: ~6:1.
• Repeated testing of the dark reddish stains confirms they are blood but cannot confidently determine the blood type or any DNA features.
• The presence of blood is exactly as expected for a genuine.  Probability estimate: 99%.
• A forger probably would paint with at least some blood to make a Shroud look like Jesus’. The forger was claimed, as it happens, to have been a murderer, so him getting blood is not surprising. Probability estimate: 60%.
• Likelihood ratio for this piece of evidence: ~5:3.
• No chemical traces of bodily decomposition such as occurs in the first hours after death are found on the shroud.
• There’s no indication from the gospels that Jesus’ body was preserved from any decomposition. It seems fitting, though. But it’s still surprising; no one predicted it.  Probability estimate:  15%.
• Whereas if it’s a forgery, the lack of bodily decomposition chemicals is nearly guaranteed. Probability estimate: 90%.
• Likelihood ratio for this piece of evidence:  1:6.
• There are no bodily proteins or fluids other than blood on the shroud.
• If it were genuine, surely some other organic traces besides blood would get embedded in the cloth.  There were other tissues embedded in the confirmed 1st century Jewish shroud.  Probability estimate:  15%.
• But if it’s a forgery, that’s unsurprising because it’s easy to paint with blood whereas the artist would have no reason to rub flesh on the cloth. Probability estimate: 85%.
• Likelihood ratio for this piece of evidence: ~1:5.

OK, time to multiply up all the odds. My final estimate comes to: 1:1,143,000,000,000 or 99.99999999991% confidence it’s a forgery. The exact number is unimportant.  The reason it can be such an extreme value is that there are many pieces of evidence available for the Shroud of Turin.  Most subjects you examine will have far fewer pieces of evidence!  Particularly compared to extreme values like that one, it’s far more likely that I’ve made math errors, acted systematically on unconscious biases, or that I’m dreaming or hallucinating right now.  What matters from the Fermi estimate is that it should point in the right direction.  I thought I was being really really generous to the pro-genuine evidence!  So my conclusion is this: the balance of the available evidence is strongly against the Shroud of Turin being the burial shroud of Jesus of Nazareth.

Have you ever tried tallying up pros and cons in a list to help you make a decision?  I have, many times.  It’s usually worthless, because it’s easy to invent new pros and new cons to balance out the list.  The combined Fermi-Bayes method offers a better tool to help you make a decision when you can’t weigh all the evidence in mind at once.  It can be particularly valuable when you and another person initially disagree, because if you can come to agreement on your likelihood estimates, then you can be more assured that your individual biases will have canceled out.

I’m unusually gratified by the only response I got on another forum when I mentioned this matter:

I’m glad you’re no professor or scholar. If you’re idea of research is Wikipedia & saying crap like “the odds are one chance in millions of being genuine” (after ignoring the evidence presented to you), please keep your job at McDonald’s & don’t even think about becoming a researcher/scholar. You’re too lazy & close-minded. Please, look at the evidence- not some Wikipedia piece. I don’t mean to insult you, but yeah. BTW I have nothing against working in McDondald’s, I use to h
― “Tom Avery”

Popular legend has it that there was an ancient Chinese curse, “May you live in interesting times.”. The backwardsness of the curse, plus the above idiot’s insult, suggest an equally backwards blessing: “May you have Internet blog commenters for enemies.”.