Good afternoon, we're going to be talking about understanding the carbon dating of the Shroud today. And the outline of this presentation is, first of all, in general we're going to be talking about what is carbon dating, and specifically about the Shroud. We'll talk about the details of the 1988 carbon dating of the Shroud of Turin. We'll then go over the objections to the carbon dating, and then explanation of the carbon dating. I made a list of eight different objections that I commonly hear to the authenticity of the Shroud of Turin, and this is kind of in the sequence of how frequently I hear them. Miracles are impossible, the carbon dating of the Shroud to 1260 to 1390 AD. Shroud's history only goes back to about 1350. What I'm saying is, these are all the objections. I don't believe any of these are legitimate. The Diarchus Memorandum, Walter McCrone's painting hypothesis, oh it's just another relic in the Catholic Church. Luke 24.12 refers to multiple clauses. Fabric would have decayed by now. I think there's good responses to all of these, but the most difficult one to respond to for the layman is the second one, carbon dating to 1260 to 1390. And that is because people are not familiar with statistical analysis of scientific measurements. And because I could explain what the problem is in one sentence, but you wouldn't understand it. So therefore, we have to go through quite a bit of detail on this to try and explain it all. So first of all, as we go into what is carbon dating, we have to understand what carbon is. So carbon is an element. An element is defined as all the atoms of that element respond chemically to other atoms in certain ways. So that all carbon atoms respond to other atoms in certain ways. And they respond to the other atoms based upon their electrons. Now an atom looks like a little solar system. The heavy mass of the atom is in the center called the nucleus. The electrons circle around it. Now carbon atoms have six protons in the nucleus. Each of those protons has a positive charge. And because each atom has to be neutral, then there has to be six electrons, each with a negative charge, circling around it. Two electrons are in the inner orbit, as shown in the diagram. Four electrons are in the outer orbit. The outer orbit can contain up to eight electrons, which then those outer electrons in the outer orbit then bind to the surrounding atoms. And in a cellulose molecule, you will have those four outer electrons binding to four different atoms surrounding the carbon atom, typically, so that there's one electron bound to each of those four atoms around it. Now, carbon can also have various numbers of neutrons in the nucleus. We have carbon-12. Now, you see that the carbon right here. Lower left subscript is six. That means that there's six protons in the nucleus. To the right of the superscript, 12 means that there's 12 protons plus neutrons in the nucleus. So there's carbon-12, carbon-13, and carbon-14 because there are either 6, 7, or 8 neutrons in the nucleus. So that's what a carbon atom is. Typically, carbon is carbon-12 with just 6 neutrons, but you can have carbon with eight neutrons. And the problem with that is that the ratio of neutrons to protons is too high so that the atom gradually decays. And across the bottom I list the decay scheme. Carbon-14 simply goes to nitrogen-14 when it ejects an electron. The key item here is the ratio of carbon-14 to carbon-12. That's what is actually measured in what's called carbon dating. Now, in living plants, what you have is over to the far right-hand side, you see, we list over here the isotopic fraction, fraction of the atoms, essentially, that are carbon-12. 98%, 99% carbon-12, about 1% carbon-13. Carbon-14 is down in the very small range, about 1 part in 10 to the 12th. So it's extremely small. But what we're interested in here is the ratio of carbon-14 to carbon-12. So it's this number divided by that number, which essentially equals 1 times 10 to the minus 12, or 1 part per trillion. is carbon-14, and that's what is measured in carbon dating. That ratio is what's measured. Now, so what happens, as a plant is growing, for example, the Shroud of Turin is made out of linen, which is made from the flax plant. So as the flax plant is growing, the carbon-14 that's already in the plant is decaying, but there's new carbon, including carbon-14, being brought into the plant in photosynthesis. So that an equilibrium is reached with some cocaine and some new coming in. So what I'm plotting here up to point zero when I'm saying let's cut down the flax at point zero. there would be a uniform amount, let's call it a hundred percent, actually one part per trillion. And so that then when you cut down the plant, then the carbon-14 decays along this curve, typically, with a half-life of years, which means that in 5,730 years, should you live that long, you would have half as much carbon-14 at that point as you started with. And then in another 5,730 years, it would be decreased by half again. So that you can see here, by measuring the amount of current carbon-14 that you have in the plant, in measuring the ratio of carbon-14 to carbon-12, whatever value you come out with along this y-axis, you then simply come across to this point and that gives you the age. And that's what they did in carbon-14 dating. They measured about 92% of what they would expect the amount of carbon-14 to be, actually measuring the ratio of carbon-14 to carbon-12. So instead of one part per trillion, it was 0.92 parts per trillion. So they came at this point from 0.92, came across, down, get to the age of 1260. Very simple. But the problem is there's assumptions in this. The assumption is that the ratio of carbon-14 to carbon-12 has not been altered by anything. So how is carbon dating done? The carbon-14 to carbon-12 ratio is what's measured experimentally using equipment people and procedures, standards and chemicals. Now I'm saying that all that process was correct. They used the equipment, had no fault in it, the people and procedures were proper, the standards and the chemicals were proper. So once they determined the correct ratio of carbon-14 to carbon-12, then they used that ratio to then calculate the date based upon this previous graph. Now I'm showing it graphically here, but it's normally done by equation. And the assumption is that the carbon-14 to carbon-12 ratio has only changed due to decay of carbon-14, but it's not been altered by other factors. And most other factors that people can think of have a very small effect on this ratio of carbon-14 to carbon-12. But I'm going to give you another option that I think is actually the case. So as a nuclear engineer, I'm often asked, is carbon dating accurate? And I say, yes, it's accurate, provided that the sample's carbon-14 to carbon-12 ratio is changed only by decay of the carbon-14. It hasn't been altered by anything else. That's the assumption that has to be made. So the measurement of the carbon-14 to carbon-12 ratio in the samples is accurate within the stated uncertainty. And so that whenever they give you a date, they've already calculated forward the uncertainty on that. And we'll talk about uncertainty in just a second. But the carbon-12, 14 to carbon-12 ratio in the sample may have been altered, and that's the issue. This would result in the carbon date not being the true date, and that's what we're after, what is the true date. So, let's go into a little bit on uncertainty in the measurements. Now, there's two sources of errors in scientific measurements. There are random errors and there are systematic errors. Now, random errors is usually what you think of. And it's random in the sense that it can be a little bit high, it can be a little bit low on the measurement. Measurements can be a little bit high, a little bit low. They're kind of random. There's various sources of these random errors. And so it's very easily dealt with by taking many measurements and then averaging the result. Because in taking many measurements, sometimes the error's going to be a little bit high, sometimes it's going to be a little bit low, but in many measurements, Those that are high will cancel those that are low, in general. So that's how scientific measurements are done. And that's why they don't just take one measurement. Isn't that interesting? On the carbon dating of the Shroud of Turin, they took 16 measurements by three different laboratories. The total of the three different laboratories. Now the other type of air is a systematic air, and this is where it becomes a little bit, maybe a little bit more difficult to understand. It would be like if I gave you a ruler and asked you to measure the dimension of this room, and you take the rule, you lay it down on one side, you put your finger here, then take the ruler, move it over, put your finger again, move the ruler over, and you get a number when you get down to the end. Now the random error would be in the process of putting your finger down and moving the ruler from one side to the other side of your finger. That would be the random error. It can be a little bit off one way or another. But then after you finish the measurement, if I told you that the ruler that I gave you was not a true 12 inches, It was only 10.5 inches in reality, though you look at it, and it looked like it was 12 inches. That would be a systematic error. No matter how many times you did the measurement, no matter how many different people did the measurement with that ruler, it would always be off. That's a systematic error. Now, systematic errors are not random. Little bit high, little bit low. No. In general, they're in one direction only, and they're a function of something else. And on the Shroud of Turin, it was a function of the location according to our neutron absorption hypothesis. So that we did encounter a systematic error and the problem with the way that they did it was that they did the statistical analysis in a way that didn't recognize that they had a systematic error. If there's a systematic error, if I just told you that the ruler was not a true tool of inches, then how would you correct the dimension that you obtained? If I didn't tell you how much off it was, you'd have no way to correct it. You'd simply have to reject the number. And that was the problem with the carbon dating of the shrub. They failed to recognize that there was a systematic error, that they should have simply rejected the data. Period. But they didn't. Matter of fact, one of the reviewers required them to reject the data. But his requirement was rejected when they published it. Interesting how science is done sometimes. So a systematic error is a function of something such as location. It's usually all in one direction, either positive or negative. It cannot be minimized by doing many measurements. And it produces a systematic bias. So that if you did your measurement across the room and then I told you the room was only 10.5 inches, then you could correct it. The difference between your, let's see, 93 feet that you read from your ruler, and the actual value of 105 feet, that difference would be the bias, it'd be the systematic bias. And so, that if there's a systematic bias, and you don't know what that bias is, you would have no assurance that the measurement value is the true value. The only option would be to reject the data, and that's what they should have done. Now, why is there uncertainty in measurements? Typically what you have, as I said, a random error can be a little bit high, a little bit low, to varying degrees. And this is the typical type of curve that turns out to be true, that at this point you have a peak value of this curve, but it can be a little bit high or a little bit low. Across this range, about 68% of the data will fall into that range. That's called 1 plus or minus 1 sigma. Within twice that range, plus or minus 2 sigma, you have about 95% of the data. And within plus or minus 3 sigma, you have about 99.7% of the data. And this is just a normal distribution, also called a Gaussian distribution, also called a bell curve. Perhaps you've seen this in some of the literature. So that any measurement that you take, if you take a measurement and you say it's this value, you're not sure that the true value is exactly that value because of the measurement errors, those random errors and systematic errors. Due to random errors alone, the true value could be anywhere along this curve if your actual measurement is right there. I hope that's clear enough. So, to try and make this clear, let's take an example from my background. This would be something that could have happened. It didn't actually. But let's say that you're working in the nuclear industry, as I did for 38 years. Your boss comes in and says, we have an old tank that's 14 feet 3 inches high, just happens to be at the same height of liquid in the tank as the dimension of the Shroud of Turin. This is interesting. Okay, and your boss says, we have to do this right, go in and take three measurements, and to be accurate, let's send them out to three different laboratories, make sure we get the right analysis on the material in the tank. Because we're concerned about it. If the amount of uranium in that tank is too high, we'll have to clean it out. And that'll cost hundreds of millions of dollars. And with the economic situation of the company, that could force us into bankruptcy. There could be 12,000 people laid off in the company worldwide if we have to clean that tank out. That's the human factor coming into how you interpret the data. So take three measurements on this tank. So you do. You go out and you take three different measurements. Now what you do is you insert a a little item, a little volume that you open the door and the material flows into it, then you take it out and you send it to the laboratory for measurement. Now, before you do this, you know that there's a concern over material settling in the tank. So you turn on the mixer. Now, the mixer is just bubbling air up through the tank, and that's supposed to mix it all, okay? So you let that run for a day. 24 hours. You then go in and you take these measures. You take three different measurements, and I list the results here. Sample one that you take is 1,200.8 milligrams per gram of liquid. That's milligrams of uranium per gram of liquid. The uncertainty there is 30.7. That talks about the width. That's the one sigma uncertainty on that normal distribution. And that was taken just 5 centimeters into the tank. The next one is 1,273.9 with the uncertainty of 23.7. That was taken just 6.4 centimeters into the tank. The third one is 1,303.5 with an uncertainty of 17.2. And that was taken only 7.7 centimeters into the tank. Okay, now you may start to wonder, suspect what the problem here is. So the question, when your boss comes in, he says, and you show him the results, your boss says, what do these results mean? Okay, so you draw a graph of it. So this is the graph. There are the three different points on the scale of uranium concentration of micrograms per gram of solution. This is the distance from the top of the tank. Okay? Now, what do the results mean? Would you simply take those three different values and average them to get that value? 1,260 micrograms per gram. The boss likes that because he would then conclude, okay, we know what's in the tank. There's no problem with excess uranium in the tank. All you have to do, he says to you, assure me that that is a correct answer for those three points. How do you approach this? And then your boss says, oh by the way, if you tell me that this curve is not the correct curve, but that it should be this curve, your job could be in jeopardy. That's the human factor coming into it. Now you may have suspected already that Those are the same values as were obtained for the Shroud of Turin, though not uranium concentration micrograms per gram. It was actually the dates that were obtained. So again, what's the correct answer? Now, this is the uncertainties. on this hypothetical example, as well as on the Shroud of Turin. This was the uncertainty. Now, if the uncertainties were one-third as high, if it was like this, then you could definitively say that that black curve is not correct, because it has to be this curve. And you don't need high-powered mathematics for it. Now, there are mathematical formulations that can solve this problem. But you just kind of look at it with your eye and you say, yeah, that's the correct curve. Now, if the uncertainties were three times as high, you'd get this. And then you'd say, well, gee whiz, it could be either one. And because of the human factor, because my job's at stake, we're going to call this one as being correct. And that's how science is done. Unfortunately. Okay, so if we go back, this is a curve that will show the same curve with a different X and Y labels on the axis later on for the Schrödinger-Turin results. So, now you would think that when they did the carbon dating in 1988, that the goal would it be to obtain the correct date for the Shroud of Turin? Wouldn't that be a reasonable assumption? Unfortunately, they had no such idea. Their main goal was not even related to the Shroud of Turin. Isn't that interesting? For example, their main goal was to validate the accuracy of what they called the small sample dating technique. It was a brand new dating technique. Instead of requiring a dating of a very large piece, they could date a very small piece. They wanted to validate that, and why would they like to validate that? Financial gain. Big money, hundreds of, I would assume millions of dollars involved in proving the small sample dating technique. Now to prove the small sample dating technique, what they wanted was to accurately date a very high profile item. And at that point in time, what higher profile item could there be in the Shroud of Turin? I showed you the four-page foldout yesterday from National Geographic. It was a very high profile item at that point. But you notice, their means is to accurately date a very high profile item, but in choosing the Shroud of Turin, When I say that, to accurately date, what does that mean? You have to know what the date is. You have to do the experiment, do the calculation, and have it turn out right, whatever right means. So you have to know the date of the Shroud of Turin. So what they did was that they assumed that the earliest date for the continuous history of the Shroud, which was mentioned yesterday, about 1355 to 1356, was the earliest date for the continuous known history of the Shroud of Turin. That's when they showed it up in Le Ray, France as the Buried Cloth of Jesus. But as I showed yesterday, it is, I believe, well historically attested that it was in Constantinople long before that 1355 or 1356 date. So what they did in their experiments, they used the accelerator mass spectroscopy, that's AMS, to accurately date the shroud. Now, in accurately dating the shroud, what were they measuring? The ratio of carbon-14 to carbon-12. But then they took that ratio and applied it using their assumption that the shroud of Turin, now listen, the shroud of Turin was just a normal piece of cloth and had not gone through anything unusual. That's the assumption. To allow them to use what I showed you on the black curve as it gradually decayed. So their assumption was that it was a normal piece of cloth that was first shown in Lorraine, France, 1355-56. Now this is the paper that came out in 1989. reporting the values and doing the statistical analysis to the extent that they wanted to report it from the 1988 carbon data in the shroud. They sent it off to three different laboratories. The averages of the three different laboratories was 1260 Nd. It was 31 years. so that that value is then corrected for the changing carbon-14 in the atmosphere and so that based on the assumption that the 1260 was correct, they then corrected that to obtain a range of 1260 to 1390 AD and they said that that was a 95% curve, which means that there was a 95% probability, they said, that the true date falls within that range. So they concluded then, these results provide conclusive evidence that the linen of the Shroud of Turin is medieval. Now this is the statement that one of the reviewers required to be deleted because this conclusion does not follow from the inadequate statistical analysis. But nature wanted to publish it, and so they did, with that statement in it. Now, this is how they cut the sample. This is an actual picture of them cutting the shrub from the lower corner, below the foot on the front image, which would be right about there. That's where they made the cut. The next one, I'm going to show you this area. closer of that diagram that I made up. What you see here, this is the main shroud piece. This is a side strip that was evidently cut off during the manufacturing process and then reattached. That's what we think happened. And so this is the seam that reattaches that side strip to the main shroud piece, they would always hold it up from the side so the two corners I think just tore off due to use so that this part here is actually, you're seeing the backing cloth. on the Shroud of Turin when you look up here. Anyway, this is where they made the cut, right here, about eight centimeters by about 1.2 centimeters, 1.5 centimeters, somewhere in there. They then cut the seam off. They cut here to send to Arizona. They then cut here and here to send to Zurich and Oxford. In measuring them, they found that the samples for Zurich and Oxford were a little bit larger than 50 milligrams. They wanted to send at least 50 milligrams. But the sample that they had cut for Arizona was only about 35 milligrams. It was inadequate. So they cut a second piece to go to Arizona. So A1 and A2 went to Arizona. They actually took A2 and simply put it into the vault. It's in the vault to this day, which is very interesting. So that each of the laboratories then cut subsamples from each of those for dating. So these are the results that we obtained. So at Oxford they did three different measurements, Zurich five, and Arizona, which is interesting, in the publication they said that Arizona only dated four, but they dated eight. Why would they deceive us like that? That really was a deception as far as I'm concerned. Why couldn't they tell the truth about it? Well, because there's problems in their statistical analysis. So that when we take all eight values, it took, what, 25 years to get the values for the eight values instead of the four? They wouldn't release them. So it took, I think it was several Freedom of Information Acts submitted to the British Museum to actually get the hundreds of pages of all the background data to the measurements and the statistical analysis. And that was just obtained two years ago and the experiments were done in 1988. Amazing how they could be withheld for that long. It kind of indicates that something is going on. So these are the values. When you just average them, these are the values. And those are the same values that I used on the hypothetical example of testing the tank of uranium in liquid. And so let's see what else we can see here. Oh, you can see that the values are increasing from one to the other. Let's see. Part of the reason for them reporting only four values, Arizona tested two samples, two subsamples, each day for four days. And so the British Museum said, well, yeah, you've got problems here. Just average the values from each day. So that's what they did. And in the process, they eliminated both the high and the low values from Arizona, trying to bring everything into agreement. The problem was that the range of the data exceeded what there should be based upon the measurement uncertainties. And that was the problem because that indicated the presence of a systematic bias. Interesting. Let's go into objections to the 1988 carbon dating. Well, we have historical evidence that the shroud existed long before 1260 AD. The image could not have been made in the range of 1260 to 1390. They didn't have the technology to do it. We don't have the technology to do it today. There's 13 other contradictory date indicators. Since I made up this slide, there's probably one or two more. The different laboratories don't agree with each other. The date depends on the sample location. Detailed statistical analysis shows that the constant value of 1260 has a very low probability of being true, and that there are many different proposed explanations for the carbon dating. I'm going through this very quickly, but that's the sequence that I want to talk to you about. Let's go into the history of the Shroud of Turin before 1260. So that I talked to you a little bit about the Hungarian pre-mourning script yesterday, and I showed you just the bottom page. I'm showing you the full page now. The upper scene is the three men doing the burial. The bottom page is what I showed you yesterday. It shows you the herringbone pattern on the top cloth and the three the four holes in an L-shaped pattern that was evidently copied from the Shrine of Turin. Thus, this, which is dated to 1192-1195, is 65 years or so before the carbon date. And that 65 years being before the carbon date is actually 2 sigma and the range of 12, I'm talking a little bit of technical here for those people who might follow me. The range of 12, remember the range of 1260 to 1390 was already a 2 sigma. This then takes you another 2 sigma below that. So you're now 4 sigma below the carbon dating. And that's not going to occur by probability. At least that's the normal criteria. Only 2 sigma is your normal acceptance criteria. But now we're 4 sigma. The history, based on the Hungarian Prey Manuscript, is 4 sigma below the carbon dating. So based on the historical evidence of the Hungarian Prey Manuscript, the carbon dating should be rejected. This is the coin that I carry in my pocket. I've shown some of you. And this was an authentic Byzantine coin minted under Constantine VIII between 1025 and 1028, according to experts on coins. So that again, with this date down at 1025 to 1028, compared to the carbon dating to 1260, this coin that I carry in my pocket disproves the carbon dating. Now coins like this actually go back to about 675 A.D. Only they're gold and cost about $2,000 on eBay, whereas this cost about $150 on eBay. This is the Pantocrator image found in a monastery down in Sinai, dated approximately to 500 A.D. The image on this has all the characteristics of the Shroud of Turin. Before this, Jesus was pictured as bald with no facial hair at all. like the Emperor. When they found the Shroud of Turin, evidently hidden in a wall to avoid persecution, the painters then knew what Jesus looked like and painted him just like the Shroud of Turin. Full frontal appearance, parted hair and middle hair, longer on one side, full beard, mustache, long nose, large owl-like eyes, they're called So there are many different similarities. Even this little piece down here made out to be part of his clothing is shown on the Shroud of Turin though it's probably just a crease. So let's go into the image could not be made in 1260 to 1390. Now there's so many different features of the shroud like this. An artist or forger in 1260 to 1390 would not have known or been able to do so many different things, create a negative image without pigment, chemicals, liquid, or scorch that contains 3D information of the body to claw at the distance. create fiber discoloration caused by a change from single to double electron bonds in the cellulose. That's actually what's causing the discoloration in the fibers. It's the carbon atoms that are in the cellulose. Normally the four different outer orbit electrons are connecting to four different atoms, but when you change those four surrounding atoms, only three, then one of the electrons has to move over. So you create a double electron bond. That carbon atom then vibrates differently when excited by light coming in. So it fluoresces differently or it reflects differently. That's why we see a different color. because the single electron bonds have been changed to double electron bonds that were in the carbon atoms that were already in the cellulose. And how do you do that to create the image of a naked crucified man? Isn't that interesting? Interesting question. Well, so the forger would not have known about flogging or crucifixion as it was done in the first century because it was outlawed about 377 AD. And he would not have put the nails in the correct locations in the wrist with thumbs folded over, contrary to all the paintings from the Middle Ages. An artist or forger in 1260-1390 would not have known to add pollen that is unique to Jerusalem on the shroud, would not have known to add pollen from a plant with long thorns around the head. He would not have known to put microscopic dirt into abrasions on the nose and the knee in anticipation of the invention of the microscope, for example. He would not have known to put chips of Jerusalem limestone on the shrine of Turin. He would not have known to put bilirubin and nanoparticles of creatine and ferritin in the blood, indicating torture. And he would not have known to use a unique stitch from the first century to connect the side piece onto the main shroud. So we have all these aspects of the Shroud of Turin that indicate that it can't possibly be from 1260 to 1390. Let's go into 13 other dates that are contradictory to the Shroud of Turin. And I'm just going to pick out maybe one or two from each one. The Hungarian primary manuscript was 1192 to 1195. And let's see, the original painting goes back to 550. So yes, the Shroud of Turin goes way back before the carbon dating. Number 13. Testing was done by Giulio Fonti in Italy using three different tests on reflectance and tensile strength of lino as it ages and the results of his scientific experiments was that the chart of Turin dates to 33 B.C. plus or minus 250 years. Let's go into the different laboratories, don't agree with each other. If we compare the value from Arizona and Oxford, 1303 plus or minus 17, 1200 plus or minus 30.7, the difference is 102.7. When you calculate the uncertainty of the difference, you take the square of the uncertainties, add them, and take the square root. That answer is 35. So the difference between Arizona and Oxford was 102.7 divided by 35.2 equals 2.9 sigma, which exceeds the normal 2 sigma acceptance criteria, thus disproving that even the two laboratories don't agree with each other. So that indicates that there's something going on, such as a systematic bias. The date depends on the sample location. Now, this is a curve that I've now relabeled distance from the bottom of the shroud, carbon-14 date as they calculated for the samples. So I'm saying that the ratio of carbon-14 to carbon-12 was correctly determined experimentally for each of the samples. But the ratio had been altered for each of those samples so that it ought not to have been dated to 1260 by simply averaging them. And that's the problem with it. Using the uncertainties. I can calculate using a chi-squared statistical analysis technique the probability of this curve being correct or the probability of this curve being correct. Now the answer is the probability that this is the correct curve, which is what they used, is 1.4%. The probability that this curve is correct is 78%. Now if I went to a horse race and there were two horses and God told me one horse was 78% chance of winning, the other was multiple horses. One was 78%, the other was 1.4%, which should I bet on if there was the same return? The one that had the higher probability. Same thing here. They should have said, yes, there's a distribution of the dates. And you see, it's a function or depends on the position on the Shrine of Turin. Detailed statistical analysis. That's what I just did. Proposed explanations. We have eight different proposed explanations. that have been considered since 1988. The first one that was proposed was neutron absorption by creation of new carbon-14. six other proposals that have been considered and rejected. Currently, the most common explanation that you'll hear is the invisible re-weave concept, but that is that there was new material invisibly re-weaved woven into old material so that when they cut it, they got both, therefore it dated to the values that it did. I don't think that's true. There really is no such thing as an invisible re-weave. You can always see it. on the back of the cloth or by use of a microscope. The only one that's a legitimate option here is neutron absorption, but that was not followed up on until I did it in 2014. I spent about six months doing nuclear analysis, computer calculations on the Shroud of Turin to resolve the carbon-14 dating problem. So that what we're saying, the neutron absorption hypothesis is that neutrons If neutrons were included in the burst of radiation that caused the image, then some of them would have been absorbed in nitrogen-14 in the shroud to produce new carbon-14 atoms on the cloth. By the process, nitrogen-14 plus a neutron gives carbon-14 plus a proton. It's an immediate reaction. This would shift the carbon-14 date forward by up to thousands of years. So what I'm saying here is that when they found that it was 92% of the carbon-14 on the cloth that would be there for a living plant and came over to this black curve, that's where the error was made. they should have come over to the red curve because in a fraction of a second the carbon-14 was increased by about 16% and then it would have decayed according to the normal decay curve. So they should have, if they had known that the carbon had been increased, carbon-14 had been increased by 16%, they would have dated it correctly to 3080.