Reply to Art Snyder’s Note “On Ken Rahn’s Statistical Analysis of the Neutron Activation Data in the JFK Assassination” of 27 May 2001

Kenneth A. Rahn
(With help from Larry Sturdivan)
28 October 2001

At the outset, I would like to thank Art Snyder for producing his note, for only through questioning ideas can we refine and strengthen them. The fact that his criticisms work out oppositely from what he intended (most of them turning out to be wrong or irrelevant) does not diminish the inherent worth of the process he started. This is how we have to work with scientific ideas.
This document first considers Art’s major points, and then turns to his other remarks in roughly the order they appear in his note. At the end, it will be clear that Art’s note illustrates the dangers of focusing too heavily on statistics for their own sake, at the expense of basic reasoning and familiarity with the literature on the topic. The “comprehensive rebuttal” to my monograph on NAA (neutron activation analysis) and the JFK assassination, as Stuart Wexler has described it to one of the newsgroups, is neither comprehensive nor a rebuttal. It is flawed at every turn. It is, to say the least, a nonstarter. Stuart and the others who so reflexively endorsed Art’s note as destroying my monograph now need to seriously reconsider their standards for accepting and rejecting arguments, for they have erroneously accepted arguments they were predisposed toward and erroneously rejected arguments they were predisposed against.

Misdirected criticisms
One of the biggest errors in Art’s note is that it was misdirected. The NAA monograph presented two independent statistical analyses of the same NAA results, a simplified one by me and a more sophisticated one by Larry Sturdivan. The introduction to the methods stated clearly that mine sacrificed accuracy for understandability, and that Larry’s was sounder. It also noted that both approaches gave essentially the same answers. Art limited himself to mine, claiming that it gave the wrong answer because of a number of statistical errors. He didn’t touch Larry’s. But if mine was wrong and Larry’s was right, then their results could not agree. Art avoided dealing with this inconvenient truism. More importantly, if I said that we should rely on Larry’s (“it gives the best available answer”), then Art should have dealt with Larry’s rather than mine. Art avoided this problem, too. These omissions alone make Art’s note irrelevant.

NAA much broader than its statistics
The narrowness of Art’s note is another of its biggest errors. The NAA monograph constructs a multipronged argument for the correctness of the NAA and Dr. Vincent P. Guinn’s interpretation of it, but Art ignores everything except the statistics. This is no more valid than cutting off one head of a hydra and claiming that you’ve killed it—you haven’t even begun. Statistics is no substitute for gray cells.

Art’s basic conclusion
Art’s basic conclusion is that my statistical analysis was flawed and led to the false conclusion that the NAA results were definitive (that the fragments came from two and only two bullets) when in fact they were inconclusive. Anyone (he says) can see the inconclusiveness just by examining Guinn’s results from 14 different bullets, which Art reproduces in his Appendix A. I (he says) used “elaborate statistical arguments” that obscured his obvious conclusion. In other words, both Guinn and I, who have made their careers in NAA, somehow missed this “fact” that was so obvious to physicist Art. At best, this conclusion is highly questionable. Art erred by not checking himself. He should have taken the scientific approach and considered other possible reasons why his conclusions differed so much from Guinn’s and mine.

Wrong appeal to “straw man”
Art identifies four major “problems” in the monograph. The first is that it allegedly introduced and refuted a “straw man” of five separate bullets being responsible for the five fragments recovered. Art states that this only confuses the issue because no one is seriously proposing that scenario.
The problem with this criticism is that it ignores context. That particular scenario was offered solely for illustrative purposes: “The above calculations are illustrative only, and for the specific case where all five fragments fell into place ‘randomly,’ whatever that means.” My text then went on to consider in more detail a series of six graded scenarios, beginning with all five fragments being genuine and ending with two genuine and three false positives. Art doesn’t tell you that. He makes it seem as though I made a big deal out of five false positives, which I obviously did not. It’s easy to score points if you attack a nonexistent target.

Creating statements out of whole cloth
Art’s second “major problem” is that I purportedly assumed an errant probability of one for genuine matches between fragments and thereby failed to properly compare competing hypotheses. In other words, by arbitrarily setting P = 1 for true matches even though the actual probability was much lower than that, I preordained the outcome to the explanation that I liked. Or, as Art says it, I failed to consider the possibility of my “preferred hypothesis” failing.
The problem with this criticism is that I did no such thing. I did not assume any probability for a “preferred” hypothesis. I restricted myself to calculating probabilities for hypotheses with false positives (accidental matches) and showed that they were too small to accept. I added that none of these alternative scenarios could be taken seriously because no solid evidence for any of them has been produced, even after 38 years of trying. I coupled these considerations with overwhelming reasoning in favor of the genuineness of the fragments and their matches. By creating things that I didn’t do and leaving out things that I did do, Art seriously trivialized my efforts.

Misguided criticism of Ptightness
Art’s third “major problem” is that my probability for the tightness of a group of fragments, Ptightness, is a poor way to discriminate genuine and accidental matches because it allegedly is insensitive to separations that are too big for genuine matches. While there may be some truth to this, the monograph showed that it can serve as a reasonable introduction to the subject. It also gave the same basic answer as Larry’s better approach. Ironically, Art’s approach shows the definitiveness of the NAA better than mine did. He missed this because he used the wrong data. Our right data coupled with his approach confirm our earlier results and rebut his.

Confusing treatment of a priori probabilities
Art’s fourth “major problem” is my alleged use of a priori probabilities, or the probabilities for getting the actual situation that we stated with (two hits, five fragments, etc.). I found this section to be particularly confusing. By definition, an a priori probability is one that exists before one gets new information that allows one to refine the calculations. The problem I see here is that one could in principle have more than one stage of new information and refined calculations. The a posteriori probability from the first round would then become the a priori probability for the next round, and so on. Art seemed to be using a priori to refer to the situation before the shots were fired. If Art is interested in continuing this discussion, it would be very helpful for him to state exactly what he means by a priori probabilities so that we can all be talking about the same thing.
That said, it appears that Art misread the monograph, for I don’t believe I used a priori probabilities in any sense that he may define them. I used his conditional probabilities instead, as he recommended, by starting with the actual situation of five fragments and examining competing explanations for their origins. A priori probabilities would have considered the chances of having gotten five fragments, four fragments, etc., which I definitely did not do. It does not seem germane to determine how improbable the actual result was relative to other ways the assassination might have played out, because it didn’t played out those other ways. Starting with the five actual fragments removes a priori probabilities from consideration.
But there is something much more important here that Art doesn’t tell you. After calculating all those probabilities that Art complains about, I stated explicitly that we should not take any of them seriously, for all the cases with planted fragments or fragments from additional rifles represent hypothetical situations with absolutely no documentation. Statistics applied to these ungrounded ideas will be just as hypothetical as the ideas themselves are. The chance that a particular fragment might have come from another rifle means nothing until we have reason to believe that another rifle was involved, and we have no such reason. Thus Art’s whole note is criticizing an approach that I had already dismissed as moot. Major false target!

Art’s only two issues
Art concludes his opening section by stating that only two issues are relevant to the case for or against conspiracy: whether the group of three fragments could have contained any accidental matches from additional bullets, and whether the group of two fragments could have contained an accidental match. I believe he is trying to say that only a certain number of false matches are of interest to him, maybe only one, and specifically that the case of five false fragments is irrelevant to these issues. He thus seems to be interested only in low-level conspiracies even though that restriction does not follow from his two issues. I consider it arbitrary, dogmatic, and unjustified to so limit the questions beforehand. Art is saying “My issues are the only issues,” and this is patently untrue.

Misquoted assumption
In referring to my simplified picture that antimony in WCC/MC bullet ranges smoothly between 0 ppm and 1200 ppm, Art misquotes the monograph. He said that I asserted that the simplification “doesn’t matter,” whereas I actually stated that “it would not change the basic sense of the answer, which appears very clearly.” Big difference! Art is shooting at another false target.

Blind statistics
In a misguided attempt to demonstrate the uselessness of my Ptightness, Art at the bottom of his page 5 tries to claim that its small value for the “group” composed of the Walker fragment and the unfired round would somehow lead to the “absurd” conclusion that “the bullet found in General Walker’s wall and the unfired bullet found in the Carcano rifle left on the 6th floor are the same bullet.” The only absurd thing here is this blind use of statistics. Statistics enters only after reasonable and competing hypotheses are formulated and justified, not before. Like drinking fine wine, thou must not use statistics “before its time.” But Art tries it here, even if he is using it only to cast aspersions of Ptightness. Art surely knows that he will find no such use of Ptightness in the monograph, and the effort to imply otherwise does not become him.
On a more fundamental level, Art erred here by applying his statistical test inappropriately. His test required samples to be chosen randomly, but he specifically selected the Walker bullet and the unfired round for their similarity. Statistical tests used by any of us are invalidated when we use nonrandom samples.

Art’s basic calculations
The problems with Art’s basic calculations can be discussed in four steps. First, he uses a technique for calculating accidental matches that is unjustified because it does not take account of the underlying log-normal distribution of antimony in the fragments. Second, he inserts wrong data into his wrong equations and so gets seriously wrong answers. Third, the right data used in his equations provide an answer that confirms our answers. Fourth, the right data in the right equations show more properly and more clearly that the two groups are distinct and composed of genuine fragments—our conclusion reached in our way. Let us walk through Art’s reasoning and calculations and see where he goes off the track.
We begin with an overview of the probability calculations. Given two or more fragments with concentrations of antimony that are close together (that form a group), we need to be able to estimate (a) the probability that any two of these fragments actually represent the same starting material (are a genuine match) and (b) the probability that the two fragments represent different starting materials such as different bullets (are an accidental match). Dr. Guinn claimed, as do Larry and I, that the groups are what they seem—genuine matches. Critics such as Art Snyder and Stuart Wexler think otherwise, and feel that it is likely or even probable that one or more of the five fragments came from outside sources (another gunman or a plant). At the minimum, the critics claim that the NAA cannot demonstrate definitively that the fragments are genuine. If probabilities (a) and (b) can be calculated reliably, they may resolve the question.
The traditional statistical view is that probability (a) cannot be estimated reliably because it amounts to trying to prove a negative to a certainty, a phrase familiar from the Warren Commission Report. The negative here would be that no more than two bullets are represented in the five fragments. I did not attempt this in the monograph, but Art claims that I did (see above), and tries to show in his note that even when that probability is calculated correctly, it leads to flawed conclusions. His improved method, which I think is reasonable extension of what I was trying to do, is to reduce the negative to a positive at a lower level. He starts with the two fragments having the same true concentration of antimony, and then allows each concentration to be degraded (made uncertain) by the vagaries of the analytical procedure. He then calculates a joint analytical uncertainty for the fragments and uses the normal distribution of uncertainty (valid for NAA) to find the probability that their actual separation can be explained solely in this way. (In other words, they are really the same concentration, but the analysis made them look different.) It’s like a Gaussian tightness approach. His new positive is their difference from the same concentration. Credit to Art for coming up with a good way to test for a genuine match.
But then he goes off the track. First, and most importantly, he uses a seriously wrong value for the analytical uncertainty. He went to Guinn’s report to the HSCA, found his table with concentrations and uncertainties, which Art reproduces as his Appendix B, and takes them at face value. This is a very serious error, for Guinn stated explicitly in his report and his testimony to the HSCA, and I reiterated in the monograph, that those values are for counting statistics only, and so represent only part of the analytical uncertainties. Guinn emphasized that the actual uncertainties of measurement are about two to three times the uncertainties from counting, which in turn are about 1% of the concentration. Thus we have to use measurement uncertainties of 2%–3%, not 1%. Art’s error showed that he hadn’t read Guinn’s report, his testimony, or my monograph carefully enough. (Art also claimed to be using the values of Appendix B only for the sake of argument, but he actually went on to draw conclusions from them.)
To the nonspecialist the difference between 2%–3% and 1% may not seem like a big deal, but it made the difference between getting the right answer and one that was completely wrong. Art calculates that the joint uncertainty for the two fragments is 11.4 ppm of antimony. Since the two fragments differ by 35 ppm, that makes them appear to be 3.1 standard deviations apart (35 ppm divided by 11.4 ppm). That is a very big separation, and gives a high probability that they were from the same source. To get that value, Art skips over the Gaussian formula he has just presented as his equation 3. Instead, he takes the 3.1 standard deviations of separation, goes to a table of statistics for the normal distribution, and finds that the area from 0 to 3.1 standard deviations is about 99.7% (0.997) of the total area under the normal curve (but using a simplified (standardized) version of the formula that he didn’t show). That allows him to state that the probability of getting a separation of 35 ppm or less (with that standard deviation) is about 0.997. In other words, the probability that two fragments could differ by up to 35 ppm and still represent a genuine match was 0.997. This answer is wrong because the standard deviation of 11.4 ppm is wrong. In any event, Art’s probability (a), for a genuine match between the stretcher bullet and the wrist fragment with the tightness approach, is 0.997.
Art then calculates his probability (b), of an accidental match between the stretcher bullet and the wrist fragment. For this he uses my tightness approach directly, whose resulting probability is [2 x 35 ppm]/1200 ppm = 0.058. This value, he notes, is some 17 times lower than the probability for the genuine match (0.997) calculated above. That is nonsensical, he says. Why? I think because he realized that the 3.1 standard deviations of separation for the fragments must mean that it is highly unlikely they represented the same source. In that he is both right and wrong, right with respect to the 3.1 standard deviations but wrong because it is really 1.25 standard deviations (35 ppm divided by the 28 ppm derived below). He is also wrong because my “linear tightness” approach was noted in the monograph not to be the best way to calculate. Thus, Art is wrong to use it here. In effect, the numerator of his ratio is wrong because of incorrect data, and the denominator because of improper theory. The ratio of two improper numbers can never be meaningful.
Art then starts down the right road (I think) by reasoning that we don’t care so much about probabilities of separations up to a particular value (whether from a genuine match or an accidental one) as about separations of that value. He correctly notes that it is rather improbable (about 0.003) to have a separation of 35 ppm.
Art stops this line of reasoning here, leaving us with a sort of apples-and-oranges comparison, or a reasonable comparison of areas followed by an implied comparison of an ordinate with an area. The result is confusion.
Then he returns to “likelihood ratios,” the approach that he had just dropped, but does not connect the new material to the old. To simplify a bit, a likelihood is the probability that a given separation (35 ppm of antimony in this case) is found where it is. It is something like the value of the probability curve at the specified separation, where separation is usually expressed in standard deviations from zero. (He calls it the “probability density function,” or PDF.) The likelihood ratio is just the ratio of the PDFs for two competing scenarios, the two here being a genuine match and an accidental match.
Art now calculates the PDFs and their ratio in order to drive home his point that either the stretcher bullet or the wrist fragment probably came from an external source. For the numerator, the probability of a genuine match, he returns to his Gaussian with the same wrong standard deviation, but this time uses a different formula that gives an answer an order of magnitude lower—0.0003 vs the earlier 0.003. The PDF for the accidental match he calculates (incorrectly) as 1/1200 (0.00083)—incorrect for the reason noted above that will be described in detail below). Now the ratio for genuine/accidental is about 1/3, which means that the accidental match (from the external source) is about three times as probable as the genuine match. He notes with evident satisfaction that his likelihood ratio (of PDFs) has changed the odds of an accidental match from 17:1 against to 3:1 for.
The problem with this great turnaround is that it is wrong for two reasons, either of which would disqualify it. The first error lies in the likelihood of a genuine match. To get the true value, we must use the proper standard deviation. We can assume that the starting numbers are close to Guinn’s overall estimate of 1% of the concentration (which they are). We can then keep things general by using an average antimony concentration of 800 ppm for the fragments. Lastly, we can assume that the typical analytical uncertainty will be the average of Guinn’s range of 2% to 3%, or 2.5%. For a concentration of 800 ppm, that works out to be 20 ppm, or 28 ppm for the joint uncertainty of the two measurements (1.4 x either uncertainty). That makes the true value of the PDF for the genuine match either 0.0065 or 0.1827, depending on which of Art’s formulas for the normal distribution you use.
The second error in the likelihood ratio is the value of its denominator, which is the PDF for an accidental match. Art again used 1/1200, which is correct for a uniform distribution of antimony in WCC/MC bullets, but is incorrect because the antimony is not distributed uniformly between 0 and 1200 ppm. We explained that in detail in the monograph, but Art ignores it and thereby shoots at a false target. But even if we accept Art’s way of calculating, the proper value of his likelihood ratio would change to 0.0065/0.000833 or 0.1827/0.000833, which amounts to 8/1 or 220/1 in favor of a genuine match. Thus with either of Art’s formulas, the two fragments are much more probably a genuine match than an accidental match, the reverse of what Art had calculated. I repeat that he got this wrong answer and Stu Wexler agreed with it because neither one had sufficiently read Dr. Guinn’s testimony to the HSCA, his report to the HSCA, or my monograph, all of which presented the proper standard deviations.
But all these calculations are flawed because they involve the simplified assumption that antimony in WCC/MC lead is distributed uniformly between 0 and 1200 ppm, which was shown in the monograph to be incorrect. Let us now briefly review what the true distribution is and how to properly calculate the probability of getting an accidental match. The best available estimate of the distribution comes from Dr. Guinn’s 14 “background” bullets that he reported to the HSCA. A plot of these 14 concentrations of antimony shows that they are not really distributed uniformly, although that simplification forms a good starting point. The next-best guess would be that they are distributed normally (in Gaussian fashion). This can be checked by plotting the data on a “normal probability plot,” as Larry Sturdivan did. That plot shows that they are also not distributed normally, for they have a sharp downturn at low concentrations as well as one or more outliers at the upper end. The next-best guess is that they are distributed log-normally, a pattern that would also be expected from the statistics of mixing virgin lead and its low antimony with recycled hardened lead and its much higher antimony. A normal probability plot with logs of concentrations confirms that the distribution is nearly log-normal. (At the time of this writing, Larry and I are evaluating the possibility that the distribution is actually bimodal, with two separate normal or log-normal zones representing the incompletely mixed starting materials. I hope to be able to report on this at the Lancer conference.)
From the normal probability plot with logs can be read the mean and standard deviation, which then can be used to construct a regular normal (Gaussian) distribution. The stretcher bullet and the wrist fragment can then be “positioned” on this distribution, with the “distance” between them representing one-half the probability that one of them is an accidental match with the other. This probability works out to be just under 2%. But this is the most optimistic value for this probability, however, for it assumes maximum knowledge on the part of whoever was firing another rifle or planting a fragment. Specifically, it assumes that the person knew of the special properties of WCC/MC lead and took pains to duplicate it in his weapon or fragment. To put it mildly, it is problematic whether any conspirator in 1963 or 1964 could have known this information or been able to put it into practice in such a short time after the assassination. For example, had the person selected a weapon that used hardened lead, or planted a fragment of hardened lead, the probability of an accidental match would have declined to zero because antimony in hardened lead does not overlap antimony in WCC/MC lead. Similarly, the probability of an accidental match within the fragments of the head-shot group works out to be about 3%, again under the most optimistic scenario. Although these most-optimistic probabilities are not vanishingly small, they are low enough to generally be regarded as statistically insignificant. The others are far smaller, if not zero. Probabilities of multiple external fragments are the products of the separate probabilities. Thus it is easy to see how the probabilities of various conspiracy scenarios can easily reach the one-in-a-million point, with probabilities of one in a hundred million not being impossible.
Thus, there is no statistical support for the idea of accidental matches from external bullets or fragments. Since the only other possibility is that all the fragments are genuine, this is the hypothesis that we must accept.

“Sampling errors”
Art then claims that “sampling errors,” or heterogeneities within WCC/MC lead, have to be considered, and that they are large enough and unpredictable enough to invalidate all attempts to find a definitive answer from the NAA. This is totally false. Again he did not read other parts of the monograph, where it is explained, with reasons and mechanisms, why the scale of these heterogeneities is too large to affect the suite of particles produced when WCC/MC bullets shatter. Art’s error can serve as a lesson for all of us—read the whole document before getting into detailed statistics that may be irrelevant. One should also know something about how bullets break before assuming some specific behavior on their part.

“Ringers” in the group of three
Here Art considers accidental matches in the group with three fragments. He uses an irrelevant “sampling error” of 30 ppm, irrelevant because the physical scale of the heterogeneities in WCC/MC lead is too large (as noted above). As a result, the inconclusive answers he gets have to be disregarded. Because the fragments in this group have the same kind of spread seen in the group of two, the answers here will be similar to that one, namely that the probabilities are 100 to 1 or so in favor of genuine matches over accidental matches. No contest!

Other types of lead
Art considers only WCC/MC lead. That narrow approach eliminates scenarios in which a conspirator planted or fired a bullet with a different type of lead. As shown in the monograph, this lowers the probabilities of a false match by a factor of something like five. (There are other reasons why it may lower the probability to zero.) That changes the roughly 1:100 likelihood ratio of accidental match to genuine match to something like 1:500, which is a significant reduction.

False prospects
Art closes his note with a discussion of the future. He says that the probabilities can be calculated better with two types of additional measurements, “more and more accurate measurements of repeated samples from the same bullet,” especially for CE 399, and “more measurements of a larger number of [WCC/MC] bullets.” But these projections are based on the flawed calculations and improper understanding that characterize his entire note. This invalidates them. The proper probabilities are so clear-cut that no more measurements are needed. It’s the old story that appears so often in JFK “research,” when results are wrongly interpreted and additional research is unnecessarily called for. We have everything we need to understand the strong message that the NAA data are trying to tell us.

The major characteristics of Art’s note include:

1.      It is narrowly focused, not broad in any sense.

2.      It wrongly states that only two question are of interest to conspiracy.

3.      It displays ignorance of Guinn’s work and my monograph.

4.      It is misdirected enough to be meaningless.

5.      It attacks at least one major argument that I didn’t make.

6.      It fails to deal with several important things that I did.

7.      It uses statistics blindly and wrongly on the Walker fragment and the unfired round.

8.      It overemphasizes the role of the five-false-positive argument in the monograph.

9.      It misstates the role of a priori probabilities.

10.  It misquotes my statement on the assumption of smoothly varying antimony between 0 and 1200 ppm in WCC/MC bullets.

11.  It seriously miscalculates the probabilities of genuine matches because it uses wrong analytical uncertainties, even though the proper values were available from both Guinn and me.

12.  It considers only WCC/MC lead.

13.  It misunderstands the irrelevance of large-scale heterogeneities.

14.  It properly proposes the use of likelihood ratios but calculates them wrongly.

All in all, the note manages to get nearly everything it touches wrong or irrelevant, primarily because it focuses too narrowly on pure statistics at the cost of ignoring the data and reasoning in the rest of the monograph and in Guinn’s testimony and report to the HSCA. In the process, an important opportunity to engage in critical dialog is lost.

How did my predictions fare?
My initial post to the newsgroups noted that Art’s critique would not be understood by most JFK “researchers.” The responses so far have abundantly confirmed that prediction. It is clear that none of the responders have understood his statistics enough to see where he went wrong. More tellingly, none of them spotted that he had used wrong data and thereby gotten wrong answers. Moreover, none of them spotted his basic statistical errors, either. That’s what can happen when you use fancy statistics, omit major steps, and don’t explain your procedures in terms that others can grasp.
My initial post to the newsgroups also predicted that the final discussion could come down to narrow statistics versus broader logical thinking, and that is the first part of what has happened. On one level, Art has been narrow by not reading the available literature enough to know the correct values to insert into his formulas. I find it ironic, and extremely illustrative, that the right values totally reverse his answer and turn it into our earlier one. On a deeper level, Art has neglected the reasoning in the NAA monograph that show that most of these statistics are worthless because they apply to completely hypothetical situations. Art’s note became irrelevant the moment he began to critique something that didn’t matter. It also didn’t help when he obscured things by failing to note this extremely important aspect of the monograph. One must spend a lot of time with the monograph in order to grasp its full reasoning, and I do not apologize for this.
But the final discussion must also deal with Art’s statistical errors. I was surprised by this. I had expected that Art’s long experience in physics would prevent him from making the errors that his note revealed. I was wrong here, however.

How to respond to my response
Since I have noted here that one of Art’s big errors was to not check himself by considering alternative explanations for his major points, I will show good faith by offering a self-critique of this response to him.
First, I admit that neither Larry Sturdivan nor I were able to understand everything in Art’s note. I would be grateful if Art would clarify some of these points, which include his seeming use of two forms of the Gaussian formula where only one is needed, and his meaning of a priori probabilities. Neither response will affect the basic soundness of my original conclusions, and particularly so for Larry’s, however, the first for mathematical reasons and the second for conceptual reasons.
Second, Art may wish to comment further on his contention that I arbitrarily set P = 1 for genuine matches. I am convinced that I did not, but if he can show convincingly that I did and was not aware of it, I will listen.
I may add to this list of weak points of my response in the future.

What’s to come
Art’s note and my response will form part of my presentation at JFK Lancer. They won’t be a big part, however, because his note doesn’t warrant it. Preparing this response has offered an opportunity for me to review once again the NAA and its place in the physical evidence from the JFK assassination, and this has proven to be a valuable exercise. In the spirit of getting as many ideas as possible onto the table well before the conference, I offer a summary of the broad train of thought that I plan on giving in Dallas.
In the broadest sense, JFK conspiracists should be terrified of the NAA and its strong links to other physical evidence and basic logic, for it knocks the legs out from under most, if not all, contemporary JFK “research.” I know that is an extremely strong statement, but I intend to make it and to justify it.
I will begin by addressing the two groups of fragments found by both the FBI and Dr. Guinn’s NAA. I will first demonstrate that once the large-scale heterogeneities are removed from the picture, as they must be because they do not affect the properties of the tiny fragments generated as jacketed bullets break when encountering bone, the groups are revealed to be extremely robust statistically (odds of something like 400:1 that they are distinct groups). Second, I will use logic and statistics to demonstrate that all the fragments are genuine (incorporating pieces of Art’s note and our proper calculations). Third, I will show the importance of the physical meaning of the two groups, by noting all the other ways the fragments might have arranged themselves but didn’t. Fourth, I will show how this means that every fragment recovered came from Oswald’s rifle to the virtual exclusion of other rifles. (The best scenarios of a plant are something like 2% to 3%; the worst, and probably the most realistic, are orders of magnitude lower.)
Then I will turn more general and consider the implications of these results. I will first review the extremely important logical dictum that without specific physical evidence for an idea, we may not consider it with any legitimacy. (Speculation is easy but meaningless without evidence.) I will combine this with the NAA data to show that we may not consider anything beyond a single shooter.
Then I will take an aggressive next step and show how the NAA knits together all the rest of the physical evidence into an extremely strong wall that no one has been able to break in 38 years of trying. I will also show that the NAA at the same time puts most or all of the other physical evidence into the category of “doesn’t matter.” This includes but is not limited to details of most of the wounds, the photos and X-rays from the autopsy, the Zapruder film, and the chains of custody. For example, since we now know that the head shot came from Oswald’s rifle, left telltale fragments in the brain, and deposited two large fragments in the front seat, it no longer matters just where it entered the head and just where it exited. It makes no sense to continue to fight over these immaterial details. That same approach can be combined with one or two other pieces of physical evidence to demonstrate the double-body hit, or DBH (formerly the single-bullet theory, or SBT).
I will conclude by moving to the most general level, of considering all other scenarios that lack physical evidence. This of course includes everybody’s favorite conspiracy theories as well as all those smaller and smaller details that are now being discussed on the newsgroups. Since they are purely speculative in nearly all cases, they are wasting everybody’s time and, worse, giving them a false sense of doing something meaningful about the assassination. Images of Nero fiddling while Rome burned come to mind.
I will then summarize as follows. (1) The NAA settles the question of the fragments—two groups representing two bullets from Oswald’s rifle. (2) The NAA knits together the rest of the physical evidence and simultaneously renders most of it moot. (3) All scenarios other than the lone gunman must be summarily rejected because they lack physical evidence.
For the record, I am continually astonished by the emerging power of the NAA to affect our interpretation of the JFK assassination. I had no such idea when I began to study the NAA data a few years ago, and am coming to terms with it just as everyone else is (or should). In other words, it is as much of a learning experience for me as for anyone else.

Responsibilities of Stu Wexler and Stewart Galanor
I have now put the thrust of my presentation on the table for all to see, at least to the extent that I can determine it three weeks ahead of the Lancer conference. Since this is supposed to be an open discussion whose only goal is to ascertain the truth (Debra Conway), it is incumbent on the other two panelists to similarly lay their cards on the table as early as possible so that I and others can evaluate them thoroughly beforehand. Only in that way can we have an open, honest dialog at the high level that Debra is expecting and that every attendee deserves. If someone springs something during the panel, I will not hesitate to declare dirty pool and that the person was more interested in winning the debate than in understanding the assassination. So I expect to see any new information from Stu and Stewart well before the conference, and preferably in these newsgroups. In this category, for example, would fall results from the “work” of Albert Frasca that we keep getting hints about. Is he really doing anything? If so, let’s see it early.

Work in progress
As the reader can see, this response to Art Snyder and the whole explanation of the NAA and its implications for the assassination are very much works in progress. That does not mean that their basic result is in doubt, but rather that they are constantly being refined. Minor updates will be posted on my web site (, major updates to the newsgroups.
I also want it to be clear that I am posting this response earlier than I would prefer, so that others attending the Lancer conference will have three weeks to evaluate it and respond from positions of greatest strength. I judge that the greater good is served in this way.

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