[Editor’s Note: This is the ninth in a series of 23 essays summarizing and evaluating Book of Mormon-related evidence from a Bayesian statistical perspective. See the FAQ at the end of the introductory episode for details on methodology.]
It seems unlikely that Joseph or his scribes could fill the Book of Mormon with examples of grammar and word use that fit better in Early Modern English than in the nineteenth century.
Stanford Carmack and Royal Skousen have painstakingly documented a strange argument—that much of the language used in the Book of Mormon reflects usage patterns that align with the sixteenth and seventeenth centuries, making it unlikely that Joseph or anyone else in the nineteenth century authored the book. The statistical case they make is extremely strong. Even assuming that they’re missing a substantial amount of evidence that doesn’t fit their narrative, the probability that Joseph produced those patterns by trying to copy biblical style are vanishingly small (p = 5.24 x 10-24). Evidence of Early Modern English can be counted as powerful evidence in favor of the Book of Mormon’s authenticity.
Evidence Score = 20+ (A critical strike in the Book of Mormon’s favor, increasing the probability of authenticity by over 20 orders of magnitude).
When last we left you, our brave skeptic, you had left behind deep thoughts about the absurdity of amateur boat-building just as this Nephi and his family entered what you assumed to be the New World. You almost can’t wait to see how this fractured family deals with life in paradise, and just how much (or how little) of a paradise this promised land turns out to be. It’s far too early in the book for there to be any hint of a happy ending.
But you don’t make it more than a few verses before you stumble onto a strange turn of phrase in the text. The stumbling part was more than a metaphor—you can almost feel your mind tripping over the words and falling flat on its face, your weary mind unable to move past them or parse the meaning.
"Wherefore, I speak unto all the house of Israel, if it so be that they should obtain these things.”
The phrase “if it so be that” may have sounded biblical, but you are pretty sure that you haven’t seen it in the Bible. You’d noticed archaic phrasing like that before, but this is the first time you stopped to think about it. You had assumed that much of the bad or strange grammar you’d encountered up to this point had been a mixture of Smith’s clearly insufficient backcountry education and his attempts to emulate biblical style.
But you realize something strange. You’d seen that turn of phrase before—not in any other book of the modern era—but you’d seen it, nonetheless. You put down the book and turn again to the small but trusty bookshelf at the edge of the cabin, thumbing through the worn spines of the oldest tomes in your collection. You come quickly to the one you’d been thinking of, The Canterbury Tales, published in 1400. You wonder if you will be able to find what you’re looking for, but as you crack open the aging book your finger lands almost miraculously on the passage you’d been thinking of.
“Thus moche amounteth al that ever he ment, if it so be that I have it in mynde.”
Had Smith read his Canterbury Tales? You suppose that he might have. But the thought doesn’t leave you as you move again to the Book of Mormon and pore over the page you’d been reading. Were there more of these? And if there were, what on earth were you to make of them?
What you experience next can only be described as transcendental. A window opens in your mind and you find your thoughts transported to an other-worldly realm. It’s as if you’re awash in a sea of words from thousands of books, and as your thoughts swim through them you can feel and know them all, their meaning filling every pore. As the literary waves crash over you, you feel a familiar linguistic thread in the water—they’re the words from Smith’s book, not just the ones you’d read, but all of them—every syllable that lay within the covers. Your skin pricks with its phrases, many of them unfamiliar, many of them strange, and as they penetrate you feel the same phrases reaching into you from dozens of other books. Their titles flash before your mind’s eye. Some you had read; many of them you hadn’t. But somehow you knew that all of them were old, almost archaic—older even than the King James itself. The phrases had a ring of authenticity that you couldn’t dismiss as facsimile or forgery.
And as soon as that thought hits you, your find your mind back in Vermont, the memory of the experience already fading. But one indelible question remains as you look back on the book in a strange mix of fascination and horror. How on earth would Joseph have been able to make use of these archaic phrases, and to have done so with such consistency?
The Book of Mormon is a strange book, and it only becomes stranger to those who become familiar with the work of Royal Skousen and Stanford Carmack, two of the key scholars involved in the Book of Mormon Critical Text Project, a project which systematically documents the features and differences between all the available editions of the Book of Mormon. In their thorough analysis, they claim to have found strong evidence that much of the English of the book’s translation is not that of Joseph’s time, nor is it of the Bible. It instead contains semantic and syntactic features that best align with those of the 1500s and 1600s, during a linguistic period identified as Early Modern English or EModE. This evidence is difficult to grapple with, not just because of its highly technical nature, but also in terms of its implications. No one knows what it would mean to have authentic, non-biblical sixteenth-century English in the Book of Mormon, but if it really is there, it would place the book far beyond the authorial reach of Joseph or his scribes. Could this evidence be a fluke? Could it be successfully imitated? We turn to Bayes to help with the answer.
Skousen and Carmack lay out their evidence in an exceedingly thorough fashion, whether in a number of articles, in a set of presentations available on YouTube, or in hundreds of pages of reference volumes. The articles are not for the faint of heart, and I’ll admit that technical nuances of Carmack’s linguistic analysis are beyond me. I believe, however, that I’m able to understand the broad strokes well enough. According to them, the Book of Mormon displays deep syntactic patterns that match the sixteenth century and are a poor fit for either the English of the King James or for eighteenth- and nineteenth-century imitations of biblical style. They also assert that the book contains unusual word meanings and phrasing that are completely unattested in either Joseph’s time or in the eighteenth century, yet can be commonly found in the centuries before that time. These two connections to EModE provide independent evidence that Joseph was not the author of the Book of Mormon.
In terms of syntax, Carmack identifies nine key syntactic features that characterize EModE, comparing the frequency of their use in the Book of Mormon, in the Bible, and in four important nineteenth-century works that critics have alleged were sources for Joseph’s writing: The First Book of the American Chronicles of the Times, The American Revolution, The First Book of Napoleon, and The Late War. These latter works each consciously imitate a biblical style, providing good comparison cases for the claim that Joseph imitated King James English when writing the Book of Mormon. (Carmack has since expanded his corpus to 25 pseudo-biblical works, and the features in these support the overall narrative on display here.) Each of these syntactic features represent deep and subtle usage patterns that would be difficult to consciously imitate over the course of a novel-length work. They include such syntax as whether the work prefers using agentive of vs. by, the use of periphrastic did, frequencies of personal which, that, and whom, and the use of finite vs. infinitive verb complementation. Carmack finds that the four eighteenth- and nineteenth-century works are very similar in the relative lack of archaic features, and that these features are also not frequently found in the King James. They are, however, extremely common in the early manuscripts and the 1830 edition of the Book of Mormon. Joseph, himself uncomfortable with this syntax, would remove many of these characteristics for the 1837 edition.
In fact, we have at least one good example of Joseph trying to emulate biblical style. Joseph Smith’s personal history is just such an attempt, and gives us a small window into what it would be like for Joseph to attempt to emulate biblical grammar. As Carmack notes, Joseph’s efforts lack these syntactic EModE features.
Skousen and Carmack also identify at least 26 semantic use cases which can’t be found anywhere in nineteenth-century literature and are also completely absent from the Bible. All of these cases are attested in literary and academic literature in EModE. They include the use of “depart” to mean "divide" (changed in our current version to “parted”), the use of “mar” to mean "hinder or stop," and the use of the phrase “but if” to mean "unless."
It’s important to note, however, that these archaic features do not make the Book of Mormon purely a product of the early modern period. There are a number of Hebraic grammatical and poetic features that are far more ancient than EModE. There are also many other sixteenth-century features of syntax and spelling that are missing from the text. Whatever is going on, the text of the Book of Mormon remained generally readable by nineteenth-century audiences.
Here are the two hypotheses we’ll consider:
The Book of Mormon was not written by Joseph or his contemporaries—This hypothesis is broad, but it has to be. What little we know about the translation process doesn’t let us say much about how the words themselves were translated into English. But there are a couple things that would be required here to be consistent with the Early Modern English evidence. The first is that Joseph is not involved in producing the wording of the text, or at least any of the words that involve EModE syntax or word meanings (which, when you get down to it, covers a very large proportion of the book). The second is that the text is not actually a true Early Modern English text. Regardless of how the text was produced, the hypothesis is that it’s been filtered or managed in some way so that the words and spellings themselves would remain recognizable to nineteenth-century readers. This would explain how the underlying syntactic structure of the text could show EModE forms, and how many recognizable words could have truly archaic meanings, while sparing us the true strangeness of EModE.
Early Modern English syntax in the Book of Mormon also happens to carry some strange implications about who and how the translation of the Book of Mormon was produced. None of these explanations are likely to make us comfortable, but that sort of speculation doesn’t matter for our purposes here. (Mathematical analysis, after all, doesn’t care whether we are comfortable or not.) All we’re concerned with is that the book didn’t come from the mind of Joseph or his scribes.
The Book of Mormon was written by Joseph using an imitation of Biblical style—According to this theory, any ancient grammatical forms in the Book of Mormon can be explained by Joseph’s (imperfect) imitation of biblical style. It doesn’t matter much whether this imitation was intentional or was merely a reflection of how steeped Joseph and others in the nineteenth-century were in biblical language—the result should be fairly similar. By this theory, Joseph’s grammar should line up well with those of others in his era who imitated biblical style, or should line up well with the Bible itself, and any deviations from those tendencies would be essentially due to chance—that Joseph’s way of imitating biblical forms happened to deviate from those used by others.
This could be framed as two separate hypotheses, but I think it works better as one. It’s not as if Joseph is copying either the Bible directly or the language of his contemporaries—it’s that he’s imitating the style and just happening to match (or not match) either of those sources. We’ll consider how it aligns with both and give critics the benefit of the doubt by using the more likely option.
With those hypotheses in hand, we can take a look at our prior probabilities:
PH—Prior Probability of Non-Joseph Authorship—So far, the probability of an authentic Book of Mormon has increased overall, but in the grand scheme it hasn’t moved all that far from where we initially started. Based on our estimates up to this point, the probability of a non-Joseph authored Book of Mormon stands at p = 1.97 x 10-30. Here’s where we’ve been thus far:
PA—Prior Probability of Joseph as Author—That would leave the remainder for our alternative hypothesis, meaning our prior would be p = 1 – 1.97 x 10-30.
CH—Consequent Probability of Non-Joseph Authorship—In part because of how vague we’ve made the hypothesis, it would be really hard to say that the evidence under examination doesn’t fit the theory of authenticity. But that vagueness doesn’t do much to alleviate the raw strangeness that this hypothesis seems to exude, at least at first glance. For whatever reason, it’s easier for us to imagine God providing a metaphysically perfect translation that placed the Book of Mormon in the exact linguistic environment of its 19th century readers, or for Joseph to have rendered the ideas of the book directly into his own speech. When we get down to it, though, those are just assumptions we bring to the text as modern (and often implicitly mystical) readers. Gods ways are not our ways–we should be open to translation mechanisms that don’t fit whatever preconceptions we’ve held in the past, instead allowing the text itself to inform our beliefs about how it came to be.
Though the use of Early Modern English isn’t the only way we could’ve gotten an authentic Book of Mormon, I submit that, given how little we know about how the book was ultimately translated, we’d be as likely to end up with that rendering as any other. In fact, just to emphasize that point, I’m going to be assigning a consequent probability of p = 1 for this hypothesis, a value that reflects the idea that there’s nothing the least bit strange about the presence of EModE in an authentic Book of Mormon text. I imagine critics (and maybe some faithful scholars) will cry foul at such a move, but with the amount of a fortiori stretching I end up doing in their behalf later on, I think I’ll be able to live with the guilt.
There’s another point worth discussing here, and it’s how the linguistic features of the text compare to other Early Modern English works. Carmack has worked hard to provide examples of Early Modern texts that show the archaic features he highlights, but I don’t believe he’s conducted the sort of frequency analysis for non-biblical 16th and 17th century texts that he’s done for 19th century ones. It’s possible that the frequency of the Book of Mormon’s archaic features would be considered too archaic, even for the Early Modern period. If so, we would have to adjust this consequent probability. Until we get better data on that front, though, I’ll be content for my substantial a fortiori efforts to make up for that possibility. (And, as we’ll soon see, this consequent probability could be as low as p = .0005 and it still wouldn’t alter my overall evidence score.)
CA—Consequent Probability of Joseph as Author—So how unexpected is the presence of EModE under the assumption that Joseph is the author? Thankfully Skousen and Carmack give us all the information we need to produce a decent estimate. We’ll consider the two main types of evidence separately, looking at the syntactic evidence first, followed by the semantic.
Syntactic evidence. Carmack’s article comparing syntactic patterns between the Book of Mormon, the King James Bible (1611; KJB), and the four pseudo-biblical works provides plenty of quantitative fodder for this analysis. He conducted relatively comprehensive searches of these texts using WordCruncher, providing frequencies or frequency percentages for each of the nine syntactic features and for each class of work—what he doesn’t report directly I was generally able to estimate based on other clues in the article, generally by assuming that opportunities for those features to appear (e.g., a choice between agentic by vs. of) occurred at the same rate per million words in the Book of Mormon, the Bible, and the pseudo-biblical works. You can see how those ended up in the table below, with cells containing my estimates shaded in orange.
For many of the syntactic features he discusses, Carmack is able to report the number or proportion of times that the feature either aligns with archaic EModE usage or whether it follows more biblical patterns. A good example of this is the case of finite vs. infinitive verb usage, where finite verbs (e.g., “causing that they should” vs. “causing them”) are more common in EModE and infinite verb use is more common in modern contexts. That type of reporting is great for a chi-square analysis. What are less amenable to that type of analysis are features that don’t have an alternative form, and that exist only rarely in modern or biblical contexts, like the plural form of -th (e.g., “Nephi’s brethren rebelleth” from the original heading of 1 Nephi). It would be possible to get probabilities for that kind of evidence—we’re going to do something similar for the semantic type of evidence later on—but trying to mix the two types of evidence would get tricky. Leaving out the four features that fall in that latter category (lest-shall usage, more-part usage, had (been) spake usage, and the -th plural) will be one way that we cut the critics some serious slack.
What I did for the remaining evidence was categorize the different forms of each feature as either EModE or as a better match for biblical or pseudo-biblical usage. I then summed the frequency with which archaic and non-archaic forms appear in the Book of Mormon, the King James, and in each of the four pseudo-biblical works, and used that as the basis for the chi-square analysis. You can see those frequencies in the table below.
Note: Values for the BoM differ slightly for the two comparisons, as there is one syntactic feature for which a lower frequency indicates archaic usage relative to the Bible. The frequency counts for that feature were reversed in the comparison with the KJV.
The chi-square values in each case are pretty astronomical; χ2(1) = 1186 for pseudo-biblical; 2337 for the King James (note that the values in the parentheses when reporting chi-square values represent the degrees of freedom for the test); that leaves us with probabilities so small that they have negative exponents in the hundreds (p = 6.46 x 10-260 and 5.35 x 10-510). If we lined up all the particles in the universe (of which there are about 1080), treated each particle like a lottery ball, and then had to correctly select the right ball, we would have to pick the correct one at least 3 times in a row to get a similarly improbable outcome. Clearly, we can be confident that the differences in syntactic usage in the Book of Mormon don’t differ from the Bible or the pseudo-biblical works on the basis of chance. It just so happens that the probability for the pseudo-biblical works is somewhat higher (because it has a smaller sample size overall), so for the critics’ sake we’ll ignore the comparison with the King James.
But leaving things there hardly seems fair. After all, maybe Carmack is being selective in his choice of evidence. How about we assume that there’s a ton of evidence within the Book of Mormon that he missed, or that he saw and isn’t reporting on, evidence that contradicts his conclusion. To that end, I assumed that our sample of syntactic examples, for both the Book of Mormon and the pseudo-biblical texts, was magically increased by a factor of five. We’ll use these extra syntactic items as a proxy for our missing evidence.
Now, there are a few ways we could handle (read: manipulate) that evidence so that it “contradicts” Carmack’s conclusion. We could, for example, assume that all of those additional items are non-archaic in both cases. It turns out, though, that the way to best water down the chi-square test (and thus help the critics’ case) is to have half of the additional items be archaic and half be non-archaic. You can see that represented below:
That assumption would probably never hold (see, for example, all the features we already excluded from our analysis), but in this case I’m willing to yield an unreasonable amount of ground to the critics, just to see what might happen. In that case, if we run the chi-square, we get a considerably higher (though still extremely small) probability at χ2(1) = 186, p = 2.63 x 10-42.
Also, chi-square analyses are notoriously sensitive. Once you get sample sizes this high, almost any difference is bound to be statistically significant. One way we can get around that is to adjust our results based on how different the four pseudo-biblical works are from each other. It’ll help if we continue with our assumption that there are a ton of other syntactic features to explore in these works, so I multiplied the number of both archaic and non-archaic items for those works by five (keeping the ratio of archaic to non-archaic items the same). If those works showed extremely large statistical differences, then that would undercut Carmack’s argument considerably. Sure enough, if you do the chi-square test comparing those four works, you get a highly significant result at χ2(3) = 135.7, p = 3.19 x 10-29.
But even though 29 and 42 seem like similar numbers, those probabilities are very different from each other—the differences between the Book of Mormon and the pseudo-biblical works would still be quadrillions of times less likely to occur by chance than the differences between the pseudo-biblical works themselves. Adjusting for the differences we might expect between the eighteenth- and nineteenth-century pseudo-biblical works, the probability of seeing EModE patterns even one fifth as pronounced as the ones Carmack found would be p = 8.24 x 10-14. We’re playing it incredibly safe with this estimate, but that’s the probability we’ll use for the syntactic portion of the evidence.
Semantic evidence. We turn now to the semantic evidence—the archaic meanings contained in the text. As noted above, Carmack and Skousen identify many different examples of archaic word meanings in the Book of Mormon (at least 26, for our purposes) that cannot be attested in either biblical or modern works. It’s safe to presume that that sort of thing would be pretty rare in nineteenth-century works—it’s not likely that many authors would consciously use words in ways that they aren’t familiar with and that their audience is unlikely to understand. You would essentially be using a word in a way that no one else in your century has used it, and in a manner that happens to match how it was used in the past. Hard to do unless you’re steeped in and consciously trying to imitate that specific literature, which neither Joseph nor his scribes would’ve done or had a reason to do.
Thankfully, we have ways of estimating the probability of rare events. There are a number of probability distributions that are used to model those sorts of relatively rare phenomena. In this case, we’ll assume that the frequency of unattested archaic word meanings would follow a Poisson distribution similar to how other relatively rare events (such as suicide and criminal acts) tend to function in the real world. If we know, or can reasonably guess, the average number of times that a rare event is likely to occur, we can use that distribution to estimate the probability of that event occurring a certain number of times (or more). The question, for us, is how often we would expect an archaic meaning to show up in an early nineteenth-century work. That sort of thing could be estimated by someone with the necessary expertise, access to solid databases, and a lot of time on their hands (like, say, Stanford Carmack), but for the moment we’ll have to pick the highest value that seems reasonable—for the benefit of the critics, of course. In a work the size of the Book of Mormon, I’d imagine the average number of unique archaic meanings would be at most 1.
But let’s assume, for the sake of argument, that Carmack and Skousen are wrong. Let’s say that, despite all their additional searching and revision efforts, their search remains incomplete, and that fully half of the 26 examples aren’t as archaic as they think. That would leave 13 valid examples of what should be a relatively rare occurrence. Even then, the probability of seeing that many examples of archaic word meaning, as calculated using this online calculator, would be p = 6.36 x 10-11. You can see what that looks like below:
Summary. Taken together, the syntactic and semantic evidence of EModE provide two strong, independent lines of evidence against Joseph authoring the Book of Mormon. The probability of seeing both kinds of evidence by chance would be the product of their respective probabilities, or p = 5.24 x 10-24.
PH = Prior Probability of the Hypothesis (our prior estimate of the likelihood of an authentic Book of Mormon, based on prior evidence, or p = 1.97 x 10-30)
CH = Consequent Probability of the Hypothesis (the likelihood of observing the evidence given a non-Joseph authored Book of Mormon, or p = 1)
PA = Prior Probability of the Alternate Hypothesis (our prior estimate of the likelihood of a Joseph-authored Book of Mormon, or p = 1 – 1.97 x 10-30)
CA = Consequent Probability of the Alternate Hypothesis (the likelihood of observing the evidence given a 19th century author of the Book of Mormon, or p = 5.24 x 10-24)
PostProb = Posterior Probability (our new estimate of the probability of an authentic Book of Mormon)
|PH = 1.97 x 10-30
|PH * CH
|(PH * CH) + (PA * CA)
|(1.97 x 10-30 * 1)
|((1.97 x 10-30) * 1) + ((1 – 1.97 x 10-30) * 5.24 x 10-24)
|7.96 x 10-5
Lmag = Likelihood Magnitude (an estimate of the number of orders of magnitude that the probability will shift, due to the evidence)
Lmag = log10(CH/CA)
Lmag = log10(1/5.24 x 10-24)
Lmag = log10(1.91 x 1023)
Lmag = 23
It looks like we have our first critical strike in the Book of Mormon’s favor, a piece of evidence that meets the statistical bar set by critics for belief in the unusual and the supernatural. Of course, critics would likely beg to differ on that front—evidence against nineteenth-century authorship isn’t evidence of ancient authorship, particularly when that evidence points to the sixteenth and seventeenth centuries. But without a clearly articulated theory that explains the source of this evidence, critics should rightly take pause. This should especially be the case given how hard we stomped on the scale in favor of the critics. Theories that don’t rely on Joseph’s authorship of the book are greatly strengthened by the presence of Early Modern English, including the theory of authenticity.
This evidence also gets us much, much closer to an authentic Book of Mormon, in conjunction with the other evidence we’ve considered. We’re not there yet; we haven’t tipped the scale from disbelief to belief—and that kind of tipping isn’t necessarily inevitable at this point. But evidence as apparently strong as this should motivate further investigation. No matter is ever truly closed for the honest skeptic, and we should remain open to evidence that could effectively counter what we’ve discussed here, as well as evidence that could further support it. Yet with this evidence is the promise that we’ve just uncovered a minor peak of a mountain of transcendent truth, one whose slope may have just gotten a whole lot steeper. One can’t help but wonder if critics are up for the climb.
When it comes to exercising skepticism in this case, the first realistic step is probably to try and redo this analysis with a more complete set of linguistic features, using hard frequency counts instead of estimates, using Carmack’s full set of 25 pseudo-biblical texts, and trying to get a sense of how rare semantic archaisms actually are in modern texts.
After that, though? I’m not gonna lie; I have tremendous pity for critics trying to demonstrate the weakness of this particular class of evidence. The skeptical responses I’ve seen so far have done little more than handwave without meaningfully grappling with the full scope of the evidence. The only path that I see to negating EModE is to produce even more thorough and rigorous work than what’s already been done in this space. However, working harder, longer, and better than the combined efforts of Royal Skousen and Stan Carmack would probably be fatal to most mortals. Keep in mind, too, that this work is ongoing, and in the year or so since I first drafted this essay the corpus of evidence in favor of EModE in the Book of Mormon has only expanded.
But if there are any chinks in the heavy dragonplate of the EModE armor, they’re as follows. The EModE hypothesis is not particularly concrete—we have a much better sense of what the translation process didn’t look like than we do of how it actually worked. The current best contenders—such as an early-modern post-mortal translation committee—sound just as strange as positing the existence of angels and gold plates, and they give us little sense of what we’d actually expect the Book of Mormon to look like if the hypothesis was true. We don’t have many examples where a text has been: 1) translated from an ancient language into Early Modern English translations and 2) has had its spelling and word use largely edited to make it more comfortable for nineteenth-century eyes and ears. It’s a small enough niche that there’s probably nothing to which we can meaningfully compare the Book of Mormon to see if the syntactic and semantic patterns match. Should an army of critics track down a sizable corpus of such material, and it turned out not to look much like the Book of Mormon, that would substantially weaken the EModE position.
We also have quite a few people, including faithful scholars, who remain opposed to the logical implications of EModE. The traditional crux of those arguments is the presence of purported bad grammar in the text, grammar which is attributed to Joseph’s backcountry upbringing. The issue here is that nearly all of the purported “bad grammar” in the Book of Mormon is explainable as mainstream EModE usage, and comparatively little of its EModE is usefully accounted for by frontier American grammar, at least not in the proportions we see in the Book of Mormon. What’s more, the vast majority of the EModE syntax hasn’t been found in any of Joseph’s other writings. Finding further EModE features within frontier dialects or within the (somehow) unexamined writings of Joseph Smith would certainly weaken Skousen and Carmack’s argument. Just don’t be surprised if those efforts are as successful as a duck flapping its way to the moon.
Next Time, in Episode 10:
When next we meet, we’ll have our skeptic re-examine his 1769 King James Bible, to see how likely it would be to have an ancient book rely on a modern translation of yet another ancient text.
Questions, ideas, and arcane secrets can be quietly deposited within BayesianBoM@gmail.com or submitted as comments below.