Bad Math and the Premature Dismissal of Brian Stubbs’ Work on Uto-Aztecan Languages

In my previous post on the negative review by BYU professor Chris Rogers regarding Brian Stubbs’ work on ancient connections between Uto-Aztecan languages and three Old World languages, some comments point to Rogers’ Table 6 as key evidence for dismissing the correspondences detailed by Stubbs. Table 6 appears to present evidence that chance similarities could account for what Stubbs has found.

As a reminder, the key to establishing genuine connections between ancient languages is not finding a bunch of random words that can appear to be related, but establishing meaningful relationship with many examples of consistent sound changes. Here is an excerpt from Wikipedia’s article on the “Comparative Method” describing how to establish legitimate connections:

Step 2, establish correspondence sets

next step involves determining the regular sound-correspondences
exhibited by the lists of potential cognates. For example, in the
Polynesian data above, it is apparent that words that contain t in most of the languages listed have cognates in Hawaiian with k
in the same position. This is visible in multiple cognate sets: the
words glossed as ‘one’, ‘three’, ‘man’, and ‘taboo’ all show this
relationship. This situation is termed a regular correspondence between k in Hawaiian and t in the other Polynesian languages. Similarly, in those data a regular correspondence can be seen between Hawaiian and Rapanui h, Tongan and Samoan f, Maori ɸ, and Rarotongan ʔ.

Mere phonetic similarity, as between English day and Latin dies (both with the same meaning), has no probative value.[31] English initial d- does not regularly match Latin d-[32]—it is not possible to assemble a large set of English and Latin non-borrowed cognates such that English d repeatedly and consistently corresponds to Latin d
at the beginning of a word—and whatever sporadic matches can be
observed are due either to chance (as in the above example) or to borrowing (for example, Latin diabolus and English devil—both ultimately of Greek origin[33]). English and Latin do exhibit a regular correspondence of t- : d-[32] (where the notation “A : B” means “A corresponds to B”); for example,[34]


 English   ten   two   tow   tongue   tooth 
 Latin   decem   duo   dūco   dingua   dent-  

If there are many regular correspondence sets of this kind (the more
the better), then a common origin becomes a virtual certainty,
particularly if some of the correspondences are non-trivial or unusual.[21]

This is at the heart of what Stubbs has done, presenting extensive data on widespread, consistent sound changes that link cognates between Uto-Aztecan languages and three Old World languages (that happen to have Book of Mormon ties). Many are non-trivial, detailed, involve lengthy words and sometimes surprising parallels in meanings and multiple meanings. But Rogers seems to treat this work as amateur excitement over chance parallels.

Suppose, for example, that the German had gone completely extinct a couple hundred years ago and only now had scholars recovered and deciphered a handful of texts. Suppose you are working on the language and begin to notice parallels with English, such as “das Buch” = book, “kochen” = to cook, and “suchen” = to seek. These show a consistent relationship between German “ch” and English “k,” which is far more meaningful than if book, cook, and seek seemed to align with, say, “ubakr,” “kouki,” and “zeqqol.” With chance finds, of course, it is unlikely that consistent patterns will arise. So even if your list of cognates was still small, the pattern of sound changes could help you realize that perhaps more than chance was at play.

But chance is always a possibility. In fact, false cognates due to chance can be found without too much trouble. In Chinese, “fei” can mean “fee,” but there’s no evidence that any legitimate relationship is behind this and many other chance parallels. How often can chance lead to a false cognate? Stubbs suggests it is 1% to 3% of the time. OK, but I think it would be very hard to contrive English-Chinese parallels for 1% of either language. But accepting that range, Rogers crunches some numbers to suggest that the 1500+ cognates presented by Stubbs are meaningless. To do this, he considers that the Uto-Aztecan language family has 30 languages and that Stubbs is scanning 3 Old World languages, which greatly increases the potential for finding parallels. Rogers argues that at a 3% rate of chance cognates, we might expect nearly 5,000 chance parallels, making 1,500 completely pathetic. Here’s the relevant portion of his paper from pages 255-256 (click to enlarge):

There’s clearly something wrong when he reports that 2,598 similarities are expected by chance alone, for that number is the number with a minus sign (i.e., 2,598 less than zero) is the number Table 6 shows remaining after subtracting the actual calculated number of possible false cognates, 4,126, from the number of cognates presented by Stubbs, 1,528. But much more trouble is occurring here than just reporting the wrong sum. This number of over 4,000 false cognates is based on rather spurious math, IMO.

The first additional problem is that Rogers is using the wrong base in calculating potential false cognates. He treats 1,528 as that base, but the base should be the number of words in the language family being considered, which is an even bigger number. But let’s assume that Rogers math is correct and that there’s a base of only 1,528 Uto-Aztecan words, incorrectly implying that Stubbs is proposing that 100% of the UA vocabulary is related to Egyptian and Semitic. Even in that case, Rogers obliterates any cause for excitement by multiplying the upper limit of 3% chance of a random correspondence by 30 Uto-Aztecan languages and by 3 Old World languages, in other words, 0.03 * 30 * 3 = 2.70, giving 270% of the entire vocabulary being subject to false cognates with Stubb’s 3 Old World languages by chance. That’s how 1,528 cognates from Stubbs becomes a potential 4,126 false cognates in the crazy math of Table 6. Something is out of touch with reality here.

Part of the problem here is that the 30 languages of Uto-Aztecan are all related, and that Stubbs is not creating an additional entry and claim for each related cognate in each language. Worse than double jeopardy, Rogers would give a false cognate a penalty of 30 * 3 = 90 words to deduct from Stubbs’ list. Note that almost each of the 1500+ cognates from Stubbs involve multiple languages and usually involve reconstructed Proto-Uto-Aztecan words; he’s not counting a cognate as, say, 15 cognates when half of Uto-Aztecan languages seem to share it, but lists it as one entry.

Further, great weight should be given to cognates that involve Proto-Uto-Aztecan, which would naturally tend to involve multiple modern UA languages. Rogers should consider the high number of cognates that are related to Proto-Uto-Aztecan, where it makes even less sense to conjure up huge numbers of expected false cognates with the multiply-by-30 tactic.

To get a feel for what Stubbs is reporting and how he counts multiple related hits in multiple languages, below is a randomly selected section from Stubbs’ more technical book (I scrolled to a random place and then picked a contiguous section that included discussion of the sound change rule under consideration), where you can see for yourself. Many of those two- and three-letter abbreviations in his explanations are abbreviations referring to specific languages, and UACV followed by a word with a leading asterisk refers to a reconstructed Proto-Uto-Aztecan word from his definitive publication on the language, which is used in each of these entries and I believe the majority throughout the book. Here’s the excerpt from pages 80-81 of Exploring the Explanatory Power of Semitic and Egyptian in Uto-Aztecan, which can be downloaded at for free, courtesy of Jerry Grover (click to enlarge):

Sadly, even some highly educated people have jumped on Table 6 and feel that Rogers with his reported gargantuan numbers for expected false cognates (up to 270% of the vocabulary) has provided compelling reasons to dismiss Stubbs’ work as meaningless garbage all due to chance alone. You can always find a reason to dismiss something you don’t like, but relying on preconceived notions coupled with bad math is not the most accurate way to reinforce your views. These kind of math errors are easy to make, I’ll admit, but it’s unfortunate that they survived peer review for the Maxwell Institute’s publication. What Stubbs gives us requires more thoughtful attention that this. Yes, it’s counter to so much that we think we know so it’s easy to want to dismiss it, but the data is not readily explained by chance cognates, and the patterns of consistent sound changes add a great deal that Rogers is missing. I hope Rogers will give Stubbs a closer look! I think he missed some significant aspects of the work he criticizes. Hoping for a round 2!

I also have to point out that Rogers’ comment on pp. 255-256 about not accounting for the impact of borrowing is quite puzzling. Stubbs is arguing that there was an infusion of ancient languages, not a genetic relationship. Read Stubbs’ response on my previous post to get into that issue more fully. But for today, I’m just addressing the issue of Table 6 and its faulty math.

Author: Jeff Lindsay

84 thoughts on “Bad Math and the Premature Dismissal of Brian Stubbs’ Work on Uto-Aztecan Languages

  1. Golly gee, Jeff, it sure looks like Stubbs’s work is so solid, and the criticisms so lame, that it should have no trouble at all with independent peer review.

    Such an exciting discovery he’s made! He’s revolutionized our understanding not only of New World linguistics, but also New World archaeology, history, genetics….

    It must all be re-thought in light of this amazing discovery!

    Academia must be alerted immediately!

    So why is this amazing discovery being held so close to the vest? Why not share it with the world? Why keep it cloistered?

    Seriously, Jeff, without genuine peer review, you’ve got nothing. The continued avoidance is extremely telling.

    — OK

  2. The wish is that people who claim to follow the truth could actually SEE the truth that the BOM is a big fat fairy tale promoted by people touting the most arcane and tortured logic possible and avoiding any legitimate test of its premises.

  3. Anonymous,

    I am assuming you meant to answer my question.

    Is "I wish for the Book of Mormon to be inauthentic because the Book of Mormon is inauthentic" a fair rephrasing of your answer to the question "What reasons might someone give for wishing the Book of Mormon to be inauthentic?"

  4. Jared,

    There is no wishing involved. I think most are simply trying to point out that the emperor has no clothes.

  5. Jeff and others, don't worry about OK's biased and bone-headed responses.

    Brian Stubbs has sent his 2015 book out for peer review, and some didn't respond to him, but some did, and did so favorably:

    After 35 years of research, I published Exploring the Explanatory Power of Semitic and Egyptian in Uto-Aztecan (2015b), which linguistically establishes a Northwest Semitic (Hebrew/Aramaic) and an Egyptian infusion, language mix, or massive borrowing into UA. Though skepticism was always the initial reaction, those who actually examined the data, among both LDS and non-LDS linguists, Uto-Aztecanists, and Semitists, offered favorable assessments or silence.

    This is solid, important work. But no matter what the quality of work, when it impinges on things that academia is uncomfortable with, academia largely ignores it. That's the way it goes.

  6. Anonymous,

    If you do not agree that someone can possibly have reasons for wishing the Book of Mormon to be inauthentic, you need not respond to my question.

    For anyone else – what reasons might someone give for wishing the Book of Mormon to be inauthentic?

  7. OK,

    Your comments come across as sounding like an elementary school yard bully. You've posited lots of hypotheses over the years but I have yet to see any peer reviewed scholarly articles that support your claims. You want all of us to take your comments


  8. Jared,

    Your question is inadequately framed as it assumes that the BoM is "authentic," and that any thought contrary is merely a "wish." There are those who know that the BoM is "inauthentic," and have multiple evidences that demonstrate it. Why would someone "wish" it were authentic?

  9. Anonymous,

    My question only assumes the BoM may be authentic. It may be false indeed, but so long as its falseness is not demonstrated – either by direct, firsthand experience or by proof by contradiction with direct, firsthand experience – its falsehood is only wished for.

    Let us examine the Book of Mormon, treating its sentences as propositions. Which specific proposition, or set of propositions, from the text of the Book of Mormon have those falsified who "know" – know by direct firsthand experience – that the Book of Mormon is inauthentic, and how, exactly, was their falsity demonstrated?

    Please bear in mind that the Book of Mormon makes no unambiguous internal claim to any known location for its narrative events other than, for the most part, "not Jerusalem," and "not the Tower of Babel." In particular, the Book of Mormon does not seem to make any unambiguous claims that necessitate an ancient American setting.

    So, please tell me by what direct firsthand experience those who know the Book of Mormon is inauthentic came to the knowledge of its inauthenticity.

    1. What constitutes “direct firsthand experience” to you? When I read it I have the direct firsthand experience of reading a 19th century text. That tells me that it is inauthentic in that it is not what it claims to be.

      Do you have “direct firsthand experience” of its authenticity?

  10. Sigh … Jared all you have stated is you don't know what it means for the bom to b authentic, which is telling. As you demonstrate, the nephite lands appear to be ever disappearing, which is not a characteristic of authentic things.

  11. Jared –

    "It may be false indeed, but so long as its falseness is not demonstrated"

    Instead of listing all the ways you believe it cannot be determined to be nauthentic why not describe what you had it mind about how it's falseness could be demonstrated?

  12. Anonymous,

    I hereby relinquish my request to you for you to substantiate your claim that someone, somewhere, both knows the Book of Mormon is inauthentic and has multiple evidences to demonstrate its inauthenticity.

    Does anyone else have an answer as to what reasons someone might give for wishing the Book of Mormon to be inauthentic?

  13. Haha, you see how bogus you are being. You failed to produce a single item that if so, indicates falseness, despite previously claiming it could be possible. Therefore it can not be indicated to be "authentic" either, as you once claimed. So, as the Anon try to help you, your question is loaded, it is not others that wish it to be inauthentic, it is you doing the wishing. Running away from people pointing this fact out to you and seeking imaginary validation.

  14. Jared Livesey @ 6:55

    Fawn Brodie once admitted to Dale Morgan that, after leaving the Church, she had a psychological need to distance herself from Joseph Smith. She ended up meeting that need by writing No Man Knows My History and declaring all out war. Sounds like a reason for someone to want the Book of Mormon to be inauthentic.

  15. Jared that's got to be the stupidest question I've ever heard in my entire life. You should be ashamed of yourself for being so manipulative and fallacious. Do you think you're clever? Do you think you control this conversation? You're not and you don't. Stop thinking you have any sort of upper hand. You're on the losing team.
    There's no wishing involved in any of this. Only truth. Truth will out. The truth is already been out and it has been for a long time. The fruits of this truth are all around you. People are leaving your church in droves. 2 more families in my Utah stronghold ward this summer.
    Keep asking stupid questions, but be sure to look up once in a while. You'll notice the crowd is thinning.
    No one likes being lied to. No one likes being manipulated. No one likes being gas lit.

  16. Direct, firsthand experience is actual sensory experience – seeing, hearing, or touching, for example. Direct, firsthand experience is knowledge, and nothing else is; you know something if, and only if, you are experiencing it – this is definitional. The purpose of this definition is to exclude from that which is called "knowledge" anything which can possibly be false – hence, properly speaking, one only knows what one is presently experiencing, as memory could potentially be faulty.

    It follows that for humans of normal lifespan and sensory capacity that things happening outside of their senses – howsoever defined – cannot be known by definition. Thus unless it is by revelation, which is experienced, no man knows the Book of Mormon to be inauthentic; likewise, no man without revelation knows it to be authentic. And if revelations do not occur, no knowledge about the authenticity of the Book of Mormon – or knowledge about anything outside of our normal sensory operations – is possible. It follows also that knowledge is nontransferrable between humans. All that is available outside of knowledge is superstition, heresay, reports of knowledge, lies, inferences, potentially flawed memories, and the like.

    1. “that things happening outside of their senses – howsoever defined – cannot be known by definition. Thus unless it is by revelation, which is experienced, no man knows the Book of Mormon to be inauthentic;”


      Your reasoning is again problematic. You’re implying that the only way one can quantify an external phenomenon is by means of an internal, non-quantifiable phenomenon. Trusting in revelation to provide accurate, reliable information has been proven historically to be extremely foolhardy. Your likelihood of being correct would be better if you tossed a coin.

  17. Hoosier 8:40 –

    Circular reasoning: "she had a psychological need to distance herself from Joseph Smith" (no reference given) Why did she have a need to distance herself from Joseph Smith? Therefore, all you have done is repeated Jared's manipulative, fallacious reasoning.

    Why do the two of you wish the Koran to be inauthentic. Asked a 100 times, but never answered.

  18. Jared –

    "All that is available outside of knowledge is superstition, heresay, reports of knowledge, lies, inferences, potentially flawed memories, and the like."

    Given that you have no knowledge of what it is you mean by "authentic" all you have is superstition, heresay, lies, inference, flawed memories and the like. As anon 3:28 pointed out, we do indeed have strong evidence that you are not asking a question, but fulfilling a strong psychological need to declare those with knowledge that differs from your belief liars. The way you ran away above (6:55) shows you know you are wrong and are in serious need of psychological help.

  19. Jared – your inability to describe what you mean by authentic proves you are only resorting to semantics to ease your own personal frustrations, which frustrations may be why you wish things to be the way you wish them. Your supposed question answered.

  20. OK, I understand that peer review is in the works in some way — these things take time. But you should know that Stubbs has widely disseminated his work to pretty much all the experts in UA asking for feedback. But in Rogers' peer review process shown in the article in question, we see some of the unfortunate limitations of peer review when one is clearly departing from the "common knowledge" of the field. The problem is introducing advances that cause reflex reactions due to defying old paradigms is that peer review will often not be real review at all, nor thoughtful consideration of the evidence, but a reflex assertion that the work must be completely fallacious, as I think we have beautifully illustrated here. How could Rogers make such glaring mistakes, while being a very smart guy, unless it's just the old story of thinking one knows and defending the common knowledge of the field without giving a fair short to the work. Stubbs knows he has been up against this and yes, it has been difficult, but he's definitely trying, so be patient.

    Peer review was very much the problem that kept the cause and cure for scurvy away from the very intelligent British medical establishment for about two centuries while thousands of men continued to die unnecessarily. Everyone knew, back then, that scurvy had nothing to do with diet, and had already been explained based on Aristotle's theories as due to bad vapors or something equally mysterious. Experimental evidence regarding limes were dismissed as ridiculous, crackpot stuff.

    Peer review held back advances in basic sanitation in hospitals, resulting in thousands of needless deaths while Semmelweis went crazy trying to get people to cleanse their hands to stop spreading germs and killing their patients. Nope, didn't fit the established science and was rejected for way too long. It may take many tries before we can get the extensive evidence from Stubbs to be considered by intellectuals who really don't want to look at such a crackpot idea. Even you, OK, were so quick to bury Stubbs work based on the numbers from Table 6 without being able to see what deeply messed up math was at work. Confirmation bias is hard to shake off, and opening eyes to completely new paradigms is never easy.

    But I share your desire to see this go through further thoughtful peer review and finally be formally published in a solid journal. I believe this will happen, so be patient. But until then, we have much more than nothing. That added recognition will be nice but not essential for intelligent people to consider and debate what Stubbs has published.

    1. "intelligent people" probably prioritize what they will "consider and debate" better …. No wait, on second thought there are intelligent people religiously declaring global warming a bigger existential threat than nuclear weapons , poverty, war, biological outbreaks … May be while people are dying of these actual problems we should have a religious discussion to debate and consider what it means to be an intelligent person.

  21. Holy cow, all this time peer review was the real enemy! The murderer was calling from inside the house, to put it colloquially.
    Way to poison the well, Jeff. When this supposed peer review finally happens, if it ever does, you've propped up an excuse just in case it's less than glowing. Ridiculous.

  22. Stubbs: I have made an astounding discovery that revolutionizes several academic fields!

    OK: Um, I think there might be some problems with your methodology. We need peer-review.

    Steve: It is not Stubbs's work that needs to be peer-reviewed, it is OK's call for peer review that needs to be peer-reviewed.

    Usually you're more sensible than this, Steve.

    — OK

  23. Jeff, you write, Peer review was very much the problem that kept the cause and cure for scurvy away from the very intelligent British medical establishment for about two centuries while thousands of men continued to die unnecessarily.

    This is called "blowing smoke."

    Then you write, But I share your desire to see this go through further thoughtful peer review.

    Wait, what? What about all those poor, scurvy-ridden British sailors? Seriously, if you agree with me that Stubbs's work should be peer-reviewed, why the clumsy, anachronistic effort to discredit peer review?

    You ask, How could Rogers make such glaring mistakes, while being a very smart guy…? I would blame any mistakes (if they are such–you're assuming the facts under dispute) on a lack of peer review. Book reviews are themselves generally not peer-reviewed, nor do book reviews constitute peer review. In fact, instead of assigning book reviews to top scholars in a field, journal editors generally farm them out to advanced grad students and junior faculty like Rogers. (And FWIW, outside of Provo, BYU Studies is not considered a "solid" academic journal.)

    Perhaps most crucially here, Jeff, you say that Stubbs has widely disseminated his work to pretty much all the experts in UA asking for feedback.

    So what you're saying is that "pretty much all the experts in UA" have been exposed to an amazing discovery that completely revolutionizes their field. And yet, several years after having their professional world rocked to its foundations by the knowledge that UA was significantly shaped by a hitherto completely unsuspected infusion of Semitic, all those experts are proceeding as if that discovery had never been made.

    How can we explain this curious indifference? How can Stubbs's work be both so revolutionary and so sound, and recognized by his peers as sound, without in the least influencing their work? The most obvious answer here is that those peers do not believe his work to be sound.

    If these experts found Stubbs's work sound, would they not be proceeding differently than they are? If they found Stubbs credible, wouldn't his discovery be shaping contemporary UA research? Remember, Stubbs's claim is not that he's showed them his work and they've rejected it (as the early British medical establishment rejected basic sanitation). His claim is that they've seen his work and told him it's sound.

    And yet these experts are not factoring this profound Semitic influence into their own work. How very odd!

    My guess is that these experts have not found Stubb's work credible. My guess is that they would not have expressed their rejection to him directly. Out of respect and affection for an old and otherwise competent colleague., they would have praised what they found praiseworthy in his work, been silent about the rest, and then gone on about their own work exactly as before.

    But at least you agree with me about the desirability of "thoughtful peer review." Hasten the day.

    — OK