The Book of Abraham and the Great Toilet Paper Test

In light of the recent controversy over whether and how the length of the original scroll of Hor (the source of Facsimile 1) can be determined, I thought I would have a little fun and try my hand at the problem. (For background see here, here, and here.) However, not having any papyri to measure, I decided to use toilet paper as a model. Below I describe my procedure and present my results.

Methods
I did not want to use a complete roll of toilet paper because that would be a lot of work, so I searched my house for a partially used one. Having located a suitable roll, I located the end of the roll and drew a line along the edge to the cardboard center. I knew that I would not be able to draw a precise line because I needed to use a marker, which bled a little. In order to have a better defined mark along the edge, I used a knife to cut along the line. I then gradually unrolled the roll and measured the length between marks (winding length), rounding to the nearest millimeter (0.1 cm). I found that this particular brand of toilet paper could stretch a few millimeters, so I tried to always measure it while it was relaxed but straight.

The last winding was not directly measured; the circumference of the cardboard tube was used instead. This alternate method was used because it was difficult to obtain an accurate measure of the last winding due to the way the toilet paper was glued to the tube. A small length of paper extended beyond the last mark, but was ignored for convenience. Having completed this series of measurements, I rewound the toilet paper. Anyone who has rewound toilet paper knows that it is never the same as before, with the windings being somewhat more loose. The purpose of this was to simulate thicker toilet paper of the same length. I cut and marked the opposite end of the roll, and measured the new winding lengths. This time I was able to measure the last (innermost) winding length directly.

Exterior windings can be used to calculate the maximum length of missing inner roll using the Hoffmann formula. John Gee has given the formula as Z=((E²-6.25)/2S)-E, where Z = the missing remainder of the roll, E = the length of the last existing winding, and S = the average change in winding length. Andrew Cook has given the Hoffmann formula as Z=(E²–6.25)/(2S)–E+S/2. Not having access to Hoffmann's original publication, I can't say which is correct. However, I found that the two formulas agreed to within a centimeter, so for my purposes the difference is irrelevant. Here I report the form given by Gee.

Cook and Smith expressed their formula as L_n = (W_n²-W_N²)/(4piT). Although it looks different, this formula is almost identical to the Hoffmann formula, which is illustrated to the right where I have colored identical terms. Hoffmann uses 6.25 (i.e. 2.5²) assuming that the missing innermost winding would be no less than 2.5 cm. For the toilet paper, I used the actual last winding measurement in its place. T represents the change in radius, while change in winding length (S) can be thought of as circumference. Thus S = 2(pi)T (i.e. circumference = 2(pi)r), and 2S = 4(pi)T. According to Cook,

Our centered convention for the winding numbers and definition of where the missing section begins removed the factor of –E+S/2 from the right-hand side.

I don't quite understand how that works, so I just went ahead and compared the results of the equations in a straightforward manner. I don't know which is most appropriate, but I found that using Cook's expression yielded a remainder of zero on the last winding, while Hoffmann's (via Gee) gave a negative number, which suggests to me that Cook's expression is better.

Results
The results of my two tests are shown below (click for large). Each graph represents the predicted maximum length of roll remaining at each winding based on the two formulas, compared to the actual remaining length. For each test, S (or T) was calculated from either a running average of change in winding length (i.e. average of all previous windings), or as a sliding window of the average of the three previous windings. (Note that the sliding window begins at winding 4; the running average begins at winding 2.)

The Hoffmann and Cook formulas gave nearly identical results, which is not surprising since the equations are essentially the same. Test 1 using a running average S (or T) tended to overestimate the maximum remaining length, but gave fairly consistent results. In contrast, the sliding window of S (or T) gave predictions that often varied from the true remainder, sometimes dramatically.

Results for the running average S (or T) for Test 2 tended to underestimate the maximum remaining length, while the running average gave more accurate predictions. I believe that this can be accounted for by the fact that I rerolled the toilet paper by hand, which resulted in the outer windings being looser than the inner ones. The initially large changes in winding length (S) of the outer windings--as the winding became tighter--had a large impact on the running average S (and T). The sliding window, in contrast, used only local changes in S (or T) and so calculations for inner windings were not affected by the loose outer windings.

In his rebuttal to Gee, Cook wrote:

Another way of determining a scroll’s original length, which involves less math, is to plot the lengths of the extant windings and fit a straight line to the results. The missing windings will reliably lie along the straight line.

I tested this by doing a linear regression (using the spreadsheet trend function) on either the first (outer) 3 or 10 windings. Using only 3 windings yielded a prediction that was reasonably accurate for Test 1, but clearly inaccurate for Test 2. However, in both cases using 10 windings yielded predictions that agreed well with the actual length.

Cook's rebuttal contains the first seven measured winding lengths of the Hor scroll, as well as 12 remaining interpolated winding lengths. I applied the Cook/Smith formula to the first seven windings using the T value reported in their original article. I then compared that to the length given by linear regression based on the same seven windings. Agreement between the two was quite good. Finally, I compared these results to a linear regression based on only the first three winding lengths, which gave the same result to within 3 cm of the other regression.

Note: Spreadsheet is available here

Conclusions

I undertook this toilet paper test primarily as a fun exercise, and its results are only as good as my competence and accuracy, both of which may be called into question. Nevertheless, based on my exercise I conclude the following:

1. The Hoffmann and Cook/Smith formulas are essentially the same and give very similar results. Why exactly Gee found otherwise will remain unknown until he is more specific about his method. Cook has suggested that Gee mistakenly applied Cook and Smith's derived value of T for the Hor scroll to the Royal Ontario Museum, not understanding that T is unique to each scroll and derived from the winding lengths.

2. Although they may be sound in theory, these formulas can give inaccurate results, which I think can partially be attributed to uneven tightness in winding. Whatever the source of error, I think it is wise to treat the results with caution, as my results in some ways mirror those of Gee's for the Royal Ontario Museum scroll.

3. Linear regression based on as few as 10 windings gave reasonably accurate results in both tests. This may represent a better approach and, at the very least, can serve as a cross-check.

4. In the particular case of the Hor scroll, linear regression based on Cook and Smith's measurements of extant winding lengths agrees well with results obtained from using their formula, even when the regression is done using as few as three windings. I therefore think that their conclusion that the missing inner portion of the scroll was 56 cm is correct to within 10 cm. (Cook has revised the length to 51 cm because of a calculation error. My linear regression using seven windings put the missing portion at 60 cm. However, if we assume that winding lengths could be as small as an unrealistic 0.2 cm, the linear regression puts the missing length at 65 cm.)

In summary, although I believe Gee has legitimate reason to be wary of the application of these formulas, Cook and Smith's estimate of the lost portion of the Hor scroll seems correct. What, if anything, this means for the Book of Abraham depends on other assumptions and considerations.

References:
1. John Gee, Some Puzzles from the Joseph Smith Papyri.

2. Andrew Cook and Chris Smith, The Original Length of the Scroll of Hôr (pdf).

3. John Gee, Formulas and Faith.

4. John Gee, Book of Abraham, I Presume.

5. Andrew Cook, Formulas and Facts: A Response to John Gee.

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The Joseph Smith Papyri: Updating the Length Controversy

Last June I blogged about attempts to determine the original length of a scroll of papyrus that Joseph Smith possessed, and from which he may have derived the Book of Abraham. At the very least we know it is the source of Facsimile 1. Andrew Cook and Chris Smith (neither of which are believing Church members, as I understand) developed a mathematical approach to determining the winding length of the scroll, which is more precise and sophisticated than simply eyeballing the papyri, and then applied a formula to determine the original length of the scroll. Their conclusion was that the scroll of Hor was too short to have contained the Book of Abraham.

John Gee, an Egyptologist associated with FARMS/Maxwell Institute, published an article in which he criticized Cook and Smith's method. According to Gee, their formula gave inaccurate results when applied to an actual complete scroll. However, I noted that I found Gee's article unsatisfactory because it did not engage Cook and Smith's article in the level of detail that it deserved. Further, in laboring to discredit their work, Gee missed or ignored the fact that their conclusion was compatible with what Gee claims to be a popular LDS view: that the Book of Abraham was more a product of revelation than a translation of text.

There have been a couple of additional developments in this little controversy, and so the story needs updating. I will take them in chronological order.

Last month Gee spoke at the annual FAIR conference and his talk touched on this issue. After briefly introducing his own attempts to apply a standard mathematical formula (developed by someone named Hoffmann), Gee said,

Andy Cook developed a slightly different formula and he and Chris Smith applied it to one of the papyri and they’ve been loudly proclaiming that they who have never worked with papyri know more than I who have been working with papyri for a quarter of a century.

Gee then showed his previously published figure that compares a known full scroll with application of Hoffmann's formula compared to Cook and Smith's. Gee claimed to have found 5 errors in Cook and Smith's work, though he did not specify what they were. He then showed the results of fixing one of those unspecified errors, which greatly improved the results (red), compared to the real scroll length (blue) and Cook and Smith's original formula (green). (For some reason, he could not be bothered to label his data series or axes.)

Gee commented:

The errors are therefore something in Cook’s formula and methodology and not something in the papyrus measurements. It shows us that Cook’s methodology is fundamentally flawed.

Now, I attribute Cook’s mistakes to working in a new field, where neither he nor Chris Smith have had any experience working with papyrus before. And there were some math mistakes that for some reason Cook did not catch. As you can see, if he corrected one mistake it would have made a big difference in his results.

Gee concluded by saying that both the Hoffmann and Cook/Smith formulas make some "fallacious assumptions" and that they can, at best, "give a ballpark estimate."

Andrew Cook has responded in the most recent issue of Dialogue. The article, "Formulas and Facts: A Response to John Gee" (subscription required) hits back at Gee on several counts. According to Cook,

1. Gee misunderstands the Cook/Smith equation, not realizing that it is the same as the Hoffmann equation, though expressed slightly differently.

2. As a corollary, Gee's representation of differences of result between the Hoffmann and Cook/Smith formulas is incorrect. They should be exactly the same.

3. Gee erroneously accuses Cook and Smith of estimating the thickness of the papyri in order to derive winding lengths, when in reality Cook and Smith measured winding lengths in order to derive thickness.

4. Differences in the smoothness of the two lines suggest that Gee did not treat the formulas consistently, which had the effect of exaggerating the alleged inferiority of Cook and Smith's formula. Further, it appears that he applied the thickness derived by Cook and Smith for the Hor scroll to the known Royal Ontario Museum (ROM) scroll instead of deriving a new value for the ROM scroll.

5. Cook obtained winding measurements for the same ROM scroll, and applied the Hoffmann and Cook/Smith formulas, and compared the results to the actual scroll length. The results of the two formulas were identical, and both were nearly identical to the actual scroll.

6. The novel contribution of the Cook/Smith paper was the autocorrelation method of identifying the winding lengths, which has been mostly overlooked. Accurate measurement is important for the reliability of the result.

7. Cook concedes that their paper contains a calculation error. However, it is not known whether that was among the errors Gee claimed to find, and anyway it only made a difference of 5 cm in the final result.

I can't adjudicate all of these points, but I think Cook makes a good case. For example, take point #3. In his "Formulas and Faith" article, Gee wrote:

Cook and Smith use the thickness of the papyri (which they did not measure but only estimated) as an indication of the change in diameter to calculate the difference between the lengths of successive windings in the scroll. Hoffmann—knowing that most papyri are already mounted, thus rendering it impossible to measure the thickness—uses the average difference between successive windings for the same purpose....

With the data gleaned from this intact roll in Toronto (that is, the individual winding lengths), I applied each of the mathematical formulas, using the assumptions made by the authors of the formulas concerning papyrus thickness, air-gap size, and size of smallest interior winding.

But as Cook correctly points out, they clearly did not begin by estimating the thickness and air-gap size. Rather, they used a similar method to that of Hoffmann--using winding length to derive effective thickness (i.e. change in radius). "Our primary task therefore, is to determine the effective thickness of the papyrus from the winding lengths." I can't help but conclude that Gee is wrong here.

It appears to me that on the technical merits Cook and Smith really do have the upper hand. Gee may have a quarter of a century experience working with papyri, but it's not obvious to me why that should give him mathematical superiority, particularly when his adversary (Cook) is apparently a theoretical physicist. We are talking about physical dimensions here, after all. If Gee ends up eating humble pie after having trashed Cook and Smith's work, he's only got himself to blame.

However, I do think that Gee's sense of caution is legitimate. I will explain why in my next post.

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The Book of Abraham: FARMS Phones It In

The most recent issue of the Maxwell Institute (FARMS) publication Journal of the Book of Mormon and Other Restoration Scripture (21:1) is now available online, and it has an article by LDS Egyptologist John Gee titled, "Formulas and Faith." Here, Gee addresses mathematical attempts to determine the length of the Joseph Smith papyri (which I discussed earlier). I should make clear that I am not any kind of expert on the papyri or the running arguments surrounding them. Nor do I know much about the persons involved. Nevertheless, I'm sorry to say that I was disappointed in this article for reasons that I will explain below.

Gee sets the issue up as follows:

One of the more prominent issues with the Book of Abraham is the relationship of the Book of Abraham to the Joseph Smith Papyri. There are three basic positions here:

1. The text of the Book of Abraham was translated from papyri that we currently have. (Or, from the unbelieving perspective, Joseph Smith thought that the text of the Book of Abraham was on papyri that we currently have.)

2. The text of the Book of Abraham was translated from (or Joseph Smith thought the text of the Book of Abraham was on) papyri that we do not currently have.

3. The text of the Book of Abraham was received by revelation independent of the papyri.

Gee notes that hardly any informed Mormons accept the first proposition. It may come as a surprise that Gee claims that the third option is held by a majority of Church members (something that may be worth some further attention later). From that perspective, the issue of scroll length is moot, but in light of the second theory Gee is willing to discuss the matter anyway (though I think I detect a sigh and roll of the eyes).

The crux of Gee's argument is that the formulas developed by Cook and Smith, and others, have not been tested on papyrus scrolls of known length. But Gee says that he has done so.

In November of 2010, I had the privilege of measuring the interior seventy-three windings of [a scroll at the Royal Ontario Museum] (after that point the scroll is no longer contiguous).

With the data gleaned from this intact roll in Toronto (that is, the individual winding lengths), I applied each of the mathematical formulas, using the assumptions made by the authors of the formulas concerning papyrus thickness, air-gap size, and size of smallest interior winding. I then compared the outcome with the actual interior length of the scroll. The results are shown on the graph.

I have to admit that I'm not entirely clear on how to interpret this graph--I think it shows the predicted remaining length as each additional winding is included in the calculation, with the outermost winding being number 72. Nevertheless, Gee's message is clear: neither formula is perfect, but Cook and Smith's formula is not even close.

On the basis of observations I have made while measuring various scrolls, I am not convinced that these formulas can ever yield anything more than rough approximations. More empirical data is needed to make refinements in the formulas.

Fair enough. It's worth noting, however, that if Cook and Smith's method underestimates true length by up to 75% (as Gee claims), that still puts the Hor scroll length at only 600 cm, less than half of Gee's estimate using the Hoffman formula, and perhaps a little cramped for the Book of Abraham. Nevertheless, Gee's caution is a point well taken. However, if you recall my previous post, Cook and Smith were explicit about their methodology, spelling out measurements, assumptions, and formulas. They wanted others to be able to reproduce their work. Now if you were Cook and Smith (or an interested third party) you might want to know where their formula breaks down, or how to adjust it to make it more accurate. Unfortunately you won't get any help from Gee in this article. Aside from the number of windings and the total length of the scroll, no measurements or details of how the winding locations were identified are given, nor is there any hint that they are forthcoming. All we have to go on is a graph and his assurance that it doesn't work. Nor does Gee address Cook and Smith's different winding length measurements for the Hor papyri. That seems like an insufficient response to me.

Moving on, I think Gee's article mis-characterizes the Cook and Smith article. First let's review the basic argument of Cook and Smith (my paraphrase):

1. Based on our calculations, the Hor scroll is too short to contain the Book of Abraham.
2. There is reason to think that the Hor scroll was the one identified as having the writings of Abraham.
3. Therefore, the Book of Abraham is probably not a direct translation of Egyptian text.

Before we look at Gee's further criticisms, you need to know that one witness described seeing a "long roll" (the apparent source of the Book of Abraham) and "another roll." Now let's look at Gee's criticisms, which are mostly confined to three paragraphs. We'll take them one at a time.

Although the Cook and Smith method of determining scroll length is anything but accurate[,]...even if it had been successful, it would have created other problems. Cook and Smith fail to establish which was the long roll because they applied their formula only to the Horos scroll; they did not apply it to any of the other extant scrolls and thus fail to meet another of the necessary conditions.... They measured only the Horos scroll because they assumed it to be the source of the Book of Abraham. Yet the eyewitnesses identify the long roll as the source. Bent on proving that the Horos scroll was not the long roll, they overlooked the implications of such a view. If the scroll of Horos is not the long roll, it simply cannot be the source of the text of the Book of Abraham (according to the accounts of the eyewitnesses). By endeavoring to prove that the Horus scroll was not the long roll, they would have undermined their own case, which depended on the Horos scroll being the proposed source of the text of the Book of Abraham.

'Long' is a relative term, and it seems to me that Gee is perhaps putting more weight on the distinction between a roll and a long roll than is warranted. (Wouldn't five feet be long to a non-Egyptologist?) Be that as it may, I don't see any evidence that Cook and Smith were "bent" on proving the Hor scroll was not the long roll. They don't frame the question in that way and, in fact, they don't even address the issue of the long roll until the end of their article when, lo and behold, they suggest that the Hor scroll was indeed the long one. But even if Gee is right about Cook and Smith disqualifying the Hor scroll as the long one, does that undermine their case? I guess it depends on what you interpret their case to be. Gee seems to imply that their case is that the Book of Abraham is bogus. But whatever the authors think personally, their article does not argue such a thing. At any rate, their immediate conclusion is that the Hor scroll did not contain the text of the Book of Abraham. If they unwittingly demonstrated that the other scroll was longer, then by Gee's criteria their conclusion is actually stronger.

Cook and Smith would like to minimize the length of the Horos scroll because they believe that finding would eliminate the possibility that the Book of Abraham was translated from a scroll that we do not currently have (theory 2). Even if their calculations had been correct and thus had shown that the scroll of Horos was not the long roll observed by the witnesses, that simply would have meant that another scroll would have been the scroll containing the Book of Abraham. So their attempt to eliminate theory 2 as a possibility would not, in fact, have actually been successful even had their formula correctly predicted a short length for the scroll of Horus.

Here Gee makes a logical leap of his own, which is to assume that if the Hor scroll was too short to contain the Book of Abraham, then another scroll must be longer. What is the justification for that? Gee makes a good point--that it would have been better if Cook and Smith had also evaluated the other fragments for comparison. But if Cook and Smith had determined that another scroll was longer, would that necessarily mean anything? I guess it depends on how much longer. But at the very least, someone would need to explain why the Book of Abraham referred to a vignette (Facsimile 1) on a totally different scroll, which was owned by a different person [1].

Furthermore, their attempt, even if successful, would not have eliminated the most popular theory—that Joseph Smith received the Book of Abraham by revelation unconnected with the papyri (theory 3). It certainly cannot force anyone to accept the theory that the Book of Abraham was translated from the extant fragments of the Joseph Smith Papyri (theory 1) since that theory is excluded by the historical evidence. So for those who care about such matters, there are still two theories (2 and 3) that are not excluded from consideration.

Here we come to the reason I quoted the conclusion of Cook and Smith in my previous post. Having ruled out the scroll of Hor as the source of the text, they listed several alternatives. Here they are again:

(1) the Document of Breathing served as a mnemonic device for the Book of Abraham, (2) the Breathing text served as a catalyst (rather than source text) for the Book of Abraham, (3) the Document of Breathing is a corrupted version of the Book of Abraham, which Smith restored to its pristine state, or (4) the Book of Abraham is simply an imaginative mistranslation of the hieratic script.

Hey, I recognize that second option and it looks a lot like Gee's theory 3. Gee doesn't seem to recognize that Cook and Smith's work supports his preferred theory (at least by popularity--allegedly), by their own admission.

All of this leads me to conclude that Gee's article does not engage Cook and Smith's work in a fair or convincing manner. People who only read Gee's article will get the impression that he has bested bumbling critics who can't construct a coherent argument. However, having read both articles, I get the impression that Gee didn't read theirs very carefully.


Notes:

1. One suggestion that I have seen is that Abraham referred to a figure that was missing from the papyri, so Joseph adapted by using a different illustration.

Further Reading:
A Guide to the Joseph Smith Papyri by John Gee

Eyewitness, Hearsay, and Physical Evidence of the Joseph Smith Papyri by John Gee

Some Puzzles from the Joseph Smith Papyri by John Gee

I Have a Question: Why doesn’t the translation of the Egyptian papyri found in 1967 match the text of the Book of Abraham in the Pearl of Great Price? by Michael D. Rhodes

Criticisms of Joseph Smith and the Book of Abraham, by W. V. Smith

FAIR Wiki: Book of Abraham Papyri

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Was the Book of Abraham Too Long for its Papyrus?

While the saints were in Kirtland, Joseph Smith acquired some Egyptian mummies and papyri from a traveling showman. Having examined the papyri, he said that they contained the writings of Abraham and Joseph of Egypt. The Book of Abraham, now in the Pearl of Great Price is the product of Joseph's translation work. Because the outermost portions of the scrolls of papyri were fragile, they were separated from the rolls and mounted on paper. Following Joseph's death, the papyri were divided up and some of them ended up at a museum in Chicago, where they were apparently destroyed in the Chicago Fire of 1871. However, at least some of the mounted fragments of papyri eventually made their way to the Metropolitan Museum of Art in New York City in 1918, and were later given to the Church in 1967. One of the fragments of papyri is immediately recognizable as Facsimile 1 in the Book of Abraham.

The re-discovery of the papyri was exciting because it offered an opportunity to check Joseph's translation against that of modern scholars. It quickly became apparent that the surviving fragments did not contain the Book of Abraham. At first glance it appeared that Joseph Smith was proven wrong. However, although one might expect the writing surrounding the vignette that became Facsimile 1 to be the Book of Abraham, defenders have noted that the Egyptians often placed vignettes next to unrelated text. It is therefore possible that the text of the Book of Abraham came from another portion of the papyrus. But how much papyrus was there?

Joseph originally had at least five different documents, with only three of them represented by surviving fragments of papyri. Facsimile 1 comes from a document called the Book of Breathings made by Isis and was owned by a man named Hor. Facsimile 3 also comes from this scroll, but it was destroyed in the fire with the rest of the scroll. Facsimile 2 was an independent document. Given that the Hor scroll contains (or contained) Facsimiles 1 and 3, it is natural to assume that this scroll was the source of the Book of Abraham. This assumption is strengthened by the book itself, which says:

12. And it came to pass that the priests laid violence upon me, that they might slay me also, as they did those virgins upon this altar; and that you may have a knowledge of this altar, I will refer you to the representation at the commencement of this record.

13. It was made after the form of a bedstead, such as was had among the Chaldeans, and it stood before the gods of Elkenah, Libnah, Mahmackrah, Korash, and also a god like unto that of Pharaoh, king of Egypt.

14. That you may have an understanding of these gods, I have given you the fashion of them in the figures at the beginning, which manner of figures is called by the Chaldeans Rahleenos, which signifies hieroglyphics. [Abraham 1:12-14]

So how long was the Hor scroll? The surviving portions of this scroll apparently come from the outer end, as mentioned above. Although its original length is unknown, one can take a couple of approaches to estimating. One way is to compare to similar scrolls of the same period. You can also take a mathematical approach to the question because when the scroll was wrapped up, the outermost portion of the scroll contained the rest within it. With an idea of the winding length and the thickness of the papyri, one can estimate the maximum length of the scroll. (Imagine taking a roll of toilet paper and using a marker to draw a line from the cardboard tube to the outer edge--but just on one side so that the line roughly represents the radius. When unrolled, you would see a repeating pattern of marks at one of the edges. The distance between marks would be the winding length, which shortens as you progress toward the original center.)

LDS Egyptologist (and FARMS associate) John Gee originally went with a generic estimate of 320 cm (10.5 ft). However, after applying a published mathematical formula, he updated his estimate to 1250.5 cm (41 ft).

So far so good.

In the Winter 2010 issue of Dialogue: A Journal of Mormon Thought, independent researchers Andrew W. Cook and Christopher C. Smith published a paper, "The Original Length of the Scroll of Hôr," that took another look at the question [1]. They wrote:

Gee reported 9.7 and 9.5 cm as the lengths of the first and seventh windings, respectively, but offered no details regarding identification of winding locations. When we attempted to replicate Gee’s results, we found that his measurements did not seem to be accurate, and in fact required that the papyrus be impossibly thin.

In the rest of their paper, Cook and Smith described in detail how they attacked the question. Briefly, they traced the original papyri (because they were not permitted to photograph them) and then digitized their tracings to convert them into a grid of measurements. To determine winding locations (i.e. repeating patterns of damage to the upper and lower edges), they used a mathematical autocorrelation formula in order to reduce subjectivity. Let's look at an example. First we have a tracing of the papyri overlaid onto an independently obtained photograph.

Next, the upper portion of the of the tracing has been digitized into a coordinate system that matches the contour of the of papyri (though it is a little vertically stretched). The dotted lines show the same tracing shifted 10.42 cm to the right. Note the general agreement in contour.

Here is the output of the correlation function, which has a peak at 10.42 cm. This is the winding length, and was used in the last figure to determine the winding location.

Cook and Smith applied this method to the top and bottom of each fragment from the Hor roll. A cursory examination of the paper reveals lots of mathematical formulas and figures. The authors wrote:

Our choices are based on a desire to provide all details necessary for others to verify our work and duplicate our results.

In endnote 39 they add:

We are happy to make our data available to anyone interested in verifying our results.

I'm not going to pretend that I fully understand their method. Math is not a strength of mine. But those who do understand should be able to replicate their results.

When it's all put together, Cook and Smith estimate that the Hor scroll was approximately 150 cm (4.9 ft). Their estimate is within 3 cm of that of Klaus Baer (Hugh Nibley's Egyptology tutor). Based on the width of the surviving columns of text, and how it correlates to English translation, Cook and Smith estimate that the Book of Abraham would have required at least 511 cm (16.8 ft). Therefore, they argue that the Hor scroll is too short to have contained the Book of Abraham.

I don't know whether they are right or not, but it's a fun and interesting exercise. Their concluding paragraphs will be important later, so I quote them in full.

In recognition of the unlikelihood that there ever was a Book of Abraham source text on the inner section of the Hôr scroll, several alternative theories have been put forth to the effect that: (1) the Document of Breathing served as a mnemonic device for the Book of Abraham, (2) the Breathing text served as a catalyst (rather than source text) for the Book of Abraham, (3) the Document of Breathing is a corrupted version of the Book of Abraham, which Smith restored to its pristine state, or (4) the Book of Abraham is simply an imaginative mistranslation of the hieratic script. The ultimate success of any existing or future theory will depend on its ability to account for all of the evidence, including the fact that there was simply no room on the papyrus for anything besides the Breathing text.

Irrespective of Joseph’s method of translation, it is clear that he sensed in the Hôr scroll a richness of symbolic and religious potential that contemporary scholars could not see. To the experts who viewed Chandler’s collection in New York and Philadelphia, the Hôr scroll was a cryptic relic of a dead religion from a dusty tomb. Joseph, however, breathed fresh meaning into the crumbling little scroll, giving it new life as powerful scripture for the latter days. Perhaps the Egyptian vision of the afterlife, described in Hôr’s Document of Breathing, is not so far-fetched after all.

In my next post we will look at the FARMS response.

Notes:

1. Cook is a physicist and Smith is a graduate student in religious studies. Smith is not LDS; I don't know about Cook.

Further Reading:
A Guide to the Joseph Smith Papyri by John Gee

Eyewitness, Hearsay, and Physical Evidence of the Joseph Smith Papyri by John Gee

Some Puzzles from the Joseph Smith Papyri by John Gee

I Have a Question: Why doesn’t the translation of the Egyptian papyri found in 1967 match the text of the Book of Abraham in the Pearl of Great Price? by Michael D. Rhodes

Criticisms of Joseph Smith and the Book of Abraham, by W. V. Smith

FAIR Wiki: Book of Abraham Papyri

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What the Big Bang Means for Mormons

Since we're on the topic of the Big Bang, I want to highlight an article from the FARMS Review (now Mormon Studies Review) in 2004: The Big Bang: What Does It Mean for Us? by Hollis R. Johnson, an emeritus professor of astronomy at Indiana University. The essay is a response to an evangelical critique of LDS doctrine, but it serves as a nice accessible introduction to cosmology. You should read the whole thing, but I'll give you the nickel version.

To understand the evangelical critique, you have to know that the original formulation of the Big Big bang envisioned the initial state of the universe as infinitely dense and infinitely small, known as a singularity. This fit nicely with creation ex nihilo, and also implied that if God exists in space and time, then he was a product of the Big Bang.

This notion of singularity has had a lot of staying power in the popular understanding of the Big Bang, but Johnson points out that science has moved on and the singularity has been discarded. For one thing, the notion of a singularity is at odds with quantum mechanics because it would violate the Heisenberg uncertainty principle. (I presume that this holds for black holes as well?) This and other questions gave rise to inflationary cosmology, and the concept of the multiverse.

So what does the multiverse mean for our theology? Well it supports the teaching that matter (i.e. energy) is eternal. It's less clear to me what it means for God or our future in this universe, but Johnson thinks it's premature to take a strong stand on these things anyway. He chastises critics for assuming any particular scientific model as the final truth, especially when dealing with a topic as large and mysterious as cosmology. His frustration with theologians comes through in these two gems:

Creation from nothing is clearly a fantasy devised by certain theologians, perhaps in a misguided attempt to glorify God by making of him a fantastic magician.

How long is eternity? Theologians can speculate forever, while scientists continue to provide a factual time line.

The straightforward and unapologetic explanation of cosmology makes this essay one of my favorite FARMS Review essays.

Note:

I found a minor mistake that is hardly worth bringing up, but I'm going to anyway. Footnote 7 says: "Note that numbers in an exponent simply show the number of zeros after (+) or before (-) the given digits. For example, 10⁵ means 1 followed by 5 zeros (100,000), and 10^—9 means 1 preceded by a period and 9 zeros (.0000000001)." The first part is correct, but the second is not. 10^—9 = .000000001; one preceded by eight zeros.

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Spend an Evening with Daniel Peterson

It's been a little while since I've checked in on the Mormon Stories podcast, and boy have I been missing out. Today I want to highlight a 4-part interview with Daniel C. Peterson. That works out to about 4.5 hours of discussion with one of the Church's chief (if not the chief) apologists. It's a wide-ranging and pretty frank discussion, and I thought it was just delightful. Here are a few of the gems that I picked out:

- He has an abiding interest in astronomy, cosmology, and geology. In fact, he originally intended to be a cosmologist.

- A desire that we teach our history better (i.e. warts and all), and that Sunday school in general be improved. In connection with this, Peterson tells some amusing stories about his time on the Sunday school manual-writing committee.

- While serving as a gospel doctrine teacher, he talked about the human side of prophets (e.g. Nephi probably was a really annoying younger brother). A contingent of the class complained to their bishop that he was teaching "secular humanism."

- Speaking of humanism, Peterson sees Mormonism as a kind of theistic humanism, and thinks that non-religious humanists have important things to say.

- His opinion that many prophecies, and their fulfillment, are often a reflection of God's power to bring things to pass in the way he chooses, rather than some kind of predestined future.

- A second-hand story that President Eyring remarked that most high priest groups have more doctrinal certainty than the First Presidency.

I want to dwell on one part of the interview for a moment, because I think it needs some challenging. In defense of Joseph Smith's use of folk-magic, Peterson pointed out that dowsing for water is still a wide-spread practice, and told of a personal experience where dowsing for water seemed to work. First I should note that although that line of defense might work well with religious critics, it makes things worse for someone of a scientific skepticism orientation. This is because dowsing appears to be a phenomenon that can be attributed to subconscious cues and muscle movements, and retrospective justification. In short, it appears to be a psychological illusion, similar to facilitated communication and Ouija boards.

I don't doubt Peterson's sincerity (and to be clear, he does not claim that dowsing does in fact work), nor am I in a position to judge his experience, but his story does raise some red flags. For example, he and others may have received subtle cues as to where the water pipe was. Did the dowsing rods cross at exactly the right spot, or was there an element of 'close enough,' that artificially inflates the number of hits? Further, Peterson discounts the guy for whom the dowsing failed, attributing the failure to his not holding it right. As convincing as the experience sounds, a lot of ordinary possibilities remain. So, I agree that Joseph's use of folk-magic is not, in and of itself, any more scandalous than dowsing, but let's be careful in comparing him to a practice that controlled tests have repeatedly shown to be illusory. (Actually, I'm open to the possibility that many of Joseph's magical experiences were honest illusions, but that's another discussion.)

Anyway, my overall impression of the discussion is that Daniel Peterson and I think a lot alike, and his view of Mormonism resonates with me in many ways. I don't say that as though he should be flattered or to inflate my own status. I simply mean that Peterson has impeccable LDS credentials, so when I agree with him about something that isn't the company line, so to speak, I think I'm in good company.

In the spirit of this blog, I want to finish with a couple of quotes that I really liked.

To the extent that there is an anti-scientific, anti-intellectual strain in CES [the Church Educational System], that's something that needs to be rooted out. This does not help us. And I know that there is a movement on in the Church right now with some people pushing certain geographical theories of the Book of Mormon, and a component of that is young-earth creationism, anti-evolutionism. This worries me enormously, because it can't be sustained.

And later:

We're not fundamentalist Protestants who happen to have an extra book, and maybe an extra wife.

...Mormonism itself is bigger than that. And I object to it when critics try to paint us as a narrow-minded little fundamentalist sect, and I really object to it when Mormons try to do it. And I don't like it from either side. That's why I object to some of this young-earth creationist stuff that I'm hearing recently. No, no, that's not us.

Preach it, brother!

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Abraham's Allegorical Astronomy

Several years ago I highlighted three chapters from the FARMS book, Astronomy, Papyrus, and Covenant. One of the chapters, "'And I Saw the Stars': The Book of Abraham and Ancient Geocentric Astronomy," by John Gee, William J. Hamblin, Daniel C. Peterson, argues that the Book of Abraham (specifically, chapter 3) is best read in the context of a geocentric astronomy. I've felt that this chapter is an important example of putting scripture into an ancient context that does not fit with modern science, and it is done so by LDS scholars of unquestioned faith.

This week I came across an article that takes this a step further. In his 2009 article, Encircling Astronomy and the Egyptians: An Approach to Abraham 3, BYU Associate Professor of Ancient Scripture and Egyptologist, Kerry Muhlestein, argues that the astronomical paradigm is irrelevant to the meaning of the Book of Abraham.

I think we stumble when we attempt to understand Abraham’s vision in terms of astronomic paradigms. It is quite likely that the Lord was describing astronomy and the heavens allegorically in order to teach doctrinal, not astronomical, principles. While attempting to understand astronomical principles has merit...and while there may be an understandable cosmic paradigm to be teased out of the narrative, it seems that the allegorical teachings are the weightier matters as far as the gospel classroom is concerned.

Muhlestein goes on to explain the importance of the planets and stars to the Egyptians and how, in chapter 3, God was preparing Abraham to be able to teach the Egyptians using astronomy as basis for communication.

I was slightly surprised to find that this thesis--a rejection of scriptural literalism and concordism--was published by the Religious Studies Center, an arm of the BYU Religion Department. Good on them. As I have noted on several occasions, other Christians have been taking this basic approach with the creation scriptures for a while now. I know of only a couple of attempts by LDS authors to do similarly, but most Church members would probably consider them unorthodox at best.

Muhlestein's article gives me hope that what's good for Abraham chapter 3 will also be good for chapters 4 and 5.

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FARMS Review on the Book of Mormon, DNA, and Creationism

FARMS Review Vol. 22 No. 1 is up on the FARMS website. Two reviews are of particular interest here.

First is The Book of Mormon and the Origin of Native Americans from a Maternally Inherited DNA Standpoint by Ugo A. Perego, who is a geneticist at the Sorenson Molecular Genealogy Foundation. This article does not review a particular publication; rather, it is more of a topical review. Actually it has been available at FAIR for a few months now, and I have been remiss in not pointing it out. In fact, I recommend that you look at the FAIR version because it has some figures not contained in the FARMS version. (The FARMS PDF version has the figures, but the resolution is better at FAIR.)

This article ranks high on my list of authoritative articles about DNA and the Book of Mormon. It's written for lay people, but I'm afraid many will still find it too technical. (If anyone need help translating the jargon, I'm happy to help.) One of the things I love about the article is that from what I can tell it is straightforward and true to the science. For example, let's look at Figure 1.

Click to enlarge.

This figure shows how mitochondrial DNA lineages are related to one another. Not only does the Y axis show the appropriate timescale (200,000 years), but it also helps to show how we know that all of humanity originates in Africa. See that cluster of lineages on the left? Those are African lineages. The extended group of lineages on the right are the rest of the world. You can see that they are basically a subset of the African lineages. (See also Figure 4.) Anyway, kudos to Perego.

Next there is an extended, withering criticism of Rod Meldrum's book, Rediscovering the Book of Mormon Remnant through DNA, in Often in Error, Seldom in Doubt: Rod Meldrum and Book of Mormon DNA, by Gregory L. Smith.

Meldrum quit his day job to become a full-time for-profit (but still amateur) Book of Mormon geography researcher. He has formed his own organization, The Foundation for Indigenous Research and Mormonism (FIRM) Foundation--OK, really. FIRM? And yes, the redundancy of FIRM Foundation is of his own making--that has three emeritus Seventies on its board. Meldrum places the Book of Mormon in the Great Lakes area (dubbed the "Heartland model.") and FIRM sells a variety of books and videos pushing their view (along with right-wing politics). This model has previously been highly criticized by FAIR, and others.

Smith's criticism extends beyond issues of geography to the young earth creationism (YEC) pushed by Meldrum, and the sanctimony it is all wrapped in. The connection between evolution, creationism, and Book of Mormon geography may seem strange at first glance, but it ultimately makes sense. In order to make his theory work, Meldrum has to savage multiple fields of science because they are interconnected. He can cherry-pick certain scientific findings to support him and justify it by asserting that scientists have been interpreting the facts all wrong because they labor under an atheist conspiracy. I should also note that evolution often serves as the whipping boy for all of the natural sciences. Got a problem with the Big Bang, or radiometric dating? Blame evolution.

I find this sort of fundamentalist thinking and distortion extraordinarily troubling, and it is one reason why I consider Meldrum's theories worthy of review. He distorts the status of this teaching for the Latter-day Saints, refrains from quoting any authorities who differ with his views, portrays his sources as more authoritative than they are, and insists that the scriptures require it, making any other reading or view "impossible." Therefore, anyone who disagrees is ignoring the "clear" teachings of scripture. And anyone who differs is automatically less zealous in upholding the scriptures than Meldrum. "There are faithful members of the Church that have a deep belief in evolution and have been able to reconcile their beliefs. . . . Please know that your beliefs are respected," we are assured (p. 149). Yet if my beliefs differed from Meldrum's absolutism, I wouldn't find much respect in his caricatured treatment.

It seems clear that Smith does not share Meldrum's (YEC) views. With that in mind, I think Smith hits the nail squarely on the head with this passage.

At the same time, we cannot always allow misrepresentation of a point of view to proceed unchallenged, lest some be misled. Those given false information often learn later that their trust was misplaced. They then complain that "the church" (rather than "a member of the church") taught them falsehoods because misinformation was presented in a church context draped in the trappings of the gospel. Even if evolutionary theory is false in every particular, we do the cause of truth no service by creating strawmen, misrepresenting it, or minimizing the evidence offered in its behalf. We must deal with its most robust case if we are not to lead others to assume we were either ignorant or disingenuous—neither state being a good apologetic. And if we are right to oppose evolution, any efforts that do not fully address the depth and breadth of the best evidence are doomed to failure.

I have not read the whole review yet, but what I have has been excellent, and I already know that I will have more to say, either about it or based on it.

Also, check out the Editor's Introduction where the "Heartland model" is compared to a weed that needs to be pulled from the garden of Mormon scholarship.

Finally, I offer my praise to FARMS and FAIR for providing a platform for the criticism that this kind of stuff deserves, and for joining the atheist conspiracy taking a general stance that is largely consonant with science.

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FARMS: Of Science, Scripture, and Surprise

The FARMS Review (2008, Volume 20, Issue 2) contains a thoughtful and articulate essay by Duane Boyce titled, "Of Science, Scripture, and Surprise." It is ostensibly a review of Evolution and Mormonism: A Quest for Understanding, by Trent D. Stephens and D. Jeffrey Meldrum. However, discussion of the book is so superficial that I can't help but think that the book is mentioned simply to serve as justification for including the essay in a review publication. In fact, the essay gives much more attention to Stephen Jay Gould's The Structure of Evolutionary Theory.

Most of the essay can be boiled down to this: science is a messy process that is subject to all manner of human foibles.

To one degree or another, these [foibles] are all inevitable realities of intellectual inquiry. They are unavoidable. But recognizing and explicitly acknowledging such tensions and discontents is preferable to ignoring them. By ignoring them we are apt, in our naïveté, to ascribe more certainty than is warranted at any given moment to a particular discipline's range of intellectual conclusions (as happened with psychoanalytic theory, for example) and to risk developing an attitude of dogmatism and defensiveness as a result.

Recognizing such factors, on the other hand, we can be saved from such dogmatism and instead attain something approaching wisdom: a lingering tentativeness and humility about many of the beliefs we hold at any one time. In other words, we can be sure we are mistaken in one way or another even if we cannot be sure exactly where.

This is all well and good, though it can be taken too far. As Timothy Ferris has written,

The empirical spirit on which the Western democratic societies were founded is currently under attack, and not just by such traditional adversaries as religious fundamentalists and devotees of the occult. Serious scholars claim that there is no such thing as progress and assert that science is but a collection of opinions, as socially conditioned as the weathervane world of Paris couture. Far too many students accept the easy belief that they need not bother learning much science, since a revolution will soon disprove all that is currently accepted anyway. In such a climate it may be worth affirming that science really is progressive and cumulative, and that well-established theories, though they may turn out to be subsets of larger and farther-reaching ones--as happened when Newtonian mechanics was incorporated by Einstein into general relativity--are seldom proved wrong. As the physicist Steven Weinberg writes, "One can imagine a category of experiments that refute well-accepted theories, theories that have become part of the standard consensus of physics. Under this category I can find no examples whatever in the past one hundred years." Science is not perfect, but neither is it just one more sounding board for human folly.

I was pleased that toward the end of the essay Boyce balances his critique of scientific certitude with a critique (though brief) of scriptural certitude. His examples are two of my favorites: the degrees of glory described in D&C 76 and the re-definition of eternal punishment in D&C 19. Both revelations fundamentally altered the way previous scripture was understood. In summary,

...we are likely to understand new truths and experience new perspectives that will dramatically inform and revise matters that we think we understand now: subsequent revelations have a way of informing previous ones.

Next, Boyce takes issue with an interpretation advanced by Stephens and Meldrum of 2 Nephi 2:22, the preeminent 'no death before the fall' scripture. Although he tries to be fair, I don't think that Boyce quite does justice to the interpretation of Stephens and Meldrum. But the strengths and weaknesses of alternative interpretations does not concern me here. What I wish to point out is that this wrangling over interpretation concerns a single, short passage concerning a largely figurative story. To paraphrase B.H. Roberts, I think it is a thin thread to hang heavy weights on.

Moving on, toward the end of the essay Boyce expresses two concerns about evolution, and I will consider his questions in turn.

1. What are we to make of Moroni and Jacob, who both speak of the creation as miraculous?

To begin with, we might consider something Brigham Young said about miracles [1]:

The providences of God are all a miracle to the human family until they understand them. There are no miracles, only to those who are ignorant. A miracle is supposed to be a result without a cause, but there is no such thing. There is a cause for every result we see; and if we see a result without understanding the cause we call it a miracle.

It is not clear to me that Jacob and Moroni had special insight into the creation, as Boyce seems to assume. Both passages occur in a context of the prophet extolling the greatness and power of God. Given their scriptural heritage (especially the creation as depicted in Genesis) and the state of their scientific understanding [2], what choice would they have but to see the creation as miraculous? And if you are looking for examples of miracles, what better example could you find than the creation of the earth and life on it? Processes that we might call ordinary (though still wonderous) were apparently unknown to Jacob and Moroni. If our estimation of God is based on the impressiveness of his miracles (rather than his character and attributes), Brigham Young's statement suggests that we eventually may be disappointed.

2. Since the scriptures relate many miracles where God accomplished great feats quickly, why would he use such a long and wasteful method of creation?

In my mind, this is a more difficult question. It plays a role in some people's disbelief in God, and I don't know of an obvious answer to it. Nevertheless, the view that God as been at work for extremely long periods of time has early support in the Church. For example, we have the statement in a letter from W. W. Phelps [3] that,

...eternity, agreeably to the records found in the catacombs of Egypt, has been going on in this system, (not this world) almost two thousand five hundred and fifty five millions [2,555,000,000] of years: and to know at the same time, that deists, geologists and others are trying to prove that matter must have existed hundreds of thousands of years;—it almost tempts the flesh to fly to God, or muster faith like Enoch to be translated and see and know as we are seen and known!

It is unclear exactly what "system" Phelps was referring to, but this passage has been used by commentators such as Elder Bruce R. McConkie as support for God's vast experience, knowledge, and work. And of course there is also the statement in scripture that "all is as one day with God, and time only is measured unto men" (Alma 40:8). Why the quick miracles then? At least one reason might be that God desired results relevant to human timescales rather than his.

I don't know why God would use such a long process of creation. Presumably, God could have created the earth and life on it in six literal days, which would be quite a miracle. We could draw up a list of reasons why one way would glorify God more than the other. However, as I have argued previously, the issue is not what God could do. The issue is what the surviving evidence suggests. Happily, well-represented portions of Mormonism are quite at home with the vast timescale of creation suggested by the evidence.

Ultimately, I fundamentally agree with Boyce: we will continue to be surprised. I would simply ask that we not lose sight of the well-supported surprises that have already come.

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Notes:
1. This sentiment has been echoed by other Church leaders, and the link provided is to Teachings of Presidents of the Church: Brigham Young. This is not an attempt to settle the question by an appeal to authority; it is simply to show that Brigham Young's sentiment is still welcome within mainstream Mormonism.

2. As an example, both prophets appear to believe that God speaking was the direct cause of man's creation from dust, which is a straightforward interpretation of Genesis. Other modern scriptures suggest a more indirect relationship between God's words and the desired result. Further, Brigham Young called the idea that Adam was made from dust "baby stories." It may be that on the topic of the creation, Jacob and Moroni wrote 'pre-surprise.'

3. Times and Seasons, vol. 5 (January 1844-January 1, 1845) No. 24.

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FARMS Reviews "The Case for Divine Design"

The Case for Divine Design: Cells, Complexity, and Creation, by Frank B. Salisbury, is reviewed in the most recent FARMS Review (2008, Volume 20, Issue 1). The review article is "The Clockmaker Returns," by James L. Farmer. Dr. Salisbury is an emeritus professor of plant physiology, and Dr. Farmer is a BYU emeritus biology professor.

I have read The Case for Divine Design completely through once, mostly through a second time, and bits and pieces even more. I think the review is pretty straightforward and even-handed, and I generally agree with it. My one quibble is that toward the end Dr. Farmer seems to see Intelligent Design (ID) as only associated ("guilty by association") with Creationism. However, the fact is that ID grew out of creationism in response to court decisions that prevented the teaching of creationism in public schools.

Now for some of my own comments on The Case for Divine Design:

The main point of the book is to argue that science does not disprove God--not that there is scientific evidence for God (Salisbury rejects ID as legitimate science), but that the history of life is not known in sufficient detail to rule out divine intervention. It is in that sense that he seems to feel affinity toward ID.

He describes his worldview as follows (pg 22):

My belief also includes the idea that an Intelligent Creator, God, played a critical role in this process. I have no conclusion about what that role might have been. Did he engineer the first life on Earth and then let evolution take over, as deists and others believe? Or did he intervene in other ways intelligently creating every species? My attitude is that we simply lack enough information to speculate at this time.

It comes as no surprise that science cannot refute such a position.

Although I am less attracted to ID than Salisbury (and I am repelled by the ID movement), my own view is actually quite similar. Yet in spite of that core agreement, I have a few reservations about the book. First let me say that I appreciate the thought that Dr. Salisbury put into the book. There are a shortage of public LDS-scientist role models and his effort to communicate his years of thinking to another generation is to be commended, and his arguments are worth considering.

In a different FARMS Review article that was written by Dr. Salisbury, he suggested that the authors "are so busy defending evolutionary theory that it never seems to occur to them that there might still be problems with the theory." I think I would turn that around here: Dr. Salisbury is so busy trying to find problems with evolution that he misses some of its strengths. To be clear, he assures us that he is not a "bitter anti-evolutionist," and in an interesting end note, he writes that he "was personally deeply troubled" by Joseph Fielding Smith's book, Man, His Origin and Destiny. (He later met with then-Apostle Spencer W. Kimball, who told Salisbury "that he knew little about the science...and had no personal convictions on the matter," and that President Smith's book was "not to be considered Church doctrine" [quotations from the book, which paraphrased Elder Kimball].) Nevertheless, in my opinion his treatment of evolutionary theory is incomplete, as the following two examples illustrate.

1. Adaptationism and genetic drift. Salisbury repeatedly expresses concern that plausible "just-suppose stories"--especially in regard to the power of natural selection--are accepted too readily as final explanations. You could argue that holding a provisional position (and rejecting others) based on existing knowledge and pending additional information, is not a bad thing--and science is not about achieving metaphysical certainty anyway. But that aside, he seems unaware that scientists such as Stephen J. Gould have made similar criticisms. Probably the most famous example is a paper Gould and Richard Lewontin wrote in 1979 called, "The Spandrels of San Marco and the Panglossian Paradigm: A Critique of the Adaptationist Programme," in which Gould and Lewontin argued for a pluralistic approach to evolution that does not entail explaining every detail in terms of natural selection.

This is relevant because Salisbury seems unaware of a significant alternative to natural selection: genetic drift, which is where the frequency of a particular gene can become the norm (or driven to extinction) due to chance events. Imagine an animal hunted to near-extinction; that species will have restricted genetic diversity going forward. In many cases, the reason certain genes will be most frequent in the recovering population will have nothing to do with natural selection. They will be predominant simply because animals with alternate versions happened to get killed by hunters.

This failure to consider genetic drift, in turn, leads him to puzzle over what in my opinion are probably non-existent problems. For example, Salisbury seems to wonder how natural selection can account for the gene that causes Huntington's disease, which kills people in mid-life (i.e. post-reproduction). Although I can imagine a genetic scenario that could lead to the Huntington's gene being spread by natural selection, it is also quite possible that natural selection has nothing to do with it. The gene might simply have spread by chance (i.e. genetic drift). Likewise, Salisbury worries about how a selectively neutral mutation in cytochrome c can spread until it becomes fixed (i.e. present in all individuals of a population). Again, this is the domain of genetic drift, which becomes a dominant factor in small populations.

Salisbury might accuse me of spinning just-suppose stories--which I guess I am, since I haven't looked into the scientific literature concerning the evolution of these genes. However, the point is that once we release ourselves from explaining everything in terms of natural selection and turn to other established evolutionary principles, some otherwise perplexing problems evaporate. Moreover, scientists have devised various statistical tests for differentiating between natural selection and genetic drift.

2. Genetic relatedness. Before genes were understood to be coded by DNA, copies of which are inherited by offspring, evolutionary relationships were determined primarily by comparative anatomy. In the second chapter Salisbury uses a literary device to express his internal deliberations and pondering by putting arguments in the mouths of "the Biologist" and "the Skeptic." The Biologist discusses the relationships inferred by anatomy and the fossil record, but the Skeptic argues (at least twice) that anatomical similarities do not prove genetic relatedness. Inexplicably, the Biologist never points out the evidences of genetic relatedness! The closest we get is a brief treatment of an evolutionary tree generated from cytochrome c sequences in the fourth chapter. He writes:

The conclusion is that, because humans and chimpanzees have identical sequences, they must be closely related, while humans and higher plants must be distantly related, since they have the fewest sequences in common. Stories such as this are compelling and are among the most impressive and plausible evidences that an evolutionist can produce, which is not to say that an Intelligent Creator could not have designed things that way.

This is quite unsatisfactory. Genetic sequences contain treasure troves of evidence suggesting common descent and genetic relatedness, and by and large the inferred relationships match those that were previously determined by comparative anatomy. He may be correct (for now) that we cannot demonstrate a genetic relationship between us and other hominans (for lack of surviving genetic material to study), but if the genetic trail goes cold at Homo erectus, it gets rather hot again with chimpanzees and gorillas. A genetic relationship with a cousin implies a genetic relationship with a common grandparent, even if the exact identity of the parents or grandparents remain uncertain.

In summary, I think that The Case for Divine Design makes some interesting points that are worth considering. However, in the examples I have discussed, as well as some I have not, I think the book raises needless doubt as to why evolution is the central organizing principle of biology. Given the wide range of material that the book covers in so short a space, readers should use the book as a springboard rather than an ending point.

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Review of FARMS Review 19:2

I don't know how long it has been available online, but I noticed a few days ago that FARMS Review 19:2 (2007) is on the FARMS website. It seems new to me, but perhaps I just missed it. Anyway, only one review is directly related to science and that is David Grandy's "Ideology in the Guise of Science," a review of The God Delusion by Richard Dawkins. Having recently read the book, I was interested to read this review. FARMS Review is gradually attempting to address secular anti-Mormonism--something I think is important, and this review is part of that effort. [Also of note, don't miss Daniel Peterson's take-down of Christopher Hitchens.]

David Grandy is a professor of philosophy at BYU (my inference). For someone who has taught courses on the history and philosophy of science (Grandy, not me), I have to admit that I was disappointed with his review. I think the whole thing could be summed up with the response, "Oh yeah?!"

A central argument of The God Delusion is that the existence of a supernatural personal God is--in principle--a scientific question, and that although current science cannot disprove his existence, it allows us to say that such a God probably does not exist. In addition, Dawkins makes these additional "consciousness-raising" points (as summarized at Wikipedia):

- Atheists can be happy, balanced, moral, and intellectually fulfilled.

- Natural selection and similar scientific theories are superior to a "God hypothesis" — the illusion of intelligent design — in explaining the living world and the cosmos.

- Children should not be labelled by their parents' religion. Terms like "Catholic child" or "Muslim child" should make people flinch.

- Atheists should be proud, not apologetic, because atheism is evidence of a healthy, independent mind.

None of this is really addressed by Grandy. He demurs at the idea that natural selection has as much explanatory power as Dawkins argues it does, but does not provide a basis for thinking otherwise other than to point to holes in our knowledge and play games with analogies. He charges that the book "is ideology poorly disguised as science." I think it would be more accurate and fair to say that it is ideology informed by science. His introductory story insinuates that Dawkins has attacked a caricature of God, and that the book is not threatening, but he does not elaborate.

Certain passages make me wonder how much attention Grandy paid to what he was reading. For example, he writes,

In the latter part of the book, Dawkins offers an explanation for religion. Believing that only Darwinian evolution can get to the bottom of this matter, he weaves an interesting story. But this is not to say that others, working from different principles, could not weave equally interesting but very different stories.

In fact, Dawkins argued that religion was not directly selected by natural selection, but is a by-product of something else that was. Further, Dawkins wrote,

If, then, religion is a by-product of something else, what is that something else?... I shall offer one suggestion by way of illustration, but I must stress that it is only an example of the kind of thing I mean, and I shall come on to parallel suggestions made by others. I am much more wedded to the general principle that the question should be properly put, and if necessary rewritten, than I am to any particular answer.

In other words, it sounds to me like Dawkins is proposing a hypothesis.

Perhaps I am being too critical. After all, taking on The God Delusion properly would probably require a book of its own; no doubt Professor Grandy has other interests, and this was just a quick summary of his opinion. Further, you ask, "if you're so critical, why don't you write a better review?" My reply would be what I wrote previously: "I do not want to add my voice to those of his critics who obviously miss his point or offer up lame counter-arguments, nor am I equal to the task of taking him on."

I hate to end on a negative note, so I will close with a passage I agreed with.

The goal of harmonizing faith and reason is an old one, but there are pitfalls along the way; and to his credit, Dawkins does a good job of pointing some of them out. If we invest faith in, say, intelligent design, irreducible complexity, or certain versions of the anthropic principle, all of which lean on God to make sense of things, what happens when persuasive naturalistic explanations emerge?

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Welch on Evidence and Faith

For some time now, I've been coveting the online essay of the week feature at Dave's Mormon Inquiry. I'm going to adopt a similar feature here that I will call "Essay Notes" (in keeping with my Book Notes and Quote Notes categories).

First up is The Power of Evidence in the Nurturing of Faith, by John Welch, from the FARMS book, Echoes and Evidences of the Book of Mormon. Welch gives some of his thoughts on the relationship of evidence and faith. The basic thesis is summed up in the title, that the role of evidence--in particular, in support of the Book of Mormon--is to maintain enough of a sense of plausibility to allow faith to become established and grow. Along the way he draws on the role of evidence in the law to argue that evidence is not a black-or-white thing, but something that has greater or weaker strength depending on a number of contexts, and that ultimately a subjective judgment must be made. For example, after listing various degrees of certitude required in different legal circumstances, he writes:

In a religious setting, no arbiter prescribes or defines the level of evidence that will sustain a healthy faith. All individuals must set for themselves the levels of proof that they will require. Yet how does one privately determine what burden of proof the Book of Mormon should bear?... Few people realize how much rides on their personal choice in these matters and that their answer necessarily originates in the domain of faith.

The essay does takes a faith-first approach; much of the essay seems to treat evidence as useful only insofar as it builds faith. But is it only a one-way street? Shouldn't evidence also inform faith? Welch seems to imply that it should, at least to some degree. For example:

Caution is also advised on the side of faith. Revealed knowledge must be understood and interpreted correctly. What has actually been revealed?... Moreover, the implications of revelation are not always clear.

And one that I have highlighted before (quoting Sydney Sperry):

Too many persons in every generation, including our own, hope for things—fantastic things—in the name of faith and religion, but give little thought as to whether or not they are based on truth.

As President Packer said, mixing these two things is like mixing oil and water. Although it is certainly not the last word, in my opinion Welch's essay is one of the better attempts in LDS literature.

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FARMS Reviews "Voices from the Dust"

Another installment of FARMS Review is available online. The one that caught my eye was Brant Gardner's review of Voices from the Dust: New Insights into Ancient America by David G. Calderwood. You may remember that I attended a presentation by Calderwood last fall and reported on it here. (I'd like to claim that I was prescient in my looking forward to the FARMS review, but alas, no genius was needed to call that one.)

Gardner has two chief methodological criticisms:

1. By including material from all over the Americas, Calderwood is implicitly endorsing a hemispheric model--something that is contradicted by what many would consider much stronger evidence (either from within or without the Book of Mormon). Conversely, rejecting a hemispheric model calls into question his methods.

Either Calderwood defends the hemispheric geography of the Book of Mormon by default, or he forfeits the ability to pull information from texts so far distant as those from Peru and Central Mexico.

2. Calderwood accepts the Spanish accounts uncritically and dismisses the argument that the writers were projecting their own religious background onto the natives. You'll have to read Gardner's review for more on that.

As a side note, in response to a passage in the introduction, Gardner writes, "I confess that I am nervous when the introduction of any book on history blithely dismisses years of scholarship." There was a taste of that in the presentation I attended as well. From my report:

Early in the talk he said that researchers are tied to "make-believe histories." The first is evolution and that there was no creation. The second is that Native Americans migrated from Asia 15,000 years ago and that there were no significant outside contacts until Columbus. (He did not specify whether he objected to the early migration, or just the isolation.)

Gardner concludes:

Calderwood sees only the parallels. He neglects to consider any other reason for the apparent similarities in his sources. In the historical materials from Mesoamerica, with which I am most familiar, I find much stronger evidence that it really was the common perceptual layer imposed by the Spaniards that created the parallels in the chroniclers' accounts.

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Mormons and the Multiverse

The physical plausibility of the Mormon conception of God appears to be inversely proportional to his necessity. Let me explain.

The Big Bang poses some problems for Mormon theology. Run the tape of time backwards and the universe reaches a point where it is so hot and dense that it is hard to see how God could exist within the universe, to say nothing of an infinite hierarchy of gods or eternal intelligences (whatever those are). Last year Dialogue: A Journal of Mormon Thought published "Eternal Progression in a Multiverse: An Explorative Mormon Cosmology," (pdf link) by Kirk D. Hagen. The basic idea is that this universe is only a part of a larger multiverse, and this gives our theology a door out of this universe. (See also Clark's post on this topic at Mormon Metaphysics.)

Creationists of various stripes (including intelligent design) have argued that certain aspects of this universe (eg. fundamental constants) that are conducive to life on this planet have been designed--that the universe just happens, by chance, to have the features necessary to make our existence possible seems too improbable. Therefore it is likely that God designed the universe.

Some scientists have responded that--whatever the merit of that argument--the concept of a multiverse renders the argument irrelevant. Of all the universes that make up the multiverse, some will have the properties needed for life. We live in one of those universes. (For a recently published example of this kind of argument, see here.)

But Richard Sherlock doesn't like this argument at all. In his FARMS Review essay, "Mormonism and Intelligent Design", he writes:

What critics have resorted to is a wildly imaginary but inventive claim that there may be an infinite number of parallel universes. At one time it was suggested that the universe might go through an infinite number of expansions followed by contractions, a big bang and a big crunch, if you will. This idea, however, has been refuted by recent data. But no problem. The hypothesized infinite multiverses will do equally well. We might be simply the universe that was "organized" in the design-specific manner that it appears to be. The other universes or multiverses as they are called may be "organized" in much less inviting ways. Or maybe they started and failed, collapsing back on themselves or flying apart. The question is why would one want to multiply entities for which we have absolutely no evidence? The reason for the multiplication is not science, for the appeal to hidden entities or forces violates what scientists claim to seek above all else: explanation, not mystery. The reason is the deeply held faith in materialism and in the equally strong article of faith by some against God or divine design.

And so we come full circle. Do we insist on God's necessity and accept the problems of the Big Bang, or do we invoke the idea of a multiverse and give up cosmic improbability?

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FARMS and Physics

I recently highlighted several essays in the FARMS publication, Astronomy, Papyrus, and Covenant. I want to return, briefly, to the chapter, "'And I Saw the Stars': The Book of Abraham and Ancient Geocentric Astronomy," by John Gee, William J. Hamblin, Daniel C. Peterson.

The essay argues that the Book of Abraham is presented from a geocentric point of view. In answer to the question of why God would teach Abraham using a "false" conception, the authors suggest that (i) God teaches according to our human limits of understanding, and (ii):

the geocentric view of the cosmos is not, strictly speaking, false. If modern relativistic physics has taught us anything, it is that there is no absolute space, and thus no privileged point for observation of the cosmos except as has been established by convention. The geocentric system was abandoned, in the last analysis, not because it was incorrect but because, as it had developed with its cycles and epicycles, it was too complex and cumbersome. ...it would still be possible today, in light of modern relativistic physics—and if we were willing to subject ourselves to the difficulty of doing so—to construct a description of the universe that assumes the earth to be at the center.

As currently indicated on the sidebar, I am reading Timothy Ferris's Coming of Age in the Milky Way, and he made a point that I had not thought of before, and if I understand correctly, means that the quote above is incorrect (aside from the historical reason for rejecting geocentrism).

(Note: you physicists and astronomers out there--tell me if I've got this right or not.)

From a geocentric point of view, the farther away the stars are, the faster they have to move in order to circle the earth. Astronomically speaking, you don't have to get very far (I guess a circumference of one light year) before the velocity of the stars would have to exceed the speed of light in order to circle the earth every year. This would violate a fundamental principle of relativity. So the irony here is that the authors invoke relativity to support a notion that actually contradicts relativity. Sure, we could generate such a description, but it would remain "false."

Is this right or am I missing something?

Update: Whether the issue I raise has merit or not may depend on the assumptions of the model. But I'm encouraged that at least one person has noticed the problem before. See A Critique of Geocentricity.

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