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Mortal Man

Winding Measurements

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I believe in establishing the facts before arguing about them. Therefore, I am starting this thread in order to focus specifically on the winding measurements for the scroll of Horos. I hope this thread will serve as a place where we can work together to definitively establish an upper bound on the original length of the scroll. I think that coming to an agreement on this is in everyone's best interest.

Here is how it will work. I'll lay out some initial observations, measurements and analysis for everyone to scrutinize and critique. I invite all to point out any errors, misjudgements or miscalculations that they can find. As each correction/improvement comes in, I will update this OP accordingly, such that the length estimates reflect our current best understanding. I will acknowledge each contributor and/or provide links to your posts. This thread should serve to address all of the issues raised in the FAIR Wiki. http://en.fairmormon.org/Book_of_Abraham/S...missing_papyrus

Ground Rules:

1. Forget that the length of the snsn scroll has anything to do with the veracity of the church.

2. Don't try to prove that the scroll was either very long or very short.

3. Focus on physical observations and measurements of the papyri.

4. Provide constructive criticism.

5. If you disagree with the estimates then provide a detailed description of your concern(s) backed up with high-quality pictures.

6. If you agree with the estimates then say so in order that your voice be counted.

Here is my analysis.

OBSERVATIONS

After staring at many different images from many different sources, I am of the opinion that the lacuna in the chest of Anubis provides the clearest indicator of the windings. In the image below I have layered JSP I & XI to show how these lacunae would have lined up for the scroll in its rolled-up state.

IXI_layers_line.jpg

I aligned the images by blowing them up in Photoshop and selecting the lightest line of pixels extending down into the crack at the bottom tip of each lacuna. The blue line is drawn along these lines of pixels. Notice how well the humps to the right line up as well as the stair-step patterns past the humps. Now look at the left end of the second-to-bottom layer and notice how its lacuna is displaced slightly to the right of the corresponding lacuna in the bottom layer. Imagine how these lacunae would shift to line up if the layers were rolled into a cylinder with the correct radius of curvature. It is thus possible to directly visualize the S factor in Hoffmann's equation.

As further evidence of the unambiguous alignment of these lacunae, notice the cracks which extend down from the bottoms of the first two gaps.

W14_cracks.jpg

The crack on the left causes a misalignment between Osiris' ankle and leg. I have traced the cracks to bring out their similar shape.

W14_cracks_green.jpg

MEASUREMENTS

Now that we've established the azimuthal coincidence of these cracks/lacunae, let's turn to their distance measurements. The Improvement Era image of JSP I contains a ruler which allows the distance between the first two lacunae to be readily measured. The ruler was fortuitously placed along the top side in close proximity to the lacunae. Although some distortion is apparent on the right end, the middle section between the lacunae appears quite straight (a stroke of luck ;) ).

W14.jpg

I will refer to this winding as W1.4 to reflect that fact that it begins roughly four-tenths of a winding-distance from the rightmost edge of the scroll. Subsequent windings in this sequence will be referred to as Wn.4. Taking a close look in Photoshop, I measured this winding to be W1.4 = 10.21 cm (1 in = 2.54 cm).

In order to measure W2.4 and W3.4, I placed fiducials along the lightest line of pixels extending down from the bottom dips in the 3rd and 4th lacunae.

three_windings.jpg

Using the W1.4 measurement, I determined the scaling factor for my Photoshop ruler to be 1.0104 (remarkably close to unity :P ). Using the Photoshop ruler together with the scaling factor, I get W2.4 = 10.06 cm and W3.4 = 9.98 cm. It should be noted here that I and XI are mounted separately; hence, if the photographic joining in the above Larsen photo is not exact, then there will be some error in the W2.4 measurement.

CROSS CHECKS

In the Improvement Era photo of JSP XI the ruler is placed long the bottom and is significantly distorted at the right end.

W34_ruler.jpg

Nevertheless, we are once again fortunate that the ruler segment between the ends of W3.4 is relatively straight. Placing the fiducials as before and measuring off the embedded ruler yields W3.4 = 9.70 cm. Hence, there is a 2.8 mm discrepancy that needs to be resolved between the two measurements of W3.4. Feel free to chime in on this point.

SHIFTED SEQUENCE

Shifting the Wn.4 lines to the right yields this sequence of windings.

W1234_composite.jpg

The first winding begins at the edge of the papyrus and ends at the belly of the Duamutef canopic jar. The end of this winding is marked by a prominent crack, which displaces the horizontal lines in front of the nose of the Sobek crocodile.

Duamutef_crack-1.jpg

This crack, which is repeated at the end of the second winding, may have been caused by the edge of the scroll sticking to the second and third layers when the scroll was first unwound. If this is in fact what happened, then it appears that a portion of the original outside edge of the papyrus scroll has been preserved.

CROSSING THE GAP

According to Nibley and Rhodes, the gap between X and XI is about 6 cm.

columns_parallax.jpg

Column2.jpg

However, according to Chris Smith's counting of hieratic characters, the gap is more like 12 cm. http://www.mormonapologetics.org/index.php...mp;p=1208660150

Chris_15gap.jpg

If Chris is correct, then there are actually 8+ windings.

JSP X PLUS FRAGMENTS FROM IV

The remaining columns of the extant snsn text have suffered some damage since they were first mounted.

X_IV_RGBY.jpg

The outlined fragments became unglued from the backing paper and were subsequently reglued upside down into IV.

IV_RGB.jpg

Can anyone find the yellow piece?

There appear to be several other pieces out of place here as well. Where do they go?

You can see the glue marks in X where the red fragment fell off.

JSPX-Larson.jpg

There is "good" damage and there is "bad" damage.

Damage done do the scroll in its wound-up state imprints a repeating pattern in the layers, which is useful for identifying the windings.

Damage done to the scroll after it is unwound obscures the repeating pattern, thus introducing ambiguity in the windings.

Hence, before attempting to locate the windings in X, it is desirable to first replace the fragments that flaked off. Rhodes' high-quality images contain the missing pieces, thus we'll start with a composite of his photos.

X_composite.jpg

Layering the images as before, in order to show how the lacunae would have aligned for the wound-up scroll, we get the following.

X_layers_line.jpg

The blue line here corresponds to the same Wn.4 pattern depicted in the first figure. These lacunae are not as distinct as they were for I & XI and there are no obvious cracks to work with; however, the humps on either side of the blue line provide excellent alignment guides when viewed close in.

In order measure the windings, let's take a look at the Improvement Era photo with its embedded ruler.

W84.jpg

The three blue lines bounding W6.4 & W7.4 correspond to the alignment determined from the layering analysis. Yet again, we are fortunate that the embedded ruler for this section is straight and lies in close proximity to the lacunae. The winding lengths are: W6.4 = 9.02 cm & W7.4 = 8.54 cm. The break in W8.4 makes it difficult to determine its length precisely. Guessing the end point from the glue mark, we get W8.4 = ~8.05 cm.

THICKNESS INDICATORS

The papyrus contains fibers running both lengthwise and spanwise, indicating that it is a typical 2-layer laminate. In the hieroglyphic column to the left of Anubis, some of the top layer has peeled off exposing the bottom layer. The bottom layer is completely opaque and no ink has seeped through. You can sense the three-dimensionality of the material. It is worth mentioning that papyrus such as this had to be tough enough to endure stone burnishing to make it smooth enough to write on.

delamination.jpg

PHOTOGRAPHIC DISTORTION

The FAIR Wiki raises the issue of photographic distortion as a serious concern to be addressed. http://en.fairmormon.org/Book_of_Abraham/S...missing_papyrus

For the Improvement Era photos, with their embedded rulers, this is largely a moot point. However, after experimenting a bit with my camera, I've come to appreciate how focal length, angle of view etc. can be a serious concern for photographs with no fiducials. The Wiki points out that no technical details of the BYU photographs (distance, angle, lensing etc. ) are known. Nevertheless, I see four ways in which confidence can be established in the measurements:

1. Employ scaling factors to tie measurements to photos with fiducials (as done here with the Improvement Era photos).

2. Compare measurements for many different photos. It is unlikely that photos taken by different people many years apart would exhibit exactly the same distortion. Thus, consistency between photos would suggest that distortion is a minor effect.

3. Measure the originals. (Not likely to happen but we can always hope.)

4. In some cases it may be possible to correct for parallax using a simple cosine correction...

OPEN QUESTIONS

1. Are the papyri pressed tightly by the glass?

2. Have they experienced any shrinkage or additional wrinkling since they were mounted?

3. What is the observable thickness of the snsn fragments mounted in IV compared to the Book of the Dead papyrus?

4. Has anyone asked Prof. Rhodes his opinion on the measurements?

SUMMARY OF WINDING LENGTHS

BYU Studies Photos:

W1.4 =

W2.4 =

W3.4 =

W4.4 =

W5.4 =

W6.4 =

W7.4 =

W8.4 =

Improvement Era Photos:

W1.4 = 10.21 cm (from embedded ruler)

W2.4 =

W3.4 = 9.70 cm (from embedded ruler)

W4.4 =

W5.4 =

W6.4 = 9.02 cm (from embedded ruler)

W7.4 = 8.54 cm (from embedded ruler)

W8.4 = 8.05 cm (from embedded ruler, questionable due to the break in the photo.)

Larson Copies:

W1.4 = 10.21 cm (imputed from Improvement Era photo)

W2.4 = 10.06 cm (from scaled Photoshop ruler)

W3.4 = 9.98 cm (from scaled Photoshop ruler)

W4.4 =

W5.4 =

W6.4 =

W7.4 =

W8.4 =

Nibley Photos:

W1.4 =

W2.4 =

W3.4 =

W4.4 =

W5.4 =

W6.4 =

W7.4 =

W8.4 =

Rhodes Photos:

W1.4 =

W2.4 =

W3.4 =

W4.4 =

W5.4 =

W6.4 =

W7.4 =

W8.4 =

Originals:

W1 = 9.7 cm (Gee's measurement, not counted in average)

W2 =

W3 =

W4 =

W5 =

W6 =

W7 = 9.5 cm (Gee's measurement, not counted in average. This measurement may actually correspond to W8.)

W8 =

Average over all photos:

W1.4 = 10.21 cm (1)

W2.4 = 10.06 cm (1)

W3.4 = 9.84 cm (2)

W4.4 = ?

W5.4 = ?

W6.4 = 9.02 cm (1)

W7.4 = 8.54 cm (1)

W8.4 = 8.05 cm (1) (not used in determination of S)

HOFFMANN EQUATION

Hoffmann's length formula is

Z = (E2 - 6.25)/(2S) - E

Z is the maximum possible length of the papyrus interior to the winding of length E.

S is the average difference between winding lengths.

The formula is derived via a path integral along a spiral. http://www.mormonapologetics.org/index.php...mp;p=1208633398

The empirical correction factor of 6.25=2.52 accounts for the fact that "the windings can not be put into practice under 2.5 cm." http://www.mormonapologetics.org/index.php...mp;p=1208654896

CURRENT LENGTH ESTIMATES:

Average difference in winding lengths: S = (10.21 - 8.54)/6 = 0.278 cm (from Improvement Era W1.4-W7.4)

Total length of extant fragments excluding gap between X and XI: Le = 68 cm (includes fragments from IV)

Length of gap between X and XI: Lg = 12 cm (from column 2 to fragment from IV)

Maximum possible length of original pristine scroll: Lo = 182 cm (from Hoffmann formula)

Maximum possible length of missing interior papyrus: Lm = Lo - Le - Lg = 102 cm

Length of missing columns from Book of Breathings: Lc = 40 cm (from Rhodes' estimate of two 20 cm columns)

Length of facsimilie 3: Lf = 20 cm (from Rhodes' estimate)

Length available for Book of Abraham: La = Lm - Lc - Lf = 42 cm (about 2 columns of hieratic text)

ACKNOWLEDGEMENTS

I am grateful to Chris Smith for his many helpful comments and for sending me his images plus the Hoffmann paper.

Also, thanks to dblagent007 and William Schryver for steering me towards photobucket to get around my attachment bug.

REFERENCES

1. Improvement Era, February (1968).

2. Charles M. Larson, "By His Own Hand Upon Papyrus: A New Look at the Joseph Smith Papyri," (1992)

3. Hugh Nibley, John Gee and Michael D. Rhodes, "The Message of the Joseph Smith Papyri: An Egyptian Endowment," (2005)

4. Michael D. Rhodes, "The Hor Book of Breathings: A Translation and Commentary," (2005).

5. John Gee, "Some Puzzles from the Joseph Smith Papyri," FARMS Review: 20, 113-137 (2008). http://ispart.byu.edu/publications/review/...d=699#_ednref25

6. Christopher C. Smith, "The Myth of the Missing Book of Abraham Papyrus," Sunstone West Symposium, 2009

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MM,

You've done some great work here.

Just to clarify my methodology for finding the length of the "gap": Rhodes reconstructs the text of column 2 such that on line 8, there are about twenty characters/character groupings between the eleven or so on the JSP XI fragment and the six or seven on the small, misplaced fragment that has been inserted into the gap in the reconstructions MM posted. In other words, the length of the missing portion of column 2, line 8 should be almost double the length of the portion of that line on JSP XI. Compare this expectation to the Nibley reconstruction, and you'll see that he hasn't allowed enough space between the fragments to accommodate the necessary characters.

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My initial reaction is that an "upper-limit" estimate of ~400 cm (~13 ft.) of missing scroll is sufficient to accord with the testimony of the eyewitnesses to a "long roll."

That said, I have some reservations about the accuracy of the images you have been compelled to use in order to make your measurements. I would prefer that independent measurements of the original papyri could take place.

Nevertheless, my preliminary judgment is that your methodology seems reasonable, although an elucidation of Gee's corresponding measurement methodology would be valuable for comparison.

Still, an informed critic's concession of ~13 ft. of missing scroll is probably all a Book of Abraham apologist could ever hope to obtain.

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MM:

So while Brent and Brian are skulking about in their little spy vs. spy operation, we civilians are going to take the bull by the horns and conduct our own analysis using publicly available images.

I'm not sure exactly what this is supposed to mean, to tell you the truth.

To my knowledge, there has been no "skulking about" going on. And I'm not certain what you are suggesting with the phrase "their little spy vs. spy operation." Maybe you could elaborate. I've been pretty conscious of what Professor Hauglid has been doing for the past three years, and it's basically what he was publicly known to be doing: preparing a critical edition of the Kirtland Egyptian Papers, and conducting systematic analysis of the same. The project is well under-way, and the first publications should appear before the end of the year. That's pretty good progress if you ask me: four years from start to finish on a huge textual criticism project, and a considerable body of analysis to accompany it.

I realize that the mentality forged in the message board environment wants results now, but that just isn't how it works -- at least as I have come to understand these things.

Also, and you must not have realized this, but Dr. Hauglid has had very little to do with the papyri themselves. They are outside the scope of his project.

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Chris Smith:

You've done some great work here.

Really? To what â??great workâ? could Chris be referring?

All I can see MM has done is to rework the numbers between his initial post and his final(?) post until a result was achieved that corresponds more or less to Ritnerâ??s estimate and his preconceived notions.

Congratulations for such â??great work.â? (By the way, whatâ??s that smell? Smells like confirmation bias to me.)

The bottom line is that he is asserting that Geeâ??s measurements of the original papyri are wrong by a total of 1.5 cm (9.7 cm [Gee] vs. 10.2 cm [MM] and 9.5 cm [Gee] vs. 8.5 cm [MM]).

The initial measurements Mortal Man posted returned a missing scroll length of ~400 cm. (My first post on this thread references his first set of conclusions.) That, of course, was not deemed a satisfactory answer, and so he wiped the slate clean and started over, ultimately settling upon his current set of measurements, as performed against various photographic images of the papyri. Now we are assured that the total missing scroll length was no more than ~100 cm!

And so here we are again: he is essentially asserting that Professor Geeâ??s measurements (performed multiple times on the original papyri) are incorrect to a degree that could only be explained by either gross ineptitude, intentional deception, or (I suppose) both.

In my judgment, there is no demonstrable reason yet presented to question the reliability of Geeâ??s measurements. And if there is any error in those measurements, I can see no reason to suppose that it approaches the magnitude Mortal Man asserts. Indeed, I am incredulous that he continues to argue for an error of such proportions!

As I hinted in my paper, a mistake of .1 cm on any given measurement is a reasonable margin of error to assume, especially when considering the inherent difficulties that he and I have both described. Anything beyond that encroaches the realm of special pleading. His assertion of a total error of 1.5 cm is, in my estimation, utterly spurious.

Given the reality that Professor Gee had access to the originals, and assuming even moderate competence as a technician, and given the probable margin of error, I can accept an â??Sâ? factor in the range of 0.05 cm â?? 0.15 cm. But 0.28 cm? I donâ??t think so. Unless, of course, John Gee is a bumbling fool or an inveterate liar.

But perhaps suggesting that conclusion is the real objective of this entire exercise. I wonder â?¦

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Hi Will,

MM didn't rework his numbers between his initial and final post. Rather, his initial post included measurements only from JSP I and XI, whereas his final post incorporated JSP X. This is why I praised MM's work prior to his final edit, and didn't respond to your gloating in post # 3: because I knew that the measurements from JSP X change the estimate considerably. (I've done these measurements myself, so I knew what to expect.) If you have a problem with MM's measurements or his choice of anchor points, I encourage you to look at the pictures and do some measurements of your own. Accusing MM of dishonesty without justification is not a valid counterargument.

Best,

-Chris

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Hi Will,

MM didn't rework his numbers between his initial and final post. Rather, his initial post included measurements only from JSP I and XI, whereas his final post incorporated JSP X. This is why I praised MM's work prior to his final edit, and didn't respond to your gloating in post # 3: because I knew that the measurements from JSP X change the estimate considerably. (I've done these measurements myself, so I knew what to expect.) If you have a problem with MM's measurements or his choice of anchor points, I encourage you to look at the pictures and do some measurements of your own. Accusing MM of dishonesty without justification is not a valid counterargument.

Best,

-Chris

I understand completely that, from your perspective, Professor Gee is the only person that can be accused of ineptitude or dishonesty when it comes to these things.

In any case, I have not implied that either you or "Mortal Man" have been dishonest. I fully accept the alternative possibility of ineptitude. Either that, or you're simply working with an unreliable source for your measurements: photographs of the papyri.

As I see it, given the huge discrepancies that you assert, there are only three possibilities here:

1. Gee is dishonest or inept.

2. Gee's critics are dishonest or inept.

3. There is an extraordinarily significant difference between measurements done from photographs and measurements done from the original papyri.

It's obvious which of these options you have settled on, but I remain unconvinced.

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Wow! I'm impressed with how careful and systematic you've been, Mortal Man. And I'm not sure why you're being criticized here for ignoring Gee's measurements when you actually factor them into your average.

In any case, laying things out step by step in this way should allow anyone to see just where they differ from your analysis and make the appropriate evidentiary challenges or calculation adjustments.

Cheers,

Don

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Wow! I'm impressed with how careful and systematic you've been, Mortal Man. And I'm not sure why you're being criticized here for ignoring Gee's measurements when you actually factor them into your average.

In any case, laying things out step by step in this way should allow anyone to see just where they differ from your analysis and make the appropriate evidentiary challenges or calculation adjustments.

Cheers,

Don

Give me a break!

There are only two sets of measurements: those of Gee and those of Cook.

And Cook asserts that Gee's measurements are incorrect by an incredible 1.5 cm!

I hope any casual observers of the thread are not fooled by this meaningless exercise.

Cook initially promised to show where Gee's measurement methodology was flawed, but all he did in the end was assert a set of measurements (based on two different sets of unreliable photographs) that differ from those made by Gee. And they don't just differ slightly. They differ to an astounding degree! A degree of error that, in my judgment, can only be explained by the three options I listed in my previous post.

Frankly, I cannot see how this thread has advanced the discussion one iota beyond where it was previously. We've simply returned to the question of whether or not Professor Gee is a bumbling fool. And, clearly, the critics are content to continue using the "Gee is inept" gambit as their primary counter-argument to the conclusions outlined in my paper.

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I understand completely that, from your perspective, Professor Gee is the only person that can be accused of ineptitude or dishonesty when it comes to these things.In any case, I have not implied that either you or "Mortal Man" have been dishonest. I fully accept the alternative possibility of ineptitude. Either that, or you're simply working with an unreliable source for your measurements: photographs of the papyri.As I see it, given the huge discrepancies that you assert, there are only three possibilities here:1. Gee is dishonest or inept.2. Gee's critics are dishonest or inept.3. There is an extraordinarily significant difference between measurements done from photographs and measurements done from the original papyri.It's obvious which of these options you have settled on, but I remain unconvinced.
William,You could have made this point much earlier, and much more charitably, and it would have served your cause much better.All you have to say is: The problem I have with your analysis is that there are large discrepancies between Gee's measurements and those done from examining poor photographs. Following the calculations, but using just Gee's measurements, we arrive at X for the length of the scrolls. etc...
Wow! I'm impressed with how careful and systematic you've been, Mortal Man. And I'm not sure why you're being criticized here for ignoring Gee's measurements when you actually factor them into your average.In any case, laying things out step by step in this way should allow anyone to see just where they differ from your analysis and make the appropriate evidentiary challenges or calculation adjustments.Cheers,Don
Don,I have serious misgivings when someone averages measurements that apparently radically differ from one another.

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It doesn't look to me like MM has averaged Gee's measurements with his own. Rather, he has averaged his measurements from Larson with his measurements from Improvement Era.

MM also hasn't argued that Gee is dishonest or incompetent. That is merely William's strawman. Rather, MM has discussed the difficulty of choosing good anchor points on a doubly damaged papyrus, and implied that Gee may simply have chosen incorrectly. That does not require incompetence. It simply requires a mistake. I think MM has very compellingly identified the best anchors available to us, but he did so only after a careful and time-intensive analysis of all the lacunae, in dialogue with other folks here on the forum. If Gee did not pour the same amount of time and energy into this vortex as MM did, he might simply have chosen incorrectly. That is not the horrific, ghastly, impossible scenario William is trying to make it out to be. It's simply the sort of thing that happens to the best of us from time to time.

In any case, I will allow that William's third option (that the photographs are inaccurate) remains a possibility, and I look forward to making measurements from additional photographs when they become available to me. In the meantime, I'm sure William will be happy to entertain us with further demonstrations of his gift for obloquy.

Best,

-Chris

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Zeta:

William,You could have made this point much earlier, and much more charitably, and it would have served your cause much better.All you have to say is: The problem I have with your analysis is that there are large discrepancies between Gee's measurements and those done from examining poor photographs. Following the calculations, but using just Gee's measurements, we arrive at X for the length of the scrolls. etc...

Zeta buddy, you must not be following these threads all that closely, because I have already done precisely what you suggest, numerous times. But always with the same result. And you know what they say about people who insist on iterating the same action despite unchanging results ... well, let's just say that it seems appropriate to try something different. :P

And so I will. But it's not going to play out any further on message boards. I have come to see that, as it pertains to this particular ongoing controversy, the potential purposes of the message board environment have been served to the maximum degree possible.

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CS:

In the meantime, I'm sure William will be happy to entertain us with further demonstrations of his gift for obloquy.

As I'm sure you will continue to entertain us with further demonstrations of your gift for applying double standards. :P

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As I'm sure you will continue to entertain us with further demonstrations of your gift for applying double standards. :P

You're right to expect that my palpable hypocrisy will continue indefinitely. After all, I wouldn't want to disappoint anyone for whom my active and misguided persecution of the Saints is an important reinforcement of Mormon particularity. We all have our roles to play in this cosmic drama of ours, and I could hardly let mine go unfulfilled.

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Wow! I'm impressed with how careful and systematic you've been, Mortal Man.
Thanks Don, it's nice to hear an encouraging word after sinking so much time into this.
And I'm not sure why you're being criticized here for ignoring Gee's measurements when you actually factor them into your average.
As Chris mentioned, I listed Gee's measurements for completeness but did not factor them into S.
In any case, laying things out step by step in this way should allow anyone to see just where they differ from your analysis and make the appropriate evidentiary challenges or calculation adjustments.
That's exactly what I'm hoping for. The more I work with these images the more I realize what a wealth of information they contain. Every time I look at something I see two or three other things that ought to be examined, such that my current "To Do" list is longer than when I started.
MM didn't rework his numbers between his initial and final post. Rather, his initial post included measurements only from JSP I and XI, whereas his final post incorporated JSP X.
Also, the initial post used a measurement for W3.4 which I now believe was in error.
All I can see MM has done is to rework the numbers between his initial post and his final(?) post until a result was achieved that corresponds more or less to Ritner's estimate and his preconceived notions.
I underestimated how much time this would take when I began. I can see that the number quoted in my early partial analysis has caused some confusion. In retrospect, I should have refrained from stating the length estimate until all the measurements were in and the numbers settled down. I still expect the estimate to bounce around a bit, but probably not by more than 20 cm.
The bottom line is that he is asserting that Gee's measurements of the original papyri are wrong by a total of 1.5 cm (9.7 cm [Gee] vs. 10.2 cm [MM] and 9.5 cm [Gee] vs. 8.5 cm [MM]).
I have my suspicions as to where Prof. Gee made his measurements, but rather than offer them up here, I think we should give him the opportunity to join this conversation and explain them himself. It does appear, however, that his 9.5 cm measurement was more in the vicinity of W8 than W7.
In my judgment, there is no demonstrable reason yet presented to question the reliability of Gee's measurements.

All we know about his measurements is what he wrote in the Wiki:

"The lacuna and any partial measurements involving lacunae were dropped from the evaluation which I made."

If this was indeed the case, then what exactly did he base his measurements on? Wrinkle patterns only observable in the originals? Fourier or wavelet analysis of ink smears? Infrared/ultraviolet absorption in the backlit papyrus? Microscopic pagination encoded by the scribe?

Unless, of course, John Gee is a bumbling fool or an inveterate liar.
You seem determined to steer this discussion into a referendum on Prof. Gee's compentence. This is not helpful.

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All we know about his measurements is what he wrote in the Wiki:

"The lacuna and any partial measurements involving lacunae were dropped from the evaluation which I made."

If this was indeed the case, then what exactly did he base his measurements on? Wrinkle patterns only observable in the originals? Fourier or wavelet analysis of ink smears? Infrared/ultraviolet absorption in the backlit papyrus? Microscopic pagination encoded by the scribe?

I'm fairly certain this refers to what you have dubbed "the gap".

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MM (on Professor Geeâ??s winding measurements):

â?¦ what exactly did he base his measurements on? Wrinkle patterns only observable in the originals? Fourier or wavelet analysis of ink smears? Infrared/ultraviolet absorption in the backlit papyrus? Microscopic pagination encoded by the scribe?

Clever.

Kind of a variation on the â??Gee is a clownâ? theme you and Chris love to reprise from time to time.

In any case, his measurements (as dictated by the Hoffmann formula) were based on his judgment of the distance between corresponding salient points in the repeating patterns of the lacunae.

We get that you reject the accuracy/reliability of Geeâ??s measurements. That much is clear.

What is not clear is the strength of the rationale you have used for your own measurements. Try as I might (and I have now read through the latest incarnation of your evolving post several times) I cannot see that your assignment of the points of measurement amounts to anything more than arbitrary. Oh, I understand what you believe you are doing with the overlay business illustrated above. But your resulting measurements do not demonstrate the expected properties and consistency of a spiral wrap of papyrus. This leads me to believe that your selected points of measurement are essentially arbitrary, and therefore unreliable. The points you have selected for the measurements of windings 3, 6, and 7 seem particularly problematic.

In a typical wound scroll, we would expect the â??Sâ? factor (the space between successive windings) to be the largest for the outside windings, since it is the outside windings that have less tension holding them in the spiral pattern, whereas the inner windings are held in place by all of the material wrapped around them. Therefore, any â??emptyâ? space (space not occupied by the actual papyrus material itself) between successive layers should be less and less until you reach the umbilicus.

But you have this expected pattern completely reversed!

Your â??Sâ? factors are actually increasing the further inside the spiral you get. It starts out at .15 between 1 and 2, then rises to .22 between 2 and 3, then to .27 between 3 and 4, finally rising to .48 and .49 for the last two windings whose measurements you provide. Your measurements suggest that the scrollâ??s outer windings were considerably tighter than the inner windings! And, of course, that just doesnâ??t make sense.

I can only conclude that youâ??ve got a serious flaw in your methodology.

You seem determined to steer this discussion into a referendum on Prof. Gee's compentence. This is not helpful.

Right. The underlying implication of your entire series of posts on this message board for the past few months has served to put into question Professor Geeâ??s competence, which both you and Chris Smith have explicitly ridiculed on occasion (I would refer our readers to your posts on the MDB). And yet I am now the one who wants to steer the discussion in the direction youâ??ve both been taking it for all this time? Are you serious? Or was this some attempt at humor gone awry?

As for steering the discussion into a referendum on someoneâ??s competence, I think that is the general thrust of my comments above. :P

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Edit: I have added this image of a scroll to illustrate my point from above. Our readers will note that, in a rolled scroll, the outer windings are much looser; the inner windings quite tight, especially the closer to the center you go. Mortal Man's measurements seemingly reverse this condition.

PapyrusScroll.jpg

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In any case, his measurements (as dictated by the Hoffmann formula) were based on his judgment of the distance between corresponding salient points in the repeating patterns of the lacunae.

Did he tell you this? If so, where exactly are these "salient points"?

your resulting measurements do not demonstrate the expected properties and consistency of a spiral wrap of papyrus.

...

In a typical wound scroll, we would expect the "S" factor (the space between successive windings) to be the largest for the outside windings, since it is the outside windings that have less tension holding them in the spiral pattern, whereas the inner windings are held in place by all of the material wrapped around them. Therefore, any "empty" space (space not occupied by the actual papyrus material itself) between successive layers should be less and less until you reach the umbilicus.

But you have this expected pattern completely reversed!

Your "S" factors are actually increasing the further inside the spiral you get. It starts out at .15 between 1 and 2, then rises to .22 between 2 and 3, then to .27 between 3 and 4, finally rising to .48 and .49 for the last two windings whose measurements you provide. Your measurements suggest that the scroll's outer windings were considerably tighter than the inner windings! And, of course, that just doesn't make sense.

...

Our readers will note that, in a rolled scroll, the outer windings are much looser; the inner windings quite tight, especially the closer to the center you go. Mortal Man's measurements seemingly reverse this condition.

From http://www.matse.psu.edu/matse81/Spring_20...s/CRRAFinal.pdf

"Cellulosic materials also display good dimensional stability [11], i.e., these are "elastic"

materials, because of the hydrogen bonding. Most plant fiber materials will revert to their

original shape after stressing, when the stress is removed, because the hydrogen "cross-links"

keep the chain molecules together whilst being deformed. However, the hydrogen bonds may be

disrupted by water, and the material can become plastic (as opposed to elastic). Hence the need

for pressing the "papyrus paper" whilst wet; the hydrogen bonding network is disrupted, and the

"paper" will plastically deform. Once dry, the papyrus may be elastically formed into a scroll,

but will not be permanently deformed by the rolling." (emphasis mine)

The elastic strength of papyrus causes each winding in a scroll to "press out" against the outer windings in an attempt to return to its original shape; hence, the Horos scroll probably had to be bound or placed in a tube to prevent it from unrolling (you show an unbound scroll). This means that the outer windings were subject to the cumulative force of all inner windings and hence were pressed more tightly together. If you've ever rolled up a poster and placed it in a tube, you may have noticed that the outer windings are tight against the outside while the inner windings sometimes spiral in loosely. This is a result of the inner radius of curvature exceeding the elastic strain limit of the material, which results in plastic deformation. Also, the inner end is often a straight segment, passing along a chord of the hollow core. This configuration minimizes the strain energy in the material. Therefore, the inverse relation between S and the radius of curvature is as expected.

(I would refer our readers to your posts on the MDB).

CFR

I'd be very interested in seeing these posts, since I've never been a member of that board.

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So, now we've transformed the assumptions concerning this question from a traditional papyrus scroll wrapped around a wooden umbilicus to a three-foot wide papyrus sheet, rolled up and stuffed in a tube.

Mmmmm ......

Not sure where to go from here.

When it becomes possible to continuously modify the parameters of the debate to meet any exigency, it then becomes a debate with no end in sight.

I suppose I will terminate my participation in this discussion by simply stating that I do not accept the various speculative rationales you have employed. Nor do I believe they will stand up to scrutiny if presented outside the domain of a message board. I will present my findings for publication. I invite you to submit yours as well. Perhaps by advancing the debate to that level we'll be more likely to reach a satisfactory conclusion.

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That the papyrus was in a tube is well-attested by contemporary sources. And although the use of a wooden umbilicus has been suggested, I don't think that anyone has committed themselves to that possibility. I personally think the use of an umbilicus unlikely.

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That the papyrus was in a tube is well-attested by contemporary sources.

I don't dispute that the scroll is reported to have been anciently placed in some kind of tube, from which it was extracted (and damaged) in 1835. But until now, the question of the tube, per se, never formed part of the argument. Now it has, along with MM's new argument about how that sheet of papyrus was "rolled up" and placed in said tube. You're no longer talking about a "papyrus scroll," but rather a ~3-foot-long papyrus "poster" rolled up and placed inside a tube. I view that as a fundamental alteration of the argument.

And although the use of a wooden umbilicus has been suggested, I don't think that anyone has committed themselves to that possibility. I personally think the use of an umbilicus unlikely.

Sure you do.

Now.

I get that.

MM's measurements absolutely require the papyrus to be liberated from an umbilicus. It remains to be seen if the argument will stand up to the scrutiny that will now be applied to it.

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Sure you do.

Now.

I get that.

Now, and over the entire course of the argument. Although in a few posts I pointed out that Gee's equation argument assumed that there was no umbilicus, I have not pressed that argument for precisely the reason that no eyewitnesses reported an umbilicus, and I do not have any particular reason to believe that the use of an umbilicus was commonplace. Most of the pictures I've seen of papyrus rolls do not feature an umbilicus (although I admittedly have not studied the use of umbilici in any great detail).

In any case, if you expect the critics to make no modifications of their argument whatsoever, then you do not understand the nature of scholarship. We all alter our views to accommodate new evidence, arguments, and considerations. If those new considerations are minor, they will require only minor adjustments. If they are more significant, then they will require a more significant shift. Bring me something more substantial than a complaint that MM's measurements do not fit your expectations, and I will modify my view accordingly. In the meantime, you can't seriously expect me to abandon my position on account of your misgivings.

-Chris

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Now, and over the entire course of the argument. Although in a few posts I pointed out that Gee's equation argument assumed that there was no umbilicus, I have not pressed that argument for precisely the reason that no eyewitnesses reported an umbilicus, and I do not have any particular reason to believe that the use of an umbilicus was commonplace. Most of the pictures I've seen of papyrus rolls do not feature an umbilicus (although I admittedly have not studied the use of umbilici in any great detail).

In any case, if you expect the critics to make no modifications of their argument whatsoever, then you do not understand the nature of scholarship. We all alter our views to accommodate new evidence, arguments, and considerations. If those new considerations are minor, they will require only minor adjustments. If they are more significant, then they will require a more significant shift. Bring me something more substantial than a complaint that MM's measurements do not fit your expectations, and I will modify my view accordingly. In the meantime, you can't seriously expect me to abandon my position on account of your misgivings.

-Chris

The point is not whether there was an umbilicus present with the scroll when it was entombed with its accompanying mummy. The issue is that a long scroll would have been rolled using an umbilicus, which can be removed after the scroll is rolled. It's obvious that, for example, Papyrus Greenfield was wound using an umbilicus, but the umbilicus had been removed.

Mortal Man's assertions vis-a-vis his measurements do not an argument make. Nor is it aided greatly by this late theory of a 3-4 ft. long sheet of papyrus--a Book of Breathings Poster, if you will--being rolled up and placed inside a tube. That is just an ad hoc reaction to the unforeseen difficulties imposed by his measurements.

Of course, the theory of the BoB Poster is entirely dependent on the accuracy of Mortal Man's measurements of the grafted photos.

That is the question.

It is clear that they differ greatly from Professor Gee's measurements. Gee's measurements predict a long scroll wrapped around a center core. Mortal Man's measurements indicate a relatively short length of papyrus sheet rolled into a tube.

It's hard to know how to respond to direct contradiction, which is what we see here. I suppose, in many minds, it all depends on which way you lean on the greater question of Book of Abraham authenticity. Everyone roots for their own "home team."

I guess that's the way it's meant to be ...

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Edited to clarify some clumsy phrasing.

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So, now we've transformed the assumptions concerning this question from a traditional papyrus scroll wrapped around a wooden umbilicus to a three-foot wide papyrus sheet, rolled up and stuffed in a tube.
You're no longer talking about a "papyrus scroll," but rather a ~3-foot-long papyrus "poster" rolled up and placed inside a tube.
Nor is it aided greatly by this late theory of a 3-4 ft.

182 cm = 5.97 ft

Why do you keep insisting that the sheet was only 3 feet long? Are you trying to disprove the existence of Facsimile 3? I think that it must have been at least 4.8 ft to accommodate the remainder of the BoB. Do you have some sort of vested interest in the scroll being very short? :P

But until now, the question of the tube, per se, never formed part of the argument. Now it has, along with MM's new argument about how that sheet of papyrus was "rolled up" and placed in said tube... I view that as a fundamental alteration of the argument.
...a Book of Breathings Poster, if you will--being rolled up and placed inside a tube. That is just an ad hoc reaction to the unforeseen difficulties imposed by his measurements.

Far from being an "ad hoc reaction," the tube first came to my attention when Chris told me about it last January. http://www.mormonapologetics.org/index.php...mp;p=1208569209

Anyway, the papyrus itself informs us that the scroll was bound on the outside.

From Rhodes' translation of the instructions column: http://home.comcast.net/~michael.rhodes/SnsnTranslation.pdf

"...after his two hands have been clasped to his heart. The Document of Breathing which <Isis> made shall (also) be buried, which is written on both the inside and outside of it, (and wrapped) in royal linen, being placed <under> his left arm near his heart..." (emphasis mine)

MM's measurements absolutely require the papyrus to be liberated from an umbilicus.

How so?

The point is not whether there was an umbilicus present with the scroll when it was entombed with its accompanying mummy. The issue is that a long scroll would have been rolled using an umbilicus, which can be removed after the scroll is rolled. It's obvious that, for example, Papyrus Greenfield was wound using an umbilicus, but the umbilicus had been removed.

No argument here. That's how I'd do it.

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I wrote:

That is just an ad hoc reaction to the unforeseen difficulties imposed by his measurements.

To which MM replies:

Far from being an "ad hoc reaction," the tube first came to my attention when Chris told me about it last January.

This is a complete non sequitur, since the issue isn't the tube. The issue is that, whereas Gee's measurements very clearly indicate a long scroll wound rather tightly around an inner core; your measurements indicate a short scroll which was loosely rolled up and placed in a tube. Your measurements show a steadily increasing "S" factor, which suggests ever-increasing space between windings from the outside to the inside--just the opposite of what would be seen in a traditional scroll configuration; very much the opposite of what we see in the scroll image I have posted numerous times:

PapyrusScroll.jpg

You never made any mention of the tube and the idea of the scroll exhibiting the properties of a rolled-up poster until AFTER I explained the implications of your measurements.

In any event, it all comes down--AGAIN--to whose measurements are correct. And, as I've already noted several times, the difference between the two sets of measurements is HUGE! Someone is very, very, very wrong here. Not just a little mistaken, but very, very, very wrong.

It remains to be seen who that party is.

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