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William Schryver

Missing Papyrus

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Missing Papyrus

- Calculating the Length of the Lost Scroll of Horos -

Version 1.1

William Schryver

The History

In 1967, the New York Metropolitan Museum of Art formally bequeathed to The Church of Jesus Christ of Latter-day Saints a quantity of ancient Egyptian papyri representing an unknown fraction of the collection of Egyptian textual material originally purchased by the church in 1835 from an antiquities dealer by the name of Michael Chandler. Chandler arrived in Ohio in search of Joseph Smith for the ostensible purpose of requesting the Prophet to translate the Egyptian writings on the papyri, which papyri had been found in conjunction with the mummified remains of four persons entombed in the area of ancient Thebes. Chandler sold the mummies and papyri to a consortium of church members for $2400.

Within a year, and in consequence of frequent handling and transport, the papyri began to exhibit signs of decomposition. In response, the most severely damaged outer windings were cut from the rolls, glued to a stiff paper backing, and permanently mounted inside glass frames.1

According to various eyewitness accounts, the textual material consisted of:

â??â??â?¦ a quantity of records, written on papyrus, in Egyptian hieroglyphics,â??2 including (1) some papyri â??preserved under glass,â??3 described as â??a number of glazed slides, like picture frames, containing sheets of papyrus, with Egyptian inscriptions and hieroglyphicsâ??;4 (2) â??a long roll of manuscriptâ??5 that contained the Book of Abraham;6 (3) â??another rollâ??;7 and (4) â??two or three other small pieces of papyrus, with astronomical calculations, epitaphs, &c.â??â?8

After the death of Joseph Smith, the Egyptian material remained in the possession of his mother, Lucy Mack Smith, who, until her death in May 1856, lived with the Prophetâ??s widow, Emma. Shortly after Mother Smithâ??s death, Emma and her second husband, Lewis C. Bidamon, sold the Egyptian materials to one Abel Combs, who subsequently divided the collection. Combs sold some of the material to the St. Louis Museum, including the two rolls of papyrus, but apparently retained most of the mounted fragments. The St. Louis Museum ultimately sold the rolls to the Wood Museum in Chicago, which burned in the fire of 1871, presumably reducing the majority of the original collection to ashes. The mounted fragments passed through several hands, and were ultimately purchased by the New York Metropolitan Museum of Art in 1947.9

It is these glass frames and their papyri contents that were given to the Church on November 27, 1967.10 In February 1968, the Church historianâ??s office discovered another fragment of the papyri in its files, and likewise publicized it.11

None of these extant papyri fragments contain an Egyptian text of the Book of Abraham, a fact first pointed out by Hugh Nibley, who authored articles on the papyri which were serialized in the Church's official magazine beginning in January 1968. Nibley repeatedly emphasized that the documents did not contain the Book of Abraham, but that some of the fragments contained a text he identified as "The Book of Breathings.â?12

Critics of the church, employing a variety of arguments, insist that the extant papyri are what Joseph Smith believed to be the source of his translation of the Book of Abraham.13 Most LDS scholars and apologists have long argued that such a conclusion is unwarranted by the evidence, and that the vast majority of original Egyptian textual material has been lost or destroyed.

In 2007, Brigham Young University Professor of Egyptology, John Gee, presented evidence that the scroll of Horos was considerably longer than the three mounted fragments that survive.14 This would mean that the scroll of Horos was the â??long scrollâ?â??the one upon which the text of the Book of Abraham was found, according to the preponderance of the contemporary eyewitness testimony.

Geeâ??s argument employs a standard formula developed by Egyptologist Friedhelm Hoffmann.15 Hoffmannâ??s formula determined the outside circumference of successive windings by measuring between salient points in the lacunae. 16

Plate #1

JSP_Lacunae.jpg

Lacunae are indicated by red outlines.

He then averaged the difference in the decreasing winding measurements in order to produce a factor he nominated â??S.â? Then, employing the relatively simple mathematics involved in determining the length of a spiral, he claimed to be able to reliably calculate the missing length of any substantial remnant of a papyrus scroll.

Without explicitly endorsing the accuracy of the formula, Gee used his own measurements of the winding lengths of the extant portions of the scroll of Horos and reported the result. Since this initial report, and without directly addressing the reliability of Hoffmannâ??s formula, critics have consistently disputed Professor Geeâ??s arguments concerning the likelihood of a significant amount of missing scroll material.

The Formulae

The Hoffman theory utilizes a series of measurements of the circumference of successive scroll windings. The difference between each successive winding, as measured between corresponding salient points in the lacunae, is then averaged. This result (â??Sâ?) becomes the factor representing the combination of the thickness of the papyrus and the relative tightness of the winding.17

Plate #2

JSP_Lac_Windings.jpg

Corresponding points in the repeating patterns are selected for measurement.

In the case of the Joseph Smith Papyri, Professor Gee is presently the only technician to perform measurements on the original documents, with the intent of gathering data to supply the Hoffmann equation. His measurements showed seven total windings, with the initial winding totaling 9.7 cm and the final winding 9.5 cm, which ultimately produces an â??Sâ? factor of 0.03333.18

A simpler formula is available, based on the thickness of the papyrus material in combination with the known circumference of a single winding. If the initial winding circumference is known and if a constant papyrus thickness is assumed, then the calculation of the spiral becomes a rudimentary application of mathematics.

The two formulae should be mutually supporting. The Hoffmann formula ought to accurately predict the relative thickness of the papyrus material; the spiral calculation, armed with a single accurate circumference measurement and a known papyrus thickness, ought to confirm the results of the Hoffmann formula. However, in practice the Hoffmann formula predicts a longer scroll length than the simple spiral calculation. The discrepancy appears to be due to the acute sensitivity to measurement errors inherent in the formula. (See footnote 23 below.)

The Hoffmann formula returns a missing scroll length result of ~1250 cm (41 ft.), which seems to suggest a papyrus thickness of ~53 microns.19 Known papyrus examples of traditional manufacture range between 100 â?? 200 microns in thickness.20 Utilizing Geeâ??s initial winding measurement of 9.7 cm in conjunction with the lower limit of this range, the spiral calculation returns a missing scroll length of ~750 cm (~25 ft.). Using the upper limit of the range, the formula returns a value of ~380 cm (~12.5 ft.). In either case, this range of lengths is consistent with the known eyewitness testimony of a â??long roll.â?

Traditional production methods produced a very thin papyrus material, as seen in the examples cited above. However, beginning in the Greco-Roman period, Greek-style pens became popular, eventually supplanting the traditional Egyptian brushes or â??rush pens.â? The propensity of these pens to tear the thinner traditional papyrus prompted the introduction of a thicker product. There are samples of papyrus from the Greco-Roman period that measure up to 500 microns or more in thickness.21

However, it is unlikely that the Joseph Smith Papyri are of the thicker variety, for the following reasons:

  • The Joseph Smith Papyri date to the early Greco-Roman era, ~200 B.C.
    -
  • They were written using the old-style Egyptian brushes.
    -
  • Most significantly, the average winding length difference suggests that the thickness of the papyrus in the scroll of Horos was at the extreme low end, rather than the high, of the spectrum of papyrus thickness.22

Conclusions

  • Both the Hoffmann formula and the simple spiral calculation appear theoretically sound. The difference in results between them appears to center on the Hoffmann formulaâ??s sensitivity to precise measurements.
    23

    -

  • Professor Geeâ??s assertion that the total length of the scroll of Horos greatly exceeds the total length of the extant fragments is vindicated. Using Geeâ??s 9.7 cm circumference measurement in conjunction with a papyrus thickness of 100 micronsâ??the lowest value in the range of known samples of traditionally manufactured papyrusâ??the missing length of the scroll of Horos would have been ~750 cm, or ~25 ft.
    24

    -

  • The contemporary eyewitness reports of a â??long rollâ? are confirmed.

    -

  • Even assuming the highest value in the range of known samples of traditionally manufactured papyrus (200 microns in thickness), the extant fragments of the scroll of Horos represent only 25% of the original length of the whole.

(I gratefully acknowledge the invaluable assistance and insights of Kevin Barney, John Gee, David Keller, Matthew Roper, Gregory Smith, and Edwin Slack.)

Appendix I25

PapyrusScrollLengthTable.jpg

End Notes:

1 See John Gee, "Eyewitness, Hearsay, and Physical Evidence of the Joseph Smith Papyri," in The Disciple as Witness, Essays on Latter-day Saint History and Doctrine in Honor of Richard Lloyd Anderson (Provo: FARMS, 2000), 181.

2 William S. West, A Few Interesting Facts Respecting the Rise, Progress, and Pretensions of the Mormons (Warren, OH, 1837), cited in Jay M. Todd, The Saga of the Book of Abraham (Salt Lake City: Deseret Book, 1969), 196.

3 Josiah Quincy, Figures of the Past from the Leaves of Old Journals (Boston: Roberts Brothers, 1883), 386.

4 Henry Caswall, The City of the Mormons; or, Three Days at Nauvoo, in 1842 (London: J. G. F. & J. Rivington, 1842), 22.

5 Charlotte Haven to her mother, 19 February 1843, "A Girl's Letters from Nauvoo," Overland Monthly and Out West Magazine, December 1890, 624.

6 Jerusha W. Blanchard, "Reminiscences of the Granddaughter of Hyrum Smith," Relief Society Magazine 9/1 (1922): 9; Charlotte Haven to her mother, 19 February 1843, Overland Monthly, 624.

7 Charlotte Haven to her mother, 19 February 1843, Overland Monthly, 624.

8 Oliver Cowdery to William Frye, 22 December 1835 in Latter Day Saints' Messenger and Advocate 2/3 (1835): 234; as cited in John Gee, "Some Puzzles from the Joseph Smith Papyri."

FARMS Review 20 no. 1 (2008) 113â??137, on-line at http://farms.byu.edu/publications/review/?...p;id=699#_edn12

9 See John Gee, A Guide to the Joseph Smith Papyri, (Provo, Utah: FARMS, 2000), 9.

10 Jay M. Todd, "Egyptian Papyri Rediscovered," Improvement Era (January 1968): 12â??16.

11 Jay M. Todd, "New Light on Joseph Smith's Egyptian Papyri: Additional Fragment Disclosed," Improvement Era (February 1968): 40; Jay M. Todd, "Background of the Church Historian's Fragment," Improvement Era (February 1968): 40Aâ??40I.

12 Hugh Nibley, "A New Look at the Pearl of Great Price," Improvement Era (August 1968): 53â??63, for example, contains multiple references to the papyri as part of the Book of the Dead (pp. 55â??59). Reprinted in Hugh Nibley, An Approach to the Book of Abraham, Collected Works of Hugh Nibley 18 (Salt Lake City: Deseret Book and FARMS, 2009).

13 For example, see Jerald and Sandra Tanner, â??The Fall of the Book of Abraham,â? online at: http://www.utlm.org/onlineresources/fallofbookabraham.htm

14 See John Gee, "Some Puzzles from the Joseph Smith Papyri," 113â??137

15 Ibid.

16Lacunae is the plural of lacuna, meaning "a blank space" or missing part of the papyrus material. Because the lacunae were formed when the scroll was still rolled together, the â??missing partsâ? tend to exhibit repetitive patterns along the edges of the papyrus material. (See Plate #1) The total length of a single winding can be determined by measuring between common points in the repeating patterns. (See Plate #2)

17 See Plate #2 for a graphic representation of the process involved.

18 See John Gee, "Some Puzzles from the Joseph Smith Papyri," 113â??137.

19 1000 microns = 1 mm; 10000 microns = 1 cm; 50 microns = 0.005 cm.

20 New Kingdom papyri measured by Jaroslav Cerny averaged 125 microns in thickness. (See A. Lucas, J. R. Harris, Ancient Egyptian Materials and Industries, 4th Edition, (Dover Publications, 1999), 139. n. 7). The papyri discovered in the Villa dei Papyri at Herculaneum have been measured via Micro CT scan and average 150 microns in thickness. (See Herculaneum Archaeology, Issue 3 (Summer 2005): 5)

21 â??A feature that is quite noticeable is the great thickness of certain papyri of the Late Period or Greco-Roman period. There are certainly only two layers, but the strips themselves must have been sliced very thickly. It is widely accepted that the Greek style of reed pen (which in the Ptolemaic period quickly ousted the traditional Egyptian rush pen â?? even, eventually, for the writing of Demotic â?? was likely to puncture the thinnest qualities of papyrus, and that this led to a general increase in the thickness of papyrus.â? Paul T. Nicholson and Ian Shaw, Ancient Egyptian Materials and Technology (Cambridge University Press, 2000) 232.

22 One may justifiably wonder why the question isnâ??t resolved simply by measuring the thickness of samples of the Joseph Smith Papyri. Such measurements are greatly complicated by the fact that the papyri have been glued to a stiff backing paper and permanently mounted in glass frames since 1836. The understandable objections of the conservators, combined with the difficulties inherent in removing samples for measurement may prove insuperable in the near future. However, the Micro CT scan process utilized by the scientists working with the Herculaneum scrolls may yet be seen as a possible avenue for measuring the thickness of the JSP.

23For example, if we round the Gee measurements up and down .1 cm (9.8 and 9.4 cm, respectively) the Hoffmann formula returns a result more comparable to the spiral calculation: a length of ~720 cm and a papyrus thickness of ~0.100 mm.

24 See Appendix I.

25 Thanks to Edwin Slack for preparing the data from which this table is derived, and for the derivation thereof included in Appendix II.

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Thanks, William, for the posting. Takeaways from this paper:

1) Gee's measurements require a papyrus thickness significantly thinner than known examples from even the New Kingdom period, let alone the Greco-Roman period from which the Hor papyrus dates. This is consistent with what Chap and I previously argued, but not with what William previously argued. Thus it is very likely that Gee's measurements are inaccurate.

2) William has not taken any measurements of the papyrus, nor has anyone yet attempted to confirm Dr. Gee's measurements from the original. Thus the only numbers we really have to work with remain Gee's measurements and my and Mortal Man's measurements from the various sets of photographs.

A few points of critique:

1) William's estimates of the papyrus length are based solely on the highly questionable assumption that the papyrus is consistent with New Kingdom papyri rather than with papyri of the Greco Roman Period. There is no reason to accept this assumption except that the missing papyrus theory requires it.

2) William acknowledges contributions from his fellow apologists but not from critics, who evidently are not important enough to have their contributions to this discussion acknowledged. This despite the fact that he uses references I and others here provided over the course of our discussion, and relies on an understanding of the issue that he obtained from the critics.

3) He assumes that the change in circumference between two wraps (Will's "Delta C", Hoffmann's S-value) can be directly derived from a measurement of papyrus thickness taken with a micrometer. This assumption requires that there is no air space or "breathing room" between papyrus layers. If he really wants to draw comparisons to New Kingdom papyri, he should measure New Kingdom S-values directly rather than deriving them from micrometer measurements. Or, at the very least, he should verify his assumption by checking it in several specific cases.

4) William makes the statement that "in practice the Hoffmann formula predicts a longer scroll length than the simple spiral calculation." This is incorrect. The Hoffmann formula actually predicts a shorter length than the simple spiral calculation. Hoffmann's formula actually is a simple spiral calculation, but with the innermost windings subtracted. That's because, to quote my translation of him, "the windings can not be put into practice under 2.5 cm. (The actual value permitted for all intents and purposes lies higher. I might have recommended over 3 cm.) As in the graphical reconstruction, we must subtract this innermost range from the total expanse." William's statement that "the Hoffmann formula seems to assume a thinner product of papyrus than is attested by the known examples thereof" illustrates, quite frankly, that he does not yet understand how the Hoffmann formula works. The formula involves no such assumption, but rather requires that its users input actual measurements from the papyrus itself. The reason the Hoffmann result is so implausible is that Gee inputted implausible measurements. It is no fault of Hoffmann's or of the formula itself.

5) William's summary of the eyewitness evidence of the papyri (lifted from Gee) not only conflates different time periods (namely, before the papyrus fragments were mounted and after they were mounted) but ignores some crucial eyewitness evidence, including several witnesses who were told that the mounted fragments included portions of the writings of Abraham.

To summarize:

Aside from conceding that Gee's measurements are implausible (which admittedly is progress), William's paper does not appear to significantly advance the discussion beyond what we've already debated on this and the other board.

Brent Metcalfe informs me that he intends to provide me with two more sets of (unpublished) photographs that have rulers in them, so that I can repeat my measurements and obtain more accurate figures. Assuming Brent comes through, this will allow for a much more definitive evaluation.

Peace and best wishes to William,

-Chris

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Chris,

I will respond to your post when time permits. You have made several statements that are either unwarranted or untrue. But you should also note that I apparently made some changes to the paper between when you first read it and when you wrote your post. My understanding of the Hoffmann formula was greatly enhanced by a discussion with a colleague, David Keller. And, accordingly, I modified some of the language concerning the formula.

I wlll state, categorically, that you are mistaken when you write:

William's estimates of the papyrus length are based solely on the highly questionable assumption that the papyrus is consistent with New Kingdom papyri rather than with papyri of the Greco Roman Period.

This is simply not true. I also cited examples from Herculaneum (79 A.D.) -- where many scrolls were measured and averaged 100 - 200 microns in thickness.

Furthermore, I specifically addressed your argument about the Greco-Roman period papyri:

Traditional production methods produced a very thin papyrus material, as seen in the examples cited above. However, beginning in the Greco-Roman period, Greek-style pens became popular, eventually supplanting the traditional Egyptian brushes or â??rush pens.â? The propensity of these pens to tear the thinner traditional papyrus prompted the introduction of a thicker product. There are samples of papyrus from the Greco-Roman period that measure up to 500 microns or more in thickness.21

However, it is unlikely that the Joseph Smith Papyri are of the thicker variety, for the following reasons:

  • The Joseph Smith Papyri date to the early Greco-Roman era, ~200 B.C.
    -
  • They were written using the old-style Egyptian brushes.
    -
  • Most significantly, the average winding length difference suggests that the thickness of the papyrus in the scroll of Horos was at the extreme low end, rather than the high, of the spectrum of papyrus thickness.22

The last bullet point is the most important one of all, as I indicate.

You can claim that Gee's measurements are wrong from now until judgment day. But the fact remains that he measured the originals -- multiple times! And the measurements, even if off by a minor degree, still indicate a papyrus thickness on the extreme low end of the spectrum: 100 - 200 microns.

I will address the remainder of your arguments as soon as possible ...

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CS:

1) Gee's measurements require a papyrus thickness significantly thinner than known examples from even the New Kingdom period, let alone the Greco-Roman period from which the Hor papyrus dates. This is consistent with what Chap and I previously argued, but not with what William previously argued. Thus it is very likely that Gee's measurements are inaccurate.

As I noted in footnote #23, If we assume an error of 1/10th of a centimeter in the Gee measurements (rounding up and down to 9.8 and 9.4 cm, respectively) then the Hoffmann formula returns a value much more in accord with the spiral calculation. I am willing to concede that an error in measurement on that order is possible. We are, after all, talking about tenths of a centimeter.

But you're going to have to establish the fact that Gee was absolutely inept in order to create an inaccuracy sufficient to shrink the length of missing papyrus down to where you'd like it.

I want our readers to understand that Gee's measurements of the winding lengths confirm that the JSP are quite thin -- like traditionally-manufactured papyrus. If the papyrus were 500 microns thick, as you would like us to believe, then Gee's measurements are not just incorrect, they would have to be outright misrepresentations. Is that what you're going to argue? That Gee is a liar, or (at the very least) an incompetent bungler?

That's a bold claim coming from someone who has performed his measurements on photos from a book versus someone who has had numerous opportunities to measure the original documents.

Are you sure you want to go down that road?

.

.

.

Edit: Incidentally, you wrote:

... he uses references I and others here provided ...

What are you talking about?

I have used no references that you provided me.

I did a Google search using the search terms (IIRC) "ancient" "Egyptian" "papyrus" and "thickness" and returned -- on the first page of results, the same books you have previously cited. But I had already read the references before you cited anything. So, you're just plain wrong about your allegation. I would love to credit "Chap" for his assistance in helping me to understand the math behind some of these questions. Unfortunately, I don't think it is appropriate to credit an anonymous message board poster.

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William,

With respect to the scrolls at Herculaneum, please see my third point of critique. I would also be quite interested in seeing the article you reference, if you don't mind emailing me a copy.

As I pointed out a while ago on MDB, the Dead Sea Scroll papyri tend to have S-values of .5 cm (which would translate to a maximum thickness of .08), well beyond the range that you seem to allow in your chart. And, as I pointed out and you repeated in your OP here, papyri of the Greco-Roman period tend to be thicker than earlier period papyri due to the increased use of Greek reed pens. So while I will concede that your citation with respect to the Herculaneum papyri makes it seem plausible that the thickness is between 100 and 200 microns, you also have not excluded the possibility that the thickness was significantly greater than that. You also have not vindicated Gee's smaller value. All you have done is shown that it is possible that Gee's measurements were only a little carelessly mistaken rather than severely so.

You can claim that Gee's measurements are wrong from now until judgment day. But the fact remains that he measured the originals -- multiple times!

It is remarkable, then, that even your generous analysis has to correct his measurements in order to place them within the realm of plausibility.

As I stated before, I will hopefully soon be provided with two more sets of photographs that include rulers for scale. These should make possible a definitive evaluation of Dr. Gee's measurements well before judgment day. In the meantime, your faith in the accuracy of his measurements is touching but is "evidence of things unseen" only in the minds of those who share that faith. The rest of us will hold out for independent verification.

Best,

-Chris

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But you're going to have to establish the fact that Gee was absolutely inept in order to create an inaccuracy sufficient to shrink the length of missing papyrus down to where you'd like it.

Given the subjectivity involved in identifying reference points for measurement, Dr. Gee's very small sample size of only two windings, and his longstanding tendency to find what he wants to find, this sort of inaccuracy is more likely than you might be inclined to believe.

If the papyrus were 500 microns thick, as you would like us to believe, then Gee's measurements are not just incorrect, they would have to be outright misrepresentations.

Actually, my measurements have thus far suggested a maximum thickness of about 290 microns. But since my E-value also differs from yours, and you don't appear to be taking into account Hoffmann's correction factor, this results in a significantly lower estimate of the length of the missing portion than your table suggests.

What are you talking about?

I have used no references that you provided me.

I was the one who made the argument about Ptolemaic papyri being thicker and who first cited the source about the Greek reed pens-- exactly the same words from that source that you yourself cite above. Incidentally, I made this argument at Sunstone well before our message board conversation. In that thread you and Chap had been discussing a different book with a similar title and format before I brought this citation to your attention, so perhaps you are confusing the two works. In any case, I really don't care that much about getting credit for the use of this particular source. I just find it a little personally offensive that you acknowledge the contributions of several apparent latecomers to the conversation, but act as though I and other critics have contributed nothing. It's rude, and suggests a disregard for those with whom you disagree.

Best,

-Chris

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Chris Smith wrote

"As I pointed out a while ago on MDB, the Dead Sea Scroll papyri tend to have S-values of .5 cm (which would translate to a maximum thickness of .08), well beyond the range that you seem to allow in your chart. And, as I pointed out and you repeated in your OP here, papyri of the Greco-Roman period tend to be thicker than earlier period papyri due to the increased use of Greek reed pens."

The Dead Sea Scrolls are not papyrus, but parchment made from goats skins.

Would they not be thicker than papyrus?

Danite

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The Dead Sea Scrolls are not papyrus, but parchment made from goats skins.

Would they not be thicker than papyrus?

There are both leather and papyrus scrolls among the Dead Sea Scrolls. The leather documents are actually thinner than the papyrus ones.

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Regarding footnote 23, Gee clearly rounded to the nearest mm as his use of significant figures shows. I don't expect those not trained in the hard sciences or engineering to understand the implications, but I feel a little embarrassed for Chris continuing making an issue about papyrus thickness, when feasible ones are readily available for the margin of error that is implied in those significant figures. Theoretically Gee could have been off in his measurements by only 1/20th of a cm (not 1/10 as suggested above). But that is assuming perfect measuring conditions, which I think should not be taken for granted, why would lacunae or some other reference points have frayed or aged exactly the same way between layers such that it can really be measured in mm anyway?

I don't think it will really help to get photographs with rulers in them for arriving at the precision necessary for running an adequate check on Gee. It is not the scale of the photos that is the problem, it is the nonlinear distortion that is caused by camera angles. So unless you have a way of estimating the camera parameters from info in the picture (not an easy digital image processing task judging from some of the journal articles I have read or skimmed), you may be mathematically in over your head.

edit: hard to keep the right magnitudes in straight :P

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Just as an example of how nonlinear camera distortion can come into play. Some grad students (in computer science I think) developed a system where they spied on people coming into an out of a building and took pictures of their keys. The goal was to find the bitting code which involves measuring the depth of the key groove at uniformly distributed positions. But before they could perform those measurement they had to compensate for the distortion there unknown camera angle created. They had some clues available to them that aren't known in scroll measurement problem from photos. First they had a standard key pattern for a few common brands that provided a mapping frame of reference like the back, straight side of the key and a distinct head shape. From there they used canned (but expensive, software) to perform the necessary mathematical transformations to rotate and remove the non-linear distortion. Only then could they make adequate measurements and even then it was hit and miss whether they could make a key that worked.

See:

http://vision.ucsd.edu/~blaxton/pagePapers...age_ccs2008.pdf

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mormon fool,

First of all, William's footnote is inaccurate. Plugging his corrected figures into Hoffmann's equation produces a result of 607 cm, or about 20 feet. Compare this to Gee's estimate of 41 feet. Thus a very tiny difference in our input values results in a dramatic difference in our results. A larger sample size (i.e. measuring more wraps) might have helped Gee ensure the accuracy of what are actually very difficult measurements due to the subjectivity of the choice of reference points. Accurately measuring to the nearest mm quite simply is not feasible given a sample size of only two wraps.

I feel a little embarrassed for Chris continuing making an issue about papyrus thickness, when feasible ones are readily available for the margin of error that is implied in those significant figures.

William's correction of Gee's figures within his implied margin of error may indeed bring the maximum papyrus thickness into the very bottom of William's range of known papyrus thicknesses, but its bare-minimum level of feasibility does not translate to plausibility or probability. So don't feel too embarrassed for me.

But that is assuming perfect measuring conditions, which I think should not be taken for granted, why would lacunae or some other reference points frayed or aged exactly the same way between layers such that it can really be measured in microns anyway?

This is precisely my point when I say that when William extrapolates from Gee's S-value to the papyrus thickness and then compares that to papyri measured with a micrometer, he is engaging in a highly dubious exercise. Extrapolation from the change in circumference gives us a maximum papyrus thickness that would only apply if there were no air or unevenness or other material intervening between successive papyrus wrappings. In other words, the 100 micrometer value William extrapolates from his measurements is actually the average difference in radius between successive wrappings, not the actual thickness of the papyrus we would find if we measured it with a micrometer. Delta R and Measured Thickness will only be identical under ideal circumstances; in every other case Measured Thickness will be < Delta R. The difference between the two values might be significant, for all we know. William has not done the work required to find out how closely the one approximates the other. What's my point? My point is that even though William's corrections bring Gee's Delta R value into the very bottom of his range of known measured thicknesses, the actual measured thickness implied by that Delta R likely still remains below that range.

The maximum Gee would have been off in his measurements is 1/20th of a mm (not 1/10 as suggested above).

I assume you mean cm, not mm.

Adjusting Gee's figures an extra tenth of a centimeter in both directions beyond what William has already done brings the length of the missing portion down to about 13 feet and Delta R up to about 160 microns. This is a much more believable Delta R figure, though it is still quite low in comparison to the Dead Sea Scrolls and many other papyri of the Greco-Roman period, including the Semminis and Noufianoub Books of the Dead that were found at the same site and date to about the same period as the Hor document. Gee's figures for the Seminnis document imply a Delta R of 400 microns, and his numbers for the Noufianoub text suggest a Delta R of 525 microns. To borrow the words of an old Sesame Street song, "One of these things is not like the others." I don't think I'm being unreasonable in pointing that out and raising questions about it. Do you?

I don't think it will really help to get photographs with rulers in them for arriving at the precision necessary for running an adequate check on Gee. It is not the scale of the photos that is the problem, it is the nonlinear distortion that is caused by camera angles. So unless you have a way of estimating the camera parameters from info in the picture (not an easy task judging from some of the journal articles I have read or skimmed), you may be mathematically in over your head.

It is true that camera angles can introduce distortion. That is part of the problem with the Improvement Era photographs, in which the distortion is significant. You can tell by looking at the rulers in the photographs and gauging them against an undistorted ruler. The IE photographs appear to create serious problems for Gee's measurements, but my hope is that given additional photos taken by a more careful photographer using the right focal length and angle, I can correct for the IE distortion and confirm or disconfirm Gee's measurements.

I have a request pending to see the originals, but since the Church did not allow Robert K. Ritner to see them I am not hopeful that I will be treated better. So I will make do for the time being with the hopefully more-than-adequate resources to which I can obtain access.

Best,

-Chris

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And now that I've wasted a large portion of my day on this, I'm done. Have fun.

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CS:

It is remarkable, then, that even your generous analysis has to correct his measurements in order to place them within the realm of plausibility.

Why do you think I have â??correctedâ? Geeâ??s measurements? I have not. I simply pointed out that were they rounded differently, the subsequent result would still indicate a scroll of great length. Until proven otherwise, Geeâ??s measurements must be assumed to be correct, indicating a papyrus thickness of about 53 microns. You claim that is implausible. On what basis? We know of several samples as thin as 100 microns. What evidence do you have that it was not possible to manufacture papyrus even thinner than that? None.

Incidentally, Iâ??m all for having anyone and everyone measure the winding lengths on the JSP. I even look forward to your measurements of the photos, notwithstanding the inherent unreliability of such a methodology.

Our readers should understand (and I must give credit to David Keller, again, for providing me with these figures â?? I confess to relying on others to crunch the numbers in this discussion) in order to achieve a papyrus thickness of 500 microns, Geeâ??s measurements for the windings must be incorrect by 1.9 cm! In order to achieve a papyrus thickness of 800 microns, his measurements must be incorrect by 3 cm!

That, my friend, is a serious order of error that you are alleging.

Given the subjectivity involved in identifying reference points for measurement, Dr. Gee's very small sample size of only two windings, and his longstanding tendency to find what he wants to find, this sort of inaccuracy is more likely than you might be inclined to believe.

1.9 - 3 cm inaccuracy? That is a HUGE discrepancy.

Actually, my measurements have thus far suggested a maximum thickness of about 290 microns.

Which, assuming it is true, would predict a total length of missing scroll of ~8 feet! In my judgment, even that figure is sufficient to accord with the eyewitness testimony of the â??long roll.â? 8 feet of scroll with unknown contents! This is a major concession in and of itself. Nevertheless, the measurements made by Gee must be considered authoritative until proven otherwise.

I was the one who made the argument about Ptolemaic papyri being thicker and who first cited the source about the Greek reed pens-- exactly the same words from that source that you yourself cite above.

Believe what youâ??d like, but I was not led to that source by you. I already had the source in hand when you made your post. As I have already indicated, both sources I cited are returned on the first page of a single Google search. But if you are so hungry for credit, you are free to as much as youâ??d like. :P I donâ??t see as it matters much anyway. The evidence speaks for itself, regardless of who feels they found it first.

I just find it a little personally offensive that you acknowledge the contributions of several apparent latecomers to the conversation, but act as though I and other critics have contributed nothing. It's rude, and suggests a disregard for those with whom you disagree.

Stop your freaking whining about this. You and one of your anonymous buddies focused me on the topic, for that I give you full credit. â??Chapâ? very much helped me understand the issues, which I had largely ignored previous to that time. For that I give him credit. But the fact is that you and your anonymous friends, contrary to your opinion otherwise, contributed very little to my research and understanding of this question. For that I must credit my own hard work and the help of several others with whom I have consulted extensively in the past several days.

This is precisely my point when I say that when William extrapolates from Gee's S-value to the papyrus thickness and then compares that to papyri measured with a micrometer, he is engaging in a highly dubious exercise.

Iâ??m comparing the results of two separate formulae. The Gee measurements indicate a papyrus thickness of 53 microns. Known samples of traditionally manufactured papyrus from both the New Kingdom period (Cerny) and the Greco-Roman period (the Herculaneum Micro CT scan measurements of several scrolls) are as thin as 100 microns. Until Geeâ??s measurements are shown to be incorrect, I donâ??t see how it is â??implausibleâ? to believe that papyrus could have been manufactured to a ~50 micron thickness. And were his measurements to be â??correctedâ? by future, more precise, measurements, youâ??re still facing the reality that his measurements must be incorrect to an almost implausible degree: 2 â?? 3 cm!

Youâ??ve got quite a task ahead of you in that respect. I look forward to the results of your measurements. I hope you feel confident in publicizing them, and will then be prepared to stand by them.

One final query: why have you ignored the fact that the JSP were written with old-style Egyptian brushes and not the Greek pens that were used for the thicker late Greco-Roman period papyrus samples? You see, itâ??s not just Geeâ??s measurements that argue for thin Joseph Smith Papyri. As I noted in the paper:

â?¦ it is unlikely that the Joseph Smith Papyri are of the thicker variety, for the following reasons:
  • The Joseph Smith Papyri date to the early Greco-Roman era, ~200 B.C.
    -
  • They were written using the old-style Egyptian brushes.
    -
  • Most significantly, the average winding length difference suggests that the thickness of the papyrus in the scroll of Horos was at the extreme low end, rather than the high, of the spectrum of papyrus thickness.22

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mormon fool,

First of all, William's footnote is inaccurate.

Actually William's footnote, which I helped formulate, may be the most correct observation to how you have gotten so utterly off on the wrong track in your critique of Gee. You would do well to study it out until your orientation towards this problem changes.

Whether one uses Hoffmann's equation, the calculus equation, or your friend's spread sheet the final result is very sensitive to the measurement of the S parameter.

For the equations the dominant term is inversely proportionate to S>=2*pi*T. Since S is small, doubling S is still in the margin error implied in Gee's significant figures and I see that you agree that an measuring error of 1 mm is no big deal. Doubling S actually halfs the dominant term in the formulas so yes, going from 40 to 20 feet is approximately what I expect to happen. before I even touch a calculator.

Plugging his corrected figures into Hoffmann's equation produces a result of 607 cm, or about 20 feet. Compare this to Gee's estimate of 41 feet. Thus a very tiny difference in our input values results in a dramatic difference in our results.

As we should expect.

A larger sample size (i.e. measuring more wraps) might have helped Gee ensure the accuracy of what are actually very difficult measurements due to the subjectivity of the choice of reference points. Accurately measuring to the nearest mm quite simply is not feasible given a sample size of only two wraps.

I agree that it would be very difficult to measure to the nearest mm. I have a hard enough time when I am doing carpentry where you measure twice and cut once and are still lucky if you are in an 8th of an inch, even if you have a laser guided saw or have set up a fence. Even little things conspire to throw the measurement off from the thickness of my marker to the heat which can expand or contract my tape measure, to the angle I am looking from, or whether my ruler is being held at the right angle.

Interestingly enough, measuring multiple wraps does not help that much if each independent measurement is associated with its own independently distributed random error. I would quantify that for you but I would have go back and review Cramer-Rao bounds on an over-determined system of equations. But perhaps I should let you do some homework on that and report back to us?

William's correction of Gee's figures within his implied margin of error may indeed bring the maximum papyrus thickness into the very bottom of William's range of known papyrus thicknesses, but its bare-minimum level of feasibility does not translate to plausibility or probability.

What did Sherlock Holmes always say? "Once you eliminate the impossible, what remains must be true, however improbable." .

So don't feel too embarrassed for me.

I feel a little better now.

This is precisely my point when I say that when William extrapolates from Gee's S-value to the papyrus thickness and then compares that to papyri measured with a micrometer, he is engaging in a highly dubious exercise.

Actually this precisely the type of thing one should be doing as a check on whether observed measurements or theoretic upper bounds are reasonable or not. If you want to perform additional tests that show that whether or not tight wrapping is feasible or not, knock yourself out. I do not know why Will should have to satisfy your shifting skeptical demands every time he debunks your old requirements.

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Actually, given the nature of papyrus, I suspect it is quite likely that any given roll of papyrus would vary in width.

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Plugging his corrected figures into Hoffmann's equation produces a result of 607 cm, or about 20 feet. Compare this to Gee's estimate of 41 feet. Thus a very tiny difference in our input values results in a dramatic difference in our results.

To which Mormon fool replied: "As we should expect."

I'm getting the feeling that Chris has never spent much time in an undergraduate university physics lab dropping masses from various heights, swinging pendulums, and trying to get the answers which the formulas tell us we should get. I get PTSD just thinking about it, along with the 10x10 calculation matrix which we were to do by hand--no spreadsheets.

The imprecision in all measurement, and the large effects which even small variance can make, are simply a fact of life in the real world, even under ideal conditions. Would you trust anyone who claimed to be able to measure this stuff to more accuracy than the nearest mm? I wouldn't.

(In an organic chem lab I once got 10% of the predicted yield of a compound, and considered myself fortunate.)

Let's not miss the forest for the trees:

1) we have here two formulae, based on different measurements and different principles, that converge at a common answer: that there was a great deal of scroll missing.

2) This also matches what the eyewitnesses reported.

Whether it is 10 feet, 20 feet, or 40 feet, seems rather immaterial.

And, I await with bated breath the reconstruction of all unknown non-linear camera distortion via a single reference point (the ruler). THAT will be good times. :-) As I understand it, that is an exceedingly difficult computational problem. Break out your Cray. :-)

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Will,

Which, assuming it is true, would predict a total length of missing scroll of ~8 feet! In my judgment, even that figure is sufficient to accord with the eyewitness testimony of the â??long roll.â?

Actually, my measurements from the IE and Larson photos from which the 290 micron figure was derived predict a much shorter missing length, on the order of three feet.

Youâ??ve got quite a task ahead of you in that respect. I look forward to the results of your measurements. I hope you feel confident in publicizing them, and will then be prepared to stand by them.

I intend to publicize my measurements and stand by them regardless of the results. If it turns out I have been hopelessly wrong about all this, I will eat my shorts and apologize to Dr. Gee on this very board.

One final query: why have you ignored the fact that the JSP were written with old-style Egyptian brushes and not the Greek pens that were used for the thicker late Greco-Roman period papyrus samples?

I discussed it on the other board when you first raised this argument a while ago. The bottom line is that I'm not convinced that the type of writing implement used is a predictor for the thickness of the papyrus used. No doubt those who used reed pens sought out thicker qualities of papyrus, but is there any reason that users of brushes should seek out thinner ones? Did the scribe(s) of the Noufianoub and Ta-shere-min document(s) seek out thin papyrus?

Mormon fool,

Actually William's footnote, which I helped formulate, may be the most correct observation to how you have gotten so utterly off on the wrong track in your critique of Gee.

You misunderstand me. William's footnote stated that his corrected measurements, when plugged into Hoffmann's formula, returned a length of 720 centimeters. Actually, the length returned is 607 centimeters.

Interestingly enough, measuring multiple wraps does not help that much if each independent measurement is associated with its own independently distributed random error.

I don't know anything about Cramer-Rao bounds. What I do know is that when I measured the papyri, the initial reference points I chose were not good anchors, but that only became clear to me when I increased my sample size and compared the results across several wrappings. Careful study of repeated lacunae over all the extant wrappings helped me choose a variety of much better anchors that returned more consistent results.

I also know enough math to know that a line of best fit will be more accurate when you have more data points. Inputting two data points is inferior to inputting seven. When enough data points are inputted, eventually errors of measurement can be expected to more or less average themselves out.

The snideness is getting pretty thick in here, so I'm going to bow out of this conversation before it gets the best of me. I'll report back if and when I've taken further measurements.

Best,

-Chris

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Mormon fool,

You misunderstand me. William's footnote stated that his corrected measurements, when plugged into Hoffmann's formula, returned a length of 720 centimeters. Actually, the length returned is 607 centimeters.

Chris, thanks for the clarification, that helps me understand where we have had a failure to communicate. You may want to go back and re-read the footnote, the 720 cm figure is not said to have come from the Hoffmann formula, the Hoffmann result is said to be comparable to the 720 cm figure. The difference between 720 and 607 is not a big deal as the figures your post brought up and emphasized (~20 ft and ~40 ft) and it was this that I was responding to, unaware that you had misread the footnote.

Hoffmann's equation calculates the missing scroll length and not the total scroll length, like the various versions of the spiral equation do, although they all can be adjusted to do either. So about 65 cm of the difference is in the 7 windings of 9 + cm. The remaining difference is that one of Hoffman's terms appears to subtract out an inner core of about r=.4 cm (all assuming that we are talking about the limiting case that S = 2piT as footnote 23 says upfront).

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Actually, given the nature of papyrus, I suspect it is quite likely that any given roll of papyrus would vary in width.

Someone go and get Hamblin a playbill so he can read the synopsis before he comes back for the second act. :P

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I also know enough math to know that a line of best fit will be more accurate when you have more data points. Inputting two data points is inferior to inputting seven. When enough data points are inputted, eventually errors of measurement can be expected to more or less average themselves out.

The expected error in estimating S doesn't average out very fast because additional measurements become additional sources of error. Just to give you an idea of how much I did a 1000 simulations that compared just using the last two measurement with using all 7 measurements. I assumed measurement errors as IID RVs with a gaussian distribution of zero mean and std of 1 mm. This resulted in the standard deviation of error in the S estimate that only made a 20% difference by using the extra measurements. However if my zero bias assumption doesn't hold then using additional measurements can actually make things worse. Even under the optimal conditions I ran it under, 38% of the time using extra measurements made the estimate worse.

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The snideness is getting pretty thick in here, so I'm going to bow out of this conversation before it gets the best of me. I'll report back if and when I've taken further measurements.

No one is being snide, but your argument is crumbling. I suppose that claiming everyone is nasty is an attempt to seize the high ground, but it doesn't look very persuasive given your history on this and other topics.

There are people here who know far more math and the necessary modeling than you do. You might try learning from them.

Take a deep breath. The Church can still be false if there was extra scroll. :-)

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I wrote:

Our readers should understand (and I must give credit to David Keller, again, for providing me with these figures â?? I confess to relying on others to crunch the numbers in this discussion) in order to achieve a papyrus thickness of 500 microns, Geeâ??s measurements for the windings must be incorrect by 1.9 cm! In order to achieve a papyrus thickness of 800 microns, his measurements must be incorrect by 3 cm!

That, my friend, is a serious order of error that you are alleging.

And also:

The Gee measurements indicate a papyrus thickness of 53 microns. Known samples of traditionally manufactured papyrus from both the New Kingdom period (Cerny) and the Greco-Roman period (the Herculaneum Micro CT scan measurements of several scrolls) are as thin as 100 microns. Until Geeâ??s measurements are shown to be incorrect, I donâ??t see how it is â??implausibleâ? to believe that papyrus could have been manufactured to a ~50 micron thickness. And were his measurements to be â??correctedâ? by future, more precise, measurements, youâ??re still facing the reality that his measurements must be incorrect to an almost implausible degree: 2 â?? 3 cm!

To which Christopher Smith replied: _____________________________________

So Chris, I ask you: Are you suggesting that Professor Gee's measurements are incorrect to such a pronounced degree? Have your measurements to date indicated such a possibility?

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No one is being snide[...]

Take a deep breath. The Church can still be false if there was extra scroll. :-)

Hmm.

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(Greg Smith @ May 8 2009, 11:57 AM)

No one is being snide[...]

Take a deep breath. The Church can still be false if there was extra scroll. :-)

Hmm.

How outrageous of the moderators to permit such over-the-top, beyond-the-pale snidenesses like this one from the despicable Greg Smith!

I wouldn't blame poor Chris if he never came back to this uncivilized cesspool of unbridled rhetorical excess.

:P

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The smiley indicates that I'm joking.

But, I am joking to make a quite serious point--Chris is insisting far too much on a losing point. This isn't a hill worth dying on. (Those who have followed the discussion elsewhere will understand why he is reluctant to lose face on the issue, given the amount of crowing and posturing that has gone on.)

This doesn't prove the Church is true or false. It merely proves that the eyewitness accounts about the scrolls are accurate, and also provides validation for an Egyptologial formula for scroll rolling. (I always believed there were more scrolls because there are witnesses who said so, and why would they lie? At the time, it had no apologetic interest on one side or the other. It's the sort of incidental detail that is likely to be accurately reported.)

And, it proves John Gee isn't a completely incompetent hack or liar on this point. (Those concerned can rest assured, however, that he could certainly be an incompetent hack or liar on every other point.)

I suspect, actually, that that was the whole point of the exercise in some minds--discrediting Gee.

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