Ludd wrote:I haven't been able to find anything over there where he describes the methodology you're talking about. If someone knows where his method is described, I would appreciate a link.
Your method developed over the course of
this thread, where you were essentially equating measured thickness with change in radius, such that measured thickness and outer circumference can be used to extrapolate scroll length.
By the end of the thread you were telling us about a new methodology developed by George and Howard Fisher, which did not use measured thickness as an input, but rather merely as a control. But you also seemed to say that you would still be publishing your unamended paper using the earlier thickness method. Here are some relevant quotes:
[Professor Gee's] measurements showed seven total windings, with the initial winding totaling 9.7 cm and the final winding 9.5 cm, which ultimately produces an "S" factor of 0.03333.
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. Known papyrus examples of traditional manufacture range between 100 - 200 microns in thickness. Utilizing Gee'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 "long roll." . . .
Professor Gee's assertion that the total length of the scroll of Horos greatly exceeds the total length of the extant fragments is vindicated. Using Gee's 9.7 cm circumference measurement in conjunction with a papyrus thickness of 100 microns—the lowest value in the range of known samples of traditionally manufactured papyrus—the missing length of the scroll of Horos would have been ~750 cm, or ~25 ft.
The contemporary eyewitness reports of a "long roll" 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.
For those who are interested, Brian Hauglid and I spent part of today in a private room at the new Church History Library. The Kirtland Egyptian Papers were our primary focus of attention. More to come later on that.
We also spent a considerable amount of our allotted time examining the Joseph Smith Papyri. We requested and were granted permission to make precision measurements of several fragments of the papyri. We employed a micrometer and measured two samples still attached to the thick backing paper. They measured 394 and 368 microns, respectively. We were not able, at this time, to isolate a sample containing only backing paper in order to measure it and, by subtraction, determine the thickness of the attached papyrus. But we were able to measure two samples no longer attached to the backing paper. Those two samples meaured 97 and 127 microns, respectively, about half the thickness of the "average" of Greco/Roman papyri for which I have previously been able to obtain measurements (see above for details). Combined with John Gee's initial measurement of the outermost winding of the scroll of Horos (9.7 cm), the simple calculation of a spiral returns an upper-bound length of approximately 18-25 feet for the missing portion of the scroll.
The outer winding length is somewhere in the neighborhood of 10 cm, by your own admission.
The intact portions of the papyri we have measured attest to a very thin stock of papyrus used for all of the extant scroll remnants.
The combination of a 10 cm outer winding circumference with a very thin stock of papyrus equates to a substantially long scroll, assuming it was a typical example of comparable Ptolemaic-era documents, which, in all material respects, it appears to be.
Until just recently, no one in the field of Egyptology had ever really concerned themselves with things such as the thickness of papyrus, the length of windings, or the length of missing portions of scrolls for which only fragments remain. As a result of the controversy surrounding the Joseph Smith Papyri (specifically the original length of the scroll of Hor), impetus has now been given for more systematic study of these questions. Consequently, it has been possible, through a comparative analysis of scrolls of known lengths, to not only develop a reliable methodology for estimating the missing length of a papyrus scroll, but also to test the methodologies employed by the competing Schryver and Cook/Smith teams. I can therefore report, absent any detail or further elaboration at this juncture, that the methodology I describe in my forthcoming paper has been shown to produce reasonably accurate results. My having averaged all the papyrus thickness measurements, instead of using only the ones from undamaged areas of the papyrus, caused me to underestimate the original length of the scroll of Hor by about 1 meter.
As I presently understand it (and I must emphasize that I have not yet had the opportunity to sit down with the papyrologist to discuss the specifics) the thickness of the papyrus is not a necessary measurement in the methodology that has been developed. However, the formula does give a reasonably accurate estimate of the papyrus thickness. Therefore, knowing the thickness of the papyrus is an important element of confirming data. Furthermore, as I illustrate in my forthcoming article, if you do know the thickness of the papyrus and at least the first three winding lengths, you can very accurately estimate the original length of the scroll. The original length was in the neighborhood of 500 cm. . . . The method I describe in my paper actually rests on no assumptions at all. It is based on nothing more than four objective measurements: the thickness of the papyrus and the length of the first three windings. Its simplicity is its virtue, and explains why it is superior (by several orders of magnitude) to the methodology you and Cook employed.
In short, your method was apparently to average the outer windings in order to get an outer circumference, and then plug this value and the measured thickness of the papyrus into the spiral formula in order to get an estimate of papyrus length. Although Andrew and I repeatedly pointed out that you were assuming a rough equivalency between measured and effective thickness, you persisted in arguing that your method rested on "no assumptions at all." You clung to your method even when some papyrologists with whom you were collaborating developed a different method, which used measured thickness only as a control.
By the way: as usual, your "Ludd" pseudonym's fixation on all things William Schryver is a dead giveaway.