Scroll Length?

[William Schryver]

Just draw a spiral with an outer circumference of ~10.5 cm and a change in radius of 701 microns per winding.

I invite someone with the necessary skills and software to do exactly this and post the results on this thread.

[wenglund]

Just draw a spiral with an outer circumference of ~10.5 cm and a change in radius of 701 microns per winding.

Assuming that the thickness of the papyrus averages, conservatively, 167 micron, that leaves a space of 534 micron (equivalent to five sheets of printer paper) between each winding. That seems pretty loosely wrapped to me--so loose as to seemingly defy the laws of physics for the item involved (maybe the Egyptian scribes used hair spray to maintain the even spacing between windings.

Thanks, -Wade Englund-

[William Schryver]

As I understand it, for this kind of test to have any meaning, someone would have to have taken a precise measurement of the scroll before it was originally unrolled. Also, the top and bottom borders of the scroll would have to be significantly damaged before the scroll is unrolled. Are there any scrolls available that meet these requirements, which a researcher would be able to handle sufficiently to conduct this test?

The Toronto scroll to which I have referred multiple times in this thread meets these requirements. A researcher would not need to "handle" the papyrus any more than Cook/Smith "handled" the Joseph Smith papyri.

[wenglund]

That's why the winding lengths are so much more important than anything else.

...at the very least it is why they are most vulnerable to distorting the results.

Thanks, -Wade Englund-

[Chris Smith]

Do you intend to argue that those measurements produce a total scroll length of ~300 cm?

I just ran a quick regression analysis using your measurements (along with Hoffman's rule that windings can't be implemented under 2.5 cm) and got 304 cm. How did you get your 600 cm figure?

The images I have are superior to any photographs you have. I used them to measure the winding lengths. They are exactly to scale.

Care to share how exactly you went about your measurements?

The edge is barely discernible. I’m fascinated by the fact that you apparently believe it is sufficient to perform measurements.

It's sufficient to be included in the correlation analysis, if that's what you mean. There may be some minor secondary damage to the edge, but that should average out in the analysis.

[William Schryver]

Assuming that the thickness of the papyrus averages, conservatively, 167 micron, that leaves a space of 534 micron (equivalent to five sheets of printer paper) between each winding. That seems pretty loosely wrapped to me--so loose as to seemingly defy the laws of physics for the item involved (maybe the Egyptian scribes used hair spray to maintain the even spacing between windings.

Thanks, -Wade Englund-

Good observation, Wade. Cook/Smith describe a scenario that is effectively impossible given the measured thickness of the papyrus of the scroll of Hor, that is why they continue to subtly insinuate that my reports of the thickness measurements are either grossly in error or fraudulent.

What is also interesting is that the scroll of Hor was sealed on the ends with bitumen, which was routinely employed to seal Egyptian scrolls as seen here:

If, as Cook/Smith report, the papyrus in question was so loosely rolled as to have over 500 microns of empty space between each layer, the bitumen would, first of all, have had no purpose, and were it applied, it would have been pressed between each layer of papyrus well onto the text of the scroll itself.

Cook/Smith keep insisting that our papyrus thickness measurements are neither relevant nor useful, but then they keep providing examples of where those measurements prove very relevant indeed. Cook/Smith are convinced that our report of the papyrus thickness is a fraud. I have chosen to publicize those measurements: Scroll of Hor - Papyrus Thickness Measurements

According to their calculations, the papyrus thickness is somewhere in the neighborhood of 700 microns. Cook/Smith attempt to dance around this figure by telling us that it merely amounts to the "effective thickness," but the fact is that their calculations require the papyrus to attest a physical thickness of approximately 700 microns. Therefore I point out again that our thickness measurements are a very important "control" value for their methodology as well as the methodology of anyone else who attempts to propose an original length for the scroll of Hor.

Edited November 11, 2011 by William Schryver

[wenglund]

I just ran a quick regression analysis using your measurements (along with Hoffman's rule that windings can't be implemented under 2.5 cm) and got 304 cm. How did you get your 600 cm figure?

See my comparative calculations, which includes my formula (see above). In that example I calculated the length based on Will's prior mention of the papyri averaging a thickness of 167 microns. whereas at 125 microns the length shows at 663 cm.

Thanks, -Wade Englund-

Edited November 11, 2011 by wenglund

[Mortal Man]

Your methodology produces a length for the winding that departs radically from the gradual decrease seen between the first and second windings

Regarding the "cracks" method that Chris illustrated, note that the seams wander a bit, such that they can only be used to estimate the windings to within about a millimeter. Also note that the second winding spans the joint between pJS 1.1 and 1.2 (with a visible gap in between). I suspect that the joint is adding a bit to the second winding, such that the first three windings from the cracks method should be:

106 mm

102 mm

98 mm

give or take half a millimeter for any particular winding.

--reporting a winding length that is significantly shorter than what Gee and I report using our respective methodologies,

The only windings Gee has thus far reported in print are significantly shorter than yours.

[Mortal Man]

As I understand it, for this kind of test to have any meaning, someone would have to have taken a precise measurement of the scroll before it was originally unrolled.

Yes, that would be helpful. Unfortunately, it appears this was not done for the Toronto scroll. I don't doubt that the Toronto scroll is 6 m, since that is an easy measurement to verify; however, I'm quite certain it could not be rolled up into a 3.3 cm diameter scroll. It would have to be thinner than a human hair to do so. Remember that papyrus is made by placing two layers together, with the fibers running crossways, then burnishing the recto layer with a stone to make it smooth enough to write on. It has to be thick enough not to fall apart during this process.

Also, the top and bottom borders of the scroll would have to be significantly damaged before the scroll is unrolled.

Even minimal damage would do.

[Mortal Man]

Assuming that the thickness of the papyrus averages, conservatively, 167 micron, that leaves a space of 534 micron (equivalent to five sheets of printer paper) between each winding. That seems pretty loosely wrapped to me--so loose as to seemingly defy the laws of physics for the item involved (maybe the Egyptian scribes used hair spray to maintain the even spacing between windings.

Wade, if you assume that the thickness of the papyrus averages, conservatively, 1 micron then you can claim that our results are even more absurd and use additional emoticons.

[Mortal Man]

...at the very least it is why they are most vulnerable to distorting the results.

...which is why Gee is using them to claim a circumference of 3.3 cm for the Toronto scroll.

[shalamabobbi]

I invite someone with the necessary skills and software to do exactly this and post the results on this thread.

I get about 1.3m

Consider each layer a concentric cylinder. This approximation errs on the long side. Also each radius is to the outside of each layer, an approximation that errs on the long side.

Everything in meters:

Circumference = C = 0.105

outermost radius = r1 = C/2pi = 0.0167

Thickness = t = 0.000701

Length = L

r1/t = 23 highest whole integer (number of concentric cylinders)

L = 2pi[r1+r2+r3+...+r23] (summation of circumferences of concentric cylinders)

where r2 = r1 - t

r3 = r1 - 2t

...

r23 = r1 - 22t

L = 2pi[r1 + r1-t + r1-2t + ... + r1-22t]

= 2pi*r1[1 + 1-t/r1 + 1-2t/r1 + ... + 1-22t/r1]

let a = t/r1

L = 2pi*r1[1 + 1-a + 1-2a + ... + 1-22a]

L = 2pi*r1[23 -a -2a ... -22a]

L = 2pi*r1[23 - (a + 2a + 3a + ...+ 22a)]

L = 2pi*r1[23 - a(11*23)]

L = 2pi*r1[23-10.613]

L = 2pi*r1[12.387]

L = 77.83r1 = 1.3 meters

Edited November 12, 2011 by shalamabobbi

[Mortal Man]

I don’t know what methodology Professor Gee used for his original report of the winding length measurements, or what images he was using. I know he has acknowledged that those measurements were not accurate, but (IIRC) he attributes it to the fact that he was using images that were not to scale.

Wait a minute, hold on. Before the FAIR WIKI was updated, Gee went on and on about how hopeless it was to use photographs, what with all the distortion and all, and he laid into the critics for even attempting such a thing. He trumpeted the fact that all his measurements were taken directly from the originals and insisted that was the only reliable way to go. Now, after all that preaching, you are telling us he measured his windings from photographs?!?!?!?!?!

Yes, we understand that you are insinuating that Professor Gee’s is lying concerning his report of the Toronto scroll.

I am insinuating that if the Toronto scroll really is 6 meters then it's circumference is greater than 3.3 cm. I keep asking you to take a 6 m sheet of papyrus and roll it up into 3.3 cm; I've yet to see your results.

I haven’t seen his report on the Toronto scroll, but he told me that he was permitted to measure the actual scroll; that its lacunae were very regular, and that he measured (IIRC) a total of 73 windings.

My question was, why should we believe Gee's report of 10.4 cm for the outermost winding?

My measurements for the first three windings are:

10.48 cm

10.30 cm

10.13 cm

Do you intend to argue that those measurements produce a total scroll length of ~300 cm?

I don't intend to argue anything. I intended to simply plug your numbers into the formula, which I did. I think that you should intend to plug your numbers into the formula as well, unless you find it more satisfying to argue.

[A] I have never reported that I basing my winding length measurements on photographs,

let alone the same one you have.

The images I have are superior to any photographs you have.

[A] I used them to measure the winding lengths.

You made another chiasmus!

So despite not reporting that you used "photographs" for your winding measurements you now admit to using "images" to measure your windings.

What is the provenance of these "images"? When were they taken? By whom were they taken? Are the "images" digital scans or, in fact, photographs?

They are exactly to scale.

Oh really? Do they match our tracings of the originals? You ought to find out before proceeding to publication, don't you think?

[wenglund]

Wade, if you assume that the thickness of the papyrus averages, conservatively, 1 micron then you can claim that our results are even more absurd and use additional emoticons.

I could also assume an average thickness of closer to 1000 micron (equivalent to 10 sheets of copy paper) so you can feel a lot better about yourself. However, I am trying to be reasonable. Perhaps you should give it a try.

Thanks, -Wade Englund-

[wenglund]

...which is why Gee is using them to claim a circumference of 3.3 cm for the Toronto scroll.

I am not sure that is a reasonable comparison. Using one of them to determine the circumference is far less vulnerable (exponentially) to significant distortion than using two or three of them to estimate over-all length. .

Thanks, -Wade Englund-

Edited November 12, 2011 by wenglund

[wenglund]

Oh really? Do they match our tracings of the originals? You ought to find out before proceeding to publication, don't you think?

Since when did hand tracings become the gold standard of measurement? Forget digital technology when Chis has got a #2 pencil ready.

Thanks, -Wade Englund-

Edited November 12, 2011 by wenglund

[Mortal Man]

The scroll in Toronto unrolled to a length of over 600 cm.

I haven’t seen his report on the Toronto scroll, but he told me that he was permitted to measure the actual scroll; that its lacunae were very regular, and that he measured (IIRC) a total of 73 windings.

It is simply a derived value from the measurement of the first winding, which was ~10.4 cm.

If your first two numbers are correct then the average winding length for this scroll is 600/73=8.22 cm. Assuming an arithmetic (linear) progression of windings (which, according to Dr. Stegemann, is the case for all of the larger Qumran scrolls) then this would correspond to the value of the center winding and the outermost winding would be double this; i.e., 16.44 cm.

Gee's three numbers are not consistent. If the scroll really is over 600 cm long with a total of 73 windings then the outer circumference must be at least 16.44 cm.

If the Toronto scroll is similar to the Hor scroll, with T=701 microns, then the outermost winding would be 22.99 cm. This is pretty close to twice Gee's estimate. This fact, combined with the reported ellipticity of the scroll, leads me to conclude that Gee has mistakenly measured the half-winding length!

Edited November 13, 2011 by Mortal Man

[Mortal Man]

To me, the notion that a rolled up papyri would form an Archimedian spiral with "white space" (gaps between windings) that is uniformly or on average more than three times the average thickness of the papyrus, seems questionable to me.

I think you did this once. Is that image still available online? I think it would be valuable for our readers to see even a crude drawing. Crayon will do, if that's all you've got.

But I'm serious. Show people an end view of what your calculations suggest the scroll looked like.

Ok, here you go.

Notice that the white space is pretty thin.

Now show us how far you can unroll it!

Edited November 12, 2011 by Mortal Man

[Zeta-Flux]

Ok, here you go.

Notice that the white space is pretty thin.

Now show us how far you can unroll it!

The only way you made that work is fill in the gaps with a substance. That is completely unworkable in this case. Firstly, because of the bitumen. Secondly, because there is no evidence of a separating substance.

[William Schryver]

If your first two numbers are correct then the average winding length for this scroll is 600/73=8.22 cm. Assuming an arithmetic (linear) progression of windings (which, according to Dr. Stegemann, is the case for all of the larger Qumran scrolls) then this would correspond to the value of the center winding and the outermost winding would be double this; i.e., 16.44 cm.

Gee's three numbers are not consistent. If the scroll really is over 600 cm long with a total of 73 windings then the outer circumference must be at least 16.44 cm.

If the Toronto scroll is similar to the Hor scroll, with T=701 microns, then the outermost winding would be 22.99 cm. This is pretty close to twice Gee's estimate. This fact, combined with the alleged ellipticity of the scroll, leads me to conclude that Gee has mistakenly measured the half-winding length!

I'm sorry that you misunderstood what I said and then went to so much trouble in your attempts (once again) to establish that either John Gee or I are lying about something.

I said John measured 73 windings. I didn't say there were only 73 windings in the scroll! There were many more. John simply got weary of measuring windings after he had done 73--especially since he realized 73 was already overkill in terms of acquiring enough to validate the calculations.

I also searched through my old e-mails and found that John simply said that the scroll was 3.3 cm prior to being unwound. He didn't say if it was ellliptical. He didn't say if the 3.3 cm measurement was for a minor or major axis. He just said it was 3.3 cm in diameter. That calculates to a ~10.4 cm circumference. He said nothing about the length of the first winding. I'll call him later today or Monday and see if I can get that value from him. But, obviously, it had to be somewhere in the neighborhood of 10.4 cm.

No matter how you try to twist it, the simple fact is that the scroll had a pre-unwinding diameter of ~3.3 cm and it unrolled to over 6 meters in length. Yes, that makes for a very thin stock of papyrus.

You keep making repeated references to the thickness of a human hair, blah, blah, blah. But the simple fact is that papyrus has been measured to less than 120 microns. The scroll of Semminis in the Church History Library was even thinner than that in most places. Some portions measured to less than 100 microns. Modern printer paper (100 microns) is thinner than the figures you list for "human hair." The paper in your scriptures is about 50 microns--much thinner than the figures you list for "human hair." Yes, papyrus was routinely manufactured to a thickness less than that of the hair of my Navajo friends, but thicker than my own hair. It was an amazing technology those Egyptians had.

You continue to cast doubt (albeit obliquely) on our report that the physical thickness of the papyrus of the scroll of Hor was between 100 and 200 microns. And yet it is. Only one locus measured over 300 microns. It was where the two layers of the papyrus had completely separated and the two separated layers themselves were separating into multiple additional layers. Very few loci measured over 200 microns. The average thickness of JSP I = 185 microns; JSP XI = 165 microns; JSP X = 152 microns. Several loci (the loci that attested the least papyrus layer separation) measured under 150 microns, some as little as 101 microns.

These are, of course, verifiable facts. It will yet be seen that the methodology we employed is beyond reproach. Again, the simple fact is that the physical thickness of the scroll of Hor was ~150 microns, not the 700 microns predicted by your calculations. This is why a knowledge of the papyrus thickness becomes so important as a control in our attempts to calculate the original length of the scroll.

Edited to fix a badly worded phrase.

Edited November 12, 2011 by William Schryver

[William Schryver]

The only way you made that work is fill in the gaps with a substance. That is completely unworkable in this case. Firstly, because of the bitumen. Secondly, because there is no evidence of a separating substance.

QFT

[William Schryver]

Ok, here you go.

Notice that the white space is pretty thin.

Now show us how far you can unroll it!

This is how the Egyptians rolled papyrus:

I can conceive of no way for papyrus to be rolled in the fashion your photo demonstrates.

[William Schryver]

Two slightly larger photos of an unopened Egyptian scroll, sealed with bitumen:

This is how they rolled and sealed scrolls in ancient Egypt, my friends.

[J Green]

Mortal Man's rolled scroll doesn't appear to exert much tensile pressure on the windings, either. And yet the measurements in Will's paper that demonstrate a progressive thinning toward the center (along with less separation) point to a tightly wound scroll, just like in the picture above. It would imply windings just like that picture with very little space in between. So if the actual thickness is around 160 microns, well, then the whole 700 effective thickness measurement appears rather unrealistic. At least from my perspective.

[William Schryver]

By the way, Andrew, is that chewed-up, then spit-out Tootsie Roll between your layers of "papyrus"?

But seriously, folks, Andrew's little illustration (although he certainly didn't intend it to do so) has done much to illustrate the strength of my argument on this thread, and to underscore the importance of our knowledge of the papyrus thickness as a control on our attempts to calculate the original length of the scroll of Hor.

I have opted to share here a brief portion of my article treating upon the topic of papyrus thickness, especially because it elaborates on J Green's comment above:

The subsequent analysis of the measurements of the thickness of the papyrus fragments from the original scroll of Hor revealed much more than was originally expected. That said, in order to correctly interpret and extrapolate meaning from the raw data of the measurements, it is essential to have at least a fundamental understanding of the nature of papyrus and the manner of its production. Unfortunately, there is still much uncertainty and debate, even among modern papyrologists, as to how ancient Egyptian papyrus was manufactured. The manufacturing techniques were closely guarded secrets, and the Egyptians left no known record of the process.

The only surviving ancient account of the manufacture of papyrus is given by Pliny. This problematic description has been much discussed. Many modern writers consider this account to be correct in basic method, but ambiguous in detail. However, from examination of the ancient examples, and from the experience of various individuals who have made papyrus sheets in more recent years … the basic method can reasonably be deduced to have been as follows:

- Cut the stems into manageable lengths and peel away the rind.

- Thinly slice the pith into strips longitudinally, along one of its three flat sides.

- Lay a series of the strips onto a board, side by side, just touching each other, or slightly overlapping, to make the first layer.

- Lay a second similar layer of strips over them at right angles.

- Press or beat the two layers together and allow them to dry.[1]

No adhesive was applied to the overlapping layers of papyrus. The natural adhesive properties of the papyrus sap was sufficient to bind together the layers. However, over course of time, it is evident that this bond can lose its adhesion. It is readily observed that all three sheets of the extant portion of the scroll of Hor attest separation of the fibers of the papyrus. Many loci attest the separation of the two perpendicular layers of original papyrus strips. There is also layered fragmentation within each of the two larger layers.

It is my observation that a substantial portion of the surviving scroll, if not the majority, attests some degree of layered fragmentation. That said, it is possible to identify those loci on the sheets where there is little, if any, apparent damage via layered separation of the papyrus. Measurement of those loci consistently returned the lowest thickness values, in relation to all the measurements taken. The average thickness of the least damaged portions of the papyrus, as represented by the lowest 25% of the total number of measurements from all three fragments (24 of 96), was 123 μm (micrometers).

We made every effort to measure only points attesting no apparent loss of papyrus, notwithstanding the fact that fiber separation was evident. In other words, we consciously did not measure any point where the top, ink-bearing, layer of papyrus was not present.

As opposed to the consistently lower measurements returned at those loci attesting no visible fiber separation, measurement points where much separation was observed consistently returned the highest values of the study. The average thickness of the highest 25% of the total number of measurements was 221 µm.

In addition, it was observed that the relative degree and incidence of fiber separation steadily decreased the further into the roll the measurements were taken. The average thickness of each successive fragment was as follows: JSP I = 185 µm; JSP XI = 165 µm; JSP X = 152 µm.[2]

I propose that the logical explanation for the decreasing incidence of fiber separation towards the inside of the scroll is that the tighter inner windings of the scroll exerted their stored tensile energy such that a “clamping effect” was exerted on the papyrus—an effect that would have diminished toward the outer windings of the scroll. Only a considerable quantity of scroll material, rolled tightly upon itself from a center core, could possibly produce the tensile energy sufficient to explain the observed effect on the papyrus.

[1] Paul T. Nicholson and Ian Shaw, Ancient Egyptian Materials and Technology, Cambridge University Press, Cambridge, UK, 2006: 231, bibliography references in original omitted in this citation.

[2] See Appendix II for the detailed results of the papyrus thickness analysis.

Copyright 2011 by William Schryver - All Rights Reserved

Edited November 12, 2011 by William Schryver