Scroll Length?

[wenglund]

Is there agreement on the length or circumference of the outer wrap (~10.5 cm)?

Is there also agreement on the length or circumference of the innermost wrap (2.5 cm)? (I ask because the image of the scroll Will has posted in the past seem a bit smaller.)

If so, it seems to me, then, that disputes over the thickness of the papyri and the tightness of the windings can have a profound impact on calculations of the numbers of windings and the length of the scroll.

I have a clarifying question for Mortal Man. When you speak about "effective thickness", is that the sum of the thickness of the papyri plus the thickness of the space between each wrap--the white space in your Archamedian spiral, or is it just the thickness of the "white space"?

Also, what do you estimate are the lengths of each of the outer three windings of the Joseph Smith papyri.

Thanks, -Wade Englund-

Edited November 9, 2011 by wenglund

[Mortal Man]

I think I know what you're talking about, and it is related to the Toronto scroll I talked about above. I actually didn't have anything to do with what happened, and I don't even claim to understand what was done. But as I understand it, Professor Gee came up with a way to test the Cook/Smith methodology (very complex), the Friedrich Hoffmann methodology (moderately complex), and the Schryver/Slack methodology (fairly simple) against a scroll of known dimensions. If I'm not mistaken, he intends to report his results along with the publication of my article. I don't know how soon that will occur.

No offense to Prof. Gee, but from what he has written, both to me personally and in publication, I'm quite certain he doesn't understand our methodology sufficiently to apply it properly. It is (unfortunately) rather complicated and tedious and you have to be very careful in how you proceed. The only person I've seen on the apologetic side with the requisite background to fully understand our paper is Prof. William V. Smith of BYU's math department. He has stated that "the physical conclusions of the article seem reasonable to me as far as the Hor papyrus" and "on the whole it seems to be a careful analysis of the problem of the length of Hor."

Edited November 10, 2011 by Mortal Man

[Bill Hamblin]

No offense to Prof. Gee, but from what he has written, both to me personally and in publication, I'm quite certain he doesn't understand our methodology sufficiently to apply it properly. It is (unfortunately) rather complicated and tedious and you have to be very careful in how you proceed. The only person I've seen on the apologetic side with the requisite background to fully understand our paper is Prof. William V. Smith of BYU's math department, and he has stated that "the physical conclusions of the article seem reasonable to me as far as the Hor papyrus."

In other words, you haven't actually tested your methodology empirically, right?

[Mortal Man]

I believe Smith/Cook traced the scroll on a transparency laid over the scroll, then adjusted digital copies to the tracing, then adjusted for camera angle, topping it off with a formula to adjust for error.

There was no camera involved nor any "formula to adjust for error." We scanned the tracings and then digitized the scans to produce X-Y lists of numbers. Then we printed out the digitized curves to scale and overlaid them on the original tracings. We repeated this procedure several times to remove some minor errors which had crept in during the scanning-digitizing-printing process. In the end we had a set of digital curves exactly matching our original tracings. We invite everyone and anyone with access to the papyri to check our digital data for themselves.

Yours was fairly straight forward, and the two-winding measurement (green line) appeared to be a good control on the three-winding measurement, which was more important.

It appears that Will is simply following the method I outlined here and here (and Chris Smith performed before that). This "anchor points" method is obsolete.

And your thickness measuements that point to a progressive thinning toward the interior of the scroll imply a compactness and density that would appear to contradit an 800-micron effective thickness when the actual thickeness is only 150 microns, right?

This "progressive thinning" of William's imagination appears to derive from comments Chris and I made in the earliest threads on this topic to the effect that pJS 1.3 appeared to be more tightly wound that pJS 1.1-1.2. It turned out that secondary damage (after the scroll was unwound) to the upper edge of pJS 1.2 was skewing the winding measurement, making the outermost windings appear looser than they really were. (See Figure 27 on page 33.) The bottom edge actually yields cleaner data than the top edge and by analyzing both edges, the pattern becomes clear.

[Mortal Man]

Have YOU actually tried this?

Yes and no. I've performed many consistency checks and tests for accuracy. But I haven't performed a blind test because that would require someone other than me to administer.

[Mortal Man]

If I'm not mistaken, he intends to report his results along with the publication of my article.

Is he publishing his own article or putting his results into your article?

When are where will this/these article(s) appear?

[Mortal Man]

From what I understand, the Cook/Smith methodology did not perform well. (Again, I don't understand how it was tested. I was only told that it was tested against the Toronto scroll and that it predicted a length less than 25% of the actual.)

That's because the Cook/Smith methodology has not been applied to this scroll. If this were a good-faith effort then Gee would have sought our feedback to ensure he applied our method properly. Chris and I would have been happy to help.

Getting the winding lengths is one thing, getting the winding numbers is more difficult. Everything you need to know is spelled out in our paper (in excruciating detail) but you have to meet all the constraints we specified or the results won't be valid.

As I recall, you also flatly claimed that a wound papyrus scroll only 3.3 cm in diameter could not possibly measure over 6 meters when unrolled. Do you still stand by that claim?

The diameter of human hair ranges from 17 to 181 microns. It varies with color, temperature and humidity. A 6 m strand of 142 micron hair could theoretically be rolled up into 3.3 cm.

I also suppose that you might get the minor axis of a Ptolemaic papyrus scroll down to 3.3 cm if you used the right equipment.

Edited November 10, 2011 by Mortal Man

[wenglund]

Let me ask again:

Is there agreement on the length or circumference of the outer wrap (~10.5 cm)?

Is there also agreement on the length or circumference of the innermost wrap (2.5 cm)? (I ask because the image of the scroll Will has posted in the past seem a bit smaller.)

If so, it seems to me, then, that disputes over the thickness of the papyri and the tightness of the windings can have a profound impact on calculations of the numbers of windings and the length of the scroll.

I have a clarifying question for Mortal Man. When you speak about "effective thickness", is that the sum of the thickness of the papyri plus the thickness of the space between each wrap--the white space in your Archamedian spiral, or is it just the thickness of the "white space"?

Also, what do you estimate are the lengths of each of the outer three windings of the Joseph Smith papyri.

Thanks, -Wade Englund-

[Mortal Man]

Is there agreement on the length or circumference of the outer wrap (~10.5 cm)?

I think so. Although I haven't seen Will's paper, I think we're pretty close on that.

Is there also agreement on the length or circumference of the innermost wrap (2.5 cm)?

That number is what Hoffmann quoted based on his observations of various scrolls. It doesn't make much difference to the length estimate; i.e., you could set it to zero without changing the answer much.

If so, it seems to me, then, that disputes over the thickness of the papyri and the tightness of the windings can have a profound impact on calculations of the numbers of windings and the length of the scroll.

The thickness/tightness dispute is a red herring. Only the winding lengths matter.

I have a clarifying question for Mortal Man. When you speak about "effective thickness", is that the sum of the thickness of the papyri plus the thickness of the space between each wrap--the white space in your Archamedian spiral, or is it just the thickness of the "white space"?

It is none of those things. It is simply a parameter derived from the winding lengths. You can think of it as the mean change in radius from one winding to the next, but the important point is that it comes from the winding measurements and cannot be defined/measured independent of the windings.

Also, what do you estimate are the lengths of each of the outer three windings of the Joseph Smith papyri.

Our winding numbers are not integers. Also, we use an angularly centered definition to eliminate the extraneous terms in Hoffmann's derivation. What you call winding 1 we call W_0.5. So, for example, along the bottom edge we have:

W_0.8704=10.49cm

W_2.601=9.74cm

[Mortal Man]

In other words, you haven't actually tested your methodology empirically, right?

Wrong.

Why don't you try reading our paper, instead of sowing FUD?

[Mortal Man]

You need to add another factor to your test in order to make it analogous to the scroll of Hor: the damage to both ends must be highly irregular, making it very difficult to establish common recurring points for your winding length measurements.

The type of damage makes no difference, so long as you don't go in with a scalpel and cut individual layers independent of their neighbors.

[Bill Hamblin]

Wrong. Why don't you try reading our paper, instead of sowing FUD?

My real question was: have you tried your methodology on a papyrus of known length to see if it actually works? As far as I can tell from your article, you didn't. But I might have missed something. I was really boring and I skimmed a bit.

So, will you answer my real question?

PS It is amazing how my simple question can create such fear, uncertainty and doubt.

[JeremyOrbe-Smith]

Gentlemen, gentlemen! Please! This is a family board! The length of your scrolls doesn't matter, it's all in how you use 'em!

[Bill Hamblin]

Gentlemen, gentlemen! Please! This is a family board! The length of your scrolls doesn't matter, it's all in how you use 'em!

Well, my scroll is longer than Mortal Man's. And I read my scrolls. He simply measures his.

[JeremyOrbe-Smith]

Yeah, well, I've got you both beat: despite the rules of mathematics, the law of mass conservation and the topological limitations of our three-dimensional universe, I know from experience that there is nothing preventing my scroll from being long enough to span the entire U.S. highway system.

[Edit: I politely decline, however, to let Smith, Schryver, or anyone else on this board verify the circumference empirically. O ye of little faith.]

Edited November 10, 2011 by JeremyOrbe-Smith

[J Green]

Mortal Man,

Thanks for the clarification.

There was no camera involved nor any "formula to adjust for error."

My bad. Sorry. I went back to your paper to see where I got it wrong and then realized I was conflating it with a remark by Chris in this thread from 2009.

This "progressive thinning" of William's imagination appears to derive from comments Chris and I made in the earliest threads on this topic to the effect that pJS 1.3 appeared to be more tightly wound that pJS 1.1-1.2. It turned out that secondary damage (after the scroll was unwound) to the upper edge of pJS 1.2 was skewing the winding measurement, making the outermost windings appear looser than they really were. (See Figure 27 on page 33.) The bottom edge actually yields cleaner data than the top edge and by analyzing both edges, the pattern becomes clear.

Will appears to be drawing conclusions based on his own measurements rather than on any previous discussion. He takes around a 100 measurements of actual thickness with the various fragments and observes the nature of the separation. He reports less separation as you progress toward the inner portion of the scroll as well as a decrease in the actual thickness. Average thickness for JSP I (1.1) = 185, JSP XI (1.2) = 165, and JSP X (1.3) = 152 (all in microns). If we get less separation and less thickness as we progress inward, doesn't that suggest a stronger tensile strength exerting pressure on the inner windings? And if the actual thickness is around 160 microns but the effective thickness is 700, doesn't that seem like a scenario that isn't exerting much pressure on the windings? I.e., if you have a coiled spring and relax the tension over 300%, does the spring exert that much pressure any more? I realize that I may be really off base with this question but I'm asking it because it seems like a logical conclusion and because exposing my ignorance by asking the stupid question is sometimes the best way to learn.

As for the math in both papers, I plead abject failure. I thought I was following it pretty well, but at the point that I had either rediscovered cold fusion or invented a great alternative to hummus, I realized I was lost.

Cheers

[Zeta-Flux]

Bill Smith is a friend, so I'll have to ask him about his take on this subject. Being a mathematician myself I should probably delve into these two papers.

[William Schryver]

Mortal Man:

This "progressive thinning" of William's imagination appears to derive from comments Chris and I made …

No, it doesn’t. And the “progressive thinning” is not imaginary. It is a measured phenomenon, and (I believe) a rather significant one.

The bottom edge actually yields cleaner data than the top edge and by analyzing both edges, the pattern becomes clear.

I would like to plot the measurement points you propose on the backdrop of the images of the papyri. I think that might be a rather illustrative thing to do.

You seem to believe that you have removed the “human element” from the act of determining the measurement points for the winding lengths you propose. I am very doubtful of that.

The diameter of human hair ranges from 17 to 181 microns. It varies with color, temperature and humidity. A 6 m strand of 142 micron hair could theoretically be rolled up into 3.3 cm.

I also suppose that you might get the minor axis of a Ptolemaic papyrus scroll down to 3.3 cm if you used the right equipment.

So it would require a steamroller, huh?

I am puzzled that you so confidently dismiss Professor Gee’s report of the 3.3 cm diameter (while still rolled/sealed) Ptolemaic-era scroll that unrolled to a length over 6 meters.

I am also puzzled that you so confidently dismiss (as you have on several occasions) my report that the actual physical thickness of JSP I, JSP XI, and JSP X averages 167 microns.

After all, (assuming John Gee and I are not simply lying) these are presumably demonstrable facts.

You do agree with me and Professor Gee that the scroll of Hor, when rolled, measured more or less 3.3 cm in diameter. I’m glad we agree on at least that point.

The thickness/tightness dispute is a red herring. Only the winding lengths matter.

I think you may be surprised at how much the questions of thickness/tightness can tell us. That said, I agree 100% that the difference in our results is related to the difference in our winding length measurements.

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.

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Zeta-Flux:

Bill Smith is a friend, so I'll have to ask him about his take on this subject. Being a mathematician myself I should probably delve into these two papers.

I consulted with Bill somewhat. Bill read an early draft of my paper, and I believe he read the Cook/Smith paper—although my impression is that he was not nearly as approving of its conclusions as Mortal Man has made him out to be.

Since the point when I believed my paper was completed, I have envisioned further analysis I would like to see brought to bear on this problem. If you are willing to examine the problems, I would very much appreciate it. PM me if you are interested, and I will give you a current e-mail address and we can correspond on this issue.

Edited November 10, 2011 by William Schryver

[wenglund]

Our winding numbers are not integers. Also, we use an angularly centered definition to eliminate the extraneous terms in Hoffmann's derivation. What you call winding 1 we call W_0.5. So, for example, along the bottom edge we have:

W_0.8704=10.49cm

W_2.601=9.74cm

I am a little confused. In your article you said: "In an Archimedean spiral, the length and radius of each winding (proceeding inward) decreases by a constant amount per revolution. Note that the first (blue) winding is slightly longer than the second (red) winding and that there are twelve windings in total. We could compute the length of each black winding if we knew the lengths of the blue and red windings. Equivalently, we could compute the radius of each black winding if we knew the radii of the blue and red windings, since the distances across the white gaps (differences in radii between successive windings) are all the same.

I bolded where you used integers to refer to the windings, and your measurement reference seems to be the beginning point and end of the winding rather than the angular.ly centered point. Be that as it may, I don't really care what you call the windings or where you place your measurement points. I am just trying to find out what you calculate as the length for what is equivolent in the Hor scroll to the blue and red and first black windings in your Archimedien example--or, if you prefer, the distances between each of the 1st through 4th angularly centered points. Thus far you have given me 10.49cm and 9.74cm, so all I need is the next measurement (I am trying to figure out if there is some consistency or pattern to the decline in length for each successive wrap, which may provide a formula for predicting the lengths of missing wraps and thus the length of the scroll.)

I don't know, but perhaps that is why you asked: "Send me at least 3 outer windings and I'll tell you the length to within 10%."

Thanks, -Wade Englund-

[William Schryver]

/snip/ questions to Mortal Man about his winding length measurements

Wade,

I will be glad to share with you my three successive winding length measurements:

10.48 cm

10.30 cm

10.13 cm

[Zeta-Flux]

Questions I had while reading the Cook/Smith paper.

1. Were the computations also carried out using the bottom edge function? (ah, I see later that you did do this! Good.)

2. How was equation (7) derived? Also, some of the terminology is hard to follow. For example, the sentence after equation (7) has n=0. But then in the next sentence you derive n=0.8983. So where is it you use n=0 in equation (7) to get n=0.8983? (If only in the derivation of \zeta, then that was an unfortunate use of n twice.)

3. Do we know that the scroll was wound from the right edge to the left?

4. I'm not sure I followed the discussion at the bottom of page 15. Are you assuming that JS 1.2 follows directly after JS 1.1? (As a mathematician, it is hard for me to follow some of the formulas because the variables are being using in multiple different contexts. In the future, for example, it might be better to write n_{b1} and n_{b2}, where b1 and b2 refer to the ends of JS 1.1 and JS 1.2 respectively.) In particular, I don't understand how you get n_{b2} by taking 18.72/10.42.

5. Using the top edge and bottom edge, the derived lengths of the first winding are (respectively) 10.42cm and 10.49cm. There is a discrepancy of 0.05cm. I imagine this is not unusual, but can anyone confirm that this sort of error is natural?

6. Page 22, why is the winding length on the top of JS 1.2 anomalously large, as opposed to the winding length on the bottom being anomalously small (especially since the bottom edge admittedly has more damage)?

7. Using JS 1.3, we have two consecutive windings. Isn't that sufficient to tell us how much material could appear later? (Modulo possibilities like a tight inner wind, followed by a looser outer wind.)

Okay, it is bed time. My brain has stopped trying to parse the math so I have to quit. If I missed something or skipped something while reading, please take mercy.

Goodnight.

[Zeta-Flux]

Will,

I'd be happy to help. I'll PM you now (then go to bed).

[wenglund]

Wade,

I will be glad to share with you my three successive winding length measurements:

10.48 cm

10.30 cm

10.13 cm

Excellent. Are the next two by chance:

9.96

9.78

Thanks, -Wade Englund-

[wenglund]

5. Using the top edge and bottom edge, the derived lengths of the first winding are (respectively) 10.42cm and 10.49cm. There is a discrepancy of 0.05cm. I imagine this is not unusual, but can anyone confirm that this sort of error is natural?

The discrepancy may be accounted for naturally by considering the scroll as being rolled up asymmetrically, into a slight conical shape. This happens to me pretty much every time I try to roll up a sleeping bag--one side tends to roll up tighter than the other, with the tighter side typically on the left (my left hand tends to be stronger than my right, though it isn't my dominant hand). The same thing happens when I roll up carpets. Just a guess.

Thanks, -Wade Englund-

Edited November 10, 2011 by wenglund

[Olavarria]

The way to resolve part of this problem is to use the rival methods on actual papyri of know length. My understanding is that Schriver and Gee (and others) have used their method on papyri of known length with good accuracy, while Smith and Cook have not.

Excellent point, we need a control.