Scroll Length?

[wenglund]

I'm probably missing something here because I don't understand the math. (My choice was calculus or Hebrew.) But it seems obvious to me that a variable in these formulas would be how tightly wound the papyrus was. A loosely wound scroll with a 3cm diameter would have less papyrus than a tightly wound scroll with a 3cm diameter. If the measurements were taken only from the outermost three windings of the scroll--which seems to be the case here with Chris and Andrew's experiment--then it couldn't tell us about the length of the scroll unless we knew how tightly or loosely wound the inner part of the scroll was. Wouldn't a 3cm diameter scroll produce the same measurements on the outermost three rings of the scroll regardless of how tightly wound it was in the interior?

As I understand it, Andrews formula doesn't require measurements of looseness or tightness (in my formula the looseness or tightness is accounted for by the "distance between the spiral branches" or rings), though the results of his calculations produce a relatively loose spiral, which to me makes his measurements somewhat suspect.

Thanks, -Wade Englund-

[Bill Hamblin]

As I understand it, Andrews formula doesn't require measurements of looseness or tightness (in my formula the looseness or tightness is accounted for by the "distance between the spiral branches" or rings), though the results of his calculations produce a relatively loose spiral, which to me makes his measurements somewhat suspect.

Thanks, -Wade Englund-

Loose winding = short scroll. Tight winding = long scroll, right?

Also, it seems to me that it would be more accurate if these types of calculations should produce a range of possible lengths, rather than a single number, since there are always unknown variables.

I'd still like to see their formulas tested on a scroll of known length, loosely and tightly wound.

[William Schryver]

The lacunae on pJS X aren't that irregular.

Yes, they most certainly are. And the problem for your methodology is that, at the point of the last large lacuna on JSP-XI, the whole bottom part is missing:

And at the point of the first large lacuna of JSP-X, the whole top part is missing:

The homologies are actually fairly obvious when you look closely.

Something is quite obvious when you look closely, I’ll grant you that.

I do think it is telling that you throw out a term (“homology”) that you know most of the readers will not even understand in the context of this discussion. Why? Because you know you can bluff confidence in the face of the fact that most people are simply too intimidated by the subject matter to question you further. This is where the obtuse impenetrability of your paper also serves you well. I’m convinced that, of all the people on your home message board who triumphally proclaim the Cook/Smith paper the “final word” as to the original length of the scroll of Hor, no one is able to understand it. Literally no one. I’m convinced its overwhelming opaqueness reflects a deliberate strategy.

Furthermore, the results agree for the top and bottom edge functions and can be confirmed by visual examination of obvious measurement points. In short, there's no indication that the irregularity of pJS X compromised our analysis.

So you assert. And I admit I, myself, am not able to make a mathematical counter-argument in terms of the flaws in your methodology. I only know it is incorrect because I am so certain that my measurements of the first three winding lengths are at least in the general neighborhood of correct, whereas your measurements leave that neighborhood entirely, and wind up in the ghetto of “just plain wrong.” My measurements are confirmed by Professor Gee, who employs an entirely different methodology (as I understand it, he’s no longer attempting to match up common recurring points in the lacunae).

In any case, I have recruited and continue to attempt to recruit qualified people to examine the issues, and hope to include some of their criticisms of the Cook/Smith winding length acquisition methodology as an appendix to my paper when it is published.

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Cook:

I'll try to make this as plain as I possibly can.

More likely you’ll try to make it as patronizing as you possibly can. That is, after all, your strong suit.

By forcing your thickness into the formula, you have effectively altered the winding lengths.

You don’t know what I have done.

At any rate, I don’t “force” the thickness value into anything. It serves as a valuable “control” and, to the extent it is a rather conservative value (I will argue that the actual original thickness of the papyrus was ~125μm), it can be used in conjunction with the first winding length in a very simple formula to calculate the original length of the scroll. I will provide that value for comparison purposes to the result returned from the employment of the first three winding lengths alone.

I am puzzled that, after several inquiries, you still won't say if 3.3 cm corresponds to the major or minor axis of this (presumably) elliptical scroll.

Neither. It is simply a derived value from the measurement of the first winding, which was ~10.4 cm.

Yup, given that we agree on the outermost winding, this whole argument boils down to Wm. (Of course, I'm talking about a Wm for each section.)

I started with no presuppositions, and very little understanding of the mathematics involved. I simply assembled a team of qualified people to perform the measurements of the various physical properties of the scroll of Hor. Those measurements, when analyzed, indicate a very typical, tightly wound Ptolemaic-era scroll of 500 - 600 cm.

I am convinced that you, on the other hand, commenced with an objective to prove this same scroll was not much longer than the fragments that have survived, and I believe the integrity of your methodology was corrupted by this overriding objective. I also believe this will yet be demonstrated empirically. The evidence is already emerging.

However, I already know that your results cannot be harmonized with the multiple historical accounts of a long roll separate and distinct from the mounted fragments that survive to the present day. Nor can your results be harmonized with the measurements we performed on the scroll of Hor—measurements I am convinced will be shown to have employed simpler and more reliable methodologies than those you have applied to the question.

So continue your patronizing ways to your heart’s desire. As I have often said in relation to my research (and specifically in respect to the concerted efforts to silence it), I am confident that the truth will eventually come out. The winding length measurements can be used to reliably determine the original length of the scroll. They represent empirical values. Eventually a consensus will develop around those values and, in the process, the flaws of your methodology will become apparent.

Edited November 11, 2011 by William Schryver

[William Schryver]

Loose winding = short scroll. Tight winding = long scroll, right?

Also, it seems to me that it would be more accurate if these types of calculations should produce a range of possible lengths, rather than a single number, since there are always unknown variables.

I'd still like to see their formulas tested on a scroll of known length, loosely and tightly wound.

I'll have to talk to John about this, but I've seen nothing in my reading that would indicate that scrolls were wound with widely varying degrees of "tightness." From what I have read, and what he has told me previously, the Egyptians had a single, simple method for winding papyrus, and it produced a fairly uniform, tightly wound roll.

Cook/Smith would have us believe the scroll of Hor represents a departure from that norm. If the original papyrus was only 125 cm long, then, given the normal rolling methodology, it should have been rolled into a scroll whose diameter, when sealed, was less than 1 cm, with a first winding length of about 3 cm. That's not what we see with the scroll of Hor. It, when it was rolled and sealed--much like that other Ptolemaic-era scroll unrolled in Toronto in 2009--had a diameter of ~3.3 cm. The scroll in Toronto unrolled to a length of over 600 cm. We calculate that the scroll of Hor was originally about the same length.

It is the Cook/Smith methodology that produces an anomaly here.

[William Schryver]

Loose winding = short scroll. Tight winding = long scroll, right?

I think I would modify this statement to read:

Short scroll = short scroll. Long scroll = long scroll.

I don't believe the tightness of the winding is the real problem here. I think the problem is that the scroll was either short or long to begin with. The measurement of the outer circumference (a measurement everyone more or less agrees on) indicates a long scroll, if one assumes we are dealing with a typical Ptolemaic-era scroll. The Cook/Smith paper simply argues that the scroll was not typical; that it was more like the rolled diploma held in the hand of my avatar: a short sheet of papyrus rolled up like a poster.

[Bill Hamblin]

I'll have to talk to John about this, but I've seen nothing in my reading that would indicate that scrolls were wound with widely varying degrees of "tightness." From what I have read, and what he has told me previously, the Egyptians had a single, simple method for winding papyrus, and it produced a fairly uniform, tightly wound roll.

Cook/Smith would have us believe the scroll of Hor represents a departure from that norm. If the original papyrus was only 125 cm long, then, given the normal rolling methodology, it should have been rolled into a scroll whose diameter, when sealed, was less than 1 cm, with a first winding length of about 3 cm. That's not what we see with the scroll of Hor. It, when it was rolled and sealed--much like that other Ptolemaic-era scroll unrolled in Toronto in 2009--had a diameter of ~3.3 cm. The scroll in Toronto unrolled to a length of over 600 cm. We calculate that the scroll of Hor was originally about the same length.

It is the Cook/Smith methodology that produces an anomaly here.

In other words, a c. 10 cm first winding (like the JS Papyri) would produce a c. 3 cm diameter (based on Pi). We have known scrolls with this same 3 cm diameter that have a 600 cm length. It seems to me the case is closed. The JS papyri certainly could have been 600 cm. That's empirical and indisputable, right? So why are we bothering with hypothetical mathematical formulae?

Edited November 11, 2011 by Bill Hamblin

[Mortal Man]

If I'm understanding you correctly, using the lacunae on the top and bottom of JSP 1.1, the measurements suggest a first winding length of approximately 10.48cm (or close enough, that you could agree with William on that point). Is that correct?

Almost.

We use the shape of the whole edge (not just certain lacunae or points in the lacunae), top and bottom, to compute winding lengths slightly to the left of the first winding. But all quibbling aside, we're in pretty close agreement on the outermost winding.

However, it is the second winding length that you and Chris differ from William on. He suggests 10.30cm and 10.13cm for the next two windings. Your correlation function using the top edge suggests something similar, but your correlation function on the bottom edge yields something significantly smaller. Is that correct?

Our correlation function for the top edge of pJS 1.2 gives something similar to William's values. However, we know for a fact that secondary damage occurred to this area of the papyrus and that the nature of the damage is such that it increases the apparent winding length. The seams in the papyrus suggest that the third winding should be closer to 9.8 cm (see Figure 26 on page 32). Our correlation analysis of the bottom edge returns an average winding length of 9.74 for pJS 1.2, which closely matches the seams. William is basing his whole analysis on the most problematic area of the papyrus.

If so, would you say that this single difference is one of two root causes in the difference in the total length computations, the other being calculations involving JSP X?

Yes, that is the heart of the issue.

The length formula calls for two winding lengths, which you want to be as far-separated as possible in order to generate the most accurate prediction. William's inputs to the length equation are (as far as I can tell, not having seen his paper):

n = 1.0

m = 3.0

W₁ = 10.50

W₃ = 10.13

which gives

L₁ = 298 cm.

This value is too large because W₃ is too large. Using the more accurate value of W₃=9.8 yields L₁=158 cm. Hugh Nibley's mentor and John Gee's mentor have both estimated an original scroll length of about 155 cm.

(It seems to me that your equation (7) relies heavily on the computation of T, and this computation relies heavily on the winding lengths.

T can be eliminated from the equations, such that nothing really depends on it. Equation (7) depends solely on the length of the section of papyrus being fed into the correlation function and the mean winding length returned by that function.

If we agree on winding lengths, we are likely to agree on what happens afterwards.)

Yes, everything follows from the winding lengths.

[Mortal Man]

Have you used your drawing program to plot out an end view of your Hor scroll calculations in spiral form so as to see what I mean?

It's not that great of a drawing program.

[William Schryver]

In other words, a c. 10 cm first winding (like the JS Papyri) would produce a c. 3 cm diameter (based on Pi). We have known scrolls with this same 3 cm diameter that have a 600 cm length. It seems to me the case is closed. The JS papyri certainly could have been 600 cm. That's empirical and indisputable, right? So why are we bothering with hypothetical mathematical formulae?

I probably shouldn't refer to the diameter that much, since (as Cook as noted above) the wound scroll would almost certainly have been elliptical in shape. In any case, the diameter value is derived from the length of the first winding (the circumference). The scroll in Toronto and the scroll of Hor had an initial winding > 10 cm. The scroll in Toronto unrolled to over 600 cm. We argue, based on the gradual decrease in the first 3 winding lengths of the scroll of Hor, that it was also originally ~600 cm. The thickness measurements we performed are consistent with a 500 - 600 cm scroll.

[William Schryver]

It's not that great of a drawing program.

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.

[Mortal Man]

I'm probably missing something here because I don't understand the math. (My choice was calculus or Hebrew.) But it seems obvious to me that a variable in these formulas would be how tightly wound the papyrus was. A loosely wound scroll with a 3cm diameter would have less papyrus than a tightly wound scroll with a 3cm diameter.

Our results make it pretty clear that the missing interior section must have been wound at least as tightly as the middle (pJS 1.3) and outer (pJS 1.2 & 1.1) sections. That is the only way to get enough papyrus for the rest of the BoB plus Fascimile 3. So we are already giving Schryver/Slack/Gee the maximum benefit of the doubt regarding the tightness/looseness of the inner windings; i.e., any assumption that the missing section was wound differently leads to a shorter scroll than what we are predicting.

If the measurements were taken only from the outermost three windings of the scroll--which seems to be the case here with Chris and Andrew's experiment--

We examined all of the extant papyrus, including the middle section of the scroll (pJS 1.3) as well as the outer windings (pJS 1.2 & 1.1). We measured 8 windings in total, 4 along the top and 4 along the bottom. Each pair of windings gave us an estimate of the scroll length, or if you prefer, the effective thickness parameter. Three of these four estimates were in close agreement. The fourth was an outlier, which we threw out because of the known secondary damage to the upper side of pJS 1.2. We averaged the three consistent estimated to get our final result.

Then see if the formulas accurately predict the length of the papyri.

The formulas are not in dispute, only the length of William's third winding.

Edited November 11, 2011 by Mortal Man

[William Schryver]

The formulas are not in dispute, only the length of William's third winding.

More accurately stated, what is in dispute are the respective methodologies for producing winding length measurements. It so happens that the discrepancy between the methodologies manifests itself at the third winding. Your methodology produces a length for the winding that departs radically from the gradual decrease seen between the first and second windings--reporting a winding length that is significantly shorter than what Gee and I report using our respective methodologies, and resulting in a significant difference in the total length of the scroll. I don't believe your measurement will hold up under closer scrutiny. Time will tell ...

[Calm]

The formulas are not in dispute, only the length of William's third winding.

Are you claiming that all agree the formulas are valid in their usage to estimate length? And that no one is disputing the other set of measurements?

If so, would this not mean if you plug the same numbers into both formulas, the result would be identical? If not identical, then there has to surely at least be a dispute over which will yield the best estimate given a set of circumstances.

Edited November 11, 2011 by calmoriah

[Mortal Man]

Yes, they most certainly are. And the problem for your methodology is that, at the point of the last large lacuna on JSP-XI, the whole bottom part is missing:

And at the point of the first large lacuna of JSP-X, the whole top part is missing:

Something is quite obvious when you look closely, I’ll grant you that.

I invite everyone to examine Figures 2, 3 and 4 in our paper to see if Chris's tracings are reasonable. We have made our digitized tracings freely available for anyone to compare to the originals.

I do think it is telling that you throw out a term (“homology”) that you know most of the readers will not even understand in the context of this discussion. Why?

Yeah Chris, stop using words that aren't in William's vocabulary.

My measurements are confirmed by Professor Gee

Let me see, is this the same Professor Gee who claims that "the initial winding length is 9.7 cm, the last winding is 9.5 cm"? Wouldn't that make the third winding somewhere between 9.5 and 9.7 cm?

In any case, I have recruited and continue to attempt to recruit qualified people to examine the issues

You haven't recruited Chris or myself. Don't you like us?

Neither. It is simply a derived value from the measurement of the first winding, which was ~10.4 cm.

I see, now that you've admitted this, the legerdemain involving the Toronto scroll is becoming clear. You have trumpeted over and over and over that the circumference of the Toronto scroll is 3.3 cm and now we find out that this is not a direct measurement but only inferred based on Gee's estimate of 10.4 cm for the outer winding. Given Gee's abysmal record on winding lengths, why should any of us believe this one?

I started with no presuppositions, and very little understanding of the mathematics involved. I simply assembled a team of qualified people to perform the measurements of the various physical properties of the scroll of Hor. Those measurements, when analyzed, indicate a very typical, tightly wound Ptolemaic-era scroll of 500 - 600 cm.

Except that your measurements indicate a ~300 cm scroll.

I am convinced that you, on the other hand, commenced with an objective to prove this same scroll was not much longer than the fragments that have survived, and I believe the integrity of your methodology was corrupted by this overriding objective.

It's called "projection" Will, imputing your own motives to others.

The winding length measurements can be used to reliably determine the original length of the scroll. They represent empirical values.

It appears to me that you only took thickness measurements of the originals (papyrus+paper+glue+two layers of mylar on each side) and not winding measurements, is that correct? Are you basing all of your winding measurements on your photographs? If so, you have a problem. I think your photographs may be the same ones we have and they are not exactly to scale.

[wenglund]

Loose winding = short scroll. Tight winding = long scroll, right?

Yes--assuming the same average thickness of the papyri, because the looseness or tightness of the spiral changes the number of windings within a fixed circumference, and thus a disparity in scroll lengths that may fit within that same fixed circumference..

The same is true of thick verses thin scrolls--think of the difference in length between 1 and 2 ply rolls of toilet paper.

In short, whether due to thickness of the item being rolled and/or the tightness/looseness of the roll, the distance between each ring of the spiral will affect the calculated length of the spiral (see my comparison above between Andrew and Will, and the difference in variables T and R.

Thanks, -Wade Englund-

Edited November 11, 2011 by wenglund

[Chris Smith]

Will,

While there is substantial damage in the areas of the papyrus you highlighted, the edge is all that matters. Fortunately, the edge is still evident there.

As for the opaqueness of our paper, I would have greatly preferred it were simpler. I tried repeatedly to make it so. But the strength of the methodology was its ability to account for many different variables, and we finally erred on the side of exhaustiveness rather than readability. So yes, you're correct that the complexity of the method was a deliberate strategy-- a strategy to get accurate results.

Edited November 11, 2011 by Chris Smith

[Chris Smith]

Bill,

As Andrew noted earlier in this thread, Hartmut Stegemann says that short scrolls tend to be loosely wound, whereas long ones are more tightly wound. So the apparent discrepancy between the winding-tightness of the Hor scroll and Gee's Toronto scroll is consistent with what we'd expect from scrolls of different lengths.

Peace,

-Chris

Edited November 11, 2011 by Chris Smith

[Bill Hamblin]

Will,

While there is substantial damage in the areas of the papyrus you highlighted, the edge is all that matters. Fortunately, the edge is still evident there.

As for the opaqueness of our paper, I would have greatly preferred it were simpler. I tried repeatedly to make it so. But the strength of the methodology was its ability to account for many different variables, and we finally erred on the side of exhaustiveness rather than readability. So yes, you're correct that the complexity of the method was a deliberate strategy-- a strategy to get accurate results.

So have you tested your method on several papyri of known and different lengths, all rolled in scrolls with 3 cm diameter. Seems like this is a very simple way to actually test the formula.

[Mortal Man]

I've seen nothing in my reading that would indicate that scrolls were wound with widely varying degrees of "tightness." From what I have read, and what he has told me previously, the Egyptians had a single, simple method for winding papyrus, and it produced a fairly uniform, tightly wound roll.

That is consistent with our findings.

Cook/Smith would have us believe the scroll of Hor represents a departure from that norm.

No, not at all.

[Mortal Man]

The Cook/Smith paper simply argues that the scroll was not typical; that it was more like the rolled diploma held in the hand of my avatar: a short sheet of papyrus rolled up like a poster.

Will, you're just embarrassing yourself with these gross misrepresentations of our paper.

[Mortal Man]

Show people an end view of what your calculations suggest the scroll looked like.

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

[Cobalt-70]

So have you tested your method on several papyri of known and different lengths, all rolled in scrolls with 3 cm diameter. Seems like this is a very simple way to actually test the formula.

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?

Edited November 11, 2011 by Cobalt-70

[Mortal Man]

Are you claiming that all agree the formulas are valid in their usage to estimate length?

Yes, all of the various formulas people are using can be reduced to this formula.

And that no one is disputing the other set of measurements?

What other set of measurements?

If so, would this not mean if you plug the same numbers into both formulas, the result would be identical?

Either identical or very close, depending on whether you assume a nonzero value for the innermost winding and other minor details.

If not identical, then there has to surely at least be a dispute over which will yield the best estimate given a set of circumstances.

For the purpose of this discussion, everyone should just stick to the formula linked above.

[Mortal Man]

Yes--assuming the same average thickness of the papyri, because the looseness or tightness of the spiral changes the number of windings within a fixed circumference, and thus a disparity in scroll lengths that may fit within that same fixed circumference..

The same is true of thick verses thin scrolls--think of the difference in length between 1 and 2 ply rolls of toilet paper.

In short, whether due to thickness of the item being rolled and/or the tightness/looseness of the roll, the distance between each ring of the spiral will affect the calculated length of the spiral (see my comparison above between Andrew and Will, and the difference in variables T and R.

All of the relevant physical characteristics of the scroll are captured in the winding lengths. IOW, the windings contain information about the thickness, tightness, looseness, embedded salve, wrinkles etc. An accurate measure of the winding lengths automatically accounts for all of these details. That's why the winding lengths are so much more important than anything else.

[William Schryver]

Mortal Man:

Yeah Chris, stop using words that aren't in William's vocabulary.

Well, as everyone well knows, it’s hard for him to not use words that are outside the limited realm of my vocabulary.

Let me see, is this the same Professor Gee who claims that "the initial winding length is 9.7 cm, the last winding is 9.5 cm"? Wouldn't that make the third winding somewhere between 9.5 and 9.7 cm?

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.

… the legerdemain involving the Toronto scroll is becoming clear.

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

You have trumpeted over and over and over that the circumference of the Toronto scroll is 3.3 cm and now we find out that this is not a direct measurement but only inferred based on Gee's estimate of 10.4 cm for the outer winding. Given Gee's abysmal record on winding lengths, why should any of us believe this one?

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.

Except that your measurements indicate a ~300 cm scroll.

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?

It appears to me that you only took thickness measurements of the originals (papyrus+paper+glue+two layers of mylar on each side) and not winding measurements, is that correct?

I think it is rather understandable that the methodology for determining the papyrus thickness was not the same as the one used to determine the winding lengths.

Are you basing all of your winding measurements on your photographs? If so, you have a problem. I think your photographs may be the same ones we have and they are not exactly to scale.

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. I used them to measure the winding lengths. They are exactly to scale.

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Chris Smith:

While there is substantial damage in the areas of the papyrus you highlighted, the edge is all that matters. Fortunately, the edge is still evident there.

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