Some Puzzles from the John Gee Paper

[Chris Smith]

I do find it intriguing how you seem to privilege certain historical sources while simultaneously rejecting those that tend to disagree with your favorites. I guess that's all part and parcel of crafting history, though, isn't it?

I rarely reject sources wholesale. Entirely discounting certain witnesses on the basis of their distance from the events they describe or of their biases in reporting those events (as some apologists have been wont to do) usually isn't good historical methodology. Most witnesses mix accurate memory with distorted memory, understatement with exaggeration, truth with fiction. The historian, then, attempts to understand the complexities of witnesses' memories and motives not for the purpose of sorting the witnesses themselves into binary "reliable" and "unreliable" categories, but rather for the purpose of assessing the meaning and significance of specific memories and specific statements that the various witnesses make. There are individual statements made by the witnesses that I discount or interpret differently than John Gee does. For example, when Charlotte says that the walking serpent's head was in Eve's ear, I think she simply fudged this detail in her memory. And when she says she was shown vignettes "from another roll", I think that she was merely told that these vignettes were from another roll, not that she actually viewed that roll while it was still intact. Believe it or not, I have pretty good reasons for making these kinds of interpretive decisions. Whereas the identification of the framed fragments as the writings of Abraham is independently corroborated by three independent witnesses, the existence of a second intact roll in the Nauvoo period is contradicted at least implicitly by both Appleby and Seyffarth. Oliver Cowdery's 1835 letter also indicates that the judgment vignette of Book of the Dead 125 was at "the inner end of the same roll, (Joseph's record)". Since Book of the Dead 125 is the last chapter in the extant Ta-shere-min Book of the Dead fragments, Cowdery's statement implies that there can't have been a lengthy intact interior portion following those fragments. But of course even if I am dismissing or re-interpreting a few details of Charlotte's statement, that does not mean that I reject her report outright. Actually, I think her report is extremely valuable and provides some very important historical information about the mummies and papyri in the Nauvoo period.

I guess what I'm trying to say, Will, is that I'm not just privileging the sources I agree with and rejecting the ones I don't. Rather, the way that I'm using the sources here is carefully considered and follows the standard rules and methods of the historical discipline. Privileging sources on the basis of ideological preconceptions, however, does appear to me to be the modus operandi required to arrive at the missing papyrus theory.

I think this is hyperbole, and that your sense of certainty far exceeds your capacity to substantiate your conclusions.

I'm sure I am sometimes guilty of bombastic certitude. I think, though, that my certitude on this subject has substantial evidentiary warrant, and I don't expect I will ever have to revise any of the major outlines of my conclusions about the source of the Book of Abraham.

Best,

-Chris

[Mortal Man]

I appreciate Prof. Gee taking the time to respond to my email; I imagine he gets inundated with these kinds of inquiries.

I will respond to the math issue now, and the rest of his concerns as I find the time.

(2) I understand your attempt at calculation and it is a good first step, but you are

operating only with geometry when the continually changing radius demands the use of

calculus.

The calculus is trivial so we might as well do it.

Assume a papyrus of uniform thickness T is wound into a perfect spiral.

Let dL = Rn*dTHETA be a differential arc length along the spiral, where dTHETA is the angle subtended by dL.

The radius of a differential segment on the n^th winding (counting out from the core) is Rn = n*T, where n = THETA/(2*pi).

Letting N denote the number of windings out to the innermost extant winding, the length of the spiral interior, Lm, is given by the path integral (using "I" for the integral sign, with sub and super-scripts to express the limits of integration)

Lm = I₀^2*pi*N Rn*dTHETA = I₀^2*pi*N T*THETA*dTHETA/(2*pi) = T*THETA²/(4*pi)|₀^2*pi*N = pi*T*N²

Converting to Gee's notation,

T = S/(2*pi)

N = E/(2*pi*T) = E/S

Lm = Z + E

Hence,

Z = E²/(2*S) - E

Comparing this to Hoffmann's equation,

Z ≈ (E²-6.25)/(2*S) - E

we see that the perfect-spiral approximation differs only by an empirical correction factor (6.25). I assume that Hoffmann's correction factor accounts for the looseness of the innermost windings and is based on observations and measurements of actual scrolls. I agree with Prof. Gee in that Hoffmann's formula is probably more accurate and I have no problem using it. Employing Hoffmann's formula, my estimate for the maximum length of the original papyrus from point D to the left end is:

E_D = 9.49 cm

S_D = 0.251 cm

Z_D = 157 cm

The length of the extant portion to the left of point D is ~45 cm. Hence, my estimate for the maximum length of the missing section becomes 112 cm (compared to 124 cm from my OP estimate). Hoffmann's formula, with its empirical correction, predicts a missing section 9.7% shorter than the perfect-spiral idealization.

Note that the formulas in my OP, which were obtained "operating only with geometry" are identical to the formulas obtained through "the use of calculus." A simple way to see this, without doing the math, is to imagine cutting a spiral scroll through its radius, and then reconnecting each of the windings to the winding just inside it. The result is a set of concentric cylinders with the same total length and area as the original spiral.

[dblagent007]

So MM, the bottom line, after much math, is that you and Gee measured the length of the windings in the pictures differently. Isn't that right? Gee pegged the length of the initial winding at 9.7 cm and the length of the seventh winding at 9.5 cm, while you pegged the length of the initial winding at about 10 cm and the length of the third winding at about 9.5 cm. You didn't provide a length for the seventh winding, but if you did it would have been much smaller than Gee's 9.5 cm.

So, how come you and Gee are so far apart on the winding measurements?

[Mortal Man]

Does Gee or Hoffman provide a way to calculate the average thickness of the paper from the different winding lengths? Using MM's method, the papyrus would have been as thick as 8lb paper today. I would be interested to know if there is a better way to calculate the thickness.

dblag,

The effective average thickness of the papyrus is

T = S/(2*pi) = (Wm-Wn)/[2*pi*(m-n)]

where Wm and Wn are the lengths of the m^th and n^th windings, respectively (m>n). Gee, Hoffmann, Chris and I all agree on this.

Note that since the thickness is two orders of magnitude smaller than the windings, two digits of accuracy are lost in the subtraction in the numerator. A digit of accuracy can be recovered if n and m are sufficiently far apart and another digit can be recovered by averaging a large number of measurements or through a linear regression as Chris has done.

MM

[William Schryver]

dblag,

The effective average thickness of the papyrus is

T = S/(2*pi) = (Wm-Wn)/[2*pi*(m-n)]

where Wm and Wn are the lengths of the m^th and n^th windings, respectively (m>n). Gee, Hoffmann, Chris and I all agree on this.

Note that since the thickness is two orders of magnitude smaller than the windings, two digits of accuracy are lost in the subtraction in the numerator. A digit of accuracy can be recovered if n and m are sufficiently far apart and another digit can be recovered by averaging a large number of measurements or through a linear regression as Chris has done.

MM

So how and why -- assuming you're correct -- is Gee so far off? He asserts a length 10x your result. Have you replied back to him and included your calculations in order to obtain his reaction?

Again, I won't even permit myself to try to understand the math; it looks painful to me. But I am interested in coming to understand why we're seeing such a radical difference in results when supposedly you're both using the same Hoffmann formula. Are you saying that Gee has made a mistake that has pushed the decimal one position to the right?

[Mortal Man]

So MM, the bottom line, after much math, is that you and Gee measured the length of the windings in the pictures differently. Isn't that right? Gee pegged the length of the initial winding at 9.7 cm and the length of the seventh winding at 9.5 cm, while you pegged the length of the initial winding at about 10 cm and the length of the third winding at about 9.5 cm. You didn't provide a length for the seventh winding, but if you did it would have been much smaller than Gee's 9.5 cm.

Correct

So, how come you and Gee are so far apart on the winding measurements?

It depends on exactly where, in each of the lacunae, you locate the end points of the windings. I chose to begin my study with JSP I & XI because the lacunae in that section look very similar, which makes it easy to locate the points. If you look closely at the first image I posted, you'll notice a little ledge near the groin area of Osiris (end-point B ). This ledge is clearly repeated in the lacunae at A, C & D. In order to reduce my end-point location error, I took six measurements for each winding at points above, on and below the ledge. Then I threw out the min and max and averaged the remaining four measurements.

Chris included JSP X in his analysis, which gives him greater accuracy potential for three reasons: (1) His first and last windings are more widely separated (as are Gee's), which reduces the statistical error in the winding measurements; i.e., you gain an order of accuracy when you average the results over many windings. (2) More windings enables you to improve the accuracy of each measurement by ensuring consistency between successive windings; i.e., proceeding from the outside in, each winding must be shorter than the previous one and the change in length should be nearly constant (or slightly increase) from one winding to the next. (3) As Chris has mentioned, a linear regression accounts for the looser inner windings (increase in apparent thickness) as you approach the core. My length estimate is probably a bit too long because it assumes the inner windings are as tightly wound as the outer ones.

In the end, you should arrive at a thickness in the allowable range for papyri produced during the Ptolemaic era. I seem to recall reading somewhere that such papyri are between 0.2 and 0.8 mm thick. My estimate of 0.4 mm falls within this range.

[dblagent007]

So how and why -- assuming you're correct -- is Gee so far off? He asserts a length 10x your result. Have you replied back to him and included your calculations in order to obtain his reaction?

Again, I won't even permit myself to try to understand the math; it looks painful to me. But I am interested in coming to understand why we're seeing such a radical difference in results when supposedly you're both using the same Hoffmann formula. Are you saying that Gee has made a mistake that has pushed the decimal one position to the right?

The reason the results are different is because the input is vastly different. Gee says the first winding length is 9.7 cm and the seventh winding length is 9.5 cm. MM says that the first winding length is about 10 cm and the third winding length is about 9.5 cm.

I assume that both MM, Chris, and Gee obtained their raw data measurements from the photos, but I could be wrong. Either way, the question that must be answered is why Gee's raw data measurements are so different from the others.

If the thickness calculations are correct, I can't help but think there is something wrong with Gee's raw data. I can't imagine the Egyptians creating papyrus that is equivalent in thickness to 8lb paper today (common copy paper is 20 lb).

[dblagent007]

It depends on exactly where, in each of the lacunae, you locate the end points of the windings. I chose to begin my study with JSP I & XI because the lacunae in that section look very similar, which makes it easy to locate the points. If you look closely at the first image I posted, you'll notice a little ledge near the groin area of Osiris (end-point B ). This ledge is clearly repeated in the lacunae at A, C & D. In order to reduce my end-point location error, I took six measurements for each winding at points above, on and below the ledge. Then I threw out the min and max and averaged the remaining four measurements. Since the equations are linear, this process is formally equivalent to Chris' linear regression. Chris, however, extended his analysis to JSP X, which gives him greater accuracy potential for two reasons: (1) His first and last windings are more widely separated (as are Gee's), which reduces the statistical error in the winding measurements; i.e., you gain an order of accuracy when you average the results over many windings. (2) More windings enables you to improve the accuracy of each measurement by ensuring consistency between successive windings; i.e., proceeding from the outside in, each winding must be shorter than the previous one and the change in length should be nearly constant from one winding to the next.

In the end, you should arrive at a thickness in the allowable range for papyri produced during the Ptolemaic era. I seem to recall reading somewhere that such papyri are between 0.2 and 0.8 mm thick. My estimate of 0.4 mm falls in the middle of this range.

Thanks for the explanation. We know how MM and Chris determined the winding lengths. Now, does anyone know how Gee determined the winding lengths?

[William Schryver]

The reason the results are different is because the input is vastly different. Gee says the first winding length is 9.7 cm and the seventh winding length is 9.5 cm. MM says that the first winding length is about 10 cm and the third winding length is about 9.5 cm.

I assume that both MM, Chris, and Gee obtained their raw data measurements from the photos, but I could be wrong. Either way, the question that must be answered is why Gee's raw data measurements so different from the others.

If the thickness calculations are correct, I can't help but think there is something wrong with Gee's raw data. I can't imagine the Egyptians creating papyrus that is equivalent in thickness to 8lb paper today (common copy paper is 20 lb).

So, if I understand correctly, it simply comes down to the fact that Gee is arguing for a much more tightly-wound roll, thereby containing many more windings. And that can account for over a 1000cm difference?

[dblagent007]

So, if I understand correctly, it simply comes down to the fact that Gee is arguing for a much more tightly-wound roll, thereby containing many more windings. And that can account for over a 1000cm difference?

That's close but Gee is arguing that the Hor scroll used much thinner paper (not much more tightly-wound), thereby containing many more windings. Using Gee's data the papyrus is about 0.05 mm thick. MM's data shows it is about 0.4 mm thick. That is an enormous difference in thickness that would allow for a lot more windings.

Think of it this way. Gee is saying the papyrus is effectively as thick as the paper used to print your bible. MM and Chris are saying the papyrus is as thick as heavy card stock. The difference is that you could wind a lot more bible paper around a spool before reaching the edges than you could heavy card stock.

Edited to add: the thickness of the papyrus directly influences the length of each winding. Gee says that the length of the windings changes very little (9.7 cm for the initial winding and 9.5 cm for the seventh winding - so after seven windings the length of has only changed 0.2 cm!), which means the paper is very thin. MM says the length of the windings changes much more (10 cm for the initial winding and 9.5 cm for the third winding - so after only three windings the length has already change 0.5 cm), which means the paper is much thicker.

[Mortal Man]

So how and why -- assuming you're correct -- is Gee so far off?

I believe his value of 9.5 cm for the 7^th winding is too large. I suspect that if he were to measure the 2^nd through 6^th windings, the intermediate lengths would not all be consistent; e.g., he might find his 5^th winding to be longer than his 4^th winding (which is physically impossible). His computed thickness is 0.053 mm. I don't think the Egyptians had the technology to produce papyri that thin, and even if they did, they wouldn't have been able to write on it without tearing it to shreds. Also, keep in mind that we are estimating the apparent thickness, not necessarily the actual thickness. The apparent (or effective) thickness may be greater than the physical thickness due to wrinkling, inhomogeneities and the tightness of the wrapping. There are good reasons to believe that the apparent thickness increases toward the interior.

Have you replied back to him and included your calculations in order to obtain his reaction?

Not yet, because I simply have not had the time. I will, however, try to send him a reply tonight.

Are you saying that Gee has made a mistake that has pushed the decimal one position to the right?

No, I checked his math and it is correct. Once again, I believe the primary source of error is in his 7^th winding measurement.

[William Schryver]

While taking time off from preparing his upcoming presentation at the British Museum*, Professor Gee contacted me and elaborated on why he feels both Mortal Man and Chris Smith are coming up with results that are less than 10% of the value Gee himself has calculated. He has reviewed the pertinent posts on this thread. Without going into detail that I don't really understand anyway, suffice it to say that John asserts that your measurements are incorrect. He further asserts that it is essential for the measurements to be correct to the 1/10th of a millimeter.

Needless to say, he stands by his published figure for the length of the Horos scroll.

* - Professor Gee, knowing of his reputation for buffoonery among critics on this message board and others, wants to assure everyone that he will merely be providing the comic relief in between the presenters of greater stature and professional reputation. He has purchased a new cap and some special shoes for the occasion:

[dblagent007]

Without going into detail that I don't really understand anyway, suffice it to say that John asserts that your measurements are incorrect. He further asserts that it is essential for the measurements to be correct to the 1/10th of a millimeter.

I would be very interested in the details of Gee's measurements. It would shed a lot of light on this subject.

[William Schryver]

I would be very interested in the details of Gee's measurements. It would shed a lot of light on this subject.

Here's what John says:

The average difference between the windings is in the denominator, so as the denominator approaches zero, the total gets larger. When the denominator is between one and zero, the effect is multiplying the numerator by increasingly larger numbers. Putting 0.1 in the denominator is the same as multiplying by 10. Putting 0.01 in the denominator is the same as multiplying by 100. The difference between the first winding and the last winding is very small (2 millimeters) thus the average difference is also quite small. By increasing the initial measurement, they more than quadruple the average difference, as a result, they end up cutting the size of the roll [to] an eighth of my estimate.

The difference in our measurements is less than half a centimeter (hardly what can be termed a serious error) but that is why the estimates vary so much.

Again, this calculus stuff makes my head hurt, and besides, I don't really care that much about this particular issue. I think the critics' arguments are vulnerable on many different fronts besides this; the length of the Horos scroll is, for the most part, immaterial to my apologetic defense of the Book of Abraham. I have always argued that I believe the scrolls contained Abraham material, but that neither Joseph Smith nor his associates would necessarily have known where it was. I think the arguments advanced by critics, that attempt to tie the Abraham material to the Sensen text, are unfounded in the extreme, and can and will be shown deficient.

Incidentally, I read this interesting quote from Zahi Hawass today:

" (...) Professional Egyptologists consult scientific publications, or at least confer with their colleagues, before jumping to conclusions on any matter related to the discipline of Egyptology. Amateur Egyptologists, on the other hand, often speak and write without thinking. (...)"

http://weekly.ahram.org.eg/2009/941/he3.htm

[Mortal Man]

John asserts that your measurements are incorrect.

Which measurements? All of my measurements? All of Chris' measurements?

He further asserts that it is essential for the measurements to be correct to the 1/10th of a millimeter.

That is why I reported my winding measurements to 1/10th of a millimeter. John, however, only reported his measurements to 1 millimeter. I discussed the order of accuracy and the loss/recovery of significant digits in my earlier post.

Needless to say, he stands by his published figure for the length of the Horos scroll.

Can he provide examples of 0.05 mm papyri from the Ptolemaic period?

[dblagent007]

Here's what John says:

Thanks, Will. Unfortunately, we already know that MM's measurements are vastly different than Gees and that this is what is causing the discrepancy (this is basically all Gee is saying with the explanation of the numerator/denominator stuff).

What I would like to know is how did John obtain the 9.7 cm and 9.5 cm measurements of the Hor scroll? What points on the scroll did he measure between? Did he obtain the measurement from pictures of the scroll or from physical inspection at the church archives? If the measurements came from pictures, how did he determine the length of the first and seventh windings?

I agree that this is not the most critical issue, but it would be good to put to bed.

[William Schryver]

What I would like to know is how did John obtain the 9.7 cm and 9.5 cm measurements of the Hor scroll? What points on the scroll did he measure between? Did he obtain the measurement from pictures of the scroll or from physical inspection at the church archives? If the measurements came from pictures, how did he determine the length of the first and seventh windings?

First of all, the answer is that I don't know how John arrived at his figures.

I do know that John has relatively unhindered access to the original papyri, and that he has examined them on numerous occasions in the past few years. That being the case, and until I have reason to conclude otherwise, I think it is reasonable to assume that his measurements are the most accurate of anyone currently opining on the topic.

[Mortal Man]

I do know that John has relatively unhindered access to the original papyri, and that he has examined them on numerous occasions in the past few years. That being the case, and until I have reason to conclude otherwise, I think it is reasonable to assume that his measurements are the most accurate of anyone currently opining on the topic.

Has he measured the thickness? Is it 0.05 mm?

John reports the 1st and 7th windings as 9.7 cm and 9.5 cm, respectively. Given only two significant digits, there is only one number between 9.7 and 9.5; i.e., 9.6. Since John has unhindered access to the original papyri and examines them on numerous occasions, could you ask him what his measurements are for the 2nd, 3rd, 4th, 5th and 6th windings? Given that they must all fall between 9.5 and 9.7 cm, how will he assign a unique two-digit length to each winding?

Has anyone else measured the windings on the originals? Who else has access?

[William Schryver]

MM:

Has he measured the thickness? Is it 0.05 mm?

Dunno.

Since John has unhindered access to the original papyri and examines them on numerous occasions, could you ask him what his measurements are for the 2nd, 3rd, 4th, 5th and 6th windings?

I donâ??t think so. Not because Iâ??m not interested, but because I only feel like Iâ??m entitled to so many questions per year when it comes to Professor Gee, and Iâ??ve already spent several of them on this subject that holds only tangential interest for me.

Given that they must all fall between 9.5 and 9.7 cm, how will he assign a unique two-digit length to each winding?

Could it be that he simply rounded off the amounts for the published version of his findings, but that his private notes have more exact measurements? I think that is probably likely. But since he has already established a precedent for responding to your queries, perhaps you could pose this question to him yourself. Iâ??ve found John to be a very personable and helpful guy â?? for an academic. Iâ??ll bet, if you give him a chance, heâ??ll prove equally helpful to you in your investigations into these things.

Has anyone else measured the windings on the originals?

Dunno.

Do you speculate that John is either inept or dishonest when it comes to his published measurements? I donâ??t believe that would be a justifiable conclusion.

Who else has access?

Dunno. Not I.

[Mortal Man]

perhaps you could pose this question to him yourself.

I'm still waiting for his response to my latest email. Though I doubt that it will be substantially different than what he told you.

Do you speculate that John is either inept or dishonest when it comes to his published measurements?

No.

Do you speculate that it is unreasonable to ask for a second opinion?

[William Schryver]

Do you speculate that it is unreasonable to ask for a second opinion?

Not at all. Indeed, of all the questions that have been debated in reference to the JSP and the KEP, it would seem that this one is the most amenable to an objective and definitive answer. I'm all for getting the papyri measured to within a micrometer of accuracy, and then plugging the results into the formula. Personal opinion should not be a factor when it comes to this particular issue.

[Mortal Man]

Not at all. Indeed, of all the questions that have been debated in reference to the JSP and the KEP, it would seem that this one is the most amenable to an objective and definitive answer. I'm all for getting the papyri measured to within a micrometer of accuracy, and then plugging the results into the formula. Personal opinion should not be a factor when it comes to this particular issue.

YES! THANK YOU! HALLELUJAH! Will, you are my new best friend!

This is not something we should have to argue about. Those with access have it within their power to conclusively determine the maximum length of the papyrus, probably to within 1 centimeter.

[William Schryver]

MM:

Will, you are [my] new best friend!

Hey, buddy ... settle down there, would ya? I mean, I know nothing about you. Maybe we should do dinner and a movie first before we advance to the next stage of our relationship. Ya think?

And, be forewarned, I am the Apollyon of Apologetics! If you have any faith remaining, I will destroy it. (See my sig line for any needed explanation.)

[Mortal Man]

MM:

Hey, buddy ... settle down there, would ya? I mean, I know nothing about you. Maybe we should do dinner and a movie first before we advance to the next stage of our relationship. Ya think?

But that's just not the Mormon way.

And, be forewarned, I am the Apollyon of Apologetics! If you have any faith remaining, I will destroy it. (See my sig line for any needed explanation.)

I keep my friends close and my enemies closer.

[William Schryver]

MM:

I keep my friends close and my enemies closer.

Or, as someone else once put it:

You gotta be crazy, you gotta have a real need.

You gotta sleep on your toes, and when you're on the street,

You gotta be able to pick out the easy meat with your eyes closed.

And then moving in silently, down wind and out of sight,

You gotta strike when the moment is right without thinking.

And after a while, you can work on points for style.

Like the club tie, and the firm handshake,

A certain look in the eye and an easy smile.

You have to be trusted by the people that you lie to,

So that when they turn their backs on you,

You'll get the chance to put the knife in.

Still, I have no worries. I've been impregnable ever since I stopped cutting my hair. Now, my wife kind of likes it (she is a child of the 70s, after all) but my daughters don't quite know what to think about Dad playing the organ in Sacrament Meeting with long flowing curls streaming down the back of his suit jacket.