The Missing Papyrus Equation

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_CaliforniaKid
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The Missing Papyrus Equation

Post by _CaliforniaKid »

Some time ago there was a lot of noise about an equation that supposedly proved that the Hor Book of Breathings was originally some 41 feet in length. Even John Gee, who gave the FAIR presentation that highlighted this equation, was surprised by this result, but after checking and rechecking his figures as well as the assumptions on which the equation is based, he claims to be sold. Last night I was up altogether too late listening to Gee's talk and trying to figure out what in the world he's talking about.

I should begin by highlighting the historical evidence with respect to the missing portion of the roll. After our present fragments of the Hor Book of Breathings (from the front end of the Book) were preserved under glass, the end of the Book remained intact as a roll. We have two eyewitness accounts of this remainder that might help us gauge what was left. In the first place, A Nauvoo visitor named Charlotte Haven described it as a "long roll of manuscript" in her journal. Secondly, Gustavus Seyffarth called it "an invocation to the Deity Osirus, in which occurs the name of the person, (Horus,) and a picture of the attendant spirits, introducing the dead to the Judge, Osirus." This appears to describe the end of the Hor[us] Book of Breathings, followed by Facsimile 3, the closing vignette. Michael D. Rhodes estimates in his critical text that we can expect that there are about 60 cm (or roughly two feet) of writing missing from the end of the Book of Breathings. In looking at Rhodes' transcription of Louvre 3284, a copy of the BoB very similar to the Hor text, I think he may be underestimating by ten centimeters or so. But his figure is believable. Certainly a lower limit for the missing text would be one and a half feet, and an upper limit might be two and a half or three feet. Seyffarth's testimony suggests that there was no other text after the Book of Breathings on the remainder of the roll, so this was probably its total length (unless there was unused space at the end). Would a two-foot text explain Charlotte Haven's testimony that Mother Lucy unrolled a "long roll of manuscript"? It might. We would probably expect something at least three feet in length, but someone like Charlotte who is not familiar with papyrus just might describe a two-foot roll as "long," especially since it may have been wrapped almost twenty-five times. (By the number of "wraps", I mean the number of full rotations required to unroll the text.)

In any case, there's certainly no eyewitness testimony that nails down the existence of a missing text at the end of the Hor scroll. So Gee presents us instead with his mathematical equation. In his words, "the circumference of a scroll limits the amount of scroll that can be contained inside it. Thus we can determine by the size of the circumference and the tightness of the winding how much papyrus can be missing at the interior end of a papyrus roll." Notice that Gee is here careful to say that our result will be an upper limit: it tells us how much papyrus "can be" missing from the interior of the Hor roll. He does not continue to use such reserved language, however. The remainder of his presentation treats his result as the actual amount of missing papyrus.

Gee does not give an explicit reference for his equation, but does mention a couple details. He states, for example, that the study was more than a decade old, that it was written by somebody with a Germanish name that sounds like "Fredam Holfman", and that it was created in order to gauge the original length of "Papyrus Spiegelberg". I haven't tried very hard yet to track this reference down, but since I know little about Egyptology and I don't speak German, it may prove difficult do so. Gee unfortunately also does not give the derivation of his equation. Here's the equation he proffers:

E - length of the last/interior extant winding
S - average diff. b/w successive winding lengths
Z - length of the missing portion

Z = (e^2 - 6.25)/(2s) - e

The idea here seems to be that as you get closer to the interior of a roll, your wraps get continually shorter. If we know the length of the missing portion's outer wrap (E) and the difference in length between each successive wrap (S), we can calculate the number of missing wraps and the approximate length of each of them. (S should be a constant as long as the change in radius for each wrap also remains constant-- i.e., as long as the tightness of the wrapping remains the same throughout the roll. There is some reason to doubt that the tightness of the Hor roll's wrappings were uniform over its entire length, but it was probably close enough for our purposes.) I confess I don't know exactly how Holfman/Gee arrived at the above equation. In working this problem out myself, I came up with the following formula that should give the length of the missing portion: Z = [e^2-e*s]/2s. This is the number of missing wraps, e/s, multiplied by the average circumference of the missing wraps, [e-s]/2. But the results Gee's formula produces are very similar to the results produced by mine. The fault in his analysis does not appear to lie with the formula itself.

Gee gives 9.5 as the value of E, and places S somewhere between .033 and .05. He says that inputting these figures gives us between 835 cm and 1250 cm for the length of the missing portion. It would be fair, I think, to ask how he arrived at his values of S and E. Presumably, it was by measuring the distance between matching lacunae, as shown in the image below.

Image

In order to check Gee's figures, I whipped out my copy of By His Own Hand Upon Papyrus and a handy-dandy ruler and came up with some figures of my own. Larson says his images are 78% of actual size, so all of my measurements below have been multiplied by 1.282 in order to compensate for scale. Obviously it would be better to have had access to the originals, but I think we can get reasonable figures from the photographs, anyway. In the extant portion of the Hor BoB, there are 7 wraps. A lacuna in the middle makes it impossible to gauge the length of wraps # 4 and 5, except by extrapolation (thus the brackets). Anyway, here are my figures:

-----

Lengths of Wraps:

#1: 10.11 cm
#2: 9.98 cm
#3: 9.9 cm
#4: [9.5?]
#5: [9.1?]
#6: 8.7
#7: 8.32

Diffs b/w each wrap:

#1 & 2: .13
#2 & 3: .08
#3 & 4: [.4?]
#4 & 5: [.4?]
#5 & 6: [.4?]
#6 & 7: .38

Note: The three figures in brackets here must add up to 1.2, but may not have been as evenly distributed as I have suggested above.

-----

My numbers are obviously very different from Gee's. Feel free to do some measurements of your own and report back here if you find I'm way off. It's a little hard to match up the lacunae perfectly, so this isn't an exact science. But I have done my best to be as accurate as possible. Plugging my figures into Gee's equation gives us 79.14 as the length of the missing portion of the roll. (Plugging them into my formula gives us 91.97.) I should emphasize that I made my measurements before I even started playing with equations, so my numbers were not selected in order to give the results I wanted. An 80-centimeter figure (about two and a half feet) is precisely what we would expect based on Michael D. Rhodes' predictions, cited above.

In conclusion, it appears that Gee's vastly inflated length for the missing portion is the result of faulty measurement. Properly considered, the missing-papyrus-equation seems to leave his theory fatally crippled and without a leg to stand on.

Best,

-Chris
Last edited by Guest on Fri Jul 18, 2008 5:10 am, edited 2 times in total.
_Boaz & Lidia
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Post by _Boaz & Lidia »

Gee has a very explicit need to believe. Everything he produces is done to satisfy that need.

He exits every corner that he logically paints himself into by using the age old self induced emotional epiphany. "The holy ghost has bore witness to me that _________ is true".

He has waaaay more at risk than the average member. Not only would he lose his wife, family on both sides, job, BYU colleagues, he would lose the majority of his life that he spent defending this malarkey.
Last edited by Guest on Thu Jul 17, 2008 11:59 pm, edited 1 time in total.
_truth dancer
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Post by _truth dancer »

Hi CK..

Nice work.

Have you shared this info with Gee or any other apologists? Any response?

:-)

~dancer~
"The search for reality is the most dangerous of all undertakings for it destroys the world in which you live." Nisargadatta Maharaj
_CaliforniaKid
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Post by _CaliforniaKid »

truth dancer wrote:Hi CK..

Nice work.

Have you shared this info with Gee or any other apologists? Any response?

:-)

~dancer~


Nope. Y'all are the first. I tried emailing Gee a couple times to find out his source for the equation, but he never answered. I've given up trying to get ahold of the man.
_Boaz & Lidia
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Post by _Boaz & Lidia »

CaliforniaKid wrote:
truth dancer wrote:Hi CK..

Nice work.

Have you shared this info with Gee or any other apologists? Any response?

:-)

~dancer~


Nope. Y'all are the first. I tried emailing Gee a couple times to find out his source for the equation, but he never answered. I've given up trying to get ahold of the man.
You are too nice, calling him a man. :p
_Scottie
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Post by _Scottie »

Did you post this at MAD?

I'm awfully curious now.
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_Chap
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Post by _Chap »

I should be interested to check the validity of these formulae myself, but unfortunately I do not yet fully understand the problem they are trying to solve. In CK's terms:

E - length of the last/interior extant winding
S - average diff. b/w successive winding lengths
Z - length of the missing portion

Is the papyrus we have today supposed to be a continuous length without any gaps, so that the Z we are trying to estimate is a length of papyrus that was originally (when wrapped) either inside or outside the extant portion?

Clearly, if the missing portion was wrapped outside the extant papyrus, we have no way of calculating its length. If the missing portion was wrapped inside the extant papyrus, there is obviously a physical limit to what could have been fitted in, but I am not sure that any simple formula will predict it. The only thing I can imagine a formula predicting is the length of a missing portion between two extant portions. If we have at least one complete wrap on one side of the missing portion, and two complete wraps on the other, the prediction can be done. Is that the situation?

Looking at Gee's formula:

Z = (E^2 - 6.25)/(2S) - E

I can see an immediate problem. Unless the 6.25 is an area (that is, a length times a length) in some unspecified units, the equation does not work dimensionally: E^2 would be (for instance) in centimeters squared if E is in centimeters, so 6.25 cannot be a pure number as it is presented here.

But where on earth (in a general formula) could 6.25 come from? It looks suspiciously like 2π, which is 6.28 to 3 sig figs. - but in that case it absolutely cannot be meaningfully subtracted from E^2. If 6.25 does have the dimensions of area, then the terms on the right hand side will have the dimensions of length, and all is well in that respect - though of course that does not guarantee the formula is correct.

CK's formula Z = [E^2-E*S]/2S has no such problems: dimensions are consistent and correct - although again that does not guarantee the formula is right.

But I am afraid I still fail to understand the physical situation clearly enough to have a stab at writing my own formula. What exactly is going on, please? Can CK please take it from the top?
_CaliforniaKid
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Post by _CaliforniaKid »

Chap,

The extant portion of the BoB is the outer portion of the roll. The inner portion is what's missing. You have to understand that papyrus is much more flexible than paper. So when you roll it, it's not like rolling a piece of paper, where you'll have a big gap in the middle of the roll. Either you roll it like you might a towel, or you roll it around some kind of hard core, like a wooden stick. Both Gee's formula and mine assume that there was no core in the case of the Hor BoB. When this assumption is admitted, I think the length of the interior portion of the scroll is probably predictable enough for our purposes.

Hope that helps,

-Chris
_Mad Viking
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Post by _Mad Viking »

Chap wrote:I should be interested to check the validity of these formulae myself, but unfortunately I do not yet fully understand the problem they are trying to solve. In CK's terms:

E - length of the last/interior extant winding
S - average diff. b/w successive winding lengths
Z - length of the missing portion

Is the papyrus we have today supposed to be a continuous length without any gaps, so that the Z we are trying to estimate is a length of papyrus that was originally (when wrapped) either inside or outside the extant portion?

Clearly, if the missing portion was wrapped outside the extant papyrus, we have no way of calculating its length. If the missing portion was wrapped inside the extant papyrus, there is obviously a physical limit to what could have been fitted in, but I am not sure that any simple formula will predict it. The only thing I can imagine a formula predicting is the length of a missing portion between two extant portions. If we have at least one complete wrap on one side of the missing portion, and two complete wraps on the other, the prediction can be done. Is that the situation?

Looking at Gee's formula:

Z = (E^2 - 6.25)/(2S) - E

I can see an immediate problem. Unless the 6.25 is an area (that is, a length times a length) in some unspecified units, the equation does not work dimensionally: E^2 would be (for instance) in centimeters squared if E is in centimeters, so 6.25 cannot be a pure number as it is presented here.

But where on earth (in a general formula) could 6.25 come from? It looks suspiciously like 2π, which is 6.28 to 3 sig figs. - but in that case it absolutely cannot be meaningfully subtracted from E^2. If 6.25 does have the dimensions of area, then the terms on the right hand side will have the dimensions of length, and all is well in that respect - though of course that does not guarantee the formula is correct.

CK's formula Z = [E^2-E*S]/2S has no such problems: dimensions are consistent and correct - although again that does not guarantee the formula is right.

But I am afraid I still fail to understand the physical situation clearly enough to have a stab at writing my own formula. What exactly is going on, please? Can CK please take it from the top?


I can't get it any longer than 7 ft.
"Sire, I had no need of that hypothesis" - Laplace
_Mad Viking
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Post by _Mad Viking »

CaliforniaKid wrote:Chap,

The extant portion of the BoB is the outer portion of the roll. The inner portion is what's missing. You have to understand that papyrus is much more flexible than paper. So when you roll it, it's not like rolling a piece of paper, where you'll have a big gap in the middle of the roll. Either you roll it like you might a towel, or you roll it around some kind of hard core, like a wooden stick. Both Gee's formula and mine assume that there was no core in the case of the Hor BoB. When this assumption is admitted, I think the length of the interior portion of the scroll is probably predictable enough for our purposes.

Hope that helps,

-Chris


It would be interesting to see his list of assumptions. I perform and check calculations for a living and assumptions put a calc in the proper context.
"Sire, I had no need of that hypothesis" - Laplace
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