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Length of the Lost Scroll of Horos


William Schryver

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To whom it may concern:

Since I know that the School of the Pundits if often ignored, I did want to alert everyone in the discussion forum that there is a new thread where I have posted a paper I have just completed: Missing Papyrus - Calculating the Length of the Lost Scroll of Horos.

The paper argues that, in consequence of recent developments, we can now assert with considerable confidence that the scroll of Horos -- the roll from which the "Book of Breathings" fragments were cut -- was the "long roll," the one which the preponderance of the eyewitness testimony identifies as the source of the text of the Book of Abraham. In fact, the missing portion is at least 3x as long, and possibly 7x as long as the ~100 cm represented by the surviving fragments.

This means that, contra Robert Ritner and others, Professor John Gee is correct in his claims concerning a large quantity of missing material from the collection of papyri originally in the possession of Joseph Smith.

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Great work William. I read them and all looks sound (the math does, I'm not a expert on the scrolls so I go by what you guys say, but the math looks good.)! I always look forward to your posts.

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Will,

I'm glad to see that you're still interested in this subject; however, after reading through your post in the pundits forum, it appears that not much has changed since the last thread. http://www.mormonapologetics.org/index.php...mp;p=1208629246

Both the Hoffmann formula and the simple spiral calculation appear theoretically sound. The difference in results between them appears to center on the Hoffmann formulaâ??s sensitivity to precise measurements.

Chris'/Chap's linear regression is superior to the Hoffmann formula because it provides a means for error estimation. The problem with the Hoffmann formula is that it takes only two windings as inputs. If the measurements are exact, then the prediction will be accurate; however, if either of the measurements is off, then the formula can give a wildly inaccurate result and the user will have no way of knowing it. The Hoffmann formula essentially fits a line to two data points and then looks far out on the line to see where it crosses the abscissa (see his Abb. 3 drawing). Since two points precisely define a line, there is no inherent error gauge in this method. On the other hand, if measurements are made for 3 or more windings, then it becomes possible to put an error bar on the estimate by looking at the residual "goodness of fit" variable as well as other indicators. You can also compute exactly how much the estimate would change for a given change in any one of the winding measurements. Increasing the number of winding measurements decreases the sensitivity to error in any particular measurement. Furthermore, by looking at many windings, you enforce consistency in the measurements from one winding to the next; i.e., successive windings should differ by ~2*pi*T, where T is the apparent thickness, which, as Chris has repeatedly pointed out, must be greater than or equal to the actual thickness, depending on wrinkling, inhomogeneities etc.

the measurements made by Gee must be considered authoritative until proven otherwise.

You must show your work to get credit. Prof. Gee has done nothing but quote two numbers; i.e., the lengths of the 1st and 7th windings (to two significant figures). I have sent him three emails requesting information on his methodology. He responded to my first two emails but gave no indication as to how he measured the windings. Chris and I have shown exactly how we made our measurements and described in detail our reasoning and methodology. Gee must do the same if he wants his estimate to be taken seriously. It is insufficient and inappropriate to simply say "I have examined the originals and you have not, therefore you must take my word for it."

Now look closely at the papyrus. You'll notice fibers running both lengthwise and spanwise, indicating that it is a typical 2-layer laminate. Look at the hieroglyphic column to the left of Osiris' feet. You'll see where the top layer has peeled off exposing the bottom layer. Notice the opacity of the bottom layer and the fact that no ink has seeped through. Also consider the fact that papyrus such as this must endure stone burnishing to make it smooth enough to write on. Do you think you could do all that with a page from your triple combination?

I have done some experimentation taking photographs of the plates in Nibley's book in order to assess the potential magnitude of distortion effects. There does appear to be a minor issue of parallax between the top and bottom of the papyrus. (I'd show an example but I get an error when I try to upload an attachment..) The parallax is reduced by increasing the distance from the page to the camera lens and properly centering the camera over the image. Nevertheless, if any new photographs are taken, I highly recommend placing rulers along both the top and bottom edges. Better yet, put both rulers in place and scan the papyri.

I hope that in the future this topic will be something we can work on together, rather than arguing about. I think it is an issue that can be definitively resolved. It's really all about the winding measurements, everything else is a minor issue and/or red herring.

Best Regards,

MM

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EbedQuestion.png

Chris'/Chap's linear regression is superior to the Hoffmann formula because it provides a means for error estimation.

I know who Friedhelm Hoffmann is. But who is "Chris/Chap"? I cannot find anything on him or his formula in any publication. Can someone point me to his work? Thanks.

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I know who Friedhelm Hoffmann is. But who is "Chris/Chap"? I cannot find anything on him or his formula in any publication. Can someone point me to his work? Thanks.

I was referring to Chris Smith's regression analysis, which was discussed on "the board that shall not be named."

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I read the thread in the Pundits forum and thought of this quote from Patton:

"Untutored courage is useless in the face of educated bullets."

To Chris Smith: Chris, your fine education is showing. Your posts are, as ever, cogent and refined.

Judging from the amount of condescension in Will Schryver's posts, I'd say your bullets are hitting their mark.

Frij

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Interestingly enough, measuring multiple wraps does not help that much if each independent measurement is associated with its own independently distributed random error. I would quantify that for you but I would have go back and review Cramer-Rao bounds on an over-determined system of equations. But perhaps I should let you do some homework on that and report back to us?

This is incorrect. If the measurements are independent, then the errors will be randomly distributed, unless there is some systematic bias in the methodology. Random errors; e.g., a Gaussian distribution about the mean, are subject to cancellation upon integration or least-squares fitting. The net result is that you gain an order of accuracy (an extra digit) by measuring multiple windings. If the skewness of the error probability density function is zero, then the net error goes to zero in the limit of an infinite number of measurements. If the distribution has non-zero skewness (there is a bias), then the net error doesn't go to zero but significant cancellation still occurs.

Is there anyone here who is actually interested in the real answer to this question or is it too much fun beating up on Chris?

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Is there anyone here who is actually interested in the real answer to this question or is it too much fun beating up on Chris?

I certainly am, and I am extremely disheartened to see Chris's post on the board that shall not be named indicating that the 'beating' is apparently beginning to take its toll and may affect his future participation in these discussions. A real shame, and a loss for all those interested in this discussion.

(BTW - Is it actually a rule that we not name the other board? If it is an actual rule, I'll certainly abide by it, but I hope I won't get in trouble for thinking it more than a tad ridiculous.)

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I certainly am, and I am extremely disheartened to see Chris's post on the board that shall not be named indicating that the 'beating' is apparently beginning to take its toll and may affect his future participation in these discussions. A real shame, and a loss for all those interested in this discussion.

(BTW - Is it actually a rule that we not name the other board? If it is an actual rule, I'll certainly abide by it, but I hope I won't get in trouble for thinking it more than a tad ridiculous.)

I have no sense of decorum, but then again, they have no issues with mentioning this board.

censored

Have a nice day!

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(BTW - Is it actually a rule that we not name the other board? If it is an actual rule, I'll certainly abide by it, but I hope I won't get in trouble for thinking it more than a tad ridiculous.)

From the MADB Guidelines:

Do not start board wars or cross-posting (duplicate discussions from other boards on the MADB boards or vice versa in order to continue an argument). Links to other discussion boards will not be permitted in most cases.
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Frij:

I read the thread in the Pundits forum and thought of this quote from Patton:

"Untutored courage is useless in the face of educated bullets."

To Chris Smith: Chris, your fine education is showing. Your posts are, as ever, cogent and refined.

Judging from the amount of condescension in Will Schryver's posts, I'd say your bullets are hitting their mark.

;) Donâ??t look now, but your sycophant is showing.

And if thereâ??s one thing Iâ??ve learned in my years dealing with exmormons on message boards, itâ??s that one manâ??s self-deprecation can be and often is another manâ??s hubris.

In any case, I can quote Patton, too â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦ but I donâ??t think Iâ??ll do it here. :crazy:

You have a unique perspective on this discussion. Iâ??ll grant you that. Youâ??re obviously passionate for â??your sideâ? in this controversy. And thatâ??s perfectly fine with me.

Unfortunately for your perspective (as well as Smithâ??s arguments) thereâ??s the dispassionate matter of the objective mathematics to deal with.

And Mortal Manâ??s objections above entirely miss the point emphasized so succinctly by Greg Smithâ??s late night post in the Punditâ??s thread:

Let's not miss the forest for the trees:

1) we have here two formulae, based on different measurements and different principles, that converge at a common answer: that there was a great deal of scroll missing.

2) This also matches what the eyewitnesses reported.

Whether it is 10 feet, 20 feet, or 40 feet, seems rather immaterial.

Hear, hear.

As Iâ??ve made perfectly clear on several occasions, I believe the eyewitness testimony can be accorded with a missing scroll length of as little as ~10 feet -- although itâ??s beginning to look as though there was quite probably a great deal more than that.

OK, Iâ??m going to take my condescension ball and get back to work â?¦

.

.

.

But wait, one more thing:

Mortal Man:

Is there anyone here who is actually interested in the real answer to this question or is it too much fun beating up on Chris?

:P

Please spare us the theatrics.

Chris has no idea what it means to get "beat up" on a message board.

Although if he persists in this particular argument, he might find out in time.

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Is there anyone here who is actually interested in the real answer to this question or is it too much fun beating up on Chris?

Have you stopped beating your spouse?

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Frij:

;) Donâ??t look now, but your sycophant is showing.

And if thereâ??s one thing Iâ??ve learned in my years dealing with exmormons on message boards, itâ??s that one manâ??s self-deprecation can be and often is another manâ??s hubris.

In any case, I can quote Patton, too â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦â?¦ but I donâ??t think Iâ??ll do it here. :crazy:

You have a unique perspective on this discussion. Iâ??ll grant you that. Youâ??re obviously passionate for â??your sideâ? in this controversy. And thatâ??s perfectly fine with me.

Unfortunately for your perspective (as well as Smithâ??s arguments) thereâ??s the dispassionate matter of the objective mathematics to deal with.

And Mortal Manâ??s objections above entirely miss the point emphasized so succinctly by Greg Smithâ??s late night post in the Punditâ??s thread:

Hear, hear.

As Iâ??ve made perfectly clear on several occasions, I believe the eyewitness testimony can be accorded with a missing scroll length of as little as ~10 feet -- although itâ??s beginning to look as though there was quite probably a great deal more than that.

OK, Iâ??m going to take my condescension ball and get back to work â?¦

.

.

.

But wait, one more thing:

Mortal Man:

:P

Please spare us the theatrics.

Chris has no idea what it means to get "beat up" on a message board.

Although if he persists in this particular argument, he might find out in time.

I am passionate about well-reasoned and well-stated arguments, Will, which is why yours leave me less than excited.

Do you deal only in dispassionate objectivity when you believe it suits your agenda? Were you to confront the many phenomenal claims of Joseph Smith with the same dispassionate objectivity with which you claim to deduce the length of the scrolls you might just find yourself right outside the church.

Oh, and that's not my sycophant showing. It's something else. (I've read enough of your posts here and yon to know math isn't your only weakness.)

Frij

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And Mortal Manâ??s objections above entirely miss the point emphasized so succinctly by Greg Smithâ??s late night post in the Punditâ??s thread:

non se⋅qui⋅tur

[non sek-wi-ter, -toor; Lat. nohn se-kwi-toor]

â??noun

1. Logic. an inference or a conclusion that does not follow from the premises.

2. a statement containing an illogical conclusion.

Mortal Man:

:P

Please spare us the theatrics.

My memory is a little vague here; perhaps you can help me out and remind me who posted this:

80082.jpg

Chris has no idea what it means to get "beat up" on a message board.

Although if he persists in this particular argument, he might find out in time.

Will, you are an attorney, correct?

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AC:

My memory is a little vague here; perhaps you can help me out and remind me who posted this:

80082.jpg

Have you forgotten already? That's John Gee at the most recent Book of Abraham apologetics meeting at BYU.

I really like the color combination.

Will, you are an attorney, correct?

What ever gave you that idea?

BTW, I'll see if I can't fetch my main math man, mormonfool, to address your specific mathematics questions. That's his forte, not mine.

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Now look closely at the papyrus. You'll notice fibers running both lengthwise and spanwise, indicating that it is a typical 2-layer laminate. Look at the hieroglyphic column to the left of Osiris' feet. You'll see where the top layer has peeled off exposing the bottom layer. Notice the opacity of the bottom layer and the fact that no ink has seeped through. Also consider the fact that papyrus such as this must endure stone burnishing to make it smooth enough to write on. Do you think you could do all that with a page from your triple combination?

Will, any response to this?

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I certainly am, and I am extremely disheartened to see Chris's post on the board that shall not be named indicating that the 'beating' is apparently beginning to take its toll and may affect his future participation in these discussions. A real shame, and a loss for all those interested in this discussion.

Indeed. Going over to the "other board" is almost certainly associated with a sneaking suspicion that one needs greener pastures in which to make his case, ie., a choir to preach to.

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Frij:

;) Don’t look now, but your sycophant is showing.

And if there’s one thing I’ve learned in my years dealing with exmormons on message boards, it’s that one man’s self-deprecation can be and often is another man’s hubris.

In any case, I can quote Patton, too ………………………………… but I don’t think I’ll do it here. :crazy:

You have a unique perspective on this discussion. I’ll grant you that. You’re obviously passionate for “your side” in this controversy. And that’s perfectly fine with me.

Unfortunately for your perspective (as well as Smith’s arguments) there’s the dispassionate matter of the objective mathematics to deal with.

And Mortal Man’s objections above entirely miss the point emphasized so succinctly by Greg Smith’s late night post in the Pundit’s thread:

Hear, hear.

As I’ve made perfectly clear on several occasions, I believe the eyewitness testimony can be accorded with a missing scroll length of as little as ~10 feet -- although it’s beginning to look as though there was quite probably a great deal more than that.

OK, I’m going to take my condescension ball and get back to work …

.

.

.

But wait, one more thing:

Mortal Man:

:P

Please spare us the theatrics.

Chris has no idea what it means to get "beat up" on a message board.

Although if he persists in this particular argument, he might find out in time.

Yes, those nineteenth century eyewitnesses to all the now missing material. Pity those exist, as without them the critic's forensic preoccupations would have greater plausibility then at present. With them, the whole theory that all presently existing material is the source/origin of the ideas and text represented in the BofA are in danger, at any time, of disappearing in a puff of oily smoke.

The critics know this too, which accounts for a great deal of the snottyness, intellectual snobbery, and professed cognitive superiority to their interlocutors. They'd prefer, like the always irrepressible and annoying KG (he who must not be named, who spends much of his posting time on the board which must not be named), to engage in an endless orgy of name calling, internet shouting matches, and effervescent smarm, all of which seems to indicate a rather telling lack of confidence in their own position.

This is, in a way, quite fitting, as the more people talk up their own position and express grand certitude regarding their own theories and guesses, the greater the ultimate fall will be.

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I hope that in the future this topic will be something we can work on together, rather than arguing about. I think it is an issue that can be definitively resolved. It's really all about the winding measurements, everything else is a minor issue and/or red herring.

Excellently said, MM.

And thanks to those who offered their encouragement and votes of support.

I really genuinely do want to see this argument correctly and definitively resolved, regardless of who is right. Based on the testimony of Gustavus Seyffarth and on my measurements from the photographs so far, I fully expect further investigation to find that there was no other text on the Hor roll after the Book of Breathings. But if it should turn out that I am wrong, it certainly would not be the end of the world.

Best,

-Chris

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Will,

I'm glad to see that you're still interested in this subject; however, after reading through your post in the pundits forum, it appears that not much has changed since the last thread. http://www.mormonapologetics.org/index.php...mp;p=1208629246

Chris'/Chap's linear regression is superior to the Hoffmann formula because it provides a means for error estimation.

I don't see it this way. The estimation of the S parameter is independent of whatever formula or method used to calculate scroll length. Hoffmann's equation doesn't dictate how it should be done. The expression Gee (not to be confused with the Hoffmann formula) published for estimating S is merely a convenient way that makes use of the first and last winding length. The Hoffmann equation utilizes the final winding term to find the missing length rather than total length, but an easy tweak will give total length if desired. If the user wants to calculate the S parameter some other way (than just using first and last measure), it is a mathematically simple matter to do so. I haven't see Hoffmann's derivation, but I am comfortable drawing such conclusions from Gee's summary.

With the spread sheet program I saw in use, the problem I see using it is that there is no real understanding gained about how results can change dramatically in terms of the controlling variables. For example, the dependence on scroll length to imprecision in the S estimate appears to have been misunderstood. It is very sensitive at such small values because the dominant term in Hoffmann equation or the equation derived from modeling with an Archimedes spiral equation is inversely proportional to S (or maximum value that T can obtain). This insight isn't immediately apparent in playing around with spread sheets. I don't think I would have made any message board appearance if I hadn't noticed the Gee debunking party has demonstrated a lack of awareness about this insight.

The problem with the Hoffmann formula is that it takes only two windings as inputs.

I am editting my response here because I ran (assumed you were right about 2 windings) with this my first pass through. In fact the Hoffmann equation as expressed in Gee's paper only uses the final winding length (E).

If the measurements are exact, then the prediction will be accurate; however, if either of the measurements is off, then the formula can give a wildly inaccurate result and the user will have no way of knowing it.

One can do a perturbation analysis to see how small measurement errors can result in large differences in scroll length. Users who don't know how to analyze the results of a formula are not particularly unique to Hoffmann's equation.

The Hoffmann formula essentially fits a line to two data points and then looks far out on the line to see where it crosses the abscissa (see his Abb. 3 drawing). Since two points precisely define a line, there is no inherent error gauge in this method. On the other hand, if measurements are made for 3 or more windings, then it becomes possible to put an error bar on the estimate by looking at the residual "goodness of fit" variable as well as other indicators. You can also compute exactly how much the estimate would change for a given change in any one of the winding measurements. Increasing the number of winding measurements decreases the sensitivity to error in any particular measurement. Furthermore, by looking at many windings, you enforce consistency in the measurements from one winding to the next; i.e., successive windings should differ by ~2*pi*T, where T is the apparent thickness, which, as Chris has repeatedly pointed out, must be greater than or equal to the actual thickness, depending on wrinkling, inhomogeneities etc.

See my pundit post on why, even though this method is a slight improvement over just using the first and last measurements to estimate S, it is hardly worth making a big deal about. For example, I am working on a parameter estimation paper myself where at one point I do a linear best fit on some data at one state and do a parameter search to minimize weighted least squared error. Yet I doubt it is all that necessary in my paper to describe my precise method for obtaining the data I used or spell out a step-by-step procedure of all the steps I took. My readers won't be interested in such matters and amateurs won't be competent in duplicating them anyway. Linear best fits are so trivial and routine that the word "estimate" or "interpolate" usually do the trick.

But what I am trying to say is that using linear interpolation that will only theoretically provide a modestly better estimate of S is nothing to get excited about. There really is no merit in using an ubiquitous method on bad data (Garbage in Garbage out). It really is not all that big of a contribution that advances our knowledge on subject, neither are the various formulas for scroll length that differ (as I have explained rather artificially) from Hoffmann's.

The observation that T <= S/2pi was a nice contribution as it allows a feasibility check on the estimation of S. It is also a nice contribution that scrolls that meet this requirement have been identified.

The camera angle problem sounds fun and could be a contribution if it is at all tractable. I have my preliminary doubts, but I would rather somebody more motivated expend their effort at it. I do not have much reason to distrust Gee, so at this stage it much more parsimonious for me to believe Chris et als. measurements are foo-barred with inferior resources than Gee's.

The estimate of how tightly something can be rolled is interesting, but it seems to me that paper conforms rather nicely. That is one of the reasons for its popularity. You can't stick a fresh stack of typing paper in a vice (or a book) and get much compression. I don't think curvature fundamentally affects much how seemlessly layers of paper can mesh together. Paper being my frame a reference for the papyrus... But if you guys find out differently let us know.

edit: adding some clarity to difference between estimating S and using a formula to evaluate scroll length which is dependent on S.

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Mortal Man:

Now look closely at the papyrus. You'll notice fibers running both lengthwise and spanwise, indicating that it is a typical 2-layer laminate. Look at the hieroglyphic column to the left of Osiris' feet. You'll see where the top layer has peeled off exposing the bottom layer. Notice the opacity of the bottom layer and the fact that no ink has seeped through. Also consider the fact that papyrus such as this must endure stone burnishing to make it smooth enough to write on. Do you think you could do all that with a page from your triple combination?

dblagent007:

Will, any response to this?

Only that I don't really get what point MM is trying to make here. The photos I have seen of the scroll of Horos seem to show a very fine, thin material was used. Papyrus was manufactured by laying two layers of the plant fibers crossways of each other and pressing them together until they were essentially "welded" to each other. They are known to have -- over the course of millenia -- produced papyrus of an exceedingly thin quality. I have documented samples as thin as .10 mm (100 microns) from the New Kingdom to the Roman era. Gee's measurements, if absolutely accurate, indicate a thickness of 53 microns for the scroll of Horos. Despite the dearth of specimens quite that thin, I don't know that papyrus cannot be manufactured that thin. I do know it can be manufactured to a thickness of 100 microns.

Is that the kind of response you're looking for?

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Am I missing something, or does CS' argument largement consist of ignoring actual observation of real data and the reasonable extrapolations drawn therefrom in favor of 150+ years ago 3rd party tendentiousness?

USU "Holy Aristotle, Batman!" 78

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Just for the sake of the argument, were is Tarski, he has a PhD in math. Just currious what he would make of all of this. Not taht I think CS or MM aren't capable.

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