The Length of a Papyrus Scroll

A while ago, someone asked me a question about determining the length of a papyrus scroll  (before you unroll it obviously). The question pertained specifically to, you guessed it, P. Joseph Smith (the document of breathing part). I thought about this for a few minutes and it’s really not a hard problem.

The inverse problem, deciding what a scroll looked like in its rolled state, if you encounter it unrolled may be of interest, but both problems are connected to basically the same set of measurements.

Some of you geeks might be interested in how it goes, if you haven’t already guessed it.  This of course is clearly connected to the name of this blog, if not to the charter, but, rules are made to be broken (again and again).  Have a little sleep-inducing fun: (Note, the presentation has been updated based on various email responses and misunderstandings, etc., etc.)


19 Responses to The Length of a Papyrus Scroll

  1. Matt W. says:

    How do you account for tightness/looseness of the role?

  2. Matt W. says:

    ie- I am not a math person/you lost me coach.

  3. W. V. Smith says:

    The epsilon function is the distance from the inner radius (which can relate to any fixed axis which runs through the region inside of all windings) to the inner side of a winding. So if there is slop, it can be built into the measurement.

  4. Tod Robbins says:

    Bill, this is like Galileo all over again. Superb!

  5. W. V. Smith says:

    Are you suggesting I will come under Church discipline??

  6. Tod Robbins says:

    No, we like mathematicians in this Church. 😉

    • W. V. Smith says:

      “I’ve never known a mathematician who didn’t go too far.” -Brigham Young. (In a negative way – going beyond the bounds of propriety….)

  7. Tod Robbins says:

    That is NOT a real quotation! Really? Ha ha!

  8. MM says:

    It appears to me that the integrand in the length equation at the bottom of page 1 is a distance function for the differential segment of an elliptical spiral subtended by angle dt; i.e., the squared terms inside the square root represent the rates of change of the x and y coordinates of the spiral, is that correct?

  9. Tod Robbins says:

    Oh goodness MM, 100 points. Amen.

  10. WVS says:

    Ok, I can’t believe the amount of email I’ve gotten over this thing. Even though the post is probably dead, I revised the computation business, making it more complicated, formal and harder to understand. You asked for it.

  11. “File not found” when I try to download the new version.

    • W. V. Smith says:

      WordPress had a crash the other day, and the link didn’t come back. In the meantime, I was asked to do a rewrite in a more formal way for an Egyptological journal and then another request of the same sort by an LDS source, so I’m going to leave it down for the time being until those issues take shape at some point. If nothing goes forward, I may do the rewrite anyway and just repost it.

  12. MM says:

    I’d be interested in your comments on this article:

    • WVS says:

      The upshot of the article appears to be that the Document of Breathing from P. Joseph Smith didn’t have enough room on it even under ideal conditions, to contain a hieratic version of the Book of Abraham text. I think that’s probably the case even if you allow for a fairly long scroll. Under perfect conditions, I think you might get 17 feet or so at the outside in addition to what has survived. Not enough. But that would still seem pretty long without speculating about what Charlotte Haven or others might have interpreted “long” to mean as the article seems to want to do. But the physical conclusions of the article seem reasonable to me as far as the Hor papyrus. Side issues in the article are more fuzzy I think, but on the whole it seems to be a careful analysis of the problem of the length of Hor. I can’t personally vouch for the measurements of course. But I assume they are good.

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