Chap wrote:Re-reading that post, I think its value, if it had any, was in showing that it was possible to talk fairly precisely about scroll length without using algebraic formulae.
Yup, the spiral formula is just a convenient way of adding up all the missing windings. A simpler method, albeit more cumbersome, is to write them out by hand (or use a spreadsheet like Chris originally did).
I was trying to write a kind of Scroll Length for Dummies. (NB - I am happy with formulae myself, but I know that lots of people aren't. Including Gee, I suspect.)
Gee has trumpeted the accuracy of the Hoffmann formula in his "puzzles" paper, in his 2009 FAIR talk and on the FAIR Wiki. He thought we were using a different formula because of our different
notation and centered
convention for the winding numbers. This misperception inspired him to demonstrated that there is something wrong with the Cook/Smith formula, that it is based on incorrect assumptions etc. The fact is, the formulas are mathematically equivalent; they give
identical predictions if correctly applied. Nevertheless, Gee managed to generate a difference by feeding the formulas different inputs. Chris actually discovered this right away.
The take-home point, so far as I could see, was that Gee's work (as it was then) seemed to require papyrus that was implausibly thin, in order to get all the windings he needed for his preferred total length into the space available.
Yes, Gee's Hor papyrus from the "puzzles" paper is impossibly thin.