William Schryver wrote:I'm not John Gee. And I haven't made this argument concerning a 1200cm scroll. In fact, I've never been entirely comfortable with it because I didn't really understand it, and it seems like a 40ft. roll of papyrus would have been larger in circumference, when rolled up, than 9.7cm.
As my calculations show, you are entirely right about that!
Suppose the scroll is made of papyrus of thickness t, and that it has a total of N wraps.
That means that if it is tightly wound, the radius of the scroll must be New Testament. Thus the outer circumference must be:
C = 2πNt
Now the average length of a wrap is halfway between the outer value, C, and the value of the innermost wrap, which is effectively zero. It is therefore
C/2 = 2πNt/2 = πNt
The total length is thus:
L = NC/2 = π(N^2)t
Suppose we have L = 1200 cm
so 1200 cm = π(N^2)t,
=> N^2 = 1200 cm/ πt
Let us take the plausible value of 0.05cm (half a mm) for the papyrus thickness t
Then N^2 = 1200 cm/ (π*0.05cm)
=> N^2 = 7650 (3 sig figs, probably not justified)
=> N = 87 (2 sig figs)
Using our previous result that
C = 2πNt
we have C = 2π*87*0.05cm = 27 cm
So the outermost wrap should be about three times the length we actually find (about 9 cm), if want a tight roll of papyrus 1200 cm long and about 0.05 cm thick.