2) The mean you cite is meaningless without error bars and any insistence on even the second decimal is unrealistic:
The K.C. was not a perfect rectangle when Petrie was there and his measurements despite adjustments show that. The top length south is almost an inch shorter than the north base. Not that I care all that much for my purposes, but taking a look at the numbers since this matters so much to you: Differences top to bottom each wall.
North: 0.64 inches
South: 0.65 inches
If we take the extremes of these four measurements we get a cubit range of 20.594 - 20.639 inch
West: 0.12 inches
East: 0.14 inches
The cubit range is 20.604 - 20.643 inch
What this means is that the true variance due to all variations is 0.049 inch (error +/- 0.025) 6 times what Petrie reported...0.008, +/- 0.004.
Therefore, the real error bars on Petrie's overall average value, 20.632, are 20.594 - 20.643. The geometric definition is actually more centered relative to that range, ie -20 parts ppm/rc/+ 29 ppm, versus Petrie's overall average which is approaching the upper bracket to within 11 ppm.
What Petrie did is to assume that the base measurements were more accurate than the ceiling measurement. His average value for the cubit is derived from those four measurements at the base.
Probably the base of the chamber was the part most carefully adjusted and set out; and hence the original value of the cubit used can be most accurately recovered from that part. The four sides there yield a mean value of 20-632 ± "004, and this is certainly the best determination of the cubit that we can hope for from the Great Pyramid.
He eliminated four data points on a hunch. Why?
Gantenbrink's analysis of structure points shows that the ceiling measurements were the better anchors. Regardless, in the absence of knowing which, you have had to treat all 8 observation as equally valid to feed into the confidence interval of the metric used.
A similar issue came up when measuring the perimeter. He assumed that the pyramid corners fell on the diagonals. As a result, his error bars are artificially small, because he eliminated the variance of the corners from the diagonals, which Lehner and Goodman accounted for.
MJT: This conversation continues after I read your published work and not one day earlier.
Stop fussing around behind the curtain. Just do it and get it done. I am actually looking forward to it!
Edited 8 time(s). Last edit at 20-Mar-18 11:24 by Manu.