Background

In my previous post, I have presented metrological data, which indicated that vessels from Matt Beall’s ancient Egyptian stone vase collection fall into two distinct categories:

• ‘precise’, which are consistent in quality with modern-day stone vases that are made on a lathe;
• ‘imprecise’, which are consistent in quality with manual labor using stones and sticks.

In this post, I am going to refine this conclusion and argue that the quality of the ancient Egyptian stone vessels that I deem ‘precise’ is inconsistent with the quality of modern-day machining; it is demonstrably higher.

Ever-Growing Data Set

I have added more 3D scans to my dataset, which now includes a vase labeled ‘J1’ from Jordan Moras (magenta), two more modern vases ‘M4’ and ‘M5’ (orange), and 13 more vases from Matt Beall’s collection (blue), Fig. 1.

This time, the vertical scale of the chart in Fig. 1 is not logarithmic, but linear. I have chosen it to emphasize the gap in quality between the ‘precise’ (green) and the ‘imprecise’ (blue) classes.

When I have switched from the logarithmic to the linear vertical scale, something else became evident: the modern vases (orange) seem to form aclass of its own, which fits between the ‘precise’ and the ‘imprecise’ classes – Fig. 2; the manually made vases by Olga Vdovina, however, fit right in with the ‘imprecise’ class, whereas the ‘J1’ vase bought by Jordan Moras fits with the ‘precise’ class.

Note that the scatter plot on Fig. 2 is logarithmic; a linear plot squishes all the ‘precise’ artifacts into just one green dot. This happens because of the HUGE gap in quality between the two classes, which makes the linear scale impossible to use. To see what I mean, take a look at Fig. 3.

By limiting the range of the plot to 100 on the x and y axes, I can illustrate how the ‘precise’, ‘modern’, and ‘imprecise’ objects cluster together, although at the expense of omitting many ‘imprecise’ artifacts, which fall outside the 100/100 inner/outer quality range. To show how big the gap between the classes is, I had to zoom in some more, Fig. 4.

Fig. 4 illustrates how distinct the ‘precise’, the ‘modern’, and the ‘imprecise’ classes truly are (the ‘imprecise’ class does not even fit into the zoomed-in portion of the scatter plot, save for one object).

Conclusion

It is safe to say that the developed metrological analytical technique of evaluation of the quality of ancient artifacts can clearly distinguish between the modern stone vases and those of purported ancient Egyptian origin. As such, the analysis of forty-three 3D scans uncovered three classes of objects:

1. ‘precise’ class, M ≤ 15, characterized by extremely high precision;
2. ‘modern’ class, 15 < M ≤ 50, consistent with modern machining on a lathe;
3. ‘imprecise’ class, M > 50, consistent with manual fashioning.

In terms of the total quality metric M, the ancient Egyptian stone vessels that I deem ‘precise’ are 5 to 10 times more precise than modern-day stone vases made on a lathe and out of softer stones (two modern vases were onyx and three were marble). This is a difference of 500 to 1000 percent!

Several objects in Matt’s Beall collection are characterized by circularity and concentricity of 10-20 microns ON AVERAGE. Let the meaning of the word ‘on average’ sink in; this means that half the slices examined by the algorithm were circular and concentric with the accuracy greater than 10-20 microns! As I have shown in my previous post, the accuracy of the vase ‘V18’ from Matt Beall’s collection is basically beyond the measurement capability of a CAT scanner… and beyond the rounding error arising from dealing with the floating point math on a computer.

At the same time, modern-day stone vases are circular and concentric to within 50-200 microns, a big difference.

By comparison, the hand-made vases and the rest of the objects in the ‘imprecise’ class are 50 to 100 times less precise in terms of the total quality metric as compared to the ‘precise’ class and 5 to 10 times less precise as compared to the ‘modern’ class.