Pottery Analysis using Mathematical and Computational tools

1. Pottery Analysis using Mathematical and Computational tools • Ayelet Gilboa • Avshalom Karasik • Ilan Sharon • Uzy Smilansky

2. Drawbacks of Traditional Typology • The traditional methods used for pottery description, typology and classification, are subjective and qualitative. • The huge amount of data in published archaeological reports renders impossible any exhaustive comparison of assemblages.

3. Main Goals and Motivations • To develop new objective and quantitative tools for morphological description, classification and analysis of archaeological artifacts. • Considering the overwhelming abundance of data in the archaeological reports, we would like to implement comparative, typological analysis on a computer aided basis.

4. Acquisition of the Data

5. Curvature function computation Acquisition of the Data

6. Curvature Function Computation The curvature function k(s) provides the curvature k as a function of the arc-length s along the line. The curvature is the rate of change of the direction q (s) of the tangent at the point s: k is positive at convex sections and negative at concave sections.

7. The curvature as a function of the arc-length Alternatively, the curvature is the (signed) inverse of the radius of the osculating circle.

8. 20 15 10 5 0 -10 -5 0 5 10 15

9. A profile of a bowl and its graph of curvature.

10. Why Curvature ? • Efficiency - the most efficient and economic way to specify a planar curve is by its curvature, one variable describing two dimensional line. • Invariance - the curvature holds all the information about the curve and it does not changes under translations or rotations. • Uniqueness - the original curve and its curvature function are in one-to-one relation. Each can be uniquely and accurately reconstructed from the other. • Archaeological relevance – the curvature emphasizes features, which are relevant to the archaeological analysis such as: rim, base, carination etc.

11. Comparing Vessels • The correlation between two curvature functions is defined in terms of the scalar product. • The range of C is

12. New Method for Defining Prototypes • The fact that vessels are represented by numerical functions, enables us to calculate the “mean” of a group of vessels. • One can define this mean as representing a prototype which is specified by the group. • The “mean” vessel is virtual. However, we can plot it and compare it both visually and quantitatively to other real or virtual vessels.

13. A prototype generated as a mean of two rims.

14. Boring Bowls – A Test Case The assemblage: 87 Iron age I-IIa bowls from Tel Dor. Goal: To test the hypothesis that there is a morphological development along the period, from a “complex” rim to a “smooth” one.

15. Tel Dor prototypes

16. Virtual evolution of the rims, from “complex” to “smooth”.

19. Bowls distribution by periods, along the ‘complex-smooth’ axis. 10 Iron Ia 9 Iron Ib Iron I/II 8 Iron IIa 7 6 5 4 3 2 1 0 smooth complex

20. Hazor – Tyre “torpedo” storage jars The assemblage: 24 (Tyre) and 53 (Hazor) storage jars, which were the subject of several scientific articles *. Goal: To shed new light on this problematic issue, using our objective tool for ceramic comparison and classification. * See: Geva S. BASOR 248; Bikai P. BASOR 258; Gilboa A. In QEDEM Reports 2.

21. Hazor – Tyre “torpedo” storage jars The procedure Step 1: scanning all the jars published in the respective excavation reports, and calculating their curvature functions. Step 2: computing the correlation matrix for the combined assemblage. It represents the correlation for every pair of jars Step 3: A cluster analysis of the correlation matrix reveals the inner structures of the assemblages, demonstrated on a “cluster tree” where distinct branches indicate well-segregated morphological types .

22. Hazor / Tyre colored matrix of correlations Hazor Tyre

23. Hazor / Tyre “tree” of correlations correlation 0.95 0.9 0.85 0.8 Tyre: red Hazor: black 0.75

24. Hazor / Tyre – Possible Conclusions • The lack of a significant typological overlap raises doubts about the claims that the 'torpedo' jars indicate commercial links between Hazor and Tyre. • The higher inner similarities observed in the assemblage of Tyre’s jars supports the possibility that they were produced locally, by a workshop which follows a well defined tradition, as suggested by Bikai. • In the Tyre assemblage there are three jars, which differ from the rest. These may possibly be of foreign origin.

25. Problems and Inaccuracies • Every drawing includes interpretation of the artist. Different drawers emphasize different features. • Many inaccuracies derive from the poor quality of the published drawings and from its small scale in the publications. • The pottery published in the archaeological reports is partial and therefore biased.

26. Profile drawing from a 3D scanner

27. Summary We have developed new methodological tool for typological analysis and classification. This objective and quantitative method has been proved to be archaeologically meaningful and even more sensitive than the human eye. A large digital database of ceramic drawings will enables automatic search for parallels. Modern devices such as 3D scanners have a great potential in the field of pottery analysis.