The Numbers Ain’t Enough

Reporting the arguments in a new comment paper on geochemical similarity methods

A comment paper has now been published in the Journal of Archaeological Science: Reports examining an arithmetic method for assessing geochemical similarity between artefacts and potential sources.

Pearce, N. J. G., Bevins, R. E., Ixer, R. A., and Pirrie, D. 2026. “Arithmetic Approaches Alone Are Inadequate in Defining Similarity: A Comment on Ciborowski and Nash 2026 ‘Defining Similarity: An Arithmetic Method for Archaeological Source Provenance Targeting Using Geochemical Data’.” Journal of Archaeological Science: Reports: 105874. 10.1016/j.jasrep.2026.105874 (ScienceDirect)

The method under discussion

Ciborowski and Nash (2026) proposed an arithmetic method that uses ratios of selected elements to zirconium, converts differences into percentages, and calculates the geometric mean of those percentages. They presented it as a straightforward way to compare artefacts with potential sources.

Pearce et al. (2026) assessed the application of this method to examples included in the Ciborowski and Nash paper.

Examples examined in the comment

The comment analyses two published datasets.

In the case of Neolithic and Bronze Age obsidian artefacts from Ustica, Pearce et al. report that the arithmetic method produced different source assignments from those reached through bivariate plots of elements such as Rb, Ba, Zr, Nd and U.

In the case of Stonehenge Stone 62 (a non-spotted dolerite), the comment notes that the arithmetic method identified Carn Goedog as a relatively close match. Pearce et al. point out that Carn Goedog is a spotted dolerite and that Stone 62 belongs to a different petrographic group, with differences also visible in compatible elements such as Ni and Cr.

Issues raised by the comment

Pearce et al. raise several points about the arithmetic approach:

• The results can change with small variations in input data, including those caused by rounding or normal analytical precision.
• The use of many rare earth elements can influence the outcome because these elements tend to behave similarly.
• The method as applied in the examples focuses on incompatible elements and does not incorporate compatible elements that may show variation between sources.
• Every element contributes equally to the final geometric mean, without adjustment for differences in analytical precision.
• Petrographic information is not included in the calculation.

The authors of the comment argue that these factors limit the reliability of the method when used on its own.

Alternative approach described

Pearce et al. advocate what they term a “total” approach, combining petrographic examination, mineralogical data, geochemical analysis and geological context.

Summary of the debate

Year	Paper	Main development reported
2020	Nash et al., Science Advances	West Woods suggested as source for most sarsens using pXRF and statistical analysis.
2024–2025	Hancock et al., Archaeometry	Re-examination of data for Stone 58 and discussion of methodological choices.
2025	Harding et al.	Additional stones linked to West Woods area.
Early 2026	Ciborowski & Nash	Arithmetic similarity method proposed.
June 2026	Pearce et al.	Comment examining the arithmetic method and its application to published examples.

Note on the paper

The comment by Pearce et al. (2026) focuses on the application and limitations of one specific arithmetic method. It does not claim to resolve the broader question of sarsen sources at Stonehenge.

References

• Ciborowski, T. J. R., and Nash, D. J. 2026. “Defining Similarity: An Arithmetic Method for Archaeological Source Provenance Targeting Using Geochemical Data.” Journal of Archaeological Science: Reports 69: 105513. 10.1016/j.jasrep.2025.105513
• Hancock, R. G. V., et al. 2024. “Stonehenge Revisited: A Geochemical Approach to Interpreting the Geographical Source of Sarsen Stone #58.” Archaeometry 67(1): 1–19. 10.1111/arcm.12999
• Harding, P., et al. 2024. “Earliest Movement of Sarsen Into the Stonehenge Landscape: New Insights from Geochemical and Visibility Analysis of the Cuckoo Stone and Tor Stone.” Proceedings of the Prehistoric Society 90: 229–251 (published online January 2025). 10.1017/ppr.2024.13
• Nash, D. J., and Ciborowski, T. J. R. 2025. “Comment on: Stonehenge Revisited.” Archaeometry 67: 1423–1436. 10.1111/arcm.13105
• Nash, D. J., et al. 2020. “Origins of the Sarsen Megaliths at Stonehenge.” Science Advances 6(31): eabc0133. 10.1126/sciadv.abc0133
• Pearce, N. J. G., Bevins, R. E., Ixer, R. A., and Pirrie, D. 2026. “Arithmetic Approaches Alone Are Inadequate in Defining Similarity: A Comment on Ciborowski and Nash 2026 ‘Defining Similarity: An Arithmetic Method for Archaeological Source Provenance Targeting Using Geochemical Data’.” Journal of Archaeological Science: Reports: 105874. 10.1016/j.jasrep.2026.105874
• Pearce, N. J. G., Bevins, R. E., and Ixer, R. A. 2022. “Portable XRF Investigation of Stonehenge Bluestone 62 and Potential Source Outcrops in the Mynydd Preseli.” Journal of Archaeological Science: Reports 44: 103525.