Pattern recognition of universal mathematical constants in Acheulean biface formats

  • Alan Edward Cannell Independent Researcher Owner Director Transcraft Engineering Curitiba, Parana
Keywords: Acheulean, biface, geometry, format, mathematical constant, aesthetics


The similar design formats of many Acheulean bifaces has prompted several studies into the use of ‘mental templates’, leading to controversial claims that there may be a relation between length and width equal to the Golden Ratio. To avoid subjectivity, these studies have used aggregate data from assemblages that, by definition, mask the individuality of each tool, its material, any retouching and the original imposed design. Visual pattern recognition is widely used in psychological research and some branches of engineering and a similar technique is presented to highlight the formats of two samples of the Boxgrove assemblage (one random) and examine the presence of universal mathematical constants. A probabilistic analysis suggests that the repeated use of the numbers 2, Pi and Phi and the relationship between them could not have been produced by chance. These relationships appear to be constant over very long time periods and are still used today in modern gemstone design.



Author Biography

Alan Edward Cannell, Independent Researcher Owner Director Transcraft Engineering Curitiba, Parana

MSc Engineering

20 years of research in paleoanthropology

special interests in  manuports and throwing, an engineering analysis of acheulean bifaces and, in particular, pattern recognition of biface formats


Blodgett, T.A., Gilbertson, A., Geurts, R. & Goedert, B. 2011, Preferred Length-to-Width Ratios Among Fancy Shape Diamonds. Gems & Gemology; Proceedings of the Fifth International Gemological Symposium, 47(Summer): 129.
Boismier, W.A., Gamble, C. & Coward, F.S., (Eds.) 2012, Neanderthals among mammoths : excavations at Lynford Quarry, Norfolk. English Heritage, Swindon, 529 p.
Cannell, A.E. 2014, Proboscidean resources and the engineering of Acheulean lithic technology. Lithic Technology, 39(1): 39-45. doi:10.1179/0197726113Z.00000000031
Costa, A.G. 2010, A Geometric Morphometric Assessment of Plan Shape in Bone and Stone Acheulean Bifaces from the Middle Pleistocene Site of Castel di Guido, Latium, Italy. In: New Perspectives on Old Stones : Analytical Approaches to Paleolithic Technologies (Lycett, S.J. & Chauhan, P., Eds.), Springer New York, New York, NY: p. 23-41. (in English) doi:10.1007/978-1-4419-6861-6_2
Emery, K. 2010, A re-examination of variability in handaxe form in the British Palaeolithic. Doctoral thesis no. 19299 at the Institute of Archaeology, University College London, London, 388 p. URL:
Gowlett, J.A.J. 2011, Special Issue: Innovation and the Evolution of Human Behavior The Vital Sense of Proportion: Transformation, Golden Section, and 1: 2 Preference in Acheulean Bifaces. PaleoAnthropology (Special Issue: Innovation and the Evolution of Human Behavior), 174. doi:10.4207/pa.2011.art51
Iovita, R. & McPherron, S.P. 2011, The handaxe reloaded: A morphometric reassessment of Acheulian and Middle Paleolithic handaxes. Journal of Human Evolution, 61(1): 61-74. doi:10.1016/j.jhevol.2011.02.007
Lycett, S.J. 2008, Acheulean variation and selection: does handaxe symmetry fit neutral expectations? Journal of Archaeological Science, 35(9): 2640-2648. doi:10.1016/j.jas.2008.05.002
Lycett, S.J. & von Cramon-Taubadel, N. 2008, Acheulean variability and hominin dispersals: a model-bound approach. Journal of Archaeological Science, 35(3): 553-562. doi:10.1016/j.jas.2007.05.003
Machin, A.J., Hosfield, R.T. & Mithen, S.J. 2007, Why are some handaxes symmetrical? Testing the influence of handaxe morphology on butchery effectiveness. Journal of Archaeological Science, 34(6): 883-893. doi:10.1016/j.jas.2006.09.008
McNabb, J., Binyon, F. & Hazelwood, L. 2004, The Large Cutting Tools from the South African Acheulean and the Question of Social Traditions. Current Anthropology, 45(5): 653-677. doi:10.1086/423973
McPherron, S.P. 2000, Handaxes as a Measure of the Mental Capabilities of Early Hominids. Journal of Archaeological Science, 27(8): 655-663. doi:10.1006/jasc.1999.0467
Mithen, S.J. 2006, The singing Neanderthals: the origins of music, language, mind, and body. Weidenfeld & Nicolson, London, 374 p.
Pope, M., Russel, K. & Watson, K. 2006, Biface form and structured behaviour in the Acheulean. Lithics, 27: 44-57. URL:
Le Tensorer, J.-M. 2006, Les cultures acheuléennes et la question de l'émergence de la pensée symbolique chez Homo erectus à partir des données relatives à la forme symétrique et harmonique des bifaces. Comptes Rendus Palevol, 5(1-2): 127-135. (in French) ("Emergence of symbolic thought in Acheuean biface formats") doi:10.1016/j.crpv.2005.12.003
Wenban-Smith, F. 2004, Handaxe typology and Lower Palaeolithic cultural development: ficrons, cleavers and two giant handaxes from Cuxton. Lithics, 25: 11-21.
White, M.J. 1998, On the Significance of Acheulean Biface Variability in Southern Britain. Proceedings of the Prehistoric Society, 64: 15-44. doi:10.1017/S0079497X00002164
Wynn, T. & Tierson, F. 1990, Regional Comparison of the Shapes of Later Acheulean Handaxes. American Anthropologist, 92(1): 73-84. doi:10.1525/aa.1990.92.1.02a00050
How to Cite
Cannell, A. (2015). Pattern recognition of universal mathematical constants in Acheulean biface formats. Journal of Lithic Studies, 2(1), 17-44.
Research Articles