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      Handbook of the Mathematics of the Arts and Sciences 

      Projections of Knots and Links

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      Springer International Publishing

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          U-series dating of Paleolithic art in 11 caves in Spain.

          Paleolithic cave art is an exceptional archive of early human symbolic behavior, but because obtaining reliable dates has been difficult, its chronology is still poorly understood after more than a century of study. We present uranium-series disequilibrium dates of calcite deposits overlying or underlying art found in 11 caves, including the United Nations Educational, Scientific, and Cultural Organization (UNESCO) World Heritage sites of Altamira, El Castillo, and Tito Bustillo, Spain. The results demonstrate that the tradition of decorating caves extends back at least to the Early Aurignacian period, with minimum ages of 40.8 thousand years for a red disk, 37.3 thousand years for a hand stencil, and 35.6 thousand years for a claviform-like symbol. These minimum ages reveal either that cave art was a part of the cultural repertoire of the first anatomically modern humans in Europe or that perhaps Neandertals also engaged in painting caves.
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            Symmetry

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              A female figurine from the basal Aurignacian of Hohle Fels Cave in southwestern Germany.

              Despite well over 100 years of research and debate, the origins of art remain contentious. In recent years, abstract depictions have been documented at southern African sites dating to approximately 75 kyr before present (bp), and the earliest figurative art, which is often seen as an important proxy for advanced symbolic communication, has been documented in Europe as dating to between 30 and 40 kyr bp. Here I report the discovery of a female mammoth-ivory figurine in the basal Aurignacian deposit at Hohle Fels Cave in the Swabian Jura of southwestern Germany during excavations in 2008. This figurine was produced at least 35,000 calendar years ago, making it one of the oldest known examples of figurative art. This discovery predates the well-known Venuses from the Gravettian culture by at least 5,000 years and radically changes our views of the context and meaning of the earliest Palaeolithic art.
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                Book Chapter
                2018
                May 25 2018
                : 1-31
                10.1007/978-3-319-70658-0_16-1
                6c8f4d8f-156a-4c23-b466-31cd881f648e
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