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Becker–Blaschke problem of space |
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| Institution: | 1. Aix-Marseille Université, CEPERC, UMR 7304. 29, avenue Robert Schuman 13621 Aix-en-Provence Cedex 1. France;2. Zukunftskolleg, University of Konstanz, Box 216, 78457 Konstanz, Germany;1. Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA;2. Division of Science, New York University Abu Dhabi (NYUAD), Saadiyat Island, P.O. Box 129188 Abu Dhabi, United Arab Emirates;1. Biozentrum, University of Basel, Klingelbergstrasse 50/70, 4056 Basel, Switzerland;2. Quantitative Gene Expression Group, MRC Clinical Sciences Centre, Imperial College London, Hammersmith Hospital Campus, Du Cane Road, London W12 0NN, UK |
| Abstract: | In a letter to Weyl, Becker proposed a new way to solve the problem of space in the relativistic context. This is the result of Becker?s encounter with the two traditions of thinking about space: Husserlian transcendental phenomenology and Blaschke?s equiaffine differential geometry. I reconstruct the mathematical content of the Becker–Blaschke solution to the problem of space and highlight the philosophical ideas that guide this construction. This permits me to underline some common properties of Riemannian and Minkowskian manifolds in terms of an unusual notion of isotropy. Finally, I will use this construction as a support to analyze several philosophical differences between Weyl?s and Becker?s proposals. |
| Keywords: | Problem of space Phenomenology Affine differential geometry Oskar Becker Wilhelm Blaschke Hermann Weyl |
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