Hermann Günther Graßmann (1809–1877): Visionary Mathematician, Scientist and Neohumanist Scholar: Papers from a Sesquicentennial Conference

In this volume specialists in mathematics, physics, and linguistics present the first comprehensive analysis of the ideas and influence of Hermann G. Graßmann (1809-1877), the remarkable universalist whose work recast the foundations of these disciplines and shaped the course of their modern development. Front Matter....Pages i-xxx Front Matter....Pages 1-2 A Survey of Grassmann’s Lineale Ausdehnungslehre ....Pages 3-6 On Hermann Grassmann’s Life and His Work as a Mathematics Teacher....Pages 7-18 Remarks on the Fate of Grassmann’s Nachlaß ....Pages 19-26 Front Matter....Pages 27-28 The Influence of Grassmann’s Theory of Tides on the Ausdehnungslehre ....Pages 29-36 The Influence of Justus Grassmann’s Crystallographic Works on Hermann Grassmann....Pages 37-45 Geometrical Product — Exponentiation — Evolution. Justus Günther Grassmann and Dynamist Naturphilosophie ....Pages 47-58 The Cooperation between Hermann and Robert Grassmann on the Foundations of Mathematics....Pages 59-70 The Origins of Colorimetry: What did Helmholtz and Maxwell Learn from Grassmann?....Pages 71-86 Hermann Grassmann’s Contribution to the Construction of a German „Kulturnation“. Scientific School Grammar between Latin Tradition and French Conceptions....Pages 87-113 Front Matter....Pages 115-115 The Reception of H. Grassmann’s Mathematical Achievements by A. Clebsch and His School....Pages 117-130 On the Reception of Grassmann’s Work in Germany during the 1870’s....Pages 131-145 Reception of Grassmann’s Ideas in Bohemia....Pages 147-153 The Influence of H. Grassmann on Italian Projective N -Dimensional Geometry....Pages 155-163 Hermann Günther Grassmann and the Theory of Hypercomplex Number Systems....Pages 165-173 Basis and Dimension — From Grassmann to van der Waerden....Pages 175-196 The Emergence of Vector Calculus in Physics: The Early Decades....Pages 197-210 Where does Grassmann Fit in the History of Logic?....Pages 211-216 The Influence of Hermann Günther Grassmann and Robert Grassmann on Ernst Schröder’s Algebra of Logic....Pages 217-227 Front Matter....Pages 229-230 Grassmann Progressive and Regressive Products and CG-Algebras....Pages 231-242 Grassmann’s Vision....Pages 243-254 Front Matter....Pages 229-230 Grassmann’s Dialectics and Category Theory....Pages 255-264 The Completion of Grassmann’s Natur-Wissenschaftliche Methode ....Pages 265-280 Grassmannian Manifolds in Geometry....Pages 281-283 Regressive Products and Bourbaki....Pages 285-295 The Grassmann Product in Physics....Pages 297-301 Invariance under Nesting — An Aspect of Array-Based Logic with Relation to Grassmann and Peirce....Pages 303-335 An Application of Grassmann Geometry to a Problem in Robotics....Pages 337-343 Back Matter....Pages 345-369