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.

Inhalt

Introduction. I: Biography. A Survey of Graßmann's Ausdehnungslehre; A. Beutelspacher. On Graßmann's Life and His Work as a Mathematics Teacher; H. Schwartze. Remarks on the fate of Graßmann's Nachlaß; G. Schubring. II: Emergence of Graßmann's Ideas and Their Context. The Influence of Graßmann's Theory of Tides on the Ausdehnungslehre; A.C. Lewis. The Influence of Justus Graßmann's Crystallographic Works on Hermann Graßmann; E. Scholz. Geometrical Product - Exponentiation - Evolution. Justus Günther Graßmann and Dynamist Naturphilosophie; M.-L. Heuser. The Cooperation between Hermann and Robert Graßmann on the Foundations of Mathematics; G. Schubring. The Origins of Colorimetry: What did Helmholtz and Maxwell Learn from Graßmann? R.S. Turner. Hermann Graßmann's Contribution to the Construction of a German `Kulturnation' - Scientific School Grammar Between Latin Tradition and French Conceptions; E. Hültenschmidt. III: Historical Influences of Graßmann's Work. The Reception of Graßmann's Mathematical Achievements by A. Clebsch and His School; R. Tobies. The Reception of Graßmann's Work in Germany During the 1870s; D. Rowe. Reception of Graßmann's Ideas in Bohemia; Z. Nádeník. The Influence of Graßmann on Italian Projective n-Dimensional Geometry; A. Brigaglia. Hermann Günther Graßmann and the Theory of Hypercomplex Number Systems; K.-H. Schlote. Basis and Dimension - From Graßmann to Van der Waerden; J.-L. Dorier. Emergence of Vector Calculus in Physics: The Early Decades; K. Reich. Where Does Graßmann Fit in the History of Logic? I. Grattan-Guinness. The Influence of Hermann Günther Graßmann and Robert Graßmann on ErnstSchröder's Algebra of Logic; V. Peckhaus. IV: Influences of Graßmann's Work on Recent Developments in Science. Algebra Graßmann Progressive and Regressive Products and CG-Algebras; A. Brini, A.G. B. Teolis. Graßmann's Vision; D. Hestenes. Graßmann's Dialectics and Category Theory; F.W. Lawvere. Geometry The Completion of Graßmann's Naturwissenschaftliche Methode; A. Swimmer. Graßmannian Manifolds in Geometry; W. Klingenberg. Regressive Products and Bourbaki; A. Zaddach. Physics, Technology £/LIST£ The Graßmann Product in Physics; G. Braunss. Array-Based Logic; O.I. Franksen. An Application of Graßmann Geometry to A Problem in Robotics; J. Pfalzgraf. Index.