„Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i. e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.“

The Philosophy of Space and Time (1928, tr. 1957)

Última atualização 22 de Maio de 2020. História
Hans Reichenbach photo
Hans Reichenbach
professor académico alemão 1891 - 1953

Citações relacionadas

Hans Reichenbach photo
David Hilbert photo
Hermann Grassmann photo
Subrahmanyan Chandrasekhar photo

„all the standard equations of mathematical physics can be separated and solved in Kerr geometry.“

—  Subrahmanyan Chandrasekhar physicist 1910 - 1995

From Chandrasekhar's Nobel lecture, in his summary of his work on black holes; Republished in: D. G. Caldi, ‎George D. Mostow (1989) Proceedings of the Gibbs Symposium: Yale University, May 15-17, 1989 p. 230

Albert Gleizes photo
Jean Metzinger photo
Albert Einstein photo

„Development of Western Science is based on two great achievements, the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (Renaissance). In my opinion one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all.“

—  Albert Einstein German-born physicist and founder of the theory of relativity 1879 - 1955

Letter to J.S. Switzer (23 April 1953), quoted in The Scientific Revolution: a Hstoriographical Inquiry By H. Floris Cohen (1994), p. 234 http://books.google.com/books?id=wu8b2NAqnb0C&lpg=PP1&pg=PA234#v=onepage&q&f=false, and also partly quoted in The Ultimate Quotable Einstein edited by Alice Calaprice (2010), p. 405 http://books.google.com/books?id=G_iziBAPXtEC&lpg=PP1&pg=PA405#v=onepage&q&f=false
1950s

G. H. Hardy photo
Hans Reichenbach photo
Robert Chambers (publisher, born 1802) photo
Charles A. Beard photo
René Descartes photo
Stephen Hawking photo

„Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.“

—  Stephen Hawking British theoretical physicist, cosmologist, and author 1942 - 2018

As quoted in Stephen Hawking: A Biography (2005) by Kristine Larsen, p. 43

Hermann Weyl photo
David Eugene Smith photo
Joseph Louis Lagrange photo

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“