Monistic conception of geometry

 Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences
 101-1 ,Vernadskii Ave., Moscow, 119526, Russia
 email: rylov@ipmnet.ru
 Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm
or mirror Web site: http://gasdyn-ipm.ipmnet.ru/~rylov/yrylov.htm

Updated September 15, 2010

abstract

One considers the monistic conception of a geometry, where there is only one fundamental quantity (world function). All other geometrical quantities a derivative quantities (functions of the world function). The monisitc conception of a geometry is compared with pluralistic conceptions of a geometry, where there are several independent fundamental geometrical quantities. A generalization of a  pluralistic conception of the proper Euclidean geometry appears to be inconsistent, if the generalized geometry is  inhomogeneous. In particular, the Riemannian geometry appears to be inconsistent, in general, if it is obtained as a generalization of the pluralistic conception of the Euclidean geometry.

There is text of the paper in English (pdf, ps) and in Russian (ps, pdf)