„That the existence of these motions (the "axiom of free mobility") is a desideratum, if not… a necessity, for a geometry applicable to physical space, has been forcefully argued on a priori grounds by von Helmholtz, Whitehead, Russell and others; for only in a homogeneous and isotropic space can the traditional concept of a rigid body be maintained.“

Geometry as a Branch of Physics (1949)

Citações relacionadas

Hans Reichenbach photo
Newton Lee photo
Hans Reichenbach photo
Willem de Sitter photo
William Kingdon Clifford photo
Philip Warren Anderson photo
Paul Carus photo

„The truth is that other systems of geometry are possible, yet after all, these other systems are not spaces but other methods of space measurements. There is one space only, though we may conceive of many different manifolds, which are contrivances or ideal constructions invented for the purpose of determining space.“

—  Paul Carus American philosopher 1852 - 1919

Science, Vol. 18 (1903), p. 106, as reported in Memorabilia Mathematica; or, The Philomath's Quotation-Book https://archive.org/stream/memorabiliamathe00moriiala#page/81/mode/2up, (1914), by Robert Edouard Moritz, p. 352

Thomas Young (scientist) photo
Hans Reichenbach photo
Frank Wilczek photo
Gerald James Whitrow photo

„Galileo had raised the concepts of space and time to the status of fundamental categories by directing attention to the mathematical description of motion.“

—  Gerald James Whitrow British mathematician 1912 - 2000

The Structure of the Universe: An Introduction to Cosmology (1949)
Contexto: Galileo had raised the concepts of space and time to the status of fundamental categories by directing attention to the mathematical description of motion. The midiaevel qualitative method had made these concepts relatively unimportant, but in the new mathematical philosophy the external world became a world of bodies moving in space and time. In the Timaeus Plato had expounded a theory that outside the universe, which he regarded as bounded and spherical, there was an infinite empty space. The ideas of Plato were much discussed in the middle of the seventeenth century by the Cambridge Platonists, and Newton's views were greatly influenced thereby. He regarded space as the 'sensorium of God' and hence endowed it with objective existence, although he confessed that it could not be observed. Similarly, he believed that time had an objective existence independent of the particular processes which can be used for measuring it.<!--p.46

Hans Reichenbach photo
Pythagoras photo

„There is geometry in the humming of the strings. There is music in the spacings of the spheres.“

—  Pythagoras ancient Greek mathematician and philosopher -585 - -495 a.C.

As quoted in the preface of the book entitled Music of the Spheres by Guy Murchie (1961)
The Golden Verses

„The philosophy of the foundations of probability must be divorced from mathematics and statistics, exactly as the discussion of our intuitive space concept is now divorced from geometry.“

—  William Feller Croatian-American mathematician 1906 - 1970

Introduction, The Nature of Probability Theory, p. 3.
An Introduction To Probability Theory And Its Applications (Third Edition)

Robert Grosseteste photo
Arundhati Roy photo

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