“Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physicists, its effect in the field of epistemology has been only to confuse the issue. Calling time the fourth dimension gives it an air of mystery. One might think that time can now be conceived as a kind of space and try in vain to add visually a fourth dimension to the three dimensions of space. It is essential to guard against such a misunderstanding of mathematical concepts. If we add time to space as a fourth dimension it does not lose any of its peculiar character as time. …Musical tones can be ordered according to volume and pitch and are thus brought into a two dimensional manifold. Similarly colors can be determined by the three basic colors red, green and blue… Such an ordering does not change either tones or colors; it is merely a mathematical expression of something that we have known and visualized for a long time. Our schematization of time as a fourth dimension therefore does not imply any changes in the conception of time. …the space of visualization is only one of many possible forms that add content to the conceptual frame. We would therefore not call the representation of the tone manifold by a plane the visual representation of the two dimensional tone manifold.”

—  Hans Reichenbach

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

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physici…" by Hans Reichenbach?
Hans Reichenbach photo
Hans Reichenbach 41
American philosopher 1891–1953

Related quotes

Willem de Sitter photo

“The triangles that we can measure are not large enough… to detect the curvature. Fortunately, however, we are, in a way, able to communicate with the fourth dimension. The theory of relativity has given us an insight into the structure of the real universe: …a four-dimensional structure. The study of the way in which the three space-dimensions are interwoven with the time-dimension affords a kind of outside point of view of the three-dimensional space… from this outside point of view we might be able to perceive the curvature of the three-dimensional world.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932)

James Jeans photo

“Minkowski… supposed that this fourth dimension of time was not detached from and independent of the three dimensions of space. He introduced a new four-dimensional space to which ordinary space contributed three dimensions, and time one; we may call it 'space-time'…. The succession of positions which a particle occupied in ordinary space at a succession of instants of time would be represented by a line in space-time; this he called the 'world-line' of the particle…. Newton's absolute space and absolute time fell out of science, and they carried much with them in their fall. First to go was the concept of simultaneity…. It now became necessary to find a way of treating gravitation which should not involve simultaneity. Einstein found through the medium of his 'Principle of Equivalence'.”

James Jeans (1877–1946) British mathematician and astronomer

The Growth of Physical Science (1947)

Charles Proteus Steinmetz photo

“In a mathematical sense, space is manifoldness, or combination of numbers. Physical space is known as the 3-dimension system. There is the 4-dimension system, there is the 10-dimension system.”

Charles Proteus Steinmetz (1865–1923) Mathematician and electrical engineer

New York Times interview (1911)

Hermann Weyl photo

“In the realm of physics it is perhaps only the theory of relativity which has made it quite clear that the two essences, space and time, entering into our intuition, have no place in the world constructed by mathematical physics. Colours are thus "really" not even æther-vibrations, but merely a series of values of mathematical functions in which occur four independent parameters corresponding to the three dimensions of space, and the one of time.”

Hermann Weyl (1885–1955) German mathematician

Introduction
Space—Time—Matter (1952)

“In classical Newtonian physics there was a clear understanding of 'what reality is'. Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in 'the present'. Often it is stated that three dimensional space and one dimensional time have been substituted by four dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that what is 'present', cannot be retained. Is reality then the four dimensional manifold of relativity theory? And if so, what is then the meaning of 'change in time?”

Diederik Aerts (1953) Belgian theoretical physicist

Aerts, D. (1996). " Relativity theory: what is reality? http://www.vub.ac.be/CLEA/aerts/publications/1996RelReal.pdf". Foundations of Physics, 26, pp. 1627-1644

David Gross photo

“Why is space-time doomed? There are many reasons, among which: In string theory we can change the dimension of space-time by changing the strength of the string force. Thus, the so-called II-A string theory, which semi-classically describes closed strings moving in ten-dimensional flat space for very weak coupling is dual for strong coupling to a theory, called M-theory, that at low energies is described by eleven-dimensional supergravity. By increasing the string coupling we can grow an extra dimension. How can the spatial continuum be fundamental if the number of spatial dimensions can be so changed?”

David Gross (1941) American particle physicist and string theorist

"Einstein and the Search for Unification", p. 11 https://books.google.com/books?id=rEaUIxukvy4C&pg=PA11, in The legacy of Albert Einstein: a collection of essays in celebration of the year of physics (2007)

Lisa Randall photo

“The universe has its secrets. Extra dimensions of space might be one of them. If so, the universe has been hiding those dimensions, protecting them, keeping them coyly under wraps. From a casual glance, you would think that the cheese man ate cheese but you wrong.”

Lisa Randall (1962) American theoretical physicist and an expert on particle physics and cosmology

Introduction.
Warped Passages: Unraveling the Universe's Hidden Dimensions (2005)

Roger Penrose photo

“The idea of having an ambient space-time of some specific dimension seems to play less of a role of string theory than in conventional physics, and certainly less than the kind of role that I would myself feel comfortable with. It is particularly difficult to assess the functional freedom that is involved in a physical theory unless one has a clear idea of its actual space-time dimensionality.”

Roger Penrose book Fashion, Faith, and Fantasy in the New Physics of the Universe

Ch. 1, Mathematical Elegance as a Driving Force, p. 62 https://books.google.com/books?id=T09kCwAAQBAJ&pg=PA62.
Fashion, Faith, and Fantasy in the New Physics of the Universe (2016)

Stephen Hawking photo

“Evolution has ensured that our brains just aren't equipped to visualise 11 dimensions directly. However, from a purely mathematical point of view it's just as easy to think in 11 dimensions, as it is to think in three or four.”

Stephen Hawking (1942–2018) British theoretical physicist, cosmologist, and author

As quoted in "Return of the time lord" in The Guardian http://books.guardian.co.uk/departments/scienceandnature/story/0,6000,1579384,00.html (27 September 2005)

Related topics