# „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.“

1891 - 1953

### „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 Dutch cosmologist 1872 - 1934

### „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 Mathematician and electrical engineer 1865 - 1923

### „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 Belgian theoretical physicist 1953
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

### „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 British mathematician and astronomer 1877 - 1946

### „We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.“

—  Hans Reichenbach American philosopher 1891 - 1953

### „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 American particle physicist and string theorist 1941
"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)

### „Time is not a line but a dimension, like the dimensions of space.“

—  Margaret Atwood Canadian writer 1939
Cat's Eye (1988)

### „Some philosophers have believed that a philosophical clarification of space also provided a solution of the problem of time. Kant presented space and time as analogous forms of visualization and treated them in a common chapter in his major epistemological work. Time therefore seems to be much less problematic since it has none of the difficulties resulting from multidimensionality. Time does not have the problem of mirror-image congruence, i. e., the problem of equal and similarly shaped figures that cannot be superimposed, a problem that has played some role in Kant's philosophy. Furthermore, time has no problem analogous to non-Euclidean geometry. In a one-dimensional schema it is impossible to distinguish between straightness and curvature.... A line may have external curvature but never an internal one, since this possibility exists only for a two-dimensional or higher continuum. Thus time lacks, because of its one-dimensionality, all those problems which have led to philosophical analysis of the problems of space.“

—  Hans Reichenbach American philosopher 1891 - 1953

### „Time and space are finite in extent, but they don't have any boundary or edge. They would be like the surface of the earth, but with two more dimensions.“

—  Stephen Hawking, Black Holes and Baby Universes

### „No man can visualize four dimensions, except mathematically … I think in four dimensions, but only abstractly. The human mind can picture these dimensions no more than it can envisage electricity. Nevertheless, they are no less real than electro-magnetism, the force which controls our universe, within, and by which we have our being.“

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

### „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 German mathematician 1885 - 1955
Introduction<!-- p. 3-4 -->

### „Dada is able to mobilize the optical and dimensional static viewpoint which keeps us imprisoned in our [three-dimensional] illusions. Thus it became possible t0 perceive the entire prism of the world instead of just one facet at a time. In this connection Dada is one of the strongest manifestations of the fourth dimension, transposed onto the subject.... Dada is 'yes-no', a bird on four legs, a ladder without steps, a square without angels. Dada possesses as many positives as negatives. To think that Dada simply means destruction is to misunderstand life, of which Dada is the expression.“

—  Theo van Doesburg Dutch architect, painter, draughtsman and writer 1883 - 1931
Quote from Van Doesburg's article 'What is Dada?????????????????', in Dutch art-magazine De Stijl, The Hague, 1923; as quoted in "Theo van Doesburg", Joost Baljeu, Studio Vista, London 1974, p. 134

### „Material, space, and color are the main aspects of visual art. Everyone knows that there is material that can be picked up and sold, but no one sees space and color. Two of the main aspects of art are invisible; the basic nature of art is invisible.“

—  Donald Judd artist 1928 - 1994
In: Artforum International. Vol. 32 (1994), p. 38

### „The manner in which time and space are bound up with each other in the four-dimensional continuum is variable. It is difficult to express this variability of the cross-connections between space and time in simple language, and different interpretations of it are possible, corresponding to different mathematical transformations of the fundamental line-element, e. g. a different choice of the variable which we interpret as "time." Perhaps the best way we can express it is by saying that the solution of the field-equations of the theory of relativity shows that there is in the universe a tendency to change its scale, which at the present time results in an expansion, but may perhaps at other times become, or have been, a shrinking. This is true of the grand scale model of the universe.“

—  Willem de Sitter Dutch cosmologist 1872 - 1934