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
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Suppose a person of the Fourth Dimension, condescending to visit you, were to say, 'Whenever you open your eyes, you see a Plane (which is of Two Dimensions) and you INFER a Solid (which is of Three); but in reality you also see (though you do not recognize) a Fourth Dimension, which is not colour nor brightness nor anything of the kind, but a true Dimension, although I cannot point out to you its direction, nor can you possibly measure it.' What would you say to such a visitor? Would not you have him locked up? Well, that is my fate: and it is as natural for us Flatlanders to lock up a Square for preaching the Third Dimension, as it is for you Spacelanders to lock up a Cube for preaching the Fourth. Alas, how strong a family likeness runs through blind and persecuting humanity in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes — we are all liable to the same errors, all alike the Slaves of our respective Dimensional prejudices, as one of your Spaceland poets has said —
Edwin Abbot
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
The 4D style, or cosmic comics and relativistic humor, is based on Einstein's theory of relativity and I came up with it 20 years ago. 4D works use the idea of the fourth dimension and time, playing on such surrealistic and amazing subjects as motion relativity, space curvature and time dilation.
Javad Alizadeh
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
Dada is able to mobilize the optical and dimensional static viewpoint which keeps us imprisoned in our (three-dimensional) illusions. Thus it became possible tp 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
Reichenbach, Hans
Reinfeldt, Fredrik
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