Hans Reichenbach: Spacing

Hans Reichenbach was American philosopher. Explore interesting quotes on spacing.
Hans Reichenbach: 82   quotes 3   likes

“…the differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a curve, and cannot lead to an epistemological priority of Euclidean geometry, in contrast to the views of certain authors.”

Hans Reichenbach

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

“Perceptual space is not a special space in addition to physical space, but physical space which we endow with a special subjective metric. …apart from the definition of congruence in physics and that based on perception, there is no third one derived from pure visualization. Any such third definition is nothing but the definition of physical congruence to which our normative function has adjusted the subjective experience of congruence.”

Hans Reichenbach

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

“…introduce the auxiliary concept of first-signal…defined as the fastest message carrier between any two points in space. We now send a first-signal from P, calling the event of departure E1… The event of its arrival at P' is called E'. Simultaneously with the arrival of this signal, another first signal is sent from P'. The arrival of this signal at P is the event E2. …the time interval between E1 and E2 is coordinated to the event E', [E1 is earlier than E' and E2 is later than E'] and every event of this time interval except for the endpoints is inderterminate as to the time order relative to E.”

Hans Reichenbach

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

Departure , Time

“There is no pure visualization in the sense of a priori philosophies; every visualization is determined by previous sense perceptions, and any separation into perceptual space and space of visualization is not permissible, since the specifically visual elements of the imagination are derived from perceptual space. What led to the mistaken conception of pure visualization was rather an improper interpretation of the normative function… an essential element of all visual representations. Indeed, all arguments which have been introduced for the distinction of perceptual space and space of visualization are base on this normative component of the imagination.”

Hans Reichenbach

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

Imagination , Sense

“We are frequently faced with the necessity of looking for the picture required for the visualization of an object, not in the perception of this particular object, but in a different perceptual image. …we can assert the discrepancy between the perceived picture and the objective state. This discrepancy… proves absolutely nothing against the fact that all visualizations are merely sense qualities of the perceptual space. …If the parallelism is …to be visualized, we must supplement our assertion by the description of certain qualities with which we are familiar from perceptual space.”

Hans Reichenbach

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

Sense

“This fact… proves that space measurements are reducible to time measurements. Time is therefore logically prior to space.”

Hans Reichenbach

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

Time

“The surfaces of three-dimensional space are distinguished from each other not only by their curvature but also by certain more general properties. A spherical surface, for instance, differs from a plane not only by its roundness but also by its finiteness. Finiteness is a holistic property. The sphere as a whole has a character different from that of a plane. A spherical surface made from rubber, such as a balloon, can be twisted so that its geometry changes…. but it cannot be distorted in such a way as that it will cover a plane. All surfaces obtained by distortion of the rubber sphere possess the same holistic properties; they are closed and finite. The plane as a whole has the property of being open; its straight lines are not closed. This feature is mathematically expressed as follows. Every surface can be mapped upon another one by the coordination of each point of one surface to a point of the other surface, as illustrated by the projection of a shadow picture by light rays. For surfaces with the same holistic properties it is possible to carry through this transformation uniquely and continuously in all points. Uniquely means: one and only one point of one surface corresponds to a given point of the other surface, and vice versa. Continuously means: neighborhood relations in infinitesimal domains are preserved; no tearing of the surface or shifting of relative positions of points occur at any place. For surfaces with different holistic properties, such a transformation can be carried through locally, but there is no single transformation for the whole surface.”

Hans Reichenbach

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

Way , Mathematics , Tear , Light

“Light signals alone provide the metrical structure of the four-dimensional space-time continuum. The construction may be called light axioms.”

Hans Reichenbach

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

Light , Time

“Clocks are inherently four-dimensional instruments, since the endpoints of their unit distances are events. Measuring rods, on the other hand, are three-dimensional measuring instruments; their end points are space points and they can be changed into four-dimensional measuring instruments only if events are produced at their end points according to a special rule.”

Hans Reichenbach

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

Change

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

Problem , Time

“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)

Music , Color , Mathematics , Thinking

“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

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

Mathematics , Understanding , Science

“The surfaces of three-dimensional space are distinguished from each other not only by their curvature but also by certain more general properties. A spherical surface, for instance, differs from a plane not only by its roundness but also by its finiteness. Finiteness is a holistic property.”

Hans Reichenbach

The sphere as a whole has a character different from that of a plane. A spherical surface made from rubber, such as a balloon, can be twisted so that its geometry changes. ...but it cannot be distorted in such a way as that it will cover a plane. All surfaces obtained by distortion of the rubber sphere possess the same holistic properties; they are closed and finite. The plane as a whole has the property of being open; its straight lines are not closed. This feature is mathematically expressed as follows. Every surface can be mapped upon another one by the coordination of each point of one surface to a point of the other surface, as illustrated by the projection of a shadow picture by light rays. For surfaces with the same holistic properties it is possible to carry through this transformation uniquely and continuously in all points. Uniquely means: one and only one point of one surface corresponds to a given point of the other surface, and vice versa. Continuously means: neighborhood relations in infinitesimal domains are preserved; no tearing of the surface or shifting of relative positions of points occur at any place. For surfaces with different holistic properties, such a transformation can be carried through locally, but there is no single transformation for the whole surface.
The Philosophy of Space and Time (1928, tr. 1957)