Hans Reichenbach - Space Quotes

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

Hans Reichenbach
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
This fact... proves that space measurements are reducible to time measurements. Time is therefore logically prior to space.

Hans Reichenbach
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
It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.

Hans Reichenbach