Space and Geometry in the Light of Physiological, Psychological and Physical Inquiry

Ernst Mach

janv. 1906 · Open Court Classics

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This historic book may have numerous typos, missing text, images, or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1906. Not illustrated. Excerpt: ... SPACE AND GEOMETRY FROM THE POINT OF VIEW OF PHYSICAL INQUIRY.1 Our notions of space are rooted in our physiological organism. Geometric concepts are the product of the idealization of physical experiences of space. Systems of geometry, finally, originate in the logical classification of the conceptual materials so obtained. All three factors have left their indubitable traces in modern geometry. Epistemological inquiries regarding space and geometry accordingly concern the physiologist, the psychologist, the physicist, the mathematician, the philosopher, and the logician alike, and they can be gradually carried to their definitive solution only by the consideration of the widely disparate points of view which are here offered. Awakening in early youth to full consciousness, we find ourselves in possession of the notion of a space surrounding and encompassing our body, in which space move divers bodies, now altering and now retaining their size and shape. It is impossible for us to ascertain how this notion has been begotten. Only the most thoroughgoing analysis of experiments purposefully and methodically performed has enabled us to conjecture that inborn idiosyncracies of the body have cooperated to this end with simple and crude experiences of a purely physical character. Sensational And Locative Qualties. An object seen or touched is distinguished not only by a sensational quality (as "red," "rough," "cold," etc.), but also by a locative quality (as "to the left," "above," "before," etc.). The sensational quality may remain the same, while the locative quality continuously changes; that is, the same sensuous object may move in space. Phenomena of this kind being again and again induced by physico-physilogical circumstances, it is found that however ...

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Educated by his father, who stressed the importance of carpentry and farming, Ernst Mach received his Ph.D. from the University of Vienna in 1860. Mach made many contributions to science in a variety of fields, but he is best known for his powerful influence on several generations of scientists as a critic of science and as a philosopher. His initial research in experimental psychology revealed the function of the semicircular canals of the ear. Mach is best known in physics for his work on shock waves, which led to the mach number being introduced in 1929 as a measure of speed. The mach number is the ratio of the speed of an object in a fluid to the speed of sound in the fluid. Mach is also known to cosmologists for his controversial statement of the principle of inertia, called Mach's principle. The Mach principle rejected the Newtonian notion of absolute space and time. Mach's elimination of absolute space was part of his more general program in which he hoped to eliminate metaphysics (all those purely "thought-things" that cannot be pointed to in experience) from science. His views influenced the important philosophical movement of logical positivism and also had some impact on scientific practice, especially Einstein in formulating his theory of relativity. Despite his influence, Mach was a radical thinker who never accepted the existence of atoms or Einstein's theory of relativity.