Space and Geometry in the Light of Physiological, Psychological and Physical InquiryOpen Court Publishing Company, 1906 - 144 sider 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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Space and Geometry in the Light of Physiological, Psychological and Physical ... Ernst Mach Uten tilgangsbegrensning - 1906 |
Space and Geometry in the Light of Physiological, Psychological and Physical ... Ernst Mach Uten tilgangsbegrensning - 1906 |
Space and Geometry: In the Light of Physiological, Psychological and ... Ernst Mach Begrenset visning - 2004 |
Vanlige uttrykk og setninger
actually analogous angle-sum animal appear assumption biological Bolyai boundary boundary-line boundary-surface cardinal directions cepts characterized circle coincide conceived constant construction correspond curvature deductions definite determined dimensions direction displacement distance domain doubtless elementary organs elements ence equal Euclid Euclidean geometry example fact Fifth Postulate figures fundamental Gauss geometric concepts geometric space gles Greek Mathematics Herodotus ical ideal images interior angles intersection irritated Leipsic length likewise Lobachévski locative qualities logical manifold mathematician measure ment metric space metrical experiences motion move movement obtained parallel parallelograms perception perpendicular physical experience physicist physiological space plane primitive geometry properties propositions rectangle regard relations retina Riemann right angles rigid bodies rotation Saccheri sations sensational qualities sensations of space sense sensuous sides skin space-sensations spatial sphere straight line surface symmetry tactual space theorem theory three-dimensional space tion triangle Ueber visual space volume
Populære avsnitt
Side 115 - The sum of the angles of a triangle is equal to two right angles and The area of a circle J57tr2are correct only in Euclid.
Side 114 - That if a straight line meet two other straight lines, so as to make the two interior angles on the same side of it, taken together, less than two right angles...
Side 120 - ... assumption that the fourth angle was right, obtuse, or acute. The similarity of figures he finds to be incompatible with the second and third assumptions. The case of the obtuse angle, which requires the sum of the angles of a triangle to exceed 2.R, he discovers to be realized in the geometry of spherical surfaces, in which the difficulty of parallel lines entirely vanishes. This leads him to the conjecture that the case of the acute angle, where the sum of the angles of a triangle is less than...
Side 60 - If a straight line intersect two parallel straight lines, the sum of the interior angles ,on the same side will be equal to two right angles. Let the parallels AB, CD, be...
Side 135 - ... being regarded as more than intellectual scientific experiments and with no idea of being applied to reality. In support of my remark it will be sufficient to advert to the advances made in mathematics by Clifford, Klein, Lie, and others. Seldom have thinkers become so absorbed in revery, or so far estranged from reality, as to imagine for our space a number of dimensions exceeding the three of the given space of sense, or to conceive of representing that space by any geometry that departs appreciably...
Side 63 - Let ABC be a triangle, of which the side AC is greater than the side AB; the angle ABC shall be greater than the angle BCA.
Side 94 - 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.
Side 113 - Yet not only were the ways of research designedly concealed by this artificial method of stringing propositions on an arbitrarily chosen thread of deduction, but the varied organic connection between the principles of geometry was quite lost sight of.1 This system was more fitted to produce narrow-minded and sterile pedants than fruitful, productive investigators.
Side 114 - Euclid easily proves that if a straight line falling on two other straight lines makes the alternate angles equal to each other, the two straight lines will not meet but are parallel.
Side 5 - The sensible space of our immediate perception, which we find ready at hand on awakening to full consciousness, is considerably different from geometrical space. Our geometrical concepts have been reached for the most part by purposeful experience. The space of the Euclidean geometry is everywhere and in all directions constituted alike; it is unbounded and it is infinite in extent. On the other hand, the space of sight, or "visual space...
Referanser til denne boken
Angular Momentum: An Illustrated Guide to Rotational Symmetries for ..., Volum 1 William Jackson Thompson Ingen forhåndsvisning tilgjengelig - 1994 |