An Essay On the Foundations of Geometry
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And how is superposition necessary, or even possible ? A colour is fixed by its position in the spectrum : two lines in the same spectrum cannot be superposed, and two lines in different spectra need not be — their positions in their respective spectra suffice, or even, roughly, their immediate sense -quality. The fact is, Riemann had space in his mind from the start, and many of the properties, which he enunciates as belonging to all manifolds, belong, as a matter of fact, only to space. It is... far from clear what the magnitudes are which the various deter- minations make possible. Do these magnitudes measure the elements of the manifold, or the relations between elements ? This is surely a very fundamental point, but it is one which Riemann never touches on. In the former case, the super- position which he speaks of becomes unnecessary, since the magnitude is inherent in the element considered. We do not require superposition to measure quantities corresponding to different tones or colours ; these can be discovered by analysis of single tones or colours.
What to read after An Essay On the Foundations of Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Russell Bertrand to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
And how is superposition necessary, or even possible ? A colour is fixed by its position in the spectrum : two lines in the same spectrum cannot be superposed, and two lines in different spectra need not be — their positions in their respective spectra suffice, or even, roughly, their immediate sense -quality. The fact is, Riemann had space in his mind from the start, and many of the properties, which he enunciates as belonging to all manifolds, belong, as a matter of fact, only to space. It is... far from clear what the magnitudes are which the various deter- minations make possible. Do these magnitudes measure the elements of the manifold, or the relations between elements ? This is surely a very fundamental point, but it is one which Riemann never touches on. In the former case, the super- position which he speaks of becomes unnecessary, since the magnitude is inherent in the element considered. We do not require superposition to measure quantities corresponding to different tones or colours ; these can be discovered by analysis of single tones or colours.
What to read after An Essay On the Foundations of Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Russell Bertrand to read onlineMoreLess
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