Music and the Making of Modern Science
232 Chapter 15 had been revealed decades before by the work of Gauss, Nicolai Ivanovich Lobachevsky, and J á nos B ó lyai. Indee ...
Riemann and the Sound of Space 233 initiative and the premier unsolved mathematical problem up to the present day.^11 This, by i ...
234 Chapter 15 ‘ poetry of hypothesis ’ ), but rather afterwards emphasize the conditions that must be met to account for what t ...
Riemann and the Sound of Space 235 Riemann ’ s analytic program required that “ we must now derive from the empirically known fu ...
236 Chapter 15 to move in it as continuously, monodromously, and freely, as do bodies in actual space? Answer, expressed accordi ...
Riemann and the Sound of Space 237 For Helmholtz, questions about “ the origins of spatial intuition in general ” emerge from st ...
238 Chapter 15 matter or a fine point of mathematical rigor, this has deep implications for Einstein ’ s geometric account of gr ...
Riemann and the Sound of Space 239 the work as in some sense still the same, yet we cannot likewise “ transpose ” all the colors ...
240 Chapter 15 For the first time in his writings on the problem of space, Helmholtz described in detail non-Euclidean geometrie ...
Riemann and the Sound of Space 241 two points with the horizontal distance of two others, because we can apply a measure first t ...
242 Chapter 15 manifold to describe mathematically our visual experience looking “ through a pair of convex spectacles ” that ha ...
Riemann and the Sound of Space 243 light, Helmholtz with its physiology, Einstein with its speed and interactions with matter. B ...
...
By the end of the nineteenth century, the Pythagorean quest might have seemed played out. With Newtonian and Maxwellian physics ...
246 Chapter 16 A B Figure 16.1 (a) Richard Wimmer, Frauenhofer Demonstrating the Spectrograph. (b) Frauenhofer ’ s illustration ...
Tuning the Atoms 247 the spectra induced by electrical sparks in tubes containing various elemental gases, begin- ning with hydr ...
248 Chapter 16 contributions by Gustav Kirchhoff, Robert Bunsen, and others).^3 But that still avoids the question why elemental ...
Tuning the Atoms 249 one of the motions within the molecules of hydrogen. ” He notes that many other possible “ overtones ” of t ...
250 Chapter 16 surface areas of our central bodies excite, seems more qualified than any other body to open new vistas in the in ...
Tuning the Atoms 251 squares of the numbers 3, 4, 5, 6, and as denominator one of these less one of the four smaller numbers [i. ...
«
8
9
10
11
12
13
14
15
16
17
»
Free download pdf