Notes to pages 238–248 307
- For the non-Euclidean character of color space, see chapter 18.
- Helmholtz 1868; 1882, 2:616 – 617; Pesic 2007 , 50 – 51; see also Heinzmann 2001.
- The second edition (1885) of the Handbuch mentions Riemann and describes color perception as a three-
dimensional manifold comparable to space; Helmholtz 1896 , 336. - For the role of Heinrich Grassmann, see Torretti 1978 , 109; Scholz 1980.
- Helmholtz 1954 , 370, based on the fourth German edition (1877); cf. Helmholtz 1865 , 560; Helmholtz 1870 ,
- See also Vogel 1993 , 273.
- Helmholtz 1954 , 370.
- See Helmholtz 1995 , 76 – 95.
- Quoted in Pesic 2007 , 53 – 70, at 53.
- Ibid. , 64.
- Ibid. , 61.
- Ibid. , 59.
- For Immanuel Kant on space as a manifold, see Critique of Pure Reason B50; see also Lenoir 2006.
- Quoted in Pesic 2007 , 59.
- See Helmholtz 1977 , 159 – 160; Hyder 1999.
- Quoted in Pesic 2007, 68.
- See, e.g., Fullinwider 1990.
- Helmholtz writes his four-dimensional line element as ds 2 = dx 2 + dy 2 + dz 2 + dt 2 , in which he then allows
t to become imaginary ( t = i τ ), so that the four-dimensional manifold is now pseudospherical and hence
ds 2 = dx 2 + dy 2 + dz 2 − d τ 2 , exactly the form of the Lorentzian line-element used by Einstein and Minkowski, if
τ =ct , where c is the speed of light. - Abbott 1992; Pesic 2007 , 54 – 55; Reichenbach 1970, 308.
- See Hawkins 1994 ; 2000 , 124 – 130.
- See Hawkins 2000 , 34 – 42; Rowe 1992. For Clifford ’ s response, see Pesic 2007, 71 – 87.
- Quoted in Pesic 2007 , 109 – 116, at 110.
- Heinzmann 1992 , 2001.
- See Pesic 2007 , 100; for the Poincar é and Klein models, see Rosenfeld 1987 , 236 – 246.
- Einstein 1987 , 1:220.
- Solovine and Einstein 1956 , viii; Holton 1996 , 205; Cahan 2000 , 59 – 74.
- See Stein 1977 ; Carrier 1994 ; Friedman 2002 ; Ferreiros 2006.
- Quoted in Howard 2005 , 34.
- Einstein as quoted in Pesic 2007, 190. The mathematical details not given in his 1854 lecture are provided
in Riemann 1990 , 423 – 436; Farwell and Knee 1990. - Einstein 1987 , 6:569; second Einstein quote from Pesic 2007 , 161.
16 Tuning the Atoms - Sommerfeld 1934 , v.
- Å ngstr ö m 1855 , 327.
- See Pais 1986 , 166 – 205.
- H α 6562.1 Å , H β 4860.7 Å , H γ 4340.1 Å , H δ 4101.2 Å.
- Stoney 1871 , 291.
- Helmholtz 1954 , 23 – 24.