Music and the Making of Modern Science

310 Notes to pages 272–282

3. Heisenberg 1971 , 10 – 11.


4. Moore 1989 , 18.


5. Ibid. , 120 – 129. Schr ö dinger ’ s writings on color are collected in MacAdam 1970 , 134 – 193.


6. In 1922, Schr ö dinger also was influenced by Hermann Weyl ’ s work on extending general relativity to a “ gauge
   theory ” including electromagnetism; see O ’ Raifeartaigh 1997 , 77 – 106; Moore 1989 , 146 – 148.


7. Bloch 1976 , 23.


8. Ibid. , 23 – 24.


9. He initially used relativistic expressions and found an equation (now called the Klein – Gordon equation) that
   he could not immediately interpret; in its place, he then put forward a nonrelativistic expression, now called the
   Schr ö dinger equation. See Pais 1986 , 288 – 289.


10. Schr ö dinger 1982 , 1.


11. Schr ö dinger 1928 , 7.


12. Schr ö dinger 1982 , 10.


13. Ibid. , 26.


14. Regarding the problem of visualization, see Pesic 2002 , 97 – 99. A Hilbert space comprises vectors (which
    may be real or complex) having a positive measure of distance (given by their “ inner product ” ) and is complete ,
    meaning that any Cauchy sequence (in which the successive terms become arbitrarily close to each other as the
    sequence progresses) converges to a limit within the space.


15. Dirac 1963, 47; Weyl 2009, 11 – 12; Holton 1988.


16. Kramer 1994 ; Kramer et al. 2010 ; Hermann, Hunt, and Neuhoff 2011 ; Volmar 2012, 2013a,b ; Supper 2012.


17. “ Ode to a Grecian Urn, ” lines 11 – 14. For a later physicist ’ s expression of such longings, see Wilczek and
    Devine 1988.


18. For an overview, see Vecchia 2008 ; Cappelli et al. 2012 , 221 – 235. In a 1730 letter to Goldbach, Euler first
    defined what was only named the “ beta function ” by Jacques Binet in 1839; see Cajori 2011, 271 – 272.
    19 Nambu 2012 , 279; emphasis added. Susskind (2012 ) also relied on the analogy with the harmonic oscillator.
    Nielsen (2012 ) traversed a different, but finally convergent, metaphorical path, realizing that the Feynman
    diagrams for the processes described by the Veneziano amplitude could be understood in terms of the behavior
    of an elastic sheet.


19. In popular writings, Smolin 2006 and Woit 2006 challenge the rhapsodic string encomium of Greene 2000.


20. Erlmann 2010 places this resonance in the larger context of the history of reason.


21. Brann 2011, 42 – 43.


22. I address science and the hiddenness of nature in Pesic 2000.


23. See Susskind 2005 ; Carr 2007.


24. The demiurge even “ outsourced ” to the young gods the creation of human beings; see Timaeus 42d – e.


25. A growing literature considers cosmology in terms of bubbles; see Kleban 2011, Salem 2011.


26. The valuable accounts in Daston and Galison 2007 and Daston and Lunbeck 2011 remain centered on visual
    and material modalities and evidence. The present work may complement these accounts and help situate issues
    of “ objectivity ” and “ observation ” (as post-Kantian concerns) within the larger historical and metaphysical
    framework that aural issues require.


27. Pesic in preparation-b.