Энтропия– мера беспорядка физической системы; неупорядоченные системы имеют высокую энтропию, а упорядоченные – низкую. Энтропию также можно рассматривать как число способов перестановок, составляющих систему частей (например, молекул) без изменения общих характеристик системы, таких как объем, температура или давление.

[1] Plato, Timaeus, trans. Donald J. Zeyl (Indianapolis: Hackett, 2000), p. 12.

[2] Так в книге. Правильно: «из двадцати треугольников» ( прим. Vadi. Далее множество подобных «тупых» ошибок исправляю в тексте без примечаний)

[3] Ibid., p. 46–47.

[4] Ibid., p. 44.

[5] Max Tegmark (MIT), interview with author, May 16, 2005. (Note: All interviews were conducted by Steve Nadis unless otherwise noted.)

[6] Aristotle, On the Heavens, at Ancient Greek Online Library, http://greektexts.com/library/Aristotle/On_The_Heavens/eng/print/1043.html.

[7] Michio Kaku. Hyperspace(New York: Anchor Books, 1995), p. 34.

[8] H. G. Wells, The Time Machine(1898), available at http://www.bartleby.com/1000/1.html.

[9] Abraham Pais, Subtle Is the Lord(New York: Oxford University Press, 1982), p. 152.

[10] Oskar Klein, “From My Life of Physics,” in The Oskar Klein Memorial Lectures, ed. Gosta Ekspong (Singapore: World Scientific, 1991), p. 110.

[11] Leonard Mlodinow, Euclid’s Window (New York: Simon & Schuster, 2002), p. 231.

[12] Andrew Strominger, “Black Holes and the Fundamental Laws of Nature,” Lecture, Harvard University, Cambridge, MA, April 4, 2007.

[13] Ibid.

[14] Georg Friedrich Bernhard Riemann, “On the Hypotheses Which Lie at the Foundations of Geometry,” lecture, Gottingen Observatory, June 10, 1854.

[15] E. T. Bell, Men of Mathematics(New York: Simon & Schuster, 1965), p. 21.

[16] Leonard Mlodinow, Euclid's Window(New York: Simon & Schuster, 2002), p. xi.

[17] Edna St. Vincent Millay, “Euclid Alone Has Looked on Beauty Bare,” quoted in Robert Osserman, Poetry of the Universe(New York: Anchor Books, 1995), p. 6.

[18] Andre Nikolaevich Kolmogorov, Mathematics of the 19th Century(Birkhauser, 1998).

[19] Deane Yang (Polytechnic Institute of New York University), e-mail letter to author, April 20, 2009.

[20] Mlodinow, Euclid's Window, p. 205.

[21] Brian Greene, The Elegant Universe(New York: Vintage Books, 2000), p. 231.

[22] C. N. Yang. “Albert Einstein: Opportunity and Perception,” speech, 22nd International Conference on the History of Science, Beijing, China, 2005.

[23] Chen Ning Yang, “Einstein’s Impact on Theoretical Physics in the 21st Century,” AAPPS Bulletin15 (February 2005).

[24] Greene, The Elegant Universe, p. 72.

[25] Robert Greene (UCLA), interview with author, March 13, 2008.

[26] Lizhen Ji and Kefeng Liu, “Shing-Tung Yau: A Manifold Man of Mathematics,” Proceedings of Geometric Analysis: Present and Future Conference, Harvard University, August 27-September 1, 2008.

[27] Leon Simon (Stanford University), interview with author, February 6, 2008.

[28] Greene, interview with author, March 13, 2008.

[29] Cameron Gordon (University of Texas), interview with author, March 14, 2008.

[30] Robert Geroch (University of Chicago), interview with author, February 28, 2008.

[31] Edward Witten (Institute for Advanced Study), interview with author, March 31, 2008.

[32] Edward Witten, “A New Proof of the Positive Energy Theorem,” Communications in Mathematical Physics80 (1981): 381–402.

[33] Roger Penrose, “Gravitational Collapse: The Role of General Relativity,” 1969, reprinted in Mathematical Intelligencer30 (2008): 27–36.

[34] Richard Schoen (Stanford University), interview with author, January 31, 2008.

[35] Demetrios Christodoulou, The Formation of Black Holes in General Relativity(Zurich: European Mathematical Society, 2009).

[36] John D. S. Jones, “Mysteries of Four Dimensions,” Nature332 (April 7, 1998): 488–489.

[37] Simon Donaldson (Imperial College), interview with author, April 3, 2008.

[38] Faye Flam, “Getting Comfortable in Four Dimensions,” Science 266 (December 9, 1994): 1640.