Is God a Mathematician_ - Mario Livio [130]
Since I have already discussed pure Platonism: For another excellent discussion of many of the topics in the present book, see Barrow 1992.
Tegmark argues that: Tegmark 2007a, b.
in response to a similar assertion: Changeux and Connes 1995.
concluded in his 1997 book: Dehaene 1997.
Dehaene and his collaborators: Dehaene et al. 2006.
Not all cognitive scientists agree: See Holden 2006, for example.
provided the following observation: Changeux and Connes 1995.
the most categorical statement: Lakoff and Núñez 2000.
Neuroscientists have also identified: See Ramachandran and Blakeslee 1999, for instance.
cognitive neuroscientist Rosemary Varley: Varley et al. 2005; Klessinger et al. 2007.
Here, again, is how Atiyah argues: Atiyah 1995.
Since the nineteenth century: For a very detailed description of the Golden Ratio, its history and properties, see Livio 2002, and also Herz-Fischler 1998.
Prime numbers as a concept: A good discussion of these ideas is provided in an article by Yehuda Rav in Hersh 2000.
Anthropologist Leslie A. White: White 1947.
drew attention in the 1960s to the fact: For a popularized description see Hockett 1960.
The former property represents the ability: For a readable discussion of language and the brain see Obler and Gjerlow 1999.
are also characteristic of mathematics: The similarities between language and mathematics are also discussed by Sarrukai 2005 and Atiyah 1994.
Noam Chomsky published his revolutionary work: Chomsky 1957. or more on linguistics, an excellent review can be found in Aronoff and Rees-Miller 2001. A popularized, very interesting perspective is given in Pinker 1994.
Computer scientist Stephen Wolfram argued: Wolfram 2002.
Astrophysicist Max Tegmark argues: Tegmark identified four distinct types of parallel universes. In “Level I,” there are universes with the same laws of physics but different initial conditions. In “Level II,” there are universes with the same equations of physics but perhaps different constants of nature. “Level III” employs the “many worlds” interpretation of quantum mechanics, and in “Level IV,” there are different mathematical structures. Tegmark 2004, 2007b.
to contradict what has become known as the principle of mediocrity: For an excellent discussion of this topic see Vilenkin 2006.
adopt an intermediate position known as realism: Putnam 1975.
Let me first briefly review: There are other opinions that I do not discuss. For instance, Steiner (2005) argues that Wigner does not show that the examples that he gives for “unreasonable effectiveness” have anything to do with the fact that the concepts are mathematical.
Physics Nobel laureate David Gross writes: Gross 1988. For further discussion of the relationship between mathematics and physics, see Vafa 2000.
Sir Michael Atiyah, whose views on the nature: Atiyah 1995; see also Atiyah 1993.
mathematician and computer scientist Richard Hamming: Hamming 1980.
A similar interpretation was proposed: Weinberg 1993.
Gelfand was once quoted: In Borovik 2006.
Raskin concluded that: Raskin 1998.
Hersh proposed that in the spirit: Excellent article by Hersh in Hersh 2000.
Kepler used a huge body of data: Kepler’s own books, reprinted as Kepler 1981 and 1997, make for very interesting reading in the history of science. Excellent biographies include Caspar 1993 and Gingerich 1973.
the orbits of the planets may eventually: For a review, see Lecar et al. 2001.
The answer is actually simpler: An interesting discussion of the utility of mathematics appears in Raymond 2005. Insightful perspectives on Wigner’s enigma are also found in Wilczek 2006, 2007.
Bertrand Russell in The Problems of Philosophy: Russell 1912.
BIBLIOGRAPHY
Aczel, A. D. 2000. The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity (New York: Four Walls Eight Windows).