Abstract
I always found it an interesting coincidence that the two basic ingredients of modern quantum theory, namely probability and complex numbers, were discovered by the same person, an extraordinary man of many talents, a gambling scholar by the name of Girolamo Cardano.
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Notes
- 1.
Galileo Galilei was explicitly asked, by one of the gambling noblemen at the court in Florence, to explain this puzzle, and so he did in his brief Considerazioni sopra il Giuoco dei Dadi, written around 1620.
- 2.
For more details, see David (1998).
References
Aaronson, S. (2004). Is quantum mechanics an island in theoryspace? In: A. Khrennikov (Ed.), Proceedings of the Växjö conference, Quantum Theory: Reconsideration of Foundations, (quant-ph 0401062).
Born, M. (1926). Zur Quantenmechanik der Stoßvorgänge. Zeitschrift für Physik, 37, 863–867.
Cardano, G. (1545). Artis magnae, sive de regulis algebrici liber unus. In Cardano 1663. English tanslation by T. Richard Witmer: The Rules of Algebra, (Ars Magna). New York: Dover Books on Mathematics, 2007.
Cardano, G. (1643). De propria vita. Villery, Paris. (Jean Stoner, Trans.). The Book of My Life (De vita propria liber). New York: Review Books, 2002.
Cardano, G. (1663). Opera Omnia Hieronymi Cardani, Mediolanesis, 10 vols. Spoon, Lyons. All 10 volumes can be downloaded from the website of the Philosophy Department, University of Milan (http://www.filosofia.unimi.it/cardano/).
d’Alembert, J. (1754). Croix ou Pile. In L’Encyclopédie, vol. 4. Paris: Ed. Diderot.
David, F. N. (1998). Games, gods and gambling. A history of probability and statistical ideas. New York: Dover Publications.
Deutsch, D. (1999). Quantum theory of probability and decisions. Proceedings of the Royal Society of London, A455, 3129–3137. (quant-ph 9906015).
Gleason, A. (1957). Measures on closed subspaces of a Hilbert space. Journal of Mathematics and Mechanics, 6, 885–894.
Hardy, L. (2001). Quantum theory from five reasonable axioms. (quant-ph 0101012).
Ore, Ø. (1953). Cardano, the gambling scholar. Princeton: Princeton University Press. (Contains an English translation of Liber de ludo aleæ by Sydney H. Gould).
Wallace, D. (2003). Everettian rationality: defending Deutsch’s approach to probability in the Everett interpretation. Studies in the History and Philosophy of Modern Physics, 34, 415–439. (quant-ph 0303050).
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Ekert, A. (2014). Random, Complex, and Quantum. In: Lupacchini, R., Angelini, A. (eds) The Art of Science. Springer, Cham. https://doi.org/10.1007/978-3-319-02111-9_8
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