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Published online by Cambridge University Press:  18 February 2024

Dan Gusfield
Dan Gusfield
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University of California, Davis
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Proven Impossible
Elementary Proofs of Profound Impossibility from Arrow, Bell, Chaitin, Gödel, Turing and More
 , pp. 240 - 245
Publisher: Cambridge University Press
Print publication year: 2024

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References

[1]Aaronson, S.. Quantum Computing Since Democritus. Cambridge University Press, 2013.CrossRefGoogle Scholar
[2]Ackerman, M.. Towards Theoretical Foundations of Clustering. PhD thesis, Department of Computer Science, University of Waterloo, 2012.Google Scholar
[3]Ackerman, M. and Ben-David, S.. Measures of clustering quality: A working set of axioms for clustering. Proceedings of Neural Information Processing Systems 21, Vancouver Canada, 2008.Google Scholar
[4]Arrow, K.. A difficulty in the concept of social welfare. Journal of Political Economy, 58:328–346, 1950.CrossRefGoogle Scholar
[5]Arrow, K.. Social Choice and Individual Values (1st edition). Chapman and Hall, 1951.Google Scholar
[6]Arrow, K.. Social Choice and Individual Values (2nd edition). Yale University Press, 1963.Google Scholar
[7]Attiya, A. and Ellen, F.. Impossibility Results for Distributed Computing. Morgan & Claypool, 2014.CrossRefGoogle Scholar
[8]Baez, J.. Surprises in logic, 2016. https://math.ucr.edu/home/baez/surprises.html.Google Scholar
[9]Ball, P.. Beyond Weird. The University of Chicago Press, 2018.CrossRefGoogle Scholar
[10]Barrow, J. D.. Impossibility: The Limits of Science and the Science of Limits. Oxford University Press, 1999.CrossRefGoogle Scholar
[11]Becker, A.. What Is Real? The Unfinished Quest for the Meaning of Quantum Physics. Basic Books, 2018.Google Scholar
[12]Beeson, M.. Discussion of incompleteness. Slides for a course on incompleteness and undecidability, lecture 17, Stanford University. www.michaelbeeson.com/teaching/StanfordLogic/Lecture17Slides.pdf.Google Scholar
[13]Bell, J. S.. On the Einstein Podolsky Rosen paradox. Physics, 1:195–200, 1964.CrossRefGoogle Scholar
[14]Bell, J. S.. Bertlmann’s socks and the nature of reality. Journal De Physique, 42:C2–41 C2–62, 1981.Google Scholar
[15]Bell, J. S.. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press, 1987.Google Scholar
[16]Berto, F.. There’s Something about Gödel. Wiley-Blackwell, 2009.CrossRefGoogle Scholar
[17]Boolos, G.. A new proof of the Gödel incompleteness theorem. Notices of the American Mathematical Society, 36:388–390, 1989.Google Scholar
[18]Brown, A.. The weird, but true, evidence for ‘spooky action’ at a distance (Kavli Hangout). January 8, 2016 www.space.com/31562-weird-universe-revealed-in-quantum-entanglementbreakthrough.htmlGoogle Scholar
[19]Brubaker, B.. How Bell’s theorem proved “spooky action at a distance” is real. Quanta Magazine; July 20, 2021; quantamagazine.org.Google Scholar
[20]Budiansky, S.. Journey to the Edge of Reason: The Life of Kurt Gödel. Oxford University Press, 2021.Google Scholar
[21]Calder, A.. Constructive mathematics. Scientific American, 146–171, October 1 1979.CrossRefGoogle Scholar
[22]Chaitin, G. J.. Computational complexity and Gödel’s incompleteness theorem. ACM SIGACT News, 9:11–12, 1971.CrossRefGoogle Scholar
[23]Chaitin, G. J.. Gödel’s theorem and information. International Journal of Theoretical Physics, 22:941–954, 1982.CrossRefGoogle Scholar
[24]Clauser, J.. Phone interview with John Clauser on the day the 2022 Nobel prizes in physics were announced, 2022. www.youtube.com/watch?v=ZYZiLX2uibM.Google Scholar
[25]Clauser, J., Horne, M., Shimony, A., and Holt, R.. Proposed experiment to test local hidden-variable theories. Physical Review Letters, 23:880–884, 1969.CrossRefGoogle Scholar
[26]Coy, P.. The super bowl can teach us about incompatible incentives. The New York Times, February 15, 2023.Google Scholar
[27]Cubitt, T. S., Gu, M., Perales, A., Pérez-Garcia, D., and Wolf, M. M.. Undecidability in physics: A quantum information perspective, 2022 (in preparation).Google Scholar
[28]Cubitt, T. S., Pérez-Garcia, D., and Wolf, M. M.. Undecidability of the spectral gap. Nature, 528:207–211, 2015.CrossRefGoogle Scholar
[29]Cubitt, T. S., Pérez-García, D., and , M. M. Wolf. The unsolvable problem. Scientific American, 319:28–37, 2018.CrossRefGoogle Scholar
[30]Davis, M. and Hersh, R.. Hilbert’s 10th problem. Scientific American, 229:84–91, 1973.CrossRefGoogle Scholar
[31]Dehlinger, D. and Mitchell. Entangled photons, M., nonlocality, and Bell inequalities in the undergraduate laboratory. American Journal of Physics, 70:903–910, 2002.CrossRefGoogle Scholar
[32]d’Espagnat, B.. Quantum theory and reality. Scientific American, 241:158–181, November 1979.CrossRefGoogle Scholar
[33]Einstein, A., Podolsky, B., and Rosen, N.. Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47:777–779, 1935.CrossRefGoogle Scholar
[34]Eisert, J., Muller, M. P., and Gogolin, C.. Quantum measurement occurrence is undecidable. Physical Review Letters 108, 260501, 2012.CrossRefGoogle ScholarPubMed
[35]Ekert, A.. Quantum cryptography based on Bell’s theorem. Physical Review Letters, 67:661, 1991.CrossRefGoogle ScholarPubMed
[36]Elbroch, L., Levy, M., Lubell, M., Quigley, H., and Caragiulo, A.. Adaptive social strategies in a solitary carnivore. Science Advances, 3:e1701218, 2017.CrossRefGoogle Scholar
[37]Ellenberg, J.. Does Gödel matter?, March 10, 2005. Slate Magazine. slate.com/human-interest/2005/03/the-romantic-s-favorite-mathematician.html.Google Scholar
[38]Fisher, R. A.. Statistical Methods and Scientific Inference. Oliver and Boyd, 1956.Google Scholar
[39]Franzen, T.. Gödel’s Theorem: An Incomplete Guide to Is Use and Abuse. CRC Press, 2005.CrossRefGoogle Scholar
[40]Freedman, S. J. and Clauser, J. F.. Experimental test of local hidden-variable theories. Physical Review Letters, 28:938–941, 1972.CrossRefGoogle Scholar
[41]Geanakoplos, J.. Three brief proofs of Arrow’s impossibility theorem. Economic Theory, 26:211–215, 2005.CrossRefGoogle Scholar
[42]Gilder, L.. The Age of Entanglement. Vintage, 2009.Google Scholar
[43]Gill. Statistics, R. D., causality and Bell’s theorem. Statistical Science, 29: 512–528, 2014.CrossRefGoogle Scholar
[44]Girvan, M. and Newman, M.. Community structure in social and biological networks. Proceedings of the National Academy of Sciences (USA), 99:7821–7826, 2002.CrossRefGoogle ScholarPubMed
[45]Gödel, K.. Uber formal unentscheidbare Sätze der Principia Mathematica und Verwandter, Systeme I. Montshefte für Mathematik und Physics, 38:173–198, 1931.CrossRefGoogle Scholar
[46]Greenberger, D. M., Horne, M., Shimony, A., and Zeilinger, A.. Bell’s theorem without inequalities. American Journal of Physics, 58:1131–1143, 1990.CrossRefGoogle Scholar
[47]Greenstein, G.. Quantum Strangeness: Wrestling with Bell’s Theorem and the Ultimate Nature of Reality. MIT Press, 2019.CrossRefGoogle Scholar
[48]Gusfield, D.. Integer Linear Programming in Computational and Systems Biology: An Entry-Level Text and Course. Cambridge University Press, 2019.CrossRefGoogle Scholar
[49]Hardy, L.. Non-locality for two particles without inequalities for almost all entangled states. Physical Review Letters, 71:1665–1668, 1993.CrossRefGoogle Scholar
[50]Havil, J.. Impossible? Surprising Solutions to Counterintuitive Conundrums. Princeton Press, 2008.Google Scholar
[51]Hofstadter, D.. Gödel, Escher and Bach. Basic Books, 1979.Google Scholar
[52]Hofstadter, D.. I Am a Strange Loop. Basic Books, 2007.Google Scholar
[53]Ing, S.. Stalin and the Scientists. Atlantic Monthly Press, 2016.Google Scholar
[54]Jaynes. Clearing up mysteries: The original goal. In J. Skilling, E. T., editor, Maximum Entropy and Bayesian Methods, pages 127. Kluwer Academic Publishers, 1989.Google Scholar
[55]Jaynes, E. T.. Probability Theory: The Logic of Science. Cambridge University Press, 2003.CrossRefGoogle Scholar
[56]Johannes, B., Cubitt, T. S., Lucia, A., and Pérez-Garcia, D.. Undecidability of the spectral gap in one dimension. Physical Review X (online), 10, 2020. https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.031038.CrossRefGoogle Scholar
[57]Kleinberg, J.. An impossibility theorem for clustering. In Advances in Neural Information Processing, 2002, pages 463–470, 2002.Google Scholar
[58]Kolmogorov, A. N.. Three approaches to the quantitative definition of information. Problems in Information Transmission, 1:1–7, 1965.Google Scholar
[59]Kritchman, S. and Raz, R.. The surprise examination paradox and the second incompleteness theorem. Notices of the AMS, 57:1454–1458, 2010.Google Scholar
[60]Lafitte, G.. Gödel incompleteness revisited. Journées Automates Cellulaires, pages 74–89, 2008.Google Scholar
[61]Lewis-Pye, A. and Rougharden, T.. Resource pools and the CAP theorem, 2020. arXiv:2006.10698v1.Google Scholar
[62]Liben-Nowell, D.. Connecting Discrete Mathematics and Computer Science. Cambridge University Press, 2022.CrossRefGoogle Scholar
[63]Lindsay, G.. Models of the Mind. Bloomsbury Sigma, 2021.CrossRefGoogle Scholar
[64]Lipton, R.. The P = NP Question and Gödel’s Lost Letter. Springer, 2010.CrossRefGoogle Scholar
[65]Livio, M.. The Equation That Could Not Be Solved. Simon and Schuster, 2005.Google Scholar
[66]Lloyd, S.. On the uncomputability of the spectral gap, 2016. arXiv preprint arXiv:1602.05924.Google Scholar
[67]Lynch, N.. A hundred impossibility proofs for distributed computing. In Proceedings of the Eighth Annual ACM Symposium on Principles of Distributed Computing, pages 1–28, 1989.CrossRefGoogle Scholar
[68]Mermin, N. D.. Is the moon there when nobody looks? Reality and the quantum theory. Physics Today, 38:38–47, 1985.CrossRefGoogle Scholar
[69]Mermin, N. D.. Quantum mysteries revisited. American Journal of Physics, 58:731–734, 1990.CrossRefGoogle Scholar
[70]Mermin, N. D.. What’s wrong with these elements of reality? Physics Today, 43:9–11, 1990.CrossRefGoogle Scholar
[71]Mermin, N. D.. Hidden variables and the two theorems of John Bell. Reviews of Modern Physics, 65:38–47, 1993.CrossRefGoogle Scholar
[72]Mermin, N. D.. Quantum mysteries refined. American Journal of Physics, 62:880–887, 1994.CrossRefGoogle Scholar
[73]Mermin, N. D.. What’s wrong with this quantum world? Physics Today, 57: 10–11, 2004.CrossRefGoogle Scholar
[74]Mermin, N. D.. Quantum Computer Science. Cambridge University Press, 2007.CrossRefGoogle Scholar
[75]Moore, C.. Unpredictability and undecidability in dynamical systems. Physical Review Letters, 64:2354, 1990.CrossRefGoogle ScholarPubMed
[76]Nadlinger, D. P. et al. Experimental quantum key distribution certified by Bell’s theorem. Nature, 607:682–686, 2022.CrossRefGoogle ScholarPubMed
[77]Nagel, E. and Newman, J. R.. Gödel’s Proof. New York University Press, 1958.Google Scholar
[78]Newman, M.. Modularity and community structure in networks. Proceedings of the National Academy of Sciences (USA), 103:8577–8582, 2006.CrossRefGoogle ScholarPubMed
[79]Nielsen, M. and Chuang, I.. Quantum Computation and Quantum Information. Cambridge University Press, 2000.Google Scholar
[80]Nigro, S.. Why evolutionary theories are unbelievable. The Linacre Quarterly, 71, 2004. Available at: http://epublications.marquette.edu/lnq/vol71/iss1/7.CrossRefGoogle Scholar
[81]Oberhoff, S.. Incompleteness Ex Machina. Bulletin of the European Association for Theoretical Computer Science, (128), 2019.Google Scholar
[82]Pais, A.. Subtle Is the Lord: The Science and the Life of Albert Einstein. Oxford University Press, 1982.Google Scholar
[83]Penrose, R.. The Emperor’s New Mind: Concerning Computers, Minds and the Laws of Physics. Oxford University Press, 1989.CrossRefGoogle Scholar
[84]Phys.org. Quantum physics problem proved unsolvable: Gödel and Turing enter quantum physics, December 9, 2015. https://phys.org/news/2015-12-quantum-physics-problem-unsolvable-godel.html.Google Scholar
[85]Poonen, B.. Undecidable problems: A sampler. In Kennedy, J., editor, Interpreting Gödel: Critical Essays. Cambridge University Press, 2014.Google Scholar
[86]Pour-El, M. B. and I. Richards. The wave equation with computable initial data such that its unique solution is not computable. Advances in Mathematics, 39:215–239, 1981.CrossRefGoogle Scholar
[87]Pullum, G. K.. Scooping the loop snooper. www.lel.ed.ac.uk/˜gpullum/loopsnoop.html.Google Scholar
[88]Reny, P.. Arrow’s theorem and the Gibbard–Satterthwaite theorem: A unified approach. Economics Letters, 99–105, 2001.CrossRefGoogle Scholar
[89]Richeson, D.. Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity. Princeton University Press, 2019.Google Scholar
[90]Robinson, R. M.. Undecidability and nonperiodicity for tilings of the plane. Inventiones Mathematicae, 12:177–209, 1971.CrossRefGoogle Scholar
[91]Rosenblum, B. and Kuttner, F.. Quantum Enigma. Oxford University Press, 2011.Google Scholar
[92]Roughgarden, T.. Foundations of blockchains (lecture 9.6: An impossibility result for proof-of-work protocols), 2022. www.youtube.com/watch?v=8IwnXURUzUw.Google Scholar
[93]Roy, D. V.. On Berry’s paradox and non-diagonal constructions. Complexity, 4:35–38, 1999.3.0.CO;2-8>CrossRefGoogle Scholar
[94]Russell, B.. The Philosophy of Logical Atomism. Open Court, 1985.Google Scholar
[95]Sanders, H.. Arrow’s impossibility theorem of social choice.math.uchicago.edu/may/VIGRE/VIGRE2007/REUPapers/FINALAPP/Sanders.pdf.Google Scholar
[96]Sen, A.. The professor of impossibility. The Indian Express, February 27, 2017.Google Scholar
[97]Sipser, M.. Introduction to the Theory of Computation (3rd edition). Cengage Learning, 2013.Google Scholar
[98]Smith, P.. An Introduction to Gödel’s Theorems (2nd edition). Cambridge University Press, 2013.CrossRefGoogle Scholar
[99]Smith, P.. Gödel without (Too Many) Tears. Logic Matters, 2020.Google Scholar
[100]Smullyan, R. M.. Gödel’s Incompleteness Theorems. Oxford University Press, 1992.CrossRefGoogle Scholar
[101]Smullyan, R. M.. The Gödelian Puzzle Book: Puzzles, Paradoxes and Proofs. Dover, 2013.Google Scholar
[102]Styer, D.. The Strange World of Quantum Mechanics. Cambridge University Press, 2000.CrossRefGoogle Scholar
[103]Harrison Bell’s theorem, D. M., 1999. https://faraday.physics.utoronto.ca/PVB/Harrison/BellsTheorem/BellsTheorem.html.Google Scholar
[104]Townsend, J. S.. A Modern Approach to Quantum Mechanics (2nd edition). University Science Books, 2012.Google Scholar
[105]Tumulka, R.. The assumptions of Bell’s proof. In Bell, M. and Gao, S., editors, Quantum Nonlocality and Reality: 50 Years of Bell’s Theorem. Cambridge University Press, 2016.Google Scholar
[106]Vaidman, L.. Variations on the theme of the Greenberger, Horne, Zeilinger proof. Foundations of Physics, 29:615–630, 1999.CrossRefGoogle Scholar
[107]Wikipedia. Conway’s game of life, 2023. https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life.Google Scholar
[108]Wolchover, N.. How Gödel’s proof works. Wired Magazine, July 19, 2020.Google Scholar
[109]Yu, N.. A one-shot proof of Arrow’s impossibility theorem. Economic Theory, 50:523–525, 2012.CrossRefGoogle Scholar
[110]Zachary, W.. An information flow model for conflict and fission in small groups. Journal of Anthropological Research, 33:452–473, 1977.CrossRefGoogle Scholar
[111]Zeilinger, A.. Quantum teleportation. Scientific American, April 2000.CrossRefGoogle ScholarPubMed
[112]Zeilinger, A.. Dance of the Photons: From Einstein to Quantum Teleportation. FSG, 2010.Google Scholar
[113]Zukov, G.. The Dancing Wu-Li Masters: An Overview of the New Physics. Morrow, 1979.CrossRefGoogle Scholar
[114]Zyga, L.. Classical problem becomes undecidable in a quantum setting, July 9, 2012. https://phys.org/news/2012-07-classical-problem-undecidable-quantum.html.Google Scholar

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  • Bibliography
  • Dan Gusfield, University of California, Davis
  • Book: Proven Impossible
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