Trick or Truth? pp 233-247 | Cite as
And the Math Will Set You Free
Chapter
First Online:
Abstract
Can mathematics help us find our way through all the wonders and mysteries of the universe? When physicists describe the laws governing the physical world, mathematics is always involved. Is this due to the fact that the universe is, at least in part, mathematical? Or rather mathematics is merely a tool used by physicists to model phenomena? Is mathematics just a language to tell the story of our universe, a story which could be told with the same or even more effectiveness using another language? Or quite the opposite, the universe is just a mathematical structure?
Keywords
Cellular Automaton Unify Theory Physical World Turing Machine Mathematical Structure
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Notes
Acknowledgments
I wish to thank Alma Ionescu for helpful comments.
References
- 1.G.D. Birkhoff. Universal algebra. In Comptes Rendus du Premier Congrès Canadien de Mathématiques, volume 67, pages 310–326. University of Toronto Press, Toronto, 1946.Google Scholar
- 2.L. Smolin. A naturalist account of the limited, and hence reasonable, effectiveness of mathematics in physics. Foundational Questions Institute, “Trick or Truth: the Mysterious Connection Between Physics and Mathematics” essay contest, last retrieved September 9, 2015, 2015. http://fqxi.org/community/forum/topic/2335.
- 3.R.M. Unger. A mystery demystified: The connection between mathematics and physics. Foundational Questions Institute, “Trick or Truth: the Mysterious Connection Between Physics and Mathematics” essay contest, last retrieved September 9, 2015, 2015. http://fqxi.org/community/forum/topic/2332.
- 4.R.M. Unger and L. Smolin. The singular universe and the reality of time. Cambridge University Press, 2014.Google Scholar
- 5.O.C. Stoica. On singular semi-Riemannian manifolds. Int. J. Geom. Methods Mod. Phys., 0(0):1450041, March 2014.Google Scholar
- 6.O.C. Stoica. Einstein equation at singularities. Cent. Eur. J. Phys, 12:123–131, February 2014.Google Scholar
- 7.O.C. Stoica. Singular General Relativity. Ph.D. Thesis, January 2013. arXiv:math.DG/1301.2231.
- 8.O.C. Stoica. Big Bang singularity in the Friedmann-Lemaître-Robertson-Walker spacetime. The International Conference of Differential Geometry and Dynamical Systems, October 2013. arXiv:gr-qc/1112.4508.
- 9.O.C. Stoica. Beyond the Friedmann-Lemaître-Robertson-Walker Big Bang singularity. Commun. Theor. Phys., 58(4):613–616, March 2012.Google Scholar
- 10.O.C. Stoica. Schwarzschild singularity is semi-regularizable. Eur. Phys. J. Plus, 127(83):1–8, 2012.Google Scholar
- 11.O.C. Stoica. Analytic Reissner-Nordström singularity. Phys. Scr., 85(5):055004, 2012.Google Scholar
- 12.O.C. Stoica. Spacetimes with Singularities. An. Şt. Univ. Ovidius Constanţa, 20(2):213–238, July 2012.Google Scholar
- 13.O.C. Stoica. The Geometry of Black Hole Singularities. Advances in High Energy Physics, 2014:14, May 2014. http://www.hindawi.com/journals/ahep/2014/907518/.
- 14.O.C. Stoica. Metric dimensional reduction at singularities with implications to quantum gravity. Ann. of Phys., 347(C):74–91, 2014.Google Scholar
- 15.M. Tegmark. The mathematical universe. Foundations of Physics, 38(2):101–150, 2008.Google Scholar
- 16.D.J. Chalmers. Facing up to the problem of consciousness. Journal of consciousness studies, 2(3):200–219, 1995.Google Scholar
- 17.R. Penrose. Singularities and time-asymmetry. In General relativity: an Einstein centenary survey, volume 1, pages 581–638, 1979.Google Scholar
- 18.O.C. Stoica. On the Weyl curvature hypothesis. Ann. of Phys., 338:186–194, November 2013. arXiv:gr-qc/1203.3382.
- 19.Y. Bar-Yam. A mathematical theory of strong emergence using multiscale variety. Complexity, 9(6):15–24, 2004.Google Scholar
- 20.F. Cucker and S. Smale. On the mathematics of emergence. Japanese Journal of Mathematics, 2(1):197–227, 2007.Google Scholar
- 21.G.F.R. Ellis. Recognising top-down causation. arXiv:1212.2275, 2012.
- 22.D. Dennett. Are we explaining consciousness yet? Cognition, 79(1):221–237, 2001.Google Scholar
- 23.D. Dennett. Intuition pumps and other tools for thinking. WW Norton & Company, 2013.Google Scholar
- 24.C. Hoefer. Freedom from the inside out. Royal Institute of Philosophy Supplement, 50:201–222, 2002.Google Scholar
- 25.O.C. Stoica. Flowing with a Frozen River. Foundational Questions Institute, “The Nature of Time” essay contest, 2008. http://fqxi.org/community/forum/topic/322.
- 26.O.C. Stoica. Modern Physics, Determinism, and Free-Will. Noema, Romanian Committee for the History and Philosophy of Science and Technologies of the Romanian Academy, XI:431–456, 2012. http://www.noema.crifst.ro/doc/2012_5_01.pdf.
- 27.S. Aaronson. The Ghost in the Quantum Turing Machine. To appear in “The Once and Future Turing: Computing the World,” a collection edited by S. Barry Cooper and Andrew Hodges, 2013. arXiv:1306.0159.
- 28.C.C. Chang and H.J. Keisler. Model theory, volume 73. North Holland, 1990.Google Scholar
- 29.O.C. Stoica. The Tao of It and Bit. Foundational Questions Institute, “It from Bit or Bit from It?” essay contest, fourth prize, 2013. http://fqxi.org/community/forum/topic/1627.
- 30.M. Tegmark. Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. Knopf Doubleday Publishing Group, 2014.Google Scholar
- 31.K. Gödel. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik, 38(1):173–198, 1931.Google Scholar
- 32.S. Hawking. Gödel and the end of physics. http://www.hawking.org.uk/index.php/lectures/91, last retrieved September 9, 2015, 2002.
- 33.M. Tegmark. Is "the theory of everything" merely the ultimate ensemble theory? Annals of Physics, 270(1):1–51, 1998.Google Scholar
- 34.D. K. Lewis. Convention: A philosophical study. John Wiley & Sons, 2008.Google Scholar
- 35.D. K. Lewis. Counterfactuals. John Wiley & Sons, 2013.Google Scholar
- 36.D. K. Lewis. On the plurality of worlds, volume 322. Cambridge Univ. Press, 1986.Google Scholar
- 37.M. Tegmark. On the dimensionality of spacetime. Classical and Quantum Gravity, 14(4):L69, 1997.Google Scholar
- 38.J. Conway. The game of life. Scientific American, 223(4):4, 1970.Google Scholar
- 39.M. Cook. Universality in elementary cellular automata. Complex Systems, 15(1):1–40, 2004.Google Scholar
- 40.M. Cook. A concrete view of rule 110 computation. EPTCS, 1:31–55, 2009.Google Scholar
- 41.A. Albrecht and L. Sorbo. Can the universe afford inflation? Phys. Rev. D, 70(6):063528, 2004.Google Scholar
Copyright information
© Springer International Publishing Switzerland 2016