Abstract
It would be nice if science answered all questions about our universe. In the past, mathematics has not just provided the language in which to frame suitable scientific answers, but was also able to give us clear indications of its own limitations. The former was able to deliver results via an ad hoc interface between theory and experiment. But to characterise the power of the scientific approach, one needs a parallel higher-order understanding of how the working scientist uses mathematics, and the development of an informative body of theory to clarify and expand this understanding. We argue that this depends on us selecting mathematical models which take account of the ‘thingness’ of reality, and puts the mathematics in a correspondingly rich information-theoretic context. The task is to restore the role of embodied computation and its hierarchically arising attributes. The reward is an extension of our understanding of the power and limitations of mathematics, in the mathematical context, to that of the real world. Out of this viewpoint emerges a widely applicable framework, with not only epistemological, but also ontological consequences – one which uses Turing invariance and its putative breakdowns to confirm what we observe in the universe, to give a theoretical status to the dichotomy between quantum and relativistic domains, and which removes the need for many-worlds and related ideas. In particular, it is a view which confirms that of many quantum theorists – that it is the quantum world that is ‘normal’, and our classical level of reality which is strange and harder to explain. And which complements fascinating work of Cristian Calude and his collaborators on the mathematical characteristics of quantum randomness, and the relationship of ‘strong determinism’ to computability in nature.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aspect, A., Dalibard, J., Roger, G.: Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Letters 49, 1804–1807 (1982)
Aspect, A., Grangier, P., Roger, G.: Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment; a new violation of Bell’s inequalities. Phys. Rev. Letters 49, 91 (1982)
Bell, J.: On the Einstein Podolsky Rosen paradox. Physics 1, 195 (1964)
Bell, J.S.: Einstein-Podolsky-Rosen experiments. In: Proceedings of the Symposium on Frontier Problems in High Energy Physics, Pisa, pp. 33–45 (June 1976)
Bohm, D.: A suggested interpretation of the quantum theory in terms of ‘hidden’ variables, I and II. Phys. Rev. 85, 166–193 (1952); reprinted in Wheeler, J.A., Zurek, W.H. (eds.) Quantum Theory and Measurement. Princeton University Press, Princeton (1983)
Born, M.: The Restless Universe. Blackie & Son, London (1935)
Born, M.: Natural Philosophy of Cause and Chance, Clarendon Press (1949)
Callender, C. (ed.): The Oxford Handbook of Philosophy of Time. Oxford University Press, Oxford (2011)
Calude, C., Campbell, D.I., Svozil, K., Stefanescu, D.: Strong determinism vs. computability. In: DePauli-Schimanovich, W., Köhler, E., Stadler, F. (eds.) The Foundational Debate: Complexity and Constructivity in Mathematics and Physics, pp. 115–131. Kluwer, Dordrecht (1995)
Calude, C.: Algorithmic Randomness, Quantum Physics, and Incompleteness. In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 1–17. Springer, Heidelberg (2005)
Calude, C.S., Svozil, K.: Quantum randomness and value indefiniteness. Advanced Science Letters 1, 165–168 (2008)
Cooper, S.B.: Clockwork or Turing U/universe? - Remarks on causal determinism and computability. In: Cooper, S.B., Truss, J.K. (eds.) Models and Computability. London Mathematical Society Lecture Notes Series, vol. 259, pp. 63–116. Cambridge University Press, Cambridge (1999)
Cooper, S.B.: Upper cones as automorphism bases. Siberian Advances in Math. 9, 1–61 (1999)
Cooper, S.B.: Computability Theory. Chapman & Hall/CRC, Boca Raton, London, New York, Washington, D.C (2004)
Cooper, S.B.: Definability as hypercomputational effect. Applied Mathematics and Computation 178, 72–82 (2006)
Cooper, S.B.: How Can Nature Help Us Compute? In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2006. LNCS, vol. 3831, pp. 1–13. Springer, Heidelberg (2006)
Cooper, S.B.: Computability and emergence. In: Gabbay, D.M., Goncharov, S.S., Zakharyaschev, M. (eds.) Mathematical Problems from Applied Logic I. Logics for the XXIst Century. Springer International Mathematical Series, vol. 4, pp. 193–231 (2006)
Cooper, S.B., Odifreddi, P.: Incomputability in Nature. In: Cooper, S.B., Goncharov, S.S. (eds.) Computability and Models, pp. 137–160. Kluwer Academic/Plenum, New York, Boston, Dordrecht, London, Moscow (2003)
Einstein, A.: Autobiographical Notes. In: Schilpp, P. (ed.) Albert Einstein: Philosopher-Scientist. Open Court Publishing (1969)
Einstein, A., Podolsky, B., Rosen, N.: Can quantum mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)
Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics, vol. 3. Addison-Wesley (1965)
Funtowicz, S.O., Ravetz, J.R.: A New Scientific Methodology for Global Environmental Issues. In: Costanza, R. (ed.) Ecological Economics: The Science and Management of Sustainability, pp. 137–152. Columbia University Press, New York (1991)
Jaffe, A.: Quantum Theory and Relativity. In: Doran, R.S., Moore, C.C., Zimmer, R.J. (eds.) Contemporary Mathematics Group Representations, Ergodic Theory, and Mathematical Physics: A Tribute to George W. Mackey, vol. 449, pp. 209–246 (2008)
Kleene, S.C.: Recursive functionals and quantifiers of finite types I. Trans. of the Amer. Math. Soc. 91, 1–52 (1959)
Kleene, S.C.: Recursive Functionals and Quantifiers of Finite Types II. Trans. of the Amer. Math. Soc. 108, 106–142 (1963)
Kreisel, G.: Some reasons for generalizing recursion theory. In: Gandy, R.O., Yates, C.E.M. (eds.) Logic Colloquium, vol. 69, pp. 139–198. North-Holland, Amsterdam (1971)
Kuhn, T.S.: The Structure of Scientific Revolutions, 3rd edn. University of Chicago Press, Chicago (1996)
Maudlin, T.: Quantum Non-Locality & Relativity: Metaphysical Intimations of Modern Physics, 3rd edn. Wiley-Blackwell, Malden (2011)
Meinhardt, H.: The Algorithmic Beauty of Sea Shells, 4th edn. Springer, Heidelberg (2009)
Omnès, R.: The Interpretation of Quantum Mechanics. Princeton University Press, Princeton (1994)
Penrose, R.: Quantum physics and conscious thought. In: Hiley, B.J., Peat, F.D. (eds.) Quantum Implications: Essays in honour of David Bohm, pp. 105–120. Routledge & Kegan Paul, London, New York
Post, E.L.: Degrees of recursive unsolvability: preliminary report (abstract). Bull. Amer. Math. Soc. 54, 641–642 (1948)
Richards, B.: Turing, Richards and Morphogenesis. The Rutherford Journal 1 (2005), http://www.rutherfordjournal.org/article010109.html
Rieper, E., Anders, J., Vedral, V.: Entanglement at the quantum phase transition in a harmonic lattice. New J. Phys. 12, 025017 (2010)
Slaman, T.A.: Degree structures. In: Proceedings of the International Congress of Mathematicians, Kyoto, pp. 303–316 (1990/1991)
Smolin, L.: The Trouble With Physics: The Rise of String Theory, the Fall of Science and What Comes Next. Allen Lane/Houghton Mifflin, London, New York (2006)
Taleb, N.N.: The Black Swan. Allen Lane, London (2007)
Turing, A.: On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society 42, 230–265 (1936/37); reprinted in A.M. Turing, Collected Works: Mathematical Logic, pp. 18–53
Turing, A.: Systems of logic based on ordinals. Proceedings of the London Mathematical Society 45, 161–228 (1939); reprinted in A.M. Turing, Collected Works: Mathematical Logic, pp. 81–148
Turing, A.M.: The Chemical Basis of Morphogenesis. Phil. Trans. of the Royal Society of London. Series B 237, 37–72 (1952)
van Rijsbergen, K.: The Geometry of Information Retrieval. Cambridge University Press, Cambridge (2004)
White, M.: Isaac Newton – The Last Sorcerer. Fourth Estate, London (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Cooper, S.B. (2012). Mathematics, Metaphysics and the Multiverse. In: Dinneen, M.J., Khoussainov, B., Nies, A. (eds) Computation, Physics and Beyond. WTCS 2012. Lecture Notes in Computer Science, vol 7160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27654-5_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-27654-5_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27653-8
Online ISBN: 978-3-642-27654-5
eBook Packages: Computer ScienceComputer Science (R0)