Our Mathematical Universe

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by Max Tegmark


  Suggestions for Further Reading

  This book has drawn on a huge corpus of work by the scientific community. Most of it is published in technical journal papers that you’ll find cited in my own technical papers at http://space.mit.edu/home/tegmark/technical.html. However, there’s also a rich literature of books aiming to explain the core ideas to non-experts. In addition to the references I’ve called out in footnotes, here’s a small sample of such books, from the many wonderful ones that have been written, through which you can continue exploring topics that we’ve covered. I’ve tried to group them by their main focus, even though many cover other topics as well. One or more integral symbols ∫ indicate that a book is more technical/mathematical, akin to chili-pepper symbols indicating spiciness on restaurant menus.

  COSMOLOGY (CHAPTERS 2–4)

  Adams, Fred, and Greg Laughlin. The Five Ages of the Universe. New York: The Free Press, 1999.

  Chown, Marcus. The Magic Furnace: The Search for the Origins of Atoms. New York: Oxford University Press, 2001.

  de Grasse Tyson, Neil. Death by Black Hole: And Other Cosmic Quandaries. New York: W. W. Norton & Company, 2007.

  Finkbeiner, Ann. A Grand and Bold Thing: An Extraordinary New Map of the Universe Ushering in a New Era of Discovery. New York: Free Press, 2010.

  Greene, Brian. The Fabric of the Cosmos. New York: Knopf, 2004.

  Hawking, Stephen. A Brief History of Time. New York: Touchstone, 1993.

  Kirshner, Robert P. The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Princeton: Princeton Science Library, 2004.

  Kragh, Helge. Cosmology and Controversy: The Historical Development of Two Theories of the Universe. Princeton: Princeton University Press, 1996.

  Krauss, Lawrence. A Universe from Nothing: Why There Is Something Rather than Nothing. New York: Free Press, 2012.

  Rees, Martin. Just Six Numbers: The Deep Forces That Shape the Universe. New York: BasicBooks, 2000.

  Rees, Martin. Our Cosmic Habitat. Princeton: Princeton University Press, 2002.

  Seife, Charles. Alpha and Omega: The Search for the Beginning and End of the Universe. New York: Penguin Books, 2004.

  Singh, Simon. Big Bang: The Origin of the Universe. New York: HarperCollins, 2004.

  Smolin, Lee. Time Reborn: From the Crisis in Physics to the Future of the Universe. Boston: Houghton Mifflin Harcourt, 2013.

  Weinberg, Steven. The First Three Minutes: A Modern View of the Origin of the Universe. New York: BasicBooks, 1993.

  INFLATION, MULTIVERSE LEVELS I–II (CHAPTERS 5–6)

  Barrow, John. The Book of Universes: Exploring the Limits of the Cosmos. New York: W. W. Norton & Company, 2011.

  Davies, Paul. Cosmic Jackpot: Why Our Universe Is Just Right for Life. New York: Houghton Mifflin, 2007.

  Guth, Alan. The Inflationary Universe. New York: Perseus Books Group, 1997.

  ∫∫Linde, Andrei D. Particle Physics and Inflationary Cosmology. Chur, Switzerland: Harwood Academic Publishers, 1990.

  Steinhardt, Paul J., and Neil Turok. Endless Universe: Beyond the Big Bang. New York: Doubleday, 2007.

  Susskind, Leonard. The Cosmic Landscape: String Theory and the Illusion of Intelligent Design. New York: Little, Brown and Company, 2005.

  Vilenkin, Alexander. Many Worlds in One: The Search for Other Universes. New York: Hill and Wang, 2006.

  QUANTUM MECHANICS, MULTIVERSE LEVEL III (CHAPTERS 7–8)

  Byrne, Peter. The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family. New York: Oxford University Press, 2010.

  Cox, Brian, and Jeff Forshaw. The Quantum Universe (And Why Anything That Can Happen, Does). Boston: Da Capo Press, 2012.

  Deutsch, David. The Beginning of Infinity: Explanations That Transform Our World. New York: Allen Lane, 2012.

  Deutsch, David. The Fabric of Reality. New York: Allen Lane, 1997.

  ∫∫ Everett, Hugh. “The Many-Worlds Interpretation of Quantum Mechanics.” Ph.D. diss., Princeton University, 1957. Free download at http://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf.

  ∫∫ Everett, Hugh. The Many-Worlds Interpretation of Quantum Mechanics, edited by Bryce S. DeWitt and Neill Graham. Princeton: Princeton University Press, 1973.

  ∫∫ Giulini, Domenico, and Erich Joos, Claus Kiefer, Joachim Kupsch, Ion-Olimpiu Stamatescu and H. Dieter Zeh. Decoherence and the Appearance of a Classical World in Quantum Theory. Berlin: Springer, 1996.

  Kaiser, David. How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival. New York: W. W. Norton & Company, 2011.

  ∫Saunders, Simon, and Jonathan Barrett, Adrian Kent and David Wallace. Many Worlds? Everett, Quantum Theory & Reality. Oxford: Oxford University Press, 2010.

  MULTIVERSES IN GENERAL (CHAPTERS 6 AND 8)

  ∫ Carr, Bernard J., ed. Universe or Multiverse? Cambridge, Mass.: MIT Press, 2007.

  Carroll, Sean. From Eternity to Here: The Quest for the Ultimate Theory of Time. Oxford: Oneworld Publications, 2011.

  Greene, Brian. The Hidden Reality. New York: Knopf, 2011.

  Kaku, Michio. Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos. New York: Anchor Books, 2006.

  Lewis, David. On the Plurality of Worlds. Oxford: Blackwell Publishing, 1986.

  THE MIND (CHAPTERS 9 AND 11)

  Blackmore, Susan. Conversations on Consciousness: What the Best Minds Think about Free Will, and What It Means to Be Human. New York: Oxford University Press, 2006.

  Bostrom, Nick. Anthropic Bias: Observation Selection Effects in Science and Philosophy. New York: Routledge, 2002.

  Damasio, Antonio. The Feeling of What Happens. New York: Harcourt Brace, 2000.

  Damasio, Antonio. Self Comes to Mind: Constructing the Conscious Brain. New York: Pantheon Books, 2010.

  Dennett, Daniel. Consciousness Explained. Boston: Little, Brown and Company, 1992.

  Hawkins, Jeff, and Sandra Blakeslee. On Intelligence. New York: Henry Holt and Company, 2004.

  Hut, Piet, Mark Alford and Max Tegmark. “On Math, Matter and Mind,” Foundations of Physics, January 15, 2006, http://arxiv.org/pdf/physics/0510188.pdf.

  Koch, Christof. “A ‘Complex’ Theory of Consciousness,” Scientific American, August 18, 2009, http://www.scientificamerican.com/article.cfm?id=a-theory-of-consciousness.

  Koch, Christof. The Quest for Consciousness: A Neurobiological Approach. Englewood, Col.: Roberts & Company Publishers, 2004.

  Kurzweil, Ray. How to Create a Mind: The Secret of Human Thought Revealed. New York: Viking Penguin, 2012.

  Penrose, Roger. The Emperor’s New Mind. Oxford: Oxford University Press, 1989.

  Pinker, Steven. How the Mind Works. New York: W. W. Norton and Company, 1997.

  Tononi, Giulio. “Consciousness as Integrated Information: A Provisional Manifesto,” The Biological Bulletin, 2008, http://www.biolbull.org/content/215/3/216.full.

  Tononi, Giulio. Phi: A Voyage from the Brain to the Soul. New York: Pantheon Books, 2012.

  Velmans, Max, and Susan Schneider, eds. The Blackwell Companion to Consciousness. Malden, Mass.: Blackwell Publishing, 2007.

  MATHEMATICS, COMPUTATION, COMPLEXITY (CHAPTERS 10–12)

  Barrow, John D. Pi in the Sky. Oxford: Clarendon Press, 1992.

  Barrow, John D., Theories of Everything. New York: Ballantine Books, 1991.

  Chaitin, Gregory J. Algorithmic Information Theory. (Cambridge: Cambridge University Press, 1987.

  Davies, Paul. The Mind of God. New York: Touchstone, 1993.

  ∫ Goodstein, Reuben L. Constructive Formalism: Essays on the Foundations of Mathematics. Leicester: Leister University College Press, 1951.

  Hersh, Reuben, What Is Mathematics, Really? Oxford: Oxford University Press, 1999.

  Levin, Janna. A Madman Dreams of Turing Machines. New York: Anchor Books, 2007.

  Livio, Mario. Is God a Mathematician?. New York: Simon & Schu
ster, 2009.

  Lloyd, Seth. Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos. New York: Vintage Books, 2007.

  Rucker, Rudy. Infinity and the Mind. Boston: Birkhäuser, 1982.

  Standish, Russell K. Theory of Nothing. Charleston, S.C.: BookSurge, 2006.

  ∫ Wolfram, Stephen. A New Kind of Science. New York: Wolfram Media, 2002.

  FUTURE OF LIFE (CHAPTER 13)

  Bostrom, Nick, and Milan C´irkovic´, eds. Global Catastrophic Risks. Oxford: Oxford University Press, 2008.

  Davies, Paul. The Eerie Silence: Renewing Our Search for Alien Intelligence. New York: Houghton Mifflin Harcourt, 2011.

  Drexler, K. Eric. Engines of Creation: The Coming Era of Nanotechnology. London: Fourth Estate, 1985.

  Dyson, Freeman. A Many-Colored Glass: Reflections on the Place of Life in the Universe. Charlottesville: University of Virginia Press, 2007.

  Gribbin, John R. Alone in the Universe: Why Our Planet Is Unique. Hoboken, N.J.: John Wiley & Sons, 2011.

  Kurzweil, Ray. The Age of Spiritual Machines: When Computers Exceed Human Intelligence. New York: Viking, 1999.

  Kurzweil, Ray. The Singularity Is Near: When Humans Transcend Biology. New York: Viking, 2005.

  Kurzweil, Ray, and Terry Grossman. Transcend: Nine Steps to Living Well Forever. New York: Viking, 2010.

  Moravec, Hans. Robot: Mere Machine to Transcendent Mind. Oxford: Oxford University Press, 1999.

  Rees, Martin. Our Final Hour: A Scientist’s Warning. New York: Perseus Books, 1997.

  Sagan, Carl. Pale Blue Dot: A Vision of the Human Future in Space. New York: Random House, 1997.

  FUNDAMENTAL PHYSICS, STRING THEORY, QUANTUM GRAVITY

  Barbour, Julian. The End of Time: The Next Revolution in Physics. Oxford: Oxford University Press, 1999.

  ∫ Barrow, John D., and Frank J. Tipler. The Anthropic Cosmological Principle. Oxford: Clarendon Press, 1986.

  Carroll, Sean. The Particle at the End of the Universe: How the Hunt for the Higgs Boson Leads Us to the Edge of a New World. New York: Dutton, 2012.

  ∫ Einstein, Albert. Relativity: The Special and General Theory. London: Really Simple Media, 2011.

  ∫∫Feynman, Richard, and Robert Leighton and Matthew Sands. The Feynman Lectures on Physics. 3 vols. New York: Addison-Wesley, 1964.

  Gamow, George. Mr. Tompkins in Paperback. Cambridge: Cambridge University Press, 1940.

  Greene, Brian. The Elegant Universe. New York: W. W. Norton and Company, 2003.

  Musser, George. The Complete Idiot’s Guide to String Theory. New York: Penguin Group, 1998.

  ∫∫Penrose, Roger. The Road to Reality: A Complete Guide to the Laws of the Universe. New York: Knopf, 2005.

  Randall, Lisa. Warped Passages: Unraveling the Mysteries of the Universe’s Hidden Dimensions. New York: Ecco, 2005.

  Smolin, Lee. Three Roads to Quantum Gravity. New York: BasicBooks, 2001.

  Smolin, Lee. The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next. Boston: Houghton Mifflin, 2006.

  Susskind, Leonard. The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics. New York: Little, Brown and Company, 2008.

  Weinberg, Steven L. Dreams of a Final Theory: The Scientist’s Search for the Ultimate Laws of Nature. New York: Pantheon, 1992.

  Wigner, Eugene P. Symmetries and Reflections. Cambridge, Mass.: MIT Press,1967.

  Wilczek, Frank. The Lightness of Being: Mass, Ether and the Unification of Forces. New York: BasicBooks, 2008.

  ∫ Zeh, H. Dieter. The Physical Basis of the Direction of Time. 4th ed. Berlin: Springer, 2002.

  Index

  [Page numbers followed by f, n, or t refer to figures, footnotes or tables, respectively.]

  Abel, Tom

  ACBAR

  ACT

  Adams, Douglas, 1.1, 2.1, 5.1, 8.1, 9.1, 9.2, 10.1, 11.1, 13.1

  Adams, Fred

  AdS/CFT correspondence

  Aguirre, Anthony, 6.1, 8.1, 10.1, 12.1

  Albrecht, Andy, n

  Almond, Paul, 11.1, 11.2

  Alpher, Ralph, 3.1, 3.2

  Anders, Geoff

  Anderson, Philip Warren

  Anderssen, Adolf

  Andersson, Carita

  Andromeda nebula, 2.1, 3.1, 13.1, 13.2

  angular momentum, 3.1, 7.1t, 7.2n, 7.3

  anthropic

  principle, 6.1, 11.1

  selection effect

  antimatter

  Aristarchos of Samos, 2.1f, 2.2, 2.3, 2.4f

  Asimov, Isaac

  asteroid collision with Earth

  atomic structure

  experience of physical reality versus

  fine-tuning in

  theory development

  see also particle physics

  Ball, John A.

  Bardeen, James, n

  Barrow, John, 6.1, 12.1, 12.2, 12.3

  baryon number

  Bell, John

  Bendich, Justin, 8.1, 10.1

  Bennett, Chuck

  Bergland, Per

  Berra, Yogi, 8.1, 13.1

  Bessel, Friedrich

  Bette, Andreas

  Big Bang

  course of, 3.1, 3.2, 3.3, 5.1

  cyclical model of

  evidence of, 3.1, 3.2

  flatness problem of theory of, 5.1, 5.2

  horizon problem of theory of, 5.1, 5.2

  hypothesis

  inflation theory and, 5.1, 5.2, 5.3, 5.4

  limitations of theory of, 3.1, 4.1, 5.1

  nucleosynthesis after, 3.1, 3.2, 4.1, 4.2, 7.1

  origins of theory of, 3.1, 3.2

  resistance to theory of

  singularity

  Big Chill, 5.1, 5.2f, 5.3, 13.1, 13.2f, 13.3t

  Big Crunch, 5.1, 5.2f, 5.3, 13.1, 13.2f, 13.3t

  Big Rip, 13.1, 13.2f, 13.3t

  Big Snap, 13.1, 13.2f, 13.3t, 13.4

  bit strings

  black holes

  consumption of matter by, n

  creation of, in Large Hadron Collider

  creation of universes in

  Blake, William

  Blanton, Mike

  blueshift

  Bodin, Magnus

  Bohr, Niels, 7.1, 7.2, 7.3, 7.4

  Boltzmann, Ludwig

  Boltzmann brains

  Boltzmann’s constant

  Bolyai, János

  Bond, Dick, 3.1, 4.1

  Boomerang, 3.1, 4.1, 4.2

  Borel, Émile, 8.1, 8.2n

  Born, Max

  boson, t

  Bostrom, Nick, 11.1, 11.2, 11.3, 11.4, 12.1, 13.1

  Bothner, Matthias

  bottom quarks

  Brahe, Tycho, 3.1, 3.2

  braneworld

  Brockman, John

  brown light

  Brundrit, Geoff

  Bruno, Giordano, 2.1, 2.2, 6.1, 10.1, 13.1

  Bunn, Ted, 4.1, 4.2

  carbon

  in fine-tuned Universe, 6.1, 12.1

  in formation of planets

  nucleosynthesis

  in white dwarf stars

  cardinality of mathematical structure

  Carlstrom, John

  Carr, Bernard

  Carter, Brandon, 6.1, 6.2, 11.1, 11.2, 11.3

  Cepheid variables

  CERN Laboratory, 7.1, 7.2

  Chaitin, Gregory

  change

  as illusion, 9.1, 11.1, 11.2, 11.3, 11.4

  inflation theory and

  mathematical modeling of

  physics to predict, 3.1, 6.1, 7.1

  in quantum mechanics, 7.1, 7.2, 9.1

  in spacetime perspective

  wavefunction, 7.1, 8.1, 8.2

  chaos theory

  charm quarks

  Chibisov, Gennady, 5.1n, 5.2

  Christie, Agatha

  Church, Alonzo

  C´ircovic´, Milan

  Cleland, Andrew

  clustered structure of Univer
se

  cosmic background–radiation maps and

  dark matter and

  evolution of theory of

  explained by inflation theory, 5.1, 5.2

  opportunities for research on

  origins of, 3.1, 4.1

  power-spectrum curve of, 4.1, 4.2f, 4.3

  scale-invariance in

  see also cosmic seed fluctuations

  Cohen, Marius

  color (conserved quantity)

  Columbus, Christopher, 2.1, 3.1

  Commins, Eugene, 8.1, 8.2

  complexity

  algorithmic

  definition of

  Level IV multiverse and

  of mathematical structures

  complex numbers

  Computable Universe Hypothesis, 12.1, 12.2

  appeal of

  conceptual challenges in

  definition of, 10.1t, 12.1

  mathematical structures in

  computationally generated mathematical structures, 12.1, 12.2

  computational-multiverse theories

  computer technology

  for galaxy mapping

  significance of, in cosmological modeling

  threats to human life from advance in

  computronium

  Confucius

  consciousness

  artificial intelligence and

  computing internal reality of entity with

  definition of, 11.1f, 11.2, 13.1

  evolution and, 1.1, 11.1, 13.1

  experience of spacetime in

  human understanding of capacity of

  Mathematical Universe Hypothesis and, 11.1, 11.2, 11.3

  memory and

  observation of symmetry and

  in observer moments

  in our Universe

  as phase of matter

 

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