Sources - In order of appearance
John D. Barrow, Erwin Schrödinger, Eugene Wigner, Sir Roger Penrose, Stephen Hawking, David Layzer, Marcus du Sautoy, Peter Atkins, David Deutsch, Max Tegmark, Sir Isaac Newton, James Clark Maxwell, Albert Einstein, Georg Friedrich Riemann, Edwin Hubble, Paul Dirac, Carl Anderson, Prince Louis de Broglie, Hideki Yakawa, Murray Gell-Man, John Bell, Marcus Chown, Veronica Becher, Eli Maor, Euclid of Alexandria, Georg Cantor, Galileo Galilei, David Hilbert, Herman Weyl, Paul Davies, Richard Feynman, Hugh Everett, Leonard Susskind, Joe Polchinski, Raphael Busso, Alan Guth, Andrei Linde, John Wheeler, Lord Rees of Ludlow, Kurt Gödel, Freeman Dyson, Alan Turing, Gregory Chaitin, Steven Weinberg.
References
The Mystery Beyond the Multiverse
“A mystery lurks beneath the magic carpet of science, something that scientists have not been telling, something too shocking to mention.”
John D. Barrow Professor of Mathematical Sciences, University of Cambridge.
“there lies a deeply ‘religious’ belief - a belief in an unseen and perfect transcendental world that controls us in an unexplained way, yet upon which we seem to exert no influence whatsoever.”
Ibid., p 1.
“The reason why mathematics is so successful in describing the way the world works is because the world is at root mathematical.”
Barrow, John. 1991 Theories of everything. London: Vintage. p 183.leading figure in the Quantum Revolution) believed that:
“mathematical truth is timeless, it does not come into being when we discover it.”
Schrödinger, Erwin. What is life and mind and matter? Cambridge: Cambridge University Press. p 154.
“the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it... It is difficult to avoid the impression that a miracle confronts us here.”
Wigner, Eugene. 1991. The unreasonable effectiveness of mathematics in the natural sciences. In The world treasury of physics, astronomy and mathematics. Edited by Ferris, Timothy. London: Little Brown & Co. p 527.
“the truths that mathematicians seek are, in a clear sense, already 'there', and mathematical research can be compared with archaeology; the mathematicians job is to seek out these truths as a task of discovery rather than one of invention.”
Penrose, Roger. 18th Nov. 2006. What is reality. New Scientist No 2578. p 38.
“Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe?”
Hawking, Stephen. 1988. A brief history of time. New York: Bantam Press. p 174.
“why it is that the regularities which lie deep beneath the outward appearance of our physical world are actually mathematical, and even more mysterious; why they should be in the least bit accessible to the human mind ... these are the great mysteries at the heart of humankind's most sustained and successful rational enterprise.”
Layzer, David. 1990. Cosmogenesis. Oxford: Oxford University Press. p 14.
“The fact that the code provides such a successful description of nature is for many one of the greatest mysteries of science.”
Du Sautoy, M. (Presenter), & Cooter, S. (Director). (Oct. 2011). The code, [television series episode 1]. In P. Leonard (Producer). London, BBC Studios.
“It is possibly not too extravagant to claim that the answer to the question of why mathematics works will be the final answer to all questions of being”
Atkins, Peter. 2003. Galileo's Finger. Oxford: Oxford University Press. p 355.
“the deep structure of the world is mathematics: the universe, all it contains, is mathematics, nothing but mathematics, and physical reality is an awesome manifestation of mathematics.”
Atkins, Peter. 1994. Creation revisited. Oxford: Oxford University Press. p 101.
“Mathematical entities are part of the fabric of reality because they are complex and autonomous...although they are by definition intangible, they exist objectively and have properties that are independent of the laws of physics.”
Deutsch, David. 1998. The fabric of reality. London: Peguin. p 255.
“There is nothing fuzzy about mathematical structures. They are 'out there' in the sense that mathematicians discover them rather than create them, and that contemplative alien civilisations would find the same structures, (a theorem is true regardless of whether it is proven by a human, a computer or an alien)... a mathematical structure cannot change - it is an abstract, immutable entity existing outside of space and time.”
Tegmark, Max. 2004. Parallel universes. In Science and ultimate reality. Edited by: Barrow, J., Davies, P. and Charles Harper, Jr. Cambridge: Cambridge University Press. pp 480 - 482.
“when we start to look closely at all this complexity, surprising patterns begin to emerge. It is these patterns that I believe point to an underlying code at the very heart of existence, and that controls not only our world and everything in it, but even us.”
Du Sautoy, M. (Presenter), & Cooter, S. (Director). (Oct. 2011). The code, [television series episode 3]. In P. Leonard (Producer). London, BBC Studios.
“The meaning of mathematics will emerge as a key question that must eventually be answered in any quest for a fundamental understanding of the physical world.”
Barrow, John. 1992. Pi in the sky. London: Penguin. p viii.
The Mystery in Action
Photographs & Illustrations
Figure 1. [Untitled portrait of Isaac Newton]. Retrieved April 6, 2013, from: http://www.sciencekids.co.nz/pictures/scientists.html
Figure 2. [Untitled photograph of James Clark Maxwell]. Retrieved April 6, 2013 from: http://www.sciencekids.co.nz/pictures/scientists.html
Figure 3. [Untitled photograph of Albert Einstein]. Retrieved April 6, 2013 from: http://www.sciencekids.co.nz/pictures/scientists.html
Figure 4. [Untitled photograph of Paul Dirac]. Retrieved April 6, 2013 from: http://www.sciencekids.co.nz/pictures/scientists.html
The Magic of Infinities
“Mathematicians have also had to face up to the reality of infinity. The issue was a big one, one of the biggest that mathematicians have ever faced .”
Barrow, John. 2005. The infinite book. London: Vintage. p xiv.
“computers don’t just perform finite computations, doing one or a few things, and then halt. They can also carry out infinite computations, producing an infinite series of results.”
Chown, Marcus. 10th March 2001. The omega man. New Scientist. Issue no. 2281. P28.
“many computer applications are designed to produce an infinite amount of output.”
Ibid. p28.
“To the mathematician, infinity is a reality [his emphasis]. In fact, mathematics could hardly exist without it, for it is inherent already in the counting numbers, which form the basis of practically all of mathematics”
Maor, E. 1991. To infinity and beyond. Princeton: Princeton University Press. p 233.
“bigger and bigger infinite sets from ones that we already have. There is no limit to this escalation...By this means we can create an ever-ascending staircase of infinities...There is no end to this inconceivable infinity of infinities.”
Barrow, John. 1992. Pi in the sky. London: Penguin. p 214.
“there are no more moments in all of eternity than there are in, say, one minute. In both cases there is an infinite number”
Davies, Paul. 1984. God and the new physics. London: Penguin. p 19.
“A quivering slice of mathematical stability [lost] in an infinite ocean of all possible possibility”
Aldworth, Roland. 2001. Mathematics and the real face of god. Contemporary Review. Vol. 278. No 1624; pp 283-290.
Photographs & Illustrations
Figure 1. [Untitled photograph of Professor John D. Barrow]. Retrieved April 7, 2013, from: http://www.varsity.co.uk/lifestyle/3203
Figure 2. Wikipedia: Featured Pictures. File: Mandel zoom 03 seehorse.jpg [computer image]. Retrieved April 7, 2013, from: http://en.wikipedia.org/wiki/File:Mandel_zoom_03_seehorse.jpg
Figure 3. Wiki Media. Georg Cantor [photograph]. Retrieved April 7, 2013, from: http://en.wikipedia.org/wiki/File:Georg_Cantor2.jpg
Figure 4. [Untitled portrait of Galileo]. Retrieved April 6, 2013 from: http://www.sciencekids.co.nz/pictures/scientists.html
Figure 5. Wikimedia Commons. [Diagram representing pi]. Retrieved April 7, 2013, from: http://en.wikipedia.org/wiki/Pi
Figure 6. Wikimedia Commons. [Diagram of the square root of 2]. Retrieved April 7, 2013, from: http://en.wikipedia.org/wiki/Square_root_of_2
Atoms and the Multiverse
“It is my task to convince you not to turn away because you don’t understand it. You see, my physics students don’t understand it either. That is because I don’t understand it. Nobody does. ”
Feynman, Richard., 1985. QED. Harmondsworth: Penguin. p 9.
“When all possible paths are considered, each crooked path has a nearby path of considerably less distance and therefore much less time…The nearby nearly straight paths also make important contributions. So light doesn’t really travel only in a straight line; it ‘smells’ the neighbouring paths around it.”
Ibid. p 9.
“It is the mathematics of this wave motion, which somehow controls the electron… In the case of the waves of wave mechanics we have no idea what is waving.”
Bell, J.S., 1987. Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press. p 187.
“so even material substance seems able to convert itself into something with a more theoretical mathematical actuality.”
Penrose, Roger., 1994. Shadows of the mind. Oxford: Oxford University Press. p 14.
“will be the first technology that allows useful tasks to be performed in collaboration between parallel universes. A quantum computer would be capable of distributing components of a complex task among vast numbers of parallel universes, and sharing the results.”
Deutsch, David. 1998. The fabric of reality. London: Allen Lane. p 195.
“this idea that the universe has multiple histories may sound like science fiction, but it is now accepted as science fact.”
Hawking, Steven. 2001. The universe in a nutshell. London: Bantam Press. p 80.
“Each such bubble is infinite in size, yet there are infinitely many bubbles since the chain reaction never ends. Indeed, if this exponential growth of the number of bubbles has been going on forever, there will be an uncountable infinity of such parallel universes”
Tegmark, Max. 2004. Parallel universes. In: Barrow J, Davies P, Harper Jr. C, Editors. Science and ultimate reality. Cambridge: Cambridge University Press. P
“as absurd as it seems, the vacuum energy exactly cancels for the first 119 decimal places but then in the 120th place, bingo! A bit of vacuum energy. How can such a situation possibly be explained?”
Susskind, Leonard. 1 Nov. 2003. A universe like no other. New Scientist No. 2419. p 34.
“It is not only that man is adapted to the universe. The universe is adapted to man. Imagine a universe in which one or another of the fundamental dimensionless constants of physics is altered by a few percent one way or the other? Man could never come into being in such a universe... According to this principle [the Anthropic Principle], a life-giving factor lies at the centre of the whole machinery and design of the world.”
Barrow, John., and Tipler, Frank. 1986. The anthropic cosmological principle. Oxford: Oxford University Press. p vii.
“The cosmos may have something in common with an off-the-rack clothes shop: if the shop has a large stock, we are not surprised to find one suit that fits. Likewise, if our universe is selected from a multiverse, its seemingly designed or fine-tuned features would not be surprising.”
Rees, Martin. 2001. Our cosmic habitat. London: Weidenfield & Nicholson. p 165
Photographs & Illustrations
Figure 1. Alex Wong (Getty Images). (2006). Protein mass spectrometer, George Washington University. [empirical evidence of quantum superposition]. Retrieved April 8, 2013, from: http://curiosity.discovery.com/question/what-quantum-superposition
Figure 2. Benjamin Lanyon, (photographer). (2010). quantum computer, [Science experiment]. Retrieved April 8, 2013, from: blog.cryptographyengineering.com
Figure 3. Stanford University. Leonard Susskind. [photographic portrait]. Retrieved April 9, 2013, from: https://physics.stanford.edu/people/faculty/leonard-susskind
Figure 4. Bluegrass Pundit. (August 4, 2011). Do we live inside a bubble? [Illustration of chaotic inflation]. Retrieved 9 April, 2013, from: http://scinewsblog.blogspot.com/2011/08/scientists-test-multiverse-theory.html
Figure 5. The Wheeler family. (1991.) John Wheeler. [photograph]. Retrieved April 9, 2013, from: http://www.princeton.edu/pr/pictures/s-z/wheeler_john/
Figure 6. Courtesy Prof. Rees. Martin John Rees 1993 Bruce Medalist. [Photograph]. Retrieved April 9, 2013, from: http://www.phys-astro.sonoma.edu/BruceMedalists/rees/index.html
The Final Mystery
“Gödel was one of the few indubitable geniuses of our century, the only one of our colleagues who walked and talked on equal terms with Einstein”
Rucker, Rudy. 2005. Infinity and the mind. Princeton: Princeton University Press. p 161.
“The human mind is incapable of formulating (or mechanising) all its mathematical intuitions, i.e., if it has succeeded in formulating some of them, this very fact yields new intuitive knowledge, e.g., the consistency of this formalism. This fact may be called the ‘incompletability’ of mathematics.”
Ibid. p 158.
“any limitations of mathematical reasoning, like those uncovered by Gödel, are thus not merely limitations of our mental categories but intrinsic properties of reality and hence limitations upon any attempt to understand the ultimate nature of the universe.”
Barrow, John. D. 1991. Theories of everything. London: Vintage. p 184.
“Chaitin’s discovery implies there can never be a reliable ‘Theory of Everything’, neatly summarising all the basic features of reality in one set of equations.”
Chown, Marcus. 10th March 2001. The omega man. New Scientist. Issue no 2281. p 28.
“up to now, most people have implicitly assumed that there is an ultimate theory that we will eventually discover. Indeed, I myself have suggested we might find it quite soon.”
News report. 05 April 2005. The impossible puzzle. New Scientist. p 34.
“Maybe it is not possible to formulate the theory of the universe in a finite number of statements.”
News report. 05 April 2005. The impossible puzzle. New Scientist. p 34.
“it is a matter of contention whether anything resembling a ‘theory of everything’ will ever be found.”
Penrose, Roger. 2004. The road to reality. London: Vintage. p 1028.
“I don’t think that will be possible, because we can already imagine logically consistent laws of nature that don’t quite describe the world we see [read M- Theory]. We will always be somewhat disappointed...All human beings, whether religious or not, are caught in a tragic situation of never fully being able to understand the world we are in.”
Weinberg, Steven. 15 September 2008. There will be less room for religion. Newsweek. Vol. CL11, No.11. p 51.
“Imagine if you can, four things that have very different sizes. First the entire visible universe, second, the planet Earth. Third, the nucleus of an atom. Fourth, a superstring. The step in size from each of these things to the next is roughly the same. The Earth is smaller than the visible universe by about twenty powers of ten. An atomic nucleus is smaller than the Earth by twenty powers of ten. And a superstring is smaller than a nucleus by twenty powers of ten.”
Dyson, Freeman. 1990. Infinite in all directions. London: Penguin. p 18.
Photographs & Illustrations
Figure 1. Michelangelo, Sistine Chapel ceiling. (1508). The Creation of Adam. [Painting]. Retrieved April 9. 2013, from: http://en.wikipedia.org/wiki/Sistine_Chapel_ceiling#Creation
Figure 2. Courtesy of the Kurt Gödel Papers, Princeton University. Kurt Gödel. [Photoraph]. Retrieved April 9, 2013, from: http://www.ias.edu/people/godel
Figure 3. [Untitled photograph of Alan Turing]. Retrieved April 9, 2013, from: http://www.cctvcamerapros.com/Alan-Turing-Computer-Science-s/369.htm
Figure 4. Jeff Wilson (photographer).(Scientific American, Oct. 210). Steven Weinberg. [Photograph]. Retrieved Aril 9, 2013, from: http://www.scientificamerican.com/article.cfm?id=dr-unification
