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**
A Brief History of Time
** by
Stephen Hawking

Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, bet made by Stephen Hawking and Kip Thorne, Brownian motion, cosmic microwave background, cosmological constant, dark matter, Edmond Halley, Ernest Rutherford, Henri Poincaré, Isaac Newton, Johannes Kepler, Magellanic Cloud, Murray Gell-Mann, Richard Feynman, Stephen Hawking

There are other models to explain Cygnus X-l that do not include a black hole, but they are all rather far-fetched. A black hole seems to be the only really natural explanation of the observations. Despite this, I had a bet with Kip Thorne of the California Institute of Technology that in fact Cygnus X-l does not contain a black hole! This was a form of insurance policy for me. I have done a lot of work on black holes, and it would all be wasted if it turned out that black holes do not exist. But in that case, I would have the consolation of winning my bet, which would bring me four years of the magazine Private Eye. In fact, although the situation with Cygnus X-l has not changed much since we made the bet in 1975, there is now so much other observational evidence in favor of black holes that I have conceded the bet.

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This would offer great possibilities for travel in space and time, but unfortunately it seems that these solutions may all be highly unstable; the least disturbance, such as the presence of an astronaut, may change them so that the astronaut could not see the singularity until he hit it and his time came to an end. In other words, the singularity would always lie in his future and never in his past. The strong version of the cosmic censorship hypothesis states that in a realistic solution, the singularities would always lie either entirely in the future (like the singularities of gravitational collapse) or entirely in the past (like the big bang). I strongly believe in cosmic censorship so I bet Kip Thorne and John Preskill of Cal Tech that it would always hold. I lost the bet on a technicality because examples were produced of solutions with a singularity that was visible from a long way away. So I had to pay up, which according to the terms of the bet meant I had to clothe their nakedness. But I can claim a moral victory. The naked singularities were unstable: the least disturbance would cause them either to disappear or to be hidden behind an event horizon.

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ALSO BY STEPHEN HAWKING A Briefer History of Time Black Holes and Baby Universes and Other Essays The Illustrated A Brief History of Time The Universe in a Nutshell The Grand Design FOR CHILDREN George’s Secret Key to the Universe (with Lucy Hawking) George’s Cosmic Treasure Hunt (with Lucy Hawking) A BRIEF HISTORY OF TIME A Bantam Book Publishing History Bantam illustrated hardcover edition published November 1996 Bantam hardcover edition/September 1998 Bantam trade paperback edition/September 1998 All rights reserved. Copyright © 1988, 1996 by Stephen Hawking Illustrations copyright © 1988 by Ron Miller BOOK DESIGN BY GLEN M. EDELSTEIN No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher.

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What We Cannot Know: Explorations at the Edge of Knowledge
** by
Marcus Du Sautoy

Albert Michelson, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, banking crisis, bet made by Stephen Hawking and Kip Thorne, Black Swan, Brownian motion, clockwork universe, cosmic microwave background, cosmological constant, dark matter, Dmitri Mendeleev, Edmond Halley, Edward Lorenz: Chaos theory, Ernest Rutherford, Georg Cantor, Hans Lippershey, Harvard Computers: women astronomers, Henri Poincaré, invention of the telescope, Isaac Newton, Johannes Kepler, Magellanic Cloud, mandelbrot fractal, MITM: man-in-the-middle, Murray Gell-Mann, music of the spheres, Necker cube, Paul Erdős, Pierre-Simon Laplace, Richard Feynman, Skype, Slavoj Žižek, Solar eclipse in 1919, stem cell, Stephen Hawking, technological singularity, Thales of Miletus, Turing test, wikimedia commons

In fact, there was one notable person who made a bet in 1975 to the effect that Cygnus X-1 was not a black hole: Stephen Hawking. This was somewhat odd, given that he’d dedicated much of his research to probing the nature of black holes. If Cygnus X-1 turned out to be the first example of a black hole, all Hawking’s theoretical musings would have been justified. As he explained in A Brief History of Time, the bet was an insurance policy. Betting against your football team winning the final of the FA cup is a win–win situation: if your team loses, at least you benefit financially. If it turned out that his life’s work on black holes was a waste of time, then at least he’d won the bet. His prize? A subscription to Private Eye magazine to distract him from the misery of his failed research. He made the bet with fellow cosmologist Kip Thorne. Convincing evidence that proved that Cygnus X-1 was indeed a black hole would win Thorne a subscription to the journal of his choice.

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If I throw my casino dice into the black hole, can I somehow tell how it lands from the particles emitted at the edge of the event horizon? Perhaps, like the magazines being burnt, there is in theory a way to untangle this radiation and retrieve information about everything that disappears behind the event horizon. The puzzle of what happens to the information is called the black hole information paradox. In 1997 Hawking took out another bet, and this time Kip Thorne sided with him. Their bet was with Caltech theoretical physicist John Preskill. They believed that this loss of information was inevitable. But, given that it contradicted the theory of quantum physics, Preskill wasn’t prepared to concede that information was lost. Rather than magazine subscriptions, the wager this time was an encyclopedia of the winner’s choice. The choice of an encyclopedia captured the idea that if it was thrown into a black hole, could the information contained in the encyclopedia somehow be encoded in the new particles being radiated thanks to the uncertainty principle?

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Eddington could see what the maths was implying but baulked at the implications: ‘When we prove a result without understanding it – when it drops unforeseen out of a maze of mathematical formulae – we have no grounds for hoping that it will apply.’ But in 1964 Oxford mathematician Roger Penrose proved that such singular points were a necessary consequence of the theory of general relativity. A black hole in two-dimensional space-time. The event horizon is a circle inside of which we cannot know. In collaboration with a young Stephen Hawking, Penrose went on to prove that the same infinite density is predicted when we rewind the universe back to the Big Bang. Both black holes and the Big Bang are examples in general relativity of a mathematical entity called a singularity. Singularities encompass a whole range of situations where it is impossible to work out what’s happening. A singularity is a point at which our ability to model the scenario breaks down.