The Infinite Book: A Short Guide to the Boundless, Timeless and Endless

308 Pages·2006·3.84 MB·English

by  John D. Barrow

Table of Contents
Title Page
Dedication
Epigraph
Praise
Preface
chapter one - Much Ado about Everything
THE ROUGH GUIDE TO INFINITY
INTIMATIONS OF THE INFINITE
ZENO HOUR
chapter two - Infinity, Almost and Actual, Fictitious and Factual
DARKNESS AT NOON
A PURELY ARISTOTELIAN RELATIONSHIP
INFINITY AND GOD
A LITTLE KANT
chapter three - Welcome to the Hotel Infinity
HOTELS
EXPERIENCES OF THE HOTEL INFINITY
THE HOTEL INFINITY’S ACCOUNTS
chapter four - Infinity Is Not A Big Number
AN IMMACULATE MISCONCEPTION
ALBERT OF SAXONY’S PARADOX
GALILEO’S PARADOX
CADMUS AND HARMONIA
TERMINATOR 0, ½ AND 1
COUNTABLE INFINITIES
UNCOUNTABLE INFINITIES
THE TOWERING INFINITO
chapter five - The Madness of Georg Cantor
CANTOR AND SON
THE CHRONICLE OF KRONECKER
CANTOR, GOD, AND INFINITY– THE TRINITY WITH AFFINITY
ALL’S SAD THAT ENDS BAD
chapter six - Infinity Comes in Three Flavours
TRIPLE TOP
LET’S GET PHYSICAL
NAKED INFINITIES
THE GREAT BLUE YONDER
INFINITY ON THE BACK FOOT
chapter seven - Is the Universe Infinite?
EVERYTHING THAT IS
COSMOLOGY GOES UNDERGROUND
BENT UNIVERSES
THE PROBLEM OF TOPOLOGY
THE PROBLEM OF UNIFORMITY
THE PROBLEM OF ACCELERATION
WHERE DOES THIS LEAVE US?
THE SHINING
chapter eight - The Infinite Replication Paradox
A UNIVERSE WHERE NOTHING IS ORIGINAL
THE GREAT ESCAPE
THE TEMPORAL VERSION– BEEN THERE, DONE THAT
THE NEVER-ENDING STORY
THE ETHICS OF THE INFINITE
chapter nine - Worlds Without End
OTHER WORLDS IN HISTORY
OUT OF THIS WORLD
INFLATION– HERE, THERE, AND EVERYWHERE
CONSCIOUS INTERVENTIONS– MEN IN BLACK
SIMULATED UNIVERSES
HOW SHOULD WE THEN LIVE?
chapter ten - Making Infinity Machines
SUPER-TASKS
RUBBING THOMSON’S LAMP
SOME NORSE CODE
THE END-GAME PROBLEM
RELATIVITY AND THE AMAZING SHRINKING MAN
A MATTER OF TIMING
NEWTONIAN SUPER-TASKS
RELATIVISTIC SUPER-TASKS
BIG BANGS AND BIG CRUNCHES
chapter eleven - Living Forever
CHILDHOOD’S END
THE SOCIOLOGY OF ETERNITY
THE PROBLEM-PAGE OF THE UNENDING FUTURE
THE STRANGE, FAMILIAR, AND FORGOTTEN
INCESTUOUS TIME TRAVEL
THE GRANDMOTHER PARADOX
CONSISTENT HISTORIES
TOURISTS FROM THE FUTURE
TIME TRAVELLERS IN THE FINANCIAL WORLD: PERPETUAL MONEY MACHINES
WHY YOU CAN’T CHANGE THE PAST
INFINITY – WHERE WILL IT ALL END?
Notes
Acknowledgments
About the Author
BY THE SAME AUTHOR
Copyright Page
To Luca Ronconi
for his boundless imagination
‘A lot of English writers are consigned to writing about adultery in Camden
because the big themes are elsewhere’
1
Damon Galgut
Praise for John D. Barrow’s
THE INFINITE BOOK
“Truly mind-expanding stuff. If, like Blake, you want to hold infinity in the palm
of your hand, then this is for you.”
—The Guardian (London) “For those who like some deep thinking with their
reading. . . . So engrossing, it became difficult to tear away from it.”
—Tampa Tribune
“A delight. I have read all of Barrow’s books, and this is the one I have enjoyed
the most. . . . [It] is definitely the most readable and the most fun. . . . Barrow
offers a fresh view of things. . . . Popular science doesn’t come much better than
this.”
—The Independent (London) “Provocative. . . . Barrow [is] a lucid and
compelling writer.”
—Discover
“If you enjoy a good intellectual wrestle, this book is for you. . . . [It] makes you
realise that in the wonderful and immeasurable things of life such as love, beauty
and infinity, science has nothing half as interesting to say as the imagination.”
—Daily Mail
Preface
‘I am painting the infinite’
2
Vincent van Gogh
This is a book about the biggest subject of all. It’s the ultimate traveller’s guide
to everything that could be: the rough and the smooth guide to infinity.
Infinity has haunted human minds for thousands of years. It challenges
theologians and scientists alike to understand it, cut it down to size, find out if it
comes in different shapes and sizes, and decide whether we want to outlaw or
welcome it into our human descriptions of the Universe. Is it part of the problem
or part of the solution?
It is also a live issue. Physicists’ accelerating quest for a Theory of Everything
has been primarily guided by an attitude towards infinities. Their appearance can
be a warning that you have entered a blind alley on the road to the truth. The
enthusiasm with which superstring theories were embraced was a consequence
of their ingenious evasion of the problem of infinities that had plagued all their
predecessors.
These exciting new theories leave us to decide whether we should expect
matter to be infinitely divisible. Will we always be able to find ever smaller,
more elementary, particles inside any that we have, like a never-ending sequence
of Russian dolls? Or is there a limit, a smallest ‘thing’, a smallest size, or a
shortest time, where division comes to a full stop? Or perhaps the fundamental
entities out of which the world is woven are not really little particles at all?
Cosmologists have their own problems with infinities. For decades they have
been happy to live with the notion that the Universe of space and time began at a
‘singularity’, where its temperature, its density, and just about everything else,
was infinite. But will the marriage of gravity and the quantum really permit