Acclaim for John D. Barrow’s
The Book of Nothing
“Barrow is possessed of a polymathic mind that swoops and soars as it plays in the fields of nothingness.… [He] pours this vintage wine out of a Klein bottle of imagination and whimsy, which makes the reader’s effort worthwhile.”
—The Washington Post
“Even when the science gets really difficult, Barrow explains it with great clarity, a lovely lightness of touch and enormous erudition.… He has written an eligible bachelor of a book—witty, suave, rich and immensely learned.”
—The Spectator
“Barrow… writes with liveliness and in a clear-headed, imaginative way.… He is, as clearly proven by his clever and adept references to mathematicians, experimenters, writers, poets, and dreamers throughout the ages of the study of ‘nothingness,’ a master of his art.”
—The Decatur Daily
“Barrow … is very much at home with his topic, from his splendid title onward.… Readers of popular science are well served by Barrow’s apparently effortless range of reference.”
—The Guardian
“Barrow explores, with meticulous scholarly attention to detail, thousands of years of philosophy, mathematics, physics and theology organized around the concept of Nothingness.”
—American Scientist
“A clear, well-organized narrative.… Nothing informs infinite aspects of life and the world at large, and Barrow does an excellent job of bringing its effects to light.”
—Publishers Weekly
“There’s no hotter topic in science than nothing.… And there’s no better writer to introduce it than Professor Barrow.”
—Focus
J O H N D. B A R R O W
The Book of Nothing
John D. Barrow is research professor of mathematical sciences in the Department of Applied Mathematics and Theoretical Physics at Cambridge University. His previous books include Theories of Everything, The Artful Universe, Impossibility, Between Inner Space and Outer Space, The Universe That Discovered Itself, and The Origin of the Universe. He lives in England.
Also by John D. Barrow
Theories of Everything
The Left Hand of Creation (with Joseph Silk)
The Anthropic Cosmological Principle (with Frank J. Tipler)
The World Within the World
The Artful Universe
Pi in the Sky
Impossibility
The Origin of the Universe
Between Inner Space and Outer Space
The Universe That Discovered Itself
In Memory of Dennis Sciama
“From time to time young men have brought me, for my advice, pieces of work, pretty well completed but with no title. This amazes me, for to me the title is the compass-setting by which the whole development is steered. Of course, I may change it on second thoughts, but then whatever emerges in the end is schizophrenic – one cannot serve two masters.”
John L. Synge
Talking About Relativity
Contents
Preface
0 Nothingology – Flying to Nowhere
Mysteries of Non-existence
Nothing Ventured
Nothing Gained
1 Zero – The Whole Story
The Origin of Zero
Egypt – In Need of Nothing
Babylon – The Writing Is on the Wall
The No-entry Problem and the Babylonian Zero
The Mayan Zero
The Indian Zero
Indian Conceptions of Nothingness
The Travelling Zeros
The Evolution of Words for Zero
A Final Accounting
2 Much Ado About Nothing
Welcome to the Hotel Infinity
Greeks, Bearing Gifts
Islamic Art
St Augustine
The Medieval Labyrinth
Writers and Readers
Shakespearean Nothings
Paradox Lost
3 Constructing Nothing
The Search for a Vacuum
A Tale of Two Nothings
How Much of Space Is Space?
4 The Drift Towards the Ether
Newton and the Ether: To Be Or Not To Be?
Darkness in the Ether
Natural Theology of the Ether
A Decisive Experiment
The Amazing Shrinking Man
Einstein and the End of the Old Ether
5 Whatever Happened to Zero?
Absolute Truth – Where Is It To Be Found?
Many Zeros
Creation Out of the Empty Set
Surreal Numbers
God and the Empty Set
Long Division
6 Empty Universes
Dealing With Entire Universes on Paper
Vacuum Universes
Ernst Mach – A Man of Principle
Lambda – A New Cosmic Force
Deep Connections
7 The Box That Can Never Be Empty
It’s a Small World After All
The New Vacuum
All At Sea in the Vacuum
The Lamb Shift
Forces of the World Unite
Vacuum Polarisation
Black Holes
8 How Many Vacuums Are There?
Vacuum Landscape Appreciation
The Unification Road
Vacuum Fluctuations Made Me
Inflation All Over the Place
Multiple Vacuums
Eternal Inflation
Inflation and New Lambda
Falling Downstairs
Bits of Vacuum
9 The Beginning and the End of the Vacuum
Being Out of Nothingness
Creation Out of Nothing
Philosophical Problems About Nothing and How We Escaped From It
Creation Out of Nothing in Modern Cosmology
No Creation Out of Anything?
The Future of the Vacuum
Notes
Preface
“Deciding on a book’s beginning is as complex as determining the origins of the universe.”
Robert McCrum
‘Because it’s not there’ might be reason enough to write a book about Nothing, especially if the author has already written one about Everything. But, fortunately, there are better reasons than that. If one looks at the special problems that were the mainsprings of progress along the oldest and most persistent lines of human inquiry, then one finds Nothing, suitably disguised as something, never far from the centre of things.
Nothing, in its various guises, has been a subject of enduring fascination for millennia. Philosophers struggled to grasp it, while mystics dreamed they could imagine it; scientists strove to create it; astronomers searched in vain to locate it; logicians were repelled by it, yet theologians yearned to conjure everything from it; and mathematicians succeeded. Meanwhile, writers and jesters were happy to stir up as much ado about Nothing as ever they possibly could. Along all these pathways to the truth Nothing has emerged as an unexpectedly pivotal something, upon which so many of our central questions are delicately poised.
Here, we are going to draw together some of the ways in which our conceptions of Nothing influenced the growth of knowledge. We will see how the ancient Western addiction to logic and analytic philosophy prevented progress towards a fruitful picture of Nothing as something that could be part of an explanation for the things that are seen. By contrast, Eastern philosophies provided habits of thought in which the idea of Nothing-as-something was simple to grasp and not only negative in its ramifications. From this first simple step, there followed a giant leap for mankind: the development of universal counting systems that could evolve onwards and upwards to the
esoteric realms of modern mathematics.
In science, we will see something of the quest to make a real vacuum, in the midst of a thousand years of tortuous argument about its possibility, desirability and place. These ideas shaped the future direction of many parts of physics and engineering while, at the same time, realigning the philosophical and theological debates about the possibility and desirability of the vacuum – the physical Nothing. For the theologians, these debates were, in part, the continuation of a crucial argument about the need for the Universe to have been created out of both a physical and a spiritual Nothing. But for the critical philosophers, they were merely particular examples of ill-posed questions about the ultimate nature of things that were gradually falling into disrepute.
At first, such questions about the meaning of Nothing seemed hard, then they appeared unanswerable, and then they appeared meaningless: questions about Nothing weren’t questions about anything. Yet, for the scientists, producing a vacuum appeared to be a physical possibility. You could experiment with the vacuum and use it to make machines: an acid test of its reality. Soon this vacuum seemed unacceptable. A picture emerged of a Universe filled with a ubiquitous ethereal fluid. There was no empty space. Everything moved through it; everything felt it. It was the sea in which all things swam, ensuring that no nook or cranny of the Universe could ever be empty.
This spooky ether was persistent. It took an Einstein to remove it from the Universe. But what remained when everything that could be removed was removed was more than he expected. The combined insights of relativity and the quantum have opened up striking new possibilities that have presented us with the greatest unsolved problems of modern astronomy. Gradually, over the last twenty years, the vacuum has turned out to be more unusual, more fluid, less empty, and less intangible than even Einstein could have imagined. Its presence is felt on the very smallest and largest dimensions over which the forces of Nature act. Only when the vacuum’s subtle quantum influence was discovered could we see how the diverse forces of Nature might unite in the seething microworld inhabited by the most elementary parts of matter.
The astronomical world is no less subservient to the properties of the vacuum. Modern cosmology has built its central picture of the Universe’s past, present and future on the vacuum’s extraordinary properties. Only time will tell whether this construction is built on shifting sand. But we may not have to wait very long. A series of remarkable astronomical observations now seem to be revealing the cosmic vacuum by its effects on the expansion of the Universe. We look to other experiments to tell us whether, as we suspect, the vacuum performed some energetic gymnastics nearly fifteen billion years ago, setting the Universe upon the special course that led it to be what it is today and what it will eventually become.
I hope that this story will convince you that there is a good deal more to Nothing than meets the eye. A right conception of its nature, its properties, and its propensity to change, both suddenly and slowly, is essential if we are to understand how we got to be here and came to think as we do.
The glyphs accompanying the chapter numbers throughout this book, from zero to nine, are reproductions of the beautiful Mayan headvariant numerals. They represent a spectrum of celebrated gods and goddesses and were widely used by the Mayans more than fifteen hundred years ago for recording dates and spans of time.
I would like to thank Rachel Bean, Malcolm Boshier, Mariusz Dbrowski, Owen Gingerich, Jörg Hensgen, Martin Hillman, Ed Hinds, Subhash Kak, Andrei Linde, Robert Logan, João Magueijo, Martin Rees, Paul Samet, Paul Shellard, Will Sulkin, Max Tegmark and Alex Vilenkin for their help and discussions at various times. This book is dedicated to the memory of Dennis Sciama without whose early guidance neither this, nor any of my other writing over the last twenty-five years, would have been possible.
This book has survived one move of house and three moves of office in the course of its writing. In the face of all these changes of vacuum state, I would also like to thank my wife Elizabeth for ensuring that something invariably prevailed over nothing, and our children, David, Roger and Louise, for their unfailing scepticism about the whole project.
J.D.B., Cambridge, May 2000
“As I was going up the stair,
I met a man who wasn’t there.
He wasn’t there again today,
I wish, I wish he’d stay away.”
Hughes Mearns
MYSTERIES OF NON-EXISTENCE
“You ain’t seen nothing yet.”
Al Jolson1
‘Nothing’, it has been said, ‘is an awe-inspiring yet essentially undigested concept, highly esteemed by writers of a mystical or existentialist tendency, but by most others regarded with anxiety, nausea, and panic.’2 Nobody seems to know how to handle it and perplexingly diverse conceptions of it exist in different subjects.3 Just take a look at the entry for ‘nothing’ in any good dictionary and you will find a host of perplexing synonyms: nil, none, nowt,4 nulliform,5 nullity – there is a nothing for every occasion. There are noughts of all sorts to zero-in on, from zero points to zero hours, ciphers to nulliverses.6 There are concepts that are vacuous, places that are evacuated, and voids of all shapes and sizes. On the more human side, there are nihilists,7 nihilianists,8 nihilarians,9 nihilagents,10 nothingarians,11 nullifideans,12 nullibists,13 nonentities and nobodies. Every walk of life seems to have its own personification of nothing. Even the financial pages of my newspaper tell me that ‘zeros’14 are an increasingly attractive source of income.
Some zeros seem positively obscure, almost circumlocutory. Tennis can’t bring itself to use so blunt a thing as the word ‘nil’ or ‘nothing’ or ‘zero’ to record no score. Instead, it retains the antique term ‘love’, which has reached us rather unromantically from l’oeuf, the French for an egg which represented the round 0 shape of the zero symbol.15 Likewise, we still find the use of the term ‘love’ meaning ‘nothing’ as when saying you are playing for love (rather than money), hence the distinction of being a true ‘amateur’, or the statement that one would not do something ‘for love or money’, by which we mean that we could not do it under any circumstances. Other games have evolved anglicised versions of this anyone-for-tennis pseudonym for zero: ‘goose egg’ is used by American ten-pin bowlers to signal a frame with no pin knocked down. In England there is a clear tradition for different sports to stick with their own measure of no score, ‘nil’ in soccer, ‘nought’ in cricket, but ‘ow’ in athletics timings, just like a telephone number, or even James Bond’s serial number. But sit down at your typewriter and 0 isn’t O any more.
‘Zilch’ became a common expression for zero during the Second World War and infiltrated ‘English’ English by the channel of US military personnel stationed in Britain. Its original slang application was to anyone whose name was not known. Another similar alliterative alternative was ‘zip’. A popular comic strip portrays an owl lecturing to an alligator and an infant rabbit on a new type of mathematics, called ‘Aftermath’, in which zero is the only number permitted; all problems have the same solution – zero – and consequently the discipline consists of discovering new problems with that inevitable answer.16
Another curiosity of language is the use of the term ‘cipher’ to describe someone who is a nonentity (‘a cipher in his own household’, as an ineffectual husband and father was once described). Although a cipher is now used to describe a code or encryption involving symbols, it was originally the zero symbol of arithmetic. Here is an amusing puzzle which plays on the double meaning of cipher as a code and a zero:
“U 0 a 0, but I 0 thee
O 0 no 0, but O 0 me.
O let not my 0 a mere 0 go,
But 0 my 0 I 0 thee so.”
which deciphers to read
“You sigh for a cipher, but I sigh for thee
O sigh for no cipher, but O sigh for me.
O let not my sigh for a mere cipher go,
But sigh for my sigh, for I sigh for thee so.”
The sour
ce of the insulting usage of cipher is simple: the zero symbol of arithmetic is one which has no effect when added or subtracted to anything. One Americanisation of this is characteristically racier and derives from modern technical jargon. A null operation is technospeak for an action that has no consequence. Your computer cycles through millions of them while it sits waiting for you to make the next keystroke. It is a neutral internal computer operation that performs no calculation or data manipulation. Correspondingly, to say that someone ‘is a zero, a real null op’ needs no further elucidation. Of course, with the coming of negative numbers new jokes are possible, like that of the individual whose personality was so negative that when he walked into a party, the guests would look around and ask each other ‘who left?’ or the scientist whose return to the country was said to have added to the brain drain. The adjective ‘napoo’, meaning finished or empty, is a contraction of the French il n’y a plus, for ‘there is nothing left’.
Not all nominal associations with ‘nothing’ were derogatory. Sometimes they had a special purpose. When some of the French Huguenots fled to Scotland to escape persecution by Louis XIV they sought to keep their names secret by using the surname Nimmo, derived from the Latin ne mot, meaning no one or no name.
Our system of writing numbers enables us to build up expressions for numbers of unlimited size simply by adding more and more noughts to the right-hand end of any number: 11230000000000 … During the hyperinflationary period of the early 1920s, the German currency collapsed in value so that hundreds of billions of marks were needed to stamp a letter. The economist John K. Galbraith writes17 of the psychological shock induced by these huge numbers with their strings of zeros: