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One of our foremost mathematicians and cosmologists – John Barrow has a proven ability to make complex ideas easily accessible to the reader. Beginning with ancient civilizations, he explores how the zero came into being, its rocky reception in Europe, and the early avoidance and eventual acceptance of the void by Christianity. Investigating the concept of nothing through the work of writers from the ancient Greeks to the present, he examines mathematics, cosmology, theology and physics to reveal the nothing that...
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One of our foremost mathematicians and cosmologists – John Barrow has a proven ability to make complex ideas easily accessible to the reader. Beginning with ancient civilizations, he explores how the zero came into being, its rocky reception in Europe, and the early avoidance and eventual acceptance of the void by Christianity. Investigating the concept of nothing through the work of writers from the ancient Greeks to the present, he examines mathematics, cosmology, theology and physics to reveal the nothing that is at the heart of most things. Finally, Barrow spotlights recent exciting discoveries in astronomy about the nature of the vacuum which are dramatically affecting scientific explanations of the universe.
Flying to Nowhere
'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.'Nobody seems to know how to handle it and perplexingly diverse conceptions of it exist in different subjects.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, nulliform, 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.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, nihilianists, nihilarians, nihilagents, nothingarians, nullifideans, nullibists,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'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.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.
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 source 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 writes of the psychological shock induced by these huge numbers with their strings of zeros:
"'Zero stroke' or 'cipher stroke' is the name created by German physicians for a prevalent nervous malady brought about by the present fantastic currency figures. Scores of cases of the 'stroke' are reported among men and women of all classes, who have been prostrated by their efforts to figure in thousands of millions. Many of these persons apparently are normal, except for a desire to write endless rows of ciphers."
Pockets of hyperinflation persist around the globe; indeed there are more zeros around today than at any other time in history. The introduction of binary arithmetic for computer calculation, together with the profusion of computer codes for the control of just about everything, has filled machines with 0s and 1s. Once you had a ten per cent chance of happening upon a zero, now it's evens. But there are huge numbers that are now almost commonplace. Everyone knows there are billions and billions of stars, and national debts conjure up similar astronomical numbers. Yet we have found a way to hide the zeros: 109 doesn't look as bad as 1,000,000,000.
The sheer number of synonyms for 'nothing' is in itself evidence of the subtlety of the idea that the words try to capture. Greek, Judaeo-Christian, Indian and Oriental traditions all confronted the idea in different ways which produced different historical threads. We will find that the concept of nothingness that developed in each arena merely to fill some sort of gap then took on a life of its own and found itself describing a something that had great importance. The most topical example is the physicists' concept of nothing — the vacuum. It began as empty space — the void, survived Augustine's dilution to 'almost nothing', turned into a stagnant ether through which all the motions in the Universe swam, vanished in Einstein's hands, then re-emerged in the twentieth-century quantum picture of how Nature works. This perspective has revealed that the vacuum is a complex structure that can change its character in sudden or gradual ways. Those changes can have cosmic effects and may well have been responsible for endowing the Universe with many of its characteristic features. They may have made life a possibility in the Universe and one day they may bring it to an end.
When we read of the difficulties that the ancients had in coming to terms with the concept of nothing, or the numeral for zero, it is difficult to put oneself in their shoes. The idea now seems commonplace. But mathematicians and philosophers had to undergo an extraordinary feat of mental gymnastics to accommodate this everyday notion. Artists took rather longer to explore the concepts of Nothing that emerged. But, in modern times, it is the artist who continues to explore the paradoxes of Nothing in ways that are calculated to shock, surprise or amuse.
In the 1950s artists began to explore the limiting process of going from polychrome to monochrome to nullichrome. The American abstract artist Ad Reinhardt produced canvases coloured entirely red or blue, before graduating to a series of five-foot square all-black productions that toured the leading galleries in America, London and Paris in 1963. Not surprisingly, some critics condemned him as a charlatan but others admired his art noir: 'an ultimate statement of esthetic purity', according to American art commentator Hilton Kramer.Reinhardt went on to run separate exhibitions of his all-red, all-blue and all-black canvases and writes extensively about the raison d'être for his work.It is a challenge to purists to decide whether Reinhardt's all-black canvases capture the representation of Nothing more completely than the all-white canvases of Robert Rauschenberg. Personally, I prefer the spectacular splash of colours in Jasper Johns' The Number Zero.
The visual zero did not need to be explicitly represented by paint or obliquely signalled by its absence. The artists of the Renaissance discovered the visual zero for themselves in the fifteenth century and it became the centrepiece of a new representation of the world that allowed an infinite number of manifestations. The 'vanishing point' is a device to create a realistic picture of a three-dimensional scene on a flat surface. The painter fools the eye of the viewer by imagining lines which connect the objects being represented to the viewer's eye. The canvas is just a screen that intervenes between the real scene and the eye. Where the imaginary lines intersect that screen, the artist places his marks. Lines running parallel to the screen are represented by parallel lines which recede to the line of the distant horizon, but those seen as perpendicular to the screen are represented by a cone of lines that converge towards a single point — the vanishing point — which creates the perspective of the spectator.
Musicians have also followed the piper down the road to nothingtown. John Cage's musical composition 4¢ 33? — enthusiastically encored in some halls — consists of 4 minutes and 33 seconds of unbroken silence, rendered by a skilled pianist wearing evening dress and seated motionless on the piano stool in front of an operational Steinway. Cage explains that his idea is to create the musical analogue of absolute zero of temperature24 where all thermal motion stops. A nice idea, but would you pay anything other than nothing to see it? Martin Gardner tells us that 'I have not heard 4¢ 33? performed but friends who have tell me that it is Cage's finest composition'.
Writers have embraced the theme with equal enthusiasm. Elbert Hubbard's elegantly bound Essay on Silence contains only blank pages, as does a chapter in the autobiography of the English footballer Len Shackleton which bears the title 'What the average director knows about football'. An empty volume, entitled The Nothing Book, was published in 1974 and appeared in several editions and even withstood a breach of copyright action by the author of another book of blank pages.
Another style of writing uses Nothing as a fulcrum around which to spin opposites that cancel. Gogol's Dead Souls begins with a description of a gentleman with no characteristics arriving at a town known only as N.:
"The gentleman in their carriage was not handsome but neither was he particularly bad-looking; he was neither too fat nor too thin; he could not be said to be too old, but he was not too young either."
A classic example of this adversarial descriptive style, in which attributes and counter-attributes cancel out to zero, is to be found on a woman's tomb in Northumberland. The family inscribed the words
"She was temperate, chaste, and charitable, but she was proud, peevish, and passionate. She was an affectionate wife and tender mother but her husband and child seldom saw her countenance without a disgusting frown . . ."
Not to be forgotten, of course, are those commercial geniuses who are able to make more out of nothing than most of us can earn from anything. 'Polo, the mint with the hole' is one of the best-known British advertising pitches for a sweet that evolved independently as a 'Lifesaver' in the United States. More than forty years of successful marketing have promoted the hole in the mint rather than the mint itself. Nobody seems to notice that they are buying a toroidal confection that contains a good chunk of empty space, but then he wouldn't.
So much for these snippets of nothing. They show us nothing more than that there is a considerable depth and breadth to the contemplation of Nothing. In the chapters to come, we shall explore some of these unexpected paths. We shall see that, far from being a quirky sideshow, Nothing is never far from the central plots in the history of ideas. In every field we shall explore, we shall find that there is a central issue which involves a right conception of Nothing, and an appropriate representation of it. Philosophical overviews of key ideas in the history of human thought have always made much of concepts like infinity,but little of Nothing. Theology was greatly entwined with the complexities of Nothing, to decide whether we were created out of it and whether we risked heading back into its Godless oblivion. Religious practices could readily make contact with the reality of Nothingness through death. Death as personal annihilation is an ancient and available variety of Nothing, with traditional functions in artistic representation. It is a terminus, a distancing, suggesting an ultimate perspective or perhaps a last judgement; and its cold reality can be used to spook the complacent acceptance of a here-and-now to which listeners are inevitably committed.
One of our aims is to right this neglect of nothing and show a little of the curious way in which Nothing in all its guises has proved to be a key concept in many human inquiries, whose right conception has opened up new ways of thinking about the world. We will begin our nullophilia by investigating the history of the concept and symbol for the mathematicians' zero. Here, nothing turns out to be quite as one expected. The logic of the Greeks prevents them having the idea at all and it is to the Indian cultures that we must look to find thinkers who are comfortable with the idea that Nothing might be something. Next, we shall follow what happened after the Greeks caught up. Their battle with zero focused upon its manifestation as a physical zero, the zero of empty space, the vacuum and the void. The struggle to make sense of these concepts, to incorporate them into a cosmological framework that impinged upon everyday experiences with real materials, formed the starting point for an argument that would continue unabated, becoming ever more sophisticated, for nearly two thousand years. Medieval science and theology grappled constantly with the idea of the vacuum, trying to decide questions about its physical reality, its logical possibility and its theological desirability.
Part of the problem with zero, as with the complementary concept of infinity, was the way in which it seemed to invite paradox and confusing self-reference. This was why so many careful thinkers had given it such a wide berth. But what was heresy to the logician was a godsend to the writer. Countless authors avoided trouble with Nothing by turning over its paradoxes and puns, again and again, in new guises, to entertain and perplex. Whereas the philosopher might face the brunt of theological criticism for daring to take such a sacrilegious concept seriously, the humorist trying to tell his readers that 'Nothing really matters' could have his cake and eat it, just as easily as Freddie Mercury. If others disapproved of Nothing, then the writer's puns and paradoxes just provided more ammunition to undermine the coherence of Nothing as a sensible concept. But when it came back into fashion amongst serious thinkers, then were not his word games profound explorations of the bottomless philosophical concept that Nothingness presented?
Hand-in-hand with the searches for the meaning of Nothing and the void in the Middle Ages, there grew up a serious experimental philosophy of the vacuum. Playing with words to decide whether or not a vacuum could truly exist was not enough. There was another route to knowledge. See if you could make a vacuum. Gradually, theological disputes about the reality of a vacuum became bound up with a host of simple experiments designed to decide whether or not it was possible to evacuate a region of space completely. This line of inquiry eventually stimulated scientists like Torricelli, Galileo, Pascal and Boyle to use pumps to remove air from glass containers and demonstrate the reality of the pressure and weight of the air above our heads. The vacuum had become part of experimental science. It was also very useful.
Still, physicists doubted whether a true vacuum was possible. The Universe was imagined to contain an ocean of ethereal material through which we moved but upon which we could exert no discernible effect. The science of the eighteenth and nineteenth centuries grappled with this elusive fluid and sought to use its imagined presence to explain the newly appreciated natural forces of electricity and magnetism. It would only be banished by Einstein's incisive genius and Albert Michelson's experimental skill. Together they removed the need and the evidence for a cosmic ether. By 1905 a cosmic vacuum had become possible again.
Things soon changed. Einstein's creation of a new and spectacular theory of gravity allowed us to describe a space that is empty of mass and energy with complete mathematical precision. Empty universes could exist.
Yet something had been missed out in the world of the very small. The quantum revolution showed us why the old picture of a vacuum as an empty box was untenable. Henceforth, the vacuum was simply the state that remained when everything that could be removed from the box was removed. That state was by no means empty. It was merely the lowest energy state available. Any small disturbances or attempts to intervene would raise its energy.
Gradually, this exotic new picture of quantum nothingness succumbed to experimental exploration. The multiplication of artificial voids by scientists at the end of the nineteenth century had paved the way for all sorts of useful and now familiar developments in the form of vacuum tubes, light bulbs and X-rays. Now the 'empty' space itself started to be probed. Physicists discovered that their defensive definition of the vacuum as what was left when everything that could be removed had been removed was not as silly as it sounds. There was always something left: a vacuum energy that permeated every fibre of the Universe. This ubiquitous, irremovable vacuum energy was detected and shown to have a tangible physical presence. Only relatively recently has its true importance in the cosmic scheme of things begun to be appreciated. We shall see that the world may possess many different vacuum states. A change from one to another may be possible under certain circumstances, with spectacular results. Remarkably, it appears that such a transition is very difficult to avoid during the first moments of our Universe's expansion. More remarkable still, such a transition could have a host of nice consequences, showing us why the Universe possesses many unusual properties which would otherwise be a complete mystery to us.
Finally, we shall run up against two cosmological mysteries about Nothing. The first is ancient: the problem of creation out of nothing — did the Universe have a beginning? If so, out of what did it emerge? What are the religious origins of such an idea and what is its scientific status today? The second is modern. It draws together all the modern manifestations of the vacuum, the description of gravity and the inevitability of energy in a quantum vacuum. Einstein showed us that the Universe might contain a mysterious form of vacuum energy. Until very recently, astronomical observations could only show that if this energy is present, as an all-pervading cosmic influence, then its intensity must be fantastically small if it is not to come to dominate everything else in the Universe. Physicists have no idea how its influence could remain so small. The obvious conclusion is that it isn't there at all. There must be some simple law of Nature that we have yet to find that restores the vacuum and sets this vacuum energy equal to zero. Alas, such a hope may be forlorn. Last year, two teams of astronomers used Earth's most powerful telescopes together with the incomparable optical power of the Hubble Space Telescope to gather persuasive evidence for the reality of the cosmic vacuum energy. Its effects are dramatic. It is accelerating the expansion of the Universe. And if its presence is real, it will set the future course of the Universe, and determine its end. What better place to begin?