“‘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’,18 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.
NOTHING VENTURED
“Now, is art about drawing or is it about colouring in?”
Ali G
“Nothing is closer to the supreme commonplace of our commonplace age than its preoccupation with Nothing … Actually, Nothing lends itself very poorly indeed to fantastic adornment.”
Robert M. Adams19
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 charlatan20 but others admired his art noir: ‘an ultimate statement of esthetic purity’, according to American art commentator Hilton Kramer.21 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.22 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.23
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’.25
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 …”26
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.
NOTHING GAINED
“Nothing is real.”
The Beatles, “Strawberry Fields Forever”
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,27 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?
“Is it not mysterious that we can know more about things which do not exist than about things which do exist?”
Alfréd Renyi1
“Round numbers are always false.”
Samuel Johnson2
THE ORIGIN OF ZERO
“The great mystery of zero is that it escaped even the Greeks.”
Robert Logan3
When we look back at the system of counting that we learned first at school it seems that the zero is the easiest bit. We used it to record what happens when nothing is left, as with a sum like 6 minus 6, and anything that gets multiplied by zero gets reduced to zero, as with 5 × 0 = 0. But we also used it when writing numbers to signal that there is an empty entry, as when we write one-hundred and one as 101.
These are such simple things – much simpler than long division, Pythagoras’ Theorem, or algebra – that it would be easy to assume t
hat zero must have been one of the first pieces of arithmetic to be developed by everyone with a counting system, while the more difficult ideas like geometry and algebra were only hit upon by the most sophisticated cultures. But this would be quite wrong. The ancient Greeks, who developed the logic and geometry that form the basis for all of modern mathematics, never introduced the zero symbol. They were deeply suspicious of the whole idea. Only three civilisations used the zero, each of them far from the cultures that would evolve into the so-called Western world, and each viewed its role and meaning in very different ways. So why was it so difficult for the zero symbol to emerge in the West? And what did the difficulty have to do with Nothing?
As the end of the year 1999 approached, the newspapers devoted more and more copy to the impending doom that was to be wrought by the Millennium Bug. The reason for this collective loss of sleep, money and confidence was the symbol ‘zero’, or two of them to be more precise. When the computer programs that control our transport and banking systems were first written, computers were frugal with memory space – it was much more expensive than it is today.4 Anything that could save space was a money-saving bonus. So when it came to dating everything that the computer did, instead of storing, say, 1965, the computer would just store the last two digits, 65. Nobody thought as far ahead as the year 2000 when computers would be faced with making sense of the truncated ‘date’00. But if there is one thing that computers really don’t like, it’s ambiguity. What does 00 mean to the computer? To us it’s obviously short for year 2000. But the computer doesn’t know it isn’t short for 1900, or 1800 for that matter. Suddenly, you might be told that your credit card with its 00 expiry year is 99 years out of date. Born in 1905? Maybe the computer would soon be mailing out your new elementary-school application forms. Still, things didn’t turn out as badly as the pessimists predicted.5
The Book of Nothing Page 2