Something From Nothing
God is that which nothing is greater than. So, in essence, goes Anselm’s famous proof of God’s existence. According to the 11th-century saint, the deity was that entity of which nothing more perfect could possibly be conceived. Throughout the Middle Ages, Anselm’s argument carried enormous weight, but even in its heyday, this seemingly impregnable logic was the source of much vexation. Literal scrutiny of his words reveals why, and even Anselm himself acknowledges that there is something greater than God, namely nothing.
Anxiety about nothing-which has long been pregnant with heretical implications-has been a major theme of Western thought for close to three millenniums. It was hated, even feared, by the ancient Greek philosophers and medieval Christian theologians alike, and for much of our history, the mere possibility of nothing was strenuously denied. “Nature abhors a vacuum,” Aristotle declared in the 4th-century BC, effectively silencing dissent for the next 2,000 years.
In the “age of science,” however, attitudes toward nothingness-what the ancients called the void and what is now referred to as the vacuum-have undergone a dramatic shift. Beginning with Galileo, who made empty space the arena of reality, modern physicists have gradually raised the status of nothing. Today many physicists believe that nothingness is the foundation of everything, not just the arena in which matter resides but the substrate from which matter is actually constructed. As physicists envision the universe now, everything that exists is ultimately just a complex enfolding of the underlying substrate of empty space. This vision presents the universe, as English physicist Paul Davies has summed it up, as “nothing but structured nothingness.” Indeed, it might be said that one way of characterizing the history of modern physics is the gradual rise in the status of nothing from anathema to supreme principle.
Small wonder, then, that in the last 18 months there have been several books that have chronicled the history of nothing and our changing attitudes to this most enigmatic concept. The most recent of these texts and the widest ranging is English physicist John D. Barrow’s “The Book of Nothing.” Fans of physics will know Barrow from such previous works as “Theories of Everything” and “The Anthropic Cosmological Principle,” and here he demonstrates again his ability to explicate difficult subjects.
This time he casts his net wide, exploring the idea of nothing in natural science and mathematics (where it manifests as zero) and in theology, literature and philosophy. Although patchy in execution, Barrow’s efforts to relate scientific developments to wider cultural themes must be applauded. Some of his most fascinating chapters are those that deal with the medieval and early modern eras.
Discussing the medieval antipathy to nothing, Barrow notes that Christian attitudes were inherited not only from the Greek philosophers (many of whom agreed with Aristotle) but also from the Jewish tradition, which saw nothing as the antithesis of God: He whose defining act had been to create the world out of nothing. “What stronger evidence could there be that Nothing was something undesirable: a state without God, a state which He had acted to do away with,” Barrow writes.
For Christians, nothingness was the characteristic of being apart from God, hence it was considered atheistic to speak seriously of the void. St. Augustine equated nothing with the Devil; for him nothing represented the greatest evil. How then could it exist before the creation of the world?
The prior existence of nothing implied there was something God lacked before He created the universe, an idea so heretical it had to be combated.
Augustine’s solution to this dilemma remains one of the great leaps in Western intellectual history: The universe was not created in time, he declared, but with time. That is, when God created the world so too He created time. There was no nothing before creation because there was quite simply no before. More than 1,500 years later, physicist Stephen Hawking proposed the same idea, albeit outside the theological context, in his bestselling book, “A Brief History of Time.”
Christianity, however, is a dynamic system, and by the late 13th century, the existence of nothing-or at least the possibility of true empty space-was being championed by some of the most conservative theologians. Charles Seife, a mathematician and science writer, recounts how Aristotle’s injunction against the void itself turned out to harbor heretical implications. To his medieval disciples, the impossibility of a void implied that there could be no empty space around the universe, which people of the Middle Ages believed to be a small sphere surrounding the Earth. But if there was no space around the universe, there would be no other place to move the universe to; hence they concluded the universe could not be moved. Such a view was clearly in conflict with the idea of God’s omnipotence and, in 1277, the bishop of Paris, Stephen Tempier, issued a decree against the limiting tendencies of Aristotelian thinking. As Seife puts it, “Tempier insisted that God could break any Aristotelian law,” in particular He could create a vacuum, a genuine region of nothingness, by act of His will.
The effect of Tempier’s decrees-underplayed both by Seife and Barrow-was to initiate a new era in thinking about space and motion, an effort that culminated in the achievements of the proto-physicists of the early 14th century who first articulated the concepts of velocity and acceleration.
Three hundred years later, Galileo would complete this revolution by making empty space the foundation of his world-picture, the neutral background against which the motion of matter was mechanistically played out.
In the Newtonian world-picture that was the crowning achievement of the scientific revolution, empty space shares equal billing with matter and force as one of the three fundamental pillars of reality. With the development of 20th-century physics, the status of empty space would rise even higher, eventually eclipsing matter and force to stand alone as the ultimate foundation of all that is.
Yet while the West recoiled against the void, this horror vacui was not universally shared. Both Barrow and Seife recount how for some cultures, especially among the Arabs, the Chinese and the Indians, nothingness was a concept to be embraced and celebrated. “Rather than sweep Nothing away under the carpet as a philosophical embarrassment,” Barrow writes, “Islamic artists simply saw the void as a challenging emptiness to be filled.”
And so they covered every available surface on their temples with intricate geometric patterns, literally paying homage to the void. Buddhists too have a deep respect for the void, seeing in nothingness the ultimate reality and aiming with their contemplative practices to experience the true reality of nonbeing.
Perhaps no one has embraced nothing as strongly as the Indians who, Seife notes, “never had a fear of the infinite or of the void.” Hinduism has embedded within it, a complex philosophy of nothingness, seeing everything in the world as arising from the pregnant void, known as Sunya.
The ultimate goal of the Hindu was to free himself from the endless cycle of pain found in continual reincarnation and reconnect with the Nothingness that is the source and fundament of the All.
For Indians, the void of Sunya was the very font of all potential; nothingness was liberation. No surprise then that it is from this sophisticated culture that we inherit the mathematical analog of nothing, zero. Like Sunya, zero is a kind of place holder, a symbol signifying a pregnant space where any other number might potentially reside.
The earliest known example of zero appears in a Jain manuscript on cosmology from AD 458, though indirect evidence suggests it must have been in use in India as early as 200 BC.
In the 7th century after Christ, the Indian astronomer Brahmaghupta formally defined zero and spelled out the algebraic rules for adding, subtracting, multiplying and dividing with it. Yet the West was appalled by this enigmatic symbol when European scholars first encountered it via the Arab world.
How could you signify nothing? To do so was to acknowledge its existence, the very position early medieval thinkers had so sought to avoid.
The history of zero-the mathematical nothing-is covered briefly by both Barrow and Seife, and it is the focus of mathematician Robert Kaplan’s elegant “The Nothing That Is.” This story is also told with rare insight by Brian Rotman in his seminal 1987 book “Signifying Nothing,” which remains the benchmark in the scholarship of zero.
Kaplan traces zero’s progress through the ages, a process beset with obstacles both theological and practical. In the end it was the practical applications that won the day, for zero was the crux of that great medieval invention, double entry bookkeeping. All the priests’ arguments were finally no match for the emerging power of the modern capitalist machine.
All those zeros at the bottoms of merchants’ ledgers-each signifying a perfect balance of credits and debits-served to impart to zero the status of a true number; a status that was further enhanced by the introduction of negative numbers, which also arose naturally in the new system, as when debts exceeded earnings.
Slowly, zero came to be seen as one point along a continuous spectrum, the fulcrum of a line stretching indefinitely to the left with the negative numbers and indefinitely to the right with the positives.
With varying examples, all three authors reveal the ways in which in modern mathematics, zero has taken on a life of its own. No longer simply a number, zero has become one of the pivotal concepts in many mathematical systems. In calculus and analytic geometry, it manifests as the maxima and minima of functions (Kaplan); in set theory, it becomes the null or empty set (Barrow), and as Seife stresses, it is “infinity’s twin.” Dividing by zero always equals infinity; the two numbers are thereby conjoined in a strange symbiosis being, as Seife puts it, “equal and opposite and equally destructive.”
Perhaps nothing has surprised mathematicians so much as the fact that all the numbers can be generated from the nothingness of the empty set, a feat elegantly demonstrated by John von Neumann, the great architect of the modern electronic computer. On first encounter, many people find von Neumann’s prestidigitation unsettling, Kaplan tells us, frankly likening this mathematical hat trick to setting a host of angels “dancing on the head of a pin.” That the entire spectrum of the numbers can be created ex nihilo, as it were, remains one of the more enigmatic features of modern mathematics.
Over the last century an eerie parallel has also been found in physics, for physicists now believe that everything in our universe-every speck of matter and every active force-arose from the nothingness of empty space. One of the most important stories of modern science has been the gradual folding of more and more elements of our world-picture into the fabric of space.
Einstein began the process, inadvertently it must be said, by revealing with his general theory of relativity that gravity could be understood as a byproduct of the underlying curvature of space. Unlike Newton, for whom gravity remained the ultimate mystery, Einstein’s theory places the origin of this fundamental force in the architecture of the void. Both Barrow and Seife describe this astonishing insight, which remains physics’ most compelling and mystical achievement.
That something as powerful as gravity-the force which holds our planet in orbit around the sun and our sun in orbit around the galaxy-could be a byproduct of empty space seems to defy reason. The equations of general relativity even allow, as Barrow tells us, for the existence of empty universes: vast expanses of space and time devoid of matter and energy. Physicists refer to these as “vacuum” universes. Such a world would be Augustine’s nightmare, a pure and purposeless void, in the most profound sense.
But the pure void of general relativity is itself an abstraction; physicists have since discovered that the vacuum is far from empty. That other great pillar of 20th-century physics, quantum mechanics, showed us that the vacuum is teaming with “virtual” particles, ephemeral ghosts of ordinary matter which constitute a seemingly infinite background of energy that some people hope will one day provide the solution to all our energy needs. Though such a prospect is highly contentious (Barrow tells us that most physicists reject the idea outright), there is no doubt that the vacuum has continually surpassed physicists’ expectations; every time they think they have found nothing, it has turned out to be a very complex something. Today it looks as if Aristotle might well get the last laugh and that a true vacuum, a genuine nothingness, is little more than an illusion.
The nothingness of space seems to encode not only gravity but also all the other fundamental forces physicists recognize. The unofficial goal of physics today is indeed to find a unified theory which would integrate general relativity and quantum theory into a single mathematical framework, enfolding everything into the fabric of pure space.
The current leading contender is string theory, which describes matter as microscopic strings undulating in six infinitesimal dimensions of space, themselves embedded within the four cosmological dimensions that relativity describes.
Barrow devotes the last third of his book to the quest for this unifying vision, and readers seeking an even fuller description can turn to Times science writer K.C. Cole’s excellent work, “The Hole in the Universe.”
Such a vision would ally modern physics with ancient Indian philosophy: From the void, we were created and to the void we will return, or at least our atoms will. Sunya, the pregnant void, has been reborn in the language of mathematics.
Seeking the heart of oblivion, each of these authors is finally confronted with the riddle of non-being. As Sartre reminds us, and as these books reinforce, few subjects induce such vertiginous mind trips as the nature of nothing. Initiates might start with Seife’s breezy and accessible volume; those seeking deeper insights can turn to Barrow and Kaplan.
We have come a long way since Aristotle and Augustine, but if the last century of physics and mathematics has taught us anything, it is that nothing remains the final frontier, not only of logic but of physical possibilities.