The Book of Nothing

by John D. Barrow

  There were two threads to the theological writings: one which drew out the nature of the nothingness from which creation had sprung; another which emphasised the nothingness and ephemerality of all temporal things. Both were directed at refuting the dualist heresy that the world was created out of pre-existing matter, rather than out of Nothing. The first thread was the preserve of serious theological treatises whereas the second was the substance of metaphysical poets trying to prove the nothingness of life when viewed in the cosmic scheme of things.27

  It is important to recognise that although Christian doctrine included the notion of creation out of nothing (creatio ex nihilo), it did not include the idea that the creation was caused by nothing. The cause28 of the creation is God, not some latent property of the void. God always exists but the Universe just lacks a material cause to initiate its structure. Aquinas argued that if there is absolutely nothing – no Universe, no God, no Being at all – then nothing can appear. For to cause itself, a being would have to exist in order to give itself existence and this, he claims, is absurd. So if absolutely nothing ever existed in the past, nothing exists now.29

  THE MEDIEVAL LABYRINTH

  “But if there is a void above and a void below, a void within and a void without, he who is intent on escaping void has need of a certain imaginative mobility.”

  Robert M. Adams30

  It is easy to skip over the Middle Ages as though they were a time of darkness and delusion, an antechamber in the history of scientific ideas that awaits the arrival of Copernicus, Galileo and Newton. But in order to understand why scientific ideas about space and the vacuum developed in the way they did, when they did, it is important to take some snapshots of the way in which human thinking about the concept of Nothing developed from the time when Aristotle’s ideas held sway until the early eighteenth-century arguments between Newton and Leibniz. Scholars of all complexions struggled for more than five hundred years to harmonise subjects like the nature of space, infinity and the vacuum. Their task was made more difficult by their need to relate all these concepts to the nature and capacity of God. The synthesis of Aristotle’s philosophy and Christianity created a complex web of philosophical ideas whose theological consistency was more important than the mere assimilation of experimental facts; not because those facts were regarded as of little relevance, but because their significance was often ambiguous and they could be incorporated into the World model in a variety of ways consistent with their overall World view.

  As a result of Aristotle’s rejection of the idea that a separate vacuum could exist, on the grounds that it was logically incoherent,31 it was believed almost universally in the early Middle Ages that Nature abhorred the creation or persistence of any vacuum state. Almost all scholars believed that it was not possible to create a vacuum within the universe of space that we experience and see around us, a so-called intracosmic void. Things became more complicated when attention was turned to consider the possibility that there might exist an infinite extracosmic void beyond our finite, spherical, Aristotelian universe. This idea began to have credence in the fourteenth century and became very widely accepted over the next three hundred years.

  Medieval philosophers inherited a strong Aristotelian opposition to the vacuum. In order to leave no hiding place from his arguments for its non-existence, Aristotle defined the vacuum carefully. He characterised it as that in which the presence of a body is possible, although not actual. Aristotle attempted to show that admitting the idea of a vacuum would paralyse the Universe. Motion would be impossible because there was no reason to move one way or the other in a vacuum because it was necessarily the same everywhere and in every direction. There was neither ‘up’ nor ‘down’ and so no way for things to adopt their ‘natural’ motion. In any case, if motion did occur it would continue for ever because there would be no medium offering any resistance to its motion.32 Perpetual motion was a reductio ad absurdum. Nor would it make sense for a moving body to stop anywhere in this perfectly homogeneous void: for why should it stop at one place rather than another?

  Considerable attention was devoted by scholars in the thirteenth and fourteenth centuries to the idea that Nature disliked the presence of a vacuum so acted always so as to remove it or resist its creation. As ever, there were shades of opinion. Some – strict Aristotelians – maintained that it was impossible to make a perfect vacuum for even a fleeting instant of time. Others were content to permit the ephemeral existence of a vacuum so long as events inevitably overcame it and refilled it quickly with air or other material. They did not believe in the existence of a stable vacuum.

  Some scholars like Roger Bacon were unhappy with a law of Nature that was negative. A rule like ‘no vacuums allowed’ could not be primary; it needed to be a consequence of a deeper positive principle about what Nature did. Negative principles were very powerful vetoes but they allowed too many things to happen that were not seen. As a specific example, the workings of Empedocles’ water-catcher, or clepsydra, were much debated. Bacon argued that the veto on the formation of a vacuum was insufficient to explain what is seen. The formation of a vacuum inside its walls could equally well be avoided by the walls imploding. Why does Nature choose to hang on to the water rather than cave in the walls of the vessel? What principle decides?

  Another favourite puzzle that taxed medieval scholars was a simple example noticed first by Lucretius.33 It is the problem of separating two smooth surfaces; for example, two flat sheets of glass or metal, as shown in Figure 2.5. The concern was that if they begin in perfect contact but are then suddenly pulled apart then a vacuum must be briefly formed when they separate: there must be a change from a state in which there is nothing between the sheets and one in which there is air between them. Here is Lucretius’ ancient version of the problem:34

  “If two bodies suddenly spring apart from contact on a broad surface, all the intervening space must be void until it is occupied by air. However quickly the air rushes in all round, the entire space cannot be filled instantaneously. The air must occupy one spot after another until it has taken possession of the whole space.”

  The way this problem was investigated gives a wonderful insight into the ingenuity and serious medieval interest in these problems.35 The theological stakes were surprisingly high, as we shall see.

  Figure 2.5 Two parallel sheets sliding across their surface of contact.

  The Scholastics tried hard to show that this ancient puzzle, rediscovered by Bacon and others, did not allow even a short-lived vacuum to arise. Some claimed that while a vacuum could indeed form in principle if the surfaces were slid across each other so that they remained perfectly parallel, this could never happen in practice. A slight angle would develop between the surfaces and air would enter and gradually fill the gap between the surfaces bit by bit. Bacon turned the discussion around and argued that two smooth plane parallel surfaces could not be separated if they were in perfect contact (which would have a ring of truth about it for those who had tried it) unless they were first inclined. This was Nature displaying her resistance to the creation of a vacuum.

  One of Bacon’s English contemporaries, Walter Burley, saw through this suggestion, pointing out that the inclining of the surfaces makes no difference of principle at all. The ephemeral vacuum must still form, it merely lasts for a shorter time than if the plates are parallel when separated. Probing deeper still, he pointed out that perfectly parallel surfaces don’t exist; but no matter, even though real surfaces always exhibit microscopic undulations which restrict their points of contact to occasional protrusions, all that the argument for an ephemeral vacuum needs is for there to be a single point of contact. When that point of contact is broken a vacuum must arise momentarily.

  A notable opponent of the direction of this reasoning was Blasius of Parma, a student of motion and fluid flow. He argued that it was possible for plates to be separated by parallel motion yet not form a vacuum. This requires the particles of air to move at just the right speeds at
just the right times to fill the void space immediately it forms.36 But then he resorts to a very interesting argument, reminiscent of Zeno, that the vacuum can never form because there is no first moment when it exists – if you think there is, then halve it, and so on, ad infinitum. By denying the logical possibility of a first instant of separation for the plates, Blasius tried to eliminate the possibility of an instantaneous separation of the surfaces which would have allowed a vacuum to make even the briefest appearance.

  Despite the ingenuity of these suggestions, the most widely accepted resolution of the dilemma stayed close to Aristotle’s own treatment of a very similar problem. Aristotle had argued that there would always be some air trapped between two surfaces in contact, just as two surfaces which touch under water always get wet at their interface. Most people had regarded this as a conclusive and simple resolution of the surface contact problem until Bacon raised a simple objection. Forget about the two solid surfaces, he said. They are just a device to allow some air to be trapped in between the surfaces and avoid a vacuum forming. Suppose, instead, that you have only one surface and consider its interface with the water around it. Nothing lies between the surface and the water and so whenever they are separated a momentary vacuum must form!37

  Burley responded by claiming that there was still a thin film of air at the interface between a liquid and a solid. When you began to separate them it would quickly expand to fill up any potential void space. But what if the air was as rarefied as it could be and there was no scope for further expansion? Burley responded again by claiming that the surfaces would be inseparable in this situation. The only way of parting them would be to bend one of them and so create the inclined-surface problem that he and Bacon both believed to be the only way to effect a separation without producing a vacuum.

  Despite his appeal to a specific physical process to avoid the vacuum’s appearance, Burley felt he needed more protection from uncontrollable natural events than this. What if a heavy rock should fall to the ground and expel all the air in between its surface and the ground at the point where they first made contact? Would there not be an instantaneous vacuum there? To stop all the air being expelled, he appeals to a celestial agent38 which prevents the air yielding ‘to the stone because [the stone] is held back by the superior agent, which powerfully seeks to prevent a vacuum’. If natural processes were inadequate to overcome the threat of a real vacuum forming then one needed to fall back on the cosmic censorial power of this supernatural agency to stave off the creation of Nothing from something. In the much-debated example of the water-catcher, the celestial agent could be invoked to explain why the water behaved ‘unnaturally’ by not falling downwards, rather than imploding the walls of the vessel to prevent a vacuum forming. This type of explanation, reminiscent of the Just So Stories, was not very persuasive. Unfortunately, the celestial agent was annoyingly inconsistent in policing the formation of vacua. Others were quick to point out that on other occasions the universal agent did choose to stave off the vacuum by distorting the walls of the container, as occurs if the water freezes.

  Alongside these detailed arguments about the ways in which Nature staves off the creation of an intracosmic void, there were centuries of debate about the existence of an extracosmic void – a vacuum beyond the physical Universe. Aristotle considered the idea briefly but rejected it along with the whole idea of the plurality of worlds. His definition of a vacuum as that in which ‘the presence of a body is possible but not actual’ demanded such a conclusion. For ‘outside’ the Universe there is no possibility of body and hence no vacuum. In this respect, as we have seen, he is diametrically opposed to the Stoic view that there exists an infinite extracosmic void.

  The extracosmic void introduced further dilemmas for medieval philosophers. It was imagined to consist of ‘imaginary’ space; that is, space that could be imagined to exist even when bodies did not. We can imagine all sorts of things that seem to go on for ever, like the list of all numbers, and these may be imagined to ‘live’ in this infinite imaginary space.39 Although it couldn’t contain ordinary matter it had a property that proved crucial in the subsequent development of ideas. It was completely filled with the presence of God and was both the expression of God’s immensity and the means by which His omnipresence was achieved and maintained. This considerably narrowed the options when it came to pinpointing its properties. Try to make the extracosmic void finite, or endow it with dimensions, and you risk reaching a heretical conclusion about the nature of God. For in order that God remains omnipresent yet indivisible, He needs to be wholly located at every single point of the infinite space of the extracosmic void: One who ‘is an infinite sphere whose centre is everywhere and circumference nowhere’.40

  The key moment in the early stages of these debates was the famous Paris condemnations of 1277 in which Bishop Etienne Tempier strove to reassert the doctrines of God’s power to do whatever He chooses. Before Tempier’s intervention, there was a widespread belief amongst theologians that Aristotelian philosophy showed that God was constrained in various ways. For example, God could not make two and two make five; God could not create a plurality of worlds; and, inevitably, there was a veto that God could not cause a movement of things that would produce a local vacuum. By denying these restrictions on God’s power, Bishop Tempier made space for an extracosmic vacuum. For if many worlds exist what lies between them? And if God should choose to move our whole world in a straight line then what would remain in its former place? ‘A vacuum’ was the answer that the prompter was whispering from the wings. And if you didn’t hear, then beware of suggesting to the Bishop that God could not create a vacuum. After 1277, the vacuum became admissible because any attempt to exclude it on philosophical grounds was tantamount to limiting the power of God.

  Another great medieval question was whether a vacuum had existed before the creation of the world. Aristotle had denied the possibility that the world (or anything else) could be created from Nothing. The original Aristotelian scenario of an eternal, uncreated Universe had the drawback of clashing with Christian doctrine and so the more appealing alternative was a version in which the world had been created from a pre-existing void containing nothing. Yet this was not entirely without problems of its own. It required the existence of something eternal that was seemingly independent of God. It was this stance that spawned infamous questions like ‘What was God doing before the creation of the world?’ and the development of Augustine’s response that entities like time and space were created along with the Universe so there was no ‘before’.

  By the sixteenth century the tide had begun to turn. The rediscovery of lost texts by Lucretius and accounts of Hero’s ancient experiments on pressure inspired assaults on Aristotelian dogma. The horror at allowing a vacuum to form abated and there was a change of attitude to the existence of an infinite void space which would alter the relationship of God to that space, culminating in a complete decoupling of the scientific and theological debates about the nature of space and the vacuum.

  In the sixteenth and early seventeenth centuries those who began to subscribe to the Stoic cosmology, with its finite cosmos surrounded by an infinite extended void, were all agreed on many of the attributes of the surrounding void: it was the same everywhere, immutable, continuous and indivisible, and offered no resistance to movement. But what was new was a growing disagreement as to God’s relationship to the infinite void space. Notable atomists like Pierre Gassendi denied that the infinite void had anything to do with the attributes of the Deity. A third way was provided by the philosopher Henry More who, while regarding space as an attribute of God, also regarded God as an infinite extended Being. More is interesting primarily because his views seem to have influenced Isaac Newton’s views about space. Newton introduced God as a three-dimensional presence everywhere and as the underpinning intelligence behind the mathematical laws of Nature. Indeed, he introduced a new form of the ancient Design Argument for the existence of God, appealing to the fortu
itous structure of the laws of Nature rather than their outcomes as evidence for a Grand Designer behind the scenes.41 Newton clung to the Stoic picture of a finite world surrounded by an infinite void space. He could imagine an empty space but not the absence of space itself. Thus space was something that was quite independent of matter and motion. It was the cosmic arena in which matter could reside, move and gravitate. Newton writes that,42

  “we are not to consider the world as the body of God, or the several parts thereof as the parts of God. He is a uniform Being, void of organs, members or parts, … being everywhere present to the things themselves. And since space is divisible in infinitum, and matter is not necessarily in all places, it may also be allowed that God is able to create particles of matter of several sizes and figures, and in several proportions to space, and perhaps of different densities and forces, and thereby to vary the laws of Nature, and make worlds of several sorts in several parts of the Universe. At least I see nothing of contradiction in this.”

  For Newton, the extracosmic void space was entirely real and not in the least imaginary. When he was preparing the 1706 edition of his Opticks for the press he considered adding to his list of ‘queries’ – a series of far-reaching questions and speculations about the physical world – a final question asking43

  “what the space that is empty of bodies is filled with.”

  These Newtonian views about the reality of the extracosmic void space and its relationship to God were articulated by his champion, Samuel Clarke, in a famous debate with Leibniz. Leibniz disagreed fundamentally with Newton. He denied that the infinite void even existed and objected to Newton’s idea that we equate it with the immensity of God. He saw how difficult it was to sustain a relationship between God and space and opposed any such attempt. In the end, his view about the separation of God from space prevailed amongst philosophers and theologians, even though the infinite void space of Newton was retained by scientists.