The Book of Nothing

by John D. Barrow

  Figure 3.2 Otto von Guericke.14

  The result of all this work was to convince scientists that the Earth was surrounded by a substantial body of air which exerted a significant pressure on its surface. By carefully studying its effects, it was possible to explain all sorts of behaviours of gases and liquids in detailed mechanical terms rather than merely ascribing them to the vague notion that ‘Nature abhors a vacuum’ as the ancients did. Historians of science have highlighted the mundane study of air pressure as a turning point in our study of Nature; teleological notions of the ‘inclinations’ in the natural order of things brought about by mysterious occult forces were superseded by explanations that used only the concepts of matter and motion.

  Figure 3.3 The Magdeburg Hemispheres Experiment.15

  Von Guericke was a practical engineer of great ingenuity. He both liked and invented machines. But he was still fascinated by the ancient philosophical questions about the reality of the vacuum and their implications for the Christian doctrine of the creation of the world out of nothing. In his account of his experimental investigations he devotes a substantial section16 to airing his views about the void, which have a strong affinity to the medieval scholastic ideas that formed the philosophical tradition in which he worked. Von Guericke’s book is rather overblown. He has something to say about just about everything under the sun, and a good deal about things above it as well. His position in local government ensured that there would be an effusive dedication by one of the local noblemen. Indeed, Johannes von Gersdorf is moved to poetry in his tribute to the experimenter of Magdeburg, ‘the most distinguished and excellent gentleman, Otto von Guericke’:

  “To delve into the manifold mysteries of nature

  is the task of an inquiring and fertile mind.

  To follow the tortuous paths of nature’s wondrous ways

  is work more difficult and not designed for everyone.

  You, Distinguished Sir, Magdeburg knows as its Burghermaster

  as well as an outstanding researcher in the field of science.

  Whether one speaks with you informally or studies your work alone,

  he will soon confirm your genius openly and without a feeling of doubt.

  May I make a small joke? While you prove quite clearly that a vacuum exists

  in your Book, there is not a vacuum to be seen!”

  For Von Guericke everything that existed could be put into one of two classes: it was either a ‘created something’ or an ‘uncreated something’. There could be no third way: no class that we can call ‘nothing’. Since ‘nothing’ is the affirmation of something and the opposite of something else, it must be a something. Thus it falls into the category of either the ‘created somethings’ or the ‘uncreated somethings’; or maybe, he feels, ‘nothing’ has a call on belonging to both categories. Thus an imaginary animal like a unicorn is nothing in the sense of being non-existent; that is, it is not a thing. But because it exists as a mental conception it is not absolutely nothing. It has the same type of existence as a human thought. Thus it qualifies as a created something. Von Guericke wanted to view the Nothing that was before the World was made as an uncreated something, so that he could say that before the World was created there was Nothing, or equally, there was an uncreated something. In this way he guards against sounding like a heretic.

  Von Guericke summarised his lyrical philosophy of the void in a great psalm in honour of Nothing (Nihil). It gives a flavour of thinking that one would not have immediately associated with down-to-earth experimental demonstrations that the vacuum could be controlled by air pumps. It is worth reading at length. He joins various concepts of Nothing, empty space and imagined space together into one and the same concept, for

  “everything is in Nothing and if God should reduce the fabric of the world, which he created, into Nothing, nothing would remain of its place other than Nothing (just as it was before the creation of the world), that is, the Uncreated. For the Uncreated is that whose beginning does not pre-exist; and Nothing, we say, is that whose beginning does not pre-exist. Nothing contains all things. It is more precious than gold, without beginning and end, more joyous than the perception of bountiful light, more noble than the blood of kings, comparable to the heavens, higher than the stars, more powerful than a stroke of lightning, perfect and blessed in every way. Nothing always inspires. Where nothing is, there ceases the jurisdiction of all kings. Nothing is without any mischief. According to Job the Earth is suspended over Nothing. Nothing is outside the world. Nothing is everywhere. They say the vacuum is Nothing; and they say that imaginary space – and space itself – is Nothing.”17

  Von Guericke believed that space was infinite and likely to be populated by many other worlds like our own. He used the idea of the infinite world to support his argument that there is really no difference between real and imagined space. For, although we might think that unicorns inhabit only an imaginary space, he argues that if space is infinite then we are reduced to imagining some of its properties, just like we are the unicorns. In fact, Von Guericke equated infinite space, or Nothing, the uncreated something, with God.

  A TALE OF TWO NOTHINGS

  “It is hard to think of any modern parallel to the shiver of horror engendered by the mere suggestion to a man of the seventeenth century that a vacuum could effortlessly exist and be maintained; a materialist forced to admit irrefutable evidence of life after death might offer a fair analogy.”

  Alban Krailsheimer18

  It is well to remember that these great experiments with air pressure focused attention on the problem of two Nothings. There was the abstract, moral or psychological ‘nothing’, juggled with by playwrights and philosophers. It was a Nothing entirely metaphysical in nature; one that you didn’t have to worry about if you didn’t want to. It could stay as poetry. Set in stark prosaic contrast was the problem created by the attempts to create a real physical vacuum in front of your very eyes by evacuating glass tubes or metal hemispheres. This vacuum exerted forces and could be used to store energy. This was a very useful Nothing.

  The seventeenth-century thinker who did most to join the two conceptions together was a polymath with diverse, seemingly contradictory, interests who liked to engage with problems that possessed a hint of the impossible or the fantastic. Some of those interests were physical, some were mathematical, while others were entirely theological. Blaise Pascal was born in the French town of Clermont in 1623. He died only thirty-nine years later, but in that short space of time he laid the foundations for the serious study of probability, constructed the second mechanical calculating machine, made significant discoveries about the behaviour of gases under pressure, and found new, important results in geometry and algebra. Finally, his most famous work was his unfinished collection of fragmentary ‘thoughts’, the Pensées,19 that remained incomplete at the time of his early death. All this was achieved from unpromising beginnings. Pascal’s mother died when he was just three years old, leaving the young boy at the mercy of his father’s theories of education. They moved to Paris where Etienne, a successful lawyer, decided to educate his rather sickly son himself in isolation from other children. Although Pascal Senior was an able mathematician, he was determined that his son should not study mathematics until he reached the age of fifteen, and all mathematics books were removed from their house. Not content with the diet of Latin and Greek that resulted, the young Pascal gradually came in contact with friends of his father who shared an interest in mathematics. Not to be denied, he evaded his father’s educational restrictions by rediscovering a number of geometrical properties of triangles for himself at the age of twelve. Surprised, his father relented and gave him a copy of Euclid’s book of geometry to work with. Soon afterwards the family uprooted and moved to Rouen where his father had been appointed tax collector for the region. The young Pascal prospered there. At the age of sixteen he presented his first mathematical discoveries of new theorems and geometrical constructions to a regular meeting of Paris mathema
ticians convened by Mersenne, one of the most notable number theorists of the day. His first published work, on geometry, appeared just eight months later. So began Pascal’s career of invention and discovery (see Figure 3.4).

  Pascal’s interest in air pressure and the quest to create a perfect vacuum began in 1646. Unfortunately, this work threw him on to a collision course with the views of René Descartes, the most influential French natural philosopher of his day. In Rouen, Pascal came to hear of Torricelli’s remarkable experiments, conducted a few years before. Teaming up with Pierre Petit, a fortifications engineer and friend of his father, he began a series of telling experiments.20 The most important was planned by Pascal and carried out by his brother-in-law, Florin Périer. It sought to demonstrate the claims that Torricelli was making in his letter to Ricci about the thinning out of the Earth’s atmosphere at high altitude. On 15 November 1647 Pascal wrote to Périer asking him to compare the mercury levels in a Torricelli tube at the base and at the summit of a local mountain:

  Figure 3.4 Blaise Pascal.21

  “if it happens that the height of the quicksilver [mercury] is less at the top than at the base of the mountain (as I have many reasons to believe it is, although all who have studied the matter are of the opposite opinion), it follows of necessity that the weight and pressure of the air is the sole cause of this suspension of the quicksilver, and not the abhorrence of the vacuum: for it is quite certain that there is much more air that presses on the foot of the mountain than at its summit.”22

  After a delay of several weeks due to bad weather, Périer gathered together his team in the convent garden in the town of Clermont. He prepared two identical tubes of mercury, adopting the same method as Torricelli had used. The heights of the mercury columns were measured carefully in the presence of an audience of local worthies and verified to be identical. The local priest was then left in charge of one of the mercury columns while Périer’s team headed for the summit of Mount Puy-de-Dôme in the Auvergne, 1465 metres above sea level. They read the height of mercury at different altitudes on their ascent and at the summit itself. Mission accomplished, they returned to the convent to check that the height of mercury in their instrument was the same as the one left in the priest’s care. It was. The change in level between the convent and the mountain top was a clear 8.25 centimetres.

  What these measurements established for the first time, on 9 September 1648, was that the pressure of air decreased as one ascended the mountain. This result had a tremendous impact on all involved. Pascal wrote that the experimenters ‘were carried away with wonder and delight’. The fact that the effect which they discovered was so large inspired one of them, Father de la Mare, to look for the difference in mercury level when he took a barometer from ground level to the top of the 39-metre-high tower of the cathedral of Notre Dame de Clermont. The difference was 4.5 millimetres: small but still quite measurable. When Pascal heard the result he repeated the experiment in the tallest buildings in Paris, finding a similar measurable trend: the taller the building the bigger the pressure drop at the top. He soon realised that sensitive measurements of the variation of pressure with altitude could be used to determine altitude if a detailed enough understanding of the correlation between atmospheric pressure and altitude could be obtained independently. In the 350 years since Pascal’s first measurements we have built up a detailed picture of the Earth’s tenuous atmosphere (see Figure 3.5). Subsequently, he discovered that the barometric level at one place could change with the weather conditions, a fact that our modern use of the barometer exploits. A modern weather map, laced with isobars, is shown in Figure 3.6.

  Figure 3.5 The change in the nature of the Earth’s atmosphere up to an altitude of 1000 kilometres above sea level.23

  Pascal maintained that the empty space at the top of the mercury tube was a real vacuum. Pascal’s opponents were not especially interested in the practical implications of pneumatics and hydraulics, but they were concerned about the philosophical implications of such a claim, not least because they were being made by a young man of twenty-three who possessed no formal academic qualifications, merely an extremely stubborn and persistent character. In Italy, Torricelli’s group worked on many experiments between 1639 and 1644 but they did not pursue their researches any further, probably for fear of opposition by the Church – Giordano Bruno was burned at the stake in 1600 and Torricelli’s mentor, Galileo, remained under house arrest by the Inquisition in the nine years before his death in 1642. But Pascal, encouraged by Mersenne, who had learned of the experiments carried out in Rome, held no such fears despite his deeply religious inclinations. He improved and extended Torricelli’s experiments in many ways. He experimented with water and red wine and various oils, as well as mercury. These required large, often spectacular, experiments with long tubes and huge barrels to be performed in the streets of his home town. This showmanship did not endear him to his conservative opponents.

  Figure 3.6 A weather map showing isobars, contour lines of equal atmospheric pressure. Winds blow from high to low pressure areas.24

  Pascal faced opposition to the recognition of the reality of a physical vacuum on two fronts. The traditionalist Aristotelians had long exercised a strong influence on physics and they denied the possibility of making a vacuum. They explained the observed changes in Nature by ‘tendencies’ which really explained nothing at all; things grew because of a life force, objects fell to earth because of a property of heaviness. This was just a name game that could make no decisive predictions about what would happen in situations never before observed. But the Aristotelians were not the only ones to deny the possibility of a vacuum. The Cartesians, followers of Descartes, followed a unified natural philosophy which attempted to deduce the behaviour of the physical world in mathematical terms, by means of specific universal laws. However, this modern-sounding initiative did not allow space to be discussed without matter being present. Space requires matter just as matter requires space. These properties of the world were axiomatic to the Cartesian system and ruled the vacuum out of court ab initio. Unfortunately, Pascal’s meetings with Descartes to discuss the significance of his spectacular mountain-top experiments on air pressure did not go well. Descartes maintained that he had actually proposed that experiments of this sort be performed, but refused to admit that they established the existence of a real physical vacuum, as Pascal always claimed. Pascal did not create a good impression, because after his visit Descartes wrote to Huygens in Holland that he had found Pascal to have ‘too much vacuum in his head’!

  Pascal ended up entering a public debate, conducted in print, with Descartes’ Jesuit tutor Père Noël. Noël sought to defend the non-existence of the vacuum on the ground laid out by his pupil, but also on the ground that the all-pervasive sovereignty of God prevented a vacuum forming anywhere, for this would require an abnegation of the Almighty’s power. Noël attacked Pascal’s interpretation of his experiment, making a fine linguistic distinction between a vacuum and ‘empty space’ when it came to evaluating the content of the mercury tube, denying that the space in the tube was the same vacuum that Aristotle had denied could exist:

  “But is this void not the ‘interval’ of those ancient philosophers that Aristotle attempted to refute … or rather the immensity of God that cannot be denied, since God is everywhere? In truth, if this true vacuum is nothing other than the immensity of God, I cannot deny its existence; but likewise one cannot say that this immensity, being nothing but God Himself, a very simple spirit, has parts one separate from the other, which is the definition I give to body, and not that you attribute to my authors, taken from the composition of matter and form.”25

  Pascal did not rise to the bait being dangled here to tempt him into a theological debate about the nature of God with a member of the Jesuits which would have resulted in him being tarred with the same brush as the atheistic atomists like Democritus (the ‘ancient philosophers’ that Noël mentions). Reclaiming the moral high ground, his reply to No�
�l cleverly sidestepped the problem with Jesuitical skill:

  “Mysteries concerning the Deity are too holy to be profaned by our disputes; we ought to make them the object of our adoration, not the subject of our discussions: so much so that, without discussing them at all, I submit entirely to whatever those persons decide who have the right to do so.”26

  As other commentators began to see the close connection between Pascal’s experiments and the ancient questions concerning the vacuum and the void, Pascal’s writings started to stress the ‘equilibrium’ and ‘balance’ that the experiments displayed rather than the emptiness. But he was circumspect in his views. His unpublished papers show that he held much firmer opinions than he voiced at the time. In his private writings we find him asking himself about the sense of the Aristotelian abhorrence of the vacuum:

  “Does Nature abhor the vacuum more on top of a mountain than in a valley, and even more so in wet weather than in sunshine?”

  Despite the down-to-earth nature of Pascal’s study of air pressure, his results had deep and (for some) disturbing implications. His theory of air pressure explained why the height of Torricelli’s mercury column should fall as the experiment was carried to high altitude: only the weight of air above the experiment is exerting pressure on the surface of the mercury in the bowl. Suppose that we kept on going – the change in the mercury level has so far been finite, does it not imply that the atmosphere may be finite in mass, surrounding the Earth like a hollowed-out sphere? This would mean that there was ultimately a vacuum out in space, surrounding and enclosing us. Noël argued that it led us to the dangerous conclusion that if this useless vacuum existed in outer space beyond us then it would mean that some of God’s creation was of no use. Yet Pascal’s arguments won the day. Not until the last half of the twentieth century would it be appreciated how the vastness of the Universe is necessary for the existence of life on a single planet within it.27