Empedocles was not just a philosopher. He made an important experimental discovery in the course of his researches into human breathing and the nature of air. He explains what he has observed about the behaviour of a perforated vessel used to catch water,15 displayed in Figure 2.2. He notices that if the water-catcher is submerged before the air has been expelled from it then the water cannot flow into it,16
“As when a girl, playing with the water-catcher of shining brass – when, having placed the mouth of the pipe on her well-shaped hand she dips the vessel into the yielding substance of silvery water, still the volume of air pressing
Figure 2.2 The ancient water-catcher experiment. Immerse the perforated vessel and then seal the tube with a finger. On removing it from the water the water remains trapped in the vessel but when the finger is removed from the tube it escapes. An explanation for this behaviour was a challenge to scientists and philosophers for more than 2000 years.
from inside on the many holes keeps out the water, until she uncovers the condensed stream [of air]. Then at once when the air flows out, the water flows in in an equal quantity.”
He is on the verge of deducing something about the pressure exerted by the air in the Earth’s atmosphere. Two thousand years would pass before Torricelli provided the correct explanation for the behaviour of devices like this.
Anaxagoras, like Empedocles, lived in the middle of the fifth century BC, working first in Ionia and then in Athens. Like Empedocles, he also denied the existence of empty space and believed strongly in the conservation of the ‘essence’ of the world. This conservation principle meant that things could not appear out of Nothing, or disappear into it. It is an idea that is similar in spirit to our modern concept of the conservation of energy. Anaxagoras viewed ‘creation’ as the bringing of order into a state of primordial chaos rather than as an event from which the World came into being out of Nothing. He also used this conservation principle to understand how things change from one substance into another; for example, how fruit or other forms of food that we eat can turn into flesh and bones. He believed that something must be passed on in each of these changes, that there are ‘seeds’ within all forms of matter which are passed on but neither created nor destroyed. ‘For in everything there is a portion of everything.’ One might even view these seeds as being the molecules of modern chemistry. Yet these ingredients were held to be infinitely divisible, so that space could be continuously filled with matter. No need for Empedocles’ pores, and no room for empty space either.
Anaxagoras shared Empedocles’ fascination with the water-catcher and repeated that experiment, extending it by compressing air inside wineskins so as to demonstrate that the air offers a resistance when the skins are stretched. From this, he concluded that air is not the same thing as empty space and that we have no observational evidence for the existence of empty space. A subtle thinker, he was the first philosopher to recognise that our observations of the world are conditioned by the frailty of our senses. Our ability to decide whether one thing is really different from another (his favourite example was distinguishing very similar shades of colour) is just a reflection of our senses and because of ‘the weakness of the sense-perceptions, we cannot judge truth’. Our senses are sampling partial information about a deeper reality that they cannot fully apprehend. His ideas were ones that would be used by the Greek atomists who came after him as a fundamental feature of their picture of the world.
The atomists maintained that all matter was composed of atoms, tiny indivisible particles (the Greek word atomos means having no parts), which were eternal, indivisible and unchangeable. Atoms moved through empty space and their different degree of clustering from place to place was responsible for changes in density and the distinctive properties of different forms of matter. This powerful picture of the world was appealing because of its simplicity and wide applicability. It was proposed first by Leucippus of Miletus in the mid-fifth century BC, developed further by his student Democritus, and eventually upgraded into an entire philosophical system by Epicurus of Samos (341–270 BC), after which it became extensively known. Even so, today its most memorable articulation is to be found in the remarkable poem De Rerum Natura (On the Nature of Things) composed by the Roman poet Lucretius in honour of Epicurean atomism in about 60 BC.
Leucippus has the double distinction of introducing the concept of matter being composed of identical basic units and of taking seriously the idea that there does indeed exist something called empty space in which these atoms move. Here we see for the first time the concept of a true vacuum being rigorously employed as an axiomatic part of a natural philosophy. Because the world was differentiated into atoms and the void in which they moved, the vacuum was necessary for any movement or change to be possible, and Leucippus reminds us that17
“unless there is a void with a separate being of its own, ‘what is’ cannot be moved – nor again can it be ‘many’, since there is nothing to keep things apart.”
Atoms could differ in concentration, in shape and in position, but they could not appear and disappear from or into Nothing. This immutability of atoms rules out any possibility that they contain regions of vacuum. They must be solid and finite in size. It may be significant that Leucippus spent some time as a pupil in the philosophical school of Elea where Zeno had worked, and where his paradoxes of the infinite were much studied. Zeno had demonstrated some of the bizarre paradoxes that could occur if you considered a process of halving things indefinitely. For example, one of his paradoxes of motion invites us to contemplate how it is possible to walk, say, to the door of our room one metre away. First, we must cross half a metre, then half of half a metre, then half of half of half a metre, and so on, ad infinitum. It appears that we will never be able to reach the door because we have to cover an infinite number of distances! It is possible that these awkward problems of dealing with things that were allowed to become arbitrarily small convinced Leucippus of the importance of having a smallest possible size for his atomic units of matter to avoid such paradoxes. There were physical reasons as well. Epicurus argued that allowing matter to be infinitely divisible would result in the irreversible destruction of its identity, slipping ultimately into non-existence, or give rise to aggregates of matter that were too fragile to persist. This was a far-reaching step because it drew a sharp distinction between mathematical and physical reality: in the former, infinite division of any quantity was possible; in the latter, it was not. You had to choose which mathematical structure to apply to physical existence.
According to Epicurus,18 atoms must also have a maximum possible size in order to explain why they are not seen with the naked eye. Democritus is silent19 on this point, but he agrees with all the other atomists that the number of atoms in the Universe, like its size and age, is infinite. Thus, their conception of the Universe is as a vacuum of infinite size filled with moving, solid, indivisible particles of different shapes and sizes.20 Lucretius poetically describes how it can be that the random motion of these imperceptible atoms can give rise to everyday objects that seem to be steady and unchanging:21
“Although all the atoms are in motion, their totality appears to stand totally motionless … This is because the atoms all lie far below the range of our senses. Since they are themselves invisible, their movements also must elude observation. Indeed, even visible objects, when set at a distance, often disguise their movements. Often on a hillside fleecy sheep, as they crop their lush pasture, creep slowly on-ward, lured this way or that by grass that sparkles with fresh dew, while the full-fed lambs gaily frisk and butt. And yet, when we gaze from a distance, we see only a blur – a white patch stationary on the green hillside.”
There is a curious parallel between the atomists’ picture of atoms separated by the void and Pythagoras’ picture of numbers. Pythagoras and his followers believed that everything could be expressed by numbers and these numbers possessed intrinsic meanings, they were not merely ways of expressing relationship between things.
If two quite different things possessed an element of threeness, or fiveness, then they were deeply related by a fundamental harmony. Like the atomists, the Pythagoreans required a void to exist in order to maintain the identities of things. For the atomists, it was empty space that separated atoms and allowed them to move. For the Pythagoreans, everything was number: the void existed between numbers. Aristotle reports that the Pythagoreans maintained that22
“the void exists … It is the void which keeps things distinct, being a kind of separation and division of things. This is true first and foremost of numbers; for the void keeps them distinct.”
The atomists were not the only ancient philosophers to have strong views about the vacuum. From the third century BC, there emerged a completely different theory of the nature of things. It became known as Stoicism, after its first adherents were dubbed Stoics because they chose to meet under a painted corridor (stoa) on the north side of the market place in Athens. Its founders were Zeno of Cition (not to be confused with Zeno of the paradoxes), Chrysippus of Soli in Cilicia, and Poseidonius of Apamea in Syria.
In complete contrast to the atomists’ dogma, the Stoics believed that all things were a continuum, bound together by a spirit – an elastic mixture of fire and air – or pneuma, that permeated everything. No empty space could exist within or between the component pieces of the world, but this did not mean that there couldn’t exist any empty space at all. Quite the contrary, the Stoics’ Universe was a finite continuous island of material diffused by pneuma, but sitting in an infinite empty space.23 The void was the great beyond and the pneuma bound the constituents of the world together so as to prevent them diffusing out into the formless void.
The Stoic conception is of interest to us now because the pneuma was a forerunner of the long-lasting idea that space is filled with a ubiquitous fluid, an ether, which can be acted upon and which responds to the actions of other material. The Stoics envisaged their ether as a medium through which the effects of sound or other forces could propagate, just as when we disturb the surface of water in one place we can see the waves emanating outwards over the surface to create effects elsewhere, causing a nearby floating leaf to oscillate up and down.
Remarkably, neither the views of the atomists nor those of the Stoics proved influential over the next fifteen hundred years. The dominant picture of the natural world that emerged from Greek civilisation and wedded itself to the Judaeo-Christian world view was that of Aristotle. Aristotle’s approach to natural phenomena was dominated by a search for purpose in motion and change. While this teleological perspective could be of help in understanding what was going on in the natural world, or in the study of human psychology, it was a real obstacle to the study of problems of physics and astronomy. Aristotle’s picture of Nature was extremely influential and his views about the vacuum fashioned the consensus view about it until the Renaissance.24 He rejected the possibility that a vacuum could exist, either in the world as the atomists maintained, or beyond it as the Stoics believed. The Aristotelian universe was finite in volume; it contained everything that exists; it was a continuum filled with matter; space was defined by the bodies it contained. But unlike the dynamical ether suggested by the Stoics, Aristotle’s continuous ether was static and passive, eternally at rest.
ISLAMIC ART
“Humility collects the soul into a single point by the power of silence. A truly humble man has no desire to be known or admired by others, but wishes to form himself into himself, to become nothing, as if he had never been born. When he is completely hidden to himself in himself, he is completely with God.”
Isaac of Ninevah (AD 600)25
When compared with ancient Greek or later Western representational art, the intricate mosaics and tessellations of Islamic art seem like an ancient form of mathematical art: computer art before there were computers. We can picture their teleported ancient creators manipulating fractals and modern tiling patterns to continue a tradition that vetoed the representation of living things. Their patterns are extremely revealing of their religious views. God alone was infinite. God alone was perfect. But by creating finite parts of patterns that were evidently infinite it was possible to capture a little piece of the Divine in a humble yet inspiring manner. The partial character of the design served to reinforce the frailty and finiteness of humanity in contrast to God’s infinity.
Islamic art directed the mind towards the infinite by creating regular patterns that could be infinitely repeated. These designs have become familiar to us through the work of the Dutch artist Maurits Escher and the mathematical designers he inspired. Born in Leeuwarden, Holland, in 1898, Escher began his artistic career as a landscape artist, painting little Mediterranean towns and villages. But his life’s work was changed in the summer of 1936 by a visit to see the fabulous designs of the Alhambra, in Granada, Spain (Figure 2.3).
Escher was deeply impressed by the intricate patterns he saw and the fabulous geometric precision of the creators of this fourteenth-century Moorish palace. He spent many days studying the detailed patterns and periodicities, and went away to develop his own synthesis of symmetry and impossibility. Unlike the patterns of the Alhambra, Escher animated his designs with living creatures: fish, birds, winged horses and people. This expression of the abstract by means of recognisable images was, he remarked, the reason for his ‘never-ceasing interest’ in these patterns.
In Islamic art we see how the Moslems celebrated infinity where the Greeks feared it. They made it the hidden engine of their artistic creations. While not quite on central stage, it was never far away in the wings. The treatment of zero and Nothingness is just as confident. Rather than sweep Nothing away under the carpet as a philosophical embarrassment, the Islamic artists simply saw the void as a challenging emptiness to be filled. No blank space could be left alone. They filled friezes and surfaces with intricate patterns.26 This urge seems to be shared by human cultures the world over. Wherever anthropologists look they find elaborate decorations.
Figure 2.3 Islamic decorations from (top) Badra in Azerbaijan, and (bottom) the Alhambra Palace in Granada, Spain.
We just do not like an empty space. As we saw with the Mayan need to fill their mathematical pictograms with an image for Nothing, the human mind longs for pattern and for something to fill any void. The great art historian Ernst Gombrich termed this impulse to decorate the horror vacui. It inspires a wealth of persistent procedures, sometimes linking different parts, sometimes filling in space, allowing a network of growing intricacy to emerge and develop.
ST AUGUSTINE
“Miracles are explainable; it is the explanations that are miraculous.”
Tim Robinson
In medieval and Renaissance thought the paradoxical aspects of the something that is Nothing became interwoven with the doctrines and traditions of Christian theology. These doctrines were founded upon the Jewish tradition of turning away from Nothing because it was the antithesis of God. God’s defining act was 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. Nothing was the state of oblivion to which the opponents and enemies of God were dispatched. Any desire to produce a state of nothingness or empty space was tantamount to attempting what only God could do, or to remove oneself from God’s domain. A single Divine creation of everything out of Nothing was a basic tenet of faith. To speak seriously of the void or of empty space was atheistic. It countenanced parts of the Universe where God was not present.
The most innovative thinker to grapple with the problem of synthesising the Greek horror of the void with the Christian doctrine of creation out of Nothing was Augustine of Hippo (354–430), pictured in Figure 2.4. He had a broader and deeper view of what creation should mean. It needed to be something more than the mere refashioning of primitive pre-existent materials into an ordered cosmos, something more than the unfurling of the cosmic scene at some moment in the distant past. Rather, i
t must provide the ground for the continued existence of the world and an explanation for time and space itself. It was for him a total bringing into being. Nothingness was therefore an immediate precursor state to the one that God sustains. This makes it more negative in its attributes than merely not being what is now in the Universe. It was characteristic of being apart from God.
Figure 2.4 St Augustine.
Augustine equated Nothing with the Devil: it represented complete separation from God, loss and deprivation from all that was a part of God, an ultimate state of sin, the very antithesis of a state of grace and the presence of God. Nothing represented the greatest evil. This was the ‘something’ that he believed non-Being to be. This formula led Augustine into dangerous waters because by introducing Nothing into the realm of Being he admitted that there was something that God lacked before he created the world. This difficulty he sidestepped, along with other problems about the beginning of time, by arguing that when God created the world he created time as well. There was no ‘before’ the first moment of time and so no time when God needed to change an unsatisfactory state of affairs.
These pieces of theological legerdemain were never entirely persuasive and centuries later they led Thomas Aquinas to create a fuller negative theology in which the attributes of God were only to be spoken of negatively: He was not finite, not temporal, unchangeable, and so forth. Aquinas supported the Aristotelian abhorrence of Nothing by viewing the creation of the world as an annihilation of Nothing in an act of Divine creative transformation. Yet, despite this careful circumscription, the Church was wary of Nothing and its mathematical representations during the tenth to thirteenth centuries. It tried to keep Nothing confined to the realm of arithmetic symbols where zero could be relegated to a harmless place holder on a counting board, far from the philosophical implications that the Indians had embraced but from which the Greek-Christian synthesis had recoiled.
The Book of Nothing Page 7