The Book of Nothing

by John D. Barrow

  In the earliest Christian traditions there is, accordingly, no ready-made inherited position about the creation of the world out of nothing. There is considerable freedom to develop this idea gradually during the first and second centuries, for nowhere in the New Testament writings is the doctrine of creation out of nothing explicitly taught. It began to be discussed seriously by theologians in about AD 160 as a result of the challenging questions raised by Gnostic philosophies.

  In Gnosticism the questions of ‘why’ and ‘how’ the world was created were of great significance, not because the Gnostics were especially interested in cosmology but because of their negative view of the world. They needed to have some explanation as to why this defective, immoral world came into being, and how it could result from the actions of the one true and perfect God. Gnostics maintained that the world was the creation of a group of more limited lesser beings (‘angels’) who either did not know the true God or were in rebellion against Him. They viewed matter and the physical Universe as something possessing only a partial reality which disturbed the true plan for the Universe. The ensuing process of salvation had as its primary goal the destruction of the defective material world. It was the complex evolution of the debate between the Gnostics and their opponents (and a whole spectrum of intermediate positions) in the early Church that led to the emergence in the early Christian Church of a clear doctrine of the creation of the Universe out of nothing in the writings of Basilides, Valentius and Irenaeus.

  Basilides and his school in Antioch developed a Gnostic system unlike all others. It focused on the need to determine the nature of creation itself. Basilides proposed that in the beginning there was just pure ineffable Nothing.14 It may be that he equated Nothing with God, and on one occasion he describes God as ‘non-being’. This is probably just a rather extreme use of a form of negative theology in which one defines God in terms of the things that He is not.15 Unlike other Gnostics, Basilides rejects the idea that there is some germinating world-seed or pre-existent formless matter from which the world emerges. He regarded such devices as limitations on the power and superhuman nature of God. He rejects totally the idea that God works like a human craftsman or an artist using the materials that are at hand to fashion the Universe.

  This is the earliest explicit rejection of the general idea of the formation of the world out of formless materials. From now on it became clear that divine creation must be placed on a higher plane than artistic creation.16 Basilides’ views became widely accepted and the rejection of the formation model for the origin of the world allowed the idea of creation out of nothing to become established during the second half of the second century. Quite quickly, the world-formation model came to be regarded as impossible to reconcile with the biblical concept of creation. Previously, the concept of ‘nothing’ was often defined in such a way that a formation out of pre-existent material could be accommodated within a statement of creation out of nothing, but Basilides, a non-standard Gnostic, was the first Christian theologian17 to speak unambiguously about creation out of nothing in a very inflexible sense that was designed to be exclusive.

  In less than a generation, a surprising change of attitude had occurred. In the middle of the second century, the early Christian Church had no interest in any specific doctrine of the creation of the world and would have been happy to accommodate a picture of the world forming out of pre-existent material with the Genesis account. Basilides’ careful argument turned things around. Creation ex nihilo was adopted as a central doctrine and the theories of world formation out of anything other than nothing were rejected as heretical challenges to the omnipotence of God and an adherence to the heretical theories of the godless philosophers. The resulting doctrine emerges from a synthesis of three convictions: that creation occurs ‘out of nothing’, that God is the supreme Creator, and the rejection of the tempting old idea that God acts in a way that is analogous to human creative action.

  It is curious that the Christian doctrine of creation out of nothing was introduced by a Gnostic, since the doctrine is by no means a Gnostic idea. Its Gnostic legacy is a reflection of the more sophisticated cosmological thinking that the Gnostics developed in order to deal with their own complicated doctrinal problems. They thought that the version of Christian truth that they taught was plainly superior to the insights coming from existing philosophy and science.

  The rejection of the world-formation cosmology was first made explicit in the works of Tatian and Theophilus of Antioch (Basilides’ home town also), but there would later emerge a view that formless matter was created out of nothing and then shaped into an orderly universe. Tatian claimed that matter is made out of nothing by God and Theophilus developed a solid biblical basis for the doctrine of creation out of nothing.

  From the modern perspective it is easy to wonder why early theologians seem to make such heavy weather of all this. There seem to be so few alternatives to the creation-out-of-nothing idea and it seems strange that such a complicated sequence of events was needed for the alternatives to be mapped out clearly. It is important to remember that one reason for their slowness is simply that they were not looking for such a doctrine. They were not motivated by a special interest in astronomy or natural philosophy. Parts of their doctrine were constructed occasionally when needed to defend specific theological points. It was synthesised into a fully worked-out form only when it was needed to counter the theological consequences of rival Greek views about the world being fashioned from pre-existent matter. Creation out of Nothing is one of the by-products of the early Christian Church’s disputes with the ideas of Greek philosophy.

  One must also remember the confusing background of Platonic philosophical ideas which were still very influential. The Platonic view of the world was that there exists an unseen eternal realm of ideal ‘forms’ which are the perfect blueprints of the things that we see in the material world. Thus each triangular shape that we see drawn on a piece of paper is an imperfect representation of the ideal triangular form. This makes the idea of nothing a very difficult one to entertain. Even if you wish to conceive of a moment before which the material world did not exist, the eternal forms still exist. Complete Nothingness is inconceivable. Thus the world-formation cosmologies which produce order in chaotic or unformed material can be seen as in-forming the raw material with the patterns from the eternal forms – transferring ‘information’ content as we might say today. In modern approaches to these problems the Platonic worry still exists in a slightly different form. We can perhaps imagine that no material universe exists, maybe even that no laws of Nature exist, but nothing at all is unimaginable for us because it would mean no facts could exist – not even a fact like the statement that nothing exists, in fact.

  PHILOSOPHICAL PROBLEMS ABOUT NOTHING AND HOW WE ESCAPED FROM IT

  “Every public action, which is not customary, either is wrong, or, if it is right, is a dangerous precedent. It follows that nothing should ever be done for the first time.”

  Francis Cornford18

  The question of why there is a world at all was raised in a short pamphlet by the philosopher Leibniz in 1697 entitled ‘On the Ultimate Origination of Things’.19 Leibniz realised that it did not matter whether you thought the world was eternal or appeared out of nothing as maintained by orthodox Christian doctrine. All theories and beliefs still faced the problem of why there was something rather than nothing. Philosophers took little interest in this question for a long time after Leibniz. Problems like this were not part of an analytical philosophy that built up understanding of things step by step. Leibniz’s problem needed an understanding of everything all at once. It was too ambitious. In fact, it was as good a candidate as any for an intrinsically insoluble problem.20 Philosophers who considered the question, like Wittgenstein (‘Not how the world is, is the mystical, but that it is’)21 and Heidegger, had little to say in answer to it and appear more interested in wondering about why the question is one that we find so compelling.22

  Th
e only novel contribution to this problem before the twentieth century was the consideration of whether the well-defined concept of mathematical existence had any cosmological implications. The development of axiomatic mathematical systems, in which a system of self-consistent rules (‘axioms’) were laid down and consequences deduced or constructed from them, led to a ‘creation’ of mathematical truths that ‘existed’ in a rather particular sense. Any mathematical statement that was logically consistent was said to ‘exist’. Mathematicians would produce what became known as ‘existence proofs’. This is clearly a far broader concept of existence than physical existence. Not all the things that are logically possible seem to be physically possible and not all of those now seem physically to exist. However, a philosopher like Henri Bergson clearly thought that this type of weak mathematical existence was a possible avenue along which to search for a satisfying solution to Leibniz’s problem:23

  “I want to know why the universe exists … Whence comes it, and how can it be understood, that anything exists? … Now, if I push these questions aside and go straight to what hides behind them, this is what I find: – Existence appears to me like a conquest over nought … If I ask myself why bodies or minds exist rather than nothing, I find no answer; but that a logical principle, such as A = A, should have the power of creating itself, triumphing over the nought throughout eternity, seems to be natural … Suppose, then, that the principle on which all things rest, and which all things manifest, possesses an existence of the same nature as that of the definition of the circle, or as that of the axiom A = A: the mystery of existence vanishes …”

  Unfortunately, this approach to why we see what we see is doomed to failure. As the nature of axiomatic systems has become more fully appreciated it is clear that any statement can be ‘true’ in some mathematical system. Indeed, a statement which is true in one system might be false in another.24

  As an interesting sidelight, there is an amusing dialogue reproduced in Andrew Hodges’ biography25 of Alan Turing. Turing attended Wittgenstein’s lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don’t like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russell26 pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russell replied immediately that ‘if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1’! A contradictory statement is the ultimate Trojan horse.

  This temptation to replace physical existence by mathematical existence can be taken to extremes. Suppose that we imagine that all possible mathematical formalisms are laid out in front of us. They each appear like a great network of all possible deductions that follow from their axioms. If the mathematical system is very simple then the deductions will also be very limited in their complexity. But if the axioms are rich enough then the sea of deductions will include extremely complex structures which possess the capability of self-awareness. It is as if we are building a computer simulation of how a system of planets might form around a star. We tell the computer all the laws of motion and gravity, and whatever other physics and chemistry that we want included in the story. The computer will produce a simulation, or artificial sequence of events, culminating in the formation, say, of a planet like the Earth. We could imagine a future in which the computational capability was such that the simulation could be continued in great detail. Biochemical replication could be followed and early life forms simulated. Eventually, the complexity of the replicators being modelled in the computer could reach a level that displayed self-awareness and an ability to communicate with other self-aware sub-processors in the simulation. They might even engage in philosophical debates about the nature of the simulation, whether it was designed for them, and whether there exists a Great Programmer behind the scenes. At root these ‘conscious’ subprogrammes would exist only in the logical structure of the computer. They would be part of the mathematical formalism being explored and elaborated by the machine.

  We can ask whether the possibility of containing structures able to be self-aware is a general or a rather special property of mathematical formalisms. One day it may be possible to answer this but at present we can only make rather weak statements. There have been controversial proposals27 that the Gödel incompleteness28 properties of arithmetic may be necessary for consciousness to operate as it does in humans. If true, this would be equivalent to saying that mathematical systems need to be rich enough to contain arithmetic in order to contain structures with the complexity of human consciousness. Thus, Euclidean geometry, which is smaller than arithmetic and does not possess incompleteness, would be too simple a logical system to become self-aware. If this approach could be developed further then we might be able to isolate a collection of mathematical structures which allow the possibility of encoding conscious subprogrammes. Conscious life would ‘exist’ in the mathematical sense only in these mathematical formalisms.

  Most philosophers treat such recipes with distaste. They regard real physical existence as distinct from mathematical existence. In the words of Nicholas Rescher,29

  “… getting real existence from pure logic is just too much of a conjuring trick. That sort of hat cannot contain rabbits.”

  Mathematical existence allows anything to ‘exist’. Some axiomatic system can always be framed in which any statement is true (and others found in which it is false). This type of existence does not, therefore, really explain anything. We want to know why so much of what we see around us can be explained as a truth of a particular system of logical rules with a single set of axioms. The fact that those axioms are not too exotic shows that the world can be described by quite simple ideas (that is, ones that are intelligible to human beings) to a very surprising degree.

  CREATION OUT OF NOTHING IN MODERN COSMOLOGY

  “Then God created Bohr,

  And there was the principle

  And the principle was quantum,

  And all things were quantified,

  But some things were still relative

  And God saw that it was confusing.”

  Tim Joseph30

  The discovery of the general theory of relativity by Einstein enabled the first mathematical descriptions of entire universes to be made. Only very simple solutions of Einstein’s equations have been found completely by direct calculation, but fortunately these simple solutions are extremely good descriptions of the visible part of the Universe for a considerable time in the past. They describe expanding universes in which the distant clusters of galaxies are moving away from each other at ever-increasing speeds. Deviations from the exact symmetry of the special solutions can be introduced quite easily, so long as they are small, and this results in a good description of the real non-uniformities in the Universe.

  As we try to reconstruct the past history of these cosmologies, we encounter a striking feature. If matter and radiation continue to behave as they do today, and Einstein’s theory continues to hold, then there will be a past time when the expansion must have encountered a state of infinite density and temperature. When this property was first appreciated, it sparked a number of very different reactions. Einstein31 thought that it was merely a consequence of considering expanding universes that contained matter without significant pressure. If pressure was include
d then he thought that it would resist the contraction of a universe down to infinite density, just as air pressure resists our attempts to squeeze an inflated balloon into a very small volume. It would ‘bounce’ back. But this intuition was completely wrong. When normal pressures were included in the universe models it made the singularity worse because in Einstein’s theory all forms of energy, including those associated with pressures, have mass and gravitate by curving space. The singular state of infinite density remained. Others objected that the singular ‘beginning’ only appeared because we were looking at descriptions of expanding universes which were spherical, with expansion at exactly the same rate in every direction. If the rate was made slightly different in different directions then, when the expansion was retraced backwards in time, the material would not all end up in the same place at the same time and the singularity would be avoided. Unfortunately, this also proved to be no defence against the singular beginning. Rotating, asymmetrical, non-uniform universes all had the same feature: an apparent beginning. If matter was present in the universe, its density was infinite there.

  The next attempts to evade this conclusion looked to a more subtle possibility. Perhaps it was just the way of measuring time and mapping space in the model universe that degenerated into a singularity, just as with the coordinates on a globe of the Earth’s surface. At the Poles the meridians intersect and create a singularity in the mapping coordinates; yet nothing odd happens on the Earth’s surface. Likewise, perhaps nothing dramatic happens at the Universe’s apparent beginning; you merely change to measuring time and space in a new way and repeat this process, as required, indefinitely into the past.