Human Universe - Brian Cox, Andrew Cohen (2014)

WHY ARE WE HERE?

But, after all, who knows, and who can say

Whence it all came, and how creation happened?

The gods themselves are later than creation, so who knows truly whence it has arisen?

Ancient Brahmin Verse

A NEAT PIECE OF LOGIC

There is tension at the interface between science and language. Language is concerned with human experience. Everyone understands what is meant by questions such as ‘Why are you late?’ ‘I’m late because my alarm clock didn’t go off’. But this answer is incomplete, and could be followed by a series of further questions in an attempt to establish precisely why.

‘Why didn’t it go off?’

‘Because it’s broken.’

‘Why is it broken?’

‘Because a piece of solder melted on the circuit board.’

‘Why did the solder melt?’

‘Because it got hot.’

‘Why did it get hot?’

‘Because it’s August and my room is hot.’

‘Why is it hot in August?’

‘Because of the details of the Earth’s orbit around the Sun.’

‘Why does the Earth orbit the Sun?’

‘Because of the action of the gravitational force.’

‘Why is there a gravitational force?’

‘I don’t know.’

All scientific ‘Why?’ questions end with ‘I don’t know’ if you keep pushing far enough, because our scientific understanding of the universe is not complete. The most fundamental description we have for anything comes down to a set of theories describing the smallest known building blocks of the universe and the forces of nature that allow them to interact with each other. These theories are known as laws of physics, and when we ask about the origin of these laws, the answer is ‘We don’t know’. This is because in the Big Bang model, our understanding of physics before 10-43 seconds after the origin of the visible universe is virtually non-existent, and the origin of the laws lies at some point before that. ‘The laws themselves are later than creation, and who knows truly whence it has arisen.’ Our best theory of space and time, Einstein’s General Theory of Relativity, no longer applies at the earliest times; the conditions were so extreme in those first moments, known as the Planck epoch, that some kind of quantum theory of gravity, which we do not possess, will be needed to describe it.

The universe is now 13.798 +/0.037 billion years old, according to our current best measurements and theoretical understanding, and has been gently expanding and cooling ever since the Big Bang. The universe appears to be gently increasing its expansion rate, and approximately 68 per cent of the energy in the universe is associated with this sedate acceleration. The energy has a name – dark energy – but its nature remains one of the great unsolved challenges for twenty-first-century theoretical physics. Of the 32 per cent that remains, approximately 27 per cent is in a form of matter known as dark matter. The nature of this is also unknown, but it probably comes in the form of as yet undiscovered sub-atomic particles. The remaining 5 per cent makes up the stars, planets and galaxies we see in the night sky, and of course human beings. The part of the universe we can see is around 93 billion light years across and has reached a relatively chilly temperature of 2.72548 +/0.00057 Kelvin due to its expansion.

The question of the origin of the universe is an old one in philosophy, and often framed in terms of the ‘First Cause’ argument. Leibniz is associated with a ‘proof’ of the existence of God in this context, which goes something like this:

Everything that exists must have either an external cause or must be eternal. If there are eternal things, then they must necessarily exist, because they don’t have a cause. Since the universe exists and is not eternal, it must have an external cause, and to avoid infinite regress that cause must be an eternal and necessary thing, which we’ll call God.

This is quite a neat piece of logic, obviously, because Leibniz wasn’t an idiot. I don’t consider such questions to fall necessarily within the domain of science. Rather science is concerned with answering more modest questions, and this is the reason for its power and success. The goal of science is to explain the observed features of the natural world. By ‘explain’, I mean ‘build theories that make predictions that are in accord with observation’. This is a humble idea; there is no a priori aim to discover the reason for the existence of our universe or to build theories of everything. Science proceeds in tiny steps, attempting to find explanations for the blue sky, the green leaves of plants or the stretched, red-shifted light from distant galaxies. Sometimes, those tiny steps build up to something rather grand, like a measurement of the age of the observable universe, but that’s not what anyone set out to do. This is why science is more successful than any other form of human thought when applied to questions within its domain, which is the explanation of the natural world. It starts small and works its way slowly and methodically forwards, deepening our understanding in careful increments.

Our chapter title ‘Why are we here?’ might therefore appear to be unanswerable by science; it’s too grand a question. But that may no longer be the case, because the careful steps are taking science into this territory and the scientific language is now in place to at least address the question ‘What happened before the Big Bang?’ This is clearly a prerequisite for being able to make any meaningful attempt to address the reasons for our existence, although it is surely not sufficient. Immediately, I have to explain a semantic distinction before a thousand philosophers throw their togas aside and prepare to engage in a naked yet civilised and eloquent battle of ideas. I am defining the term Big Bang as the astronomer Fred Hoyle originally introduced it into physics in 1949. It is to be understood as the beginning of the hot, dense state in which our observable universe once existed. Conventional cosmological theory, as described in Chapter 1, traces the evolution of the universe backwards in time, with conditions getting hotter and hotter and denser and denser until the point where we are unsure of the correct rules of physics. Currently this is earlier than approximately 10-10 seconds, which is associated with the current power of the Large Hadron Collider. If the universe existed in some other form before the hot, dense state came into existence 13.798 billion years ago, then that’s what I’m referring to as the time before the Big Bang. Science might accidentally wander into Leibniz’s territory if, for example, this time before the Big Bang were discovered to be infinite, or that the state before the Big Bang was logically necessary and describable by current or yet-to-be discovered laws of physics. Such a theory would also have to explain precisely all the properties of the universe we see today. From a scientific perspective of course, we don’t care about Leibniz; it is not the role of science to prove or disprove the existence of God. Rather we are only interested in taking our careful steps backwards in time as far as the evidence and theoretical understanding allow. The exciting thing is that developments in cosmology since the 1980s now point quite firmly towards the existence of a state before the Big Bang as defined above, and that is primarily what this chapter is about.

This chapter is also about you. I suspect most of us have mused about the question ‘Why are we here?’ For some, the question and answer may be absolutely central to their lives. For others, myself included, it’s something I used to think about on a hillside desolate beside a punctured bicycle whilst wearing a secondhand overcoat I bought from Affleck’s Palace, but my existentialism faded with my hair.

Having said that, a little existentialism, like the Manchester rain, never did anyone any harm, so let’s place ourselves at the centre of things for a while and explore the immense contingency of our personal existence as a warm-up for the much deeper problem of the origin of the universe itself. It’s a pretty deep chapter this, so put on Unknown Pleasures, grab a bottle of cheap cider and let’s get going.

NEW DAWN FADES

If, in a moment of solipsism, you decide to work out the odds of your own existence, you might come to the conclusion that you are astonishingly special. You began as a particular egg inside your mother, fertilised by a particular sperm from your father. There were 180 million sperm around that day, each with a different genetic code, only one of which became ‘you’ in combination with one of your mother’s million or so genetically unique eggs. So without going any further, you might feel lucky. If you chose to carry on, you might factor in the odds of your parents having sex on that particular day, because sperm are constantly manufactured. Then there are the odds of them meeting at all, and the odds of them being THEM. And whilst we’re picking up increasing armfuls of odds at the 1-in-a-100-million level, recall from Chapter 1 that there exists an unbroken line of your ancestors stretching back over 3.8 billion years to LUCA – the Last Universal Common Ancestor. If any one of those living things had died before it reproduced, you wouldn’t exist. That’s pretty lucky, but also completely devoid of any meaning at all. Yes, the odds of YOU existing are almost, but not quite, zero. But given the existence of the human race and a mechanism for procreation, someone has to be born. So whilst the probability of any given individual existing is tiny, it is inevitable that new babies will be born every day. Seen in this light, you are not special and your existence in the grand scheme of things is entirely understandable. Time for Joy Division and cider.

This demolition of your individual self-importance relied on the fact that a mechanism exists for the inevitable production of large numbers of human beings, given the important precondition that humans already exist. We’ve explored the road to human existence at length in the book already, and argued that complex multicellular life and intelligence at or beyond the level of humans may be rare in our universe. It is also clear that there are fundamental properties of the universe itself that are necessary for the existence of any form of life. The universe must live long enough and have the right properties for stars to form, and those stars must be capable of producing the chemical elements out of which living things are made, carbon being the most important. What do we mean by ‘properties’? We are back to the nature of the laws of physics once again, because they describe the behaviour of matter and forces at the most fundamental level. The laws restrict the possible physical structures that are allowed to appear in the universe, and stars, planets and human beings are all examples of such possible physical structures. Questions now naturally arise; more modest perhaps than our grand ‘Why are we here?’ puzzle, but more amenable to scientific enquiry. How do the laws of nature allow for human beings to exist, and by how much could those laws vary before life could no longer exist in the universe?

It was me, waiting for me,

Hoping for something more,

Me, seeing me this time,

Hoping for something else.

Ian Curtis, New Dawn Fades,

Unknown Pleasures

Let us begin in the spirit of taking small steps with a brief summary of the known fundamental laws of nature.

THE RULES OF THE GAME

Attempting to describe the laws that govern the existence of everything from galaxies to human beings in a single paragraph of a book of a TV series might seem overly ambitious. It is at one level; otherwise everyone would complete physics, chemistry and biology degree courses in an afternoon. What we can do, however, is to outline the known fundamental laws in a concise and accurate way, so let us do that.

There are twelve known particles of matter, listed on here. They are arranged into three families, or generations. You are made out of particles in the first generation alone. Up quarks and down quarks bind together to make protons and neutrons, which in turn bind together to form your atomic nuclei. Your atoms are composed of electrons bound to those nuclei. Molecules, such as water and DNA, are built up out of collections of atoms bound together. That’s all there is to you; three fundamental particles arranged into patterns. Particles called gauge bosons carry the forces of nature. There are four known fundamental forces: the strong and weak nuclear forces, electromagnetism and gravity. Gravity is missing from the figure here, and we’ll get to that in a moment. The other three forces are represented in the fourth column. To see how this all works, let’s focus on the familiar electromagnetic force. Imagine an electron bound to the atomic nucleus of one of your atoms. How does that binding happen? The most fundamental description we have is that the electron can emit a photon, which you can think of as a particle of light. That photon can be absorbed by one of the quarks inside the nucleus, and this emission and absorption acts to assert a force between the electron and the quark. There is a vast number of ways in which the electrons and the quarks inside the nucleus can emit and absorb photons, and these all combine to keep the electron firmly glued to the nucleus. A similar picture can be applied to the quarks themselves. They also interact via the strong nuclear force by emitting and absorbing force-carrying particles called gluons. The strong nuclear force is the strongest known force (the clue is in the name) and binds the quarks together very tightly indeed. This is why the nucleus is significantly smaller and denser than the atom. Only quarks and gluons feel the strong nuclear force. Finally, there is the weak nuclear force. This is mediated by the exchange of the W and Z bosons. All known particles of matter feel the weak nuclear force but it is extremely weak relative to the other two, which is why its action is unfamiliar, but not unimportant. The Sun would not shine without the weak nuclear force, which allows protons to convert into neutrons, or more precisely up quarks into down quarks, which has the same result. This is the first step in the nuclear burning of hydrogen into helium, the source of the Sun’s energy. During the conversion of a proton into a neutron, an anti-electron neutrino is produced along with an electron. The neutrino is the remaining particle in the first generation we haven’t discussed yet. Because neutrinos only interact via the weak nuclear force, we are oblivious to them in everyday life. This is fortunate, because there are approximately sixty billion per square centimetre per second passing through your head from the nuclear reactions in the Sun. If the weak force were a little stronger, you’d get a hell of a headache. Actually, you wouldn’t because you wouldn’t exist, and this foreshadows the subject of the fine-tuning of the laws of nature we will undertake later in this chapter. The one remaining type of particle is the Higgs Boson, on its own in the fifth column. Empty space isn’t empty, but is jammed full of Higgs particles. All the known particles apart from the photon and the gluons, which are massless, interact with the Higgs particles, zigzagging through space and acquiring mass in the process. This is the counter-intuitive picture that was confirmed by the discovery of the Higgs Boson at CERN’s Large Hadron Collider in 2012.

What really interests
me is whether God had any choice
in the creation of 
the world.

Albert Einstein

Two further generations of matter particles have been discovered. They are identical to the first generation except that the particles are more massive because they interact with Higgs particles more strongly. The muon, for example, is a more massive version of the familiar electron. The reason for their existence is unknown.

This is all there is in terms of the description of the fundamental ingredients of the universe. There are almost certainly other particles out there somewhere – the dark matter that dominates over normal matter in the universe by a factor of 5 to 1 is probably in the form of a new type of particle which we may discover at the Large Hadron Collider or a future particle accelerator. The evidence for dark matter is very strong and comes from astronomical observations of galaxy rotation speeds, galaxy formation models and the cosmic microwave background radiation that we met in Chapter 1 and will meet again later in this chapter. But because we don’t know what form the dark matter takes, we are not able to incorporate it into our list.

The mathematical framework used to describe all the known particles and forces other than gravity is known as quantum field theory. It is a series of rules that allows the probability of any particular process occurring to be calculated. The whole thing can be described in one single equation, known as the Standard Model Lagrangian. Here it is:

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It takes a lot of work to use this piece of mathematics to make predictions, but the predictions are spectacularly accurate and agree with every experimental measurement ever made in laboratories on Earth. This equation even predicted the existence of the Higgs particle; that’s how good it is. It probably looks like a set of squiggles unless you are a professional physicist, but in fact it isn’t too difficult to interpret, so let’s dig just a little deeper. The 12 matter particles are all hidden away in the symbol Ψj. The Standard Model is a quantum field theory because particles are represented by objects known as quantum fields. There is an electron field, an up quark field, a Higgs field and so on. The particles themselves can be thought of as localised vibrations in these fields, which span the whole of space. Fields will be important for us later, when we’ll want to think about a certain type of field that may have appeared in the very early universe, known as a scalar field. The Higgs field is an example of a scalar field. The mathematical terms between the two Ψjs on the second line describe the forces and how they cause the particles to interact. The forces are also represented by quantum fields. The term – gs Tj · Gµ for example, describes the gluon field that allows the quarks in the Ψj terms to bind together into protons and neutrons. The term gs is known as the strong coupling constant. It is a fundamental property of our universe that encodes the strength of the strong nuclear force. Each of the forces has one of these coupling constants. We will want to discuss these coupling constants later, because they define what our universe is like and what is allowed to exist within it. The last two lines deal with the Higgs Boson. The strength of the interaction between a matter particle and the Higgs field is contained in theyj terms, which are known as Yukawa couplings. These must be inserted to produce the observed masses of the particles of matter. That’s pretty much it.

Here ends our crash course on particle physics. The central point is that there exists a remarkably economical description of everything other than gravity, and it is contained within the Standard Model.

We considered the gravitational force in some detail in Chapter 1. It is described by Einstein’s Theory of General Relativity, which is what physicists call a classical theory. There are no force-carrying particles in Einstein’s theory; instead the force is described in terms of the curvature of spacetime by matter and energy and the response of particles to that curvature. A quantum theory of gravity, which we have already noted will be necessary to describe the first fleeting moments in the history of the universe, would involve the exchange of particles known as gravitons, but as yet nobody has worked out how to construct such a description. This is why Einstein’s theory remains the only fundamental non-quantum theory we have.

For completeness, let’s refresh our memory of Einstein’s Theory of General Relativity:

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General Relativity, like the Standard Model, contains a coupling constant encoding the measured strength of gravity: G, Newton’s gravitational constant. The amount of dark energy is inserted by hand, in accord with observations, as was the case for the strengths of the forces and the masses of the particles in the Standard Model.


THE STANDARD MODEL

The Standard Model of particle physics is a theory that explains the interactions between subatomic particles in the form of the strong, weak and electromagnetic forces. The original theory has been tested experimentally since it was first postulated and has proven extremely robust. In 2013 the Higgs Boson that had been predicted by the theory was discovered using the Large Hadron Collider at CERN.

INSIDE THE ATOM

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General Relativity and the Standard Model are the rules of the game. They contain all our knowledge of the way that nature behaves at the most fundamental level. They also contain almost all the properties of our universe that we think of as fundamental. The speed of light, the strengths of the forces, the masses of the particles (encoded as the strength of their interaction with the Higgs Bosons via the Yukawa couplings) and the amount of dark energy are all in these equations. In principle, any known physical process can be described by them. This is the current state of the art, but it doesn’t mean that we know how everything works and can all retire, by a long shot or well-timed cover drive.

Most games are skin-deep, but cricket goes to the bone.

John Arlott and Fred Trueman

I timed a cover drive properly once when I was 14 years old playing at Hollinwood Cricket Club near Oldham. Front foot, head in line with the ball, sweet sound of the middle, four runs. I know what I have to do, but I never did it quite as well again. Cricket is an art built on simple rules, first codified by the members of the Marylebone Cricket Club on 30 May 1788; a significant date in world history according to historians with good taste. Those original laws still form the basis of the game today. There are 42 of them, and they define the framework within which each game evolves. Yet despite the rigid framework, no two games are ever alike. The temperature and humidity of the air, a light scatter of dew on the grass, the height of grass on the wicket, and hundreds of other factors will subtly shift and change throughout the game. More importantly, the players and umpires are each complex biological systems whose behaviour is far from predictable, with the exception of Geoffrey Boycott. The presence of so many variables makes the number of possible permutations effectively infinite, which is why cricket is the most interesting of human pursuits excluding science, sex and wine tasting.

Knowledge of the laws is therefore insufficient to characterise the infinite magic of the game. This is also true for the universe. The laws of nature define the framework within which things happen, but do not ensure that everything that can happen will happen in a finite universe – that rather obscure ‘finite’ caveat will be important for us later on. Virtually all of science beyond particle physics and theoretical cosmology is concerned with the complex outcomes allowed by the laws rather than the laws themselves, and in a certain sense our solipsistic initial question ‘Why are we here?’ is also a question about outcomes rather than laws. The answer to the question ‘Why did England beat Australia in the great Ashes series of 2005?’ is not to be found in the MCC rule book, and similarly the natural world that emerges from the Standard Model and General Relativity cannot be understood simply by discovering the laws themselves.

It’s worth noting that the laws of nature were not written by the MCC, or even the committee of Yorkshire County Cricket Club. We had to work them out by watching the game of the universe unfold, which makes their discovery even more wonderful. Imagine how many matches would have to be viewed in order to deduce the laws of cricket, including but not restricted to the Duckworth Lewis method? The great achievement of twenty-first-century science is that we’ve managed to work out the laws of nature by doing just this; observing many millions of complex outcomes and working out what the underlying laws are.

The Standard Model, then, cannot be used to describe complex emergent systems such as living things. No biologist would attempt to understand the way that ATP is produced inside cells using the Standard Model Lagrangian and no telecommunications engineer would use it to design an optical fibre. They wouldn’t want to even if they could; you wouldn’t gain any insight into how a car engine works by starting off with a description of its constituent subatomic particles and their interactions. So whilst it is important that we have a detailed model of nature at the level of the known fundamental building blocks, we must also understand how the complexity we observe around us emerges from these simple laws if we are to make progress with our difficult ‘Why?’ question.

NATURE’S FINGERPRINT

On Monday 27 March 1905 at 8.30am, William Jones arrived at Chapman’s Oil and Colour Shop on Deptford High Street ready for a day’s work. Jones normally arrived a few minutes after the shop manager Thomas Farrow had raised the shutters. On this particular Monday, however, the shutters were down. Farrow lived with his wife Anne above the shop, but no matter how hard Jones knocked on their door, there was no response. This was a most unusual start to the day, and his concern increased when a glimpse through a window revealed chairs strewn across the floor of the normally tidy shop. Jones and another local resident forced the door, to be confronted by Farrow lying dead in a pool of blood. Anne had been similarly bludgeoned in her bed, although she clung to life for four more days without regaining consciousness.

Such scenes were not uncommon in Edwardian London. The reason that this crime is of note is because it was the first in the world to use a new technology to catch and convict the killers. On an inner surface of the empty cash box, the police noticed a fingerprint. They already had a suspect: a local man named Alfred Stratton, who was arrested three days later along with his brother Albert. The Strattons’ fingerprints were taken, and a positive match was made between the cash-box print and Alfred Stratton’s right thumb. Although fingerprints were never used before in a murder case, expert witnesses convinced the jury that the complex patterns of the cash-box fingerprint could only belong to Alfred Stratton. The jury took just two hours to find the Stratton brothers guilty of murder, and the pair were sentenced to death by hanging, with justice swiftly dispatched on 23 May.

Take a look at your fingerprints now; there is seemingly endless complexity in the swirls and ridges. Since every human being carries different fingerprints on the hands and the soles of their feet (which aren’t fingerprints, but there isn’t a word for them), the size of database required to characterise every human being’s fingerprints would be colossal. One of the most important properties of nature, however, is that the blueprints for the construction of the natural world are far simpler than the natural world itself. In modern language, there is a tremendous amount of data compression going on. The instructions to create fingerprints are far simpler than the fingerprints themselves, and more than that, the same instructions, run over and over again from slightly different starting points in the embryonic stage of our development, always lead to different fingerprints. This behaviour shouldn’t come as a surprise. The sweep of desert dunes or the patterns in summer clouds are all described by a handful of simple laws governing how sand grains or water droplets behave when agitated by shifting air currents, buffeted by chaotic thermals and winds and re-ordered by the action of the forces of nature. And yet from a simple recipe, complexity emerges.

When you have eliminated
the impossible, whatever 
remains, however improbable, 
must be the truth.

Sherlock Holmes

The quest to understand how the boundless variety of the natural world emerges from underlying simplicity has been a central theme in philosophical and scientific thought. Plato attempted to cast the world available to our senses as the distorted and imperfect shadow of an underlying reality of perfect forms, accessible through reason alone. The modern expression of Plato’s ethereal dualism was captured eloquently by Galileo, 500 years ago: ‘The book of nature is written in the language of mathematics’. The challenge is not only to discern the underlying mathematical behaviour of the world, but also to work back upwards along the chain of complexity to explain how those forms that Plato would have defined as imperfect arise from the assumed lower-level perfection. A rather beautiful early example of this quest is provided by Galileo’s illustrious contemporary, Johannes Kepler.

A BRIEF HISTORY OF THE SNOWFLAKE

Johannes Kepler is rightly best known for his laws of Planetary Motion that paved the way for Newton to write Principia. Hidden within his illustrious CV, however, is a publication that had a rather more whimsical earthbound ambition. Two years after publishing the first part of Astronomia Nova in 1609, Kepler published a short 24-page paper entitled De nive sexangula – On the Six-Cornered Snowflake. It is a beautiful example of a curious scientific mind at work. In the dark December of 1610, Kepler was walking across the Charles Bridge in Prague when a snowflake fell on the lapel of his coat. In the freezing night he stopped and wondered why this ephemeral sliver of ice possessed a six-sided structure, in common with all other snowflakes, notwithstanding their seemingly infinite variation. Others had noticed this symmetry before, but Kepler realised that the symmetry of a snowflake must be a reflection of the deeper natural processes that underlie its formation.

‘Since it always happens when it begins to snow, that the first particles of snow adopt the shape of small six-cornered stars, there must be a particular cause,’ wrote Kepler, ‘for if it happened by chance, why would they always fall with six corners and not with five, or seven?’ Kepler hypothesised that this symmetry must be due to the nature of the fundamental building blocks of snowflakes. This stacking of frozen ‘globules’, as he referred to it, must be the most efficient way of building a snowflake from the ‘smallest natural unit of a liquid like water’.

To my mind, this is a leap of genius and a tremendously modern way of thinking about physics. The study of symmetry in nature lies at the very heart of the Standard Model, and abstract symmetries known as gauge symmetries are now known to be the origin of the forces of nature. This is why the force-carrying particles in the Standard Model are known as gauge bosons. Kepler was searching for the atomic structure of snow before we knew atoms existed, motivated by the observation of a symmetry in nature – the six-sided shape of all snowflakes. The inspiration for this idea, which is way ahead of its time, came from a peculiar source. In the years leading up to the publication of De nive sexangula, Kepler had been in communication with Thomas Harriot, an English mathematician and explorer. Amongst multiple claims to fame, Harriot was the navigator on one of Sir Walter Raleigh’s voyages to the New World, and had been asked to solve a seemingly simple mathematical problem. Raleigh wanted to know how best to stack cannonballs to make the most efficient use of the limited space on the ship’s deck. Harriot was driven to exploring the mathematical principles of sphere packing, which in turn led him to develop an embryonic model of atomic theory and inspire Kepler’s consideration of the structure of snowflakes. Kepler imagined replacing cannonballs with globules of ice, and supposed that the most efficient arrangement creating the greatest density of globules was the six-sided hexagonal form he observed in the snowflake on his shoulder. Kepler also observed hexagonal structures across the natural world, from beehives to pomegranates and snowflakes, and presumed that there must be some deeper reason for its ubiquity.

As I write it has begun to 
snow, and more thickly 
than a moment ago. I have 
been busily examining the 
little flakes.

Johannes Kepler

‘Hexagonal packing’, as Kepler referred to it, must be ‘the tightest possible, so that in no other arrangement could more pellets be stuffed into the same container’. This became known as the Kepler Conjecture. It took almost 400 years to prove Kepler’s conjecture, and this required the help of a 1990s supercomputer. Despite the time lag, Kepler’s work had a more immediate impact, inspiring the beginnings of modern crystallography that led eventually to the discovery of the structure of DNA. What a lovely example of serendipity coupled with curiosity and a sprinkling of genius; from cannonballs to snowflakes to the code of life.

As for Kepler’s original thought on that frozen bridge, he never found the connection between the underlying structure of his ice globules and the hexagonal symmetry of snowflakes. Even though he realised that the regular patterns must reveal something about the shape of the building blocks of snowflakes and the details of the packing, he couldn’t explain the ornate complexity or the flatness of the structure. Instead he acknowledged his failure with the good grace of a true scientist: ‘I have knocked on the doors of chemistry’ he writes at the end of his paper, ‘and seeing how much remains to be said on this subject before we know the cause, I would rather hear what you think, my most ingenious man, than wear myself out with further discussion.’

Three and a half centuries later, Japanese physicist Ukichiro Nakayara made the first artificial snowflakes in a laboratory. Writing in 1954, he describes a process that begins not with the snowflake itself but with smaller substructures called snow crystals, which are in turn built up from collections of ice crystals – the globules Kepler was searching for. The hexagonal packing that Kepler suspected to be the origin of the snowflakes’ symmetry begins with the formation of these ice crystals, when water molecules link together in a hexagonal structure via hydrogen bonds. Hydrogen bonding occurs because of the structure of the water molecules themselves, with a greedy oxygen atom hungry for electrons grabbing them off two hydrogen atoms, forming covalent bonds that lock the H2O molecules together, leaving a residual positive electrical charge in the vicinity of the two protons and a negative charge in the vicinity of the oxygen. This slight separation of charge in the water molecules allows them to bind together into larger structures through the mutual attraction and repulsion of the electrical charges, just as an electron is bound into its position around an atomic nucleus. The entire configuration, including the structure of the oxygen nucleus and the single protons that comprise the hydrogen nuclei, can be predicted in principle by the Standard Model of particle physics. Yet the details of any particular snowflake are beyond computation, because the seemingly infinite variety reflects the precise history of the snowflake itself. Once ice crystals form as agglomerations of water molecules held together by hydrogen bonds, they cluster around dust particles in the air, building on their underlying hexagonal symmetry to form larger snow crystals. As the crystals begin the long journey down to Earth they join in ever-larger, more complex combinations, shaped by endless variations of air temperature, wind patterns and humidity into myriad unique forms. The symmetry is all that remains of the simplicity, and it takes a careful and patient eye to see the endless variation for what it is: a reflection of the complex history of the snowflake convoluted with the underlying simplicity of the laws of nature.

The most vivid example of emergent complexity, and the closest to our hearts, is life. As we discussed in Chapter 2, the origin of life on Earth has a sense of inevitability about it, because its basic processes are chemical reactions that will proceed given the right conditions. Those conditions were present in the oceans of Earth 3.8 billion years ago, possibly earlier, and they led to the emergence of single-celled organisms. The fateful encounter which produced the eukaryotic cell around 2 billion years ago looks rather more like blind chance, but it happened here and laid the foundations for the Cambrian explosion 530 million years ago. There is a bit of hand-waving going on here, though, and to make a more persuasive case that all the complexity of Darwin’s endless forms most beautiful can at least in principle emerge from simple underlying laws, one more example is in order.

Perhaps the most beautiful manifestation of the artful complexity of nature can be found in the spots, stripes and patterns on the coats and skin of living things; emergent pattern writ large across venomous striped surgeonfish, emperor angelfish, zebra swallowtail butterflies and the big cats of Africa and Asia. Everyone agrees that these patterns evolved as a result of natural selection of one form or another, and the raw material for the variation was provided by random mutations in the genetic code. But a very challenging scientific question of fundamental importance in modern biology is precisely how patterns such as these appear.

HOW THE LEOPARD GOT ITS SPOTS

Rudyard Kipling’s Just So story, ‘How The Leopard Got His Spots’, tells the story of an Ethiopian man and a leopard. They went hunting together, but one day the man noticed that the leopard wasn’t very successful. The reason, he deduced, was that the leopard had a plain sandy coat, whereas all the other animals had camouflage. ‘That’s a trick worth learning, leopard’ he said, taking his fingers and thumb and pressing them into the leopard’s coat to give it the distinctive five-pointed pattern. If you don’t believe in evolution by natural selection, this is the most plausible theory open to you. If you do, then what remains is to identify the mechanism by which the pattern is formed. The answer might appear to be solely a matter of genetics, but genes are not the whole story. It would take a terrific amount of information to instruct every single cell to colour itself according to its position on the leopard’s skin, and this is indeed not what is done. Nature is frugal and deploys a much more efficient mechanism for producing camouflage patterns. As with so many things in this book, I get to say yet again that this is an active area of research, and therefore exciting. The reason for the attention is that camouflage patterns on the skin self-organise during the development of the embryo, and embryonic development is of course fundamental to an understanding of biology. In the case of the leopard, it is thought, though not proven, that the camouflage is an example of a Turing pattern, named after the great Bletchley Park code-breaker and mathematician Alan Turing.

In 1952, Turing became interested in morphogenesis – the process by which an animal develops its shape and patterning. He was particularly interested in the mathematics behind regularly repeating patterns in nature such as the Fibonacci numbers and golden ratio in the leaf arrangements of plants and the scales of pineapples, and the appearance of camouflage patterns such as the tiger’s stripes and the leopard’s spots. Turing’s influential and ground-breaking paper, ‘The Chemical Basis of Morphogenesis’, published in March 1952, begins with a simple statement. ‘It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.’ These systems are known as reaction-diffusion systems, and they can produce patterns from a featureless initial mixture if the two reactants diffuse at different speeds. There is a nice analogy that describes how such a system can work.fn1 Imagine a dry field full of grasshoppers. They are strange grasshoppers, because when they get warm they sweat, generating a large amount of moisture. Now imagine that the field is set alight in several different places. The flames will spread at some fixed speed, and if there were no grasshoppers the whole field would be charred. As the flames approach the grasshoppers, however, they will start to sweat, dampening the grass behind them and inhibiting the flames as they hop away ahead of the approaching flames. Depending on the different parameters, including the different speeds of the flames and the grasshoppers, and the amount of sweat necessary to quell the advancing flames, a Turing pattern can be formed, with areas of charred grass and green areas where the inhibiting grasshoppers prevented the fire from taking hold.

… Zebra moved away to some little 
thorn-bushes where the sunlight fell 
all stripy and the giraffe moved off to 
some tallish trees where the shadows 
fell all blotchy.

‘Now watch,’ said the zebra and
the giraffe. ‘This is the way it’s done. 
One … two … three! And where’s your 
breakfast!’ … All they could see were 
stripy shadows and blotched shadows 
in the forest, but never a sign of 
Zebra and Giraffe.

‘That’s a trick worth learning.

Take a lesson from it, Leopard!’

… Then the Ethiopian put his five 
fingers close together and pressed 
them all over the leopard, and 
wherever the five fingers touched, they 
left five black marks, all close together

Rudyard Kipling

It is thought that the leopard gets its spots in this way during embryonic development: an activator chemical (fire) spreads through the skin and stimulates the production of the dark pigmented spots (charred grass) but is inhibited by another chemical (sweating grasshoppers) spreading with a higher diffusion rate. The precise pattern produced depends on the ‘constants of nature’ of the system, such as the speeds at which the chemicals diffuse, and on what a mathematician would call the boundary conditions: the size and geometry of the grassy field in our analogy. In embryonic development, it is the size and shape of the embryo when the reaction-diffusion begins that determines the type of pattern produced. A long and thin domain produces stripes. A domain that is too small or too large produces uniform colour. In between can be found the distinctive coat patterns of cows, giraffe, cheetah and, of course, the leopard. Computer simulations of Turing patterns have been remarkably successful, not only in describing the generic features, particularly of mammalian coats, but also some of the interesting details seen in nature. For example, the mathematical models predict that it is possible for spotted animals to have striped tails, as cheetahs do, but not for striped animals to have spotted tails; and indeed, no such examples exist.

Kepler’s snowflakes and the leopard’s spots are two picturesque examples of emergent complexity: the appearance of intricate, ordered patterns from the action of simple underlying laws. Nature contains systems far more complex than these, of course: you being a case in point. But to return to the question at the beginning of our solipsistic meander, the reason that you exist, given the laws of nature, is that you are allowed to. Just as all snowflakes and all leopards’ coats are unique in detail because of their individual formation histories, so you are unique because no two human beings share a common history. But we wouldn’t read any deep meaning into the existence of one particular snowflake in a snowstorm, and the same is true for you. Our focus should therefore shift from trying to explain the appearance of humans, or our planet, or even our galaxy, to a rather deeper question: the origin of the whole framework – of spacetime and the laws that govern it and the allowed structures within it. What properties of the laws themselves are essential for galaxies, planets and human beings to exist? After all, as we’ve noted, the laws might be mathematically elegant and economical, but they do contain a whole host of seemingly randomly chosen numbers, discovered by experimental observation and with no known rhyme or reason to them – the constants of nature such as the strengths of the forces, the masses of the particles and the amount of dark energy in the universe. How dependent is our existence on these fundamental numbers?

A UNIVERSE MADE FOR US?

Our universe appears to be made for us. We live on a perfect planet, orbiting around a perfect star. This is of course content-free whimsy. The argument is backwards. We have to be a perfect fit for the planet because we evolved on it. But there are interesting questions when we look deeper into the laws of nature and ask what properties they must have to support a life in the universe. Take the existence of stars, for example. Stars like the Sun burn hydrogen into helium in their cores. This process involves all four forces of nature working together. Gravity kicks it all off by causing clouds of dust and gas to collapse. As the clouds collapse, they get denser and hotter until the conditions are just right for nuclear fusion to occur. Fusion starts by turning protons into neutrons through the action of the weak nuclear force. The strong nuclear force binds the protons and neutrons together into a helium nucleus, which in itself exists on account of the delicate balance between the strong nuclear force holding it together and the electromagnetic force trying to blow it apart because of the electrically charged protons. When stars run out of hydrogen fuel, they perform another series of equally precarious nuclear reactions to build carbon, oxygen, and the other heavy elements essential for the existence of life. What happens if the strengths of the forces, those fundamental constants of nature we met earlier in the chapter, are varied a bit?

There are many examples of apparent fine-tuning in nature. If protons were 0.2 per cent more massive, then they would be unstable and decay into neutrons. That would certainly put an end to life in the universe because there would be no atoms. The proton mass is ultimately set by the details of the strong and electromagnetic forces, and the masses of the constituent quarks, which are set by the Yukawa couplings to the Higgs field in the Standard Model. There really isn’t much freedom at all.

The mother of all fine-tunes, however, is the value of our old friend dark energy, the thing that is causing our universe to gently accelerate in its expansion. Although dark energy contributes 68 per cent of the energy density of the universe, the amount of dark energy in a given volume of space is actually small. Very small: 10–27kg per cubic metre to be precise. The point is that every cubic metre of our universe has this amount of dark energy in it, and that adds up! Explaining why dark energy has this small, but non-zero, value is one of the great problems in cosmology, not least because if a particle physicist sits down with quantum field theory and decides to calculate how big it should be, it turns out that it would be more naturally of the order of 1097kg per cubic metre. That’s a lot bigger than 10–27kg per cubic metre. Over a million million million million million million million million million million million million million million million million million million million million times bigger, in fact. That’s embarrassing for the particle physicists, of course, but from the perspective of fine-tuning it’s even worse. If the value of dark energy were only 50 times larger than it is in our universe, rather than somewhere else in this immensely large theoretical range, then it would have become dominant in the universe around one billion years after the Big Bang during the time that the first galaxies were forming. Because dark energy acts to accelerate the universe’s expansion and dilute matter and dark matter, gravity would have lost the battle in such a universe and no galaxies, or stars, or planets or life would exist. What could possibly account for this incredible piece of luck? It can’t really be luck – the odds are too long by a Geoffrey Boycott innings. One possibility is that there is some as yet unknown physical law or symmetry that guarantees that the amount of dark energy will be very close to, but not quite, zero. This is certainly possible, and there are physicists who believe that this may be the case. The other possibility, which was raised by one of the fathers of the Standard Model, Steven Weinberg, is that the value of dark energy is anthropically selected. Anthropic arguments appear at one level to be a statement of the obvious: the properties of the universe must be such that human beings can exist because human beings do exist. This is, of course, true, but it is fairly devoid of content from a physical perspective unless there is some way in which all possible values of dark energy, and indeed all the other constants of nature, are realised somewhere. If, for example, there exists a vast, possibly infinite swathe of different domains in the universe, or indeed an infinity of other universes, each with a different amount of dark energy selected by some mechanism from the span of allowed values, then we would indeed have a valid anthropic explanation for our ‘special’ human universe. It must exist, because they all do, and of course we appear in the one that permits our existence.

But surely it makes no sense to take refuge in a vast infinity of universes to explain our existence? Absolutely correct, if that’s why the idea is introduced – it’s no better than a God-of-the-gaps explanation. If, however, there were some other reason, based on observations and theoretical understanding, that suggested an infinity of universes, then such an anthropic explanation for our perfect, human universe would be admissible. Remarkably – and that remarkably overused word is appropriate for once – this outlandish suggestion is a widely held view amongst many cosmologists.

A DAY WITHOUT YESTERDAY?

If we look at our universe on the largest distance scales, by which I mean at distance scales far larger than the size of single galaxies, it has a number of properties that any theory of its origin has to explain. The most precise picture of the young universe we have is the photograph of the Cosmic Microwave Background Radiation (CMB) taken by the Planck satellite.

This is the afterglow of the Big Bang, a photograph of the universe as it was 380,000 years after the initial hot, dense phase when the expansion had cooled things down sufficiently for atoms to form. The most obvious feature of the CMB is that it is extremely uniform, glowing at a temperature of 2.72548 degrees above absolute zero, with small fluctuations at the level of 1 part in 100,000. Those very tiny temperature differences are represented by the colours in the photograph. This uniformity is extremely difficult to explain in the standard Big Bang model for a simple reason. Our observable universe today is 90 billion light years across. This means that if we look out to the CMB from opposite sides of the Earth, we are looking at two glowing parts of the ancient sky that are now separated by 90 billion light years. The universe, however, is only 13.8 billion years old, which means that light, the fastest thing there is, has only had time to travel 13.8 billion light years. Two ‘opposite’ parts of the CMB could therefore never have been in contact with each other in the standard Big Bang model, and there is absolutely no reason why they should be almost precisely the same temperature. I’ve italicised ‘almost’ in the previous sentence because, as we noted, there are very slight variations in the CMB at the level of 1 part in 100,000, and these are very important. The universe was never completely smooth and uniform everywhere, and these variations in density are encoded into the CMB as differences in temperature. The regions of slightly greater density ultimately seeded the formation of the galaxies, and so without them we wouldn’t exist. What caused these small variations in the otherwise ultra-smooth early universe?

Another fundamental property of the universe that is difficult to explain is its curvature – or lack of it – which can also be measured from the CMB. Space appears to be absolutely flat; a veritable ice rink. Recall from Chapter 1 that the shape of space is related to the density and distribution of matter and energy in the universe through Einstein’s equations. In the standard Big Bang theory, the universe doesn’t have to be flat. In fact, it requires a great deal of fine-tuning to keep it flat over 13.8 billion years of cosmic evolution. Instead, the radius of curvature is measured to be much greater than the radius of the observable universe – more than sixty orders of magnitude larger. That’s a big problem!

It suddenly struck me that 
that tiny pea, pretty and blue, was
the Earth. I put up my 
thumb and shut one eye and 
my thumb blotted out the 
planet Earth. I didn’t feel like a 
giant. I felt very, very small.

Neil Armstrong

In the early 1980s, the need to explain these and other properties of the observable universe led a group of Russian and American physicists to propose a radical idea. The modern version, the best-known proponents of which are Alan Guth, Andrei Linde and Alexei Starobinsky, is known as the Theory of Inflation. We’ll describe a particular version of inflation below, driven by something called a scalar field, which was first described by Andrei Linde.

Spacetime existed before the Big Bang, and for at least some of that time was described by Einstein’s Theory of General Relativity and a quantum field theory like the Standard Model. The central idea in quantum theory is that anything that can happen does happen. Everything that is not explicitly ruled out by the laws of nature will happen, given enough time. One of the types of things permitted to exist in quantum field theory are scalar fields. We’ve met an example of a scalar field earlier in the chapter in the guise of the Higgs field, which we know to exist because we’ve measured it at the Large Hadron Collider. Scalar fields have the property that they can cause space to expand exponentially fast. We touched on such a scenario in Chapter 1 without being explicit about the mechanism – it is the de Sitter’s matter-less solution to Einstein’s field equations first discovered in 1917. Given General Relativity and quantum field theory, therefore, it must be the case that scalar fields will fluctuate into existence in such a way that an exponential expansion of spacetime is triggered. In this exponential phase, spacetime expands faster than the speed of light. This might sound problematic if you know some relativity, but it isn’t. The universal speed limit exists for particles moving through spacetime, but does not apply for the expansion of spacetime itself. In a tiny fraction of a second – around 10–35 seconds in fact – an exponential expansion of this type can inflate a piece of spacetime as tiny as the Planck length to a quite mind-boggling size: trillions of times larger than the observable universe. Any pre-existing curvature is completely washed out, leading to a flat observable universe. It’s like looking at a square centimetre-sized piece of the surface of a balloon of a light year in radius; you won’t see any curvature, no matter how hard you try.

Likewise any variations in density will be washed out, leading to the smooth and uniform appearance of the CMB. Perhaps the greatest triumph of inflationary models such as these, however, is that they don’t predict a completely uniform, homogeneous and isotropic universe. Quantum theory doesn’t allow for absolute uniformity. Empty space is never empty, but a fizzing, shifting soup of all possible quantum fields. Like the surface of a stormy ocean, waves in the fields are constantly rising and falling, and the exponential expansion can freeze these undulations into the universe. Remarkably, when calculations using the known laws of quantum theory are carried out, the sort of density fluctuations that result from such a mechanism are precisely of the form seen in the CMB. These quantum fluctuations are the seeds of the galaxies and therefore the seeds of our existence, frozen into the oldest light in the cosmos and photographed by a satellite built by the people of Earth 13.8 billion years later.

Inflation in this guise explains the observable properties of our universe, and in particular all the details of the CMB, which has been measured to high accuracy. This is why it is currently widely accepted as an essential ingredient by many cosmologists. As if this wasn’t enough to get excited about, however, there is much more.

One obvious question that arises is this: if inflation gets going, how does it stop? The answer is that inflation stops completely naturally, but with a fascinating twist that drives right to the heart of our ‘Why are we here?’ question. The scalar field driving inflation fluctuates up and down in accord with the laws of quantum theory, just like the waves on the surface of an ocean. If the energy stored in the field is high enough, inflation begins. One might expect that such a rapid expansion would dilute the energy extremely rapidly, causing inflation to stop. But scalar fields have the interesting property that their energy density can stay relatively constant as space expands. You can think of the expanding space as doing work on the field, pumping energy into it and keeping its level high. And in turn, the high level of the field’s energy continues to drive the expansion. This might sound like the ultimate free lunch, and in a sense it is, almost, although gradually the energy will become diluted and decay away. The time this takes depends on the size of the initial fluctuation in the field and the details of the field itself, but in general the higher the initial energy, the longer the field takes to fall in value as the expansion continues. An analogy often used to picture this scenario is to imagine a ball rolling down the side of a valley. The height of the ball up the valley side represents the energy density of the scalar field. When the ball is high up, the energy in the field is high, driving the inflationary expansion. As the ball rolls slowly down the valley the energy reduces and inflation turns off. At the valley floor, the ball oscillates back and forth until it comes to rest. The scalar field likewise oscillates and in so doing dumps its energy into the universe in the form of particles. In so doing it creates a hot dense soup, which we identify as the ‘Big Bang’. In other words, inflation ends naturally and the standard Big Bang follows. The decay of the scalar field that drove inflation is the cause of the Big Bang!

Let us step back for a moment and recap with broad brush-strokes, because we seem to be wandering onto Leibniz’s territory, and that’s an astonishing place for physics to have arrived at. Our claim is that there exists a quantum field that causes the universe to expand exponentially fast for some period of time, and in doing so produces all the features of the universe we observe today, including the existence of galaxies and the matter out of which they are made. This is a triumph, and is now part of cosmology textbooks. Before the Big Bang, there was inflation. Fine, our philosopher friends would say, but what happened before inflation? Here, we must leave the textbooks and become a little more speculative, but not too speculative. We are still going to be working within the domain of mainstream physics.

There is an extension of what we might term standard inflationary theory. It is known as eternal inflation. Put simply, there seems to be no reason why inflation should stop everywhere at the same time. There should always be regions of the universe where the scalar field fluctuates to such high values that the exponential expansion continues, and these regions will always come to dominate the universe, however rare they may be, because they are exponentially expanding. Where inflation stops, Big Bangs herald the beginning of more sedately expanding regions like ours. But elsewhere, there is an ever-growing exponentially expanding universe, constantly spawning an infinity of Big Bangs. This theory, known as eternal inflation, leads to an infinite, immortal multiverse, growing fractal-like without end. This is truly mind-numbing, but we must emphasise that it is an entirely natural extension of standard inflationary cosmology.

Eternal inflation opens up even more exciting possibilities. As we discussed above, one of the great mysteries in physics today is the origin of the constants of nature such as the strength of gravity, the masses of the particles and the value of dark energy. These values appear to be fine-tuned for the existence of life, and understanding where they come from is a prerequisite for understanding our existence. In eternal inflationary models, each mini-universe can have different values of these constants and different effective laws of physics. The word ‘effective’ is important. The idea is that there is some overarching framework, out of which our laws and the constants of nature are selected randomly. If this is correct, then each of the infinite number of mini-universes that branch off the fractal inflationary multiverse can have different effective laws of physics, and all possible combinations will be realised somewhere. No matter how fine-tuned our laws appear for the existence of life, it is inevitable that such mini-universes as ours will exist, and there will be an infinite number of each possible set of combinations. There is no fine-tuning problem. Given the multiverse, we are inevitable. This is reminiscent of our rejection of your own personal uniqueness whilst listening to Joy Division at the beginning of the chapter. Yes, in isolation, the odds of you existing are almost vanishingly small. But given a mechanism for producing human beings, babies are born all the time and their existence is not surprising. Here, we have a mechanism for producing universes – and with an even greater statistical sledgehammer, the mechanism doesn’t simply produce a few billion of them, it produces a potentially infinite number.

This is a quite stunning theoretical model, and I understand that it sounds like wild speculation. It isn’t, though. Inflation is probably correct in some form, in the sense that before what we call the Big Bang, there was an exponential expansion of spacetime. Scalar fields, which are known to exist, have the correct properties to drive such an expansion, although there are other theoretical models of inflation, as well. Theoretical physicists studying inflationary models have discovered that almost all of them are eternal, in the sense that they stop inflating in patches rather than all at once. This means that the potential for creating universes, in the guise of inflation, is always expanding faster than it is decaying away, and it will therefore never stop. We live in an infinite, eternal, fractal multiverse comprised of an infinite number of universes like ours, alongside an infinite number of universes with different physical laws. We exist because it is inevitable. Almost.

There is one very important caveat to this picture. Recent research suggests that eternal inflationary models may be eternal in the future, but not in the past. They never stop, but they may have to start. I can’t give you a definitive answer to this ultimate question, because nobody yet knows. I can quote from Andrei Linde’s recent review of inflationary cosmology, published in March 2014.fn1

‘In other words, there was a beginning for each part of the universe, and there will be an end for inflation at any particular point. But there will be no end for the evolution of the universe as a whole in the eternal inflation scenario, and at present we do not know whether there was a single beginning of the evolution of the universe as a whole at some moment t=0, which was traditionally associated with the Big Bang.’

And so we reach the end. Defining the Big Bang as the initial hot, dense phase of our observable universe that gave rise to the CMB 380,000 years later, we understand what happened before. There was a period of inflationary expansion, which could have been driven by a scalar field in accord with the known laws of physics. That inflationary expansion is probably still going on somewhere, spawning an incalculable number of universes as we speak, and it will continue doing this forever. We live in an eternal universe, in which everything that can happen does happen. And we are one of the things that can happen. Did the whole universe have a beginning, an essential, external cause in the spirit of Leibniz’s God? We still don’t know. Possibly there was a ‘mother of all Big Bangs’, and if so, we will certainly need a quantum theory of gravity to say anything more.

What does this mean? The wonderful thing for me is that nobody knows, because the philosophical and indeed theological consequences of eternal inflation have not been widely debated and discussed. My hope is that in trying to summarise the issues, regrettably briefly and necessarily superficially in the television series and in a little more depth here, these ideas will be accessible to a wider audience and stimulate discussion.

This is desirable and necessary, because ideas are the lifeblood of civilisation, and societies assimilate ideas and become comfortable with their implications through understanding and debate. If eternal inflation is the correct description of our universe, it will be the artists, philosophers, theologians, novelists and musicians, alongside the physicists, who explore its meaning. What does it mean if the existence of our universe is inevitable? What does it mean if we are not special in any way? What does it mean if our observable universe, with all its myriad galaxies and possibilities, is a vanishingly small leaf on an every-expanding fractal tree of universes? What does it mean if you are, because you have to be? I can’t tell you. I can only ask – what does it mean to you?

For small creatures such as we,
the vastness is bearable only through love.

Carl Sagan