The Science of Discworld IV Judgement Da

TWENTY-TWO



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FAREWELL, FINE-TUNING





They didn’t make it; it made them.

Pastor Oats, a truly wise man, has put his finger on a deep, often unappreciated, truth, which illuminates the misty borderland where science and religion meet. Here lie some of the most perplexing riddles of modern cosmology, where the austere workings of fundamental physics collide with the richness of human experience.

At the heart of this collision is an astonishing coincidence: universes that can sustain living creatures are extraordinarily unlikely. This coincidence violates, in the most dramatic manner possible, the Copernican principle that humans aren’t special.

Before Nicholas Copernicus published On the Revolutions of the Celestial Spheres in 1543, with a few honourable exceptions, almost everyone viewed humanity as the centre of the universe. This was so obviously true that it seemed ridiculous to deny it. Look around you. Everything else trails off into the distance, and you are smack bang in the middle. Your own senses prove that the stars and other celestial bodies revolve around the Earth. The natural shape for their orbits must surely be a circle, a perfect geometric figure; its perfection provides yet more evidence that everything was created for us, and that we are located at the heart of creation.

However, ancient astronomers were excellent observers, and when they looked at what the universe was actually doing, they realised that circles don’t fit. But they could save the ‘perfect form’ theory, because combinations of circles agree very closely with observations. In the second century AD, Claudius Ptolemaeus (Ptolemy) wrote the Almagest (‘the greatest’), which represented the movements of the Sun and planets around a stationary Earth. To match the complex trajectories observed, he employed several geometric constructions, involving spheres rotating on axes that are supported by other spheres. In a simplified form, the most important features of the Ptolemaic system were epicycles: circular orbits whose centres themselves revolved in circular orbits. If necessary, those centres might also revolve in circular orbits, and so on. In total, Ptolemy needed more than eighty spheres, but the resulting system was very accurate. Especially at a time when Earth was not recognised as a planet. That term referred to wandering stars, and the Earth was neither a star, nor a wanderer. It was fixed.

We are special.

Copernicus was clearly a contrarian, and he realised that everything makes a lot more sense if we’re not special, and the Earth is not at the centre. This is an instance of the mediocrity principle: as a working heuristic, it is best to avoid assuming that any given phenomenon has unusual, special features, or violates the laws of nature. One feature of Ptolemy’s system that may have led Copernicus to this view was a suspicious coincidence. The numbers associated with most of the epicycles – size, speed of rotation – were rather haphazard, with no clear patterns. But Copernicus noticed that identical copies of one particular set of epicycle data occurred many times over: in the motion of the Sun and of all the planets. He could cut the number of epicycles down from Ptolemy’s eighty to a mere thirty-four by transferring this one to the Earth. The Sun then became stationary, and everything else (bar the Moon) revolved around it – Earth included. By adopting an Earth-centred frame of reference, Ptolemy had been obliged to transfer the Earth’s motion round the Sun to every other body, by adding a single extra epicycle to all of them. Remove this common epicycle, and the description would be much simpler. But then you are faced with a radical change to the theory: among the many celestial bodies, only the Moon revolves around the Earth. Everything else revolves around the Sun.

That statement is open to challenge, on grounds discussed for flat Earths in chapter 8. You can represent the universe in any frame of reference you wish. There is nothing to stop you choosing a coordinate system in which the Earth is stationary, and you can even decide – depending on your assessment of your own importance in the scheme of things – that you are at the origin. It is entirely straightforward, for those who play this kind of game, to rewrite all of the laws of nature within that you-centred frame of reference. So there is a sense in which what’s in the middle and what goes round what is entirely arbitrary.

However, another philosophical principle, Occam’s razor, suggests that this freedom to choose is not terribly meaningful. William of Occam (or Ockham) is credited with the philosophical principle ‘entities should not be multiplied beyond necessity’.fn1 This tends to be interpreted as ‘simple explanations are better than complex ones’, but that goes beyond what William actually said. His point was that it is silly to include features that can be removed without making any significant difference. Complex explanations are often better than simple ones, but only when simpler ones won’t do the job. Interpreting Occam’s razor either way, lots of copies of an epicycle are trumped by just one copy, even if it has to be attached to a different body.

In a frame attached to the Earth, the laws of motion become extraordinarily complicated. The nearest major galaxy, M31 in Andromeda, about 2.6 million light years away, has to whiz all the way round the Earth once every 24 hours. More distant objects – the current record is about 13.2 billion light years – must undergo even more outlandish gyrations. In contrast, if we choose a frame of reference centred on the Sun, making it stationary relative to the average positions of the stars, the mathematics becomes far simpler and the physics and metaphysics far more reasonable. Ignoring the gravitational influences of any other bodies, the Sun and Earth both orbit their mutual centre of gravity in ellipses. But because the Sun is so much more massive than the Earth, that centre lies well inside the Sun. So … the Earth goes round the Sun. We foolishly think the Earth is stationary because it is, relative to us. (Sorry, still too human-centred: make that ‘we are stationary, relative to it’.)

Lesson learned – after several centuries, a few burnings and a lot of fuss and bother. But that was just the warm-up act. When astronomers realised that distant blobs of light were galaxies – swirling masses composed of billions of stars – it eventually dawned on them that the familiar Milky Way’s river of light is no accident: it is our own galaxy seen edge-on, from inside. Naturally our Sun will be at the galactic centre … Well, no, it is actually in a very nondescript region about two thirds of the way towards the rim: 27,000 light years from the galactic core, close to one of the galaxy’s spiral arms, the Orion Arm. The glorious Sun is merely one star (and a pretty feeble one at that) among thousands in the Local Fluff, which itself lies inside the Local Bubble. The Sun is not even in the galactic plane, though it’s fairly close – about sixty light years.

After several centuries in which every successive attempt to portray humanity as special was debunked, the Copernican principle became embedded in fundamental physics as a generalisation of Einstein’s basic principle of relativity: there is no such thing as a privileged observer.

We said earlier that a major motivation behind the scientific method is a conscious awareness that people tend to believe things because they want to, or have been socially brainwashed into wanting to. Religions exploit this tendency by making faith paramount: strength of belief trumps contrary or absent evidence. Science deliberately tries to counteract it by demanding convincing evidence. The Copernican principle is one extra reminder about what not to assume. It doesn’t always apply, but it punctures our sense of self-importance.

Broad quasi-philosophical principles like those of Copernicus and Occam are guidelines, not hard-and-fast rules. And, wouldn’t you just know it: as soon as we started to get used to the idea that in the vast scheme of things we are pretty ordinary, evidence began to turn up that this wasn’t a done deal. Maybe we are special. Maybe the Earth is in a privileged position, or a privileged state. Maybe it has to be.

By the time this line of reasoning had run its course, we seemed to be so special that the entire universe must somehow operate in precisely the manner that can give rise to … us. It is as though the universe were created with humanity in mind.

To those of a religious persuasion, this was hardly news, and they welcomed the partial conversion of the scientific world with open arms. But even atheists were coming round to the idea that if the universe were even slightly different from what it is, we wouldn’t be here. There’s even a general principle, a distinctly non-Copernican one, that can be used to justify these claims. It’s called the Anthropic Principle.

There are two flavours. The Weak Anthropic Principle states that the universe has to be of a kind that can give rise to creatures like us, because if it weren’t, we wouldn’t be here to ask awkward questions. The Strong Anthropic Principle states that the universe was in some sense designed for us. We are not just an accidental by-product; we are what it’s all for. In 1986 John Barrow and Frank Tipler compiled an impressive, highly technical, analysis: The Anthropic Cosmological Principle. It discussed the view that in several respects our universe – as opposed to innumerable conceivable alternatives – is uniquely fine-tuned for life to arise. Many scientists and most cosmologists now seem to accept that.

A common image dramatises the point. Take a shiny metal rod and a sharp knife. Rest the rod on the knife’s edge, and try to balance it. You can’t. Unless the rod’s centre of mass is exactly above the edge of the blade, the rod will slip, then slide and fall to the ground.

Life is balanced on a cosmic knife edge.

Less metaphorically: the laws of nature are exquisitely finely tuned. Change any of the fundamental constants of nature by the smallest amount, and life’s delicate cycles will fail. Poise humanity one micron away from cosmic perfection, and it will topple.

Alongside this human-centred view of the universe goes a human-centred view of humans. Forget all those weird and wonderful aliens that infest science fiction, living in the hydrogen-helium atmospheres of gas giants, or the frigid cold of worlds so far from their suns that the temperature is barely above absolute zero. It’s much simpler than that. The only viable aliens will be just like us. They will live on a rocky world with oceans and plenty of oxygen in its atmosphere; it will need to be just the right distance from its sun. The world will need a strong magnetic field to keep radiation at bay, a large companion like our Moon to keep its axis stable, and a gas giant like Jupiter to protect it from comets.

The aliens’ sun will also have to be special. Remarkably like ours, in fact. Not just in its spectral type, its general shape, size, and the kind of nuclear reaction it uses, but in its location. The sun needs to be reasonably far away from any of its galaxy’s spiral arms, because the process of star formation creates a lot of radiation, and most stars form in the spiral arms. On the other hand, it can’t be too far away, as our own Sun demonstrates. Moreover, the aliens’ sun must be near enough to the galactic centre for there to be enough heavy elements to provide the planet with a rocky core, but far enough from the centre to avoid being subject to intense radiation, which would destroy life.

Well, carbon-based life, like ours … but that’s the only kind that can exist. The element carbon is unique: it forms the complex molecules required to make living creatures. Carbon is a key element in the claim that life anywhere on the universe has to be much like life on Earth. But in the cosmic scheme of things, carbon is highly unlikely. It exists only by virtue of a remarkably precise alignment of the energy levels of nuclear reactions inside stars. So stars are special, and the reason is life.

Not just stars. The whole universe is special, finely tuned for life to exist. The basic physics of our universe, on which everything else rests, depends on about thirty fundamental constants: numbers such as the strength of gravity, the speed of light and the strength of atomic forces. Those numbers appear in the deep laws of nature, relativity and quantum theory, and there seems to be no clear mathematical reason why they might not be different. They are ‘adjustable parameters’ – knobs that a creator god could twiddle to any value He/She/It desired. But, tellingly, if you do the sums, it turns out that if any of these constants were even slightly different from its actual value, then not only would life be impossible: there would be no planets for life to inhabit, no stars to provide energy, and no atoms to assemble into matter.

Our universe, like life, is also improbably balanced on the finest of knife edges, and the slightest deviation would have spelled disaster.

This scenario of cosmological fine-tuning is widely viewed as one of the biggest puzzles in cosmology, a series of wildly unlikely coincidences that demands rational explanation but seems to lead only to imaginative speculations involving physics that has not yet been supported by evidence. Religious fundamentalists have seized upon it as a proof of the existence of God. It is difficult, even for atheists, not to have some sympathy with them, because the usual presentation of the science involved points unerringly towards some kind of design principle for our universe.

Fine-tuning, be it terrestrial or cosmological, makes perfect sense from a human-centred viewpoint. In contrast, it seems to pose some very difficult questions for universe-centred thinking.

Most of the scientific effort to resolve these questions starts from the premise that fine-tuning is genuine, so our universe really is virtually unique when it comes to its ability to harbour life. From here it is easy to become convinced that we are the purpose of the whole thing, or even that without us there would be no observers to collapse the quantum wavefunction of the universe and maintain its existence. Less human-centred explanations have also been offered, including a virtually endless cycle of creation and destruction of different universes, which can be noticed by their intelligent inhabitants only when they are the kind of universe that can have intelligent inhabitants, or a vast multiverse of parallel or independent universes in which every physical possibility is realised. Either removes the need to explain any particular universe. The sheer scope of the imaginative proposals that emerge from a few numbers is breathtaking.

There is, however, another way. Instead of accepting the premise of fine-tuning and trying to explain it – or explain it away – we can challenge the premise itself. For a start, it’s strange that physicists can think of no other way to make a universe than to keep ours but change a few constants. It’s even stranger that believers don’t hesitate to impose the same restriction on their omnipotent deity’s creative abilities. But even accepting this limitation, it has been clear for at least a decade that the usual description of fine-tuning is needlessly mystical, and verges on the mythical.

The issues are deep, and it is important not to avoid them by offering glib ‘explanations’ that miss the point. For example, the Weak Anthropic Principle – that we can observe a universe only if it is suited to our own existence – really does explain why our universe must satisfy some pretty stringent constraints. Since we exist, it has to. But that is just another way of saying ‘the universe is how it is’. It’s no different from reasoning from the existence of, say, sulphur, and concluding that atomic theory has to be much as we think it is. The Weak Anthropic Principle only seems different from the equally valid Weak Sulphuric Principlefn2 because it’s about us rather than a lump of yellow rock. But the Copernican principle cautions us not to imagine that there’s anything special about us, and in this case, there isn’t. We are just one piece of evidence. An equally convincing case can be made that the universe is uniquely finely tuned to make sulphur.

The Weak Anthropic Principle only goes so far. It doesn’t explain why this kind of universe exists, rather than something different – especially when almost any alternative would allegedly fall apart or explode the moment it came into being, or would be so boring that only very simple structures could form. However, the Strong Anthropic Principle – that the universe was made in order for humans to exist – doesn’t explain any of that either. We could just as readily formulate the Strong Sulphuric Principle: the universe was made in order for sulphur to exist.

Why us? The Strong Anthropic Principle just assumes it’s obvious that we are the purpose of the whole thing. Sulphur? Don’t be silly.

Let’s warm up with the carbon story, which is easier to grasp. Then we’ll take a look at those puzzling fundamental constants. We discussed both of these in The Science of Discworld II: the Globe, and we have to cover some of the same ground again before going further. We’ll keep it brief.

Astrophysicists have put together a careful account of how the chemical elements formed. Combinations of elementary particles – protons, neutrons, or their more exotic precursors – came together in vast clouds to form atoms of the lightest element, hydrogen. The early universe was hot enough for hydrogen atoms to fuse together, making the next lightest element, helium. Then the clouds collapsed under their own gravity, triggering nuclear reactions. Stars were born, and within those stars new elements assembled, with atomic weights up to and including iron. Subtler processes, occurring in red giant stars, put together heavier elements, as far as bismuth. Everything else required high-energy processes occurring only in supernovas – massive stellar explosions.

In 1954 the astronomer Fred Hoyle realised that there was a problem with carbon. The universe contains a lot more of it than the known nuclear reactions can explain. And carbon is the vital element for life. Carbon can form in red giants through the ‘triple-alpha’ process, in which three helium nuclei (atoms minus their electrons) collide, pretty much simultaneously. A helium nucleus comprises two protons and two neutrons. So three of them combined must yield a nucleus with six protons and six neutrons. This is carbon.

In the dense environment of a red giant star, nuclei collide relatively often. But it’s not terribly likely that just as two of them come together, a third joins the party. So the process has to happen in two stages. First, two helium nuclei collide and fuse, making beryllium. Then another helium nucleus fuses with that. Unfortunately for this theory, the form of beryllium involved falls apart after one tenth of one quadrillionth of a second. The chance that a helium nucleus can hit such a rapidly vanishing target is much too small.

Hoyle knew this, and he also knew that there is a loophole. If the combined energies of beryllium and helium just happen to be very close to an energy level of carbon, then the nuclei can fuse much faster and the sums work out fine. Such a near-coincidence of energies is called a resonance. No suitable resonance was then known, but Hoyle insisted that it had to be there. Otherwise Hoyle wouldn’t be there, being made from quite a lot of carbon. That led him to predict an unknown energy level of carbon around 7.7 MeV (million electronvolts, a convenient unit of energy for nuclear reactions). By the mid-1960s the experimentalist William Fowler had found such a resonance at 7.65 MeV, within 1% of Hoyle’s prediction. Hoyle presented this discovery as a triumph of ‘anthropic’ reasoning: deducing something about the universe from the existence of humans. Without that finely tuned resonance, we wouldn’t be here.

It sounds impressive, and it is when told that way. But already we see a tendency to exaggerate. For a start, the link to humans is unnecessary and irrelevant. What matters is the amount of carbon in the universe, not what it can make. We do not need to appeal to our own existence to know how much carbon there is. In The Fallacy of Fine-Tuning, Victor Stenger refers to an investigation of the history of Hoyle’s prediction by the philosopher Helge Kragh. Hoyle did not initially link the resonance to the existence of life, let alone human life. The anthropic connection was not made for nearly thirty years. ‘It is misleading to label the prediction of the 7.65 MeV state [as] anthropic, or to use it as an example of the predictive power of the anthropic principle,’ Kragh wrote. Pan narrans has been at work again, and the human love of narrativium has rewritten the historical story.

Next: it’s simply not true that ‘without that finely tuned resonance, we wouldn’t be here.’ The 7.65 MeV figure for the energy of the resonance is not what’s required for carbon-based life to exist. It is the energy needed to produce the amount of carbon actually observed. Change the energy, and carbon would still be produced … but in different quantities. Not as different as you might think: Mario Livio and co-workers calculate that any value between 7.596 MeV and 7.716 MeV would generate much the same amount of carbon. Anything up to 7.933 MeV would generate enough carbon for carbon-based life to exist. Moreover, if the energy level dropped below 7.596 MeV, more carbon would be produced, not less. The lowest energy that would produce enough carbon for life is the ground state of the carbon atom, the lowest possible energy it can have, which is 7.337 MeV. A finely tuned resonance is not necessary.

In any case, resonances are ten a penny, because atomic nuclei have lots of energy levels. Finding one in the appropriate range isn’t really very surprising.

A more serious objection arises from the calculation itself. When factors that Hoyle neglected are taken into account, the combined energies of helium and beryllium turn out to be significantly higher than the figure he used. What happens to this ‘extra’ energy?

It helps to keep the red giant burning.

The star burns at precisely the temperature required to compensate for the energy difference. This looks like an even more impressive coincidence. Forget carbon: something far deeper is going on. If the basic constants of the universe were different, then the precisely fine-tuned resonance would disappear, the red giant would fizzle out and there wouldn’t be enough carbon to make Fred Hoyle, Adam and Eve, you or the cat.

However, this argument, too, is fallacious. Changing the fundamental constants affects the red giant star as well as the carbon resonance. In fact, because the star burns helium and beryllium fuel, the star’s nuclear reactions automatically home in on the temperature that makes the fuel burn. Isn’t it amazing that a coal fire burns at exactly the temperature that makes coal burn? No. If coal burns at all, then feedback ensures that the energy balance of the reaction automatically works out correctly. It may be amazing that our universe is so rich that coal can burn, or red giants shine, but that is a very different issue from fine-tuning. In a complex universe, however it may work, complex objects can arise, and they will be beautifully suited to the rules of that universe because that is how they came to be. But that does not imply that the universe was specially chosen or created to give rise to such objects. Or that those objects are improbable, or special.

The carbon resonance of a red giant, and the energetics of burning coal, are feedback systems. Like a thermostat, they automatically adjust themselves to keep going. This sort of feedback is extremely common and not at all remarkable. No more remarkable, in fact, than the amazing way that our legs are just long enough for our feet to meet the ground. Gravity pulls us down, the ground pushes us up, and the combination perches us in just the place where our feet and the ground are in exquisite alignment.

The issue of the physical constants is deeper. Today’s picture of fundamental physics depends on a series of mathematical equations, all fairly elegant and neat. However, these equations also involve about thirty special numbers: things like the speed of light; and the fine structure constant, which governs the forces holding atoms together. These numbers appear to be pretty much random, but they matter just as much as the equations. Different values of these fundamental constants lead to very different solutions of the equations – different kinds of universe.

The differences are not just the obvious ones: gravity being stronger or weaker, light travelling faster or slower. They can be more dramatic. Change the fine structure constant even a little, and atoms become unstable and fall apart. Make the gravitational constant smaller, and stars blow up, galaxies disappear. Make it larger, and everything collapses into a single gigantic black hole. In fact – so the story goes – if you change any one of those constants by more than a very tiny amount, the resulting universe is so different from ours that it could not possibly support the organised complexity of life. Having lots of constants compounds this; it is like winning the lottery thirty times in a row. Our existence is not only balanced on a knife edge: it is a very sharp knife.

It’s a striking tale, but it’s riddled with holes. Pan narrans just can’t stop itself.

One basic, and fatal, flaw in a large portion of the literature is to consider varying the constants only one at a time, and only by a small amount. Mathematically, this procedure explores only a tiny region of ‘parameter space’, the overall range of possible combinations of constants. What you find in this limited region is unlikely to be representative.

Here’s an analogy. If you take a car, and change any single aspect even a little bit, the odds are that the car will no longer work. Change the size of the nuts just a little, and they don’t fit the bolts and the car falls apart. Change the fuel just a little, and the engine doesn’t fire and the car won’t start. But this does not mean that only one size of nut or bolt is possible in a working car, or only one type of fuel. It tells us that when you change one feature, it has knock-on effects on the others, and those must also change. So parochial issues about what happens to little bits and pieces of our own universe when some constant is changed by a very small amount and the rest are left fixed are not terribly relevant to the question of that universe’s suitability for life.

Some additional sloppy thinking parlays this fundamental blunder into a gross misrepresentation of what the calculations concerned actually show. Suppose, for the sake of argument, that each of the thirty parameters has to be individually fine-tuned so that the probability of a randomly chosen parameter being in the right range is 1/10. Change any parameter (alone) by more than that, and life becomes impossible. It is then argued that the probability of all thirty parameters being in the right range is 1/10 raised to the power 30. This is 10-30, one part in a nonillion (ten billion billion billion). It is so ridiculously small that there is absolutely no serious prospect of it happening by chance. This calculation is the origin of the ‘knife edge’ image.

It is also complete nonsense.

It’s like starting at Centrepoint, in the middle of London, and going a few metres westwards along New Oxford Street, a few metres northwards up Tottenham Court Road, and imagining you’ve covered the whole of London. You haven’t even explored a few metres in a north-westerly direction, let alone anything further away. Mathematically, what is being explored by each change to a single parameter is a tiny interval along an axis in parameter space. When you multiply the associated probabilities together, you are exploring a tiny box whose sides correspond to the changes made to individual parameters – without considering changing any of the others. The car example shows how silly this type of calculation is.

Even using the constants for this universe, we can’t deduce the structure of something as apparently simple as a helium atom from the laws of physics, let alone a bacterium or a human being. Our understanding of everything more complex than hydrogen relies on clever approximations, refined by comparison with actual observations. But when we start thinking about other universes, we don’t have any observations to compare with; we must rely on the mathematical consequences of our equations. For anything interesting, even helium, we can’t do the sums. So we take short cuts, and rule out particular structures, such as stars or atoms, on various debatable grounds.

However, what such calculations actually rule out (even when they’re correct) are stars just like those in this universe and atoms just like those in this universe. Which isn’t quite the point when we’re discussing a different universe. What other structures could exist? Could they be complex enough to constitute a form of life? The mathematics of complex systems shows that simple rules can lead to astonishingly complex behaviour. Such systems typically behave in many different interesting ways, but not in just one interesting way. They don’t just sit there being dull and boring, except for one special ‘finely tuned’ set of constants where all hell breaks loose.

Stenger gives an instructive example of the fallacy of varying parameters one at a time. He works with just two: nuclear efficiency and the fine structure constant.

Nuclear efficiency is the fraction of the mass of a helium atom that is greater than the combined masses of two protons and two neutrons. This is important because the helium nucleus consists of just that combination. Add two electrons, and you’re done. In our universe, this parameter has the value 0.007. It can be interpreted as how sticky the glue that holds the nucleus together is, so its value affects whether helium (and other small atoms like hydrogen and deuterium) can exist. Without any of these atoms, stars could not be powered by nuclear fusion, so this is a vital parameter for life. Calculations that vary only this parameter, keeping all others fixed, show that it has to lie between 0.006 and 0.008 for fusion-powered stars to be feasible. If it is less than 0.006, deuterium’s two positively charged protons can push each other apart despite the glue. If it is more than 0.008, protons stick together, so there would be no free protons. Since a free proton is the nucleus of hydrogen, that means no hydrogen.

The fine structure constant determines the strength of electromagnetic forces. Its value in our universe is 0.007. Similar calculations show that it has to lie in the range from 0.006 to 0.008. (It seems to be coincidence that these values are essentially the same as those for nuclear efficiency. They’re not exactly equal.)

Does this mean that in any universe with fusion-powered stars, both the nuclear efficiency and the fine structure constant must lie in the range from 0.006 to 0.008? Not at all. Changes to the fine structure constant can compensate for the changes to the nuclear efficiency. If their ratio is approximately 1, that is, if they have similar values, then the required atoms can exist and are stable. We can make the nuclear efficiency much larger, well outside the tiny range from 0.006 to 0.008, provided we also make the fine structure constant larger. The same goes if we make one of them much smaller.

With more than two constants, this effect becomes more pronounced, not less. Numerous examples are analysed at length in Stenger’s book. You can compensate for a change to several constants by making suitable changes to several others. It’s just like the car example. Changing any one feature of a car, even by a small amount, stops it working – but the mistake is to change just that one feature. There are thousands of makes of car, all different. When the engineers change the size of the nuts, they also change the size of the bolts. When they change the diameter of the wheel, they use a different tyre.

Cars are not finely tuned to a single design, and neither are universes.

Of course, the equations for universes might run contrary to everything that mathematicians have ever seen before. If anyone believes that, we’ve got a lot of money tied up in an offshore bank and we’d be delighted to share it with them if they will just send us their credit card details and PIN. But there are more specific reasons to think that the equations for universes are entirely normal in this respect.

About twenty years ago, Stenger wrote some computer software, which he called MonkeyGod. It lets you choose a few fundamental constants and discover what the resulting universe is capable of. Simulations show that combinations of parameters that would in principle permit life forms not too different from our own are extremely common, and there is absolutely no evidence that fine-tuning is needed. The values of fundamental constants do not have to agree with those in our current universe to one part in 1030. In fact, they can differ by one part in ten without having any significant effect on the universe’s suitability for life.

More recently, Fred Adams wrote a paper for the Journal of Cosmology and Astroparticle Physics in 2008, which focuses on a more limited version of the question.fn3 He worked with just three constants – those that are particularly significant for the formation of stars: the gravitational constant, the fine structure constant, and a constant that governs nuclear reaction rates. The others, far from requiring fine-tuning, are irrelevant to star formation.

Adams defines ‘star’ to mean a self-gravitating object that is stable, long-lived, and generates energy by nuclear reactions. His calculations reveal no sign of fine-tuning. Instead, stars exist for a huge range of constants. Choosing these ‘at random’, in the sense usually employed in fine-tuning arguments, the probability of getting a universe that can make stars is about 25%. It seems reasonable to allow more exotic objects to be treated as ‘stars’ too, such as black holes generating energy by quantum processes, and dark matter stars that get their energy by annihilating matter. The figure then increases to around 50%.

As far as stars go, our universe is not improbably balanced on an incredibly fine knife edge, battling odds of billions to one against. It just called ‘heads’, and the cosmic coin happened to land that way up.

Stars are only part of the process that equips a universe with intelligent life forms, and Adams intends to look at other aspects, notably planet formation. It seems likely that the results will be similar, debunking the almost infinitesimal chances alleged by advocates of fine-tuning, and replacing them by something that might actually happen.

What, then, went wrong with the fine-tuning arguments? Failures of imagination and blinkered interpretations. For the sake of argument, let us accept that most values of the constants make atoms unstable. Does this prove that ‘matter’ cannot exist? No, it just proves that matter identical to that in our universe can’t exist. What counts is what would happen instead, but advocates of fine-tuning ignore this vital question.

We can ask the same question for the belief that the only viable aliens will be just like us, as many astrobiologists still maintain – though fewer of them than there used to be. The word ‘astrobiology’ is a compound of astronomy and biology, and what it mostly does is put the two sciences together and see how they affect each other. To analyse the possibility of alien life, especially intelligent alien life, conventional astrobiology starts with the existence of humans, as the pinnacle of life on Earth. Then it places them in the context of the rest of biology: genes, DNA, carbon. It then examines our evolutionary history, and that of our planet, to find environmental features that helped bring life, and us, into existence.

The upshot is an ever-growing catalogue of special features of our, and Earth’s, history, alleged to be necessary for alien life to exist. We mentioned some of these features earlier; now we’ll discuss some of them in more detail. They include the following conditions. Life needs an oxygen atmosphere. It needs water in liquid form. That implies being at a suitable distance from the Sun – the much-emphasised habitable or Goldilocks zone, where temperatures are ‘just right’. Our unusually large Moon stabilises the Earth’s axis, which would otherwise change its tilt chaotically. Jupiter helps protect us from comet impacts – remember how it sucked up Shoemaker-Levy 9? The Sun is neither too big nor too small, both of which make terrestrial planets less likely. Its rather dull and boring position in the galaxy – not at its centre, but out in the boondocks – is actually the best place to be. And so on and so on and so on. As the list grows ever longer, it is hard not to conclude that life is extraordinarily unlikely.

An alternative approach, which we like to call xenoscience, reverses the direction of thought. What are the possible types of habitat? We now know, as we did not until recently, that there is no shortage of planets. Astronomers have found over 850 exoplanets – planets outside our solar system – enough to provide a statistical sample that suggests that there are at least as many planets in the galaxy as stars. The physical conditions on those planets vary enormously, but that provides new opportunities for new kinds of life. So instead of asking, ‘Is it like Earth?’ we should ask, ‘Could some form of life evolve here?’

We’re not even restricted to planets: subsurface oceans on moons whose surfaces are thick layers of ice would be a good place for life, even for Earthlike life. We should take into account local conditions, but we should not assume that features that appear favourable in our solar system necessarily apply elsewhere. Without a large moon, a planet’s axis may indeed tilt chaotically, but it could do so on a scale of tens of millions of years. Evolution can cope with that; it might even be enhanced by that. Life in a big enough ocean wouldn’t even notice. A large gas giant may sweep up comets, but that could slow evolution down, because the occasional catastrophe adds variability. Jupiter may keep comets at bay, but it greatly increases the number of asteroid impacts on the Earth. The current best estimate suggests that Jupiter has done more harm than good, with regard to life. Some life forms such as tardigrades (commonly called waterbears or moss piglets) resist radiation better than most of those on our planet. The rest don’t need to, because the Van Allen belts, regions of electrically charged particles maintained by the Earth’s magnetic field, keep radiation away. In any case, if the belts hadn’t been there, life could have become more tardigrade-like.

The so-called habitable zone is not the only region around a star where life might be possible. Some exotic chemical systems can make life-like complexity possible without water, and liquid water can exist outside the habitable zone. For example, if a world close to its star is tidally locked, so that one side perpetually faces the star and the other faces away, there will be a ring-shaped twilight zone on the boundary between the two faces, where liquid water might exist. Worlds far from the star can have liquid oceans underneath an outer coating of ice: Jupiter’s moon Europa is the best-known example in the solar system, and it is thought to have an underground ocean containing as much water as all of Earth’s oceans put together. The same goes for Ganymede, Callisto and Saturn’s moon Enceladus. Titan – another moon around Saturn – has liquid hydrocarbon lakes and an excess of methane, hinting at non-equilibrium chemistry, a possible sign of unorthodox life.

The idea of a galactic habitable zone – the claim that alien life can exist only in the region of the galaxy with enough heavy elements but not too much radiation – is especially controversial. The Danish astronomer Lars Buchhave and his team have surveyed the chemical composition of 150 stars, with 226 known planets smaller than Neptune. The results show that ‘small planets … form around stars with a wide range of heavy metal content, including stars with only 25 per cent of the sun’s metallicity’. So an excess of heavy elements is not required for Earthlike planets. NASA scientist Natalie Batalha remarked that ‘Nature is opportunistic and prolific, finding pathways we might otherwise have thought difficult’.

And so on and so on and so on.

Life adapts to its environment, rather than the other way round. Goldilocks doesn’t have the final word: Daddy Bear and Mummy Bear have valid opinions too. What is ‘just right’ for life depends on what kind of life. So-called extremophiles exist on Earth at temperatures below freezing and above boiling. It’s a silly name. To such creatures, their environment is entirely comfortable; it is we who are extreme. It’s even sillier to use the same name for creatures in two environments so different that each creature would consider the other to be even more extreme than us.

The second approach is far more sensible: instead of successively cutting down the opportunities for life, it explores the full range of the possible. That vast and impressive shopping list of features ‘necessary’ for life, making humans seem extremely special, is poor logic. Life on Earth demonstrates that the list is sufficient – but that doesn’t make it necessary.

These two ways of thinking about aliens are of course yet another example of Benford’s dichotomy. Astrobiology is human-centred, because it starts from us and narrows the universe down until it fits. Xenoscience is universe-centred: it keeps possibilities as broad as possible and sees where they lead. We are beautifully adapted for our environment because we evolved to be like that. This observation is much more reasonable than claiming that we humans are so special that the solar system, the galaxy, even the entire universe, was constructed in order to accommodate us.

Cosmic balance …

Is life really balanced on a knife edge, then? Or have we got it all wrong?

Let us go back to our rod and sharp knife experiment. It seems undeniable. Try again to balance the rod on the cutting edge of the knife. However carefully you place it, it tips and slides to the floor. There is no question: the balance has to be extraordinarily precise.

The mathematics is, if anything, even more compelling. The masses on each side, multiplied by their distances from the knife, must be equal. Exactly. The slightest imbalance leads to total failure. So, by analogy, any imbalance in the laws of nature, however insignificant, would destroy the conditions required for life to exist. Change the speed of light or various other constants by a few per cent, and the delicate carbon resonance in stars would fail. No resonance, no carbon, no carbon-based life.

Maybe, though, we’ve accepted these arguments too readily. How relevant, how sensible, is the analogy of a metal rod and a sharp knife? Straight metal rods are an artificial product of technology. In mathematics and nature, most things are nonlinear – bent. What happens if you place a bent rod on top of a knife edge? Assume the bend is not too great, and roughly in the middle. Provided you place the rod on the knife so that it’s reasonably near the balance point, as soon as you let the rod go it turns so that the free ends hang downwards. It slips sideways, but not very far, and then it stops. For a few seconds it seesaws up and down, but eventually it comes to rest.

Perfectly balanced.

Reach out a fingertip and push one end up a little. When you let go, the bent rod swings back to its original position, overshoots, reverses direction, and eventually settles back to where it was to begin with. If you push the other end down, the same thing happens.

Next, move the rod sideways on its pivot, away from the bend. The shiny metal is slippery, and the rod slides back until it balances again. It’s not necessary to arrange for the rod to balance. It does so of its own accord. At the balance point, the forces pulling it to either side cancel out just as precisely as they would have to do to balance a straight rod, but the rod no longer falls off if the balance is wrong. It just moves a little, and finds its own balance point. The mathematical reason is straightforward. The rod seeks a state of minimum energy, where its centre of mass is lowest. Because the centre of mass of a bent rod is below the pivot, it ends up hanging in a stable position.

It’s not necessary to fine-tune the universe.

It can fine-tune itself.

The ‘knife edge’ thought-experiment is rigged; the analogy with nature is false. The experiment depends on the rod being straight. Pretty much any other shape would be self-correcting. In fact, even a straight rod will balance on your finger. As long as the finger is close to the midpoint, the rod no longer slides off. Agreed, a finger is sweaty and sticky, and that can stop the rod sliding, but that’s not the main reason why the rod balances. If one end tilts upwards, the rod rolls sideways and the point of contact with the finger moves away from the raised end. The weight of rod on the raised side is now greater than that on the other side, so the combined forces conspire to return the rod to the horizontal. If it is tilted the other way, the same thing happens. Even a straight rod will find its own balance point if the pivot is not a knife-sharp edge.

Not only is the thought-experiment rigged: so is the metaphor. A universe doesn’t have to be perfectly linear, and it doesn’t have to pivot on an infinitely thin line. The anthropic, human-centred mentality has unerringly homed in on exactly the wrong metaphor. It ignores the universe’s tendency to respond to change by altering its own behaviour.

The triple-alpha reaction in the red giant star is just like that. An exact coincidence of energy levels is not necessary. The nuclear energy of beryllium plus that of helium is within a few per cent of one of the energy levels of carbon – but not spot-on. That’s where the red giant comes in. The energies balance only if the star is at the right temperature. And it is. This may seem to be even further evidence of fine-tuning: the astrophysics of the red giant has to compensate precisely for the disparity in nuclear energy levels. But the star is like the bent rod. It has a nuclear thermostat. If its temperature is too low, the reaction proceeds faster, and the star heats up until the energies become equal. If the temperature is too high, the reaction proceeds more slowly, and the star cools down until the same thing happens. It would be just as sensible to admire the exquisite precision with which a wood-burning fire adjusts its temperature to be exactly that at which wood can burn. Or to be amazed that a puddle fits exactly into the dip in the ground that contains it.

The knife edge analogy depends on linear thinking – that’s why it uses a straight rod. But we live in a nonlinear universe, in which anything that is stable automatically tunes itself so that it works. That’s what stability means.

Natural systems are like your arm, not like the knife. This is how the triple-alpha process tunes itself so exquisitely, and why your legs are exactly long enough to reach the ground. It is also why we, as evolved creatures, are so neatly adapted to the universe we inhabit. Analogous beings living in different universes would also be exquisitely adapted to their local conditions. This is why most of the Goldilocks arguments, that life elsewhere in the universe must be just like it is here, are probably nonsense.fn4 There are many genuine mysteries here, much to marvel at, and much yet to be understood. But there is no compelling scientific reason to believe that the universe was specially made for us.

We are faced with two alternatives. Either the universe was set up in order to bring us into being, or we evolved to fit it. The first is human-centred: it raises humanity above the universe in all its awe-inspiring vastness and complexity. The second, a universe-centred view, puts us firmly in our place: we are perhaps an interesting development, complicated enough that we don’t understand exactly how it all works, but hardly the be-all and end-all of existence.

We have been around for a few million years at most, perhaps only 200,000 if you restrict attention to ‘modern’ humans; the universe is about 13.5 billion years old. We occupy one world orbiting one of 200 billion stars in one galaxy, which itself is one of 200 billion galaxies. Isn’t it just a tiny bit arrogant to insist that the entire universe is merely a by-product of a process whose true purpose was to bring us into existence?

fn1 This phrase is not found in his extant writings; it probably originated with the Irish theologian John Punch. The closest phrase in Occam’s work is ‘Plurality must never be posited without necessity’ in the Sententiarum Petri Lombardi of 1495. Not as pithy.

fn2 ‘A universe containing sulphur has to be suitable for containing sulphur.’

fn3 Fred C. Adams, Stars in other universes: stellar structure with different fundamental constants, Journal of Cosmology and Astroparticle Physics 8 (2008) 010. doi:10.1088/1475-7516/2008/08/010. arXiv:0807.3697.

fn4 See Jack Cohen and Ian Stewart, What Does a Martian Look Like?