The Beginning of Infinity

by David Deutsch

  Next, experimentalists set out to measure the value of that constant directly – in laboratories, or by astronomical observation, say. What should they predict? Curiously enough, one immediate prediction from the anthropic explanation is that the value will not be exactly 137.5. For suppose that it were. By analogy, imagine that the bull’s-eye of a dartboard represents the values that can produce astrophysicists. It would be a mistake to predict that a typical dart that strikes the bull’s eye will strike it at the exact centre. Likewise, in the overwhelming majority of universes in which the measurement could take place (because they contain astrophysicists), the constant would not take the exactly optimal value for producing astrophysicists, nor be extremely close to it, compared with the size of the bull’s-eye.

  So Sciama concludes that, if we did measure one of those constants of physics, and found that it was extremely close to the optimum value for producing astrophysicists, that would statistically refute, not corroborate, the anthropic explanation for its value. Of course that value might still be a coincidence, but if we were willing to accept astronomically unlikely coincidences as explanations we should not be puzzled by the fine-tuning in the first place – and we should tell Paley that the watch on the heath might just have been formed by chance.

  Furthermore, astrophysicists should be relatively unlikely in universes whose conditions are so hostile that they barely permit astrophysicists at all. So, if we imagine all the values consistent with the emergence of astrophysicists arrayed on a line, then the anthropic explanation leads us to expect the measured value to fall at some typical point, not too close to the middle or to either end.

  However – and here we are reaching Sciama’s main conclusion – that prediction changes radically if there are several constants to explain. For although any one constant is unlikely to be near the edge of its range, the more constants there are, the more likely it is that at least one of them will be. This can be illustrated pictorially as follows, with our bull’s-eye replaced by a line segment, a square, a cube . . . and we can imagine this sequence continuing for as many dimensions as there are fine-tuned constants in nature. Arbitrarily define ‘near the edge’ as meaning ‘within 10 per cent of the whole range from it’. Then in the case of one constant, as shown in the diagram, 20 per cent of its possible values are near one of the two edges of the range, and 80 per cent are ‘away from the edge’. But with two constants a pair of values has to satisfy two constraints in order to be ‘away from the edge’. Only 64 per cent of them do so. Hence 36 per cent are near the edge. With three constants, nearly half the possible choices are near the edge. With 100 constants, over 99.9999999 per cent of them are.

  Whatever anthropic reasoning predicts about the values of multiple constants, it predicts will only just happen.

  So, the more constants are involved, the closer to having no astrophysicists a typical universe-with-astrophysicists is. It is not known how many constants are involved, but it seems to be several, in which case the overwhelming majority of universes in the anthropically selected region would be close to its edge. Hence, Sciama concluded, the anthropic explanation predicts that the universe is only just capable of producing astrophysicists – almost the opposite prediction from the one that it makes in the case of one constant.

  On the face of it, this might in turn seem to explain another great unsolved scientific mystery, known as ‘Fermi’s problem’, named after the physicist Enrico Fermi, who is said to have asked, ‘Where are they?’ Where are the extraterrestrial civilizations? Given the Principle of Mediocrity, or even just what we know of the galaxy and the universe, there is no reason to believe that the phenomenon of astrophysicists is unique to our planet. Similar conditions presumably exist in many other solar systems, so why would some of them not produce similar outcomes? Moreover, given the timescales on which stars and galaxies develop, it is overwhelmingly unlikely that any given extraterrestrial civilization is currently at a similar state of technological development to ours: it is likely to be millions of years younger (i.e. non-existent) or older. The older civilizations have had plenty of time to explore the galaxy – or at least to send robot space probes or signals. Fermi’s problem is that we do not see any such civilizations, probes or signals.

  Many candidate explanations have been proposed, and none of them, so far, are very good. The anthropic explanation of fine-tuning, in the light of Sciama’s argument, might seem to solve the problem neatly: if the constants of physics in our universe are only just capable of producing astrophysicists, then it is not surprising that this event has happened only once, since its happening twice independently in the same universe would be vanishingly unlikely.

  Unfortunately, that turns out to be a bad explanation too, because focusing on fundamental constants is parochial: there is no relevant difference between (1) ‘the same’ laws of physics with different constants and (2) different laws of physics. And there are infinitely many logically possible laws of physics. If they were all instantiated in real universes – as has been suggested by some cosmologists, such as Max Tegmark – it would be statistically certain that our universe is exactly on the edge of the astrophysicist-producing class of universes.

  We know that that cannot be so from an argument due to Feynman (which he applied to a slightly different problem). Consider the class of all possible universes that contain astrophysicists, and consider what else most of them contain. In particular, consider a sphere just large enough to contain your own brain. If you are interested in explaining fine-tuning, your brain in its current state counts as an ‘astrophysicist’ for these purposes. In the class of all universes that contain astrophysicists, there are many that contain a sphere whose interior is perfectly identical to the interior of your sphere, including every detail of your brain. But in the vast majority of those universes there is chaos outside the sphere: almost a random state, since almost-random states are by far the most numerous. A typical such state is not only amorphous but hot. So in most such universes the very next thing that is going to happen is that the chaotic radiation emanating from outside the sphere will kill you instantly. At any given instant, the theory that we are going to be killed a picosecond hence is refuted by observation a picosecond later. Whereupon another such theory presents itself. So it is a very bad explanation – an extreme version of the gambler’s hunches.

  The same holds for purely anthropic explanations of all other fine-tunings involving more than a handful of constants: such explanations predict that it is overwhelmingly likely that we are in a universe in which astrophysicists are only just possible and will cease to exist in an instant. So they are bad explanations.

  On the other hand, if the laws of physics exist in only one form, with only the values of a few constants differing from one universe to another, then the very fact that laws with different forms are not instantiated is a piece of fine-tuning that that anthropic explanation leaves unexplained.

  The theory that all logically possible laws of physics are instantiated as universes has a further severe problem as an explanation. As I shall explain in Chapter 8, when considering infinite sets such as these, there is often no objective way to ‘count’ or ‘measure’ how many of them have one attribute rather than another. On the other hand, in the class of all logically possible entities, those that can understand themselves, as the physical reality that we are in does, are surely, in any reasonable sense, a tiny minority. The idea that one of them ‘just happened’, without explanation, is surely just a spontaneous-generation theory.

  In addition, almost all the ‘universes’ described by those logically possible laws of physics are radically different from ours – so different that they do not properly fit into the argument. For instance, infinitely many of them contain nothing other than one bison, in various poses, and last for exactly 42 seconds. Infinitely many others contain a bison and an astrophysicist. But what is an astrophysicist in a universe that contains no stars, no scientific instruments and almost no evidence? What
is a scientist, or any sort of thinking person, in a universe in which only bad explanations are true?

  Almost all logically possible universes that contain astrophysicists are governed by laws of physics that are bad explanations. So should we predict that our universe, too, is inexplicable? Or has some high but unknowable probability to be? Thus, again, anthropic arguments based on ‘all possible laws’ are ruled out for being bad explanations.

  For these reasons I conclude that, while anthropic reasoning may well be part of the explanation for apparent fine-tuning and other observations, it can never be the whole explanation for why we observe something that would otherwise look too purposeful to be explicable as coincidence. Specific explanation, in terms of specific laws of nature, is needed.

  The reader may have noticed that all the bad explanations that I have discussed in this chapter are ultimately connected with each other. Expect too much from anthropic reasoning, or wonder too carefully how Lamarckism could work, and you get to spontaneous generation. Take spontaneous generation too seriously, and you get to creationism – and so on. That is because they all address the same underlying problem, and are all easily variable. They are easily interchangeable with each other or with variants of themselves, and they are ‘too easy’ as explanations: they could equally well explain anything. But neo-Darwinism was not easy to come by, and it is not easy to tweak. Try to tweak it – even as far as Darwin’s own misconceptions – and you will get an explanation that doesn’t work nearly as well. Try to account for something non-Darwinian with it – such as a new, complex adaptation of which there were no precursors in the organism’s parents – and you will not be able to think of a variant with that feature.

  Anthropic explanations are attempting to account for purposeful structure (such as the fine-tuned constants) in terms of a single act of selection. That is unlike evolution, and it cannot work. The solution of the fine-tuning puzzle is going to be in terms of an explanation that will specifically explain what we observe. It will be, as Wheeler put it, ‘an idea so simple . . . that . . . we will all say to each other, how could it have been otherwise?’ In other words, the problem has been not that the world is so complex that we cannot understand why it looks as it does, but it is that it is so simple that we cannot yet understand it. But this will be noticeable only with hindsight.

  All those bad explanations of the biosphere either fail to address the problem of how the knowledge in adaptations is created or they explain it badly. That is to say, they all underrate creation – and, ironically, the theory that underrates creation most of all is creationism. Consider this: if a supernatural creator were to have created the universe at the moment when Einstein or Darwin or any great scientist (appeared to have) just completed their major discovery, then the true creator of that discovery (and of all earlier discoveries) would have been not that scientist but the supernatural being. So such a theory would deny the existence of the only creation that really did take place in the genesis of that scientist’s discoveries.

  And it really is creation. Before a discovery is made, no predictive process could reveal the content or the consequences of that discovery. For if it could, it would be that discovery. So scientific discovery is profoundly unpredictable, despite the fact that it is determined by the laws of physics. I shall say more about this curious fact in the next chapter; in short, it is due to the existence of ‘emergent’ levels of explanation. In this case, the upshot is that what science – and creative thought in general – achieves is unpredictable creation ex nihilo. So does biological evolution. No other process does.

  Creationism, therefore, is misleadingly named. It is not a theory explaining knowledge as being due to creation, but the opposite: it is denying that creation happened in reality, by placing the origin of the knowledge in an explanationless realm. Creationism is really creation denial – and so are all those other false explanations.

  The puzzle of understanding what living things are and how they came about has given rise to a strange history of misconceptions, near-misses and ironies. The last of the ironies is that the neo-Darwinian theory, like the Popperian theory of knowledge, really does describe creation, while their rivals, beginning with creationism, never could.

  TERMINOLOGY

  Evolution (Darwinian) Creation of knowledge through alternating variation and selection.

  Replicator An entity that contributes causally to its own copying.

  Neo-Darwinism Darwinism as a theory of replicators, without various misconceptions such as ‘survival of the fittest’.

  Meme An idea that is a replicator.

  Memeplex A group of memes that help to cause each other’s replication.

  Spontaneous generation Formation of organisms from non-living precursors.

  Lamarckism A mistaken evolutionary theory based on the idea that biological adaptations are improvements acquired by an organism during its lifetime and then inherited by its descendants.

  Fine-tuning If the constants or laws of physics were slightly different, there would be no life.

  Anthropic explanation ‘It is only in universes that contain intelligent observers that anyone wonders why the phenomenon in question happens.’

  MEANINGS OF ‘THE BEGINNING OF INFINITY’ ENCOUNTERED IN THIS CHAPTER

  – Evolution.

  – More generally, the creation of knowledge.

  SUMMARY

  The evolution of biological adaptations and the creation of human knowledge share deep similarities, but also some important differences. The main similarities: genes and ideas are both replicators; knowledge and adaptations are both hard to vary. The main difference: human knowledge can be explanatory and can have great reach; adaptations are never explanatory and rarely have much reach beyond the situations in which they evolved. False explanations of biological evolution have counterparts in false explanations of the growth of human knowledge. For instance, Lamarckism is the counterpart of inductivism. William Paley’s version of the argument from design clarified what does or does not have the ‘appearance of design’ and hence what cannot be explained as the outcome of chance alone – namely hard-to-vary adaptation to a purpose. The origin of this must be the creation of knowledge. Biological evolution does not optimize benefits to the species, the group, the individual or even the gene, but only the ability of the gene to spread through the population. Such benefits can nevertheless happen because of the universality of laws of nature and the reach of some of the knowledge that is created. The ‘fine-tuning’ of the laws or constants of physics has been used as a modern form of the argument from design. For the usual reasons, it is not a good argument for a supernatural cause. But ‘anthropic’ theories that try to account for it as a pure selection effect from an infinite number of different universes are, by themselves, bad explanations too – in part because most logically possible laws are themselves bad explanations.

  5

  The Reality of Abstractions

  The fundamental theories of modern physics explain the world in jarringly counter-intuitive ways. For example, most non-physicists consider it self-evident that when you hold your arm out horizontally you can feel the force of gravity pulling it downwards. But you cannot. The existence of a force of gravity is, astonishingly, denied by Einstein’s general theory of relativity, one of the two deepest theories of physics. This says that the only force on your arm in that situation is that which you yourself are exerting, upwards, to keep it constantly accelerating away from the straightest possible path in a curved region of spacetime. The reality described by our other deepest theory, quantum theory, which I shall describe in Chapter 11, is even more counter-intuitive. To understand explanations like those, physicists have to learn to think about everyday events in new ways.

  The guiding principle is, as always, to reject bad explanations in favour of good ones. In regard to what is or is not real, this leads to the requirement that, if an entity is referred to by our best explanation in the relevant field, we must regard i
t as really existing. And if, as with the force of gravity, our best explanation denies that it exists, then we must stop assuming that it does.

  Furthermore, everyday events are stupendously complex when expressed in terms of fundamental physics. If you fill a kettle with water and switch it on, all the supercomputers on Earth working for the age of the universe could not solve the equations that predict what all those water molecules will do – even if we could somehow determine their initial state and that of all the outside influences on them, which is itself an intractable task.

  Fortunately, some of that complexity resolves itself into a higher-level simplicity. For example, we can predict with some accuracy how long the water will take to boil. To do so, we need know only a few physical quantities that are quite easy to measure, such as its mass, the power of the heating element, and so on. For greater accuracy we may also need information about subtler properties, such as the number and type of nucleation sites for bubbles. But those are still relatively ‘high-level’ phenomena, composed of intractably large numbers of interacting atomic-level phenomena. Thus there is a class of high-level phenomena – including the liquidity of water and the relationship between containers, heating elements, boiling and bubbles – that can be well explained in terms of each other alone, with no direct reference to anything at the atomic level or below. In other words, the behaviour of that whole class of high-level phenomena is quasi-autonomous – almost self-contained. This resolution into explicability at a higher, quasi-autonomous level is known as emergence.

  Emergent phenomena are a tiny minority. We can predict when the water will boil, and that bubbles will form when it does, but if you wanted to predict where each bubble will go (or, to be precise, what the probabilities of its various possible motions are – see Chapter 11), you would be out of luck. Still less is it feasible to predict the countless microscopically defined properties of the water, such as whether an odd or an even number of its electrons will be affected by the heating during a given period.