Fortunately, we are uninterested in predicting or explaining most of those properties, despite the fact that they are the overwhelming majority. That is because none of them has any bearing on what we want to do with the water – such as understand what it is made of, or make tea. To make tea, we want the water to be boiling, but we do not care what the pattern of bubbles was. We want its volume to be between a certain minimum and maximum, but we do not care how many molecules that is. We can make progress in achieving those purposes because we can express them in terms of those quasi-autonomous emergent properties about which we have good high-level explanations. Nor do we need most of the microscopic details in order to understand the role of water in the cosmic scheme of things, because nearly all of those details are parochial.
The behaviour of high-level physical quantities consists of nothing but the behaviour of their low-level constituents with most of the details ignored. This has given rise to a widespread misconception about emergence and explanation, known as reductionism: the doctrine that science always explains and predicts things reductively, i.e. by analysing them into components. Often it does, as when we use the fact that inter-atomic forces obey the law of conservation of energy to make and explain a high-level prediction that the kettle cannot boil water without a power supply. But reductionism requires the relationship between different levels of explanation always to be like that, and often it is not. For example, as I wrote in The Fabric of Reality:
Consider one particular copper atom at the tip of the nose of the statue of Sir Winston Churchill that stands in Parliament Square in London. Let me try to explain why that copper atom is there. It is because Churchill served as prime minister in the House of Commons nearby; and because his ideas and leadership contributed to the Allied victory in the Second World War; and because it is customary to honour such people by putting up statues of them; and because bronze, a traditional material for such statues, contains copper, and so on. Thus we explain a low-level physical observation – the presence of a copper atom at a particular location – through extremely high-level theories about emergent phenomena such as ideas, leadership, war and tradition.
There is no reason why there should exist, even in principle, any lower-level explanation of the presence of that copper atom than the one I have just given. Presumably a reductive ‘theory of everything’ would in principle make a low-level prediction of the probability that such a statue will exist, given the condition of (say) the solar system at some earlier date. It would also in principle describe how the statue probably got there. But such descriptions and predictions (wildly infeasible, of course) would explain nothing. They would merely describe the trajectory that each copper atom followed from the copper mine, through the smelter and the sculptor’s studio and so on . . . In fact such a prediction would have to refer to atoms all over the planet, engaged in the complex motion we call the Second World War, among other things. But even if you had the superhuman capacity to follow such lengthy predictions of the copper atom’s being there, you would still not be able to say ‘Ah yes, now I understand why they are there’. [You] would have to inquire into what it was about that configuration of atoms, and those trajectories, that gave them the propensity to deposit a copper atom at this location. Pursuing that inquiry would be a creative task, as discovering new explanations always is. You would have to discover that certain atomic configurations support emergent phenomena such as leadership and war, which are related to one another by high-level explanatory theories. Only when you knew those theories could you understand why that copper atom is where it is.
Even in physics, some of the most fundamental explanations, and the predictions that they make, are not reductive. For instance, the second law of thermodynamics says that high-level physical processes tend towards ever greater disorder. A scrambled egg never becomes unscrambled by the whisk, and never extracts energy from the pan to propel itself upwards into the shell, which never seamlessly reseals itself. Yet, if you could somehow make a video of the scrambling process with enough resolution to see the individual molecules, and play it backwards, and examine any part of it at that scale, you would see nothing but molecules moving and colliding in strict obedience to the low-level laws of physics. It is not yet known how, or whether, the second law of thermodynamics can be derived from a simple statement about individual atoms.
There is no reason why it should be. There is often a moral overtone to reductionism (science should be essentially reductive). This is related both to instrumentalism and to the Principle of Mediocrity, which I criticized in Chapters 1 and 3. Instrumentalism is rather like reductionism except that, instead of rejecting only high-level explanations, it tries to reject all explanations. The Principle of Mediocrity is a milder form of reductionism: it rejects only high-level explanations that involve people. While I am on the subject of bad philosophical doctrines with moral overtones, let me add holism, a sort of mirror image of reductionism. It is the idea that the only valid explanations (or at least the only significant ones) are of parts in terms of wholes. Holists also often share with reductionists the mistaken belief that science can only (or should only) be reductive, and therefore they oppose much of science. All those doctrines are irrational for the same reason: they advocate accepting or rejecting theories on grounds other than whether they are good explanations.
Whenever a high-level explanation does follow logically from low-level ones, that also means that the high-level one implies something about the low-level ones. Thus, additional high-level theories, provided that they were all consistent, would place more and more constraints on what the low-level theories could be. So it could be that all the high-level explanations that exist, taken together, imply all the low-level ones, as well as vice versa. Or it could be that some low-level, some intermediate-level and some high-level explanations, taken together, imply all explanations. I guess that that is so.
Thus, one possible way that the fine-tuning problem might eventually be solved would be if some high-level explanations turned out to be exact laws of nature. The microscopic consequences of that might well seem to be fine-tuned. One candidate is the principle of the universality of computation, which I shall discuss in the next chapter. Another is the principle of testability, for, in a world in which the laws of physics do not permit the existence of testers, they also forbid themselves to be tested. However, in their current form such principles, regarded as laws of physics, are anthropocentric and arbitrary – and would therefore be bad explanations. But perhaps there are deeper versions, to which they are approximations, which are good explanations, well integrated with those of microscopic physics like the second law of thermodynamics is.
In any case, emergent phenomena are essential to the explicability of the world. Long before humans had much explanatory knowledge, they were able to control nature by using rules of thumb. Rules of thumb have explanations, and those explanations were about high-level regularities among emergent phenomena such as fire and rocks. Long before that, it was only genes that were encoding rules of thumb, and the knowledge in them, too, was about emergent phenomena. Thus emergence is another beginning of infinity: all knowledge-creation depends on, and physically consists of, emergent phenomena.
Emergence is also responsible for the fact that discoveries can be made in successive steps, thus providing scope for the scientific method. The partial success of each theory in a sequence of improving theories is tantamount to the existence of a ‘layer’ of phenomena that each theory explains successfully – though, as it then turns out, partly mistakenly.
Successive scientific explanations are occasionally dissimilar in the way they explain their predictions, even in the domain where the predictions themselves are similar or identical. For instance, Einstein’s explanation of planetary motion does not merely correct Newton’s: it is radically different, denying, among many other things, the very existence of central elements of Newton’s explanation, such as the gravitational force and the uniformly flowing t
ime with respect to which Newton defined motion. Likewise the astronomer Johannes Kepler’s theory which said that the planets move in ellipses did not merely correct the celestial-sphere theory, it denied the spheres’ existence. And Newton’s did not substitute a new shape for Kepler’s ellipses, but a whole new way for laws to specify motion – through infinitesimally defined quantities like instantaneous velocity and acceleration. Thus each of those theories of planetary motion was ignoring or denying its predecessor’s basic means of explaining what was happening out there.
This has been used as an argument for instrumentalism, as follows. Each successive theory made small but accurate corrections to what its predecessor predicted, and was therefore a better theory in that sense. But, since each theory’s explanation swept away that of the previous theory, the previous theory’s explanation was never true in the first place, and so one cannot regard those successive explanations as constituting a growth of knowledge about reality. From Kepler to Newton to Einstein we have successively: no force needed to explain orbits; an inverse-square-law force responsible for every orbit; and again no force needed. So how could Newton’s ‘force of gravity’ (as distinct from his equations predicting its effects) ever have been an advance in human knowledge?
It could, and was, because sweeping away the entities through which a theory makes its explanation is not the same as sweeping away the whole of the explanation. Although there is no force of gravity, it is true that something real (the curvature of spacetime), caused by the sun, has a strength that varies approximately according to Newton’s inverse-square law, and affects the motion of objects, seen and unseen. Newton’s theory also correctly explained that the laws of gravitation are the same for terrestrial and celestial objects; it made a novel distinction between mass (the measure of an object’s resistance to being accelerated) and weight (the force required to prevent the object from falling under gravity); and it said that the gravitational effect of an object depends on its mass and not on other attributes such as its density or composition. Later, Einstein’s theory not only endorsed all those features but explained, in turn, why they are so. Newton’s theory, too, had been able to make more accurate predictions than its predecessors precisely because it was more right than they were about what was really happening. Before that, even Kepler’s explanation had included important elements of the true explanation: planetary orbits are indeed determined by laws of nature; those laws are indeed the same for all planets, including the Earth; they do involve the sun; they are mathematical and geometrical in character; and so on. With the hindsight provided by each successive theory, we can see not only where the previous theory made false predictions, but also that wherever it made true predictions this was because it had expressed some truth about reality. So its truth lives on in the new theory – as Einstein remarked, ‘There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.’
As I explained in Chapter 1, regarding the explanatory function of theories as paramount is not just an idle preference. The predictive function of science is entirely dependent on it. Also, in order to make progress in any field, it is the explanations in existing theories, not the predictions, that have to be creatively varied in order to conjecture the next theory. Furthermore, the explanations in one field affect our understanding of other fields. For instance, if someone thinks that a conjuring trick is due to supernatural abilities of the conjurer, it will affect how they judge theories in cosmology (such as the origin of the universe, or the fine-tuning problem) and in psychology (how the human mind works) and so on.
By the way, it is something of a misconception that the predictions of successive theories of planetary motion were all that similar. Newton’s predictions are indeed excellent in the context of bridge-building, and only slightly inadequate when running the Global Positioning System, but they are hopelessly wrong when explaining a pulsar or a quasar – or the universe as a whole. To get all those right, one needs Einstein’s radically different explanations.
Such large discontinuities in the meanings of successive scientific theories have no biological analogue: in an evolving species, the dominant strain in each generation differs only slightly from that in the previous generation. Nevertheless, scientific discovery is a gradual process too; it is just that, in science, all the gradualness, and nearly all the criticism and rejection of bad explanations, takes place inside the scientists’ minds. As Popper put it, ‘We can let our theories die in our place.’
There is another, even more important, advantage in that ability to criticize theories without staking one’s life on them. In an evolving species, the adaptations of the organisms in each generation must have enough functionality to keep the organism alive, and to pass all the tests that they encounter in propagating themselves to the next generation. In contrast, the intermediate explanations leading a scientist from one good explanation to the next need not be viable at all. The same is true of creative thought in general. This is the fundamental reason that explanatory ideas are able to escape from parochialism, while biological evolution, and rules of thumb, cannot.
That brings me to the main subject of this chapter: abstractions. In Chapter 4 I remarked that pieces of knowledge are abstract replicators that ‘use’ (and hence affect) organisms and brains to get themselves replicated. That is a higher level of explanation than the emergent levels I have mentioned so far. It is a claim that something abstract – something non-physical, such as the knowledge in a gene or a theory – is affecting something physical. Physically, nothing is happening in such a situation other than that one set of emergent entities – such as genes, or computers – is affecting others, which is already anathema to reductionism. But abstractions are essential to a fuller explanation. You know that if your computer beats you at chess, it is really the program that has beaten you, not the silicon atoms or the computer as such. The abstract program is instantiated physically as a high-level behaviour of vast numbers of atoms, but the explanation of why it has beaten you cannot be expressed without also referring to the program in its own right. That program has also been instantiated, unchanged, in a long chain of different physical substrates, including neurons in the brains of the programmers and radio waves when you downloaded the program via wireless networking, and finally as states of long- and short-term memory banks in your computer. The specifics of that chain of instantiations may be relevant to explaining how the program reached you, but it is irrelevant to why it beat you: there, the content of the knowledge (in it, and in you) is the whole story. That story is an explanation that refers ineluctably to abstractions; and therefore those abstractions exist, and really do affect physical objects in the way required by the explanation.
The computer scientist Douglas Hofstadter has a nice argument that this sort of explanation is essential in understanding certain phenomena. In his book I am a Strange Loop (2007) he imagines a special-purpose computer built of millions of dominoes. They are set up – as dominoes often are for fun – standing on end, close together, so that if one of them is knocked over it strikes its neighbour and so a whole stretch of dominoes falls, one after another. But Hofstadter’s dominoes are spring-loaded in such a way that, whenever one is knocked over, it pops back up after a fixed time. Hence, when a domino falls, a wave or ‘signal’ of falling dominoes propagates along the stretch in the direction in which it fell until it reaches either a dead end or a currently fallen domino. By arranging these dominoes in a network with looping, bifurcating and rejoining stretches, one can make these signals combine and interact in a sufficiently rich repertoire of ways to make the whole construction into a computer: a signal travelling down a stretch can be interpreted as a binary ‘1’, and the lack of a signal as a binary ‘0’, and the interactions between such signals can implement a repertoire of operations – such as ‘and’, ‘or’ and ‘not’ – out of which arbitrary computations can be composed.
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p; One domino is designated as the ‘on switch’: when it is knocked over, the domino computer begins to execute the program that is instantiated in its loops and stretches. The program in Hofstadter’s thought experiment computes whether a given number is a prime or not. One inputs that number by placing a stretch of exactly that many dominos at a specified position, before tripping the ‘on switch’. Elsewhere in the network, a particular domino will deliver the output of the computation: it will fall only if a divisor is found, indicating that the input was not a prime.
Hofstadter sets the input to the number 641, which is a prime, and trips the ‘on switch’. Flurries of motion begin to sweep back and forth across the network. All 641 of the input dominos soon fall as the computation ‘reads’ its input – and snap back up and participate in further intricate patterns. It is a lengthy process, because this is a rather inefficient way to perform computations – but it does the job.
Now Hofstadter imagines that an observer who does not know the purpose of the domino network watches the dominoes performing and notices that one particular domino remains resolutely standing, never affected by any of the waves of downs and ups sweeping by.
The observer points at [that domino] and asks with curiosity, ‘How come that domino there is never falling?’
We know that it is the output domino, but the observer does not. Hofstadter continues:
Let me contrast two different types of answer that someone might give. The first type of answer – myopic to the point of silliness – would be, ‘Because its predecessor never falls, you dummy!’
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