The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

So much for inductivism. And since inductivism is false, empiricism must be as well. For if one cannot derive predictions from experience, one certainly cannot derive explanations. Discovering a new explanation is inherently an act of creativity. To interpret dots in the sky as white-hot, million-kilometre spheres, one must first have thought of the idea of such spheres. And then one must explain why they look small and cold and seem to move in lockstep around us and do not fall down. Such ideas do not create themselves, nor can they be mechanically derived from anything: they have to be guessed – after which they can be criticized and tested. To the extent that experiencing dots ‘writes’ something into our brains, it does not write explanations but only dots. Nor is nature a book: one could try to ‘read’ the dots in the sky for a lifetime – many lifetimes – without learning anything about what they really are.

Historically, that is exactly what happened. For millennia, most careful observers of the sky believed that the stars were lights embedded in a hollow, rotating ‘celestial sphere’ centred on the Earth (or that they were holes in the sphere, through which the light of heaven shone). This geocentric – Earth-centred – theory of the universe seemed to have been directly derived from experience, and repeatedly confirmed: anyone who looked up could ‘directly observe’ the celestial sphere, and the stars maintaining their relative positions on it and being held up just as the theory predicts. Yet in reality, the solar system is heliocentric – centred on the sun, not the Earth – and the Earth is not at rest but in complex motion. Although we first noticed a daily rotation by observing stars, it is not a property of the stars at all, but of the Earth, and of the observers who rotate with it. It is a classic example of the deceptiveness of the senses: the Earth looks and feels as though it is at rest beneath our feet, even though it is really rotating.

But the real key to science is that our explanatory theories – which include those interpretations – can be improved, through conjecture, criticism and testing.

Discoveries such as fire, clothing, stone tools, bronze, and so on, happened so rarely that from an individual’s point of view the world never improved. Sometimes people even realized (with somewhat miraculous prescience) that making progress in practical ways would depend on progress in understanding puzzling phenomena in the sky.

This is why the Royal Society (one of the earliest scientific academies, founded in London in 1660) took as its motto ‘Nullius in verba’, which means something like ‘Take no one’s word for it.’

What was needed for the sustained, rapid growth of knowledge was a tradition of criticism. Before the Enlightenment, that was a very rare sort of tradition: usually the whole point of a tradition was to keep things the same. Thus the Enlightenment was a revolution in how people sought knowledge: by trying not to rely on authority. That is the context in which empiricism – purporting to rely solely on the senses for knowledge – played such a salutary historical role, despite being fundamentally false and even authoritative in its conception of how science works.

The Enlightenment was at root a philosophical change.

The reason that testability is not enough is that prediction is not, and cannot be, the purpose of science. Consider an audience watching a conjuring trick. The problem facing them has much the same logic as a scientific problem. Although in nature there is no conjurer trying to deceive us intentionally, we can be mystified in both cases for essentially the same reason: appearances are not self-explanatory. If the explanation of a conjuring trick were evident in its appearance, there would be no trick. If the explanations of physical phenomena were evident in their appearance, empiricism would be true and there would be no need for science as we know it.

Instrumentalism, even aside from the philosophical enormity of reducing science to a collection of statements about human experiences, does not make sense in its own terms. For there is no such thing as a purely predictive, explanationless theory. One cannot make even the simplest prediction without invoking quite a sophisticated explanatory framework.

Knowledge that is both familiar and uncontroversial is background knowledge. A predictive theory whose explanatory content consists only of background knowledge is a rule of thumb. Because we usually take background knowledge for granted, rules of thumb may seem to be explanationless predictions, but that is always an illusion.

Denying that some regularity in nature has an explanation is effectively the same as believing in the supernatural – saying, ‘That’s not conjuring, it’s actual magic.’

For a conjuring trick is a trick only if it makes us think that something happened that cannot happen. Both halves of that proposition depend on our bringing quite a rich set of explanatory theories to the experience. That is why a trick that mystifies an adult may be uninteresting to a young child who has not yet learned to have the expectations on which the trick relies.

But the sea change in the values and patterns of thinking of a whole community of thinkers, which brought about a sustained and accelerating creation of knowledge, happened only once in history, with the Enlightenment and its scientific revolution. An entire political, moral, economic and intellectual culture – roughly what is now called ‘the West’ – grew around the values entailed by the quest for good explanations, such as tolerance of dissent, openness to change, distrust of dogmatism and authority, and the aspiration to progress both by individuals and for the culture as a whole.

We call a phenomenon significant (or fundamental) if parochial theories are inadequate to explain it, or if it appears in the explanation of many other phenomena;

As the physicist Stephen Hawking put it, humans are ‘just a chemical scum on the surface of a typical planet that’s in orbit round a typical star on the outskirts of a typical galaxy’.

Consider Hawking’s remark again. It is true that we are on a (somewhat) typical planet of a typical star in a typical galaxy. But we are far from typical of the matter in the universe. For one thing, about 80 per cent of that matter is thought to be invisible ‘dark matter’, which can neither emit nor absorb light. We currently detect it only through its indirect gravitational effects on galaxies. Only the remaining 20 per cent is matter of the type that we parochially call ‘ordinary matter’. It is characterized by glowing continuously. We do not usually think of ourselves as glowing, but that is another parochial misconception, due to the limitations of our senses: we emit radiant heat, which is infrared light, and also light in the visible range, too faint for our eyes to detect. Concentrations of matter as dense as ourselves and our planet and star, though numerous, are not exactly typical either. They are isolated, uncommon phenomena. The universe is mostly vacuum (plus radiation and dark matter). Ordinary matter is familiar to us only because we are made of it, and because of our untypical location near large concentrations of it.

The universe is pervaded with microwave radiation – the afterglow of the Big Bang. Its temperature is about 2.7 kelvin, which means 2.7 degrees above the coldest possible temperature, absolute zero, or about 270 degrees Celsius colder than the freezing point of water. Only very unusual circumstances can make anything colder than those microwaves. Nothing in the universe is known to be cooler than about one kelvin – except in certain physics laboratories on Earth. There, the record low temperature achieved is below one billionth of a kelvin. At those extraordinary temperatures, the glow of ordinary matter is effectively extinguished.

And it is empty: the density of atoms out there is below one per cubic metre. That is a million times sparser than atoms in the space between the stars, and those atoms are themselves sparser than in the best vacuum that human technology has yet achieved. Almost all the atoms in intergalactic space are hydrogen or helium, so there is no chemistry. No life could have evolved there, nor any intelligence. Nothing changes there. Nothing happens. The same is true of the next cube and the next, and if you were to examine a million consecutive cubes in any direction the story would be the same. Cold, dark and empty.

Since then, there have been human populations who, for instance, knew how to survive in the Amazon jungle but not in the Arctic, and populations for whom it was the other way round. Therefore that knowledge was not part of their genetic inheritance. It was created by human thought, and preserved and transmitted in human culture. Today, almost the entire capacity of the Earth’s ‘life-support system for humans’ has been provided not for us but by us, using our ability to create new knowledge.

From the outset, it was only human knowledge that made the planet even marginally habitable by humans, and the enormously increased capacity of our life-support system since then (in terms both of numbers and of security and quality of life) has been entirely due to the creation of human knowledge.

Hence Dawkins agrees with an earlier evolutionary biologist, John Haldane, who expected that ‘the universe is not only queerer than we suppose, but queerer than we can suppose.’

A few species other than humans are known to be capable of having cultural knowledge. For example, some apes can discover new methods of cracking nuts, and pass that knowledge on to other apes.

The astrophysicist Martin Rees has speculated that somewhere in the universe ‘there could be life and intelligence out there in forms we can’t conceive. Just as a chimpanzee can’t understand quantum theory, it could be there are aspects of reality that are beyond the capacity of our brains.’ But that cannot be so. For if the ‘capacity’ in question is mere computational speed and amount of memory, then we can understand the aspects in question with the help of computers – just as we have understood the world for centuries with the help of pencil and paper. As Einstein remarked, ‘My pencil and I are more clever than I.’

It is inevitable that we face problems, but no particular problem is inevitable. We survive, and thrive, by solving each problem as it comes up.

As Charles Darwin put it in The Origin of Species, ‘On the view of each organism with all its separate parts having been specially created, how utterly inexplicable is it that organs bearing the plain stamp of inutility…should so frequently occur.’

A related misconception is that evolution is always adaptive – that it always constitutes progress, or at least some sort of improvement in useful functionality which it then acts to optimize.

So what would refute the Darwinian theory of evolution? Evidence which, in the light of the best available explanation, implies that knowledge came into existence in a different way. For instance, if an organism was observed to undergo only (or mainly) favourable mutations, as predicted by Lamarckism or spontaneous generation, then Darwinism’s ‘random variation’ postulate would be refuted. If organisms were observed to be born with new, complex adaptations – for anything – of which there were no precursors in their parents, then the gradual-change prediction would be refuted and so would Darwinism’s mechanism of knowledge-creation. If an organism was born with a complex adaptation that has survival value today, yet was not favoured by selection pressure in its ancestry (say, an ability to detect and use internet weather forecasts to decide when to hibernate), then Darwinism would again be refuted. A fundamentally new explanation would be needed.

Science continues to make progress even, or especially, after making great discoveries, because the discoveries themselves reveal further problems. Therefore the existence of an unsolved problem in physics is no more evidence for a supernatural explanation than the existence of an unsolved crime is evidence that a ghost committed it.

The growth of knowledge does not consist of finding ways to justify one’s beliefs. It consists of finding good explanations. And, although factual evidence and moral maxims are logically independent, factual and moral explanations are not. Thus factual knowledge can be useful in criticizing moral explanations. For example, in the nineteenth century, if an American slave had written a bestselling book, that event would not logically have ruled out the proposition ‘Negroes are intended by Providence to be slaves.’ No experience could, because that is a philosophical theory. But it might have ruined the explanation through which many people understood that proposition. And if, as a result, such people had found themselves unable to explain to their own satisfaction why it would be Providential if that author were to be forced back into slavery, then they might have questioned the account that they had formerly accepted of what a black person really is, and what a person in general is – and then a good person, a good society, and so on.

Mathematicians realized centuries ago that it is possible to work consistently and usefully with infinity. Infinite sets, infinitely large quantities and also infinitesimal quantities all make sense. Many of their properties are counter-intuitive, and the introduction of theories about infinities has always been controversial; but many facts about finite things are just as counter-intuitive. What Dawkins calls the ‘argument from personal incredulity’ is no argument: it represents nothing but a preference for parochial misconceptions over universal truths. In physics, too, infinity has been contemplated since antiquity. Euclidean space was infinite; and, in any case, space was usually regarded as a continuum: even a finite line was composed of infinitely many points. There were also infinitely many instants between any two times.

Before our ancestors learned how to make fire artificially (and many times since then too), people must have died of exposure literally on top of the means of making the fires that would have saved their lives, because they did not know how. In a parochial sense, the weather killed them; but the deeper explanation is lack of knowledge. Many of the hundreds of millions of victims of cholera throughout history must have died within sight of the hearths that could have boiled their drinking water and saved their lives; but, again, they did not know that.

Quantum theory is the deepest explanation known to science. It violates many of the assumptions of common sense, and of all previous science – including some that no one suspected were being made at all until quantum theory came along and contradicted them. And yet this seemingly alien territory is the reality of which we and everything we experience are part. There is no other.

Hence, for instance, an individual electron always has a range of different locations and a range of different speeds and directions of motion. As a result, its typical behaviour is to spread out gradually in space. Its quantum-mechanical law of motion resembles the law governing the spread of an ink blot – so if it is initially located in a very small region it spreads out rapidly, and the larger it gets the more slowly it spreads. The entanglement information that it carries ensures that no two instances of it can ever contribute to the same history. (Or, more precisely, at times and places where there are histories, it exists in instances which can never collide.)

Physicists, both through professionalism and through natural curiosity, could hardly help wondering about that process. But many of them tried not to. Most of them went on to train their students not to. This counteracted the scientific tradition of criticism in regard to quantum theory. Let me define ‘bad philosophy’ as philosophy that is not merely false, but actively prevents the growth of other knowledge. In this case, instrumentalism was acting to prevent the explanations in Schrödinger’s and Heisenberg’s theories from being improved or elaborated or unified.

And in Dublin in 1952 Schrödinger gave a lecture in which at one point he jocularly warned his audience that what he was about to say might ‘seem lunatic’. It was that, when his equation seems to be describing several different histories, they are ‘not alternatives but all really happen simultaneously’. This is the earliest known reference to the multiverse. Here was an eminent physicist joking that he might be considered mad. Why? For claiming that his own equation – the very one for which he had won the Nobel prize – might be true.

I have mentioned behaviourism, which is instrumentalism applied to psychology. It became the prevailing interpretation in that field for several decades, and, although it is now largely repudiated, research in psychology continues to downplay explanation in favour of stimulus-response rules of thumb.

Behaviouristic studies of human psychology must, by their nature, lead to dehumanizing theories of the human condition. For refusing to theorize about the mind as a causative agent is the equivalent of regarding it as a non-creative automaton. The behaviourist approach is equally futile when applied to the issue of whether an entity has a mind.

For example, the communist thinker Karl Marx believed that his theory of history was evolutionary because it spoke of a progression through historical stages determined by economic ‘laws of motion’. But the real theory of evolution has nothing to do with predicting the attributes of organisms from those of their ancestors. Marx also thought that Darwin’s theory of evolution ‘provides a basis in natural science for the historical class struggle’. He was comparing his idea of inherent conflict between socio-economic classes with the supposed competition between biological species. Fascist ideologies such as Nazism likewise used garbled or inaccurate evolutionary ideas, such as ‘the survival of the fittest’, to justify violence. But in fact the competition in biological evolution is not between different species, but between variants of genes within a species – which does not resemble the supposed ‘class struggle’ at all. It can give rise to violence or other competition between species, but it can also produce cooperation (such as the symbiosis between flowers and insects) and all sorts of intricate combinations of the two.