The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

In this book I argue that all progress, both theoretical and practical, has resulted from a single human activity: the quest for what I call good explanations. Though this quest is uniquely human, its effectiveness is also a fundamental fact about reality at the most impersonal, cosmic level – namely that it conforms to universal laws of nature that are indeed good explanations.

Behind it all is surely an idea so simple, so beautiful, that when we grasp it – in a decade, a century, or a millennium – we will all say to each other, how could it have been otherwise? John Archibald Wheeler, Annals of the New York Academy of Sciences, 480 (1986)

Scientific theories are explanations: assertions about what is out there and how it behaves. Where do these theories come from? For most of the history of science, it was mistakenly believed that we ‘derive’ them from the evidence of our senses – a philosophical doctrine known as empiricism: Empiricism For example, the philosopher John Locke wrote in 1689 that the mind is like ‘white paper’ on to which sensory experience writes, and that that is where all our knowledge of the physical world comes from. Another empiricist metaphor was that one could read knowledge from the ‘Book of Nature’ by making observations. Either way, the discoverer of knowledge is its passive recipient, not its creator. But, in reality, scientific theories are not ‘derived’ from anything. We do not read them in nature, nor does nature write them into us. They are guesses – bold conjectures. Human minds create them by rearranging, combining, altering and adding to existing ideas with the intention of improving upon them. We do not begin with ‘white paper’ at birth, but with inborn expectations and intentions and an innate ability to improve upon them using thought and experience. Experience is indeed essential to science, but its role is different from that supposed by empiricism. It is not the source from which theories are derived. Its main use is to choose between theories that have already been guessed. That is what ‘learning from experience’ is.

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.

The misconception that knowledge needs authority to be genuine or reliable dates back to antiquity, and it still prevails. To this day, most courses in the philosophy of knowledge teach that knowledge is some form of justified, true belief, where ‘justified’ means designated as true (or at least ‘probable’) by reference to some authoritative source or touchstone of knowledge. Thus ‘how do we know…?’ is transformed into ‘by what authority do we claim…?’ The latter question is a chimera that may well have wasted more philosophers’ time and effort than any other idea. It converts the quest for truth into a quest for certainty (a feeling) or for endorsement (a social status). This misconception is called justificationism.

Fallibilists expect even their best and most fundamental explanations to contain misconceptions in addition to truth, and so they are predisposed to try to change them for the better. In contrast, the logic of justificationism is to seek (and typically, to believe that one has found) ways of securing ideas against change.

Conan Doyle came much closer to the truth when, during ‘The Boscombe Valley Mystery’, he had Holmes remark that ‘circumstantial evidence’ (evidence about unwitnessed events) is ‘a very tricky thing…It may seem to point very straight to one thing, but if you shift your own point of view a little, you may find it pointing in an equally uncompromising manner to something entirely different…There is nothing more deceptive than an obvious fact.’

I am not asking what authority scientific knowledge is derived from, or rests on. I mean, literally, by what process do ever truer and more detailed explanations about the world come to be represented physically in our brains? How do we come to know about the interactions of subatomic particles during transmutation at the centre of a distant star, when even the tiny trickle of light that reaches our instruments from the star was emitted by glowing gas at the star’s surface, a million kilometres above where the transmutation is happening? Or about conditions in the fireball during the first few seconds after the Big Bang, which would instantly have destroyed any sentient being or scientific instrument? Or about the future, which we have no way of measuring at all? How is it that we can predict, with some non-negligible degree of confidence, whether a new design of microchip will work, or whether a new drug will cure a particular disease, even though they have never existed before? For most of human history, we did not know how to do any of this. People were not designing microchips or medications or even the wheel. For thousands of generations, our ancestors looked up at the night sky and wondered what stars are – what they are made of, what makes them shine, what their relationship is with each other and with us – which was exactly the right thing to wonder about. And they were using eyes and brains anatomically indistinguishable from those of modern astronomers. But they ...

Rejecting authority in regard to knowledge was not just a matter of abstract analysis. It was a necessary condition for progress, because, before the Enlightenment, it was generally believed that everything important that was knowable had already been discovered, and was enshrined in authoritative sources such as ancient writings and traditional assumptions. Some of those sources did contain some genuine knowledge, but it was entrenched in the form of dogmas along with many falsehoods. So the situation was that all the sources from which it was generally believed knowledge came actually knew very little, and were mistaken about most of the things that they claimed to know. And therefore progress depended on learning how to reject their authority.

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. One consequence of this tradition of criticism was the emergence of a methodological rule that a scientific theory must be testable (though this was not made explicit at first). That is to say, the theory must make predictions which, if the theory were false, could be contradicted by the outcome of some possible observation. Thus, although scientific theories are not derived from experience, they can be tested by experience – by observation or experiment.

Nevertheless, testability cannot have been the decisive factor in the scientific revolution either. Contrary to what is often said, testable predictions had always been quite common. Every traditional rule of thumb for making a flint blade or a camp fire is testable. Every would-be prophet who claims that the sun will go out next Tuesday has a testable theory. So does every gambler who has a hunch that ‘this is my lucky night – I can feel it’. So what is the vital, progress-enabling ingredient that is present in science, but absent from the testable theories of the prophet and the gambler? 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. The problem is not to predict the trick’s appearance. I may, for instance, predict that if a conjurer seems to place various balls under various cups, those cups will later appear to be empty; and I may predict that if the conjurer appea...

There is always an explanation, whether we know it or not, for why a rule of thumb works. 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.’ Also, there is always an explanation when a rule of thumb fails, for rules of thumb are always parochial: they hold only in a narrow range of familiar circumstances. So, if an unfamiliar feature were introduced into a cups-and-balls trick, the rule of thumb I stated might easily make a false prediction. For instance, I could not tell from the rule of thumb whether it would be possible to perform the trick with lighted candles instead of balls. If I had an explanation of how the trick worked, I could tell.

Popper wrote: I think that there is only one way to science – or to philosophy, for that matter: to meet a problem, to see its beauty and fall in love with it; to get married to it and to live with it happily, till death do ye part – unless you should meet another and even more fascinating problem or unless, indeed, you should obtain a solution. But even if you do obtain a solution, you may then discover, to your delight, the existence of a whole family of enchanting, though perhaps difficult, problem children… Realism and the Aim of Science (1983)

That freedom to make drastic changes in those mythical explanations of seasons is the fundamental flaw in them. It is the reason that myth-making in general is not an effective way to understand the world.

In general, when theories are easily variable in the sense I have described, experimental testing is almost useless for correcting their errors. I call such theories bad explanations. Being proved wrong by experiment, and changing the theories to other bad explanations, does not get their holders one jot closer to the truth. Because explanation plays this central role in science, and because testability is of little use in the case of bad explanations, I myself prefer to call myths, superstitions and similar theories unscientific even when they make testable predictions. But it does not matter what terminology you use, so long as it does not lead you to conclude that there is something worthwhile about the Persephone myth, or the prophet’s apocalyptic theory or the gambler’s delusion, just because it is testable. Nor is a person capable of making progress merely by virtue of being willing to drop a theory when it is refuted: one must also be seeking a better explanation of the relevant phenomena. That is the scientific frame of mind. As the physicist Richard Feynman said, ‘Science is what we have learned about how to keep from fooling ourselves.’ By adopting easily variable explanations, the gambler and prophet are ensuring that they will be able to continue fooling themselves no matter what happens. Just as thoroughly as if they had adopted untestable theories, they are insulating themselves from facing evidence that they are mistaken about what is really there in the phy...

Long before the Enlightenment, there were individuals who sought good explanations. Indeed, my discussion here suggests that all progress then, as now, was due to such people. But in most ages they lacked contact with a tradition of criticism in which others could carry on their ideas, and so created little that left any trace for us to detect. We do know of sporadic traditions of good-explanation-seeking in narrowly defined fields, such as geometry, and even short-lived traditions of criticism – mini-enlightenments – which were tragically snuffed out, as I shall describe in Chapter 9. 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. And the progress made by that multifaceted culture, in turn, promoted those values – though, as I shall explain in Chapter 15, they are nowhere close to being fully implemented.

The axis-tilt theory also predicts that the seasons will be out of phase in the two hemispheres. So if they had been found to be in phase, the theory would have been refuted, just as, in the event, the Persephone and Freyr myths were refuted by the opposite observation. But the difference is, if the axis-tilt theory had been refuted, its defenders would have had nowhere to go. No easily implemented change could make tilted axes cause the same seasons all over the planet. Fundamentally new ideas would have been needed. That is what makes good explanations essential to science: it is only when a theory is a good explanation – hard to vary – that it even matters whether it is testable. Bad explanations are equally useless whether they are testable or not.

Good explanations are often strikingly simple or elegant – as I shall discuss in Chapter 14. Also, a common way in which an explanation can be bad is by containing superfluous features or arbitrariness, and sometimes removing those yields a good explanation. This has given rise to a misconception known as ‘Occam’s razor’ (named after the fourteenth-century philosopher William of Occam, but dating back to antiquity), namely that one should always seek the ‘simplest explanation’. One statement of it is ‘Do not multiply assumptions beyond necessity.’ However, there are plenty of very simple explanations that are nevertheless easily variable (such as ‘Demeter did it’). And, while assumptions ‘beyond necessity’ make a theory bad by definition, there have been many mistaken ideas of what is ‘necessary’ in a theory.

Suppose for the sake of argument that you thought of the axis-tilt theory yourself. It is your conjecture, your own original creation. Yet because it is a good explanation – hard to vary – it is not yours to modify. It has an autonomous meaning and an autonomous domain of applicability. You cannot confine its predictions to a region of your choosing. Whether you like it or not, it makes predictions about places both known to you and unknown to you, predictions that you have thought of and ones that you have not thought of. Tilted planets in similar orbits in other solar systems must have seasonal heating and cooling – planets in the most distant galaxies, and planets that we shall never see because they were destroyed aeons ago, and also planets that have yet to form. The theory reaches out, as it were, from its finite origins inside one brain that has been affected only by scraps of patchy evidence from a small part of one hemisphere of one planet – to infinity. This reach of explanations is another meaning of ‘the beginning of infinity’. It is the ability of some of them to solve problems beyond those that they were created to solve.

The Enlightenment (The beginning of) a way of pursuing knowledge with a tradition of criticism and seeking good explanations instead of reliance on authority.

The real source of our theories is conjecture, and the real source of our knowledge is conjecture alternating with criticism. We create theories by rearranging, combining, altering and adding to existing ideas with the intention of improving upon them. The role of experiment and observation is to choose between existing theories, not to be the source of new ones. We interpret experiences through explanatory theories, but true explanations are not obvious. Fallibilism entails not looking to authorities but instead acknowledging that we may always be mistaken, and trying to correct errors. We do so by seeking good explanations – explanations that are hard to vary in the sense that changing the details would ruin the explanation. This, not experimental testing, was the decisive factor in the scientific revolution, and also in the unique, rapid, sustained progress in other fields that have participated in the Enlightenment. That was a rebellion against authority which, unlike most such rebellions, tried not to seek authoritative justifications for theories, but instead set up a tradition of criticism.

The better we come to understand phenomena remote from our everyday experience, the longer those chains of interpretation become, and every additional link necessitates more theory. A single unexpected or misunderstood phenomenon anywhere in the chain can, and often does, render the resulting sensory experience arbitrarily misleading. Yet, over time, the conclusions that science has drawn have become ever truer to reality. Its quest for good explanations corrects the errors, allows for the biases and misleading perspectives, and fills in the gaps. This is what we can achieve when, as Feynman said, we keep learning more about how not to fool ourselves.

The primary function of the telescope’s optics is to reduce the illusion that the stars are few, faint, twinkling and moving. The same is true of every feature of the telescope, and of all other scientific instruments: each layer of indirectness, through its associated theory, corrects errors, illusions, misleading perspectives and gaps. Perhaps it is the mistaken empiricist ideal of ‘pure’, theory-free observation that makes it seem odd that truly accurate observation is always so hugely indirect. But the fact is that progress requires the application of ever more knowledge in advance of our observations.

Explanatory theories tell us how to build and operate instruments in exactly the right way to work this miracle. Like conjuring tricks in reverse, such instruments fool our senses into seeing what is really there. Our minds, through the methodological criterion that I mentioned in Chapter 1, conclude that a particular thing is real if and only if it figures in our best explanation of something. Physically, all that has happened is that human beings, on Earth, have dug up raw materials such as iron ore and sand, and have rearranged them – still on Earth – into complex objects such as radio telescopes, computers and display screens, and now, instead of looking at the sky, they look at those objects. They are focusing their eyes on human artefacts that are close enough to touch. But their minds are focused on alien entities and processes, light years away.

Before anything was known about how the world works, trying to explain physical phenomena in terms of purposeful, human-like thought and action may have been a reasonable approach. After all, that is how we explain much of our everyday experience even today: if a jewel is mysteriously missing from a locked safe, we seek human-level explanations such as error or theft (or, under some circumstances, conjuring), not new laws of physics. But that anthropocentric approach has never yielded any good explanations beyond the realm of human affairs. In regard to the physical world at large, it was colossally misconceived. We now know that the patterns of stars and planets in our night sky have no significance for human affairs. We know that we are not at the centre of the universe – it does not even have a geometrical centre.

Anthropocentric misconceptions have also been overturned in every other fundamental area of science: our knowledge of physics is now expressed entirely in terms of entities that are as impersonal as Euclid’s points and lines, such as elementary particles, forces and spacetime – a four-dimensional continuum with three dimensions of space and one of time. Their effects on each other are explained not in terms of feelings and intentions, but through mathematical equations expressing laws of nature. In biology, it was once thought that living things must have been designed by a supernatural person, and that they must contain some special ingredient, a ‘vital principle’, to make them behave with apparent purposefulness. But biological science discovered new modes of explanation through such impersonal things as chemical reactions, genes and evolution. So we now know that living things, including humans, all consist of the same ingredients as rocks and stars, and obey the same laws, and that they were not designed by anyone. Modern science, far from explaining physical phenomena in terms of the thoughts and intentions of unseen people, considers our own thoughts and intentions to be aggregates of unseen (though not unseeable) microscopic physical processes in our brains.

It is easy to mistake quirks of one’s own, familiar environment or perspective (such as the rotation of the night sky) for objective features of what one is observing, or to mistake rules of thumb (such as the prediction of daily sunrises) for universal laws. I shall refer to that sort of error as parochialism.

This fundamental connection between explanatory knowledge and technology is why the Haldane–Dawkins queerer-than-we-can-suppose argument is mistaken – why the reach of human adaptations does have a different character from that of all the other adaptations in the biosphere. The ability to create and use explanatory knowledge gives people a power to transform nature which is ultimately not limited by parochial factors, as all other adaptations are, but only by universal laws. This is the cosmic significance of explanatory knowledge – and hence of people, whom I shall henceforward define as entities that can create explanatory knowledge.

Using knowledge to cause automated physical transformations is, in itself, not unique to humans. It is the basic method by which all organisms keep themselves alive: every cell is a chemical factory. The difference between humans and other species is in what kind of knowledge they can use (explanatory instead of rule-of-thumb) and in how they create it (conjecture and criticism of ideas, rather than the variation and selection of genes). It is precisely those two differences that explain why every other organism can function only in a certain range of environments that are hospitable to it, while humans transform inhospitable environments like the biosphere into support systems for themselves. And, while every other organism is a factory for converting resources of a fixed type into more such organisms, human bodies (including their brains) are factories for transforming anything into anything that the laws of nature allow. They are ‘universal constructors’.

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.’ In terms of computational repertoire, our computers – and brains – are already universal (see Chapter 6). But if the claim is that we may be qualitatively unable to understand what some other forms of intelligence can – if our disability cannot be remedied by mere automation – then this is just another claim that the world is not explicable. Indeed, it is tantamount to an appeal to the supernatural, with all the arbitrariness that is inherent in such appeals, for if we wanted to incorporate into our world view an imaginary realm explicable only to superhumans, we need never have bothered to abandon the myths of Persephone and her fellow deities.

In addition to matter and energy, there is one other essential requirement, namely evidence: the information needed to test scientific theories. The Earth’s surface is rich in evidence. We happened to get round to testing Newton’s laws in the seventeenth century, and Einstein’s in the twentieth, but the evidence with which we did that – light from the sky – had been deluging the surface of the Earth for billions of years before that, and will continue to do so for billions more. Even today we have barely begun to examine that evidence: on any clear night, the chances are that your roof will be struck by evidence falling from the sky which, if you only knew what to look for and how, would win you a Nobel prize. In chemistry, every stable element that exists anywhere is also present on or just below the Earth’s surface. In biology, copious evidence of the nature of life is ubiquitous in the biosphere – and within arm’s reach, in our own DNA. As far as we know, all the fundamental constants of nature can be measured here, and every fundamental law can be tested here. Everything needed for the open-ended creation of knowledge is here in abundance, in the Earth’s biosphere.

All people in the universe, once they have understood enough to free themselves from parochial obstacles, face essentially the same opportunities. This is an underlying unity in the physical world more significant than all the dissimilarities I have described between our environment and a typical one: the fundamental laws of nature are so uniform, and evidence about them so ubiquitous, and the connections between understanding and control so intimate, that, whether we are on our parochial home planet or a hundred million light years away in the intergalactic plasma, we can do the same science and make the same progress. So a typical location in the universe is amenable to the open-ended creation of knowledge. And therefore so are almost all other kinds of environment, since they have more matter, more energy and easier access to evidence than intergalactic space. The thought experiment considered almost the worst possible case. Perhaps the laws of physics do not allow knowledge-creation inside, say, the jet of a quasar. Or perhaps they do. But either way, in the universe at large, knowledge-friendliness is the rule, not the exception. That is to say, the rule is person-friendliness to people who have the relevant knowledge. Death is the rule for those who do not. These are the same rules that prevailed in the Great Rift Valley from whence we came, and have prevailed ever since.

Many things are more obviously significant than people. Space and time are significant because they appear in almost all explanations of other physical phenomena. Similarly, electrons and atoms are significant. Humans seem to have no place in that exalted company. Our history and politics, our science, art and philosophy, our aspirations and moral values – all these are tiny side effects of a supernova explosion a few billion years ago, which could be extinguished tomorrow by another such explosion. Supernovae, too, are moderately significant in the cosmic scheme of things. But it seems that one can explain everything about supernovae, and almost everything else, without ever mentioning people or knowledge at all. However, that is merely another parochial error, due to our current, untypical, vantage point in an Enlightenment that is mere centuries old. In the longer run, humans may colonize other solar systems and, by increasing their knowledge, control ever more powerful physical processes. If people ever choose to live near a star that is capable of exploding, they may well wish to prevent such an explosion – probably by removing some of the material from the star. Such a project would use many orders of magnitude more energy than humans currently control, and more advanced technology as well. But it is a fundamentally simple task, not requiring any steps that are even close to limits imposed by the laws of physics. So, with the right knowledge, it could be achieved. In...

Like an explosive awaiting a spark, unimaginably numerous environments in the universe are waiting out there, for aeons on end, doing nothing at all or blindly generating evidence and storing it up or pouring it out into space. Almost any of them would, if the right knowledge ever reached it, instantly and irrevocably burst into a radically different type of physical activity: intense knowledge-creation, displaying all the various kinds of complexity, universality and reach that are inherent in the laws of nature, and transforming that environment from what is typical today into what could become typical in the future. If we want to, we could be that spark.

That a gene is adapted to a given function means that few, if any, small changes would improve its ability to perform that function. Some changes might make no practical difference to that ability, but most of those that did would make it worse. In other words good adaptations, like good explanations, are distinguished by being hard to vary while still fulfilling their functions.

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 time 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.

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.

As I explained in Chapter 1, even in science, almost all rejected theories are rejected for being bad explanations, without ever being tested. Experimental testing is only one of many methods of criticism used in science, and the Enlightenment has made progress by bringing those other methods to bear in non-scientific fields too. The basic reason that such progress is possible is that good explanations about philosophical issues are as hard to find as in science – and criticism is correspondingly effective.

Certainly you can’t derive an ought from an is, but you can’t derive a factual theory from an is either. That is not what science does. 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.

Quite generally, in order to understand the moral landscape in terms of a given set of values, one needs to understand some facts as being a certain way too. And the converse is also true: for example, as the philosopher Jacob Bronowski pointed out, success at making factual, scientific discoveries entails a commitment to all sorts of values that are necessary for making progress. The individual scientist has to value truth, and good explanations, and be open to ideas and to change. The scientific community, and to some extent the civilization as a whole, has to value tolerance, integrity and openness of debate.

Beauty, right and wrong, primality, infinite sets – they all exist objectively. But not physically. What does that mean? Certainly they can affect you – as examples like Hofstadter’s show – but apparently not in the same sense that physical objects do. You cannot trip over one of them in the street. However, there is less to that distinction than our empiricism-biased common sense assumes. First of all, being affected by a physical object means that something about the physical object has caused a change, via the laws of physics (or, equivalently, that the laws of physics have caused a change via that object). But causation and the laws of physics are not themselves physical objects. They are abstractions, and our knowledge of them comes – just as for all other abstractions – from the fact that our best explanations invoke them. Progress depends on explanation, and therefore trying to conceive of the world as merely a sequence of events with unexplained regularities would entail giving up on progress.

Also, a writing system based on an alphabet can cover not only every word but every possible word in its language, so that words that have yet to be coined already have a place in it. Then, instead of each new word temporarily breaking the system, the system can itself be used to coin new words, in an easy and decentralized way.

Here is an even more speculative possibility. The largest benefits of any universality, beyond whatever parochial problem it is intended to solve, come from its being useful for further innovation. And innovation is unpredictable. So, to appreciate universality at the time of its discovery, one must either value abstract knowledge for its own sake or expect it to yield unforeseeable benefits. In a society that rarely experienced change, both those attitudes would be quite unnatural. But that was reversed with the Enlightenment, whose quintessential idea is, as I have said, that progress is both desirable and attainable. And so, therefore, is universality. Be that as it may, with the Enlightenment, parochialism and all arbitrary exceptions and limitations began to be regarded as inherently problematic – and not only in science. Why should the law treat an aristocrat differently from a commoner? A slave from a master? A woman from a man? Enlightenment philosophers such as Locke set out to free political institutions from arbitrary rules and assumptions. Others tried to derive moral maxims from universal moral explanations rather than merely to postulate them dogmatically. Thus universal explanatory theories of justice, legitimacy and morality began to take their place alongside universal theories of matter and motion. In all those cases, universality was being sought deliberately, as a desirable feature in its own right – even a necessary feature for an idea to be true – and...

Babbage originally had no conception of computational universality. Nevertheless, the Difference Engine already comes remarkably close to it – not in its repertoire of computations, but in its physical constitution. To program it to print out a given table, one initializes certain cogs. Babbage eventually realized that this programming phase could itself be automated: the settings could be prepared on punched cards like Jacquard’s, and transferred mechanically into the cogs. This would not only remove the main remaining source of error, but also increase the machine’s repertoire. Babbage then realized that if the machine could also punch new cards for its own later use, and could control which punched card it would read next (say, by choosing from a stack of them, depending on the position of its cogs), then something qualitatively new would happen: the jump to universality. Babbage called this improved machine the Analytical Engine. He and his colleague the mathematician Ada, Countess of Lovelace, knew that it would be capable of computing anything that human ‘computers’ could, and that this included more than just arithmetic: it could do algebra, play chess, compose music, process images and so on. It would be what is today called a universal classical computer.

It is a remarkable fact that, in that sense (that is to say, ignoring issues of speed, memory capacity and input–output devices), the human ‘computers’ of old, the steam-powered Analytical Engine with its literal bells and whistles, the room-sized vacuum-tube computers of the Second World War, and present-day supercomputers all have an identical repertoire of computations. Another thing that they have in common is that they are all digital: they operate on information in the form of discrete values of physical variables, such as electronic switches being on or off, or cogs being at one of ten positions. The alternative, ‘analogue’, computers, such as slide rules, which represent information as continuous physical variables, were once ubiquitous but are hardly ever used today. That is because a modern digital computer can be programmed to imitate any of them, and to outperform them in almost any application. The jump to universality in digital computers has left analogue computation behind. That was inevitable, because there is no such thing as a universal analogue computer. That is because of the need for error correction: during lengthy computations, the accumulation of errors due to things like imperfectly constructed components, thermal fluctuations, and random outside influences makes analogue computers wander off the intended computational path. This may sound like a minor or parochial consideration. But it is quite the opposite. Without error-correction all informati...

Genes in present-day organisms replicate themselves by a complicated and very indirect chemical route. In most species they act as templates for forming stretches of a similar molecule, RNA. Those then act as programs which direct the synthesis of the body’s constituent chemicals, especially enzymes, which are catalysts. A catalyst is a kind of constructor – it promotes a change among other chemicals while remaining unchanged itself. Those catalysts in turn control all the chemical production and regulatory functions of an organism, and hence define the organism itself, crucially including a process that makes a copy of the DNA. How that intricate mechanism evolved is not essential here, but for definiteness let me sketch one possibility.

Genes are replicators that can be interpreted as instructions in a genetic code. Genomes are groups of genes that are dependent on each other for replication. The process of copying a genome is called a living organism. Thus the genetic code is also a language for specifying organisms. At some point, the system switched to replicators made of DNA, which is more stable than RNA and therefore more suitable for storing large amounts of information.

In 1994 the computer scientist and molecular biologist Leonard Adleman designed and built a computer composed of DNA together with some simple enzymes, and demonstrated that it was capable of performing some sophisticated computations. At the time, Adleman’s DNA computer was arguably the fastest computer in the world. Further, it was clear that a universal classical computer could be made in a similar way. Hence we know that, whatever that other universality of the DNA system was, the universality of computation had also been inherent in it for billions of years, without ever being used – until Adleman used it.

I think we have to face the fact, both with artificial evolution and with AI, that these are hard problems. There are serious unknowns in how those phenomena were achieved in nature. Trying to achieve them artificially without ever discovering those unknowns was perhaps worth trying. But it should be no surprise that it has failed. Specifically, we do not know why the DNA code, which evolved to describe bacteria, has enough reach to describe dinosaurs and humans. And, although it seems obvious that an AI will have qualia and consciousness, we cannot explain those things. So long as we cannot explain them, how can we expect to simulate them in a computer program? Or why should they emerge effortlessly from projects designed to achieve something else? But my guess is that when we do understand them, artificially implementing evolution and intelligence and its constellation of associated attributes will then be no great effort.