The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

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.

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.

Replicator An entity that contributes causally to its own copying.

Meme An idea that is a replicator.

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

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.

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.

And indeed it seems to be a recurring theme in the early history of many fields that universality, when it was achieved, was not the primary objective, if it was an objective at all. A small change in a system to meet a parochial purpose just happened to make the system universal as well. This is the jump to universality

highest-valued symbol M for 10,000 (one myriad).

A jump to universality that played an important role in the early history of the Enlightenment was the invention of movable-type printing. Movable type consisted of individual pieces of metal, each embossed with one letter of the alphabet. Earlier forms of printing had merely streamlined writing in the same way that Roman numerals streamlined tallying: each page was engraved on a printing plate and thus all the symbols on it could be copied in a single action. But, given a supply of movable type with several instances of each letter, one does no further metalwork. One merely arranges the type into words and sentences. One does not have to know, in order to manufacture type, what the documents that it will eventually print are going to say: it is universal. Even so, movable type did not make much difference when it was invented in China in the eleventh century, perhaps because of the usual lack of interest in universality, or perhaps because the Chinese writing system used thousands of pictograms, which diminished the immediate advantages of a universal printing system. But when it was reinvented by the printer Johannes Gutenberg in Europe in the fifteenth century, using alphabetic type, it initiated an avalanche of further progress.

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.

One such catalyst happened to catalyse the formation of some of the very kinds of molecules from which it itself was formed. That catalyst was not alive, but it was the first hint of life.

Different replicators began to join forces in groups, each of whose members specialized in causing one part of a complex web of chemical reactions whose net effect was to construct more copies of the entire group. Such a group was a rudimentary organism.

The most successful replicators may have been RNA molecules.

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.

The jump to universality The tendency of gradually improving systems to undergo a sudden large increase in functionality, becoming universal in some domain.

Now known as the Turing test, it is simply that a suitable (human) judge be unable to tell whether the program is human or not.

But the joke would have quite a different significance if we knew that it was not a stock joke – because no such joke had ever been encoded into the program.

The mathematician David Hilbert devised a thought experiment to illustrate some of the intuitions that one has to drop when reasoning about infinity. He imagined a hotel with infinitely many rooms: Infinity Hotel. The rooms are numbered with the natural numbers, starting with 1 and ending with – what?

But Infinity Hotel always has room for more. One of the conditions of staying there is that guests have to change rooms if asked to by the management. So, if a new guest arrives, the management just announce over the public-address system, ‘Will all guests please move immediately to the room numbered one more than their current room.’ Thus, in the manner of the first illustration in this chapter, the existing occupant of room 1 moves to room 2, whose occupant moves to room 3, and so on. What happens at the last room? There is no last room, and hence no problem about what happens there. The new arrival can now move into room 1. At Infinity Hotel, it is never necessary to make a reservation.

However, it is mathematically possible to overwhelm the capacity of Infinity Hotel. In a remarkable series of discoveries in the 1870s, Cantor proved, among other things, that not all infinities are equal.

the number of points in a finite line (which is the same as the number of points in the whole of space or spacetime) – is much larger than the infinity of the natural numbers.

An infinity that is small enough to be placed in one-to-one correspondence with the natural numbers is called a ‘countable infinity’ – rather an unfortunate term, because no one can count up to infinity. But it has the connotation that every element of a countably infinite set could in principle be reached by counting those elements in some suitable order. Larger infinities are called uncountable

The fallacious idea of delegating all one’s work to other staff in higher-numbered rooms is called an infinite regress. It is one of the things that one cannot validly do with infinity. There is an old joke about the heckler who interrupts an astrophysics lecture to insist that the Earth is flat and supported on the back of elephants standing on a giant turtle. ‘What supports the turtle?’ asks the lecturer. ‘Another turtle.’ ‘What supports that turtle?’ ‘You can’t fool me,’ replies the heckler triumphantly: ‘it’s turtles from there on down.

The theory that the designer of the biosphere was designed by another designer, and so on ad infinitum, is another example of an infinite regress.)

The possibilities that lie in the future are infinite. When I say ‘It is our duty to remain optimists,’ this includes not only the openness of the future but also that which all of us contribute to it by everything we do: we are all responsible for what the future holds in store. Thus it is our duty, not to prophesy evil but, rather, to fight for a better world.

Martin Rees suspects that civilization was lucky to survive the twentieth century. For throughout the Cold War there was always a possibility that another world war would break out, this time fought with hydrogen bombs, and that civilization would be destroyed.

That danger seems to have receded, but in Rees’s book Our Final Century, published in 2003, he came to the worrying conclusion that civilization now had only a 50 per cent chance of surviving the twenty-first century.

Rees pointed out that, for his conclusion to hold, it is not necessary for any one of those catastrophes to be at all probable, because we need be unlucky only once, and we incur the risk afresh every time progress is made in a variety of fields. He compared this with playing Russian roulette.

The future of civilization is unknowable, because the knowledge that is going to affect it has yet to be created. Hence the possible outcomes are not yet known, let alone their probabilities.

the statesman Winston Churchill suffered from intense depression, yet his outlook on the future of civilization, and his specific expectations as wartime leader, were unusually positive.

Genetic studies suggest that our own species came close to extinction about 70,000 years ago, as a result of an unknown catastrophe which reduced its total numbers to only a few thousand.

We have such a chance because we are able to solve problems. Problems are inevitable. We shall always be faced with the problem of how to plan for an unknowable future. We shall never be able to afford to sit back and hope for the best.

Sparta was, in all the above respects, the opposite of Athens. The epitome of a pessimistic civilization, it was notorious for its citizens’ austere ‘spartan’ lifestyle, for the harshness of its educational system, and for the total militarization of its society.

All other work was done by slaves: Sparta had reduced an entire neighbouring society, the Messenians, to the status of helots (a kind of serf or slave). It had no philosophers, historians, artists, architects, writers – or other knowledge-creating people of any kind apart from the occasional talented general. Thus almost the entire effort of the society was devoted to preserving itself in its existing state – in other words, to preventing improvement.

Scientific theories are hard to vary because they correspond closely with an objective truth, which is independent of our culture, our personal preferences and our biological make-up.

Art can be literally attractive in the sense of causing people to move towards it. Visitors to an art gallery can see a painting and be reluctant to leave, and then later be caused, by the painting, to return to it. People may travel great distances to hear a musical performance – and so on. If you see a work of art that you appreciate, that means that you want to dwell on it, to give it your attention, in order to appreciate more in it. If you are an artist, and halfway through creating a work of art you see something in it that you want to bring out, then you are being attracted by a beauty that you have not yet experienced. You are being attracted by the idea of a piece of art before you have created it.

New art is unpredictable, like new scientific discoveries. Is that the unpredictability of randomness, or the deeper unknowability of knowledge-creation? In other words, is art truly creative, like science and mathematics?

the mechanism could work only because insects, at the same time, evolved genes that attracted them to flowers. Why did they? Because flowers provide nectar, which is food. Just as there is co-evolution between the genes to coordinate mating behaviours in males and females of the same species, so genes for making flowers and giving them their shapes and colours co-evolved with genes in insects for recognizing flowers with the best nectar.

Nevertheless, cultures change. People modify cultural ideas in their minds, and sometimes they pass on the modified versions. Inevitably, there are unintentional modifications as well, partly because of straightforward error, and partly because inexplicit ideas are hard to convey accurately: there is no way to download them directly from one brain to another like computer programs. Even native speakers of a language will not give identical definitions of every word. So it can be only rarely, if ever, that two people hold precisely the same cultural idea in their minds. That is why, when the founder of a political or philosophical movement or a religion dies, or even before, schisms typically happen. The movement’s most devoted followers are often shocked to discover that they disagree about what its doctrines ‘really’ are.

Thus a culture is in practice defined not by a set of strictly identical memes, but by a set of variants that cause slightly different characteristic behaviours. Some variants tend to have the effect that their holders are eager to enact or talk about them, others less so.

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.

That makes the resulting ‘natural histories’ different too. There is no close cultural analogue of a species, or of an organism, or a cell, or of sexual or asexual reproduction. Genes and memes are about as different as can be at the level of mechanisms, and of outcomes; they

In the classic 1956 science-fiction story ‘Jokester’, by Isaac Asimov, the main character is a scientist studying jokes. He finds that, although most people do sometimes make witty remarks that are original, they never invent what he considers to be a fully fledged joke: a story with a plot and a punchline that causes listeners to laugh.

As I have explained, a human brain – quite unlike a genome – is itself an arena of intense variation, selection and competition. Most ideas within a brain are created by it for the very purpose of trying them out in imagination, criticizing them, and varying them until they meet the person’s preferences. In other words, meme replication itself involves evolution, within individual brains.

But in a static society that beginning of infinity never happens. Despite the fact that I have assumed nothing other than that people try to improve their lives, and that they cannot transmit their ideas perfectly, and that information subject to variation and selection evolves, I have entirely failed to imagine a static society in this story. For a society to be static, something else must be happening as well. One thing my story did not take into account is that static societies have customs and laws – taboos – that prevent their memes from changing.

The golden ages of Athens and Florence are examples of the latter, but there may have been many others. This directly contradicts the widely held belief that individuals in primitive societies were happy in a way that has not been possible since – that they were unconstrained by social convention and other imperatives of civilization, and hence were able to achieve self-expression and fulfilment of their needs and desires. But primitive societies (including tribes of hunter-gatherers) must all have been static societies, because if ever one ceased to be static it would soon cease to be primitive, or else destroy itself by losing its distinctive knowledge. In the latter case, the growth of knowledge would still be inhibited by the raw violence which would immediately replace the static society’s institutions. For

Newton’s laws are useful for building better cathedrals, but also for building better bridges and designing better artillery. Because of this reach, they get themselves remembered and enacted by all sorts of people, many of them vehemently opposed to each other’s objectives, over many generations. This is the kind of idea that has a chance of becoming a long-lived meme in a rapidly changing society.

Present-day methods of education still have a lot in common with their static-society predecessors. Despite modern talk of encouraging critical thinking, it remains the case that teaching by rote and inculcating standard patterns of behaviour through psychological pressure are integral parts of education, even though they are now wholly or partly renounced in explicit theory. Moreover, in regard to academic knowledge, it is still taken for granted, in practice, that the main purpose of education is to transmit a standard curriculum faithfully. One consequence is that people are acquiring scientific knowledge in an anaemic and instrumental way. Without a critical, discriminating approach to what they are learning, most of them are not effectively replicating the memes of science and reason into their minds.

Moreover, during the period when creativity was evolving, the ability to replicate memes was evolving too. It is believed that some members of the species Homo erectus living 500,000 years ago knew how to make camp fires. That knowledge was in their memes, not in their genes. And, once creativity and meme transmission are both present, they greatly enhance each other’s evolutionary value, for then anyone who improves something also has the means to bequeath the innovation to all future generations, thus multiplying the benefit to the relevant genes. And memes can be improved much faster by creativity than by random trial and error. Since there is no upper limit to the value of ideas, the conditions would have been there for a runaway co-evolution between the two adaptations: creativity and the ability to use memes.