The Beginning of Infinity

by David Deutsch

  There is a saying that an ounce of prevention equals a pound of cure. But that is only when one knows what to prevent. No precautions can avoid problems that we do not yet foresee. To prepare for those, there is nothing we can do but increase our ability to put things right if they go wrong. Trying to rely on the sheer good luck of avoiding bad outcomes indefinitely would simply guarantee that we would eventually fail without the means of recovering.

  The world is currently buzzing with plans to force reductions in gas emissions at almost any cost. But it ought to be buzzing much more with plans to reduce the temperature, or for how to thrive at a higher temperature. And not at all costs, but efficiently and cheaply. Some such plans exist – for instance to remove carbon dioxide from the atmosphere by a variety of methods; and to generate clouds over the oceans to reflect sunlight; and to encourage aquatic organisms to absorb more carbon dioxide. But at the moment these are very minor research efforts. Neither supercomputers nor international treaties nor vast sums are devoted to them. They are not central to the human effort to face this problem, or problems like it.

  This is dangerous. There is as yet no serious sign of retreat into a sustainable lifestyle (which would really mean achieving only the semblance of sustainability), but even the aspiration is dangerous. For what would we be aspiring to? To forcing the future world into our image, endlessly reproducing our lifestyle, our misconceptions and our mistakes. But if we choose instead to embark on an open-ended journey of creation and exploration whose every step is unsustainable until it is redeemed by the next – if this becomes the prevailing ethic and aspiration of our society – then the ascent of man, the beginning of infinity, will have become, if not secure, then at least sustainable.

  TERMINOLOGY

  The ascent of man The beginning of infinity. Moreover, Jacob Bronowski’s The Ascent of Man was one of the inspirations for this book.

  Sustain The term has two almost opposite, but often confused, meanings: to provide someone with what they need, and to prevent things from changing.

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

  – Rejecting (the semblance of) sustainability as an aspiration or a constraint on planning.

  SUMMARY

  Static societies eventually fail because their characteristic inability to create knowledge rapidly must eventually turn some problem into a catastrophe. Analogies between such societies and the technological civilization of the West today are therefore fallacies. Marx, Engels and Diamond’s ‘ultimate explanation’ of the different histories of different societies is false: history is the history of ideas, not of the mechanical effects of biogeography. Strategies to prevent foreseeable disasters are bound to fail eventually, and cannot even address the unforeseeable. To prepare for those, we need rapid progress in science and technology and as much wealth as possible.

  18

  The Beginning

  ‘This is Earth. Not the eternal and only home of mankind, but only a starting point of an infinite adventure. All you need do is make the decision [to end your static society]. It is yours to make.’

  [With that decision] came the end, the final end of Eternity. – And the beginning of Infinity.

  Isaac Asimov, The End of Eternity (1955)

  The first person to measure the circumference of the Earth was the astronomer Eratosthenes of Cyrene, in the third century BCE. His result was fairly close to the actual value, which is about 40,000 kilometres. For most of history this was considered an enormous distance, but with the Enlightenment that conception gradually changed, and nowadays we think of the Earth as small. That was brought about mainly by two things: first, by the science of astronomy, which discovered titanic entities compared with which our planet is indeed unimaginably tiny; and, second, by technologies that have made worldwide travel and communication commonplace. So the Earth has become smaller both relative to the universe and relative to the scale of human action.

  Thus, in regard to the geography of the universe and to our place in it, the prevailing world view has rid itself of some parochial misconceptions. We know that we have explored almost the whole surface of that formerly enormous sphere; but we also know that there are far more places left to explore in the universe (and beneath the surface of the Earth’s land and oceans) than anyone imagined while we still had those misconceptions.

  In regard to theoretical knowledge, however, the prevailing world view has not yet caught up with Enlightenment values. Thanks to the fallacy and bias of prophecy, a persistent assumption remains that our existing theories are at or fairly close to the limit of what it is knowable – that we are nearly there, or perhaps halfway there. As the economist David Friedman has remarked, most people believe that an income of about twice their own should be sufficient to satisfy any reasonable person, and that no genuine benefit can be derived from amounts above that. As with wealth, so with scientific knowledge: it is hard to imagine what it would be like to know twice as much as we do, and so if we try to prophesy it we find ourselves just picturing the next few decimal places of what we already know. Even Feynman made an uncharacteristic mistake in this regard when he wrote:

  I think there will certainly not be novelty, say for a thousand years. This thing cannot keep going on so that we are always going to discover more and more new laws. If we do, it will become boring that there are so many levels one underneath the other . . . We are very lucky to live in an age in which we are still making discoveries. It is like the discovery of America – you only discover it once.

  The Character of Physical Law (1965)

  Among other things, Feynman forgot that the very concept of a ‘law’ of nature is not cast in stone. As I mentioned in Chapter 5, this concept was different before Newton and Galileo, and it may change again. The concept of levels of explanation dates from the twentieth century, and it too will change if I am right that, as I guessed in Chapter 5, there are fundamental laws that look emergent relative to microscopic physics. More generally, the most fundamental discoveries have always, and will always, not only consist of new explanations, but use new modes of explanation. As for being boring, that is merely a prophecy that criteria for judging problems will not evolve as fast as the problems themselves; but there is no argument for that other than a failure of imagination. Even Feynman cannot get round the fact that the future is not yet imaginable.

  Shedding that kind of parochialism is something that will have to be done again and again in the future. A level of knowledge, wealth, computer power or physical scale that seems absurdly huge at any given instant will later be considered pathetically tiny. Yet we shall never reach anything like an unproblematic state. Like the guests at Infinity Hotel, we shall never be ‘nearly there’.

  There are two versions of ‘nearly there’. In the dismal version, knowledge is bounded by laws of nature or supernatural decree, and progress has been a temporary phase. Though this is rank pessimism by my definition, it has gone under various names – including ‘optimism’ – and has been integral to most world views in the past. In the cheerful version, all remaining ignorance will soon be eliminated or confined to insignificant areas. This is optimistic in form, but the closer one looks, the more pessimistic it becomes in substance. In politics, for instance, utopians promise that a finite number of already-known changes can bring about a perfected human state, and that is a well-known recipe for dogmatism and tyranny.

  In physics, imagine that Lagrange had been right that ‘the system of the world can be discovered only once’, or that Michelson had been right that all physics still undiscovered in 1894 was about ‘the sixth place of decimals’. They were claiming to know that anyone who subsequently became curious about what underlay that ‘system of the world’ would be enquiring futilely into the incomprehensible. And that anyone who ever wondered at an anomaly, and suspected that some fundamental explanation contained a misconception, would be mistaken.

  Michelson’s future – our present – would have been lack
ing in explanatory knowledge to an extent that we can no longer easily imagine. A vast range of phenomena already known to him, such as gravity, the properties of the chemical elements, and the luminosity of the sun, remained to be explained. He was claiming that these phenomena would only ever appear as list of facts or rules of thumb, to be memorized but never understood or fruitfully questioned. Every such frontier of fundamental knowledge that existed in 1894 would have been a barrier beyond which nothing would ever be amenable to explanation. There would be no such thing as the internal structure of atoms, no dynamics of space and time, no such subject as cosmology, no explanation for the equations governing gravitation or electromagnetism, no connections between physics and the theory of computation . . . The deepest structure in the world would be an inexplicable, anthropocentric boundary, coinciding with the boundary of what the physicists of 1894 thought they understood. And nothing inside that boundary – like, say, the existence of a force of gravity – would ever turn out to be profoundly false.

  Nothing very important would ever be discovered in the laboratory that Michelson was opening. Each generation of students who studied there, instead of striving to understand the world more deeply than their teachers, could aspire to nothing better than to emulate them – or, at best, to discover the seventh decimal place of some constant whose sixth was already known. (But how? The most sensitive scientific instruments today depend on fundamental discoveries made after 1894.) Their system of the world would for ever remain a tiny, frozen island of explanation in an ocean of incomprehensibility. Michelson’s ‘fundamental laws and facts of physical science’, instead of being the beginning of an infinity of further understanding, as they were in reality, would have been the last gasp of reason in the field.

  I doubt that either Lagrange or Michelson thought of himself as pessimistic. Yet their prophecies entailed the dismal decree that no matter what you do, you will understand no further. It so happens that both of them had made discoveries which could have led them to the very progress whose possibility they denied. They should have been seeking that progress, should they not? But almost no one is creative in fields in which they are pessimistic.

  I remarked at the end of Chapter 13 that the desirable future is one where we progress from misconception to ever better (less mistaken) misconception. I have often thought that the nature of science would be better understood if we called theories ‘misconceptions’ from the outset, instead of only after we have discovered their successors. Thus we could say that Einstein’s Misconception of Gravity was an improvement on Newton’s Misconception, which was an improvement on Kepler’s. The neo-Darwinian Misconception of Evolution is an improvement on Darwin’s Misconception, and his on Lamarck’s. If people thought of it like that, perhaps no one would need to be reminded that science claims neither infallibility nor finality.

  Perhaps a more practical way of stressing the same truth would be to frame the growth of knowledge (all knowledge, not only scientific) as a continual transition from problems to better problems, rather than from problems to solutions or from theories to better theories. This is the positive conception of ‘problems’ that I stressed in Chapter 1. Thanks to Einstein’s discoveries, our current problems in physics embody more knowledge than Einstein’s own problems did. His problems were rooted in the discoveries of Newton and Euclid, while most problems that preoccupy physicists today are rooted in – and would be inaccessible mysteries without – the discoveries of twentieth-century physics.

  The same is true in mathematics. Although mathematical theorems are rarely proved false once they have been around for a while, what does happen is that mathematicians’ understanding of what is fundamental improves. Abstractions that were originally studied in their own right are understood as aspects of more general abstractions, or are related in unforeseen ways to other abstractions. And so progress in mathematics also goes from problems to better problems, as does progress in all other fields.

  Optimism and reason are incompatible with the conceit that our knowledge is ‘nearly there’ in any sense, or that its foundations are. Yet comprehensive optimism has always been rare, and the lure of the prophetic fallacy strong. But there have always been exceptions. Socrates famously claimed to be deeply ignorant. And Popper wrote:

  I believe that it would be worth trying to learn something about the world even if in trying to do so we should merely learn that we do not know much . . . It might be well for all of us to remember that, while differing widely in the various little bits we know, in our infinite ignorance we are all equal.

  Conjectures and Refutations (1963)

  Infinite ignorance is a necessary condition for there to be infinite potential for knowledge. Rejecting the idea that we are ‘nearly there’ is a necessary condition for the avoidance of dogmatism, stagnation and tyranny.

  In 1996 the journalist John Horgan caused something of a stir with his book The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age. In it, he argued that the final truth in all fundamental areas of science – or at least as much of it as human minds would ever be capable of grasping – had already been discovered during the twentieth century.

  Horgan wrote that he had originally believed science to be ‘open-ended, even infinite’. But he became convinced of the contrary by (what I would call) a series of misconceptions and bad arguments. His basic misconception was empiricism. He believed that what distinguishes science from unscientific fields such as literary criticism, philosophy or art is that science has the ability to ‘resolve questions’ objectively (by comparing theories with reality), while other fields can produce only multiple, mutually incompatible interpretations of any issue. He was mistaken in both respects. As I have explained throughout this book, there is objective truth to be found in all those fields, while finality or infallibility cannot be found anywhere.

  Horgan accepts from the bad philosophy of ‘postmodern’ literary criticism its wilful confusion between two kinds of ‘ambiguity’ that can exist in philosophy and art. The first is the ‘ambiguity’ of multiple true meanings, either intended by the author or existing because of the reach of the ideas. The second is the ambiguity of deliberate vagueness, confusion, equivocation or self-contradiction. The first is an attribute of deep ideas, the second an attribute of deep silliness. By confusing them, one ascribes to the best art and philosophy the qualities of the worst. Since, in that view, readers, viewers and critics can attribute any meaning they choose to the second kind of ambiguity, bad philosophy declares the same to be true of all knowledge: all meanings are equal, and none of them is objectively true. One then has a choice between complete nihilism or regarding all ‘ambiguity’ as a good thing in those fields. Horgan chooses the latter option: he classifies art and philosophy as ‘ironic’ fields, irony being the presence of multiple conflicting meanings in a statement.

  However, unlike the postmodernists, Horgan thinks that science and mathematics are the shining exceptions to all that. They alone are capable of non-ironic knowledge. But there is also, he concludes, such a thing as ironic science – the kind of science that cannot ‘resolve questions’ because, essentially, it is just philosophy or art. Ironic science can continue indefinitely, but that is precisely because it never resolves anything; it never discovers objective truth. Its only value is in the eye of the beholder. So the future, according to Horgan, belongs to ironic knowledge. Objective knowledge has already reached its ultimate bounds.

  Horgan surveys some of the open questions of fundamental science, and judges them all either ‘ironic’ or non-fundamental, in support of his thesis. But that conclusion was made inevitable by his premises alone. For consider the prospect of any future discovery that would constitute fundamental progress. We cannot know what it is, but bad philosophy can already split it, on principle, into a new rule of thumb and a new ‘interpretation’ (or explanation). The new rule of thumb cannot possibly be fundamental: it will just be another equation. Only a trained expert
could tell the difference between it and the old equation. The new ‘interpretation’ will by definition be pure philosophy, and hence must be ‘ironic’. By this method, any potential progress can be pre-emptively reinterpreted as non-progress.

  Horgan rightly points out that his prophecy cannot be proved false by placing it in the context of previous failed prophecies. The fact that Michelson was wrong about the achievements of the nineteenth century, and Lagrange about those of the seventeenth, does not imply that Horgan was wrong about those of the twentieth. However, it so happens that our current scientific knowledge includes a historically unusual number of deep, fundamental problems. Never before in the history of human thought has it been so obvious that our knowledge is tiny and our ignorance vast. And so, unusually, Horgan’s pessimism contradicts existing knowledge as well as being a prophetic fallacy. For example, the problem-situation of fundamental physics today has a radically different structure from that of 1894. Although physicists then were aware of some phenomena and theoretical issues which we now recognize as harbingers of the revolutionary explanations to come, their importance was unclear at the time. It was hard to distinguish those harbingers from anomalies that would eventually be cleared up with existing explanations plus the tweaking of the ‘sixth place of decimals’ or minor terms in a formula. But today there is no such excuse for denying that some of our problems are fundamental. Our best theories are telling us of profound mismatches between themselves and the reality that they are supposed to explain.