The Philosophers of Progress

The longitude problem

For four hundred years, sailors out of sight of land could tell you exactly how far north or south they were, and only guess how far east or west. Latitude is easy: measure the angle of the sun at noon, or the pole star at night, and the arithmetic falls out. Longitude requires knowing the time in two places at once, the time where you are and the time at some fixed reference point, because the earth turns fifteen degrees an hour and the difference between the two clocks tells you how far you have travelled around it. The trouble was that no clock built before the eighteenth century could keep reliable time on a rolling, pitching, temperature-swinging ship for the months a long voyage required. On land a pendulum clock might lose a few seconds a week. At sea the same clock, thrown about by weather and salt air, could be off by a quarter of an hour a day, which at the equator is enough to misplace a ship by two hundred and fifty miles. Men who thought they were approaching open water sailed onto rocks. In 1707 a squadron of British warships, uncertain of its longitude in fog, ran aground off the Scilly Isles and something close to two thousand sailors drowned within sight of England. It was one of the oldest and most stubborn problems in the practical world, and for most of human history it looked less like a problem than like a fact of nature, a permanent tax on anyone who went to sea.

Galileo tried to solve it by timing the eclipses of Jupiter's moons, an elegant idea that required an astronomer's patience and a dead calm sea, neither of which a working ship's captain could supply. Isaac Newton thought the answer would come from astronomy, from ever more precise tables of the moon's position against the stars, and said so to a parliamentary committee in 1714, the year Britain finally put up a prize of twenty thousand pounds, a fortune, for anyone who could solve the problem to an accuracy of half a degree. Newton, the greatest scientific mind of his age, was betting on the wrong kind of answer. The winning idea came instead from a Yorkshire carpenter's son named John Harrison, who had never attended a university and who spent four decades building a series of clocks, each one a fanatical refinement on the last, using self-lubricating woods, temperature-compensating metal strips, and a strange grasshopper-shaped escapement of his own invention, until by 1761 his fourth marine chronometer lost only five seconds on a two-month voyage to Jamaica. The Board of Longitude, dominated by astronomers with a professional stake in the astronomical answer, dragged its feet for another decade before grudgingly paying him something close to the full prize, boards being at their most deliberate when the right answer has arrived from the wrong sort of man. But the argument was already over. You could now put a clock in a box, carry it to sea, and know where you were on the earth to within a few miles. A problem that had drowned sailors for four centuries, that generations of the ablest minds in Europe had treated as a near-permanent condition of ocean travel, turned out to have a solution sitting inside a Yorkshireman's workshop the whole time. Nobody had needed a change in the laws of physics. They had needed a better idea. The deepest optimism available to a thinking person rests not on data but on epistemology, on a theory of what knowledge is and how it grows. David Deutsch's argument that all problems are soluble, given the right knowledge, is the strongest form optimism has ever taken. Ray Kurzweil's exponential curves, which promise much the same future on a fixed timetable, are a guess wearing arithmetic. And the difference between prediction and prophecy, between a forecast that inherits the precision of a good explanation and one that merely extends a line on a chart, decides which of the two men deserves to be believed.

A second story, from a different century and a different discipline, makes the same point in a different key. In 1721, a Boston minister named Cotton Mather, of all unlikely people, read an account of a practice used in Ottoman Turkey and parts of West Africa, in which a small amount of live matter from a smallpox pustule was deliberately introduced into a scratch on a healthy person's arm, producing a mild case of the disease that conferred lasting immunity against the far more lethal natural infection. Mather had learned of the practice, called variolation, partly from a Boston physician and partly from Onesimus, an enslaved African man in his own household who described undergoing exactly this procedure as a child. Smallpox at the time killed perhaps three in ten of the people it infected and scarred or blinded most of the rest, and it had done so, generation after generation, for as long as anyone could remember; a plague on this scale looked, to nearly everyone who lived through repeated outbreaks of it, like weather, an affliction to be endured rather than a puzzle to be solved. Mather's advocacy for variolation during a Boston epidemic met with fury, mob threats, and a bomb thrown through his window, because the idea of deliberately infecting the healthy struck most of his contemporaries as reckless bordering on murderous. It took the better part of a century, and then Edward Jenner's discovery in 1796 that the far milder cowpox virus could confer the same immunity with none of variolation's real risk of starting a fresh epidemic, before vaccination became a settled and rapidly spreading practice. By 1980 the World Health Organization was able to declare smallpox eradicated from the face of the earth, the only human disease ever to be deliberately erased rather than merely treated. A killer that had shaped human history for thousands of years, that the Pharaoh Ramses V appears to have died of and whose scars are visible on his three-thousand-year-old mummy, turned out not to be a fixed cost of being human at all. It was a problem waiting for an explanation, and once Jenner had the explanation, the problem, remarkably, simply ended.

That ending holds the whole claim in miniature: a problem, however old, however many generations have broken themselves against it, is not the same thing as a fate. A fate is what remains once every possible remedy has been tried and failed for reasons built into the structure of reality. A problem is what remains because nobody has yet had the right idea, and having the right idea is always, in principle, possible for a being that can think. The distinction sounds almost too simple to bear the philosophical weight I am about to put on it. It carries the weight anyway. Much of what people are inclined to call human nature, the incurable folly of politics, the fixed limits of the human mind, the assumption that certain kinds of suffering are simply the price of being alive, rests on a failure to distinguish between the two. Longitude was not solved because human beings became wiser or kinder or more patient. It was solved because one stubborn craftsman had an explanation nobody else had thought of, and the explanation, once it existed, could be checked, copied, and improved. That is nearly the entire argument of David Deutsch's The Beginning of Infinity, a book that takes this observation, so modest and so easily overlooked, and follows it all the way down to the foundations of physics and all the way up to the future of civilisation.

Deutsch's wager

David Deutsch is not a professional optimist. He is a theoretical physicist at Oxford, and among the small number of people credited with founding the field of quantum computation: in the 1980s, well before anyone had built a working quantum computer, he worked out the theoretical case for why a computer exploiting the peculiarities of quantum mechanics, in which a particle can in some sense be in several states at once, might solve certain problems no classical machine ever could. This is not the biography of a man given to wishful thinking. It is the biography of a man who spends his working life inside the most exacting and unforgiving of the sciences, where a wrong idea is not merely embarrassing but demonstrably, mathematically wrong, and where being right requires an explanation so precise it can be checked against nature and found either to survive or to fail. He conducts most of this life from a house outside Oxford that he rarely leaves, on the reasonable view that the universe is equally available from there. His first book for a general audience, The Fabric of Reality (1997), made the case, seriously and at length, for the "many worlds" interpretation of quantum mechanics, the unsettling idea that every quantum event branches the universe into multiple actual histories rather than collapsing into one. The Beginning of Infinity (2011) is its successor in spirit though not in subject, a five-hundred-page argument that ranges from the theory of knowledge to political philosophy to aesthetics to the nature of creativity, written, quite deliberately, against the grain of a fashionable pessimism that had settled over the previous few decades, the sense that human beings had overreached, that the wise course now was to learn our limits and live modestly within them.

Deutsch's answer to that mood is a sentence so plain it is easy to read past it: problems are inevitable, but problems are soluble. It sounds like a fortune cookie until you notice what work each half of it is doing. The first half is a rebuke to a certain kind of utopian thinking, the fantasy of a state of affairs in which nothing further needs fixing, a garden with no more weeds. Deutsch has no patience for this. New problems will always arise, he argues, because even a solved problem changes the conditions under which the next one appears, and because our knowledge, however good, is never complete and never will be. The second half is the rebuke to pessimism, and it is the half that gives the book its argument: a problem, properly understood, is not evidence of a limit. It is evidence of an absence, a gap where an explanation has not yet been found. And since explanations are things human minds make, and since there is nothing in principle that stops a mind from eventually making the explanation a given problem requires, no problem is fixed in place for all time. What was true of finding longitude at sea was true, on Deutsch's account, of curing smallpox, and will be true of whatever presently looks unsolvable, whether that is ageing, or catastrophic climate change, or the fact that large parts of the world remain miserably poor. He calls this the beginning of infinity: once a civilisation has acquired the knack of producing good explanations, the growth of knowledge has no discoverable endpoint, no ceiling built into the nature of things, only the boundary set by the laws of physics themselves. And that boundary, Deutsch insists, is astonishingly permissive. One of the book's most quoted claims, stated with the flatness of a theorem, is that anything not forbidden by the laws of nature is achievable, given the right knowledge. Interstellar travel is not forbidden. Lives of indefinite length are not forbidden. What stands between us and such things is not a wall; it is missing knowledge, and missing knowledge is the one deficiency that minds like ours are specifically equipped to repair.

Distinguish this at once from garden-variety optimism, the temperamental cheerfulness that expects things to work out because that is simply how the optimist is built. Deutsch's claim is not a mood. It is closer to an argument in epistemology, the branch of philosophy concerned with what knowledge is and how it grows, and it rests on a specific, contestable, and rather beautiful theory of what makes an explanation good in the first place. He borrows the theory from Karl Popper, the philosopher of science who spent much of his career arguing that scientific knowledge advances not by accumulating confirmations, the way a wall accumulates bricks, but by proposing bold explanations and then trying, as hard as possible, to prove them wrong. Deutsch's contribution, developed at length in The Beginning of Infinity, is to sharpen Popper's account of what separates a real explanation from an imitation of one, and the sharpening turns on a single, deceptively simple test: a good explanation is one that is hard to vary while still accounting for what it explains.

Deutsch returns more than once to one illustration, because it does so much work so cleanly. The ancient Greeks explained the changing of the seasons with the myth of Persephone: Demeter, goddess of the harvest, loves her daughter Persephone, who is abducted by Hades and made to spend part of each year in the underworld; while she is gone, Demeter grieves, and her grief withers the crops, and that withering is winter. It is a good story. It even fits the facts, in the loose sense that winter does indeed arrive once a year and does indeed involve the earth going quiet and cold. But notice how little of the story is actually pinned down by those facts. Why must Demeter's sorrow express itself as cold rather than, say, drought, or darkness, or plague? Why does the underworld release Persephone in spring rather than at the solstice, or at random? Why six months, why not four, why not a season that varies from year to year, as grief plausibly might? None of these details is forced by anything in the world. You could swap Persephone for another captive god, swap grief for anger, swap six months for a full year, and the story would still, after a little narrative massage, account for winter following summer and summer following winter, because it was never actually built out of the phenomenon. It was built to accompany the phenomenon, and any of a thousand variations would accompany it equally well. The myth also fails a plainer test, one Deutsch takes care to point out. Demeter's grief is the grief of a goddess, not a regional weather system, so the story implies that winter should descend on the whole earth at once. It does not. When Greece shivers, Australia bakes; the seasons of the two hemispheres run in opposite phase, a fact the myth's tellers did not know and their story never predicted. And had they learned it, no crisis would have followed: a resourceful priest could have patched the tale in an afternoon, a second goddess for the south, a quarrel between the two, the amendment ratified before dinner, and that very ease of repair is the condemnation. That, for Deutsch, is the signature of a bad explanation: it can be endlessly varied and still appear to work, because nothing in it is load-bearing.

Compare this with the modern explanation for the seasons, which is that the earth's axis is tilted at roughly twenty-three and a half degrees relative to the plane of its orbit around the sun, so that as the earth makes its year-long circuit, first the northern hemisphere and then the southern hemisphere leans toward the sun and receives more direct, concentrated light, and then leans away and receives less. Try to vary this explanation and see how far you get. Change the angle of the tilt and you change the severity of the seasons in a way that can be measured and checked against the actual variation observed. Remove the tilt altogether and the seasons disappear, which is exactly why the tropics, which face the sun at close to the same angle year-round, have no real winter. Change the shape of the orbit instead of the tilt and you get a different, wrong prediction, one that does not match what telescopes and thermometers actually record. Every element of the account, the angle, the orbit, the geometry of a sphere lit from one side, is locked into place by the others and by the observable world; alter any one piece and the explanation stops explaining, or starts predicting something false. It is, in Deutsch's phrase, hard to vary, and that hardness is not a stylistic virtue, a matter of the explanation being elegant or satisfying. It is the very thing that allows the explanation to be tested, refined, and, crucially, built upon. You cannot use the Persephone myth to predict anything you did not already know. You can use axial tilt to predict the length of the day at any latitude on any date, to calculate when the sun will fail to set above the Arctic Circle, to say what the seasons must be doing right now on Mars, a planet nobody who worked out the theory ever expected anyone to visit. Deutsch has a name for this surplus: reach. Because every part of a good explanation is pinned to reality rather than to the convenience of the teller, the explanation ends up solving problems its creators never posed, and this unearned generosity, he argues, is the most reliable mark of having explained something real rather than merely narrated it. A good explanation is not merely consistent with the world; it is entangled with it, and the entanglement is what makes further discovery possible.

This criterion becomes, over the course of the book, Deutsch's instrument for cutting through an enormous amount of confused thinking, because it turns out that a great deal of what passes for explanation, in religion, in folk wisdom, in bad science, and in much contemporary talk about artificial intelligence, fails the test. Astrology fails it: whatever a horoscope says about a Scorpio's temperament could, with minor adjustment, be said with equal plausibility of a Capricorn, which is why astrology has never once been used to predict something nobody already suspected, a record of failure it has now maintained, without a single lapse, for some four thousand years. Homeopathy fails it, for similar reasons. And Deutsch's claim, the one that gives the whole book its momentum, is that human beings are the only entities we know of capable of reliably producing explanations of the hard-to-vary kind, and that this capacity, once it exists anywhere, has no natural stopping point. A mind that can produce one such explanation can in principle go on producing them indefinitely, because the same faculty, conjecture followed by ruthless criticism, is what is doing the work each time, whether the subject is the tilt of the earth or the chemistry of a vaccine or the design of a marine chronometer.

What Popper actually added

Deutsch is scrupulous about naming his debts, and the largest of them is to Karl Popper; a reader who does not know it will miss how much of the architecture of The Beginning of Infinity was already standing before Deutsch arrived to build on top of it. Popper was a Viennese philosopher who left Austria in 1937, a year before the Anschluss, for a lectureship in New Zealand, and who spent the rest of a long career, mostly at the London School of Economics, arguing against what he took to be the dominant and mistaken picture of how scientific knowledge grows. That picture, inherited from a long empiricist tradition running back through John Stuart Mill, held that science proceeds by induction: you observe many instances of something, white swans, say, and you accumulate confidence in a general law, all swans are white, in rough proportion to the number of confirming instances you have collected. Popper thought this picture was not merely incomplete but essentially backwards, and he made his case with a memorable and now famous example: no finite number of white swans, however large, can ever logically prove that all swans are white, because the very next swan around the corner might be black, as indeed Dutch sailors found when they reached Australia in 1697 and encountered swans that were black all over, an outcome no amount of prior swan-counting had prepared them for. What actually distinguishes a scientific claim, Popper argued in his first major book, Logik der Forschung, published in 1934 and later translated as The Logic of Scientific Discovery, is not that it can be confirmed but that it can be falsified, that it forbids something, sticks its neck out and specifies in advance what observation would prove it wrong. A theory that is compatible with every possible observation, that cannot in principle be caught out by anything the world might do, is not a strong theory. It is not a theory at all, in the sense that matters, because it has not risked anything.

This is where Popper's own biography sharpens the point. He arrived at his theory partly by comparing Einstein's general theory of relativity, published in 1915, with the psychoanalytic theories of Freud and Adler that were fashionable in Vienna at the time. Einstein's theory made a frightening prediction, frightening in the exact sense that it staked the theory's life on a single measurement: light from distant stars would be measurably bent by the sun's gravity, an effect large enough to be checked by photographing a solar eclipse, which Arthur Eddington's expedition did in 1919, confirming the prediction and making Einstein famous overnight. Had the starlight not bent by the predicted amount, the theory would have been simply wrong, finished, and Einstein knew it and said so. Freudian and Adlerian psychology, by contrast, seemed to Popper capable of explaining any human behaviour whatsoever after the fact, a man who drowns a child exhibits repressed aggression, a man who dives in to save the child exhibits sublimated aggression, and a theory flexible enough to absorb both a man's cruelty and his heroism as confirming evidence had, on Popper's reading, forfeited the right to be called scientific, not because it was necessarily false but because it had made itself unfalsifiable, immune to correction by anything that could actually happen. It is, without much strain, exactly the same complaint Deutsch later levels against the Persephone myth: a story fitted to the facts after the fact, rather than a story that would break if the facts had gone differently.

From this grew Popper's account of how knowledge actually advances, which he called conjectures and refutations, the title he gave to a 1963 collection of his essays. A scientist, on this account, does not patiently accumulate observations until a theory crystallises out of them. She guesses, boldly and often wrongly, proposes an explanation that goes well beyond the available evidence, and then does everything she can to prove the guess wrong, because a conjecture that survives a serious attempt at refutation has earned, however provisionally, the right to be believed, while a conjecture that has never been seriously tested has earned nothing at all. Knowledge, in this picture, grows not by being proven but by surviving, the way a species survives not because nature has certified it fit but because it has not yet been eliminated by whatever the environment throws at it. Popper made the Darwinian comparison himself, calling the growth of knowledge a process of evolution, ideas competing, most failing, a few surviving to be varied and tested again. This is also where Popper's political philosophy connects directly to his epistemology, and it is the connection Deutsch leans on hardest. In his two-volume wartime work The Open Society and Its Enemies, written in New Zealand while the war raged and dedicated, in his own words, to the victims of an idea he considered totalitarian at its root, Popper argued that societies which suppress the criticism of their own governing ideas, whether those ideas are Plato's rule of philosopher kings, Hegel's unfolding of the world spirit through the state, or Marx's supposed laws of historical inevitability, do so at a terrible cost, because a closed society, like an unfalsifiable theory, has cut itself off from the only mechanism that ever actually corrects an error, which is exposure to the possibility of being shown wrong. Popper held this view with a fervour that, by the testimony of those who attended his seminars, he did not invariably extend to criticism of Popper; colleagues privately retitled the book The Open Society by One of Its Enemies. An open society tolerates, even institutionalises, the criticism of its own foundations, and pays for that tolerance with a permanent, low-grade discomfort, the discomfort of never being allowed to declare a question finally and forever settled. Deutsch's static and dynamic societies are Popper's closed and open societies transposed from twentieth-century political argument into a general theory of how civilisations relate to knowledge as such, and his hard-to-vary criterion is Popper's falsifiability turned around to face forward: not only must a good explanation be capable of being shown wrong, it must, by the specificity of its own construction, make plain exactly how.

One further Popperian thread runs straight into the quarrel with Kurzweil. In The Poverty of Historicism, Popper argued that the future course of human history cannot be predicted, and cannot in principle, for a reason that is logical rather than practical: the course of history is shaped, more than by anything else, by the growth of knowledge, and the growth of knowledge cannot be predicted, because predicting the content of tomorrow's discovery would amount to making that discovery today. Whoever could write down next decade's physics would not be forecasting it; he would be doing it, now, a decade early. The argument sounds like a lawyer's trick until one sees that it is airtight, and Popper drew from it a lifelong hostility toward every doctrine, Marxism above all, that claimed to have read the direction of history off its past. Hold on to that argument. Deutsch does, and it will do its heaviest work against Ray Kurzweil.

Static societies and dynamic ones

If the capacity for good explanation is, in principle, unlimited, then the obvious next question is why human history is not simply an unbroken record of accelerating discovery. Deutsch's answer is that the capacity has almost always been suppressed, deliberately, and that suppression, not stupidity, accounts for most of the long, nearly changeless centuries that make up most of the human past. He borrows from Popper the distinction between static and dynamic societies, and it is one of the more clarifying pieces of political philosophy I know, precisely because it does not sort societies by wealth, or technology, or the usual markers of progress, but by their relationship to their own ideas.

A static society, in this sense, is not one that has failed to progress out of misfortune, the way a country might fail to develop because it lacks natural resources or a temperate climate. It is one organised, often with great sophistication and considerable success on its own terms, to prevent new ideas from taking root, because new ideas are a standing threat to whoever currently holds authority. Ancient Egypt lasted, in something recognisably like its own form, for nearly three thousand years, a span of time that dwarfs the entire history of parliamentary democracy, and for most of it, art, religious practice, and the structure of political power scarcely changed at all. This was not an accident or a failure of imagination. It was an achievement, in its way: a set of institutions, a priesthood, a bureaucracy, a religious cosmology binding the pharaoh to the order of the universe itself, all working together to make deviation from precedent look not merely unwise but blasphemous. Three thousand years of successful discouragement is not nothing. A society built this way can be materially impressive. It can build pyramids. What it cannot do, by its own design, is generate the kind of criticism that would allow it to notice its own errors and correct them, because noticing an error in the received order is, structurally, indistinguishable from an act of treason.

A dynamic society, by contrast, is one that has found some way, always partial, always fragile, of making room for exactly that kind of criticism, including criticism of its own most cherished and foundational ideas, without the society tearing itself apart in the process. This is an extraordinarily unnatural thing to build, which is presumably why it has happened so rarely and so recently. Deutsch's central historical example is the European Enlightenment, the roughly hundred-and-fifty-year stretch beginning in the seventeenth century in which a loose, quarrelsome, and largely self-appointed community of astronomers, philosophers, physicians, and pamphleteers, spread across a fractured and frequently warring continent, arrived collectively at a habit of mind that had eluded nearly every other civilisation in history: the conviction that authority, however ancient or exalted, does not settle a question, and that a claim earns belief not by who states it but by whether it survives determined attempts to knock it down. Francis Bacon urging that knowledge of nature be built from observation rather than inherited from Aristotle. The Royal Society's motto, nullius in verba, take nobody's word for it. Kant, in his 1784 essay answering the question "What Is Enlightenment?", defining the whole project in a single Latin tag borrowed from Horace, sapere aude, dare to know, and diagnosing the obstacle to it not as a want of intelligence but as a want of the nerve to think for oneself instead of leaning on a guardian, whether priest, physician, or prince, to do one's thinking for a fee. This was not a smooth or a comfortable process. It got people burned, imprisoned, and exiled; Galileo, remember, spent his last years under house arrest for insisting, correctly, that the earth moves. But the institutions that eventually crystallised out of it, independent universities, learned societies that published their disagreements rather than suppressing them, a scientific method that made a virtue of trying to prove yourself wrong, gave criticism somewhere to live. And once criticism has somewhere to live, error correction stops being an occasional heroic act performed by a lone genius against the current of his age, and becomes, however imperfectly, a standing feature of how the society thinks. That, for Deutsch, is the entire difference, and it explains why the sheer volume of useful knowledge produced in the three centuries since roughly 1700 so wildly outstrips everything produced in the previous ten thousand years of settled civilisation. It was not that people got smarter. It was that a certain kind of society, for the first time, permitted itself to be wrong in public and to fix the error afterward.

Nothing illustrates how quickly a dynamic moment can be extinguished by static authority quite as starkly as the fate of the Chinese treasure fleets. Between 1405 and 1433, under the command of the admiral Zheng He, Ming China sent out seven vast maritime expeditions, fleets of hundreds of ships, some of them reportedly over four hundred feet long, dwarfing anything Europe would put to sea for another century, carrying tens of thousands of sailors as far as the Arabian Peninsula and the east coast of Africa. China at that moment possessed, by a wide margin, the most advanced shipbuilding and navigational technology on earth. Then, following a change in imperial politics after the Yongle Emperor's death, a court faction hostile to the expense and the outward-looking spirit of the voyages gained the upper hand, the fleets were dismantled, the building of large ocean-going ships was banned under severe penalty, and the detailed records of Zheng He's voyages disappeared, destroyed, according to a tradition the surviving sources leave partly uncertain, by court officials who considered them an embarrassment or a temptation to future extravagance, the two objections a bureaucracy finds easiest to hold at the same time. Within a couple of generations China had gone from the world's foremost maritime power to a state that had criminalised the very capability. This was not a failure of talent, resources, or even of accumulated knowledge, all of which China had in abundance. It was a static decision, made by a court that could not tolerate a technology, and the class of people who operated it, gaining an independent power base capable of threatening the existing order, and it stands as a reminder that a dynamic period, however impressive, confers no permanent immunity; it survives only for as long as the institutions protecting criticism and experiment continue to be defended against the people who would rather not be criticised.

This has a sharp edge, and Deutsch declines to file it down. If the capacity for unlimited growth in knowledge depends on a specific and unusual institutional arrangement, tolerance for criticism, an expectation that even foundational ideas can be challenged, mechanisms for testing claims against reality rather than against tradition, then that capacity is not a fact about human beings as a species, guaranteed by our biology, so much as an achievement, held only where the institutions that sustain it are actively maintained. The default condition of human societies across history has been static, not dynamic. The Enlightenment was not the discovery of some latent human talent that had simply been waiting to be switched on; it was a strange and, from a historical distance, rather improbable set of political and intellectual arrangements that happened to take hold in a particular place at a particular time, and that could, in principle, be lost again. This is a warning dressed as a promise: the promise is unlimited, but it comes with a receipt attached, and the receipt says the promise is honoured only for as long as we keep paying for it. It sits at the very centre of what makes Deutsch's optimism a serious philosophical claim rather than a comforting slogan, and it is also, as it happens, the exact place where his argument makes contact with a live and unresolved dispute about artificial intelligence.

Deutsch takes this framework and turns it, with evident relish, against two ideas that were fashionable when he was writing and remain fashionable now. The first is the metaphor of "spaceship Earth," the image, beloved of a certain kind of environmental rhetoric, of the planet as a sealed vessel with a fixed stock of resources that its passengers must ration carefully if they are to survive the voyage. Deutsch thinks the metaphor is not merely imprecise but actively misleading, because it smuggles in the assumption that the problem facing humanity is fundamentally one of management, of dividing a finite pie more carefully, rather than one of knowledge, of discovering how to do more with what is available, or how to obtain resources nobody currently knows how to obtain. A spaceship's fuel supply is fixed by its design and cannot be renegotiated once the vessel has left port. The metaphor is silent, too, on details no actual spaceship dispenses with, a destination, for one, or anyone at the controls. The earth's usable resources, by Deutsch's account, are fixed by nothing of the kind; they are fixed only by the current state of human knowledge about what counts as a resource and how to use it. Uranium was inert rock until physicists understood nuclear fission, at which point a substance nobody had valued became one of the most concentrated energy sources on the planet. The same will very likely be true of things that today look like waste or nuisance or simply invisible, because nobody has yet had the idea that would reveal them as valuable, the way nobody had the idea of longitude by clock until Harrison built one. Deutsch then pushes the point somewhere most of the environmental writers he is arguing with would refuse to follow: the earth, he observes, is not and never has been a life-support system for human beings. Even in the East African Rift, where our species evolved, a person stripped of knowledge, of fire, of tools, of which roots nourish and which kill, would die in short order; in Oxfordshire, where Deutsch himself lives, an unclothed and unequipped human being on an ordinary January night would be dead of exposure by morning. Everything that makes the planet habitable for people, clothing, agriculture, medicine, houses, sanitation, is knowledge made physical. The life-support system the spaceship metaphor imagines was never on board. We built it, piece by piece, and we keep it running only by continuing to know how.

The deeper target, though, is the ideal of sustainability itself, at least in the strong sense of aiming for some stable, self-perpetuating equilibrium that a wise civilisation might reach and then simply maintain. Deutsch's objection is not that stability is undesirable; it is that it is impossible, and dangerous to pursue as though it were possible. Any static arrangement, however comfortable, however carefully balanced, will eventually be undone by some problem its design could not have anticipated: an asteroid on a collision course, a new pathogen, a shift in the climate driven by forces outside anyone's calculation, the exhaustion of some input nobody thought to plan for. A civilisation that has organised itself around preserving a particular equilibrium, rather than around the perpetual capacity to solve whatever problem shows up next, has traded a real form of security for an illusory one. It has optimised for surviving the problems it can currently imagine, and left itself exposed to the ones it cannot. The dinosaurs, as Deutsch likes to point out, were exquisitely well adapted to their environment for one hundred and sixty million years, a run of stability that puts the entire history of human civilisation to shame, and it did them no good whatsoever against a piece of rock arriving from outside the system they had adapted to. The lesson he draws is not that adaptation is worthless but that the only durable form of security is the capacity to keep generating new knowledge, because only new knowledge can meet a problem nobody has met before. Sustainability, on this reading, is the wrong goal dressed up as prudence. The right goal is what he calls, elsewhere in the book, the unlimited growth of explanatory power, which sounds abstract until you notice it is just another way of saying: stay a dynamic society, and do not mistake the comfort of the present arrangement for a plan.

The second target is what Deutsch calls parochialism, by which he means the recurring, almost hypnotic tendency of every generation to mistake the current limits of its knowledge for the actual limits of what can ever be known. It is an old error with an unbroken pedigree. For most of recorded history, educated people took it as simply obvious, not a hypothesis to be tested but a fact too plain to need testing, that the earth sat motionless at the centre of the universe while the sun, the planets, and the fixed stars revolved around it; the geometry seemed to demand it, the philosophy of the age seemed to demand it, and the alternative seemed faintly absurd on its face, since nobody could feel the earth moving beneath them. It took Copernicus, and then the much harder observational and mathematical work of Kepler and Galileo, to show that the apparent absurdity was an artefact of a limited vantage point rather than a fact about the cosmos. Deutsch's point is not merely that people used to be wrong about astronomy. It is that the geocentric error is a template that keeps reappearing in new clothes: the pronouncement long attributed to Lord Kelvin, perhaps apocryphally, though it captured faithfully the settled mood of physics at the century's end, that there was essentially nothing left to discover in the field; the American physicist Albert Michelson did say, in 1894 and on the record, that the grand underlying principles had been firmly established and that future advances were chiefly to be sought in the sixth place of decimals, a judgment delivered on the very eve of radioactivity, relativity, and quantum mechanics, timing of a precision the discipline's forecasts have seldom matched since; the assumption, common enough in the middle of the twentieth century, that heavier-than-air flight, or nuclear energy, or computers smaller than a room, represented some outer edge of the practically achievable. Each of these was, at the time, not a fringe view held by cranks but the sober, mainstream judgment of serious people reasoning carefully from the best available evidence. Each was wrong in the identical way: it mistook the boundary of present knowledge for the boundary of possible knowledge, which is a category error every time, because present knowledge is, by definition, exactly the part of the territory that has already been mapped, and says nothing reliable about how much territory remains.

Out of this Deutsch draws what he regards, and what I am inclined to agree is, the single most consequential claim in the book: that human beings are universal explainers. He means something quite precise by this, not that any given person happens to be clever, but that the human mind, once it possesses language and the capacity to form and test explanations, has no principled limit on what portion of physical reality it can, in time, come to understand. This is a much stronger claim than saying humans are intelligent, in the sense of being quick at pattern recognition or good at solving puzzles, because plenty of animals show flashes of that without ever accumulating knowledge across generations or building explanations that improve on their predecessors. A beaver builds a dam exactly as well, or exactly as poorly, as beavers have built dams for a million years; a chimpanzee uses a stick to fish termites out of a mound with a skill that gets passed down and imitated but never fundamentally redesigned. No beaver has ever complained about the design. Human beings alone, so far as anyone has observed, take an explanation, subject it to criticism, replace it with a better one, and then treat the improved explanation as a new starting point from which to reach further still. Given that capacity, Deutsch argues, there is no reason internal to physics why a human mind, suitably extended by instruments, mathematics, and time, should be barred from eventually understanding anything about the universe that is physically comprehensible at all: the interior of a star, the first instant after the beginning of the universe, the chemistry of a living cell, the workings of its own consciousness. This does not mean any individual will live to see the relevant discovery, and it certainly does not mean the discovery will be easy. It means the barrier, wherever it currently sits, is a fact about how much has been figured out so far, not a fact about what is figurable. That distinction is the distinction between a fate and a problem again, the one the longitude prize turned on, now generalised into a claim about the entire universe.

A note on paradigms

Deutsch's picture of scientific progress is worth setting against the rival picture that most people who have taken a single university course in the philosophy of science carry around in their heads, because the two are often confused and they are not the same. The rival comes from Thomas Kuhn's The Structure of Scientific Revolutions, published in 1962, a monograph that sold over a million copies and gave the word paradigm a second career in management, where it still performs work Kuhn never assigned it. Science, Kuhn argued, does not progress through the patient conjecture and correction Popper describes. Most of the time it works quietly within a settled paradigm, a shared stock of assumptions, methods, and exemplary problems that a scientific community takes for granted, rather as Deutsch's static societies live within their inherited authority. Then anomalies the paradigm cannot digest accumulate past some threshold of tolerance, and the whole framework is overthrown in a comparatively sudden revolution: Newtonian mechanics giving way to relativity, phlogiston to oxygen. The paradigm that takes over is not, on Kuhn's more radical and more contested claim, simply an improvement on the old one but in some sense incommensurable with it, answering different questions in a different conceptual language, so that scientists on either side of the divide half talk past one another. Kuhn's picture is also, in its way, an optimistic one, since it does not deny that science advances. But it is a more tragic optimism than Deutsch's, because it suggests that within any given paradigm a great deal of what looks like reasoned inquiry is actually a kind of collective, half-conscious conformity, and that real advance requires not steady criticism but periodic, disorienting revolution, closer to a change of religion than to Popper's picture of one bold conjecture calmly succeeding another. Deutsch, characteristically, does not think this is quite right, and his disagreement is instructive. He does not deny that scientific communities can behave like static societies for a time, growing comfortable with an inherited framework and resistant to challenges to it; the history of science offers plenty of examples, from the resistance to continental drift that lasted decades after Alfred Wegener first proposed it in 1912, to the reluctance of an older generation of geologists to accept it even after the evidence for plate tectonics became overwhelming in the 1960s. But he insists this is a failure of institutions to live up to the Enlightenment ideal, a lapse back toward static habits, rather than a permanent and necessary feature of how knowledge must grow, as Kuhn's account sometimes seems to suggest. The difference matters practically as well as philosophically: if Kuhn is right that real advance requires periodic revolution and cannot be had merely by patient, incremental criticism, then a society's job is to wait for revolutionary geniuses and get out of their way when they appear. If Deutsch is right, a society's job is unglamorous and continuous: keep the channels for criticism open at all times, in every field, so that anomalies get noticed and addressed as they arise rather than allowed to accumulate into a crisis that can only be resolved by the sociological equivalent of a coup.

A stranger kind of optimism

This is a considerably odder and more demanding position than the word "optimism" usually suggests. Ordinary optimism is a bet about probability: things have gone reasonably well before, human beings are resourceful, so on balance expect the future to be more of the same. It is a temperament, and like all temperaments it can be argued with, mocked, or simply outgrown by events. Deutsch is not offering a temperament. He is offering something closer to a logical structure, and the structure runs like this: an evil, meaning any state of affairs we would prefer did not obtain, whether disease, poverty, cruelty, or plain ignorance, persists only because we lack the knowledge to prevent or cure it. Knowledge, being the product of conjecture and criticism, has no ceiling built into it beyond the laws of physics themselves, which forbid remarkably little of what would actually help us. Therefore no evil is a fixed, permanent feature of the human condition, only a temporary one, temporary in the sense that it will end whenever the relevant explanation is found, however long that takes. He calls this the principle of optimism, and states it with the flat, almost legalistic confidence of a man stating a theorem rather than expressing a hope: all evils are caused by insufficient knowledge.

Notice what the principle does not say. It does not say things will go well. It does not say suffering will end soon, or end painlessly, or end at all within the lifetime of anyone now living. It does not say the road ahead is smooth; Deutsch is explicit, more than once, that error, failure, and even catastrophe remain certain, not merely possible, because every explanation we currently hold is fallible, and progress happens by making mistakes and noticing them, not by getting everything right on the first attempt. What the principle claims is narrower and, in a way, colder than ordinary hopefulness: that whatever the present difficulty, it is not, in itself, proof of an unbreakable limit. It is proof only of a gap in present understanding, and gaps, unlike walls, can be closed. The promise is closer to a standing permission than a guarantee. This is why Deutsch's optimism survives contact with pessimistic facts in a way that the cheerful, temperamental kind does not. A temperamental optimist confronted with a truly intractable problem eventually has to either deny the problem or abandon the optimism. Deutsch's version has no such exposure, because it was never a claim about how things will probably go; it was a claim about what kind of thing a problem is. A hurricane is not an argument against the principle of optimism, even a hurricane that kills thousands, because the principle never promised the absence of hurricanes, only that the vulnerability to them is not eternal, that somewhere in the accumulation of better meteorology, better construction, better evacuation planning, better everything, lies the eventual reduction and perhaps the eventual elimination of hurricanes as a source of human death. That claim can be tested only across a very long stretch of time, which is either its great strength, since it cannot be falsified by any single bad decade, or its great evasiveness, since it cannot be falsified by any single bad decade. I think it is the former, but the honest reader should hold both possibilities in mind at once.

Ray Kurzweil and the arithmetic of everything

If Deutsch arrives at unlimited progress by way of epistemology, by working out what an explanation is and what follows from a mind capable of producing them, Ray Kurzweil arrives at something that sounds superficially similar by an entirely different road, and the difference in road turns out to decide everything about where the two men part company.

Kurzweil is, in the first instance, not a philosopher but an inventor, and a serious one, with the patents and the working machines to prove it. Born in Queens in 1948 to parents who had fled Austria, he was building pattern-recognition programs as a schoolboy in the early 1960s, at an age when most children are still working out long division, and went on to a career that reads like a chronicle of firsts: the first flatbed scanner capable of reading ordinary printed type in any font, developed because he wanted to build a reading machine for the blind and discovered no existing scanner could handle the variety of typefaces a blind person might actually encounter; the reading machine itself, which paired that scanner with the first practical text-to-speech synthesiser and put the combination into use at the National Federation of the Blind, where Stevie Wonder, an early and enthusiastic customer, later became a friend and collaborator; and the Kurzweil K250, a music synthesiser so successful at reproducing the sound of an acoustic piano that professional musicians, Wonder among them, could not reliably tell it apart from the real instrument in blind tests. This is not, whatever else one makes of his later forecasting, the biography of a fantasist. It is the biography of a man who has repeatedly taken an idea that sounded implausible and turned it into a functioning object that other people could buy and use, which earns him, at minimum, the right to be taken seriously when he turns his attention to the future rather than dismissed as an amateur enthusiast.

His forecasting rests on a single empirical observation that he elevates into a general law, which he calls the law of accelerating returns. The observation, familiar to most people now under the name Moore's Law, is that the density of transistors that can be etched onto a silicon chip, and with it the raw computing power available for a given cost, has roughly doubled every one to two years for decades on end, a curve so smooth and so persistent across changes in underlying technology, from vacuum tubes to transistors to integrated circuits, that it looks less like an engineering trend and more like a fact of nature. Kurzweil's move is to generalise this observation beyond computing chips into a claim about technological change as such: that each advance becomes a tool that makes the next advance easier and faster to achieve, so that the rate of progress is not merely continuous, one useful thing after another, but compounding, each cycle of improvement shortening the time needed for the cycle after it. A faster computer helps design a still faster computer. Better genetic sequencing tools produce data that trains better tools for reading and eventually rewriting genetic code. The effect, plotted over a long enough stretch of time, is not a straight line but a curve that bends ever more sharply upward, the way compound interest looks unremarkable for the first several years and then, seemingly all at once, does not.

Kurzweil is not naive about the standard objection that every exponential ends. His answer, worked out at length in the book, is that Moore's Law is merely the fifth paradigm to carry the curve. Electromechanical calculators, relay machines, vacuum tubes, and discrete transistors each enjoyed a run of exponential improvement, saturated, and handed the curve on to a successor, and the price-performance of computation, by his charts, kept doubling straight through every handover. Any single technology traces an S-curve, rising steeply and then flattening as its particular physics is exhausted; what compounds, on Kurzweil's account, is the succession of S-curves, each new paradigm arriving on cue because the wealth, the demand, and the tools generated by the old one make it findable. He pairs this with a diagnosis of why sensible people keep underestimating what is coming. They reason, he says, from the intuitive linear view, projecting the rate of change they have personally experienced forward as a straight line, when the historical record is exponential, and the gap between the two readings, negligible over a year or five, becomes the whole story over fifty. It is a diagnosis with the convenient property that disagreement confirms it.

From this single mechanism, Kurzweil builds an entire history of everything, which he divides into six epochs. The first three run from physics and chemistry through biology to the emergence of brains, each compressing the timescale of learning further than the last. The fourth epoch is technology, the externalisation of thought and memory into tools, writing, and eventually machines, which is the epoch Kurzweil considers our own, and which he thinks has already dramatically shortened, compared to the epochs before it, the interval between one major advance and the next. The fifth epoch, which Kurzweil places within the lifetimes of people alive today, is the merger of human and machine intelligence, a point at which biological and non-biological thinking become interchangeable enough that the distinction stops mattering very much in practice. The sixth and final epoch, more cosmological speculation than forecast, has intelligence spreading outward from earth to saturate the matter and energy of the universe itself, an image Kurzweil renders with the memorable and faintly religious phrase that the universe "wakes up." What the universe does after waking is not specified.

The engine that is supposed to carry human civilisation from the fourth epoch into the fifth, in Kurzweil's account, is a set of three overlapping technological revolutions he abbreviates as GNR: genetics, nanotechnology, and robotics. Genetics, in his usage, means the ability to read and eventually rewrite the software of biological life itself, treating DNA less as a mysterious substance than as a code that can, in time, be debugged and improved the way a programmer debugs a piece of faulty software. Nanotechnology means the ability to build and manipulate matter atom by atom, a capability Kurzweil imagines yielding, among other things, nanoscale robots small enough to travel through the bloodstream repairing damaged cells or clearing arterial plaque before it can cause a heart attack. Robotics, the broadest and in some ways the least literal of the three, stands in Kurzweil's usage for strong artificial intelligence generally, machines that do not merely calculate faster than a human but recognise patterns, reason, and eventually create at a level that matches and then exceeds unaided human cognition, which he regards, following a school of thought within artificial intelligence research, as fundamentally a matter of pattern recognition performed at sufficient scale and speed.

What sets Kurzweil apart from most people who traffic in this kind of speculation is his willingness to attach specific dates to it, dates precise enough to be embarrassing if they turn out wrong, which is either a mark of real intellectual courage or a serious tactical error, and probably, in fact, some of both. He predicts that a computer will pass a valid Turing test, meaning it will hold a conversation indistinguishable from a human being's to a competent human judge, by 2029. He predicts the Singularity itself, the moment at which the pace of technological change becomes so rapid that unaugmented human intelligence can no longer track or meaningfully steer it, by 2045. These dates are observed at futurist conferences with the solemnity of a liturgical calendar, which, in fairness, is roughly what they are. He is fond of a line that captures the flavour of the whole project better than any summary could: "we will not experience one hundred years of progress in the twenty-first century, it will be more like twenty thousand years of progress at today's rate." It is a sentence built for quotation, and it earns its place in every review of the book, because it states with maximum clarity exactly what a compounding exponential curve implies if you take it at face value and extend it without flinching for a hundred years.

The book is not, in the end, a purely technical document, and its most affecting passages have nothing to do with transistor counts. Kurzweil writes, more than once and with evident feeling, about his father, a conductor and composer who died when Kurzweil was twenty-two, and about a wish, expressed with unusual candour for a book otherwise given over to charts and projections, that sufficiently advanced technology might one day make some kind of reunion with his father conceivable, whether through the reconstruction of a personality from records and memories or through some future understanding of consciousness itself that renders the question less absurd than it currently sounds. It is easy, reading this passage from a professional or sceptical distance, to feel the pull of the same instinct that makes people write to the dead, or keep an old voicemail they cannot bring themselves to delete, and the passage suggests that Kurzweil's optimism, however dressed up in exponential curves and epoch diagrams, is at bottom the same kind of hope that moves most people who hope for anything at all: a wish that loss might not be final, dressed in the vocabulary of the discipline the wisher happens to know best. An engineer hopes for engineering answers to grief the way a theologian hopes for theological ones.

The book's reception tracked, roughly, the fault line you would expect between people impressed by Kurzweil's track record as a working inventor and people unimpressed by his willingness to extrapolate a chip-density curve into a theory of consciousness. Bill Gates called him, in an oft-quoted line, the best person he knew at predicting the future of artificial intelligence, which is a serious endorsement from someone who had every reason to have thought hard about the competition. Paul Allen, the Microsoft co-founder turned philanthropist and, in his later years, a serious funder of brain research through the institute that bears his name, took the opposite view, co-authoring a widely discussed rebuttal that argued Kurzweil had badly underestimated just how difficult it would be to reverse-engineer the human brain, a system whose complexity, Allen argued, was not remotely comparable to the orderly, well-understood physics of transistor scaling. Allen's essential complaint was a category error: that Kurzweil had taken a reliable empirical regularity, the doubling of transistor density, and stretched it, by force of narrative rather than force of evidence, over a phenomenon, the emergence of humanlike intelligence and eventually consciousness from a machine, about which nobody, including Kurzweil, possessed a working theory. A curve describing how small you can etch a circuit says nothing, on this view, about how a mind is made, and treating the two as points on the same graph flatters the second with the rigour that properly belongs only to the first. Allen and his co-author Mark Greaves gave the objection a memorable name, the complexity brake: the deeper science reaches into a system like the brain, the more unforeseen intricacy it finds, so that each layer of new understanding tends to slow the next rather than speed it, the exact inverse of Kurzweil's compounding. Behind their specific complaint stands a more general one, pressed independently by other critics, and the sceptics hold no stronger card. An exponential is a fact about one substrate at a time. The doubling of transistor density is underwritten by a particular, well-understood physics and by an industry that spends tens of billions of dollars a year keeping the doubling on schedule; nothing in that arrangement transfers to protein chemistry, or to clinical trials, or to the reverse-engineering of a brain wired with something on the order of a hundred trillion synapses. To point at the chip curve as evidence about those domains is not extrapolation but analogy, a far weaker instrument wearing the costume of a stronger one. And every exponential yet observed in nature, the critics add, has turned out to be the early stretch of an S-curve; bacteria double merrily until the dish runs out. Kurzweil's reply, that fresh paradigms have always arrived in time to relaunch the curve, is either the deepest insight in the book or its central circularity, since the punctual arrival of the next paradigm is precisely the thing in dispute.

Kurzweil had been rehearsing the argument since 1990, revising his estimates upward rather than downward each time, and he has never let it rest: he became a director of engineering at Google in 2012, where he worked on natural language understanding, and published a sequel, The Singularity Is Nearer, in 2024, a title that nineteen intervening years had made unavoidable, which reaffirms both headline dates, 2029 and 2045, and treats the intervening emergence of large language models as vindication rather than as cause for revision. Whatever else one thinks of the project, this is not a man who set a forecast once and quietly walked away from it; he has kept restating it, in public, against two decades of accumulating evidence, which is either the discipline of someone whose model keeps being confirmed or the stubbornness of someone who has stopped being able to hear disconfirmation, and from the outside the two are not always easy to tell apart.

Twenty years on from the book's publication, with the 2029 deadline for a passed Turing test now only three years away, readers no longer have to take either side's word for the shape of the curve, because part of the record is already in, and Kurzweil, to his credit, has submitted to audit. In 2010 he published a review of the roughly one hundred and forty-seven predictions he had made in 1999 for the year 2009, grading 86 percent of them, by his own count, essentially correct, an exercise in which he served as both candidate and examiner. Independent reviewers who worked through the same list were considerably less generous, and their complaint is instructive: the passing grades often depended on charitable readings, on counting a laboratory demonstration as an arrival, or a niche gadget as a norm. On the plain meaning of his 1999 sentences, most text in 2009 was supposed to be composed by speech rather than typed, computers were supposed to have dissolved unremarkably into clothing and jewellery, and telephones that translated between languages in mid-conversation were supposed to be in common use; none of that had happened on time, and some of it has barely happened yet. But the same record, read fairly, also contains what the mockery tends to omit. He foresaw portable computers in every size and shape, the migration of daily life onto wireless access to all the world's information, machine translation good enough for real work, and, in his 1990 book, a computer defeating the world chess champion by 1998, a call that looked extravagant until Deep Blue beat Garry Kasparov in 1997, a year ahead of schedule, a margin the futurist record has rarely enjoyed since. The pattern in the audit is almost too tidy. Where a prediction rode on computation and nothing else, Kurzweil has been right with a consistency his detractors rarely acknowledge, and roughly on time; where it required matter to cooperate, regulators to agree, or biology to give up its secrets, the dates have slipped, sometimes by decades. The biological end of the GNR triad has moved slowest of all, cellular repair by nanomachine and the genetic reprogramming of ageing remaining largely aspiration, for reasons that have little to do with computing power and much to do with the layered, stubborn complexity of systems that took evolution billions of years to tinker into existence and that do not yield their secrets merely because more computation is available to search for them. Kurzweil has arranged to be present for the verdict; for years he has taken supplement pills by the hundred each day, on the theory that he need only stay alive until staying alive becomes a solved problem, a plan with the virtue of clarity and the drawback of requiring him to be right. Whether the master curve is bending as Kurzweil promised or quietly flattening exactly where his critics said it would remains open; but the audit already suggests that the law of accelerating returns is less a law of technology as such than a law of information, holding with striking reliability inside the world of bits and losing its grip, by degrees, the further from that world it travels.

What when leaves out

Kurzweil's argument, at bottom, treats the arrival of machine minds capable of matching and exceeding human intelligence as very nearly a matter of arithmetic. Give him the doubling curve of computational power and an estimate of how much raw processing the human brain performs (he puts it in the neighbourhood of ten thousand trillion operations per second, scaling up from the best-studied neural circuits, and concedes the figure is rough), and the date at which affordable machines cross that threshold falls out of the calculation almost mechanically, the way you might work out when a population growing at a known rate will exceed a known ceiling. The considerable merit of this approach is that it does not require Kurzweil, or anyone else, to have first solved the philosophical question of what intelligence, creativity, or consciousness actually are, which is a considerable saving of time. The curve, on his account, will cross the threshold on schedule regardless of whether the theorists have caught up with a full explanation of what is happening when it does, in much the same way an aeroplane can fly perfectly well before anyone has a complete theory of turbulence, or a vaccine can work before anyone fully understands the immune response it triggers. Sufficient scale, in this view, answers the question of when, and the question of what can, without embarrassment, be left for later, or left to the machines themselves once they exist to explain their own workings back to us.

Deutsch has a name for this kind of forecast, and the name is the hinge of the whole disagreement. Following Popper, he distinguishes prediction from prophecy. A prediction is a consequence of a good explanation: astronomers can announce an eclipse to the second, decades ahead, because the theory of gravitation pins the moon's path in place and the announcement inherits the theory's precision. A prophecy is a claim about the future that flows from no such explanation of the thing being foretold, and the future of civilisation, Deutsch argues in The Beginning of Infinity, belongs to prophecy's territory irreducibly, because it depends on what knowledge will be created, and the content of knowledge not yet created is unknowable in principle, not merely in practice. This is Popper's old argument from The Poverty of Historicism doing fresh work, and it cuts at Kurzweil with precision. The curve does not escape the logic by being empirical. Its continuation is not a fact waiting in the data; it is a bet that the specific creative acts needed to relaunch it, paradigm after paradigm, will keep occurring on a schedule set by their predecessors, and a claim about the timing of ideas nobody has yet had is exactly the kind of claim that no quantity of data about past ideas can secure. To call a dated Singularity prophecy rather than prediction, as Deutsch's vocabulary invites us to do, is not to call Kurzweil a mystic. It is to make the drier and more damaging point that a date fixed for the arrival of unmade knowledge cannot, given what knowledge is, be anything better than a guess wearing arithmetic.

Deutsch finds Kurzweil's sequence of priorities exactly backwards, and says so with a bluntness he does not extend to many other subjects in the book, or in his public remarks since. In interviews and in a public dialogue with the psychologist Steven Pinker on the legacy of the Enlightenment, Deutsch has argued that the field of artificial intelligence is hyping general intelligence while standing nowhere near it, and his reasoning tracks precisely back to the theory of explanation laid out in The Beginning of Infinity. Nobody, Deutsch points out, currently has a good explanation, in his hard-to-vary sense, of what creativity actually is, of what happens, mechanically, when a mind takes existing knowledge and produces from it a new conjecture rather than a recombination of what it was given. Until somebody has that explanation, he argues, no amount of computation settles the question of when a machine will possess creativity, because you cannot reliably build, or even recognise, a thing you cannot yet explain. This is not an argument that machines will never think. Deutsch has said explicitly, consistent with the argument of his book, that there is nothing in the laws of physics preventing a machine from becoming a universal explainer exactly as human beings are. His objection is narrower and, for that reason, harder to wave away: that the specific confidence embedded in a date like 2029 or 2045 mistakes the presence of a very good imitation of understanding for the arrival of understanding itself.

And here Deutsch reaches back for the very tool his book spent five hundred pages sharpening. A large language model, trained on an almost unimaginable quantity of human writing, produces sentences that are startlingly fluent, contextually apt, and often plainly useful, and it is tempting, faced with that fluency, to conclude that something like understanding must be happening underneath it. But fluency, on Deutsch's test, is not the same thing as a hard-to-vary explanation, and the two can be pulled apart by asking a very simple question of any given output: how much of what was said was actually forced by anything, as opposed to being one plausible arrangement of words among many that would have served the conversational moment equally well? Ask a language model to explain why the seasons change and it will, with total fluency, produce a serviceable paragraph about axial tilt. Ask it a question at the actual frontier of some field, a question nobody has yet answered well, and the fluency does not disappear, but the content behind it starts to look, on close inspection, cheaply variable: confident, well formed, and only loosely tethered to anything that would resist being swapped for an equally confident, equally well formed, and equally wrong alternative. This is Deutsch's Persephone test applied to a new subject. The worry is not that the machine is unconvincing. It is nearly the opposite: that it is extremely convincing in exactly the way the Persephone myth was convincing to people who had no way of checking it against axial tilt, persuasive because it fits the shape of what a good answer looks like, not because each part of it is locked in place by anything that would break if you changed it.

Deutsch is, in this specific sense, standing in a line of argument considerably older than the current wave of language models, and the ancestor shows the objection is not a reflexive suspicion of new technology but a serious and recurring philosophical position. In 1980 the philosopher John Searle proposed a thought experiment that has become one of the most argued-over in the philosophy of mind: imagine a man who speaks no Chinese, locked in a room with a vast rulebook written in English, which tells him, for any string of Chinese characters passed to him through a slot, exactly which characters to pass back out, matching input patterns to output patterns with no understanding of what either means. From outside the room, to a Chinese speaker sliding questions in and receiving fluent, sensible answers back, the room appears to understand Chinese perfectly. Inside the room, there is no understanding whatsoever, only a man mechanically following a very large lookup table. Searle's point, deployed originally against an earlier generation of symbolic artificial intelligence, was that behaviour indistinguishable from understanding is not proof of understanding, because you can, at least in principle, produce the behaviour by pure syntax, pure pattern matching, with the semantic content, the actual meaning, entirely absent. Deutsch's hard-to-vary test is, in effect, a way of trying to look inside the room without needing Searle's thought experiment at all: instead of asking whether something that feels like a mind is in there, ask whether the specific output was forced by anything, whether the rulebook, or the training data standing in for it, actually pins the answer down the way axial tilt pins down the seasons, or whether it merely produces one fluent answer among many that would have served just as well.

It would be a mistake to present this as a dispute Deutsch has simply won, and a more serious mistake to pretend to referee it, since the honest answer is that nobody currently knows. Kurzweil's defenders have a real reply, not a rhetorical one: the history of flight, and of countless other technologies, is a history of practice consistently outrunning theory, of things working reliably before anyone possessed a complete account of why, and demanding a settled philosophical theory of creativity before conceding that a machine might possess something functionally very close to it may be asking of engineering a kind of permission that engineering has never, historically, needed to ask. It is entirely possible that something recognisable as machine creativity will exist, doing real and valuable work in the world, well before any philosopher, including Deutsch, has produced a hard-to-vary account of what that creativity actually is, exactly as pilots flew for decades on instruments and intuition before aerodynamics fully caught up with the aeroplane. Equally, Deutsch's caution has its own real force: mistaking fluency for understanding has a long and undistinguished history, from mechanical chess automatons that turned out to conceal a hidden human player, an architecture that capped each machine's playing strength at that of whoever could be persuaded to fold himself inside, to chatbots from the 1960s that convinced some of their users they were talking to an understanding presence when they were in fact talking to a script of a few hundred pattern-matched replies, and the fact that a modern system is vastly more sophisticated than either does not, by itself, prove that the underlying gap between fluent imitation and genuine explanation has actually closed rather than merely grown harder to spot.

The disagreement, stripped to its bones, is a disagreement about what kind of thing warrants confidence. For Kurzweil, a sufficiently reliable trend, once identified and extrapolated with discipline, is itself a form of knowledge, and demanding a philosophical account of the mechanism before trusting the trend is a kind of excessive scruple that would have stopped a great deal of useful engineering dead in its tracks throughout history. For Deutsch, a trend is only ever a description of what has happened so far, and describing what has happened so far tells you nothing reliable about whether the thing driving it will continue, precisely because the thing driving it might depend, at some point, on somebody, somewhere, having an idea that nobody has yet had, and ideas, unlike transistors, do not arrive on a schedule set by prior ideas' rate of arrival. You cannot compound your way to a conjecture nobody has conjectured yet. A trend, in the vocabulary established earlier, licenses prediction only for as long as the explanation beneath it holds; extended past that warrant, it becomes prophecy, however dense the data behind it.

Living as though the problem is not a fate

The principle of optimism, taken seriously rather than merely admired, does a specific piece of psychological work: it converts the word "problem" from something close to an indictment into something close to an invitation. A society, or a company, or a person, that treats an unsolved difficulty as evidence of a fixed limit, this is simply how things are, this is human nature, this industry has always worked this way, has, whether it says so or not, given up on the difficulty, and everything that follows from giving up, the search for someone to blame, the retreat into managing the difficulty rather than addressing it, the quiet decision to build institutions around accommodating the problem rather than solving it, and to staff them generously, flows from that initial, often unexamined act of treating a gap in knowledge as though it were a wall. Deutsch's reframing asks for something much harder than optimism in the loose sense of expecting things to turn out fine. It asks for the specific discipline of continuing to search for the missing explanation, indefinitely, without the comfort of a guaranteed date of arrival, because the principle promises no smooth road and no schedule, only that the road, however long, does not dead-end.

This is a demanding thing to ask of anyone, far harder in practice than in the abstract, because human institutions are not built for open-ended patience. They are built to celebrate milestones, to declare victory, to move on to the next quarter's targets, and a problem that offers no reliable timetable for its own solution is, from the point of view of an organisation that needs to report progress to somebody, an awkward and unsatisfying thing to hold. It is precisely here that Kurzweil's confident dates, whatever their scientific standing, do real psychological work that Deutsch's more austere formulation cannot, because a date, even a probably wrong one, gives people something to organise around, a horizon to point toward, a way of converting an open-ended search into a project with a deadline. There is a real courage in stating 2029 and 2045 in print and letting the calendar eventually judge you, an act of intellectual exposure that most careful thinkers, including Deutsch, decline to attempt. But there is also a real vulnerability in it, because a missed date does not merely embarrass the man who set it; it risks discrediting the underlying claim, that the problem is soluble at all, in the minds of people who cannot easily distinguish a wrong forecast about timing from a wrong belief about possibility. This is, I think, the sharpest practical tension between the two men's approaches to hope: Deutsch's version is built to survive any number of missed deadlines because it never set one, and is for that reason a poor tool for organising collective effort in the near term; Kurzweil's version is a superb tool for organising collective effort and attracting the money and attention that effort requires, and is for that reason exposed, in a way Deutsch's is not, to the risk that a broken promise about when will be mistaken, unfairly but understandably, for a broken promise about whether.

The history of cancer treatment supplies a concrete case, and it contains both failure modes in sequence. In 1971 President Richard Nixon signed the National Cancer Act, promising, in language that owed a great deal to the recent triumph of the Apollo programme, a comparison that flattered cancer by implying it had a surface to land on, a war on cancer that implied, to the public listening to the speech, something close to a Kurzweilian date: a cure, or something near enough to one, within a defined and fairly short span of years. That specific promise was not kept, and could not have been kept, because cancer turned out to be not one disease with one mechanism but an enormous family of diseases, each with its own genetic causes and its own way of evading treatment, a fact nobody fully appreciated in 1971 and that no amount of funding, by itself, could have shortcut. Measured against Nixon's implied date, the war on cancer looks like a broken promise. Measured against Deutsch's slower and more patient standard, the fifty years since have been a real, substantial accumulation of exactly the kind of knowledge his principle predicts: the decoding of the specific genetic mutations that drive particular cancers, the development of targeted therapies that attack a tumour's specific molecular vulnerabilities rather than poisoning the whole body indiscriminately, immunotherapies that recruit the patient's own immune system against the disease, and a five-year survival rate for the disease as a whole that has climbed, unevenly but steadily, decade after decade, even as certain especially stubborn cancers have barely moved. Nobody declared victory in 1976 or 1986 or 1996. Impatience is not the same thing as insight, and neither is patience. The war on cancer was, on any reasonable account, a wildly overconfident promise about timing wrapped around a perfectly sound conviction about possibility, and the useful thing to salvage from the history is not the discredited date but the undiscredited faith that kept oncologists at the bench decade after decade on the strength of a conviction that the disease was a problem and not a fate, a conviction that has been repaid, slowly, unevenly, and still incompletely, by results.

The load-bearing test, off the page

Consider how much of what passes for strategic thinking inside a large organisation is, on close inspection, closer to the Persephone myth than to axial tilt. A market falls, and by the following morning a plausible story has assembled itself to account for it, interest rates, a competitor's move, a shift in consumer mood, and the story fits the fact of the fall very comfortably, the way any of a dozen variations on Demeter's grief would have fitted the fact of winter. The test that matters, and the one people apply far too rarely under the pressure of a Monday morning meeting, is not whether the story fits, almost any sufficiently flexible story will fit, but whether the story could have predicted the fall in advance, whether removing or changing any one of its supposedly causal elements would have changed the prediction in a way that could actually be checked. Most post hoc market commentary fails this test completely; it is narrative applied after the fact to a result the narrator did not, and typically could not, have called beforehand, which is why it arrives the following morning rather than the preceding one, and its persuasiveness rests entirely on its fluency and its fit, exactly the two qualities the Persephone myth also possessed in abundance. The same test, quietly applied, does a great deal of good in punditry generally, where a commentator's confident account of why a given political event was inevitable is worth almost nothing unless you can show the same account would have ruled out the alternative outcome in advance, rather than simply accommodating whichever outcome happened to occur.

There is a related and slightly subtler version of the same failure that shows up constantly in business strategy specifically, and it wears a respectable disguise. A consulting deck arrives with a framework, four quadrants, five forces, a matrix with the promising opportunities helpfully shaded green, and the framework is presented, implicitly, as an explanation of why the company should move in the recommended direction. Frameworks of this kind are not worthless; they are often a serviceable way of organising a great deal of information into a shape a room full of tired executives can discuss in an hour. But a framework is not, by itself, a hard-to-vary explanation, and the tell is the same one Deutsch uses on the Persephone myth: could the same framework, with the labels on the quadrants barely altered, have been used to justify the opposite recommendation with equally straight-faced confidence? If a rival consultant, given the same set of facts, could have produced an equally polished deck recommending the company go the other way, as the same firm, after a decent interval, has been known to do, then the deck that was actually delivered has not explained the decision, it has decorated it, and the real reasoning, if any exists, is happening somewhere the framework does not show. This is not a reason to distrust consultants more than anyone else; the same test, applied without favour, would empty out a fair portion of what passes for analysis inside any large organisation, including plenty produced by people who have never met a consultant and would be insulted by the comparison. It is simply the discipline of asking, before accepting an explanation for why a decision is the right one, what exactly would have had to be different for the explanation to have pointed the other way, and treating an inability to answer that question as a serious warning sign rather than as a mark of the recommendation's confidence. An explanation that could have pointed either way keeps a room comfortable while it waits for winter to end on its own.

An austere kind of hope

One question remains: what would it mean to live as though Deutsch's principle of optimism were simply true, not as a slogan to repeat when the news is bad, but as a working assumption about how to spend a life or run an institution? The honest answer is that it would look far less like enthusiasm and far more like a discipline, closer to the quiet, unglamorous persistence of the Yorkshire carpenter filing yet another escapement mechanism than to any of the words, breakthrough, revolution, disruption, that modern life reaches for when it wants to sound excited about the future. Harrison did not know, in 1730, that it would take him thirty more years to win the argument he had already, privately, won in principle. He kept refining the clock because refining the clock was the only thing that had ever actually solved anything, and because he seems to have understood, whether or not he would have put it this way, that the four hundred years of drowned sailors before him were evidence of missing knowledge and not evidence of a fixed feature of the sea.

The test of whether a civilisation, or a company, or a person, still believes this is not whether they say optimistic things. It is whether they keep the argument open, whether the next unsolved problem is treated as an invitation to look harder rather than as evidence that looking has reached its limit, whether criticism, including criticism of the institution's own most comfortable convictions, is still welcome in the room. That, more than any chart of accelerating computational power, more than any date fixed twenty years in advance, is the actual measure Deutsch offers of whether a society remains dynamic rather than static, whether it is still, in the fullest sense of his phrase, at the beginning of infinity rather than quietly, comfortably, and without quite noticing it, settling into a static peace with the problems it has decided, for now, not to solve. The sailors who drowned off the Scilly Isles in 1707 were not owed a clock by the laws of physics. They were owed one, if the word owed means anything here, only by the slow, uncertain, unheralded work of a civilisation still willing to admit it did not yet know how to build one, and willing to keep trying until a stubborn carpenter's son, working largely alone and mostly unthanked, went ahead and built it anyway.