The Beginning of Infinity

by David Deutsch

  TERMINOLOGY

  Explanation Statement about what is there, what it does, and how and why.

  Reach The ability of some explanations to solve problems beyond those that they were created to solve.

  Creativity The capacity to create new explanations.

  Empiricism The misconception that we ‘derive’ all our knowledge from sensory experience.

  Theory-laden There is no such thing as ‘raw’ experience. All our experience of the world comes through layers of conscious and unconscious interpretation.

  Inductivism The misconception that scientific theories are obtained by generalizing or extrapolating repeated experiences, and that the more often a theory is confirmed by observation the more likely it becomes.

  Induction The non-existent process of ‘obtaining’ referred to above.

  Principle of induction The idea that ‘the future will resemble the past’, combined with the misconception that this asserts anything about the future.

  Realism The idea that the physical world exists in reality, and that knowledge of it can exist too.

  Relativism The misconception that statements cannot be objectively true or false, but can be judged only relative to some cultural or other arbitrary standard.

  Instrumentalism The misconception that science cannot describe reality, only predict outcomes of observations.

  Justificationism The misconception that knowledge can be genuine or reliable only if it is justified by some source or criterion.

  Fallibilism The recognition that there are no authoritative sources of knowledge, nor any reliable means of justifying knowledge as true or probable.

  Background knowledge Familiar and currently uncontroversial knowledge.

  Rule of thumb ‘Purely predictive theory’ (theory whose explanatory content is all background knowledge).

  Problem A problem exists when a conflict between ideas is experienced.

  Good/bad explanation An explanation that is hard/easy to vary while still accounting for what it purports to account for.

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

  Mini-enlightenment A short-lived tradition of criticism.

  Rational Attempting to solve problems by seeking good explanations; actively pursuing error-correction by creating criticisms of both existing ideas and new proposals.

  The West The political, moral, economic and intellectual culture that has been growing around the Enlightenment values of science, reason and freedom.

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

  – The fact that some explanations have reach.

  – The universal reach of some explanations.

  – The Enlightenment.

  – A tradition of criticism.

  – Conjecture: the origin of all knowledge.

  – The discovery of how to make progress: science, the scientific revolution, seeking good explanations, and the political principles of the West.

  – Fallibilism.

  SUMMARY

  Appearances are deceptive. Yet we have a great deal of knowledge about the vast and unfamiliar reality that causes them, and of the elegant, universal laws that govern that reality. This knowledge consists of explanations: assertions about what is out there beyond the appearances, and how it behaves. For most of the history of our species, we had almost no success in creating such knowledge. Where does it come from? Empiricism said that we derive it from sensory experience. This is false. The real source of our theories is conjecture, and the real source of our knowledge is conjecture alternating with criticism. We create theories by rearranging, combining, altering and adding to existing ideas with the intention of improving upon them. The role of experiment and observation is to choose between existing theories, not to be the source of new ones. We interpret experiences through explanatory theories, but true explanations are not obvious. Fallibilism entails not looking to authorities but instead acknowledging that we may always be mistaken, and trying to correct errors. We do so by seeking good explanations – explanations that are hard to vary in the sense that changing the details would ruin the explanation. This, not experimental testing, was the decisive factor in the scientific revolution, and also in the unique, rapid, sustained progress in other fields that have participated in the Enlightenment. That was a rebellion against authority which, unlike most such rebellions, tried not to seek authoritative justifications for theories, but instead set up a tradition of criticism. Some of the resulting ideas have enormous reach: they explain more than what they were originally designed to. The reach of an explanation is an intrinsic attribute of it, not an assumption that we make about it as empiricism and inductivism claim.

  Now I’ll say some more about appearance and reality, explanation and infinity.

  2

  Closer to Reality

  A galaxy is a mind-bogglingly huge thing. For that matter, a star is a mind-bogglingly huge thing. Our own planet is. A human brain is – in terms of both its internal complexity and the reach of human ideas. And there can be thousands of galaxies in a cluster, which can be millions of light years across. The phrase ‘thousands of galaxies’ trips lightly off the tongue, but it takes a while to make room in one’s mind for the reality of it.

  I was first stunned by the concept when I was a graduate student. Some fellow students were showing me what they were working on: observing clusters of galaxies – through microscopes. That is how astronomers used to use the Palomar Sky Survey, a collection of 1,874 photographic negatives of the sky, on glass plates, which showed the stars and galaxies as dark shapes on a white background.

  They mounted one of the plates for me to look at. I focused the eyepiece of the microscope and saw something like this:

  The Coma cluster of galaxies

  Those fuzzy things are galaxies, and the sharply defined dots are stars in our own galaxy, thousands of times closer. The students’ job was to catalogue the positions of the galaxies by lining them up in cross-hairs and pressing a button. I tried my hand at it – just for fun, since of course I was not qualified to make serious measurements. I soon found that it was not as easy as it had seemed. One reason is that it is not always obvious which are the galaxies and which are merely stars or other foreground objects. Some galaxies are easy to recognize: for instance, stars are never spiral, or noticeably elliptical. But some shapes are so faint that it is hard to tell whether they are sharp. Some galaxies appear small, faint and circular, and some are partly obscured by other objects. Nowadays such measurements are made by computers using sophisticated pattern-matching algorithms. But in those days one just had to examine each object carefully and use clues such as how fuzzy the edges looked – though there are also fuzzy objects, such as supernova remnants, in our galaxy. One used rules of thumb.

  How would one test such a rule of thumb? One way is to select a region of the sky at random, and then take a photograph of it at higher resolution, so that the identification of galaxies is easier. Then one compares those identifications with the ones made using the rule of thumb. If they differ, the rule is inaccurate. If they do not differ, then one cannot be sure. One can never be sure, of course.

  I was wrong to be impressed by the mere scale of what I was looking at. Some people become depressed at the scale of the universe, because it makes them feel insignificant. Other people are relieved to feel insignificant, which is even worse. But, in any case, those are mistakes. Feeling insignificant because the universe is large has exactly the same logic as feeling inadequate for not being a cow. Or a herd of cows. The universe is not there to overwhelm us; it is our home, and our resource. The bigger the better.

  But then there is the philosophical magnitude of a cluster of galaxies. As I moved the cross-hairs to one nondescript galaxy after another, clicking at what I guessed to be the centre of each, some whimsical thoughts occurred to me. I wondered whether I w
ould be the first and last human being ever to pay conscious attention to a particular galaxy. I was looking at the blurry object for only a few seconds, yet it might be laden with meaning for all I knew. It contains billions of planets. Each planet is a world. Each has its own unique history – sunrises and sunsets; storms, seasons; in some cases continents, oceans, earthquakes, rivers. Were any of those worlds inhabited? Were there astronomers there? Unless they were an exceedingly ancient, and advanced, civilization, those people would never have travelled outside their galaxy. So they would never have seen what it looked like from my perspective – though they might know from theory. Were any of them at that moment staring at the Milky Way, asking the same questions about us as I was about them? If so, then they were looking at our galaxy as it was when the most advanced forms of life on Earth were fish.

  The computers that nowadays catalogue galaxies may or may not do it better than the graduate students used to. But they certainly do not experience such reflections as a result. I mention this because I often hear scientific research described in rather a bleak way, suggesting that it is mostly mindless toil. The inventor Thomas Edison once said, ‘None of my inventions came by accident. I see a worthwhile need to be met and I make trial after trial until it comes. What it boils down to is one per cent inspiration and ninety-nine per cent perspiration.’ Some people say the same about theoretical research, where the ‘perspiration’ phase is supposedly uncreative intellectual work such as doing algebra or translating algorithms into computer programs. But the fact that a computer or a robot can perform a task mindlessly does not imply that it is mindless when scientists do it. After all, computers play chess mindlessly – by exhaustively searching the consequences of all possible moves – but humans achieve a similar-looking functionality in a completely different way, by creative and enjoyable thought. Perhaps those galaxy-cataloguing computer programs were written by those same graduate students, distilling what they had learned into reproducible algorithms. Which means that they must have learned something while performing a task that a computer performs without learning anything. But, more profoundly, I expect that Edison was misinterpreting his own experience. A trial that fails is still fun. A repetitive experiment is not repetitive if one is thinking about the ideas that it is testing and the reality that it is investigating. That galaxy project was intended to discover whether ‘dark matter’ (see the next chapter) really exists – and it succeeded. If Edison, or those graduate students, or any scientific researcher engaged upon the ‘perspiration’ phase of discovery, had really been doing it mindlessly, they would be missing most of the fun – which is also what largely powers that ‘one per cent inspiration’.

  As I reached one particularly ambiguous image I asked my hosts, ‘Is that a galaxy or a star?’

  ‘Neither,’ was the reply. ‘That’s just a defect in the photographic emulsion.’

  The drastic mental gear change made me laugh. My grandiose speculations about the deep meaning of what I was seeing had turned out to be, in regard to this particular object, about nothing at all: suddenly there were no astronomers in that image, no rivers or earthquakes. They had disappeared in a puff of imagination. I had overestimated the mass of what I was looking at by some fifty powers of ten. What I had taken to be the largest object I had ever seen, and the most distant in space and time, was in reality just a speck barely visible without a microscope, within arm’s reach. How easily, and how thoroughly, one can be misled.

  But wait. Was I ever looking at a galaxy? All the other blobs were in fact microscopic smudges of silver too. If I misclassified the cause of one of them, because it looked too like the others, why was that such a big error?

  Because an error in experimental science is a mistake about the cause of something. Like an accurate observation, it is a matter of theory. Very little in nature is detectable by unaided human senses. Most of what happens is too fast or too slow, too big or too small, or too remote, or hidden behind opaque barriers, or operates on principles too different from anything that influenced our evolution. But in some cases we can arrange for such phenomena to become perceptible, via scientific instruments.

  We experience such instruments as bringing us closer to the reality – just as I felt while looking at that galactic cluster. But in purely physical terms they only ever separate us further from it. I could have looked up at the night sky in the direction of that cluster, and there would have been nothing between it and my eye but a few grams of air – but I would have seen nothing at all. I could have interposed a telescope, and then I might have seen it. In the event, I was interposing a telescope, a camera, a photographic development laboratory, another camera (to make copies of the plates), a truck to bring the plates to my university, and a microscope. I could see the cluster far better with all that equipment in the way.

  Astronomers nowadays never look up at the sky (except perhaps in their spare time), and hardly ever look through telescopes. Many telescopes do not even have eyepieces suitable for a human eye. Many do not even detect visible light. Instead, instruments detect invisible signals which are then digitized, recorded, combined with others, and processed and analysed by computers. As a result, images may be produced – perhaps in ‘false colours’ to indicate radio waves or other radiation, or to display still more indirectly inferred attributes such as temperature or composition. In many cases, no image of the distant object is ever produced, only lists of numbers, or graphs and diagrams, and only the outcome of those processes affects the astronomers’ senses.

  Every additional layer of physical separation requires further levels of theory to relate the resulting perceptions to reality. When the astronomer Jocelyn Bell discovered pulsars (extremely dense stars that emit regular bursts of radio waves), this is what she was looking at:

  Radio-telescope output from the first known pulsar

  Only through a sophisticated chain of theoretical interpretation could she ‘see’, by looking at that shaky line of ink on paper, a powerful, pulsating object in deep space, and recognize that it was of a hitherto unknown type.

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

  Telescopes contain automatic tracking mechanisms that continuously realign them so as to compensate for the effect of the Earth’s motion; in some, computers continuously change the shape of the mirror so as to compensate for the shimmering of the Earth’s atmosphere. And so, observed through such a telescope, stars do not appear to twinkle or to move across the sky as they did to generations of observers in the past. Those things are only appearance – parochial error. They have nothing to do with the reality of stars. The primary function of the telescope’s optics is to reduce the illusion that the stars are few, faint, twinkling and moving. The same is true of every feature of the telescope, and of all other scientific instruments: each layer of indirectness, through its associated theory, corrects errors, illusions, misleading perspectives and gaps. Perhaps it is the mistaken empiricist ideal of ‘pure’, theory-free observation that makes it seem odd that truly accurate observation is always so hugely indirect. But the fact is that progress requires the application of ever more knowledge in advance of our observations.

  So I was indeed looking at galaxies. Observing a galaxy via specks of silver is no different in that regard from observing a garden via images on a retina. In all cases, to say that we have genuinely observed any given thing is to say that we have accurately attributed our evidence (ultimately always
evidence inside our own brains) to that thing. Scientific truth consists of such correspondence between theories and physical reality.

  Scientists operating giant particle accelerators likewise look at pixels and ink, numbers and graphs, and thereby observe the microscopic reality of subatomic particles like nuclei and quarks. Others operate electron microscopes and fire the beam at cells that are as dead as dodos, having been stained, quick-frozen by liquid nitrogen, and mounted in a vacuum – but they thereby learn what living cells are like. It is a marvellous fact that objects can exist which, when we observe them, accurately take on the appearance and other attributes of other objects that are elsewhere and very differently constituted. Our sensory systems are such objects too, for it is only they that are directly affecting our brains when we perceive anything.

  Such instruments are rare and fragile configurations of matter. Press one wrong button on the telescope’s control panel, or code one wrong instruction into its computer, and the whole immensely complex artefact may well revert to revealing nothing other than itself. The same would be true if, instead of making that scientific instrument, you were to assemble those raw materials into almost any other configuration: stare at them, and you would see nothing other than them.

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