Foreword by Herbert E. Huppert FRS
Chapter 1: The unconscious brain
Chapter 2: What is lucidity? What is understanding?
Chapter 3: Mindsets, evolution, and language
Chapter 4: Acausality illusions, and the way perception works
Chapter 5: What is science?
Chapter 6: Music, mathematics, and the Platonic
Postlude: The amplifier metaphor for climate
References and endnotes
Michael Edgeworth McIntyre FRS has written a book wide in its intellectual range and provocative in its implications. That will surprise no-one who knows him. His deep yet expansive vision of the world goes back to his ancestry and upbringing. His father, Archie McIntyre FAA, was a respected neurophysiologist and his mother, Anne McIntyre, was an accomplished visual artist. His great-grandfather Sir Edgeworth David FRS was a famous geologist and Antarctic explorer.
Michael’s childhood experiences, in Australia and New Zealand, included observing his father’s experimental skill, dissecting out individual nerve fibres in a laboratory full of electronic amplifiers and oscilloscopes. That was in the early days of micro-electrodes able to record from a single nerve cell. Michael also remembers being fascinated as a small boy by the sound of Beethoven’s Eighth Symphony made visible on an oscilloscope. He became very curious about how that sound — the sound of the “marvellously life-enhancing, energetic first movement”, as he described it — was related, somehow, to the wiggling green line on the oscilloscope tube.
In his teens Michael became a skilled violinist, and in 1960 rose to be leader of the New Zealand National Youth Orchestra. Such was his talent and his love of music that, after coming to Cambridge to work for a doctorate in fluid dynamics, he considered becoming a full-time professional musician — and indeed did become a part-time professional, and a member of the British Musicians’ Union, for some years. However, to our great good fortune, mathematics and science exerted a stronger pull in the end. He continues to play violin and viola and to passionately explore the links of music to other fields, notably neurology.
The book is divided into sections, the anecdotal narratives dancing gracefully with the scholarly enquiries, explicit or implicit, around the opening question “What is science?”
Rarely in this era of super-specialization does one encounter a true polymath, but that is a fair title to bestow on Michael. He has made original contributions to the fundamental understanding of fluid dynamics in the Earth’s atmosphere, in its oceans and in the Sun’s interior. He writes persuasively about the importance of lucidity and “lucidity principles”, whether in writing and speaking, or in designing a nuclear reactor (and everything in between). He is concerned about the unconscious assumptions that impede human progress, not least those stemming from our evolutionarily ancient dualism or “dichotomization instinct”, which “makes us stupid” in the manner now so dangerously amplified by the social media, through their “artificial intelligences that aren’t yet very intelligent”. But we can still hope that “smarter robots could be a game-changer in helping us humans to get smarter too.” Michael argues for the importance of scientific ethics, and reminds us of the limits of our epistemologies.
Michael is an engaging companion on this highly informed but charmingly informal odyssey. He invites the reader to see new landscapes through new lenses, and, crucially, to make new connections in all sorts of ways.
This book brings together a set of interconnected insights from the sciences and the arts that are so basic, I think, in so many ways, that they deserve to be better known than they are. For instance they include sharpened insights into communication skills, and into the power and the limitations of science. I go on to discuss, at the end, what science can and can’t tell us about the climate problem.
So I hope the book will interest scientifically-minded readers and especially young scientists. I’ve tried to bring out the connections in a widely understandable way that avoids equations and technical jargon. The book draws on a lifetime’s personal experience as a scientist, as a mathematician, and as a musician.
It hardly needs saying that if you’re a young scientist you need to hone your communication skills. In our complex world such skills are needed not only between scientists and the public, but also between scientists in different specialties. I’ll argue that it’s useful to know, for instance, how the skilful use of written and spoken language can be informed by the way music works.
Good communication will be crucial to tackling today’s and tomorrow’s great problems including the problems of climate change, biodiversity, and future pandemics and the problem of understanding the strengths and weaknesses of artificial intelligence.
To deepen our understanding of how communication works it’s useful and interesting to consider the origins of human language. It’s now known that biological evolution gave rise to our language ability in a manner quite different from what popular culture says. And evolution is itself now better understood. Rather than a simple competition between selfish genes it’s more like turbulent fluid flow, in some ways — a complex process spanning a vast range of timescales. I try to discuss these points very carefully, since they’re still contentious.
A further aspect of evolution is that, again contrary to popular belief, there’s a genetic basis not only for the nastiest but also for the most compassionate, most cooperative parts of human nature.
Throughout the book I’ve aimed for high-quality reasoning and respect for evidence. I’ve tried to keep the main text as short as possible, and readable without reference to the voluminous endnotes. I recommend ignoring the endnotes on a first read. However, as well as adding to the arguments, the endnotes give what I hope are enough literature references to support what I say.
Note regarding video and audio clips: Figure 1 below presents an animated video clip that is basic to many of my arguments. The QR code in the figure points to a URL that should display the video clip on any smartphone with a QR reader. Alternatively, that clip, together with some audio clips from later figures, can be downloaded from the World Scientific website as a zip file. The URL is https://www.worldscientific.com/worldscibooks/10.1142/12381#t=suppl
Acknowledgements: Many kind friends and colleagues have helped me with advice, encouragement, information, and critical comments over the years. I have learned much from experts on the latest developments in systems biology, evolutionary theory, and palaeoclimatology. Beyond those mentioned in the acknowledgements sections and endnotes of my original Lucidity and Science papers34, 75, 128 I’d like to thank Dorian Abbot, Leslie Aiello, David Andrews, Paul Ashworth, Grigory Barenblatt, Terry Barker, George Batchelor, Pat Bateson, Liz Bentley, Francis Bretherton, Oliver Bühler, Frances Cairncross, David Crighton, Ian Cross, Judith Curry, Philip Dawid, David Dritschel, Kuniyoshi Ebina, George Ellis, Sue Eltringham, Kerry Emanuel, Matthew England, Georgina Ferry, Rupert Ford, Angela Fritz, Chris Garrett, Jeffrey Ginn, Richard Gregory, Stephen Griffiths, Joanna Haigh, Peter Haynes, Brian Hoskins, Matthew Huber, Herbert Huppert, James Jackson, Sue Jackson, Peter Killworth, Kevin Laland, Steve Lay, Zheng Lin, Paul Linden, Shyeh Tjing Loi, Malcolm Longair, Jianhua Lü, James Maas, David MacKay, Normand MacLaurin, Niall Mansfield, David Marr, Nick McCave, Evelyn McFadden, Richard McIntyre, Ruth McIntyre, Steve Merrick, Gos Micklem, Alison Ming, Simon Mitton, Ali Mohebalhojeh, Ken Moody, Brian Moore, Walter Munk, Alice Oven, Tim Palmer, Antony Pay, Anthony Pearson, Tim Pedley, Sam Pegler, Max Perutz, Ray Pierrehumbert, Miriam Pollak, Vilayanur Ramachandran, Dan Rothman, Murry Salby, Adam Scaife, Nick Shackleton, Ted Shepherd, Adrian Simmons, Bill Simmons, Emily Shuckburgh, Luke Skinner, Appy Sluijs, David Spiegelhalter, Marilyn Strathern, Daphne Sulston, John Sulston, Stephen Thomson, Paul Valdes, Yixin Wan, Andy Watson, Ronald S. Watts, Estelle Wolfers, Flick Wolfers, Jeremy Wolfers, Jon Wolfers, Peter Wolfers, Eric Wolff, Toby Wood, Jim Woodhouse, and Laure Zanna. And I owe two very special debts of gratitude. One is to the clarinettist and conductor Antony Pay, a man of profound insight not only into the workings of music but also into science, humanity, and human nature. At a late stage he kindly read the entire manuscript and made many helpful suggestions. My other special debt is to Alice Oven, without whom this book would never have been written. As a young commissioning editor for World Scientific, it was she who first got me interested in embarking on this project. World Scientific’s Swee Cheng Lim, Jing Wen Soh and Rok Ting Tan have helped in numerous ways with the task of seeing the book through to press.
Cambridge, April 2021
Consider for a moment the following questions.
Good answers are important to our hopes of a civilized future; and many of the answers are surprisingly simple. But a quest to find them will soon encounter a conceptual and linguistic minefield, some of it around ideas like ‘innateness’ and ‘instinct’. Still, I think I can put us within reach of some good answers (with a small ‘a’) by recalling, first, some points about how our pre-human ancestors must have evolved — in a way that differs crucially from what popular culture says — and, second, some points about how we perceive and understand the world.
One reason for looking at evolution is the prevalence of misconceptions about it. Chief among them is the idea that natural selection works solely by competition between individuals. This ignores the many examples of cooperative behaviour among social animals, which Charles Darwin himself was at pains to point out.1 Saying that competition between individuals is all that matters flies in the face of this and much other evidence. It has also done great damage to human societies.2
On perception, understanding, and misunderstanding, and on our extraordinary language ability, it hardly needs saying that they were shaped by our ancestors’ evolution. Less obvious, however, is that the evolution must have depended not only on cooperation alongside competition but also, according to the best evidence, on a powerful feedback between genomic evolution and cultural evolution. For instance our language ability couldn’t have been invented around a hundred millennia ago, purely as a result of cultural evolution, as some researchers have argued. On the contrary, I’ll show in chapter 3 — drawing on clinching evidence from Nicaragua — that our language ability must have developed through the co-evolution of genomes and cultures, with each affecting the other over a much longer timespan, probably millions of years.
Such co-evolution is necessarily a multi-timescale process. Multi-timescale processes are ubiquitous in the natural world. They’re found everywhere. They depend on strong feedbacks between different mechanisms over a large range of timescales. Here we have slow and fast mechanisms in the form of genomic evolution and cultural evolution. I’m using the word ‘cultural’ in a broad sense, to include everything passed on by social learning. Such feedbacks have often been neglected in the literature on biological evolution. Their likely importance for pre-human evolution and their multi-timescale aspects were, however, recognized and pointed out as long ago as 1979 by the great biologist Jacques Monod,3 and by the great palaeoanthropologist Phillip Tobias.4
Another theme in this book will be unconscious assumptions. It’s clear that such assumptions underlie, for instance, the polarized debates about ‘nature versus nurture’, ‘instinct versus learning’, ‘genomic evolution versus cultural evolution’, and so on. A gut feeling that evolution is either genomic or cultural, with each excluding the other, is typical. At a deeply unconscious level, it’s assumed that you can’t have both together. Further examples will come up in chapter 3. They’re germane to some notable scientific controversies.
The dichotomization instinct, as I’ll call it, the visceral push toward polarization — toward seeing all choices and distinctions as binary and exclusive — is by no means the only source of unconscious assumptions. Much more of what’s involved in perception and understanding, and in our general functioning, takes place unconsciously. Some people find this hard to accept. Perhaps they feel offended, in a personal way, to be told that the slightest aspect of their existence might, just possibly, not be under full and rigorous conscious control. A brilliant scientist whom I know personally as a colleague took offence in exactly that way, in a recent discussion of unconscious assumptions in science — even though the exposure of such assumptions is the usual way in which scientific knowledge improves, as history shows again and again, and even though I offered clear examples from our shared field of expertise.5
Many other examples are given in the book by Daniel Kahneman.6 My own favourite example is a very simple one, Gunnar Johansson’s ‘walking dots’ or ‘walking lights’ animation. Twelve moving dots in a two-dimensional plane are unconsciously assumed to represent a particular three-dimensional motion. When the dots are moving, everyone with normal vision sees a person walking. To see the animation, point your smartphone at the QR code plus hyperlink on the right of figure 1. The animation shows a person walking from far right to near left.
Figure 1: On the left, a single frame from Gunnar Johansson’s ‘walking dots’ animation. On the right, a QR code plus hyperlink that will display the animation on any smartphone with a QR reader. (In a browser you can also click on the QR code.) The walking dots phenomenon is a well studied classic in experimental psychology and is one of the most robust perceptual phenomena known. Animation constructed by Steve Lay from data kindly supplied by Professor James Maas.
And again, anyone who has driven cars, or flown aircraft, will probably remember occasions on which accidents were avoided ahead of conscious thought. The typical experience is often described as witnessing oneself taking, for instance, evasive action when faced with a head-on collision, or other life-threatening emergency. It is all over by the time conscious thinking has begun. It has happened to me, in cars and in gliders. I think such experiences are quite common. Kahneman gives an example from firefighting.6
Many years ago, the anthropologist-philosopher Gregory Bateson put the essential point succinctly, in classic evolutionary cost-benefit terms:7
No organism can afford to be conscious of matters with which it could deal at unconscious levels.
Gregory Bateson’s point applies to us as well as to other living organisms. Why? There’s a mathematical reason, combinatorial largeness. Every living organism has to deal all the time with a combinatorial tree, a combinatorially large number, of present and future possibilities. Each branching of possibilities multiplies, rather than adds to, the number of possibilities. Being conscious of all those possibilities would be almost infinitely costly.
Combinatorially large numbers are unimaginably large. No-one can feel their magnitudes intuitively. For instance the number of ways to shuffle a pack of 52 cards is 52 × 51 × 50 × ... × 3 × 2 × 1. That’s just over 8 × 1067, or eighty million trillion trillion trillion trillion trillion.
The ‘instinctive’ avoidance of head-on collision in a car — the action taken ahead of conscious thought — is not, of course, something that comes exclusively from genetic memory. Learning is involved as well. The same goes for the way we see the walking dots animation. But much of that learning is itself unconscious, stretching back to the infantile groping that discovers the outside world and allows normal vision to develop.8 Far from being mutually exclusive, nature and nurture are intimately intertwined. That intimacy stretches even further back, to the genome within the embryo ‘discovering’ and interacting with its maternal environment.9 Jurassic Park is a great story, but scientifically wrong because you need dinosaur eggs as well as dinosaur DNA. Who knows, though — since birds are dinosaurs someone might manage it, one day, with reconstructed DNA and birds’ eggs.
My approach to questions like the foregoing comes from long experience as a scientist. Science was my main profession for fifty years or so. Although many branches of science interest me, my professional career was focused mainly on mathematical research to understand the highly complex, multi-timescale fluid dynamics of the Earth’s atmosphere and oceans. Included are phenomena such as the great jet streams and the air motion that shapes the ozone hole in the Antarctic stratosphere, and what are sometimes called the “world’s largest breaking waves”. Imagine a giant sideways breaker in the stratosphere the mere tip of which is almost as large as the entire USA. That research has in turn helped us, in an unexpected way, to understand the complex fluid dynamics and magnetic fields of something even more gigantic, the Sun’s interior. But long ago I almost became a musician. Or rather, in my youth I was, in fact, a part-time professional musician and could have made it into a full-time career. So I’ve had artistic preoccupations too, and artistic aspirations. This book tries to get at the deepest connections between all these things.
It’s obvious, isn’t it, that science, mathematics, and the arts are all of them bound up with the way perception works. That’ll be the central topic in chapter 4, where the walking dots will prove informative. And common to science, mathematics, and the arts is the creativity that leads to new understanding, the thrill of curiosity and lateral thinking, and sheer wonder at the whole phenomenon of life itself and at the astonishing Universe we live in.
One of the greatest of those wonders is our own adaptability, our versatility. Who knows, it might even get us through today’s crises, desperate though they might seem. We know that our hunter-gatherer ancestors were highly adaptable. They were driven again and again to migration and different ways of living by, among other things, rapid climate fluctuations — the legendary years of famine and years of plenty. How else did our species — a single, genetically-compatible species with its single human genome — spread around the globe in less than a hundred millennia? Chapter 3 will point to recent hard evidence for the sheer rapidity, and magnitude, of some of those climate fluctuations.
Chapter 3 will also point to recent advances in our understanding of biological evolution and natural selection, advances not yet assimilated into popular culture. One implication is that not only the nastiest but also the most compassionate, most cooperative parts of our makeup are ‘biological’ and deep-seated.2, 10, 11 There’s a popular misconception — yet another variation on the theme of nature ‘versus’ nurture — that our nastiest traits are exclusively biological and our nicest traits exclusively cultural. We’ll see that the evidence says otherwise.
Here, by the way, as in most of this book, I lay no claim to originality. For instance the evidence on past climates comes from the painstaking work of colleagues at the cutting edge of palaeoclimatology, including great scientists such as the late Nick Shackleton whom I had the privilege of knowing personally. And the points I’ll make about biological evolution rely on insights gleaned from colleagues at the cutting edge of biology, including the late John Sulston of human-genome fame, whom I also knew personally.
Our ancestors must have had not only language and lateral thinking — and music, dance, poetry, and storytelling — but also rhetoric, power games, blame games, genocide, ecstatic suicide and the rest. To survive, they must have had love and compassion too. The precise timespans and evolutionary pathways for these things are uncertain. But the timespans for at least some of them, including the beginnings of our language ability, must have been a million years or more to allow for the multi-timescale co-evolution of genomes and cultures.
As already suggested there’s been a tendency to neglect such co-evolution despite the ubiquity — the commonplace occurrence — of other multi-timescale processes in the natural world. Of these there’s a huge variety. To take one of the simplest examples, consider air pressure, as when pumping up a bicycle tyre. Fast molecular collisions mediate slow changes in air pressure, and air temperature, while pressure and temperature react back on collision rates and strengths. That’s a strong and crucial feedback across enormously different timescales.
So it never made sense to me to say that long and short timescales can’t interact. It never made sense to say that genomic evolution has no interplay with cultural evolution just because the one is slow and the other is fast. And in particular it never made sense to argue from the archaeological record, as some researchers have, that language started around a hundred millennia ago as a purely cultural invention — the sudden invention of a single mother tongue from which today’s languages are all descended, purely by cultural transmission.12, 13 I’ll return to these points in chapter 3 and will try to argue them very carefully.
When considering the archaeological record it’s sometimes forgotten that language and culture can be mediated purely by sound waves and light waves and held in individuals’ memories — as in the Odyssey or in a multitude of other oral traditions, including Australian aboriginal songlines and what Laurens van der Post called the “immense wealth” of the unwritten literature of Africa.14 That’s a very convenient, an eminently portable, form of culture for a tribe on the move. And sound waves and light waves are such ephemeral things. They have the annoying property of leaving no archaeological trace. But absence of evidence isn’t evidence of absence.
And now, in a mere flash of evolutionary time, a mere few centuries, we’ve shown our versatility and adaptability in ways that seem to me more astonishing than ever. We no longer panic at the sight of a comet. Demons in the air have shrunk to a small minority of alien abductors. We don’t burn witches and heretics, at least not literally. The Pope apologizes for past misdeeds. Genocide was avoided in South Africa. We even dare, sometimes, to tolerate individual propensities and lifestyles if they don’t harm others. We argue that tyrants needn’t always win. And they don’t always win. Indeed, headline bias and recent events notwithstanding, governments have become less tyrannical and more democratic, on average, over the past two centuries, in what political scientist Samuel Huntington has called three waves of democratization15 despite the setbacks in between, and now. And most astonishing of all, since 1945 we’ve even had the good sense so far — and very much against the odds — to avoid warfare with nuclear weapons.
We’ve marvelled at the sight of our beautiful Earth poised above the lunar horizon. We have space-based observing systems, super-accurate clocks, and super-accurate global positioning, adding to the cross-checks on Einstein’s gravitational theory, also called general relativity. And now there’s yet another, very beautiful cross-check on the theory, detection of the lightspeed gravitational ripples it predicts.16 We have the Internet, bringing us new degrees of freedom and profligacy of information and misinformation. It presents us with new challenges to exercise critical judgement and to build computational systems and artificial intelligences of unprecedented power, and to use them for civilized purposes — exploiting the robustness and reliability growing out of the open-source software movement, “the collective IQ of thousands of individuals”.17 We can read and write genetic codes, and thanks to our collective IQ are beginning, just beginning, to understand them.18 On large and small scales we’ve been carrying out extraordinary new social experiments with labels like ‘market democracy’, ‘market autocracy’, ‘children’s democracy’19, ‘microlending’ conducive to population control,20 ‘citizen science’, and the burgeoning social media. With the weaponization of the social media now upon us — and the additional threats to privacy and safety from, for instance, automated face recognition, reverse-image search, and deep-fake software — there’s a huge downside as with any new technology. But there’s also a huge upside, and everything to play for...
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What makes life as a scientist worth living? For me, part of the answer is the joy of being honest.
There’s a scientific ideal and a scientific ethic that power good science. And they depend crucially on honesty. If you stand up in front of a large conference and say of your favourite theory “I was wrong”, you gain respect rather than losing it. I’ve seen it happen. Your reputation increases. Why? The scientific ideal says that respect for the evidence, for theoretical coherence and self-consistency, for cross-checking, for finding mistakes, for dealing with uncertainty and for improving our collective knowledge is more important than personal ego or financial gain. And if someone else has found evidence that refutes your theory, then the scientific ethic requires you to say so. The ethic says that you must not only be factually honest but must also give due credit to others, by name, whenever their contributions are relevant.
The scientific ideal and ethic are powerful because even when, as is inevitable, they’re followed only imperfectly, they encourage not only a healthy scepticism but also a healthy mixture of competition and cooperation. Just as in the open-source software community, the ideal and ethic harness the collective IQ, the collective brainpower, of large research communities in ways that can transcend even the power of individual greed and financial gain. The ozone-hole story is a case in point.
So too is the human-genome story with its promise of future scientific breakthroughs, including medical breakthroughs, calling for years and decades of collective research effort. The scientific ideal and ethic were powerful enough to keep the genomic information in the public domain — available for use in open research communities — despite an attempt to lock it up commercially that very nearly succeeded.26 Our collective brainpower will be crucial to solving the problems posed by the genome and the molecular-biological systems of which it forms a part, including the interplay with diseases such as COVID-19. Like so many other problems now confronting us, they are problems of the most formidable complexity.
In the Postlude I’ll return to the struggle between open science and the forces ranged against it, with particular reference to climate change, the most complex problem of them all. Again, there’s no claim to originality here. I merely aim to pick out, from the morass of confusion and misinformation surrounding the topic,24 some basic points clarifying where the uncertainties lie, as well as the near-certainties.
This book reflects my own journey toward the frontiers of human self-understanding. Of course many others have made such journeys. But in my case the journey began in a slightly unusual way.
Music and the arts were always part of my life. Music was pure magic to me as a small child. But the conscious journey began with a puzzle. While reading my students’ doctoral thesis drafts, and working as a scientific journal editor, managing the peer review of colleagues’ research papers, I began to wonder why lucidity, or clarity — in writing and speaking, as well as in thinking — is often found difficult to achieve. And I wondered why some of my colleagues are such surprisingly bad communicators, even within their own research communities, let alone on issues of public concern. Then I began to wonder what lucidity is, in a functional or operational sense. And then I began to suspect a deep connection with the way music works. Music is, after all, not only part of our culture but also part of our unconscious human nature.
I now like to understand the word ‘lucidity’ in a more general sense than usual. It’s not only about what you can find in style manuals and in books on how to write, excellent and useful though many of them are. (Strunk and White27 is a little gem.) It’s also about deeper connections not only with music but also with mathematics, pattern perception, biological evolution, and science in general. A common thread is what I call the organic-change principle.
The principle says that we’re perceptually sensitive to, and have an unconscious interest in, patterns exhibiting ‘organic change’. These are patterns in which some things change, continuously or by small amounts, while others stay the same. So an organically-changing pattern has invariant elements.
The walking dots animation is an example. The invariant elements include the number of dots, always twelve dots. Musical harmony is another.
Musical harmony is an interesting case because ‘small amounts’ is relevant not in one, but in two different senses, as we’ll see in chapter 6. This leads to the idea of ‘musical hyperspace’. An organic chord progression, or harmony change, can take us somewhere that’s both nearby and far away. That’s how some of the magic is done, in many genres of Western music. An octave leap is a large change in one sense, but small in the other, indeed so small that musicians use the same name for the two pitches. The invariant elements in an organic harmony change can be pitches or chord shapes.
Music makes use of organically-changing sound patterns not just in its harmony, but also in its melodic shapes and counterpoint and in the overall form, or architecture, of an entire piece of music. That’s part of how it can grab our attention. Mathematics, too, involves organically-changing patterns. In mathematics there are beautiful results about ‘invariants’ or ‘conserved quantities’, things that stay the same while other things change, often continuously through a vast space of possibilities. The great mathematician Emmy Noether discovered a common origin for many such results, through a profound and original piece of mathematical thinking. Her discovery is called Noether’s Theorem and is recognized today as a foundation-stone of theoretical physics.
Our perceptual sensitivity to organic change exists for strong biological reasons. One reason is the survival value of sensing the difference between living things and dead or inanimate things. To see a cat stalking a bird, or a flower opening, is to see organic change.
So I’d dare to describe our sensitivity to it as deeply instinctive. Many years ago I saw a pet kitten suddenly die of some mysterious but acute disease — a sudden freezing into stillness. I’d never seen death before, but I remember feeling instantly sure of what had happened — ahead of conscious thought. And the ability to see the difference between living and dead has been shown to be well developed in human infants a few months old.
Notice how intimately involved, in all this, are ideas of a very abstract kind. The idea of some things changing while others stay invariant is itself highly abstract, as well as simple. It’s abstract in the sense that vast numbers of possibilities are included. There are vast numbers — combinatorially large numbers — of organically-changing patterns, musical, mathematical, visual, and verbal. Here again we’re glimpsing the fact already hinted at, that the unconscious brain can handle many possibilities at once. We have an unconscious power of abstraction. That’s almost the same as saying that we have unconscious mathematics. Mathematics is a precise means of handling many possibilities, many patterns, at once, and of discovering new things about them, in an explicit and logically self-consistent way.
The walking dots animation shows that we have unconscious Euclidean geometry, the mathematics of angles and distances. There are combinatorially large numbers of arrangements of objects, at various angles and distances from one another. The roots of mathematics and logic lie far deeper, and are evolutionarily far more ancient, than they’re usually thought to be. They’re hundreds of millions of years more ancient than archaeology might suggest. In chapter 6 I’ll show that our unconscious mathematics includes, also, the mathematics underlying Noether’s theorem, and I’ll show how all this is related to Plato’s world of perfect mathematical forms.
So I’ve been interested in lucidity, ‘lucidity principles’, and related matters in a sense that cuts deeper than, and goes far beyond, the niceties and pedantries of style manuals. But before anyone starts thinking that it’s all about Plato and ivory-tower philosophy, let’s remind ourselves of some harsh practical realities — as Plato would have done had he lived today. What I’m talking about is relevant not only to music, mathematics, thinking, and communication skills but also, for instance, to the ergonomic design of machinery, of software and user-friendly IT systems (information technology), of user interfaces in general and of technological systems of any kind — including the emerging artificial-intelligence systems, where the stakes are so incalculably high.
The organic-change principle — that we’re perceptually sensitive to organically-changing patterns — shows why good practice in any of these endeavours involves not only variation but also invariant elements, i.e., repeated elements, just as music does. Good control-panel or website design might use, for instance, repeated shapes for control knobs or buttons. And in writing and speaking one needn’t be afraid of repetition, if it forms the invariant element within an organically-changing word pattern. “If you are serious, then I’ll be serious” is a clearer and stronger sentence than “If you are serious, then I’ll be also.” Loss of the invariant element “serious” weakens the sentence. Still weaker are versions like “If you are serious, then I’ll be earnest.” Such pointless or gratuitous variation in place of repetition is what H. W. Fowler ironically called “elegant” variation, an “incurable vice” of second-rate writers.28 Its opposite can be called lucid repetition, as in “If you are serious, then I’ll be serious.” Lucid repetition is not the same as being repetitious. The pattern as a whole is changing, organically. It works the same way in every language I’ve looked at, including Chinese.29
Two more ‘lucidity principles’ are worth noting here. There’s an explicitness principle — the need to be more explicit than you feel necessary — because, obviously, you’re communicating with someone whose head isn’t full of what your own head is full of. As the great mathematician J. E. Littlewood once put it,30 “Two trivialities omitted can add up to an impasse.” Again, this applies to design in general, as well as to any form of writing or speaking that aims at lucidity. Quite often, all that’s needed is to use a noun, perhaps repeated, rather than a pronoun. With a website button marked ‘Cancel’ it helps to say what it cancels. And then there’s the more obvious coherent-ordering principle, the need to build context before new points are introduced. It applies not only to writing and speaking but also to the design of any sequential process on, for instance, a website or a ticket-vending machine.
One reason for attending to these principles is that human language is surprisingly weak on logic-checking, including checks for self-consistency.
That’s one of the reasons why language is such a conceptual minefield — something that’s long kept philosophers in business. And beyond everyday misunderstandings we have, of course, the workings of professional camouflage and deception, as in the ozone and other disinformation campaigns.
The logic-checking weakness shows up in the misnomers and self-contradictory terms encountered not only in everyday dealings but also — to my continual surprise — in the technical language used by my scientific and engineering colleagues...
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What of my other question? What is this subtle and elusive thing we call understanding, or insight? What does it mean to think clearly about a problem?
Of course there are many answers, depending on one’s purpose and viewpoint. I’ll focus on scientific understanding.
What I’ve always found in my own research, and have always tried to suggest to my students, is that developing an in-depth scientific understanding of something — understanding in detail how it works — requires looking at it, and testing it, from as many different viewpoints as possible. That’s an important part of the creativity that goes into good science. And it puts a premium on good communication, including the ability to listen, actively, to someone offering a different viewpoint or focusing on a different aspect. Another part is to maintain a healthy scepticism, while respecting the evidence. And because it respects the evidence, such creativity is to be sharply distinguished from the postmodernist ‘anything goes’.
For instance, the multi-timescale fluid dynamics I’ve worked on is far too complex to be understandable at all from a single viewpoint, such as the viewpoint provided by a particular set of mathematical equations. One needs a multi-modal approach with equations, words, pictures, and feelings all working together, as far as possible, to form a self-consistent whole with experiments and observations. And the equations themselves take different forms embodying different viewpoints, with technical names such as ‘variational’, ‘Eulerian’, ‘Lagrangian’, and so on. They’re mathematically equivalent but, as the great physicist Richard Feynman used to say, “psychologically very different”. I’ll give an example in chapter 6. Bringing in words, in a lucid way, is a critically important part of the whole but needs to be related to, and made consistent with, equations, pictures, and feelings.
Such multi-modal thinking and healthy scepticism have been the only ways I’ve known of escaping from the mindsets and unconscious assumptions that tend to entrap us, and of avoiding false dichotomies in particular. The history of science shows that escaping from mindsets has always been a key part of progress, as already remarked,5 including what Thomas Kuhn famously called paradigm shifts. And an important aid to cultivating a multi-modal view of any scientific problem is the habit of performing what Albert Einstein called thought-experiments, and mentally viewing those from as many angles as possible.
Einstein certainly talked about feeling things, in one’s imagination — forces, motion, colliding particles, light waves — and was always doing thought-experiments, mental what-if experiments if you prefer. The same thread runs through the testimonies of Feynman and of other great scientists, such as Peter Medawar and Jacques Monod. It all goes back to juvenile play — that deadly serious rehearsal for real life — young animals and children pushing and pulling things (and people!) to see, and feel, how they work.
In my own research community I’ve often noticed colleagues having futile arguments about ‘the’ cause of some phenomenon. “It’s driven by such-and-such”, says one. “No, it’s driven by so-and-so”, says another. Sometimes the argument gets quite acrimonious. Often, though, they’re at cross-purposes because — perhaps unconsciously — they have different thought-experiments in mind.
Notice how the verb ‘to drive’ illustrates what I mean by language as a conceptual minefield. ‘Drive’ sounds incisive and clear-cut, but is nonetheless dangerously ambiguous. I sometimes think that our computers should make it flash red for danger, as soon as it’s typed, along with some other dangerously ambiguous words such as the pronoun ‘this’.
‘To drive’ can mean ‘to control’, as when driving a car, or controlling an audio amplifier via its input signal. But ‘to drive’ can also mean ‘to supply the energy needed’, via the fuel tank or the amplifier’s power supply. Well, there are two quite different thought-experiments here, on the amplifier let’s say. One is to change the input signal. The other is to switch the power off. A viewpoint focused on the power supply alone misses crucial aspects of the problem.
You may laugh, but there’s been a mindset in my research community that has, or used to have, precisely such a focus. It said that the way to understand our atmosphere and oceans is through their intricate ‘energy budgets’, disregarding questions of what they’re sensitive to. Yes, energy budgets are interesting and important, but no, they’re not the Answer to Everything. Energy budgets focus attention on the power supply, making an input signal look unimportant just because it’s small.
Instead of the verb ‘to drive’ it’s often helpful, I think, to use the verb ‘to mediate’, as in the biological literature where it usually points to an important part of some mechanism.
The topic of mindsets and unconscious assumptions has been illuminated not only through the work of Kahneman and Tversky6 but also through, for instance, that of Iain McGilchrist and Vilayanur Ramachandran. They bring in the workings of the brain’s left and right hemispheres. That’s a point to which I’ll return in chapter 4. In brief, the right hemisphere typically takes a holistic view of things and is more open to the unexpected, while the left hemisphere specializes in dissecting fine detail and is more prone to mindsets, including their unconscious aspects.36, 37 The sort of scientific understanding I’m talking about — in-depth understanding — seems to involve an intricate collaboration between the two hemispheres, with each playing to its own very different strengths.
Conversely, if that collaboration is disrupted by brain damage, extreme forms of mindset can result. Clinical neurologists are familiar with a delusional mindset called anosognosia. Damage to the right hemisphere paralyses, for instance, a patient’s left arm, yet the patient vehemently denies that the arm is paralysed, and will make all sorts of excuses as to why he or she doesn’t fancy moving it when asked.
Back in the 1920s, the great physicist Max Born was immersed in the mind-blowing experience of developing quantum theory. Born later remarked that engagement with science and its healthy scepticism can give us an escape route from mindsets and unconscious assumptions. With the more dangerous kinds of zealotry or fundamentalism in mind, he said38
“I believe that ideas such as absolute certitude, absolute exactness, final truth, etc., are figments of the imagination which should not be admissible in any field of science... This loosening of thinking [Lockerung des Denkens] seems to me to be the greatest blessing which modern science has given to us. For the belief in a single truth and in being the possessor thereof is the root cause of all evil in the world.”
Further wisdom on these topics can be found in, for instance, the classic study of fundamentalist cults by Flo Conway and Jim Siegelman.39 It echoes religious wars over the centuries. Time will tell, perhaps, how the dangers from the fundamentalist religions compare with those from the fundamentalist atheisms. Among today’s fundamentalist atheisms we have not only scientific fundamentalism, saying that Science Is the Answer to Everything and Religion Must Be Destroyed — provoking a needless backlash against science, sometimes violent — but also, for instance, atheist versions of what economists now call market fundamentalism.2
Market fundamentalism is arguably the most dangerous of all because of its financial and political power, still remarkably strong in today’s world. I don’t mean Adam Smith’s reasonable idea that market forces and profits are useful, in symbiosis with the division of labour and good regulation.25 Smith was clear about the need for regulation, written or unwritten.40 I don’t mean the business entrepreneurship that can provide us with useful goods and services. By market fundamentalism I mean the hypercredulous belief, the taking-for-granted, the simplistic and indeed incoherent mindset that market forces are by themselves the Answer to Everything, when based solely on ‘deregulation’ and the maximization of individual profit — regardless of evidence like the 2008 financial crash. Some adherents consider their beliefs ‘scientifically’ justified through the idea, which they wrongly attribute to Darwin, that competition between individuals is all that matters.1 That last idea isn’t, I should add, exclusive to the so-called political right.2
Understanding market fundamentalism is important because of its tendency to promote not only financial but also social instability, not least through gross economic inequality. And the financial power of market fundamentalism makes it one of the greatest threats to good science, and indeed to rational problem-solving of any kind because, for a true believer, individual profit is paramount, taking precedence over respect for evidence — evidence about financial and social stability, or mental health, or pandemic viruses, or biodiversity, or the ozone hole or climate or anything else. The point is underlined by the investigations in refs. 24 and 41.
Common to all forms of fundamentalism, or puritanism, or extremism is that besides ignoring or cherry-picking evidence they forbid the loosening of thinking that allows freedom to view things from more than one angle. Only one viewpoint is permitted, for otherwise you are ‘impure’. You’re commanded to have tunnel vision. The 2008 financial crash seems to have made only a small dent in market fundamentalism, so far, though perhaps reducing the numbers of its adherents. Perhaps the COVID-19 pandemic will make a bigger dent. It’s too early to say. And what’s called ‘science versus religion’ is not, it seems to me, about scientific insight versus religious, or spiritual, insight. Rather, it’s about scientific fundamentalism versus religious fundamentalism, which of course are irreconcilable.
Such futile dichotomizations cry out for more loosening of thinking. How can such loosening work? As Ramachandran or McGilchrist might say, it’s almost as if the right brain hemisphere nudges the left with a wordless message to the effect that ‘You might be sure, but I smell a rat: could you, just possibly, be missing something?’
It’s well known that in 1983 a Russian officer, Stanislav Petrov, saved us from likely nuclear war. At great personal cost, he disobeyed standing orders when a malfunctioning weapons system said ‘nuclear attack imminent’. He smelt a rat and we had a narrow escape. We probably owe it to Petrov’s right hemisphere. There have been other such escapes.
Let’s fast-rewind to a few million years ago, and further consider our ancestors’ evolution. Where did we, our insights, and our mindsets come from? And how on Earth did we acquire our language ability — that vast conceptual minefield — so powerful, so versatile, yet so weak on logic-checking? These questions are more than just tantalizing. Clearly they’re germane to past and present conflicts, and to future risks including existential risks.
The first obstacle to understanding is what I’ll dare — following a suggestion from a friend of mine, the late, great John Sulston — to call simplistic evolutionary theory. The theory is still firmly entrenched in popular culture, with labels like ‘Darwinian struggle’. Many biologists would now agree with John that the theory is no more than a caricature. But it’s a remarkably persistent caricature. It’s still hugely influential. It includes the idea that competition between individuals is all that matters.
More precisely, simplistic evolutionary theory says that evolution has just three aspects. First, the structure of an organism is governed entirely by its genome, acting as a deterministic ‘blueprint’ made of all-powerful ‘selfish genes’. Second, contrary to what Charles Darwin thought,18 natural selection is the only significant evolutionary force. And third, natural selection works through ‘survival of the fittest’, conceived of solely in terms of a struggle between individuals.
Survival of the fittest would be a reasonable proposition were it not that an oversimplified notion of fitness is used. Not only is fitness presumed to apply solely to individual organisms, but it’s also presumed to mean nothing more than the individual’s ability to pass on its genes. Admittedly this purely competitive, purely individualistic view does explain much of what happens in our planet’s astonishing biosphere. But it also misses many crucial points. It’s not the evolutionary Answer to Everything.
There’s a slightly more sophisticated view called ‘inclusive fitness’ or ‘kin selection’, which replaces individuals by families whose members share enough genes to count as closely related. But it misses the same points.
For one thing, as Darwin recognized, our species and other social species, such as baboons, could not have survived without cooperation within large groups. Without such cooperation, alongside competition, our ground-dwelling ancestors would have been easy meals for the large, swift predators all around them, including the big cats — gobbled up in no time at all! Cooperation restricted to a few closely related individuals would not have been enough to survive those dangers. And Darwin gives clear examples in which cooperation within large non-human groups is, in fact, observed to take place, as for instance with the geladas and the hamadryas baboons of Ethiopia.1
Even bacteria cooperate. That’s well known. One way they do it is by sharing small packages of genetic information called plasmids or DNA cassettes. A plasmid might for instance contain information on how to survive antibiotic attack. Don’t get me wrong. I’m not saying that bacteria ‘think’ like us, or like baboons or dolphins or other social mammals, or like social insects. And I’m not saying that bacteria never compete. They often do. But for instance it’s a hard fact — a practical certainty, and now an urgent problem in medicine — that large groups of individual bacteria cooperate among themselves to develop resistance to antibiotics. For the bacteria such resistance is highly adaptive, and strongly selected for. Yes, selective pressures are at work, but at group level as well as at individual and kin level, and at cellular and molecular level,18 in heterogeneous populations living in heterogeneous, and ever-changing, ecological environments.
So it’s plain that natural selection operates at very many levels within the biosphere, and that cooperation is widespread alongside competition. Indeed the word ‘symbiosis’ in its standard meaning denotes a variety of intimate, and well studied, forms of cooperation not between individuals of one species but between those of entirely different species. And different species of bacteria share plasmids.42 The trouble is the sheer complexity of it all — again a matter of combinatorial largeness as well as of population heterogeneity, and of the complexities of mutual fitness in and around various ecological niches. We’re far from having comprehensive mathematical models of how it all works.
On the other hand, though, the models have made great progress over the past decade or so, aided by increasing computer power. There have been significant advances at molecular level.18 They’ve added to the accumulated evidence for what’s now called multi-level natural selection or, for brevity, multi-level selection.43–55 The evidence comes not only from better models at various levels but also, for instance, from laboratory experiments with heterogeneous populations of real organisms, directly demonstrating group-level selection.43
The persistence of simplistic evolutionary theory, oblivious to all these considerations, seems to be bound up with a particular pair of mindsets. The first says that the genes’ eye view — or, more fundamentally, the replicators’ or DNA’s eye view — gives us the only useful angle from which to view evolution. The second reiterates that selective pressures operate at one level only, that of individual organisms. The first mindset misses the value of viewing a problem from more than one angle. The second misses most of the real complexity. And that complexity includes not only group-level selective pressures as demonstrated in the laboratory,43 but also the group-level selective pressures on our ancestors noted by Jacques Monod3 and by palaeoanthropologists such as Phillip Tobias,4 Robin Dunbar,46 and Matt Rossano48 to name but a few.
Both mindsets seem to have come from mathematical models that are grossly oversimplified by today’s standards, valuable though they were in their time. They are the old population-genetics models that were first formulated in the early twentieth century44 and then further developed in the 1960s and 1970s. For the sake of mathematical simplicity and solvability those models exclude, by assumption, all the aforementioned complexities as well as multi-timescale processes and, in particular, realistic group-level selection scenarios.43, 52, 54 And the hypothetical ‘genes’ in those models are themselves grossly oversimplified. They correspond to the popular idea of a gene ‘for’ this or that trait — nothing like actual genes, the protein-coding sequences within the genomic DNA. Very many actual genes are involved, usually, in the development of a recognizable trait, along with non-coding parts of the DNA and the associated regulatory networks3, 9, 18...
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And what of the changing climate that our ancestors had to cope with? Over the timespan of figure 2 [omitted from this preview, 3.5Myr], the climate system underwent increasingly large fluctuations some of which were very sudden, as will be illustrated shortly, drastically affecting our ancestors’ food supplies and living conditions. In the later stages, which culminated in the runaway brain evolution and global-scale migration of our species, the increasing climate fluctuations would have been ramping up the pressure to develop tribal solidarity and versatility mediated by ever more elaborate mythologies, rituals, songs, and stories passed from generation to generation.
And what stories they must have been! Great sagas etched into a tribe’s collective memory. It can hardly be accidental that the sagas known today tell of years of famine and years of plenty, of battles, of epic journeys, of great floods, and of terrifying deities that are both fickle benefactors and devouring monsters — just as the surrounding large predators must have appeared to our early ancestors, as those ancestors scavenged on leftover carcasses long before becoming top predators themselves.67 And epic journeys and great floods must have been increasingly part of our ancestors’ struggle to survive, as they migrated under the increasingly changeable climatic conditions...
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To survive all this, our ancestors must have had not just tribal solidarity but also, at least in times of crisis, strong leaders and willing followers. Hypercredulity and weak logic-checking must have had a role — selected for as genome and culture co-evolved and language became more sophisticated, and more fluent and imaginative with stories of the natural and the supernatural.
How do you make leadership work? Do you make a reasoned case? Do you ask your followers to check your logic? Do you check it yourself? Of course not! You’re a leader because, with your people starving, you’ve emerged as a charismatic visionary. You’re divinely inspired. Your people love you. You know you’re right, and it doesn’t need checking. “O my people, I’ve been shown the True Path that we must follow. Come with me! Let’s make our tribe great again! Beyond those mountains, over that horizon, that’s where we’ll find our Promised Land. It is our destiny to find that Land and overcome all enemies because we, and only we, are the True Believers. Our stories are the only true stories.” How else, in the incessantly-fluctuating climate, I ask again, did our one species — our single human genome — spread all around the globe in less than a hundred millennia?
And what of dichotomization — that ever-present, ever-potent source of unconscious assumptions — unconscious assumptions that are so often wrong in today’s world? Well, it’s even more ancient, isn’t it. Hundreds of millions of years more ancient. Ever since the Cambrian, half a billion years ago, survival has teetered on the brink of edible or inedible, male or female, friend or foe, and fight or flight. In life-threatening emergencies, binary snap decisions were crucial. But with language and hypercredulity in place, the dichotomization instinct — rooted in the most ancient, the most primitive, the most reptilian parts of our brains — could grow into new forms. Not just friend or foe but also We are right and they are wrong. It’s the Absolute Truth of our belief system versus the absolute falsehood of theirs, with nothing in between.
You might be tempted to dismiss the last point as a mere ‘just so story’, speculation unsupported by evidence. But I’d argue that there’s plenty of evidence today. One clear line of evidence is the ease with which polarized conflicts are amplified, expanded, and intensified by the social media.
There’s also the evidence documented in the book by David Sloan Wilson.43 This carefully argued book includes detailed case studies of fundamentalist or puritanical belief systems — religious in chapter 6, and atheist in chapter 7. For instance Ayn Rand, an atheist prophet revered for her preaching of market fundamentalism, held that selfishness is absolutely good and altruism absolutely bad, for absolutely everyone. Personal greed is the Answer to Everything, and the pinnacle of moral virtue. Wilson describes how a well-intentioned believer, Rand’s disciple Alan Greenspan, was “dumbfounded” by the 2008 financial crash shortly after his long reign at the US Federal Reserve Bank. By a supreme irony Rand’s credo also says, or takes for granted, not only that ‘We are right and they are wrong’ but also that ‘We are rational and they are irrational’. Any logic-checking that considers an alternative viewpoint is ‘irrational’, something to be dismissed out of hand.
It’s the same for any other puritanical mindset. Only one viewpoint is permitted; and unless you dismiss the alternatives immediately, without stopping to think, you’re impure, aren’t you. You’re a ditherer, a lily-livered moral weakling. You’re in danger of sending a heretical ‘mixed message’ when it’s all about Us Versus Them. That’s the force behind the so-called ‘purity spirals’ seen on social media, in which reasoned debates turn into shouting matches between increasingly polarized factions.
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Yes, dichotomization makes us stupid. Luckily, however, dichotomization isn’t all there is. We don’t have to see the world this way. It’s a trap we needn’t fall into. Outside life-threatening emergencies — and far more than your average reptile — we do have the ability to stop and think. We do have the ability to see that while some issues are dichotomous many others are not. We do have the ability to see — oh shock horror — that there might be merit in different viewpoints. And surprising though it may seem just now, social media such as Facebook might, with a bit of luck, help us to strengthen those thinking abilities in the not too distant future.
For many years now, the social media have amassed vast wealth and supranational power by using the artificial intelligences, the robots, that they’ve built from their ‘large hadron collider of experimental psychology’ as I called it — experimentation on billions of human subjects.22 But those robots are not yet very intelligent! In some ways they’re downright stupid. Why do I say that? Because, as currently set up, they pose an existential threat to their own survival.
Part of that threat comes from the way the robots exploit the dichotomization instinct, alongside other primitive instincts such as fear, anger, and hatred, to make things go viral and thereby rake in advertising revenue. Like or dislike, friend or unfriend, follow or don’t follow, share or don’t share, include or exclude, and so on, are not only addictive data-gathering devices but also, in their own way, examples of what I called ‘perilous binary buttons’. Press or don’t press, and don’t stop to think. In this and in other ways of shutting off thinking, the social-media robots have become highly efficient machines for spreading misinformation and alternative ‘realities’, as well as negative emotions and mental illness, on an unprecedented scale. If it’s emotionally charged, it spreads faster and is more profitable.
All this creates a new threat to democratic social stability that adds to the older, ongoing threat from gross economic inequality. Among their billions of users the robots, functioning at lightning speed, have amplified and expanded the purity spirals, the divisive rhetoric and hatespeech, the misinformed echo chambers, the filter bubbles and preference bubbles, and the sheer anger, that’s been adding fuel to the vicious binary politics we see all around us. Ref. 72 describes recent statistical studies of these phenomena.
Just as in the 1930s, that same vicious politics could soon replace democracy by brutal autocracy — and this time even at home, even at the nerve centre of the social media, even in freedom-loving Silicon Valley. And autocracy would destroy the private autonomy of enterprises like Google and Facebook. It would destroy the freewheeling, freedom-loving, democratic business environment to which the social media owe their vast wealth and power. Please don’t get me wrong. The social media have their upside and have brought huge benefits of many kinds, such as useful networking and the videos showing kids how to make and repair things — to say nothing of new ways to resist autocracy. The threat to democratic social stability was no doubt unintended. But that doesn’t make the threat less real, and less imminent.
The social-media technocrats must surely have recognized their peril. The technocrats aren’t themselves stupid. At least I don’t think they are. There’s a good chance, I think, that they’re working to make their robots smarter and less socially destabilizing. They have the financial and technical resources to do it, difficult though the task may be. Indeed I’ve heard spokespersons for two of the media, Reddit and Google’s YouTube, saying that such work is in hand and making headway. I hope they’re right. Reddit seems to be further ahead thanks to a long-established policy of respecting user privacy, alongside the development of a multi-level robot-assisted moderation system. Social scientists are coming up with further ideas that might help.72 And the storming of the US Capitol on 6 January 2021 should focus minds along with the arrival, now, of the new deep-fake disinformation and character-assassination techniques.23
Smarter robots could be a game-changer in helping us humans to get smarter too. They could help us to escape from mindsets instead of being trapped by them. With humans and robots there’s a dystopian mindset that ‘they’ll take over’. But that’s yet another binary trap, another Us Versus Them. When, instead, humans and robots work together on solving problems, with each playing to their own very different strengths, the combination can become much more powerful and much more exciting than either alone. A robot can take on the role of a third ‘brain hemisphere’ to help with problem-solving. Included, I dare to hope, might be the problem of maintaining democratic social stability in all its complexity. Instead of shutting off our thinking, robots can open it up. They can help us to see things from more than one angle.
An early example was the famous work of the DeepMind team led by Demis Hassabis, with a robot called AlphaGo. In learning to play the combinatorially large game of Go, it discovered winning game patterns that no human had thought of. And now we have its descendant AlphaFold, which in 2020 made a breakthrough toward solving the combinatorially large, and hugely important, problem of protein folding55 — the problem of deducing the three-dimensional shapes of protein molecules solely from a knowledge of their DNA, hence amino-acid, sequences in cases where the sequence fixes the shape.
The most powerful robots are like precocious children because they work by being open to learning. As with human children, we need to get to know them and to get better at teaching them and, above all, better at choosing what to teach them and how best to incentivize them. Should we keep on pushing them to amplify misinformation and social instability just because it’s lucrative in the short term? Is that a smart thing to do? Or should we push them instead to encourage flexible, versatile lateral thinking, and critical thinking, helping to expose things that might surprise us and even make us a bit uncomfortable? Could they help us to become more skilful and adaptable in future? AlphaGo and AlphaFold show that the answer is a resounding yes.
We can engage with our own children without knowing the wiring diagrams and patterns of plasticity within their brains. Similarly, we can engage with our robots without knowing what their millions of lines of self-generated computer code look like. And we can get them to help reinforce the more civilized human instincts rather than, as at present, mostly the nastier ones to boost profits. Being superb at complex pattern-recognition, they could for instance do a better job on learning the ever-evolving patterns and contexts of hatespeech, catching it before it spreads...
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Picture a typical domestic scene. “You interrupted me!” “No, you interrupted me!”
Such stalemates can arise from the fact that perceived timings differ from actual physical timings in the outside world, as measured by clocks.74 I once tested this experimentally by secretly tape-recording a dinner-table conversation. At one point I was quite sure that my wife had interrupted me, and she was equally sure it had been the other way round. When I listened afterwards to the tape, I discovered to my chagrin that she’d been right. She had started to speak a few hundred milliseconds before I did.
Musical training includes learning to cope with the differences between perceived timings and actual timings. For instance musicians often check themselves with a metronome, a small machine that emits precisely regular clicks. The final performance won’t necessarily be metronomic, but practising with a metronome helps to remove inadvertent errors in the fine control of rhythm. “It don’t mean a thing if it ain’t got that swing...”
There are many other examples. I once heard a radio interviewee recalling how he’d suddenly got into a gunfight: “It all went intuh slowww — motion.” An example still more striking is that of the jazz saxophonist Tony Kofi. At age 16 he fell three stories from a roof-repair job. He describes how he experienced the fall in slow motion, and on the way down had visions of unknown faces and places and saw himself playing an instrument. It was a life-changing experience that made him into a musician.
A scientist who claims to know that eternal life is impossible has failed to notice that perceived timespans at death might stretch to infinity. That, by the way, is a simple example of the limitations of science. What might or might not happen to perceived time at death is a question outside the scope of science, because it’s outside the scope of experiment and observation. It’s here that ancient religious teachings show more wisdom, I think, when they say that deathbed compassion and reconciliation are important to us. Perhaps I should add that, as hinted earlier, I’m not myself conventionally religious. I’m an agnostic whose closest approach to the numinous — to the transcendent, to the divine if you will — has been through music.
Some properties of perceived time are very counterintuitive indeed. They’ve caused much conceptual and philosophical confusion. For instance, the perceived time of an event can precede the arrival of the sensory data defining the event, sometimes by as much as several hundred milliseconds. At first sight this seems crazy, and in conflict with the laws of physics. Those laws include the principle that cause precedes effect. But the causality principle in physics refers to actual times in the outside world, not to perceived times. The apparent conflict is a perceptual illusion. I’ll call it an ‘acausality illusion’.75
The existence of acausality illusions — of which music provides outstandingly clear examples, as we’ll see shortly — is a built-in consequence of the way perception works. And the way perception works is well illustrated by the walking dots animation (figure 1).
Consider for a moment what the animation tells us. The sensory data are twelve moving dots in a two-dimensional plane. But they’re seen by anyone with normal vision as a person walking — as a particular three-dimensional motion exhibiting organic change. The invariant elements include the number of dots. Also invariant are the distances, in three-dimensional space, between pairs of locations corresponding to particular pairs of dots. There’s no way to make sense of this except to say that the unconscious brain fits to the data an organically-changing internal model that represents the three-dimensional motion, using an unconscious knowledge of three-dimensional Euclidean geometry.
That by the way is what Kahneman6 calls a ‘fast’ cognitive process, something that happens ahead of conscious thought, and outside our volition. Despite knowing that it’s only twelve moving dots, we have no choice but to see a person walking.
Such model-fitting has long been recognized by psychologists as an active process involving unconscious prior probabilities, and therefore top-down as well as bottom-up flows of information,37, 76, 77 where ‘bottom-up’ refers to the incoming data. For the walking dots the greatest prior probabilities are assigned to a particular class of three-dimensional motions, privileging them over other ways of creating the same two-dimensional dot motion. The active, top-down, model-fitting aspects show up in neurophysiological studies as well.78
The term pattern-seeking is sometimes used to suggest the active nature of the unconscious model-fitting process. So active is our unconscious pattern-seeking that we’re prone to what psychologists call pareidolia, seeing patterns in random images. (People see the devil’s face in a thundercloud, then form a conspiracy theory that the government covered it up.) For the walking dots the significant pattern is four-dimensional, involving as it does the time dimension as well as all three space dimensions. Without the animation, one tends to see no more than a bunch of dots.
And what is a ‘model’? In the sense I’m using the word, it’s a partial and approximate representation of reality, or presumed reality. “All models are wrong, but some are useful.”
Models are made in a variety of ways. They’re usually made with symbols of one sort or another. The internal model evoked by the walking dots is made by activating some neural circuitry. Patterns of neural activity are symbols. The objects appearing in video games and virtual-reality simulations are models made of electronic circuits and computer code. Computer code is made of symbols. Children’s model boats and houses are made of real materials but are, indeed, models as well as real objects — partial and approximate representations of real boats and houses. Population-genetics models are made of mathematical equations, and computer code usually. So too are models of photons, of air molecules, of black holes, of lightspeed gravitational ripples, and of jet streams and the ozone hole. Any of these models can be more or less accurate, and more or less detailed. But they’re all partial and approximate. And nearly all of them are made of symbols.
So ordinary perception, in particular, works by model-fitting. Paradoxical and counterintuitive though it may seem, the thing we perceive is — and can only be — the unconsciously-fitted internal model. And the model has to be partial and approximate because our neural processing power is finite. The whole thing is counterintuitive because it goes against our subjective visual experience of outside-world reality — as not just self-evidently external, but also as direct, clear-cut, unambiguous, and seemingly exact in many cases.
Indeed, that experience is sometimes called ‘veridical’ perception, as if it were perfectly accurate. One often has an impression of sharply-outlined exactness — with such things as the delicate shape of a bee’s wing or a flower petal, the precise geometrical curve of a hanging dewdrop, the sharp edge of the full moon or the sea on a clear day and the magnificence, the sharply-defined jaggedness, of snowy mountain peaks against a clear blue sky.79
Right now I’m using the word ‘reality’ to mean the outside world. Also, I’m assuming that the outside world exists. I’m making that assumption consciously as well as, of course, unconsciously. Notice by the way that ‘reality’ is another dangerously ambiguous word. It’s yet another source of conceptual and philosophical confusion...
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And what of the brain’s two hemispheres? Here I must defer to McGilchrist36 and Ramachandran,37 who in their different ways offer a rich depth of understanding coming from neuroscience and neuropsychiatry, far transcending the superficialities of popular culture. For present purposes, McGilchrist’s key point is that having two hemispheres is evolutionarily ancient. Even fish have them. The two hemispheres may have begun with bilateral symmetry in primitive vertebrates but then evolved in different directions. If so, it would be a good example of how neutral genomic changes can later become adaptive.18
A good reason to expect such bilateral differentiation, McGilchrist argues, is that survival is helped by having two different styles of perception. They might be called holistic and fragmented. The evidence shows that the first, holistic style is a specialty of the right hemisphere, and the second a specialty of the left, or vice versa in a minority of people.
If you’re a pigeon who spots some small objects lying on the ground, then you want to know whether they are, for instance, inedible grains of sand or edible seeds. That’s the left hemisphere’s job. It has a style of model-fitting, and a repertoire of models, that’s suited to a fragmented, dissected view of the environment, picking out a few fine details while ignoring the vast majority of others. The left hemisphere can’t see the wood for the trees. Or, more accurately, it can’t even see a single tree but only, at best, leaves, twigs or buds (which, by the way, might be good to eat). One can begin to see why the left hemisphere is more prone to unconscious mindsets.
But suppose that you, the pigeon, are busy sorting out seeds from sand grains and that there’s a peculiar flicker in your peripheral vision. Suddenly there’s a feeling that something is amiss. You glance upward just in time to see a bird of prey descending and you abandon your seeds in a flash! That kind of perception is the right hemisphere’s job. The right hemisphere has a very different repertoire of internal models, holistic rather than dissected. They’re fuzzier and vaguer, but with a surer sense of overall spatial relations, such as your body in its surroundings. They’re capable of superfast deployment. The fuzziness, ignoring fine detail, makes for speed when coping with the unexpected. Ref. 36 gives many more examples.
Ref. 37 points out that another of the right hemisphere’s jobs is to watch out for inconsistencies between incoming data and internal models, including any model that’s currently active in the left hemisphere. When the data contradict the model, the left hemisphere has a tendency to reject the data and cling to the model — to be trapped in a delusional mindset. “Don’t distract me; I’m trying to concentrate!” Brain scans show a small part of the right hemisphere that detects such inconsistencies or discrepancies. The right hemisphere can interrupt the left with a wordless “Look out, you’re making a mistake!” If the right hemisphere’s discrepancy detector is damaged, severe delusional mindsets such as anosognosia can result.
Ref. 36 points out that the right hemisphere is involved in many subtle and sophisticated games, such as playing with the metaphors that permeate language or, one might even say, that mediate language. So the popular-cultural idea that language is all in the left hemisphere misses many of the deeper aspects of language...
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And what of science itself? What about all those mathematical and computer-coded models of population genetics and of photons, of air molecules, of black holes, of lightspeed gravitational ripples, of jet streams and the ozone hole, of invisible pandemic spreading and of the myriad other entities we deal with in science? Could it be that science itself is always about finding useful models that fit data from the outside world, and never about finding Veridical Absolute Truth? Can science be a quest for truth even if the truth is never Absolute? The next chapter will argue that the answer to the last two questions is an emphatic yes.
Take for instance the physicists’ Holy Grail, the ultimate model or ‘Theory of Everything’. Suppose we were to find a candidate ultimate model, consistent with everything we know today and described by a single, self-consistent set of mathematical equations. It would still be impossible to test it at infinite accuracy, in an infinite number of cases, and in all parts of the Universe or Universes past, present, and future. Within a smaller, but still wide, domain of applicability one might achieve superlative scientific confidence, with many accurate cross-checks including new predictions subsequently verified. The model might be described by equations of consummate beauty. And that would be wonderful. But in principle there’d be no way to be Absolutely Certain that it’s Absolutely Correct, Absolutely Accurate, and Applicable to Absolutely Everything.
Come to think of it, isn’t that kind of obvious?
So I’d like to replace all those books on the philosophy of science by one simple, yet profound and far-reaching, statement. It not only says what science is, in the most fundamental possible way, but it also clarifies the power and limitations of science. It says that science is an extension of ordinary perception, meaning perception of outside-world reality. Like ordinary perception, science fits models to data from the outside world.
If that sounds glib and superficial to you, dear reader, then all I ask is that you think again about the sheer wonder of so-called ordinary perception. It too has its power and its limitations, and its fathomless subtleties, agonized over by generations of philosophers.
Both science and ordinary perception work by fitting models — symbolic representations — to data coming in from the outside world. Both science and ordinary perception must assume that the outside world exists, because it can’t be proven absolutely. Models, and assemblages and hierarchies of models, schemas or schemata as they’re sometimes called, are partial and approximate representations, or candidate representations, of outside-world reality. Those representations can be anything from superlatively accurate and strongly predictive to completely erroneous — like the phlogiston theory of combustion, the microwave theory of COVID-19, and ordinary hallucinations.
The walking dots animation points to the tip of a vast iceberg, a hierarchy of unconscious internal models and model components starting with the three-dimensional motion itself, but extending all the way to the precise manner of walking and the associated psychological and emotional subtleties. The main difference between science and so-called ordinary perception lies in the range of models used, in the data to be fitted, and in a more explicit focus, by science, on estimating degrees of uncertainty.
In science today we can harness the power of Bayesian causality theory to fit sophisticated models to vast datasets in a logically self-consistent way, using the probabilistic ‘do’ operator21 to represent the actions of an experimenter. The theory also has a natural way of dealing with uncertainty. Problems of the most daunting complexity are thus beginning to be tractable. Examples include the complex biomolecular circuitry that switches genes on and off,3, 9, 18 and the interplay between small-scale ocean eddies and global-scale circulations and weather systems.81
Notice that all our ways — scientific and ordinary — of perceiving the outside world are ‘theory-laden’ as is sometimes said. One might also say ‘prior-probability-laden’. It’s a necessary aspect of any model-fitting process. Consciously or unconsciously, one has to begin somewhere when selecting models to fit. Consciously or unconsciously, one has to propose some pattern of cause and effect before it can be tested against data.21 Some postmodernist35 philosophers such as Paul Feyerabend have claimed that scientific knowledge is mere opinion, just because it’s theory-laden. The point is missed that some models fit better than others. And some have more predictive power than others. And some are a priori more plausible than others, with more cross-checks to boost their prior probabilities. And some are simpler and more widely applicable than others.
Take for instance Newton’s and Einstein’s models of gravity. Both are partial and approximate representations of reality even though superlatively accurate, superlatively simple, superlatively predictive, and repeatedly cross-checked in countless ways within their very wide domains of applicability — Einstein’s still wider than Newton’s because it includes, for instance, the orbital decay and merging of pairs of black holes or neutron stars and the resulting lightspeed gravitational ripples already mentioned, also called gravitational waves. They are ripples in the structure of spacetime itself, and were first observed in 2015 by the famous ‘LIGO’ detectors.16 Observation of the gravitational ripples has provided yet another cross-check on Einstein’s model — which predicted them over a century ago — and has opened a new window on the Universe.
Both models are not only simple but also mathematically beautiful. And their high accuracies and predictive powers are crucial, for instance, to all our achievements in space science and space travel. The way a spacecraft moves isn’t a matter of mere opinion...
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Multiple levels of description are not only basic to science but also, unconsciously, basic to ordinary perception. They’re natural. They’re basic to how our brains work. Straight away, our brains’ left and right hemispheres give us at least two levels of description, a lower level that dissects fine details, and a more holistic higher level.36 And neuroscience has revealed a variety of specialized internal models or model components that symbolically represent different aspects of outside-world reality. In the case of vision there are separate model components representing not only fine detail on the one hand, and overall spatial relations on the other but also, for instance, motion and colour. Damage to a part of the brain dealing with motion can produce visual experiences like successions of snapshots or frozen scenes — merely a nuisance if you’re trying to pour your tea, but very dangerous if you’re trying to cross the road.77 Other kinds of brain damage can produce, for instance, colours floating around by themselves and unattached to objects.85
The biological sciences well illustrate the need to consider multiple levels of description, and multiple modes of description. I’ve already mentioned molecular-biological regulatory networks, or biomolecular circuits.3, 9, 18 They depend on highly specific interactions amongst a variety of molecules including DNA and protein molecules. Shape-changing protein molecules called ‘allosteric enzymes’ function within biomolecular circuits like transistors within electronic circuits. Biomolecular circuits and their actions, such as switching genes on and off, are impossible to recognize from lower levels such as the level of genes alone, still less from the levels of chemical bonds and bond strengths within thermally-agitated molecules, jiggling around and bumping into each other on timescales of trillionths of a second, and from the still lower levels of atoms, electrons, atomic nuclei, and quarks.
And again, there are of course very many higher levels of description within the hierarchy — level upon level, with causal arrows pointing both downward and upward. There are biomolecular circuits and assemblies of such circuits, going up to the levels of archaea, bacteria and their communities, of yeasts, of multicellular organisms, of niche construction and whole ecosystems, and of ourselves and our families, communities, nations, cyberspace and the entire planet — which Newton treated as a point mass.
None of this would need saying were it not for the persistence — even today — of an extreme-reductionist view of science saying, or assuming, that looking for the lowest possible level and for atomistic ‘units’ such as quarks, or atoms, or genes, or so-called memes, gives us the Answer to Everything and is therefore the only useful angle from which to view a problem. Some of the disputes about biological evolution seem have to been disputes about ‘the’ unit of selection58 — as if such a thing could, or should, be uniquely identified within the actual complexity of multi-level selection. Yes, in many cases reductionism can be enormously useful; but no, it isn’t the Answer to Everything!
In some scientific problems, including those I’ve worked on myself, the most useful models aren’t at all atomistic. In fluid dynamics we use accurate ‘continuum-mechanics’ models in which highly nonlocal, indeed long-range, interactions are crucial. They’re mediated by the pressure field. They’re a crucial part of, for instance, how birds, bees and aircraft stay aloft, how a jet stream can circumscribe and contain the ozone hole, and how waves and vortices interact.31, 86
McGilchrist’s work tells us that extreme reductionism comes from our left hemispheres. It is indeed a highly dissected view of things. His book36 can be read as a passionate appeal for more pluralism — for more of Max Born’s loosening of thinking — for the more powerful, in-depth understanding that can come from looking at things on more than one level and from more than one viewpoint, while respecting the evidence. Such understanding requires a better collaboration, says McGilchrist, between our garrulous and domineering left hemispheres and our quieter, indeed wordless, but also passionate, right hemispheres (or vice versa in a minority of people).
Surely, then, professional codes of conduct for scientists — to say nothing of lucidity principles as such — should encourage us to be more explicit than we feel necessary regarding, in particular, which level or levels of description we’re talking about. And when the levels of description aren’t clear, or when the questions asked are ‘wicked questions’ having no clear meaning at all, still less any clear answer, it would help to say so.
Such an approach might also be helpful when confronted with all the confusion, and wicked questions, about consciousness and free will. I want to stay off those topics — having already had a go at them in ref. 75 — except to say that some of the confusion seems to come first from not recognizing the existence of acausality illusions, and second from conflating different levels of description. I like the aphorism that “free will is a biological illusion but a social reality”. There’s no conflict between the two statements once they’re recognized as belonging to different levels of description.87
And they sharply remind us of the ambiguity, and the context-dependence, of the word ‘reality’. I ask again, is music real? Is mathematics real? Is our sense of self and gender real? Is the outside world real? For me, at least, they’re all real but in four different senses. And one of life’s realities is that pragmatic social functioning depends on accepting our sense of self — our internal self-model — as an entity having, or seeing itself as having, free will or volition or agency as it’s variously called. It wouldn’t do to be able to commit murder and then, like a present-day Hamlet, to say to the jury “T’wasn’t me, t’was my selfish genes did it.”
The walking dots show that we have unconscious Euclidean geometry. We also have unconscious calculus.
Calculus is the mathematics of continuous change, as with a person walking. Calculus also, for instance, deals with objects like those shown in figure 7. They’re made of smooth curves — pathways whose direction changes continuously, the curves that everyone calls ‘mathematical’:
Figure 7: Some smooth ‘mathematical’ curves.
Such curves include perfect circles, ellipses, and portions thereof, among countless other examples. A straight line is the special case having zero rate of change of direction. A circle has a constant rate of change of direction, and an ellipse has a rate of change that’s itself changing, and so on.
Such ‘Platonic objects’, as I’ll call them, are of special interest to the unconscious brain. Whenever one sees natural phenomena exhibiting what look like straight lines or smooth curves, such as the edge of the sea on a clear day, or the edge of the full moon, or the shape of a hanging dewdrop, they tend to excite our sense of something special, and beautiful. So do the great pillars of the Parthenon, and the smooth curves of the Sydney Opera House seen from a distance. We feel their shapes as resonating with something ‘already there’.
Plato felt that the world of such ‘mathematical’ objects, shapes, or forms, and the many other beautiful entities found in mathematics, is in some sense a world more real than the outside world with its commonplace messiness. He felt his world of perfect mathematical forms to be something timeless — something already there and always there.
My heart is with Plato here, on an emotional level. When the shapes, or forms, look truly perfect, they can excite a sense of great wonder and mystery. So too can the mathematical equations describing them. How can such immutable perfection exist at all, and why do we find it awesome?
Indeed, so powerful is our unconscious interest in such perfection that we see smooth curves even when they’re not actually present in the incoming visual data. For instance we see them in the form of what psychologists call ‘illusory contours’. Figure 8 is an example. If you stare at the inner edges of the messy black marks for several seconds, and if you have normal vision, you’ll see an exquisitely smooth curve joining them:
Figure 8: An illusory contour. To see it, stare at the inner edges of the black marks.
That curve is not present on the screen or on the paper. It’s constructed by your visual system. To construct it, the system unconsciously solves a problem in calculus — in the branch of it called the calculus of variations. The problem is to consider all the possible curves that can be fitted to the inner edges of the black marks, and to pick out the curve that’s as smooth as possible, in a sense to be specified. The smoothness is specified using some combination of rates of change of direction, and rates of change of rates of change, and so on, averaged along each curve. So we have an unconscious calculus of variations. And that in turn gets us closer to some of the deepest parts of theoretical physics, as we’ll see shortly.
The existence of the Platonic world glimpsed in figures 7 and 8 is no surprise from an evolutionary perspective. It is, indeed, already there. It’s already there in the sense of being evolutionarily ancient — something that comes to us through genetic memory and the automata that it enables — genetically-enabled automata that can self-organize or self-assemble into, among other things, the special kinds of symbolic representation that correspond to Platonic objects.
Over vast stretches of time, natural selection has put the unconscious brain under pressure to make its model-fitting processes as simple as the data allow. That requires a repertoire of internal model components that are as simple as possible. Some of these components are Platonic objects, smooth curves or portions of smooth curves or, rather, their internal symbolic representations. Please remember that actual or latent patterns of neural activity are symbols — and we are now talking about mathematical symbols — even though we don’t yet have the ability to read them directly from the brain’s neural networks.
A perfect circle, then, is a Platonic object simply because it’s simple. The illusory contour in figure 8 shows that the brain’s model-fitting process assigns the highest prior probabilities to models representing objects with the simplest possible outlines consistent with the data, in this case a light-coloured object with a smooth outline sitting in front of some smaller dark objects. That’s part of how the visual system distinguishes an object from its background, an important part of making sense of the visual scene.8, 76, 77, 80 Making sense of the visual scene has been crucial to survival for hundreds of millions of years — crucial to navigation, crucial to finding mates, and crucial to eating and not being eaten. Many of the objects to be distinguished have outlines that are more or less smooth. They range from distant hills down to fruit and leaves, tusks and antlers, and teeth and claws.
“We see smooth curves even when they’re not actually present.” Look again at figure 7. None of the Platonic objects we see are actually present in the figure. Take the circle on the left, or ellipse as it may appear on some screens. It’s actually more complex. With a magnifying glass, one can see staircases of pixels. Zooming in more and more, one begins to see more and more detail, such as irregular or blurry pixel edges. One can imagine zooming in to the atomic, nuclear and subnuclear scales. Long before that, one encounters the finite scales of the retinal cells in our eyes. Model-fitting is partial and approximate. What’s complex at one level can be simple at another. Perfectly smooth curves are things belonging not to the incoming sensory data but rather — I emphasize again — to the unconscious brain’s repertoire of model components.
So I’m suggesting that the Platonic world is very different from what Plato, and others, seem to have imagined.83, 84 Rather than being timeless, it’s only hundreds of millions of years old. Rather than being external to us, it’s very internal. It’s something arising from natural selection. It’s part of the unconscious mathematics we need in order to survive. But to me that’s still wonderful, indeed even more wonderful because, for one thing, it makes a lot more sense.
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The calculus of variations is a gateway to some of the deepest parts of theoretical physics. That’s because it leads to Noether’s theorem. The theorem depends on writing the equations of physics in what’s called ‘variational’ form. That’s a form allowing the calculus of variations to be used. It’s Richard Feynman’s own example of things that are mathematically equivalent but, as he said, “psychologically very different”.
Think of playing tennis on the Moon. Air resistance is assumed negligible. After being hit, the ball moves solely under the Moon’s gravity. One way to model such motion is to use Newton’s equations. They deal with the moment-to-moment rates of change of quantities like the position and velocity of the tennis ball. In our lunar example, solving those equations produces a pathway for the tennis ball in the form of a smooth curve, very close to what’s called a parabola. Since the equations describe what happens from moment to moment, one must construct the curve bit by bit, starting at one end.
However — and this might seem surprising — the same smooth curve can also be constructed as the solution to a variational problem. It’s a problem more like that of figure 8 because it treats the curve holistically, rather than bit by bit. It deals with all parts of the curve simultaneously. That’s psychologically very different indeed...
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Music has its own Platonic objects. Prominent among them are the special sets of musical pitches called harmonic series. An example is shown in figure 9, where the leftmost hyperlinked QR-code blank points to an audio clip sounding the pitches one after another:
Figure 9: A musical harmonic series. The first hyperlinked QR-code blank, on the left, points to an audio clip sounding these harmonic-series pitches one after another. The other two audio clips present some of the pitches sounded together (see text). The first and lowest pitch, called the ‘fundamental’ or ‘first harmonic’, corresponds in this case to a vibration frequency 65.4Hz (65.4 cycles per second), the second pitch or harmonic to twice this, 130.8Hz, and the third to three times, 196.2Hz, and so on. The fundamental pitch and its octave harmonics, the 2nd, 4th, 8th and so on all have the same musical name C or Doh. If you happen to have a tunable electronic keyboard and would like to tune it to agree with the harmonic series, then you need to sharpen the 3rd, 6th and 12th harmonics by 2 cents (2/100 of a semitone) and the 9th by 4 cents — these differences are barely audible — but also to flatten the 5th and 10th by 14 cents (audible to a good musical ear), the 7th by 31 cents, and the 11th by 49 cents, relative to B flat and F sharp. The last two changes are plainly audible to just about anyone. The differences arise from the fact that the standard keyboard tuning, called ‘equal temperament’, divides the octave into twelve exactly equal ‘semitones’ with frequency ratios 21/12 = 1.059463. Equal temperament is musically useful because of a peculiar accident of arithmetic. That’s the tiny, practically inaudible 2-cent difference between the 3rd harmonic and its equal-tempered approximation, whose frequency is 27/12 = 1.49831, very nearly 3/2, times the frequency of the 2nd harmonic. The tuning of the 3rd harmonic pitch, relative to the 2nd, has critical importance in most genres of music.
The defining property of a harmonic series is that the pitches correspond to vibration frequencies equal to the lowest frequency, in this case 65.4Hz (65.4 cycles per second), multiplied by a whole number such as 1, 2, 3, etc.
A harmonic series is a ‘Platonic object’ in just the same sense as before, something that’s evolutionarily ancient and of special interest to the unconscious brain — and indeed to the brains of many non-human creatures as well. How can that be? The answer will emerge shortly, when we consider how hearing works. And it will expose more connections between music and mathematics. But first, please be sure to listen to the sounds themselves (first or leftmost audio clip in figure 9). Do they not hint at something special and beautiful? Something that could divert you, and Plato, from mundane messiness? Hints of fairy horn calls, perhaps? However they strike you, these sounds are special to the musical brain.
Also special are combinations of these sounds played together. For instance if those numbered 4, 5 and 6 are played together — they are called the 4th, 5th, and 6th harmonic pitches — then we hear the familiar sound of what musicians call a major chord, or major triad (second audio clip in figure 9). If we play instead the 1st, 2nd, 3rd, 5th, 8th, and 16th, then it sounds like a more spacious version of the same chord — more like the grand, thunderous chord that opens the Star Wars music (third audio clip in figure 9). If on the other hand we play the 6th, 7th, 9th and 10th together then we get what has famously been called the ‘Tristan chord’ (first audio clip in figure 10):
Figure 10: Audio clips of the Tristan chord made up of the 6th, 7th, 9th and 10th harmonic pitches shown in figure 9. The first clip (hyperlinked QR-code blank on the left) is the chord played with accurate harmonic-series tunings, as detailed in the caption to figure 9. The second clip is the same chord in standard keyboard or equal-tempered tuning. If the first clip is played loudly, through a distorting audio system, then one usually hears not only the chord but also a low C corresponding to the 1st or 2nd harmonic. That’s a consequence of the chord being accurately tuned to the harmonic series. The third clip (hyperlinked QR-code blank on the right) sounds the chord in the spaced-out version used by Richard Wagner in the opening of Tristan und Isolde (see text), in equal-tempered tuning, along with the subsequent organic harmony changes that complete the opening phrase.
The first chord heard in Richard Wagner’s opera Tristan und Isolde is a spaced-out version of the same chord, formed by moving the 7th and 9th harmonics down an octave and the 10th down by two octaves (third audio clip in figure 10). Some people think that Wagner invented the chord, even though it was actually invented — I’d rather say discovered — long before that. For instance the chord occurs more than twenty times, in various spacings, in another famous piece of music, Dido’s Lament, written by Henry Purcell about two centuries before Tristan...
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But — I hear you ask — why are these particular sets of pitches, such as those of figure 9, so special to the brain, and what has all this to do with evolution and natural selection? Once again, the key word is simplicity. As already said, the defining property of a harmonic series is that its frequencies are whole-number multiples of the fundamental frequency or first harmonic. It follows that a sound wave created by superposing any set of pitches from a harmonic series takes a very simple form. The waveform precisely repeats itself at a single frequency. That’s 65.4 times per second in the case of figure 9. The Tristan chord, when tuned as in the first clip in figure 10, produces just such a repeating waveform.
A famous theorem attributed to Joseph Fourier tells us that any repeating waveform corresponds to some superposition of pitches from a single harmonic series, as long as you allow an arbitrary number of harmonics. Repeating waveforms, then, are mathematically equivalent to sets or subsets of harmonic-series pitches — mathematically equivalent, even if psychologically very different.
Our neural circuitry is good at timing things. It has evolved to give special attention to repeating waveforms because they’re important for survival in the natural world.
Many animal sounds are produced by vibrating elements in a larynx, or a syrinx in the case of birds. Such vibrations will often repeat themselves, to good accuracy, for many cycles, as the vibrating element oscillates back and forth like the reed of a saxophone or clarinet. So repeating waveforms at audio frequencies are important for survival because it can be important, for survival, to be able to pick out individual sound sources in a jungle full of animal sounds. This rather astonishing feat of model-fitting is similar to that of a musician skilled in picking out sounds from individual instruments, when an orchestra is playing. It depends on having a repertoire of model components that includes repeating waveforms.
So exactly-repeating waveforms are among the simplest model components needed by the hearing brain to help identify sound sources, just as perfectly smooth curves are among the simplest model components needed by the visual brain to help identify objects. That’s why exactly-repeating waveforms have the status of Platonic objects, or forms, for the hearing brain, just as perfectly smooth curves do for the visual brain. Both contribute to making sense of a complex visual scene, or of a complex auditory scene, as the case may be, while being as simple as possible.
In summary, then, for survival’s sake the hearing brain has to be able to carry out auditory scene analysis, and therefore has to know about repeating waveforms — has to include them in its repertoire of unconscious model components — unconscious symbolic representations — available for fitting to the incoming acoustic signals in all their complexity. And that’s mathematically equivalent to saying that the unconscious brain has to know about the harmonic series, and has to recognize it as special...
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Another New Zealand bird that’s known to sing simple, accurately-pitched tunes is the North Island kokako, a crow-sized near-ground-dweller. Figure 16 presents an example:
Figure 16: North Island kokako song. The transcription corresponds only to the start of the song recorded in the audio clip, again courtesy of Les McPherson. The song continues in a more complicated way ending with the 8th harmonic of 110Hz A, to my ear creating a clear key-sense of A major. The first three notes, those shown in the transcription, are close to the 6th, 7th, and 5th harmonics of the same A. Listen carefully! The second note is an avian ‘blue note’.
I want to mention one more connection between music and mathematics. It’s another connection not mentioned in the standard accounts, confined as they are to games with numbers. Of course composers have always played with numbers to get ideas, but that’s beside the point. The point here is that there are musical counterparts to illusory contours like that in figure 8. Music has its own calculus of variations! Listen to the first audio clip in figure 17:
Figure 17: Audio clips from the opening of Mozart’s piano sonata K 545.
It’s the opening of Mozart’s piano sonata K 545, whose second movement was quoted in figure 5 [omitted from this preview]. After the first eight seconds or so one hears a smooth, flowing passage of fast notes that convey a sense of continuous motion, a kind of musical smooth curve, bending upward and downward. Mozart himself used to remark on this smoothness. In his famous letters he would describe such passages as flowing like oil when played well enough. But, as with the black segments in figure 8, there’s no smoothness in the actual sounds. The actual sounds are abrupt and percussive.
Of course hearing doesn’t work the same way as vision. The analogy is imperfect. To give the impression of smoothness, in the musical case, the adjacent notes need to have similar loudness and to be spaced evenly in time. Mozart admitted that he’d had to practise hard to get the music flowing like oil. That’s an example of what I meant by the fine control of rhythm ‘to a few milliseconds or thereabouts’, by world-class musicians.
When the notes are not spaced evenly in time, as in the second audio clip in figure 17, the smoothness — Mozart’s ‘oiliness’ — disappears. That’s perhaps reminiscent of the outer ends of the black segments in figure 8.
Coming back to musical pitch perception for a moment, if you’re interested in perceived pitch then you may have wondered how it is that violinists, saxophonists, singers and others can use the kind of frequency variation called ‘vibrato’ while maintaining a clear and stable sense of pitch...
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Let’s return for just a moment to theoretical-physics fundamentals. Regarding models that are made of mathematical equations, there’s an essay that every physicist knows of, I think, by the famous physicist Eugene Wigner, about the “unreasonable effectiveness of mathematics” in representing the outside world. But what’s unreasonable is not the fact that mathematics comes in. As I keep saying, mathematics is just a means of handling many possibilities at once, in a precise and self-consistent way, and of appreciating the associated abstract patterns.
What’s unreasonable is that very simple mathematics comes in when you build and test accurate models of, for instance, the subatomic world. It’s not the mathematics that’s unreasonable; it’s the simplicity. So I’d prefer to talk about the unreasonable simplicity of, for instance, the subatomic world.
It just happens that, at the level of electrons and other subatomic particles, things look astonishingly simple. That’s just the way the world seems to be at that level. And of course it means that the corresponding mathematics is simple too, at that level. One of the greatest unanswered questions in physics is whether things stay simple, or not, when we zoom in to the lower levels and far smaller scales at which quantum phenomena and gravity mesh together.
As is well known, and discussed under headings such as ‘Planck length’, ‘proton charge radius’, and ‘Bohr radius’, we’re now talking about lengthscales of the order of a hundred billion billion times smaller than the diameter of a proton, and ten million billion billion times smaller than the diameter of a hydrogen atom — well beyond the range accessible to observation and experimentation. At those small scales, things might for instance be complex and chaotic, like turbulent fluid flow, with order emerging out of chaos and making things look simple only at much larger scales.
Such possibilities have been suggested for instance by my colleague Tim Palmer, who has thought deeply about these issues — and about their relation to the vexed questions at the foundations of quantum theory94 — alongside his better-known work on the chaotic dynamics of weather and climate.
So let’s turn now, at last, to the climate problem, by far the most complex of all the problems that confront us, a vast jigsaw of interacting pieces, from global-scale atmospheric and oceanic circulations all the way down to the microscopic scales of bacteria, viruses, and molecules. What’s at stake is existential for human civilization even though, I’ll argue, probably not existential for life on earth. I’ve written the rather long Postlude that follows in the hope of clarifying what science can and can’t tell us, today, about the problem. I can’t entirely avoid the politics, but will nevertheless try to keep the main focus on our progress toward in-depth scientific understanding.
Journalist to scientist during a firestorm, flash flood, or other weather extreme such as Cyclone Idai or Hurricane Dorian: “Tell me, Professor So-and-So, is this a one-off extreme, pure chance, or is it due to climate change?”
Well — once again — dichotomization makes us stupid. The professor needs to say “Hey, this isn’t an either-or. It’s both. Climate change produces long-term upward trends in the probabilities of extreme weather events, and in their peak intensities.” This point is, at long last, gaining traction as devastating weather extremes become more frequent, and more intense.
Here’s one way to get at what’s involved. Chapter 2 mentioned audio amplifiers and two different questions one might ask about them: first, what powers them, and second, what they’re sensitive to. For the climate system, switching off the power corresponds to switching off the Sun. But in that system is there anything corresponding to an amplifier’s sensitive input circuit?
For many years now, we’ve had a clear answer: yes. And we have practical certainty that the upward trends will continue, that they’re mostly caused by human inputs to the sensitive parts of the system and that, as a result, weather extremes will continue to become still more frequent and still more intense. What’s uncertain is how long it will take, how far it will go, and by precisely what stages, though unfortunately the extremes now appear to be ramping up sooner rather than later. They’ve been underestimated by the climate prediction models, for reasons I’ll come to.
Broadly speaking, then, the climate system can be thought of as a powerful but slowly-responding amplifier with sensitive inputs. And it’s responding to human inputs by becoming more active, with larger fluctuations, including greater extremes, in ways beginning to be understood with increasing clarity.
Some of that understanding comes from looking at past as well as present climates and at all the inputs, human and non-human. Among the amplifier’s non-human inputs are volcanic eruptions, small changes in the Sun’s power output and, more importantly, small orbital changes — small changes in the Earth’s tilt and in its orbit around the Sun. These can be regarded as small inputs because they hardly change the total power delivered by the Sun, but do slightly change its distribution over the Earth’s surface, in ways that I’ll discuss. During the past four hundred millennia or so the response to the small orbital changes was a sequence of large climate changes, the last four glacial–interglacial cycles illustrated by the ice-core data in figure 3 [omitted from this preview], ‘glacial cycles’ for brevity. And ‘large’ is a bit of an understatement. For instance, as the ice sheets changed, some of the associated sea-level changes were well over a hundred metres as already said. That’s huge by comparison with anything projected for the current century.
The main human input today is the injection, or emission, of carbon dioxide into the atmosphere. It comes from a variety of activities but most of all from burning fossil fuels such as coal, oil, and natural gas. Carbon dioxide, whether injected naturally or artificially, has a central role in the climate-system amplifier not only as a plant nutrient but also as our atmosphere’s most important non-condensing greenhouse gas.
That central role is crucial to climate behaviour in general, and to the huge magnitudes of the last four glacial cycles in particular. Those cycles depended not only on small orbital changes but also on natural injections of carbon dioxide into the atmosphere from the deep oceans, as we’ll see.
Of course to think of such natural injections as ‘inputs’ is strictly speaking incorrect, except as a thought-experiment, but they’re part of the amplifier’s sensitive input circuitry. The ice-sheet dynamics will also prove to be sensitive.
The physical and chemical properties of so-called greenhouse gases are well established and uncontentious, with very many cross-checks. Greenhouse gases in the atmosphere make the Earth’s surface roughly 30°C warmer than it would otherwise be.95 For reasons connected with the properties of heat radiation, any gas whose molecules have three or more atoms can act as a greenhouse gas. More precisely, to interact strongly with heat radiation the gas molecules must have a structure that supports a fluctuating electric ‘dipole moment’ at the frequency of the heat radiation, of the order of tens of trillions of cycles per second. Examples include not only carbon dioxide and water vapour, each with three atoms per molecule, but also, for instance, nitrous oxide and methane, with three and five atoms respectively. By contrast, the oxygen and nitrogen molecules making up the bulk of the atmosphere have only two atoms, and are nearly transparent to heat radiation. Ref. 95 gives an authoritative discussion.
One reason for the special importance of carbon dioxide is its great chemical stability as a gas. Other natural carbon-containing, non-condensing greenhouse gases such as methane tend to be converted fairly quickly into carbon dioxide. Fairly quickly means within a decade or so, for methane. And of all the non-condensing greenhouse gases, carbon dioxide has always had the most important long-term warming effect, not only today but also during the glacial cycles. That’s clear from its chemical stability and from the ice-core data, to be discussed below, along with the well established heat-radiation physics, all cross-checked by very many accurate measurements.
The role of water vapour is also central, but entirely different. It too is chemically stable and has great importance as a greenhouse gas. But unlike carbon dioxide it can and does condense or freeze, in vast amounts, for instance as cloud, rain, and snow, while copiously resupplied by evaporation from the tropical oceans and elsewhere. This solar-powered supply of water vapour — sometimes called ‘weather fuel’ because of the ‘latent’ heat energy put in by the Sun and released on condensing or freezing — dwarfs any human input and makes it part of the climate-system amplifier’s power-supply and power-output circuitry, rather than its sensitive input circuitry.
Air can hold around six or seven percent more weather fuel for every degree Celsius rise in temperature. This comes from a robust and well established piece of physics called the Clausius–Clapeyron relation. So global warming is also global fuelling.
Some of the amplifier’s power output drawing on weather fuel takes the form of tropical and extratropical thunderstorms and cyclonic storms, including those that produce the most extreme rainfall, flooding, and wind damage. The latent energy released dwarfs the energies of thermonuclear bombs. Cyclone Idai, which caused such devastation in Mozambique, and Hurricane Dorian, which flattened large areas of the Bahamas, and other recent examples — including the typhoons impacting the Philippines — remind us what those huge energies mean in reality.
It’s reasonable to expect that more weather fuel will make extremes more extreme. An especially clear example is that of thunderstorms. A thunderstorm is like a giant vacuum cleaner, powered by the weather fuel it pulls in from its surroundings. So, if it’s surrounded by air containing more weather fuel — other things being equal — it’s more vigorous and pulls the fuel in faster. That’s a very robust positive feedback, a robust self-reinforcing process, in the runup to peak intensity. The peak intensity is greater and comes sooner. The consequences can include flash flooding. Such peak intensities are completely missed by the climate prediction models, whose spatial resolution is far too coarse to describe the airflow into thunderstorms.
Please note that I’m talking about the strongest and most devastating thunderstorms, not the average thunderstorm. This point needs to be remembered when looking at statistical summaries of data, which tend to focus on averages and to hide the extremes, even if they’re present in the data.
I’ll postpone the discussion of other examples, since they’re not so simply and robustly arguable. They depend on a more complex web of cause and effect. The same points apply, though. The most extreme behaviours, not only of thunderstorms but also of cyclones and other weather systems, tend to get hidden in statistics and in any case are outside the scope of the climate prediction models. That’s again because the most extreme behaviours usually, in one way or another, involve small spatial scales that the models cannot resolve.
The main points that will emerge are first that global fuelling is making the whole climate system more active and vigorous, second that some of the changes to the system are practically speaking irreversible,96 and third that, if we were to carry on as now, subsidizing97 and otherwise promoting fossil-fuel burning, then the resulting changes would not only be irreversible but also, sooner or later, very large indeed. The main uncertainties are not about the changes being large but only about just how large, just how soon they’ll happen, and by precisely what stages.
In particular, there’s massive uncertainty about whether or when we reach what are called ‘tipping points’ of the climate system — perhaps, as now seems increasingly likely, in succession like dominoes falling. Such a sequence of events might even develop into runaway climate change toward an ice-free, extremely stormy planet with sea levels far higher than today, as in the early Eocene around 50 million years ago. That’s very far from certain, but on present trends quite possible, as I’ll show.
In climate science the term ‘runaway’ has more than one meaning, along with other technical terms such as ‘the’ climate sensitivity to carbon dioxide. Human language is, indeed, a conceptual minefield. I’ll return to these issues and to the question of tipping points. As for storminess in the early Eocene, we’ll see that there’s strong evidence for it, consistent with the positive-feedback argument about thunderstorms and flash flooding. Part of that evidence is the existence today of whales and dolphins.
In what follows, then, I’ll try to explain in more detail what science can and can’t tell us about climate as clearly, simply, accessibly, and dispassionately as I can — along with the implications under various assumptions about the politics.
Is such an exercise useful at all? The optimist in me says it is. And I hope that you might agree because, after all, we’re talking about the Earth’s life-support system and the possibilities for some kind of future civilization. Life on Earth will almost certainly survive — even if we have runaway into a new Eocene — but human civilization might not.
To build understanding it’s useful, as already suggested, to look at past climates. In doing so I’ll draw on the wonderfully meticulous work of many scientific colleagues including the late Nick Shackleton and his predecessors and successors, who have extracted large amounts of information about past climates from the geological record.
Past climates are our main source of information about the workings of the real system, taking full account of its vast complexity all the way down to the details of thunderstorms, forest canopies, soil ecology, ocean plankton, archaea, bacteria, and viruses, and the tiniest of turbulent eddies. And in case you think tiny eddies can’t be important I should point out that they’ve long been known, from the classic work of Walter Munk, Chris Garrett, Carl Wunsch and others, to be crucial to the large-scale temperature structure of the oceans all the way down from the surface to the deepest, coldest ‘abyssal’ waters. That structure is shaped by the vertical mixing due to millimetre-scale eddy motion and is crucial, in turn, to the way the deep oceans store and release carbon...
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So we’ve been driving in the fog, scientifically speaking, but the fog is now clearing. We’re reaching a better understanding of the risks — including the risks from weather extremes, from sea-level rise, and from the massive uncertainty over tipping points. And the politics is now, at long last, changing significantly. The disinformation campaigns seem now, at long last, to be meeting the same fate for climate as they did for the ozone hole, and for tobacco and lung cancer. All three cases show the same pattern: disinformation winning at first, then defeated by a strengthening of the science along with a wave of public concern powered by real events.122
Of course climate, as such, isn’t the only challenge ahead. There’s the destruction of biodiversity. There’s the long-studied evolution of zoonotic viruses such as those giving rise to HIV–AIDS, Ebola, and the SARS–MERS–COVID diseases. The current pandemic, or something like it, had long been anticipated by the scientists concerned. The pandemic has put us on notice that playing havoc with the Earth’s life-support system might look lucrative but can actually be costly — and likely more so in future.
There’s the evolution of antibiotic resistance in bacteria. There’s the threat of asteroid strikes. There’s the enormous potential for good or ill in new nanostructures and materials,55 in artificial intelligence, and in gene editing.123 There are the threats from cybercrime, from cyberwarfare, and from automated kinetic warfare — ‘Petrov’s nightmare’, one might call it. All these things demand clear thinking, good science, and good risk management. The number of ways for things to go wrong is combinatorially large, sometimes with huge unintended consequences such as the current threats to democracy, to science, and to mental health from the social media — from their lightning-speed artificial intelligences that aren’t yet very intelligent.23 So I come back to my hope that good science, which in practice means open science, with its powerful ideal and ethic, its humility and its respect for evidence, and its ability to cope with the unexpected, will continue to survive and prosper despite all the forces ranged against it.
After all, there are plenty of daring and inspirational examples. One of them is the continuing work of the open-source software community,17 and another was Peter Piot’s work on the HIV-AIDS pandemic, not only on the science itself but also on persuading pharmaceutical corporations to make new antiviral drugs affordable worldwide. And now there’s the effort to tackle the COVID-19 pandemic — racing against the virus as it mutates under selective pressures to spread faster, and to evolve vaccine resistance. Yet another example was the human genome story, reaching its climax around the turn of the century. There, the scientific ideal and ethic kept the genomic information available to open science, including medical and virological research, in the teeth of powerful efforts to lock it up and restrict it commercially.26
When one contemplates not only human weakness but also the vast resources devoted to individual profit by fair means or foul — and to disinformation — one can’t fail to be impressed that good science ever gets anywhere at all. That it has done so again and again is to me, at least, very remarkable, and inspirational. We humans can be much, much smarter and wiser than simplistic evolutionary theory allows.
The ozone-hole story, in which I myself was involved professionally, is another example. The disinformers tried to discredit everything we did, using the power of their well-resourced political weapons. What we did was seen as heresy — as with tobacco and lung cancer — a threat to share prices and profits. And yet the science, including all the cross-checks between different lines of evidence both observational and theoretical, became strong enough, adding up to enough in-depth understanding, despite the complexity of the problem, to defeat the disinformers in the end. So we now have the Montreal Protocol to limit ozone-depleting chemicals, in a new symbiosis between market forces and regulation. That too was inspirational. Surely Adam Smith would have approved.2, 25, 40 And it has bought us a bit more time to deal with climate, because the ozone-depleting chemicals are also potent greenhouse gases. If left unregulated, they would have accelerated climate change still further.
And on climate itself, as already said, we seem at long, long last to have reached what looks like a similar political turning point. The risk-management side of the problem was clearly highlighted some time ago.124 The Paris climate agreement of December 2015, and now the schoolchildren’s and other mass movements — most recently “Count Us In” for climate — allow us to hope for another symbiosis between market forces and regulation, especially now that low-carbon ‘renewable’ energy has become cheaper than fossil-fuel energy.122 That’s a powerful push toward a ‘green’ economy and many new jobs.122, 125
My colleague Myles Allen, who was instrumental in pointing out the cumulativeness of carbon-dioxide injections and the central relevance of the carbon ‘budget’ — the need to limit total future injections, or emissions107 — has suggested that a new symbiosis could emerge from recognizing the parallel between the fossil-fuel power industry and the nuclear power industry. For a long time now, it has been unthinkable to plan a nuclear power plant without including the waste-disposal engineering and its costs. Progress, then, could come from recognizing the same thing for the fossil-fuel industry. Then carbon capture and storage,126 allowing safe fossil-fuel burning as well as, for instance, safe methane-to-hydrogen conversion and safe aircraft fuelling, could become a reality at scale by drawing on the fossil-fuel industry’s engineering skills.
And the limitless burning of fossil fuels without carbon capture and storage is increasingly seen as risky even in purely financial terms. It’s seen as heading toward stranded assets and what’s been called the bursting of the shareholders’ carbon bubble. James Thornton’s ClientEarth has been bringing successful lawsuits to stop high-carbon and other high-pollution investments in many countries, arguing irresponsibility to shareholders as well as to society. And more and more ideas are coming to maturity about diversifying and driving down the cost of low-carbon energy. Beyond renewables122 an interesting example is the Rolls Royce consortium on ‘small modular reactors’ for nuclear energy, produced cost effectively by state-of-the-art manufacturing techniques that avoid the spiralling costs of the large, one-off reactor projects.127 And now, at long last, we’re seeing the electrification of personal transport, a beautiful and elegant technology and another step in the right direction.
As regards good science in general an important factor in the human genome story, as well as in the ozone-hole story, was a policy of open access to experimental and observational data. That policy was one of the keys to success. The climate-science community was not always so clear on that point, giving the disinformers further opportunities. However, the lesson now seems to have been learned.
I don’t think, by the way, that everyone doubting climate science is dishonest. Honest scepticism is crucial to science; and I wouldn’t question the sincerity of colleagues I know personally who feel, or used to feel, that the climate-science community got things wrong. Indeed I’d be the last to suggest that that community, or any other scientific community, has never got anything wrong, even though my own sceptical judgement is that, as already argued, the climate-science consensus in the IPCC reports is mostly right apart from underestimating the problems ahead, including sea-level rise — partly because the climate prediction models have underestimated them, and partly for fear of being accused of alarmism and scaremongering.
It has to be remembered that unconscious assumptions and mindsets are always involved, in everything we do and think about. The anosognosic patient is perfectly sincere in saying that a paralysed left arm isn’t paralysed. There’s no dishonesty. It’s just an unconscious thing, an extreme form of mindset. Of course the professional art of disinformation includes the deliberate use of what sales and public-relations people call ‘positioning’ — the skilful manipulation of other people’s unconscious assumptions, related to what cognitive scientists call ‘framing’.41
As used by professional disinformers the framing technique exploits, for instance, the dichotomization instinct to evoke the unconscious assumption that there are only two sides to an argument. The disinformers then insist that their ‘side’ merits equal weight, as with flat earth versus round earth. That’s sometimes called ‘false balance’. In this and in many other ways the disinformers spread confusion, exploiting their deep knowledge of the way perception works. It’s inspirational, therefore, to see the climate disinformers, despite their mastery of such techniques, now facing defeat.
It often takes a younger generation to achieve Max Born’s ‘loosening of thinking’, exposing unconscious assumptions and making progress. Science, for instance, has always progressed in fits and starts, always against the odds, and always involving human weakness alongside a collective struggle with mindsets exposed, usually, through the efforts of a younger generation. The great population geneticist J. B. S. Haldane famously caricatured it in four stages: (1) This is worthless nonsense; (2) This is an interesting, but perverse, point of view; (3) This is true, but quite unimportant; (4) I always said so. The push beyond simplistic evolutionary theory is a case in point.
So here’s my farewell message to young scientists, and to any young person who cares about a civilized future. You have the gifts of intense curiosity and open-mindedness. You’re willing and able to think logically. You have the best chance of spotting inconsistency and misinformation, and of escaping from unconscious dichotomizations. You have enormous computing power at your disposal. You have brilliant programming tools, and observational and experimental data far beyond my own youthful dreams of long ago. You have a powerful new mathematical tool, the probabilistic ‘do’ operator, for distinguishing correlation from causality in complex systems.21 You’ll have seen how new insights from systems biology — transcending simplistic evolutionary theory — have opened astonishing new pathways to technological innovation18, 55, 123 as well as deeper insights into our own human nature, as I’ve tried to sketch in chapter 3. And above all you know how to disagree without hating — how to argue over the evidence not to score personal or political points, but to enjoy exploring things and to reach toward an improved understanding.
Whatever your fields of expertise, you know that it’s fun to be curious, to be open to the unexpected, and to find out how things work. It’s fun to do thought-experiments and computer experiments. It’s fun to develop and test your in-depth understanding, the illumination that can come from looking at a problem from more than one angle. You know that it’s worth trying to convey that understanding to a wide audience, if you get the chance. You know that in dealing with complexity you’ll need to hone your communication skills in any case, if only to develop cross-disciplinary collaboration, the usual first stage of which is jargon-busting — as far as possible converting turgid technical in-talk into plain, lucid speaking.
So hang in there. Your collective brainpower will be needed as never before.
1. Many of Darwin’s examples of cooperative behaviour, within and even across different social species, can be found in chapters II and III of his famous 1871 book The Descent of Man. Darwin’s greatness as a scientist shows clearly in the meticulous attention he pays to observations of actual animal behaviour. The animals observed include primates, birds, dogs, and ruminants such as cattle. See especially pages 74–84 in the searchable full text of the book, which is available online at http://darwin-online.org.uk/content/frameset?pageseq=1&itemID=F937.1&viewtype=text.
The contrary idea that competition between individuals is all that matters — often wrongly attributed to Darwin — goes back much further, of course. It shows up in the writings of, for instance, the philosopher Thomas Hobbes. In his 1651 book Leviathan Hobbes famously declared that human nature is innately vicious, and that only authoritarian dictatorship can save us from a dog-eat-dog life that’s “nasty, brutish and short”, or “red in tooth and claw” as Alfred, Lord Tennyson later put it. Despite his great learning, Hobbes could not have known much about actual hunter-gatherer societies, whose individuals show many instinctively compassionate and cooperative modes of behaviour that Hobbes, it seems, would have found surprising.2, 10, 11
2. See for instance Collier, P. and Kay, J., 2020: Greed is Dead: Politics After Individualism, Penguin, Allen Lane. John Kay and Paul Collier are British experts on business and economics. Their book discusses the damage done to human societies by the idea that competition between individuals is all that matters. See also economist Noreena Hertz’s 2020 book The Lonely Century: Coming Together in a World That’s Pulling Apart, Sceptre. The damage has been done not only via the gross economic inequality from what economists now call neoliberalism, or market fundamentalism25 — on the so-called political right alongside ‘possessive individualism’ or ‘greed is good’ — but also, in various ways, across a wide range of persuasions on the so-called political left and sadly, in addition, by strengthening the subcultures that tolerate or advocate violence toward individuals, including sexual violence. However, as Kay, Collier, and Hertz all point out, Darwinian evolutionary theory does not, in fact, say that competition between individuals is all that matters. On the contrary, evolution has given us not only the violent and greedy sides of human nature but also the friendly, cooperative, build-it-together, compassionate sides10, 11 — ‘ubuntu’ in the sense championed by Desmond Tutu, the instinctive feeling that ‘I am because we are’ — the denial of which, and the resulting loneliness, has been devastating for physical as well as for mental and social health. That conclusion is supported by today’s cutting-edge biology, as I’ll show in my chapter 3. Kay, Collier, and Hertz are also very clear on Adam Smith’s views which, contrary to most opinion today, recognized as important that there’s far more to human nature than simple greed or selfishness.40 The point is underlined by the young people volunteering for COVID-19 ‘challenge trials’ — deliberate infection under controlled conditions — taking personal risks to help us all by accelerating scientific understanding, and vaccine development, in the current arms race against an invisible, agile, and rapidly mutating enemy.123
3. Monod, J., 1971: Chance and Necessity. Glasgow, William Collins, beautifully translated from the French by Austryn Wainhouse. This classic by the great molecular biologist Jacques Monod — one of the sharpest and clearest thinkers that science has ever seen — highlights the “more than two million years of directed and sustained selective pressure” (chapter 7, p. 124) arising from the co-evolution of our ancestors’ genomes and cultures, entailing the gradual emergence of proto-language and then language because (p. 126) “once having made its appearance, language, however primitive, could not fail... to create a formidable and oriented selective pressure in favour of the development of the brain” in new ways — to the advantage of “the groups best able to use it”. The possibility of such group-level selective pressure is still controversial and I’ll return to it in my chapter 3, where in addition another topic from Monod’s book will come up, namely that of the regulatory ‘biomolecular circuits’ overlying the genome. Those circuits depend on transistor-like components called ‘allosteric enzymes’. Monod won a Nobel prize for his pioneering work on such enzymes.
4. Tobias, P. V., 1971: The Brain in Hominid Evolution. New York, Columbia University Press. Phillip Tobias’ famous work on palaeoanthropology led him to recognize the likely interplay of genomic and cultural evolution, despite the vast disparity of timescales. He writes that “the brain-culture relationship was not confined to one special moment in time. Long-continuing increase in size and complexity of the brain was paralleled for probably a couple of millions of years [my emphasis] by long-continuing elaboration... of the culture. The feedback relationship between the two sets of events is as indubitable as it was prolonged in time.” Evidence in further support of this picture will be summarized in my chapter 3.
5. I began with examples of unconscious assumptions I’ve encountered in my own scientific research. Their unconscious nature was very clear because making them conscious exposed them as self-evidently wrong, indeed silly. They’re discussed in a recent paper of mine, On multilevel thinking and scientific understanding, Adv. Atmos. Sci., 34, 1150–1158 (2017).
6. Kahneman, D., 2011: Thinking, Fast and Slow. London, Penguin. Daniel Kahneman’s book, based on his famous research with Amos Tversky on psychology and economics, provides deep insight into many unconscious processes of great social importance. See also ref. 41. Early in his Introduction, Kahneman gives an example of a lifesaving decision taken ahead of conscious thought. In Kahneman’s words, the commander of a team fighting a domestic fire “heard himself shout, ‘Let’s get out of here!’ without realizing why.” The commander had unconsciously sensed that the floor on which they were standing was about to collapse into a bigger fire underneath.
7. Bateson, G., 1972: Steps to an Ecology of Mind: Collected Essays on Anthropology, Psychiatry, Evolution and Epistemology. Republished 2000 by the University of Chicago Press. The quoted sentence is on p. 143, in the section on ‘Quantitative Limits of Consciousness’.
8. The unconscious learning that’s needed to acquire normal vision has been extensively studied. For instance there’s been a long line of research on whether anything like normal vision is acquired by individuals blinded in infancy by congenital cataracts, or opaque corneas, that are surgically removed later in life. Common to all such cases is the complete absence of normal vision immediately after surgery. The patient typically sees only a confused mess of shapes and colours. Many months after surgery, abilities much closer to normal vision can be acquired, especially by the youngest patients. Some older patients fail to acquire anything remotely like normal vision, as in the classic cases of middle-aged patients, including a man called Virgil, described in Oliver Sacks’ 1995 book An Anthropologist on Mars, New York, Alfred Knopf. In recent years, Project Prakash in India has encountered many cases of younger patients who do better. See for instance Sinha, P., 2013: Once blind and now they see. Scientific American, 309(1), 48–55, and Gandhi, T., Singh, A.K., Swami, P., Ganesh, S., Sinha, P., 2017: The emergence of categorical face perception after extended early-onset blindness. Proc. National Academy of Sciences, 114, 6139–6143. This last study demonstrates not the ability to distinguish the faces of different individuals from one another, but only the ability to distinguish images of human faces from images of other things. That’s typically acquired by children within a year or so after surgery. Oliver Sacks’ book also describes the case of the painter Franco Magnani, to be mentioned in my chapter 4.
9. See for instance chapter 4 of Noble, D., 2006: The Music of Life: Biology Beyond Genes. Oxford University Press. This short and lucid book by an eminent biologist clearly brings out the complexity, versatility, and multi-level aspects of biological systems, and the need to avoid extreme reductionism and single-viewpoint, hypercredulous thinking, such as saying that the genome ‘causes’ everything. A helpful metaphor for the genome, it’s argued, is a digital music recording. Yes, reading the digital data ‘causes’ a musical and possibly emotional experience but, if that’s all you say, you miss the other things on which the experience depends so strongly, many of them coming from past experience as well as present circumstance. Reading the data into a playback device mediates or enables the listener’s experience, rather than solely causing it.
10. A recent book by social commentator David Brooks contains a wealth of evidence that human compassion is just as natural and instinctive as human nastiness. Further evidence is offered in, for instance, refs. 2 and 11. Brooks regards compassion as something mysterious and beyond science because he takes for granted the narrow, simplistic, dog-eat-dog view of biological evolution that still permeates popular culture. But a more complete view of evolution beginning with Charles Darwin’s observations,1 and summarized in my chapter 3, easily explains what Brooks describes as “the fierceness and fullness of love, as we all experience it”, and the observed fact that many hundreds of people whom he’s met — he calls them social “weavers” — live for others with little material reward. As Brooks observes, they are rewarded instead by something deep in their inner nature, giving them joy in caring for others and in the spontaneous upwelling of emotions such as love and compassion. They’re at peace with themselves because this inner life is more important to them than competition for power, money and status. They radiate joy. They “seem to glow with an inner light... they have a serenity about them, a settled resolve. They are interested in you, make you feel cherished and known, and take delight in your good.” All this comes naturally and without conscious effort. It does not come from being preached at moralistically. It does not come from cynical ‘virtue signalling’. See Brooks, D., 2019: The Second Mountain: The Quest for a Moral Life. Random House, Penguin.
11. Bregman, R., 2020: Humankind: A Hopeful History. Bloomsbury. This book by Rutger Bregman assembles many examples of human behaviour that’s instinctively friendly, kind and compassionate, outside kin or family. Bregman acknowledges Hobbesian human nastiness1 but makes the point that such nastiness isn’t all there is. He gives many examples to add to those in ref. 10 and argues that our friendly, compassionate side must have been a key part of our ancestors’ extraordinary versatility and adaptability — contrary to the narrow, simplistic, dog-eat-dog view of biological evolution that still permeates popular culture. And he gives us a reassessment of what Hannah Arendt called “the banality of evil”, with a forensic re-examination of the case of Adolf Eichmann, as well as of the notorious psychological experiments of Stanley Milgram and others, in the light of newly-unearthed evidence.
12. See for instance Pagel, M., 2012: Wired for Culture. London and New York, Allen Lane, Penguin, Norton. In this book a well known evolutionary biologist, Mark Pagel FRS, describes many interesting aspects of recent cultural evolution. On human languages, though, he considers that they are all descended from a single ‘mother tongue’. That’s seen most clearly on page 299, within a section headed “words, languages, adaptation, and social identity”. The author suggests that language and the mother tongue were invented, as a single cultural event, at some time after “our invention of culture” around 160 to 200 millennia ago (page 2). This hypothetical picture is diametrically opposed to that of Monod,3 who along with Tobias4 insists on a strong feedback between genomic evolution and cultural evolution over a far longer timespan, under strong selective pressures at group level (Monod,3 pp. 126–7). Pagel’s arguments assume that group-level selection is never important. I myself find Monod’s arguments more persuasive, for reasons set out in my chapter 3. Powerful cross-checks come from recent events in Nicaragua alongside laboratory experiments that directly demonstrate group-level selection.
13. A typical range of views and controversies over the origins of language can be found in the collection of short essays by Trask, L., Tobias, P. V., Wynn, T., Davidson, I., Noble, W., and Mellars, P., 1998: The origins of speech. Cambridge Archaeological Journal, 8, 69–94. There are contributions from linguists, palaeoanthropologists, and archaeologists. Some of the views are consistent with Monod’s,3 while others (see especially the essay by Davidson and Noble) are more consistent with the idea espoused by Pagel12 that language was a very recent, purely cultural invention. See also the thoughtful discussion in ref. 61.
14. van der Post, L., 1972: A Story Like the Wind. London, Penguin. Laurens van der Post celebrates the influence he felt from his childhood contact with some of Africa’s “immense wealth of unwritten literature”, including the magical stories of the San or Kalahari-Desert Bushmen, stories that come “like the wind... from a far-off place.” See also van der Post’s 1961 book The Heart of the Hunter (Penguin), page 28, on how a Bushman told what had happened to his small group: “They came from a plain... as they put it in their tongue, ‘far, far, far away’.. It was lovely how the ‘far’ came out of their mouths. At each ‘far’ a musician’s instinct made the voices themselves more elongated with distance, the pitch higher with remoteness, until the last ‘far’ of the series vanished on a needle-point of sound into the silence beyond the reach of the human scale. They left... because the rains just would not come...”
15. Pinker, S., 2018: Enlightenment Now: The Case for Science, Reason, Humanism and Progress, Penguin Random House. In a thoughtful chapter on democracy the author discusses why, in a long-term view — and contrary to what headlines often suggest — democracy has survived against the odds and spread around parts of the globe in three great waves over the past two centuries. It seems that this is not so much because of what happens in elections (in which the average voter isn’t especially engaged or well informed) but, as pointed out by political scientist John Mueller, more because it gives ordinary people the freedom to complain publicly at any time, and to be listened to by governments without being imprisoned, tortured, or killed. In other words it’s to some degree an ‘open society’ in the sense of Karl Popper — allowing bottom-up influence or ‘accountability’ — which for one thing improves the society’s versatility and adaptability. (Of course I’m assuming that ‘democracy’ means more than just popular voting. As discussed by political scientists such as Juan Linz, in order to be more than just a sham it must include reasonably strong counter-autocratic institutions, including the separation of executive, judicial, and vote-counting powers — and a culture that allows disagreement without hating, hence acceptance of electoral wins by opponents.)
16. For this new cross-check (verifying a prediction made over a century ago by Albert Einstein from his general-relativity equations) see Abbott, B. P., et al., 2016: Observation of gravitational waves from a binary black hole merger. Physical Review Letters, 116, 061102. This was an enormous team effort at the cutting edge of high technology, decades in the making, to cope with the tiny amplitude of Einstein’s gravitational ripples. The ‘et al.’ stands for the names of over a thousand other team members. The study used three LIGO detectors (Laser Interferometer Gravitational-Wave Observatory), two in the USA and one in Italy (called Virgo). They are giant interferometers, with arms kilometres long, accommodating laser beams that can detect length changes of the order of a billion-billionth (10-18) of a metre. The first event was detected on 14 September 2015. A second event was detected on 26 December 2015. It was reported in Abbott, B. P., et al., 2016, Physical Review Letters 116, 241103. In this second event the model-fitting indicated that one of the merging black holes probably had nonzero spin. Subsequent events have corresponded to the merging not only of black holes but also of neutron stars.
17. Valloppillil, V., 1998: The Halloween Documents: Halloween I, with commentary by Eric S. Raymond. This leaked document from the Microsoft Corporation, available online, records Microsoft’s secret recognition that software far more reliable than its own was being produced by the open-source community, a major example being Linux. Halloween I states, for instance, that the open-source community’s ability “to collect and harness the collective IQ of thousands of individuals across the Internet is simply amazing.” Linux, it goes on to say, is an operating system in which “robustness is present at every level” making it “great, long term, for overall stability”. I well remember the non-robustness and instability, and user-unfriendliness, of Microsoft’s own secret-source software during its near-monopoly in the 1990s.
18. Recent advances in understanding genetic codes include insights into how they influence, and are influenced by, the lowermost layers of complexity in the molecular-biological systems we call living organisms. Some of these advances, building on those in refs. 3 and 9, are beautifully described in the book by Andreas Wagner, 2014: Arrival of the Fittest: Solving Evolution’s Greatest Puzzle, London, Oneworld. A detailed view emerges of the interplay between genes and functionality, such as the synthesis of chemicals needed by an organism, and the switching-on of large sets of genes to make the large sets of enzymes and other protein molecules required by a particular functionality. And these systems-biological insights throw into sharp relief the naivety and absurdity of thinking that genetic codes are blueprints governing everything, and that there is a single gene ‘for’ a single trait.9 Also thrown into sharp relief is the role of natural selection and, importantly, other mechanisms such as neutral mutation, in the evolution of functionality. The importance of other mechanisms vindicates one of Charles Darwin’s key insights, namely that natural selection is only part of how evolution works. In Darwin’s own words from page 421 of the sixth, 1872 edition of his Origin of Species, “As my conclusions have lately been much misrepresented, and it has been stated that I attribute the modification of species exclusively to natural selection, I may be permitted to remark that in the first edition of this work, and subsequently, I placed in a most conspicuous position — namely, at the close of the Introduction — the following words: ‘I am convinced that natural selection has been the main but not the exclusive means of modification.’” And the research by Wagner and co-workers shows clearly and in great detail the role of, for instance, vast numbers of neutral mutations. These are mutations that have no immediate adaptive advantage and are therefore invisible to natural selection, yet have crucial long-term importance through building genetic diversity.44 The research gives insights into the extraordinary robustness of biological functionality, insights that have practical technological implications. For instance they’ve led to new ways of designing, or rather discovering, robust electronic circuits and computer codes. Further such insights come from recent studies of self-organizing or self-assembling structures, as for instance with the ‘murmurations’ of flocks of starlings, and structures emerging in crowds of ‘swarm-bots’.
19. Vaughan, M. (ed.), 2006: Summerhill and A. S. Neill, with contributions by Mark Vaughan, Tim Brighouse, A. S. Neill, Zoë Neill Readhead and Ian Stronach. Maidenhead, New York, Open University Press/McGraw-Hill. Summerhill School is a boarding school founded in 1921 by Alexander Sutherland Neill and is located in Suffolk, England. It is famous for its innovative approach to education including a children’s democracy based on school meetings. Each pupil has an equal vote along with the teachers. The meetings decide the school rules and deal with those who break them. A guiding principle is “freedom, not licence”: coercion is minimized subject to not harming others.
20. Yunus, M., 1998: Banker to the Poor. London, Aurum Press. This is the story of the Grameen Bank of Bangladesh, which pioneered microlending and the emancipation of women, succeeding against all expectation.
21. Pearl, J. and Mackenzie, D., 2018: The Book of Why: The New Science of Cause and Effect. London, Penguin. This lucid, powerful, and very readable book describes recently-developed forms of Bayesian probability theory82 that make causal arrows explicit, clearly distinguishing correlation from causality. Key to this is the probabilistic ‘do’ operator, or experimentation operator as it might be called. It gives us a precise mathematical framework for dealing with experiments and experimental data. It underpins the most powerful forms of artificial intelligence and big-data analytics. It is applicable to complex problems such as a virus infecting a cell. Its power lies not only behind much of today’s cutting-edge open science but also, for instance, behind the covert behavioural experiments done by the social-media technocrats.22, 23
22. Giant behavioural experiments have been done for many years now by Google, Facebook, and other social-media platforms. Experiments using, for example, ‘like’ buttons can repeatedly test the behaviour of up to billions of subjects. By contrast with the giant hadron-collider experiments, on particle physics — whose data are released into the public domain to advance the science — the giant behavioural experiments are cloaked in commercial secrecy. The experimental techniques include not only button-pressing but also getting users to ‘make friends’ with digital ‘assistants’, as they’re called, with human-like names, and to play games such as Pokémon Go, all of which generates vast amounts of data on user behaviour. And from these experiments, using the power of the Bayesian-analytics toolkit,21 the social-media technocrats have built the artificial intelligences now in use for commercial and political gain — incorporating not only mathematical models of unconscious human behaviour but also information on the private preferences of billions of individuals. They exploit and manipulate our unconscious assumptions in a precisely targeted way. The sheer scale and power of this innovation is hard to grasp, but if only for civilization’s sake it needs to be widely understood. For more detail see refs. 23.
23. One of the important documents is the book by McNamee, R., 2019: Zucked: Waking Up to the Facebook Catastrophe, HarperCollins. [Note added in proof: See also Frenkel, S. and Kang, C., 2021: An Ugly Truth: Inside Facebook's Battle For Domination, Bridge Street Press.] Roger McNamee is a venture capitalist who helped to launch Facebook and who knows a great deal about how it works, including the way it creates socially divisive echo chambers, filter bubbles, and preference bubbles. He shows how Facebook, in particular, has used its giant behavioural experiments22 to build what I’ll call artificial intelligences that aren’t yet very intelligent. To be sure, they’re clever at exploiting human weaknesses to sell things. But they’re downright stupid in other ways, not least in undermining democratic social stability and thence, I’ll argue, in risking their very own survival as free-entrepreneurial business entities. I’ll develop that point near the end my chapter 3. Part of the problem comes from the way in which the artificial intelligences maximize profits from advertising revenue. They do so by allowing abuse and misinformation to go viral at lightning speed, often under a cloak of anonymity. Unsurprisingly, that’s also exploited by political propagandists, ‘new conspiracists’, extremists and disinformers of every kind, on a massive scale. See for instance the 2019 book by Nancy L. Rosenblum and Russell Muirhead: A Lot of People Are Saying: The New Conspiracism and the Assault on Democracy, Princeton University Press. Regarding the exploitation by propagandists, national and international, there’s a useful short summary by cyber-security expert Clint Watts: Five generations of online manipulation: the evolution of advanced persistent manipulators, Eurasia Review, 13 March 2019. There are also the commercial trollers or ‘dragging sites’, internet businesses exclusively focused on the profits from spreading anonymous lies, abuse and threats as recently documented, for instance, by journalist Sali Hughes. Journalist Helen Lewis has aptly called it “the economics of outrage”. Many ongoing developments in the disinformation and trolling industries — now including character assassination using deep-fake artificial intelligence — are documented in the important 2020 book by Nina Schick, Deep Fakes and the Infocalypse: What You Urgently Need to Know, Monoray (Octopus Publishing Group).
24. The ozone disinformation campaign is something that I myself encountered personally, back in the 1980s and 1990s. This well funded, highly professional campaign and the longer-running climate disinformation campaigns have been forensically documented in the book by Oreskes, N. and Conway, E. M., 2010: Merchants of Doubt: How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming, Bloomsbury, 2010. Using formerly secret documents brought to light through anti-tobacco litigation, the authors show how the campaigns were masterminded by the same scientists turned professional disinformers who first honed their skills in the tobacco companies’ lung-cancer campaigns. For reliable information about the ozone hole, see https://csl.noaa.gov/assessments/ozone/2018/twentyquestions/
25. The idea of a cooperative ‘symbiosis’ between market forces and regulation is hardly new, having been advocated by Adam Smith40 even if not by all his followers. See also ref. 2, and the 2020 BBC Reith Lectures by Mark Carney. The idea has been developed further by economist Mariana Mazzucato in her 2018 book The Value of Everything: Making and Taking in the Global Economy, Penguin. Chapter 9 suggests how a useful symbiosis can be encouraged when government policy is recognized as “part of the social process which co-shapes and co-creates competitive markets,” with innovation and new opportunities among its goals. Mazzucato also argues that such creative developments are being held back by the incoherent popular mythologies, or narratives, that still dominate much of our politics, especially the narratives of possessive individualism and market fundamentalism — the hypercredulous, semi-conscious beliefs that Market Forces are the Answer to Everything and that the only goal should be to maximize individual profits (and never to tax them, nor to regulate anything because, dichotomously speaking, Private is Good and Public is Bad). Another eminent economist, Nobel laureate Paul Krugman, calls these dichotomized narratives “zombie ideas” as a reminder that they should be dead ideas, according to the evidence, but are kept alive artificially — by disinformation paid for by the tiny plutocratic élites that currently take most of the profits.41
26. Sulston, J., and Ferry, G., 2003: The Common Thread: A Story of Science, Politics, Ethics and the Human Genome, Corgi edn. This important book by John Sulston and Georgina Ferry gives a first-hand account of how the scientific ideal and ethic prevailed against corporate might — powerful commercial interests that came close to monopolizing the genomic data for private profit. By shutting off open access to the data, the monopoly would have done incalculable long-term damage to biological and medical research, not least the current research on COVID-19.
27. Strunk, W., and White, E. B., 1979: The Elements of Style, 3rd edn. New York, Macmillan. I love the passage addressed to practitioners of the literary arts, whose ambitions transcend mere lucidity: “Even to a writer who is being intentionally obscure or wild of tongue we can say, ‘Be obscure clearly! Be wild of tongue in a way we can understand!’”
28. See the article headed “elegant variation” in Fowler, H. W., 1983: A Dictionary of Modern English Usage, 2nd edn., revised by Ernest Gowers, Oxford University Press. Fowler’s lucid and incisive article is not to be confused with the vague and muddy article under the same heading in the so-called New Fowler’s of 1996, written by a different author.
29. My first two examples, “If you are serious, then I’ll be serious” and “If you are serious, then I’ll be also”, roughly translate to
I don’t myself know any of the Chinese languages, but even I can see that the first sentence has an invariant element while the second does not. My Chinese colleagues assure me that the first sentence is clearer and stronger than the second.
30. Littlewood, J. E., 1953: A Mathematician’s Miscellany. London, Methuen. Republished with extra material by B. Bollobás in 1986, as Littlewood’s Miscellany, Cambridge University Press.
31. The so-called ‘slow manifold’ is a multidimensional geometrical object that has a role in the mathematics of fluid-dynamical theory. It’s important for understanding the dynamics of jet streams, ocean currents, eddies, and wave–vortex interactions, using an invariant quantity called ‘potential vorticity’. In a slightly different sense it’s also important in other branches of fluid dynamics, such as understanding the flow around an aircraft and how the aircraft stays up. It’s an object found within the space of all possible flows. It’s like something hairy, or fuzzy. More precisely, it’s a fractal object. By contrast, a manifold is non-fractal and like something bald. I’ve tried hard to persuade my fluid-dynamical colleagues to switch to ‘slow quasimanifold’, but with scant success so far. For practical purposes the thing often behaves as if it were a manifold, even though it isn’t one. It’s ‘thinly hairy’.
32. Medawar, P. B., 1960: The Future of Man: The BBC Reith Lectures 1959. London, Methuen. Near the start of Lecture 2, Medawar remarks that scientists are sometimes said to give the meanings of words “a new precision and refinement”, which would be fair enough, he says, were it not for a tendency then to believe that there’s such a thing as the unique meaning of a word — the “true” or “pure” meaning. Then comes his remark that “The innocent belief that words have an essential or inward meaning can lead to an appalling confusion and waste of time” — something that very much resonates with my own experience in thesis correcting, peer reviewing, and scholarly journal editing.
33. Hunt, M., 1993: The Story of Psychology. Doubleday, Anchor Books. The remarks about the Three Mile Island control panels and their colour coding are on p. 606. There were further design flaws, such as making warning indicators inconspicuous and even making parts of the control panels too high to be read by operators.
34. McIntyre, M. E., 1997: Lucidity and science, I: Writing skills and the pattern perception hypothesis. Interdisc. Sci. Revs. 22, 199–216.
35. See for instance Pomerantsev, P., 2015: Nothing is True And Everything is Possible — Adventures in Modern Russia. Faber & Faber. The title incorporates the postmodernist tenet that there’s just one Absolute Truth, namely that nothing is true except the belief that nothing is true. (How profound! How ineffable! How Derridian!) Peter Pomerantsev worked as a television producer in Moscow with programme makers in the state’s television monopolies, during the first decade of the 2000s. He presents an inside view of how at that time the state controlled the programming through an extraordinarily skilful propagandist, Vladislav Surkov, sometimes called ‘The Puppet Master’. Surkov’s genius lay in exploiting postmodernist ideas to build an illusion of democratic pluralism in Russia at that time, with mercurial shape-shifting and the skilful and incessant telling of lies as the predominant political weapons — promoting endless confusion — alongside the pressing of binary buttons to amplify social divisions when expedient. Some Western politicians and campaign advisers have followed Surkov’s example, developing what’s been euphemistically called a ‘post-truth’ culture of ever-changing ‘alternative facts’, central to information warfare and what’s now called the ‘infocalypse’. See the last-cited of refs. 23. Postmodernism, as expounded by philosophers such as Jacques Derrida, has provided not only a fertile source of ideas but also a veneer of intellectual respectability, over what would otherwise be described as ordinary mendacious propaganda taken to new extremes.
36. McGilchrist, I., 2009: The Master and his Emissary: the Divided Brain and the Making of the Western World. Yale University Press. Iain McGilchrist has worked both as a literary scholar and as a psychiatrist. In this vast and thoughtful book, ‘world’ often means the perceived world consisting of the brain’s unconscious internal models, to be discussed in my chapter 4. In most people, the Master is the right hemisphere with its holistic, integrated ‘world’, open to multiple viewpoints. The Emissary is the left hemisphere with its dissected, atomistic and fragmented ‘world’ and its ability to speak and thereby, all too often, to dominate proceedings with its strongly-held mindsets and unconscious assumptions.
37. See for instance Ramachandran, V. S. and Blakeslee, S., 1998: Phantoms in the Brain: Human Nature and the Architecture of the Mind. London, Fourth Estate. Ramachandran is a neuroscientist known for his ingenious behavioural experiments and their interpretation. The phantoms are the brain’s unconscious internal models that mediate perception and understanding, to be discussed in my chapter 4, and this book provides one of the most detailed and penetrating discussions I’ve seen of the nature and workings of those models and of the roles of the left and right brain hemispheres. Page 59 tells how to produce the ‘phantom nose illusion’ mentioned in my chapter 4.
38. The quote can be found in an essay by Max Born’s son Gustav Born, 2002: The wide-ranging family history of Max Born. Notes and Records of the Royal Society (London), 56, 219–262 and Corrigendum, 56, 403. Max Born was awarded the Nobel Prize in physics, belatedly in 1954; and the quotation comes from a lecture he gave at a meeting of Nobel laureates in 1964, at Lindau on Lake Constance. The lecture was entitled Symbol and Reality (Symbol und Wirklichkeit).
39. Conway, F. and Siegelman, J., 1978: Snapping. New York, Lippincott. This sociological study focusing on the American fundamentalist cults of the 1970s remains highly relevant in today’s world. Chapter 4 discusses the generic aspects in a thoughtful and interesting way. It records personal accounts of intense religious experience, and similar emotional experiences, going on to take note of their political and commercial exploitation. An ex-preacher, Marjoe Gortner, describes how the techniques of bringing a crowd to ecstasy parallel the techniques of a rock concert. Gortner eventually abandoned his preaching career because “as you start moving into the operation of the thing, you get into controlling people and power and money.”
40. Tribe, K., 2008: ‘Das Adam Smith Problem’ and the origins of modern Smith scholarship. History of European Ideas, 34, 514–525. This paper provides a forensic overview of Adam Smith’s writings and of the many subsequent misunderstandings of them that accumulated in the German, French, and English academic literature of the following centuries — albeit clarified as improved editions, translations, and commentaries became available. Smith viewed the problems of ethics, economics, politics and human nature together, as a whole, and from more than one angle, and saw his two great works The Theory of Moral Sentiments (1759) and An Inquiry into the Nature and Causes of the Wealth of Nations (1776) as complementing each other. He stood by both of them throughout his life. Yes, market forces are useful, but only in symbiosis with written and unwritten regulation,25 including personal ethics.
41. See for instance Krugman, P., 2020: Arguing with Zombies: Economics, Politics, and the Fight for a Better Future, Norton, and Lakoff, G., 2014: Don’t Think of an Elephant: Know Your Values and Frame the Debate, Vermont, Chelsea Green Publishing. Economist Paul Krugman and cognitive linguist George Lakoff show how the plutocracies exploiting market fundamentalism25 perpetuate themselves using their financial power to buy expertise in psychology and persuasion — expertise in the way perception works — exploiting lucidity principles and pressing our binary buttons in the service of disinformation. One of the techniques is to ‘frame’ things as binary, for instance setting up a ‘debate’ to decide between brutal socialism on the one hand, and free markets on the other, as if they were the only two possibilities. The same goes for climate ‘versus’ the economy, or COVID ‘versus’ the economy. Dichotomization makes us stupid, as the disinformers well know. The book by Kahneman6 provides a more general, in-depth discussion of framing, and of related techniques such as anchoring and priming.
42. See for instance Skippington, E., and Ragan, M. A., 2011: Lateral genetic transfer and the construction of genetic exchange communities. FEMS Microbiol Rev., 35, 707–735. This review article opens with the sentence “It has long been known that phenotypic features can be transmitted between unrelated strains of bacteria.” The article goes on to show among other things how “antibiotic resistance and other adaptive traits can spread rapidly, particularly by conjugative plasmids”. Conjugative means that the plasmid is passed directly from one bacterium to another through a tiny tube called a pilus, even if the two bacteria belong to different species.
43. Wilson, D. S., 2015: Does Altruism Exist? Culture, Genes, and the Welfare of Others. Yale University Press. This book by evolutionary biologist David Sloan Wilson focuses on altruism as actual instinctive behaviour, and on ways in which it can arise from multi-level natural selection in heterogeneous populations. Chapter 2 presents clear and well-verified examples of multi-level selection from laboratory experiments. The examples include the evolution of heterogeneous populations of insects, and of bacteriophage viruses, that exhibited mixtures of selfish and altruistic behaviour. Group-level selection is crucial, alongside individual-level selection, to explaining what was observed in each case. Elsewhere in the book, human belief systems and their consequences are considered. Chapter 1 examines the work of Nobel laureate Elinor Ostrom on belief systems that avoid the ‘tragedy of the commons’.54 Chapters 6 and 7 examine fundamentalist belief systems and their characteristic dichotomizations. Chapter 6 focuses on religious systems including the Hutterites of North America, and chapter 7 on atheist systems including Ayn Rand’s famous version of market fundamentalism, at variance with Adam Smith’s ideas.40 Rand’s credo, called ‘objectivism’, and its relation to Friedrich Nietzsche’s Übermensch, are discussed at some length in chapter 2 of the 2018 book by the philosopher John Gray, Seven Types of Atheism, Allen Lane. See also note 79 below.
44. Wills, C., 1994: The Runaway Brain: The Evolution of Human Uniqueness. London, HarperCollins. This wise and powerful synthesis by Professor Christopher Wills was years ahead of its time. It builds on the author’s intimate knowledge of genes, palaeoanthropology, and population genetics. The starting point is the quote from Phillip Tobias4 suggesting the crucial role of multi-timescale genome–culture feedback over millions of years. The author goes on to offer many far-reaching insights, not only into the science itself but also into its turbulent history and controversies. Sewall Wright’s discovery of genetic drift is lucidly described in chapter 8 — this was one of the successes of the old population-genetics models — along with Motoo Kimura’s work showing the importance of neutral mutations, now cross-checked at molecular level.18 As well as advancing our fundamental understanding of evolutionary dynamics, Kimura’s work led to the discovery of the molecular-genetic ‘clocks’ now used to estimate, from genomic sequencing data, the rates of genomic evolution and the times of past genetic bottlenecks. Wills describes how, prior to these developments, progress was held up by dichotomized disputes about neutral mutations versus adaptive mutations, failing to recognize that both could be important.
45. Rose, H. and Rose. S. (eds), 2000: Alas, Poor Darwin: Arguments against Evolutionary Psychology. London, Jonathan Cape. This thoughtful compendium offers a variety of perspectives on the extreme reductionism or so-called Darwinian fundamentalism of recent decades, close to what I’m calling ‘simplistic evolutionary theory’ — as distinct from Charles Darwin’s own more complete, more pluralistic view. See also chapter 10 by an eminent expert on animal behaviour, the late Patrick Bateson FRS, on the word ‘instinct’ and its controversial technical meanings.
46. Dunbar, R. I. M., 2003: The social brain: mind, language, and society in evolutionary perspective. Annual Rev. Anthropol., 32, 163–181. This review offers important insights into the group-level selective pressures on our ancestors, drawing on the primatological, palaeoanthropological and palaeoarchaeological evidence. See especially the discussion on pages 172–179. Data are summarized that reflect the growth of brain size and neocortex size over the past three million years, including its extraordinary acceleration beginning half a million years ago — by which time, as suggested on page 175, “language, at least in some form, would have had to have evolved”, in part to expand the size of the grooming cliques or friendship circles within larger social groups. Even a rudimentary level of language, as with “I love you, I love you”, would have been enough to expand such circles, by verbally grooming several individuals at once. The subsequent brain-size acceleration corresponds to what Wills44 calls runaway brain evolution, under growing selective pressures for ever-increasing linguistic and societal sophistication and group size culminating — perhaps around the time of the incipient Upper Palaeolithic a hundred millennia ago — in our species’ ability to tell elaborate fictional as well as factual stories.
47. Thierry, B., 2005: Integrating proximate and ultimate causation: just one more go! Current Science, 89, 1180–1183. A thoughtful commentary on the history of biological thinking, in particular tracing the tendency to neglect multi-timescale processes, with fast and slow mechanisms referred to as “proximate causes” and “ultimate causes”, assumed independent solely because “they belong to different time scales” (p. 1182a), respectively individual-organism and genomic timescales.
48. Rossano, M. J., 2009: The African Interregnum: the ‘where,’ ‘when,’ and ‘why’ of the evolution of religion. In: Voland, E., Schiefenhövel, W. (eds), The Biological Evolution of Religious Mind and Behaviour, Springer-Verlag, pp. 127–141. The African Interregnum refers to the time between the failure of our ancestors’ first migration out of Africa, roughly 100 millennia ago, and the second such migration a few tens of millennia later. Rossano’s brief but penetrating survey argues that the emergence of belief systems having a “supernatural layer” boosted the size, sophistication, adaptability, and hence competitiveness of human groups. As regards the Toba eruption around 70 millennia ago, the extent to which it caused a human genetic bottleneck is controversial, but not the severity of the disturbance to the climate system, like a multi-year nuclear winter. The resulting resource depletion must have severely stress-tested our ancestors’ adaptability — giving large, tightly-knit and socially sophisticated groups an important advantage. Survival strategies may have included wheeling and dealing between groups. In Rossano’s words, the groups were “collectively more fit and this made all the difference.”
49. Laland, K., Odling-Smee, J., and Myles, S., 2010: How culture shaped the human genome: bringing genetics and the human sciences together. Nature Reviews: Genetics, 11, 137–148. This review notes the likely importance, in genome–culture co-evolution, of more than one timescale. It draws on several lines of evidence. The evidence includes data on genomic sequences, showing the range of gene variants (alleles) in different sub-populations. As the authors put it, in the standard mathematical-modelling terminology, “... cultural selection pressures may frequently arise and cease to exist faster than the time required for the fixation of the associated beneficial allele(s). In this case, culture may drive alleles only to intermediate frequency, generating an abundance of partial selective sweeps... adaptations over the past 70,000 years may be primarily the result of partial selective sweeps at many loci” — that is, locations within the genome. Partial selective sweeps are patterns of genomic change responding to selective pressures yet retaining some genetic diversity, hence potential for future versatility and adaptability. The authors confine attention to very recent co-evolution, for which the direct lines of evidence are now strong in some cases — leaving aside the earlier co-evolution of, for instance, proto-language.59 There, we can expect multi-timescale coupled dynamics over a far greater range of timescales, for which direct evidence is much harder to obtain, as discussed also in ref. 50.
50. Richerson, P. J., Boyd, R., and Henrich, J., 2010: Gene-culture coevolution in the age of genomics. Proc. Nat. Acad. Sci. 107, 8985–8992. This review takes up the scientific story as it has developed after Wills’ book,44 usefully complementing ref. 49. The discussion comes close to recognizing two-way, multi-timescale dynamical coupling but doesn’t quite break free of asking whether culture is “the leading rather than the lagging variable” in the co-evolutionary system (my italics, to emphasize the false dichotomy).
51. Laland, K., Sterelny, K., Odling-Smee, J., Hoppitt, W., and Uller, T., 2011: Cause and effect in biology revisited: is Mayr’s proximate-ultimate dichotomy still useful? Science, 334, 1512–1516. The dichotomy, between “proximate causation” around individual organisms and “ultimate causation” on evolutionary timescales, entails a belief that the fast and slow mechanisms are dynamically independent. This review argues that they are not independent, even though the dichotomy is still taken by many biologists to be unassailable. The review also emphasizes that the interactions between the fast and slow mechanisms are often two-way interactions, or feedbacks, labelling them as “reciprocal causation” and citing many lines of supporting evidence. This recognition of feedbacks is part of what’s now called the “extended evolutionary synthesis”. See also refs. 47 and 53.
52. See for instance Schonmann, R. H., Vicente, R., and Caticha, N., 2013: Altruism can proliferate through population viscosity despite high random gene flow. Public Library of Science, PLoS One, 8, e72043. Improvements in model sophistication, and a willingness to view a problem from more than one angle, show that group-selective pressures can be effective.
53. Danchin, E. and Pocheville, A., 2014: Inheritance is where physiology meets evolution. Journal of Physiology, 592, 2307–2317. This complex but very interesting review is one of two that I’ve seen — the other being ref. 51 — that go beyond refs. 49 and 50 in recognizing the importance of multi-timescale dynamical processes in biological evolution. It seems that such recognition is still a bit unusual, even today, because of a widespread assumption, perhaps unconscious, that timescale separation implies dynamical decoupling (see also ref. 47). In reality there is strong dynamical coupling, the authors show, involving an intricate interplay between different timescales. It’s mediated in a rich variety of ways including not only niche construction and genome–culture co-evolution but also, at the physiological level, developmental plasticity along with the non-genomic heritability now called epigenetic heritability. One consequence is the creation of hitherto unrecognized sources of heritable variability, the crucial raw material on which natural selection depends. See also the Nature Commentary by Laland, K. et al., 2014: Does evolutionary theory need a rethink? Nature, 514, 161–164. (In the Commentary, for ‘gene’ read ‘replicator’ including regulatory DNA.)
54. Werfel, J., Ingber, D. I., and Bar-Yam, I., 2015: Programed death is favored by natural selection in spatial systems, Phys. Rev. Lett., 114, 238103. This detailed modelling study illustrates yet again how various ‘altruistic’ traits are often selected for, in models that include population heterogeneity and group-level selection. The paper focuses on the ultimate unconscious altruism, mortality — the finite lifespans of most organisms. Finite lifespan is robustly selected for, across a wide range of model assumptions, simply because excessive lifespan is a form of selfishness leading to local resource depletion. The tragedy of the commons, in other words, is as ancient as life itself. The authors leave unsaid the implications for our own species.
55. Contera, S., 2019: Nano comes to life: How Nanotechnology is Transforming Medicine and the Future of Biology. Princeton, University Press. Sonia Contera shows how cutting-edge biological and medical research are breaking free from the mindsets of simplistic evolutionary theory, with its “reductionist vision” that genes govern everything — its view of organisms as “mere biochemical computers executing a program... encoded in genes”. She points out that “current medical bottlenecks will remain blocked” until medical science completes its escape from the ‘blueprint’ or ‘genes govern everything’ mindset. She also describes amazing new experiments to explore artificial self-organizing or self-assembling nanometre-scale structures, and functional machines, made of DNA or proteins. (A nanometre is a millionth of a millimetre.) These self-assemble just as their natural counterparts do, from the most simple to the most complex including ordinary crystals, viruses, and multicellular organisms.57 Recent progress on the protein folding or self-organization problem, prior to the AlphaFold breakthrough, is discussed in the section headed Protein Nanotechnology.
56. Pinker, S., 1997: How the Mind Works. London, Allen Lane. The author invokes “mathematical proofs from population genetics” in support of what amounts to simplistic evolutionary theory (chapter 3, page 163, section on “Life’s Designer”). The author is silent on which population-genetics equations were used in these “proofs”. However, as the book proceeds, it becomes clear that the author is referring to the equations of the old population-genetics models, in their simplest versions that do not prove simplistic evolutionary theory but, rather, assume it in writing down the equations. In particular, the models exclude group-level selection by confining attention to averages over whole populations, conceived of as statistically homogeneous and as living in a fixed, homogeneous environment. Notice the telltale phrase “on average” in the section “I and Thou” in chapter 6, on page 398. Not even the famous Price equation, perhaps the first attempt to allow for population heterogeneity, is mentioned, nor multiple timescales, nor Monod’s arguments.3 Almost exactly the same critique can be made of Richard Dawkins’ famous book The Selfish Gene, which makes passionate assertions to the effect that simplistic evolutionary theory and its game-theoretic aspects, such as reciprocal altruism, have been rigorously and finally established by mathematical analysis — again meaning the old population-genetics models — and that any other view is wrong or muddled. See also ref. 57.
57. Dawkins, R., 2009: The Greatest Show On Earth. London, Bantam Press. I am citing this book alongside ref. 56 for two reasons. First, chapter 8 beautifully illustrates why emergent properties and self-assembling building blocks (automata) are such crucial ideas in biology. It becomes clear why the genetic-blueprint idea is such a gross oversimplification. Chapter 8 illustrates the point with a sequence of examples beginning with the self-assembly55 of viruses and ending with the Nobel-prize-winning work of my late friend John Sulston, on the self-assembly of an adult nematode worm, Caenorhabditis elegans, from its embryo. All this gets us significantly beyond simplistic evolutionary theory, as John suggested I call it. Second, however, the book persists with the mindset against group-level selection. Any other view is, it says, an amateurish fallacy (end of long footnote in chapter 3, p. 62). No hint is given as to the basis for this harsh verdict; but as in The Selfish Gene the basis seems to be an unquestioning faith in particular sets of mathematical equations, namely those defining the old population-genetics models. Those equations exclude group-level selection by assumption, or include at most only weak forms of it. And Jacques Monod, who argued that group-level selection was critical to our ancestors’ evolution,3 was hardly an amateur. He was a great scientist and a very sharp thinker who, as it happens, was also a Nobel laureate.
58. Segerstråle, U., 2000: Defenders of the Truth: The Battle for Science in the Sociobiology Debate and Beyond. Oxford University Press. This important book gives insight into the disputes about natural selection over past decades. It’s striking how dichotomization kept muddying those disputes, even amongst serious and respected scientists. There were misplaced pressures for parsimony of explanation, forgetting Einstein’s famous warning not to push Occam’s Razor too far. Again and again the disputants felt, it seems, that ‘we are right and they are wrong’ and that there’s only one truth, to be viewed in only one way. Again and again, progress was impeded by a failure to recognize complexity, multidirectional causality, different levels of description, and multi-timescale dynamics. And the confusion was sometimes made even worse, it seems, by failures to disentangle science from politics.
59. The Acheulean toolmaking skills call for great accuracy and delicacy in striking flakes off brittle stones such as obsidian or flint. And the point about language is not that it could have been used to describe the skills. Even today one cannot acquire such a skill just by hearing it described. Rather, language would have operated on the level of personal relations. Even a rudimentary language ability, with a rudimentary syntax, would have helped a teacher to encourage a novice in efforts to acquire the skills. “Try again. Hit it there! That’s better!” Straight away that’s a selective pressure to develop language beyond the simple I-love-you, you-tickle-me social grooming level.3, 46 And with it there’s a pressure to develop future thinking — enabling the novice to imagine becoming a good toolmaker one day. “Keep at it. You’ll get there!”60 I heard these points made in a BBC radio interview with an expert on the Oldowan and Acheulean stone tools, Dietrich Stout. Professor Stout and co-workers have done interesting work rediscovering the toolmaking skills and tracing their imprint upon brain scans, including neural pathways converging on Broca’s area.
60. On future thinking — clearly helpful in a teaching situation — there’s evidence that, as primatologist Jane Goodall puts it, “Chimpanzees can plan ahead, too, at least as regards the immediate future. This, in fact, is well illustrated at Gombe, during the termiting season: often an individual prepares a tool for use on a termite mound that is several hundred yards away and absolutely out of sight.” The quote is from chapter 2 of the famous 1990 book by Goodall, Through a Window: My Thirty Years with the Chimpanzees of Gombe, Weidenfeld & Nicholson and Houghton Mifflin. Recent field work by primatologist Catherine (Cat) Hobaiter and co-workers has revealed many more of the cognitive abilities of the great apes, including gestural proto-language. Chimpanzees, bonobos and other great apes use intentional communication via gestures, with ‘vocabularies’ of many tens of distinct gestures. Some of the gestures resemble those of human infants. And it’s well known that chimpanzees and bonobos understand rudimentary syntax, as in distinguishing ‘Me tickle you’ from ‘You tickle me.’
61. Aiello, L. C., 1996: Terrestriality, bipedalism and the origin of language. Proc. Brit. Acad., 88, 269–289. Reprinted in: Runciman, W. G., Maynard Smith, J., and Dunbar, R. I. M. (eds.), 1996: Evolution of social behaviour patterns in primates and man. Oxford, University Press, and British Academy. The paper presents a closely-argued discussion of brain-size changes in our ancestors over the past several million years, alongside several other lines of palaeo-anatomical evidence. Taken together, these lines of evidence suggest an “evolutionary arms race” between competing tribes whose final stages led to the full complexity of language as we know it. Such a picture is consistent with Monod’s and Wills’ arguments,3, 44 the final stages corresponding to what Wills44 called runaway brain evolution. Aiello cites evidence for a date “earlier than 100,000 years” for the first occurrence of art objects in the archaeological record, suggesting that language was highly developed by then.
62. Harari, Y. N., 2014: Sapiens: A Brief History of Humankind. Yuval Noah Harari’s famous book explores aspects of our ancestors’ evolution, paying careful attention to the palaeogenetic, palaeoarchaeological and archaeological records and to various attempts at explanatory theories, while being careful to note where evidence is lacking. The book puts emphasis on what’s called the ‘cognitive revolution’ near the start of the Upper Palaeolithic. That’s part of the runaway brain evolution discussed by Wills44 and also for instance by Rossano;48 see figure 2 above [omitted from this preview]. It may well have been the stage at which our ancestors developed the ability to imagine nonexistent worlds and to create stories about such worlds, promoting group solidarity and versatility in very large and powerful groups or tribes. A prerequisite would have been a language ability already well developed.
63. See for instance the short paper by Montgomery, S., 2018: Hominin brain evolution: the only way is up? Current Biology 28, R784-R802. Montgomery’s figure 1b is an updated version of figure 2 above [omitted from this preview], with data from more fossil finds and improved measurement accuracy. Apart from two recent new finds, Homo floresiensis and Homo naledi, the overall pattern is the same as in figure 2 above. Regarding recent discoveries about gene flow across different strands of our ancestry, the Wikipedia article Interbreeding between archaic and modern humans gives a useful summary, referring to events around 50 millennia ago for which DNA evidence is now available.
64. Kegl, J., Senghas, A., and Coppola, M., 1999: Creation through contact: sign language emergence and sign language change in Nicaragua. In: Language Creation and Language Change: Creolization, Diachrony, and Development, ed. Michel DeGraff, 179–237. Cambridge, Massachusetts, MIT Press. This is a detailed compilation of the main lines of evidence. Included are studies of the children’s sign-language descriptions of videos they watched. Also, there are careful discussions of the controversies amongst linguists, including those who cannot accept the possibility that genetically-enabled automata for language might exist.
65. Pinker, S., 1994: The Language Instinct. London, Allen Lane. The Nicaraguan case is briefly described in chapter 2, as far as it had progressed by the early 1990s.
66. See for instance Senghas, A., 2010: The Emergence of Two Functions for Spatial Devices in Nicaraguan Sign Language. Human Development (Karger), 53, 287–302. This later study uses video techniques as in ref. 64 to trace the development and standardization, by successive generations of young children, of syntactic devices in signing space.
67. See for instance Ehrenreich, B., 1997: Blood Rites: Origins and History of the Passions Of War. London, Virago and New York, Metropolitan Books. Barbara Ehrenreich’s insightful and penetrating discussion contains much wisdom, it seems to me, not only about war but also about the nature of mythical deities and about human sacrifice, ecstatic suicide, and so on — echoing Stravinsky’s Rite of Spring and long pre-dating Nine-Eleven and IS/Daish. (Talk about ignorance being expensive!)
68. Lüthi, D., Le Floch, M., Bereiter, B., Blunier, T., Barnola, J.-M., Siegenthaler, U., Raynaud, D., Jouzel, J., Fischer, H., Kawamura, K., and Stocker, T. F., 2008: High-resolution carbon dioxide concentration record 650,000–800,000 years before present. Nature, 453, 379–382. Further detail on the deuterium isotope method is given in the supporting online material https://science.sciencemag.org/content/suppl/2007/07/03/1141038.DC1 for a preceding paper on the temperature record.
69. See for instance Alley, R. B., 2000: Ice-core evidence of abrupt climate changes. Proc. Nat. Acad. Sci., 97, 1331–1334, and references therein. This brief Perspective is a readable summary, from a respected expert in the field, of the methods whereby measurements from Greenland ice have demonstrated the astonishingly short timescales of the Dansgaard–Oeschger warmings. They took only a few years in at least some cases including that of the most recent or ‘zeroth’ such warming, about 11.5 millennia ago. For earlier Dansgaard–Oeschger warmings see ref. 71, and references therein.
70. Alley, R. B., 2007: Wally was right: predictive ability of the North Atlantic ‘conveyor belt’ hypothesis for abrupt climate change. Annual Review of Earth and Planetary Sciences 35, 241–272. This paper incorporates a very readable, useful, and informative survey of the relevant palaeoclimatic records and recent thinking about them. Wally Broecker’s famous ‘conveyor belt’ is a metaphor for the oceans’ global-scale overturning circulation, an important part of which is the Atlantic overturning circulation. The metaphor has greatly helped efforts to understand the variability observed during the glacial cycles. My own assessment is, however, that Wally was partly right. Despite its usefulness, the metaphor embodies a fluid-dynamically unrealistic assumption, namely that shutting off North Atlantic deep-water formation also shuts off the global-scale return flow. If you jam a real conveyor belt somewhere, then the rest of it stops too. In this respect the metaphor needs refinements such as those argued for by Trond Dokken and co-workers,71 recognizing that parts of the ‘conveyor’ can shut down while other parts continue to move and transport heat and salt at significant rates. As they point out, such refinements are likely to be important for understanding the most abrupt of the observed changes, the Dansgaard–Oeschger warmings, and the similar tipping point that might soon occur in the Arctic Ocean.
71. Dokken, T. M., Nisancioglu, K. H., Li, C., Battisti, D. S., and Kissel, C., 2013: Dansgaard–Oeschger cycles: interactions between ocean and sea ice intrinsic to the Nordic Seas. Paleoceanography, 28, 491–502. This is the first fluid-dynamically credible explanation of the extreme rapidity — the abruptness — and the large magnitude of the Dansgaard–Oeschger warming events. Those events left clear imprints in ice-core and sedimentary records all over the Northern Hemisphere and were so sudden, and so large in magnitude, that a tipping-point mechanism must have been involved. The proposed explanation is not only evidence-based but represents the only mechanism suggested, so far, that can act quickly enough — involving the sudden disappearance of sea ice covering the Nordic Seas when an intrusion of warmer subsurface Atlantic water became buoyant enough to break through to the surface. Figure 4 above [omitted from this preview] is figure 2a of this paper, whose full text is open-access and available at https://doi.org/10.1002/palo.20042. The authors point out that today’s Arctic sea ice might be vulnerable to the same tipping-point mechanism.
72. Bail, C., 2021: Breaking the Social Media Prism: How to Make Our Platforms Less Polarizing. Princeton University Press. This important book by Professor Chris Bail, a sociologist at Duke University, describes recent experimental-psychological studies aimed at deepening our understanding of the social media and their political effects. The ‘prism’ is a metaphor to suggest the distorted vision via social media that highlights the extremist views of small minorities, giving them undue prominence. Professor Bail points out that tackling the problem calls for ideas far more sophisticated than the simplistic idea of breaking open the echo chambers. The last chapter suggests possible ways forward based on the experimental findings.
73. One of these experimental studies demonstrated the flexibility of group-identity feelings among Liverpool and Manchester United football fans. In an extended interview published in Social Science Space, Professor Reicher summarized the experiments thus: “I was very interested in this idea of shared identity and helping, so we did some experimental studies with a colleague, Mark Levine in Exeter. We did a series of studies on categories and helping. Very simple study: You get people who are Manchester United fans, and you talk to them as Manchester United fans, and you say well, look, we are going to do a study in another building, and as they walk along to the other building, somebody runs along, falls over, hurts themselves, wearing either a Manchester United shirt, a Liverpool shirt or a red t-shirt, and they help the person in the Manchester United shirt, not the Liverpool shirt and not the red t-shirt... but the really interesting thing... was a different condition where again, we take... Manchester United fans, but this time we address them as football fans, we say we are doing research on football fans, they go to the other building, somebody runs along, falls over wearing a Manchester United shirt, a Liverpool shirt or a red t-shirt. This time... they help the Manchester United fan, they help the Liverpool fan,” (my italics) “and they don’t help the person in the red t-shirt... evidence... showing how varying the ways in which we define identities, varies the limits of solidarity.” More recently Professor Clifford Stott, an ex-student of Reicher’s, has worked with police to demonstrate how rioting in a crowd can be reduced or prevented, through understanding the dynamics of group identities in their response to different policing methods.
Another striking demonstration of flexible group identity was a recent (22 June 2019) electoral success in Turkey where political traction came not from demagoguery and binary-button-pressing but rather, to some people’s surprise, from a politicians’ colourful handbook called the “Book of Radical Love”, switching the focus away from antagonism, and toward pluralistic core values and “caring for each other” — even for one’s political opponents! Arguably, that success was yet another demonstration of caring as a deeply unconscious, deeply instinctive, powerful part of human nature, adding to the examples in refs. 2, 10, and 11.
74. The point that perceived timings differ from physical timings is not only simple, but also easy to check experimentally as I’ll show. But it’s hard to find in the philosophical literature. Indeed, some professional philosophers such as Hugh Mellor have explicitly denied it, in his 1981 book Real Time. Others have recognized it, for instance Henri-Louis Bergson and Daniel Dennett, in publications dating respectively from 1889 and 1991. But each in his own way makes it part of something complicated. See for instance the seventy pages of discussion in chapters 5 and 6 of Dennett’s 1991 book Consciousness Explained, Penguin. Among other things the discussion gets immersed in the usual philosophical quagmire surrounding the idea of ‘free will’ and the timing of decisions to act.75 A quotation from Mellor’s book can be found on Dennett’s page 149, and the famous decisions-to-act experiment by Grey Walter is described on page 167.
75. The term acausality illusion does not seem to be in general use, but I think it helps to underline the simplicity of something often regarded as complicated and mysterious.74 See McIntyre, M. E., 1997: Lucidity and science, II: From acausality illusions and free will to final theories, mathematics, and music. Interdisc. Sci. Revs. 22, 285–303. On the issue of free will I point out that, contrary to what’s sometimes asserted in the philosophical literature, decisions-to-act experiments like those of Benjamin Libet and Grey Walter74 have nothing to say on that issue. Rather, the experiments add to our examples of acausality illusions. Patients were asked to carry out an action such as pressing a button, at a time of their choosing, while the experimenters measured the associated brain activity. The timespan of the brain activity was the usual several hundred milliseconds with, inevitably, some of the activity preceding the perceived time of willing the action. The philosophical literature tends to miss the point that perceived times are — can only be — properties of the brain’s unconscious internal models that mediate perception76, 77 and not the times of any particular brain-activity events. Of course a perceived time must come from interrogating an internal model already formed, and so is always — can only be — something within short-term or longer-term memory, as with the gunfight “in slow motion”.
76. Gregory, R. L., 1970: The Intelligent Eye. London, Weidenfeld and Nicolson. This great classic is still well worth reading. It’s replete with beautiful and telling illustrations of how vision works. Included is a rich collection of stereoscopic images viewable with red-green spectacles. The brain’s unconscious internal models that mediate visual perception are called “object hypotheses”, and the active nature of the processes whereby they’re selected is clearly recognized, along with the role of prior probabilities. There’s a thorough discussion of the standard visual illusions as well as such basics as the perceptual grouping studied in Gestalt psychology. In a section on language and language perception, Chomsky’s “deep structure” is identified with the repertoire of unconscious internal models used in decoding sentences. The only points needing revision are speculations that the first fully-developed languages arose only in very recent millennia13 and that they depended on the invention of writing. That’s now refuted by the evidence summarized in my chapter 3, showing that there are genetically-enabled automata for language, including syntactic function.
77. Hoffman, D. D., 1998: Visual Intelligence: How We Create What We See. Norton. Essentially an update to ref. 76, with further illustrations and some powerful insights into the way visual perception works. Chapter 6 describes a case in which a patient, part of whose visual cortex had been damaged by a stroke, saw moving objects as a series of snapshots. For instance when tea was being poured into a cup “the fluid appeared to be frozen, like a glacier.” The stroke damage was to a small visual-cortex area called V5. [Note added in proof: See also Seth, A., 2021: Being You: A New Science of Consciousness, Faber. Neuroscientist Professor Anil Seth aptly calls the perceptual model-fitting process ‘controlled hallucination’, referring to ‘control’ by the incoming data. He recognizes the importance of the body image and the self-model.]
78. See for instance Gilbert, C. D. and Li, W. 2013: Top-down influences on visual processing. Nature Reviews (Neuroscience), 14, 350–363. This review presents anatomical and neuronal evidence for the active, prior-probability-dependent nature of perceptual model-fitting, e.g. “Top-down influences are conveyed across... descending pathways covering the entire neocortex... The feedforward connections... ascending... For every feedforward connection, there is a reciprocal [descending] feedback connection that carries information about the behavioural context... Even when attending to the same location and receiving an identical stimulus, the tuning of neurons can change according to the perceptual task that is being performed...”, etc.
79. Beliefs about veridical perception are further discussed in ref. 75. And, strange though it may seem, veridical perception was part of the gospel according to Ayn Rand.43 In her famous writings on “objectivism” she says, in effect, that veridical perception is an Absolute Truth. As the Wikipedia article on objectivism puts it, Rand’s claim is that “human beings have direct contact with reality through sense perception... perception, being determined physiologically, is incapable of error... optical illusions are errors in the conceptual identification of what is seen, not errors of sight itself.” Notice the fluency of language alongside the absence of logic-checking. Why should a mechanism be “incapable of error” just because it works “physiologically”? I wonder what Rand and her disciples would have made of the walking dots animation. Perhaps they’d dismiss it as just an illusion, and something of no importance.
80. Marr, D. C., 1982: Vision: a computational investigation into the human representation and processing of visual information. San Francisco, Freeman. The late David Marr’s celebrated classic was a landmark in vision research, focusing on bottom-up visual processing in its earliest stages, such as edge detection and stereoscopic image-matching.
81. For the ocean-eddy problem — which is a crucial part of the climate problem — we can’t actively experiment with the real ocean but we can take what are called eddy-resolving simulations of oceanic flows, whose realism can be checked against real oceanic flows, and experiment with those simulations to find patterns of behaviour using the Bayesian causality theory.21 Work of this kind is still in its infancy. See for instance Zanna, L. and Bolton, T., 2020: Data-driven equation discovery of ocean mesoscale closures. Geophys. Res. Lett., 47, e2020GL088376.
82. Jaynes, E. T., 2003: Probability Theory: The Logic of Science. edited by G. Larry Bretthorst. Cambridge, University Press. This great posthumous work by Edwin T. Jaynes blew away much of the conceptual confusion surrounding probability theory and statistical inference, with a clear focus on the foundations of the theory in its powerful ‘Bayesian’ form, underpinned by the theorems of Richard Threlkeld Cox. That was an important step toward today’s still more powerful Bayesian causality theory.21. Much of the book digs deep into the technical detail, but there are instructive journeys into history as well, especially in chapter 16. For many decades, progress was held up by dichotomized disputes reminiscent of the disputes over biological evolution44 — and similarly damaging to progress. A narrow view of statistical inference, called ‘frequentist’, is useful in some problems but was taken by professional statisticians to be the only permissible view. As with energy budgets and selfish genes, ‘usefulness’ had morphed into ‘Answer to Everything’. And the frequentist view seems to have been further confused by the mind-projection fallacy,84 masquerading as ‘objectivity’. There are mathematical entities called probability distribution functions, and these were seen as things in the outside world rather than as components of mathematical models. Furthermore, because of dichotomization, the frequentist view was mistakenly seen as excluding the more powerful and versatile Bayesian view, even though we can now see the latter as including the former, once we make explicit the information on which all probabilities are contingent. (Explicitness principle again.) A quick introduction to the basics of this, including Cox’s theorems, is given in my 2007 paper On thinking probabilistically, in Extreme Events (Proceedings of the 15th ‘Aha Huliko‘a Winter Workshop) edited by P. Müller, C. Garrett, and D. Henderson, SOEST publications, University of Hawaii at Manoa, pp. 153–161.
83. Penrose, R., 1994: Shadows of the Mind: A Search for the Missing Science of Consciousness, Oxford University Press. This fascinating book includes a discussion of the Platonic world as seen by a great mathematician, Roger Penrose FRS, who in 2020 received a Nobel prize for his powerful black-hole singularity theorem. (That theorem, a property of the model described by Einstein’s equations, was published in 1965 and predicted that black holes can form in a huge range of circumstances, not just the special circumstances previously considered — motivating an early search for them and later the LIGO work described in ref. 16.) I’ve dared to disagree, however, with Penrose’s take on consciousness and the Platonic, for reasons given in my chapter 6 and at greater length in an appendix to ref. 75, headed On mathematical truth.
84. See for instance Unger, R. M., and Smolin, L., 2015: The Singular Universe and the Reality of Time: A Proposal in Natural Philosophy. Cambridge University Press. Roberto Mangabeira Unger and Lee Smolin — two highly respected thinkers in their fields, philosophy and physics respectively — present a profound and wide-ranging discussion of how progress might be made in fundamental physics and cosmology despite formidable conceptual difficulties (some of which, incidentally, are reduced by taking the model-fitting view as I advocate it). One of the difficulties is a tendency to conflate the outside world with our mathematical models of it, what Edwin T. Jaynes82 called the mind-projection fallacy. Thus for instance the Platonic world of perfect mathematical forms83 is seen as something external, as well as immutable and everlasting — as Plato himself seems to have thought — and something that contains the Universe we live in. According to this view, as advocated for instance by the cosmologist Max Tegmark, the Universe is a purely mathematical entity, no more and no less. Such a conclusion is arguably implausible (and see my chapter 6) but in any case, as Unger and Smolin point out, belongs to metaphysics, rather than to physics or to any other kind of science. It’s outside the scope of science because there can never be sufficient observational data against which to test it.
85. See for instance Smythies, J. 2009: Philosophy, perception, and neuroscience. Perception, 38, 638–651. Further to ref. 74, this review documents parts of what I called the quagmire of philosophical confusion about the way perception works. The discussion begins by noting, among other things, the persistence of the fallacy that perception is what it seems to be subjectively, namely veridical79 in the sense of being direct and independent of any model-fitting process, a simple mapping between appearance and reality. That’s still taken as self-evident, we’re told, even by some professional philosophers despite the evidence from experimental psychology, as summarized for instance in refs. 37, 76 and 77. Then a peculiar compromise is advocated, in which perception is partly direct, and partly works by model-fitting, so that “what we actually see is always a mixture of reality and virtual reality” [sic; p. 641]. Of greater interest, though, is a summary of some old clinical evidence, from the 1930s, that gave early insights into the brain’s different model components. Patients described their experiences of vision returning after brain injury, implying that different model components recovered at different rates and were detached from one another at first. On pp. 641–642 we read about recovery from a particular injury to the visual regions in the occipital lobe: “The first thing to return is the perception of movement. On looking at a scene the patient sees no objects, but only pure movement... Then luminance is experienced but... formless... a uniform white... Later... colors appear that float about unattached to objects (which are not yet visible as such). Then parts of objects appear — such as the handle of a teacup — that gradually coalesce to form fully constituted... objects, into which the... colors then enter.”
86. Here’s a little challenge to your powers of observation. After getting out of the bath and pulling the plug, observe the sense in which the water begins to circulate around the plughole. (It can be either way, regardless of whether you live in the Northern or the Southern Hemisphere.) If the water circulates in a clockwise vortex, what’s often most eye-catching is an appearance of anticlockwise motion. But that’s a motion not of the water but of the waves on its surface. The waves you generated when you got out of the bath are refracted by the vortex motion in such a way as to propagate against the vortex flow.
87. I owe the first part of the aphorism to consultant psychiatrist Mark Salter, whom I met at the Hay-on-Wye festival How The Light Gets In. In 2013 I gave a talk there and took part in a discussion in which the issue of free will came up. Mark provoked us with “Free will is a biologically indispensable illusion.” That struck me as a rather neat statement, albeit a touch mysterious. I took it to mean, though, that what’s indispensible is the need to regard free will as illusory when trying to understand biological functioning — that is, biological functioning in the usual sense. At the physiological and molecular levels usually considered, it’s necessary to exclude the concept of free will as irrelevant.
88. Feynman, R. P., Leighton, R. B., and Sands, M., 1964: Lectures in Physics. Addison-Wesley. The action integral and Newton’s equations are discussed in chapter 19 of volume II, Mainly Electromagnetism and Matter.
89. Platt, P., 1995: Debussy and the harmonic series. In: Essays in honour of David Evatt Tunley, ed. Frank Callaway, pp. 35–59. Perth, Callaway International Resource Centre for Music Education, School of Music, University of Western Australia. ISBN 086422409 5. Debussy also exploited, for instance, the powerful musical pattern called the octatonic scale.
90. Blue notes give us just one example, among many, of how the slight tension between harmonic-series pitches and standard ‘equal-tempered’ pitches, or keyboard pitches, creates a world of opportunities to use fine pitch variations artistically. One can play games with the harmony and with the so-called ‘expression’ — the artistic treatment of emotional affect — creating or relieving tension as the pitch is slightly pushed up or down in various ways. More subtly, fine pitch variations and fluctuations can be perceived as part of the ‘tone colour’ produced by, for instance, a violin.93 All these points tend to be missed in theoretical discussions of musical fixed tunings, or ‘temperaments’. One sometimes encounters what seems to be an unconscious assumption, at variance with actual performance practice, that non-keyboard musical performances comply rigidly with one or another fixed temperament. One also encounters an assumption that temperaments, including the standard equal temperament, are evil compromises with the ‘pure’ or ‘just’ tunings of low-order harmonic-series subsets — as if the consequences were entirely negative rather than enriching.
91. The theme of the little fugue comes from the telephone number of two dear friends — yes, playing with numbers leads to musical ideas. I wrote it partly for the friends’ wedding anniversary celebration and partly in memory of my father A. K. McIntyre, who was a respected neurophysiologist, and who was much loved as a kind and gentle man. The duration is about five and a half minutes. In the recording presented in figure 18 [omitted from this preview] Ruth McIntyre plays piano, Vivian Williams cello, and I violin, and the recording and mastering were by Jeffrey Ginn Music Studios. Score and parts are available at http://www.damtp.cam.ac.uk/user/mem/papers/LHCE/music-index.html
92. Boomsliter, P. C. and Creel, W., 1961: The long pattern hypothesis in harmony and hearing. Journal of Music Theory (Yale School of Music), 5(1), 2–31. This wide-ranging and penetrating discussion was well ahead of its time and is supported by the authors’ ingenious psychophysical experiments, which clearly demonstrate waveform-cycle counting as distinct from Fourier analysis. On the purely musical issues there is only one slight lapse, in which the authors miss the context dependence of tonal major-minor distinctions. On the other hand the authors clearly recognize, for instance, the biological relevance of “efficient listening for sensing the environment” (p. 13), what’s now called auditory scene analysis.
93. The interested reader is referred to the review by McIntyre, M. E., and Woodhouse, J., 1978: The acoustics of stringed musical instruments, Interdisc. Sci. Rev., 3, 157–173. For instance figure 3 shows why the intensities of different harmonic overtones fluctuate out of step with each other during vibrato. We carried out our own psychophysical experiments to verify the strong effect on perceived tone quality. Further work on the acoustics of vibrating strings, reeds, and air jets is reported in McIntyre, M. E., Schumacher, R. T., and Woodhouse, J., 1983: On the oscillations of musical instruments, J. Acoust. Soc. Amer. 74, 1325–1345, and in a forthcoming Reflections article to appear in the same journal.
94. Personal communication, 2001-present. Tim was elected FRS in 2003 for his work on the dynamics of weather and climate. For the quantum-theoretic issues see for instance Palmer, T. N., 2020: Undecidability, fractal geometry and the unity of physics, a prizewinning essay written for the Foundational Questions Institute Prize Essay competition and to be published by Springer-Verlag. Ideas about turbulence come in somewhat obliquely, through the use of chaos theory and through a reference to limitingly small scales of turbulent eddies. This aspect of the research is, however, still in its infancy. Some of the technicalities are further discussed in Palmer, T. N., 2020: Discretisation of the Bloch sphere, fractal invariant sets and Bell’s theorem, Proc. Roy. Soc. A 476, 20190350. Regarding possible chaos at the minuscule Planck lengthscale at which quantum effects mesh with gravity, an aspect unlike ordinary turbulence is that spacetime might itself become chaotic, with ordinary space and time as emergent properties belonging only to larger scales. See for instance chapter 5 of Carlo Rovelli’s 2015 book Seven Brief Lessons on Physics, Penguin.
95. Pierrehumbert, R. T., 2010: Principles of Planetary Climate. Cambridge University Press. Professor Raymond Pierrehumbert FRS is a brilliant thinker and a leading expert on the climate dynamics of the Earth throughout its history, and on the climate dynamics of other planets. The physics, chemistry, biology and other relevant aspects are explained in a masterly way. For instance sec. 8.4 gives the clearest explanation I’ve seen of how carbon dioxide is stored in the Earth’s deep oceans, mostly as bicarbonate ions. Some subtle and tricky chemistry is involved including great sensitivity to oceanic acidity and, on multi-millennial timescales, the solution and precipitation of calcium carbonate as limestone sludge. See also, for instance, ref. 100.
96. See for instance Archer, D., 2009: The Long Thaw: How Humans Are Changing the Next 100,000 Years of Earth’s Climate. Princeton University Press. The author is a respected climate scientist and an authority on carbon in the climate system. He considers the system as a whole, with special attention to sea levels and to what happens to the carbon dioxide we’re injecting, and to the natural mechanisms for recovery. The natural recovery timescales stretch out beyond a hundred millennia, as clearly evidenced by records of past climates. For us humans a hundred millennia is an infinite timespan, making some of the human-induced changes essentially permanent and irreversible. (That’s one reason why drastic ‘geoengineering’ options are being considered. The safest such option, artificially pulling carbon dioxide back out of the atmosphere, is, however, far more expensive than going for suitable renewable97 and nuclear127 energy technologies, and carbon capture at source.126) Regarding sea levels 130 millennia ago, see for instance Overpeck, J. T., Otto-Bliesner, B. L., Miller, G. H., Muhs, D. R., Alley, R. B., and Kiehl, J. T., 2006: Paleoclimatic evidence for future ice-sheet instability and rapid sea-level rise, Science 311, 1747–1750, and references therein.
97. Farmer, J. D. et al., 2019: Sensitive intervention points in the post-carbon transition. Science, 364, 132–134. The authors remind us that the fossil fuel industry has long been heavily subsidized, to a “far greater” extent than low-carbon energy sources such as solar photovoltaics and wind. However, they also argue that there’s now hope of reaching a socio-economic tipping point, in the near future, that will reverse the priorities in favour of low-carbon energy.
98. Shakun, J. D., Clark, P. U., He, F., Marcott, S. A., Mix, A. C., Liu, Z., Otto-Bliesner, B., Schmittner, A., and Bard, E, 2012: Global warming preceded by increasing carbon dioxide concentrations during the last deglaciation. Nature, 484, 49–55.
99. Skinner, L. C., Waelbroeck, C., Scrivner, A. E., and Fallon, S. J., 2014: Radiocarbon evidence for alternating northern and southern sources of ventilation of the deep Atlantic carbon pool during the last deglaciation. Proc. Nat. Acad. Sci., 111, 5480–5484.
100. Marchitto, T. M., Lynch-Stieglitz, J., and Hemming, S. R., 2005: Deep Pacific CaCO3 compensation and glacial–interglacial atmospheric CO2. Earth and Planetary Science Letters, 231, 317–336. This technical paper gives more detail on the role of limestone sludge (CaCO3) and seawater chemistry in the way carbon dioxide (CO2) was stored in the deep oceans95 during recent glacial cycles, and on the observational evidence. The evidence comes from meticulous and laborious measurements of tiny variations in chemicals that are important in the oceans’ food chains, and in isotope ratios of various elements including oxygen and carbon, laid down in layer after layer of ocean sediments over very many tens of millennia. Another reason for citing the paper, which requires the reader to have some specialist knowledge, is to highlight just how formidable are the obstacles to building accurate models of the carbon cycle, including for instance the plant-like phytoplankton that pull carbon dioxide from the atmosphere, then die and carry carbon into the ocean depths. Such models try to represent oceanic carbon-dioxide storage along with observable carbon isotope ratios, which are affected by the way in which carbon isotopes are taken up by living organisms via processes of great complexity and variability. Not only are we far from modelling oceanic fluid-dynamical transport processes with sufficient accuracy, including turbulent eddies over a vast range of spatial scales, but we are even further from accurately modelling the vast array of biogeochemical processes involved throughout the oceanic and terrestrial biosphere — including for instance the biological adaptation and evolution of entire ecosystems and the rates at which the oceans receive mineral nutrients from rivers and airborne dust. The oceanic upper layers where phytoplankton live have yet to be modelled in fine enough detail to represent accurately the recycling of mineral nutrients simultaneously with gas exchange rates. It’s fortunate indeed that we have the hard evidence, from ice cores, for the atmospheric carbon dioxide concentrations that actually resulted from all this complexity.
101. Le Quéré, C., et al., 2007: Saturation of the Southern Ocean CO2 sink due to recent climate change. Science, 316, 1735–1738. This work, based on careful observation, reveals yet another positive feedback that’s increasing climate sensitivity to carbon dioxide injections.
102. Skinner, L. C., et al., 2017: Radiocarbon constraints on the glacial ocean circulation and its impact on atmospheric CO2. Nature Communications, 8, 16010.
103. Watson, A. J., Vallis, G. K., and Nikurashin, M., 2015: Southern Ocean buoyancy forcing of ocean ventilation and glacial atmospheric CO2. Nature Geoscience 8, 861–864. This modelling study focuses on the amount of carbon dioxide injected from the deep ocean into the atmosphere during a deglaciation. In going from glacial to interglacial conditions, it’s estimated that the contribution from ocean-circulation changes is roughly comparable, in order of magnitude, to that from changes in phytoplankton fertilization.
104. See for instance Abe-Ouchi, A., Saito, F., Kawamura, K., Raymo, M. E., Okuno, J., Takahashi, K., and Blatter, H., 2013: Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume. Nature, 500, 190–194. Importantly, their model includes a realistic, multi-millennial delay in the so-called ‘isostatic rebound’ or viscoelastic upward displacement of the Earth’s crust as an overlying ice sheet melts, unloading the crust. Such a delay can keep the top surface of a massive ice sheet at lower, warmer altitudes long enough to enhance the melting effects of an insolation peak. The model uses an exponential time constant of 5 millennia for the rebound, a value whose order of magnitude is consistent with recent geophysical observations of the continuing rebound from the last deglaciation.
105. See for instance Schoof, C., 2010: Ice-sheet acceleration driven by melt supply variability. Nature 468, 803–806. This modelling study, motivated and cross-checked by recent observations of the accelerating ice streams in Greenland, is highly simplified but captures some aspects of subglacial meltwater flow networks and their effects on the bulk motion of the ice sheet.
106. See for instance Krawczynski, M. J., Behn, M. D., Das, S. B., Joughin, I., 2009: Constraints on the lake volume required for hydro-fracture through ice sheets. Geophys. Res. Lett., 36, L10501. The standard elastic crack-propagation equations are used to describe the downward ‘chiselling’ of meltwater, which is denser than the surrounding ice, forcing a crevasse to open all the way to the bottom. This mechanism is key to the sudden drainage of small lakes of meltwater that accumulate on the top surface. Such drainage has been observed to happen within hours, for instance on the ice sheet in Greenland. The same ‘chiselling’ mechanism was key to the sudden breakup of successive portions of the Larsen ice shelf next to the Antarctic Peninsula, starting in the mid-1990s.
107. See for instance Allen, M. R., Frame, D. J., and Mason, C. F., 2009: The case for mandatory sequestration, Nature Geoscience 2, 813–814. An interactive website tracking the estimated cumulative emissions of carbon dioxide since industrialization began, measured in tonnes of carbon, is http://trillionthtonne.org. The trillionth tonne of carbon emitted into the atmosphere is by some estimates the largest possible if climate change is to be kept within acceptable bounds.
108. Valero, A., Agudelo, A, and Valero, A., 2011: The crepuscular planet: a model for the exhausted atmosphere and hydrosphere, Energy, 36, 3745–3753. This careful discussion lists the amounts of proven and estimated fossil-fuel reserves including coal, oil, gas, tar sands and clathrates, showing that if burnt they would produce emissions vastly greater than a trillion tonnes of carbon.107 The amount of methane in clathrates is estimated to be of the order of, respectively, 40 and 100 times that in proven reserves of shale gas and conventional natural gas.
109. See for instance Shakhova, N., Semiletov, I., Leifer, I., Sergienko, V., Salyuk, A., Kosmach, D., Chernykh, D., Stubbs, C., Nicolsky, D., Tumskoy, V., and Gustafsson, O., 2014: Ebullition and storm-induced methane release from the East Siberian Arctic Shelf. Nature Geoscience, 7, 64–70.
110. See also Andreassen, K., Hubbard, A., Winsborrow, M., Patton, H., Vadakkepuliyambatta, S., Plaza-Faverola, A., Gudlaugsson, E., Serov, P., Deryabin, A., Mattingsdal, R., Mienert, J., and Bünz, S, 2017: Massive blow-out craters formed by hydrate-controlled methane expulsion from the Arctic seafloor, Science, 356, 948–953. It seems that some of the clathrates in high latitudes have been melting ever since the later part of the last deglaciation, probably contributing yet another positive feedback, both then and now. Today, the melting rate is accelerating to an extent that hasn’t yet been well quantified but is related to ocean warming and to the accelerated melting of the Greenland and West Antarctic ice sheets, progressively unloading the strata beneath. Reduced pressures lower the clathrate melting point.
111. See for instance Cramwinckel, M., Huber, M., Kocken, I. J., Agnini, C., Bijl, P. K., Bohaty, S. M., Frieling, J., Goldner, A., Hilgen, F. J., Kip, E. L., Peterse, F., van der Ploeg, R., Röhl, U., Schouten, S., and Sluijs, A., 2018: Synchronous tropical and polar temperature evolution in the Eocene. Nature, 559, 382–386. This recent data study from ocean sediment cores brings many lines of evidence together, confirming earlier conclusions that the hottest prolonged period was roughly between 53–50 million years ago, peaking around 52–51 million years ago except for a relatively brief, extremely hot ‘Palaeocene–Eocene Thermal Maximum’ (PETM)112 at the start of the Eocene 56 million years ago. Also presented are improved estimates of tropical sea surface temperatures, with maxima of the order of 35°C around 52 million years ago and nearly 38°C during the PETM. Tropical sea surface temperatures today are still mostly below 30°C.
112. See for instance Giusberti, L., Boscolo Galazzo, F., and Thomas, E., 2016: Variability in climate and productivity during the Paleocene–Eocene Thermal Maximum in the western Tethys (Forada section). Climate of the Past, 12, 213–240. The early Eocene began around 56 million years ago with the Palaeocene–Eocene Thermal Maximum (PETM), a huge global-warming episode with accompanying mass extinctions now under intensive study by geologists and palaeoclimatologists. It required a massive increase in atmospheric carbon-dioxide concentration, which probably came from volcanism added to by clathrate melting, the methane from which was then converted to carbon dioxide. Peatland burning might also have contributed. The western Tethys Ocean was a deep-ocean site at the time and so provides biological and isotopic evidence both from surface and from deep-water organisms, such as foraminifera with their sub-millimetre-sized carbonate shells. The accompanying increase in the extremes of storminess is evidenced by massive soil erosion from what the authors describe as “storm flood events”.
113. See for instance Thewissen, J. G. M., 2011: Sensor, J. D., Clementz, M. T., and Bajpai, S., Evolution of dental wear and diet during the origin of whales. Paleobiology, 37, 655–669.
114. Foukal, P., Fröhlich, C., Spruit, H., and Wigley, T. M. L., 2006: Variations in solar luminosity and their effect on the Earth’s climate, Nature, 443, 161–166. An extremely clear review of some robust and penetrating insights into the relevant solar physics, based on a long pedigree of work going back to 1977. For a sample of the high sophistication that’s been reached in constraining solar models, see also Rosenthal, C. S. et al., 1999: Convective contributions to the frequency of solar oscillations, Astronomy and Astrophysics 351, 689–700.
115. Solanki, S. K., Krivova, N. A., and Haigh, J. D., 2013: Solar Irradiance Variability and Climate. Annual Review of Astronomy and Astrophysics, 51, 311–351. This review summarizes and clearly explains the recent major advances in our understanding of radiation from the Sun’s surface, showing in particular that its magnetically-induced variation cannot compete with the carbon-dioxide injections I’m talking about.
116. Cyclonic storms, with or without embedded thunderstorms, transport heat and weather fuel poleward. For evidence that this process took place in Eocene times, as it does in ours, see for instance Carmichael, M. J., et al., 2017: Hydrological and associated biogeochemical consequences of rapid global warming during the Palaeocene–Eocene Thermal Maximum.112 Global and Planetary Change, 157, 114–138. See for instance their figure 8, showing the effects of weather-fuel transport from the tropics into middle and high latitudes.
117. Kendon, E. J., Roberts, N. M., Fowler, H. J., Roberts, M. J., Chan, S. C., and Senior, C. A., 2014: Heavier summer downpours with climate change revealed by weather forecast resolution model. Nature Climate Change, 4, 570–576. See also, for instance, Knote, C., Heinemann, G., and Rockel, B., 2010: Changes in weather extremes: assessment of return values using high resolution climate simulations at convection-resolving scale, Met. Zeitschr. 19, 11–23, and Mahoney, K., Alexander, M. A., Thompson, G., Barsugli, J. J., and Scott, J. D., 2012: Changes in hail and flood risk in high-resolution simulations over Colorado’s mountains, Nature Climate Change 2, 125–131.
118. See for instance Emanuel, K. A., 2005: Increasing destructiveness of tropical cyclones over the past 30 years. Nature, 436, 686–688. For tropical cyclones, the simple picture of a fast runup to peak intensity does not apply. Intensification is a relatively slow and complex process. Tropical cyclones scoop up most of their weather fuel directly and continually from the sea surface, making them sensitive to local upper-ocean heat content and sea-surface temperature. They are sensitive also to conditions in their large-scale surroundings including temperatures at high altitudes, which in turn are affected by complex cloud-radiation interactions, and atmospheric haze or aerosol. Our current modelling capabilities fall far short of giving us a complete picture. The author of the cited paper, Professor Kerry Emanuel, is a Foreign Member of the Royal Society and a leading expert on these matters. He tells me that the conclusions in the cited paper need modification for the Atlantic because of atmospheric aerosol issues not then taken into account. However, the conclusions for the Pacific still appear valid, he tells me (personal communication, 2020). Those conclusions still suggest a tendency for the models to err on the side of underprediction, rather than overprediction, of future extremes.
119. Abram, N. J., Wolff, E. W., and Curran, M. A. J., 2013: Review of sea ice proxy information from polar ice cores, Quaternary Science Reviews 79, 168–183. The light graph near the top of figure 20 [omitted from this preview] comes from measuring the concentration of sea salt in the Dronning Maud Land ice core from East Antarctica. The review carefully discusses why this measurement should correlate with the area of sea ice surrounding the continent, as a result of long-range transport of airborne, sea-salt-bearing powder-snow blown off the surface of the sea ice. The graph shows sea salt concentration divided by the estimated time of ice-core-forming snow accumulation in the ice-core layer measured — hence the label ‘flux’, or rate of arrival, rather than ‘concentration’.
120. A quick overview of the cross-checking can be found at http://www.climatescience.cam.ac.uk/community/blog/view/844/on-the-integrity-of-ice-core-records-by-eric-wolff. It was written by a leading ice-core expert, Dr Eric Wolff FRS, in response to criticism from another colleague.
121. See for instance Shackleton, N. J., 2000: The 100,000-year ice-age cycle identified and found to lag temperature, carbon dioxide, and orbital eccentricity. Science, 289, 1897–1902. See figure 4B.
122. Ref. 97 argues from the history of sociological tipping points that we are indeed very close, now, to finding the political will to take climate seriously. Despite the continued pressures to maintain fossil-fuel subsidies and kill renewables, countervailing pressures have been building up. In part that’s because, as the authors point out, “renewable energy sources such as solar photovoltaics and wind have experienced rapid, persistent cost declines” — and are available for use with smart grids, dynamic electricity pricing, large-scale battery storage and hydrogen production — whereas, despite “far greater investment and subsidies, fossil fuel costs have stayed within an order of magnitude for a century.” This is a new economic reality, of which for instance the state of South Australia has already taken advantage, having transitioned from coal to renewables and battery storage in just a few years, with a net reduction in the cost of electricity. And the schoolchildren’s and other mass movements suggest that a sociological tipping point is indeed very close, now that young people, especially, are making their voices heard more and more clearly.
123. Isaacson, W., 2021: The Code Breaker: Jennifer Doudna, Gene Editing, and the Future of the Human Race. Simon & Schuster. This up-to-the-minute book by Walter Isaacson describes the rapidity with which molecular biologists, using new techniques including CRISPR-Cas9 gene editing, have been building revolutionary and precisely-tailored medical tests, treatments and vaccines including those for COVID-19. At the centre of the CRISPR-Cas9 story was the work of Nobel laureate Jennifer Doudna, who has also led discussions of the far-reaching ethical issues that arise. Doudna describes having had a nightmare in which Adolf Hitler asked her to teach him how to do human gene editing. There is also the nightmare of unleashing ‘gene drives’ into ecosystems.
124. King, D., Schrag, D., Zhou, D., Qi, Y., Ghosh, A., and co-authors, 2015: Climate Change: A Risk Assessment. Cambridge Centre for Science and Policy. See also the relatively brief RS-NAS 2014 (UK Royal Society and US National Academy of Sciences), Climate Change: Evidence & Causes, and its 2020 update with the same title. All three reports come from high-powered teams of scientists, supplementing the vast IPCC reports and emphasizing the careful thinking that’s been done.
125. Stern, N., 2009: A Blueprint for a Safer Planet: How to Manage Climate Change and Create a New Era of Progress and Prosperity, London, Bodley Head. Even as early as 2009, the eminent economist Nicholas Stern was pointing out that the path to a green economy is a path to renewed prosperity.
126. Oxburgh, R., 2016: Lowest Cost Decarbonisation for the UK: The Critical Role of CCS. Report to the Secretary of State for Business, Energy and Industrial Strategy from the Parliamentary Advisory Group on Carbon Capture and Storage, September 2016.
127. Stein, P., 2020: Interview with BBC News on 24 January 2020 on the Rolls Royce consortium, a project to develop and build ‘small modular reactors’ to produce nuclear power.. Paul Stein, the Chief Technology Officer at Rolls Royce, said that the design and costing are already complete and that both have been scrutinized by the Royal Academy of Engineering and by the Treasury of the UK government. He argued persuasively that basing the design on advanced but conservative engineering and manufacturing techniques, more like car manufacture, will drive costs down — by contrast with large, one-off civil construction projects like the Hinkley Point C nuclear power station, for which “history shows that costs go up with time”.
128. McIntyre, M. E., 1998: Lucidity and science: III. Hypercredulity, quantum mechanics, and scientific truth. Interdisc. Sci. Revs. 23, 29–70. See the Corrigendum to Part III, a slightly corrupted version of which was published in the December 1998 issue of Interdisciplinary Science Reviews. Further discussion is in McIntyre, M. E., 2000: Lucidity, science, and the arts: what we can learn from the way perception works. Bull. Faculty Human Devel. (Kobe University, Japan), 7(3), 1–52. (Invited keynote lecture to the 4th Symposium on Human Development, Networking of Human Intelligence: Its Possibility and Strategy.)
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20 October 2021.