Or rather, what can we know?
Donald Rumsfeld is wrongly mocked for a “misunderstimated” quote when he served under President George Dubbya Bush. There may have been many things in his political career for which he deserved ridicule, but not for this:
as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don’t know we don’t know. And if one looks throughout the history of our country and other free countries, it is the latter category that tends to be the difficult ones.
(Donald Rumsfeld during DoD news briefing, February 2002)
The subject of Marcus du Sautoy‘s book What We Cannot Know: Explorations at the Edge of Knowledge (published by 4th Estate, 2016) takes on another category of even more difficult questions – Are there things which we know we cannot know? The alternative sub-title is From Consciousness to the Cosmos, the Cutting Edge of Science Explained. Both alternatives display the scope and ambition of this remarkable book.
Questions questions questions
It is an exploration of a wide range of scientific and philosophical fields including Chaos Theory, Particle Physics, Cosmology and Neuroscience, and poses questions about what we can know or whether certain questions hold any meaning at all. These are presented in a series of eight “Edges”, numbered (oh, mathematician!) 0 to 7 of course. In each he surveys the history of each domain, before getting to the knotty debatably unknowable stuff. The episodes are strung together with reference to the authors dice: when he throws them, can he know what will happen?
He starts with Newton’s Laws of Motion and how the subsequent views of a mechanistic and predictable universe seems to go awry due to the instability of very simple systems and sensitivity to even the tiniest error in the initial conditions. He traces the emergence of Chaos Theory (illustrated by beautiful fractal maps) through to limits on the prediction of the weather and even the behaviour of the planets of the Solar System.
Then Du Sautoy dives into Particle Physics, asking if we can ever “bottom out” the nested building blocks of matter, down into the baffling counter-intuitive conclusions of Quantum Mechanics. which shows us that we can’t just keep dividing stuff – whether energy, space or time – forever; that there are real limits of what can be measured. The includes the much-misunderstood Uncertainty Principle, which is a theory of great precision rather than (as popularly imagine) vagueness. It imposes certain limits on what are meaningful questions to ask.
If you’re not living on the edge, you’re taking up too much room
Next the author takes us to the outer reaches of space and time. There are massive puzzles in contemporary Cosmology (where the Universe came from and where it is going). Looking back was there a singularity at the Big Bang? Looking forward, why the is expansion of the Universe evidently accelerating? (“the stars are going out”). And of course who hasn’t stared up at a night sky and wondered if it is infinite. He reckons that we cannot know if it is infinite, but we may get evidence if it not.
Your calculations may be correct, but your physics is atrocious
(Albert Einstein to George Lemaitre, who first deduced the Big Bang)
But of course time and space cannot be discussed separately once Einstein’s insights into Relativity are considered. Space-time is four dimensions inextricably linked, leading to the mind-boggling facts of identical clocks running at different rates, the breakdown of causality for observers in relative motion (it really is worth a ride in Einstein’s tram!), and the leaky event horizon of a black hole.
The final two “Edges” I found most intriguing of all. First he turns inward to look for consciousness. We know a great deal about how the brain works, but consciousness? What is it? Where is it? Can machines have it? What does the famous Turing Test really tell us? One experimental outcome genuinely shocked me: some decisions we make (choosing between doing two different things) are visible in the activity of our motor cortex a full six seconds (!!!) before we consciously know about it. Is free will an illusion? Is consciousness just the “froth on reality“, as the question was posed in his famous Reith Lectures?
because our intelligence is ultimately an embodied intelligence, the knowledge we can obtain about mathematics is restricted to that which can be embodied
Last of all, Du Sautoy is on home ground with Mathematics. And yet I find these chapters the least convincing. He explains the “beauty” of mathematical proofs and the foundation-shaking emergence of Gödel’s incompleteness theorems which can prove that there are true things one can state that cannot be proven. I’ve followed it through several times and still it stretches understanding … which is of course the point! There is self-referential fun as well as the Big Questions in this section. But I also found myself frustrated by the inconsistency in applying the same levels of logical reasoning as had been used elsewhere in the book. There appears to me a shortfall in distinguishing between “unknowables” and failures to translate mathematical concepts into natural language. As Quantum Mechanics and Cosmology illustrate, it is possible to pose questions that have no logical content, a situation too long tolerated in philosophy.
So in the light of this (and the preceding quotation) I take issue with (amongst other things) …
- … the math concept of “infinite decimal expansion” which is at odds with the QM concept of quantised space-time. The smooth-functioned maths is only an approximation to the lumpiness of the Universe.
- … Cohen’s valid but contradictory models of Cantor’s “countable infinities”: Surely this demonstrates (by contradiction) that the concept of “countable infinities” is flawed?!
- … Max Tegmark’s Mathematical Universe Hypothesis (fundamentally we are all “just” equations) – yes really – is countenanced despite Du Sautoy’s own summary that:
Science does the actual, mathematics does the possible
(Marcus du Sautoy – so why does he countenance Max Tegmark’s Mathematical Universe Hypothesis (fundamentally we are all “just” equations) – yes really?)
Mathematics is traditionally divided into Applied and Pure (or Theoretical). I am more inclined to think of the distinction as “Pragmatic” maths (which can reference the Universe) and Flying Rainbow Unicorn maths which cannot. Hmphh.
The Art of the Readable
The author is a mathematician and but also, true to one of his job titles as the Simonyi Professor of the Public Understanding of Science at the University of Oxford, he is an excellent populariser of scientific ideas. He also discusses the issues on the edge of knowability with some leading thinkers – these dialogues are some of the most accessible and memorable parts of the book. The exchanges make what could be a dry and philosophical text much more human. His encounters with Sir Roger Penrose (so full of ideas and speculations), Prof John Barrow (cosmologist) and John Polkinghorne (distinguished physicist who became a priest in later life) etc., are priceless. And there is a surprising amount of discussion about Faith, always informed and respectful.
I have read enough to be familiar with most of the science and maths, but even as a trained scientist I struggled with being dragged through the entire history of each of the disciplines investigated. In my opinion this was another book in need of a strong editor. I was better engaged after 6 chapters, but I know several well-read members of my Book Group who didn’t make it that far. But if you can endure the verbosity (and some repetition) the philosophical conclusions and discussion are well worth it.
Even if, like me, you may strongly disagree with some of the more recent speculative cutting edges of science and mathematics (e.g. the Mathematical Universe Hypothesis (MUH) or Multiple Universe view of Cosmology) there is a great deal to think over. There is an excellent Further Reading section, which somehow leaves out some of the books and authors which are mentioned or alluded to in the text, including Julian Jaynes and Douglas Hofstadter. Du Sautoy’s book is not an easy read, but rewards the effort with a lifetime’s-worth of intrigue, curiosity and brain food.
Elsewhere on the shelf
- Julian Jaynes The Origin of Consciousness in the Breakdown of the Bicameral Mind (1976)
- Douglas R. Hofstadter Gödel, Escher, Bach: an Eternal Golden Braid (A Metaphorical Fugue on Minds and Machines in the Spirit of Lewis Carroll) (Penguin, 1979)
- Roger Penrose The Road to Reality: A Complete Guide to the Physical Universe (Jonathan Cape, 2004)
- Max Tegmark Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (2014; Penguin Edition 2015)
- John D Barrow & Frank J Tipler The Anthropic Cosmological Principle (Oxford University Press, 1986)
Image credits
- Book cover: Amazon stock image
- Butterfly child: Carl Court / Getty Images
- Cosmic Inflation diagram: from an article by Sabine Hossenfelder in Forbes.com
- Einstein being relatively rude: Arthur Sasse / Bettman Archive (via The Grauniad)
- Flying rainbow unicorn: stock image
- GEB book cover: Abe Books stock image
Sir Roger Penrose wrote a fine obituary of Steven Hawking for the Guardian. He was quite frank about Hawking’s complicated private life and professional disappointments and wrote, ‘…the Big Bang was not so accommodating as Hawking wished, and this was a great disappointment to him’. Nicely put.