Book Review: What We Cannot Know

Mathematician Marcus du Sautoy takes us on an amiable guided tour of the outer limits of knowledge.

In 1988, I accepted a joint position as an assistant director of the Science Museum, and as a professor of the public understanding of science at Imperial College London. It was the latter title, of course, that caught people’s attention.

One day, I was a lecturer at the University of Oxford, working on a national survey of public perceptions of science; the next, I was a leading authority on anything and everything to do with the public face of science and technology. Suddenly journalists called with all kinds of questions: What were my opinions about “cold fusion,” genetically modified foods, mad cow disease? What did I think about the supposedly parlous state of science education in British schools? After a few early missteps, I quickly learned to think twice before answering questions on the phone.

What We Cannot Know

The following is a review of Marcus du Sautoy’s new book “What We Cannot Know: Explorations at the Edge of Knowledge,” published this spring by Harper Collins.

Twenty years later, Marcus du Sautoy was appointed to the Charles Simonyi Professorship for the Public Understanding of Science at Oxford, and to judge by his new book, he had a similar experience. “It often makes me laugh,” he writes about the exalted title he holds, and adds, “There seems to be a belief that with such a title I should know it all.” He recounts how the announcement of the 2009 Nobel Prize in Physiology or Medicine for the discovery of “how chromosomes are protected by telomeres and the enzyme telomerase,” was followed — predictably, I would say — by a call from a journalist hoping for an explanation of the breakthrough.

“Biology,” du Sautoy writes, “has never been my strong point, but I was sitting in front of my computer screen and so I’m embarrassed to admit I got the Wikipedia page up on telomeres and, after a quick scan, proceeded to explain.”

How I wish we’d had Wikipedia back in the early 1990s, when I needed it most! But on second thought, how glad I am that we didn’t: The temptation to become an instant expert on everything under the sun would surely have been too great to resist. To be fair to du Sautoy, though, his is an honestly self-deprecating story. Nowhere in this book does he come across as a know-it-all. On the contrary, he’s at pains to emphasize that no one can know it all: first, for the obvious reason that the sum of scientific knowledge is too vast for any one person to master; and second, for the not-so-obvious reason that some things — interesting things, intriguing things, perhaps even important things — appear to lie beyond our collective ability ever to find out.

The context for “What We Cannot Know” is significant. Du Sautoy is not the first holder of the Simonyi Chair. That honor goes to Richard Dawkins, for whom the Chair was created in the mid-1990s. As is now well known, Dawkins soon gave up teaching to devote himself wholeheartedly to writing and public speaking; within a decade, he had become both the U.K.’s best-known public intellectual and the world’s most famous atheist.

Not surprisingly, perhaps, when Dawkins retired from the Simonyi Chair in 2008, Oxford decided to appoint a rather different kind of successor. The news article in The Guardian bore the bracing headline “Popular face of maths to succeed godless Dawkins,” and the reporter, Alok Jha, cheerily began, “Stepping into the shoes of Richard Dawkins could be intimidating for some: not so for Marcus du Sautoy.” Noting that du Sautoy was “keen to steer his own path,” Jha quoted him as follows: “I’m bracing myself for everyone asking me if I believe in God or not…But my focus is mainly on trying to excite people about science, why I do it, how it impacts on your life”.

True to his word, du Sautoy has combined mathematical research and teaching with ingenious and artful outreach, and he has generally steered clear of metaphysical mysteries. In addition to writing several books for general readers (for example, one on symmetry and another on the mathematics of everyday life), he makes regular appearances on TV, often in the company of the comedian Dara Ó Briain, with whom he presents “School of Hard Sums,” a British game show in which du Sautoy sets various mathematical puzzles for Ó Briain and his guests to solve. Du Sautoy has presented TV shows on subjects as varied as artificial intelligence and self-awareness, and this year he appeared at the Glastonbury Festival in the west of England, whose promoters say he “offers you the chance to win one million dollars if you can solve a mathematical conundrum.” As he promised at the outset, in all of this du Sautoy’s focus has been “very much on the science and less on religion.”

Until now, that is. In “What We Cannot Know,” du Sautoy finally gives in to the steady pressure to “come clean” on the question of God. He tells us about a radio interview he gave in Northern Ireland on a Sunday morning (not a particularly good assignment, one would have thought, for someone trying to avoid talking about God). Challenged to explain his thoughts on the question, he countered with the time-honored technique of asking for a definition of terms: What did the interviewer mean by “God”? The interviewer replied, “It is something which transcends human understanding.”

By this stage in his account, du Sautoy has already said enough to indicate that he is an atheist (his religion, he tells us, is Arsenal, the English soccer team). At first, he is inclined to consider the interviewer’s definition a cop-out, but then he decides to try taking it seriously: “What if you define God as the things we cannot know?” To paraphrase the former U.S. Secretary of Defense Donald Rumsfeld, are there not merely “known unknowns” and “unknown unknowns” (of which science surely has plenty), but also known unknowables? If so, what are they, and do they seem to approximate to anything that we might want to acknowledge as God?

This move defines du Sautoy’s delightful hunt for anything about the universe that we can be confident we shall never know. His quest for the unknowable involves a series of close encounters with the known, and particularly with what he terms the edges of our mathematical and scientific understanding. An amiable and entertaining guide, he takes us with him and his kids on an archaeological dig in Israel, which leads through a discussion of Neolithic sheep heel bones — once used, supposedly, for divination — to a consideration of the unavoidable uncertainties involved in throwing dice. He moves from his relative competence on the trumpet and incompetence on the cello to a consideration of continuity and discontinuity in nature, and thence to a deeper consideration of what makes the dice roll so uncertain. And in the end, he even comes clean in answer to that annoying radio interviewer in Northern Ireland.

Du Sautoy compiles a long list of things about the universe that we can be fairly confident we cannot know. The dice, of course, are easy. We know the general laws that apply to their behavior when they are thrown and land on a hard surface; these laws were supplied by Newton, and their application is (relatively) straightforward. The problem is that the system comprising the player, the dice themselves, and the surface is enormously sensitive to initial conditions. Make the tiniest alteration in these conditions, and the result may be quite different. Since we can never hope to measure the initial conditions accurately enough to discern such tiny differences, we can never hope to predict each throw with certainty. (Of course, this doesn’t mean we can’t make meaningful predictions about the results of a statistically significant large number of throws; but that’s another story.) Here, then, is one kind of unknowability.

All so-called chaotic systems that demonstrate sensitivity to initial conditions are likewise unknowable in principle. They include not only familiar examples such as the weather but also less familiar ones such as the evolutionary tree of life, whose fractal nature suggests to du Sautoy that “many of the questions of evolutionary biology could well fall under the umbrella of things we cannot know.” And chaos theory by no means defines the list. For example, du Sautoy suggests that we can never know for sure the ultimate constituents of matter. Despite the successes of particle physics, unpeeling the onion of matter reveals layer after layer of existence, and he argues that there is no reason to suppose that this layering doesn’t continue beyond our ability to detect what is happening at distances below one Planck length.

To these unknowables, du Sautoy adds many more: from physics, from biology, from brain science, and even from mathematics. In some cases, such as the ultimate nature of matter, he is definitive: He thinks we can truly never know. In others, such as whether the universe is infinite, and the nature of time before the Big Bang, he’s not so sure. In the case of consciousness, he’s impressed that science is making interesting progress, but in the end he’s genuinely unsure whether anything that we can discover will ever allow us to claim that we truly understand how sentience and subjectivity arise in the world.

The conclusion of du Sautoy’s quest, therefore, is an honest reappraisal of his own beliefs. He’s very clear that he remains skeptical about the solutions to the riddle of existence that are offered by conventional religions. However,

I wonder, whether as I come to the end of my exploration at the limits of knowledge, I have changed my mind about declaring myself an atheist. With my definition of a God as the existence of things we cannot know, to declare myself an atheist would mean that I believe there is nothing that we cannot know. I don’t believe that anymore. In some sense I think I have proved that this God does exist. It’s now about exploring what quality this God has.

I cannot pretend to know exactly how the first holder of the Simonyi Chair at Oxford will feel about his successor’s interpretation of the scope of science in “What We Cannot Know.” Where Dawkins’ writings tend to leave readers with the sense that science is all-powerful, du Sautoy presents us with a view of science as brilliant, enchanting, but not all-encompassing.

To some degree, of course, this is the difference between the optimist (the glass half full) and the pessimist (half empty). For du Sautoy, who tells us that he was initially drawn to mathematics out of a love of certainty, there is great significance in the realization that mathematics and science will never enable us to know it all. But there is more here as well: there is the difference between what might be called scientific immodesty and scientific modesty. Unlike some public representatives of science, du Sautoy is not inclined to exaggerate its power to explain. Near the end of his quest, for example, he suggests that the sciences may not even be the best guide to the behavior of some of the universe’s more unruly objects: “The humanities,” he remarks, “are the best language we have for understanding as much as we can about what it is to be human.” It is impossible to imagine Dawkins writing a sentence like that.

Of what use, then, are professors for the public understanding of science? In my view, one thing is taking seriously the task of making sense of science in the wider culture. Whatever science may be, it is not its own sufficient explanation; it does not arise from the world’s peer-reviewed journals complete with all of its meanings, significances, and larger implications.

Rather, these things remain to be negotiated through public discourse; and such discourse is by its nature philosophical, historical, social, and moral. Every time a professor for the public understanding of science (or anybody else) sallies forth into the public domain with his or her latest work of scientific interpretation, we are treated to an exercise in the making of cultural meaning. Inevitably, personality and values come into play, along with intellect and rhetorical skill. We are not to complain about this; but we will do well to be aware of it as we enjoy the work (or not, as the case may be).

Du Sautoy is an eminently enjoyable interpreter of science; and his, like others’, is a distinctive view of the place of science in human affairs. When Pierre-Simon Laplace made his famous pronouncement in 1812 about a hypothetical all-knowing intellect for whom “nothing would be uncertain and the future just like the past would be present before our eyes,” he spoke for one particular, and particularly bold, view of science. On Laplace’s deathbed, du Sautoy notes, he spoke for a different and altogether more circumspect view: “What we know is little,” he said, “and what we are ignorant of is immense.” Du Sautoy clearly prefers this more modest, “glass half empty” view; and for what it’s worth, so do I.

John Durant is director of the MIT Museum and an adjunct professor in the Science, Technology & Society Program at MIT. From 1989 to 2000, he served as Assistant Director of the Science Museum, London, and Professor of the Public Understanding of Science at Imperial College, London.

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