Do Dice Play God?: The Mathematics of Uncertainty

"In the introduction of Do Dice Play God? , Ian Stewart goes through these ‘six ages of uncertainty,’ all the way from reading entrails, to quantum mechanics at the start of the 20th century, to more recent findings like the development of chaos theory in the 60s and 70s. The book has an interesting setup in that some of the chapters are very applied. For example, he has a short chapter on math and the law. But then some of the chapters are very theoretical. The thing I’d say about Do Dice Play God? is that it is very rewarding, but you do have to invest in it. It gets very, very deep at some points—not just A-level or undergraduate-deep, but graduate school deep. He explains some really complicated concepts in the book. He goes very deep into quantum theory, deeper than I’ve ever read in a popular science book before. He really is looking at how the uncertainties that we now understand as inherent in quantum theory can stop us from predicting the future, or at least make it very challenging to do so. Another concept he goes into is chaos. Chaos is usually characterised by a dynamical system which has sensitive dependence on initial conditions. Let’s say you start two systems off very close together, like two instances of setting off a double pendulum. Even though the equations which predict the motion of these systems are deterministic—if you had perfect knowledge of where they started, you should be able to predict the state of the system as far as you like into the future—after a while, they will diverge. Support Five Books Five Books interviews are expensive to produce. If you're enjoying this interview, please support us by donating a small amount . The weather is a classic example of a chaotic system. The equations that rule the weather are all completely deterministic. There’s no probability inherent in them. But if you don’t know the exact initial conditions for the weather—what the weather doing is now—when you run these equations forward, after a day or two, they’ll become completely desynchronized. If you have even slight uncertainty in your initial conditions, when you run things forward, one prediction might predict sunshine and the other a thunderstorm. In the book, Stewart gets quite deep into the theory behind the chaos, looking at attractors, for example. Yes, but in this case it’s not because of probability or chance. It’s not like there’s someone behind the scenes flipping a coin so that we don’t know which way things will turn out. There isn’t anything inherently uncertain in the equations that govern many aspects of world. It’s because we’re looking at these complex nonlinear systems that will diverge from each other, even if they start very close together. “Chaos is inherent in these complex nonlinear systems” The motion of the planets is another example. We can actually predict where the planets are going to be in millions of years’ time. But if we have some uncertainties about their positions, then after a few million years we might predict that Mercury is on one side of the solar system when in fact it’s on the other. Chaos is inherent in these complex nonlinear systems. A bit of both. Another thing that’s really nice about the book is that Stewart uses solid mathematical arguments to make important political points. For example, he looks at climate change. He points out that we can’t infer whether climate change is happening just by looking at single weather events, because the weather does fluctuate a lot. What we need to be looking at is long-term averages and whether we see a trend in temperature increasing over time. He gets quite political at some points—about why the Trump administration is denying climate change, or not taking more action on climate change, but his points are always backed up by solid mathematical arguments. Yes, he’s written lots of popular math books. The title of this book is a play on what’s probably his most famous book, Does God Play Dice? (1989). He’s also a serious academic. He’s a fellow of the Royal Society and really well respected in his field. He’s worked on lots of different areas, including my own area of mathematical biology. So he’s highly regarded both academically and for his popular math books."