Adam Kucharski: The Uncertain Science of Certainty

“To navigate proof, we must reach into a thicket of errors and biases. We must confront monsters and embrace uncertainty, balancing — and rebalancing —our beliefs. We must seek out every useful fragment of data, gather every relevant tool, searching wider and climbing further. Finding the good foundations among the bad. Dodging dogma and falsehoods. Questioning. Measuring. Triangulating. Convincing. Then perhaps, just perhaps, we'll reach the truth in time.”—Adam Kucharski

My conversation with Professor Kucharski on what constitutes certainty and proof in science (and other domains), with emphasis on many of the learnings from Covid. Given the politicization of science and A.I.’s deepfakes and power for blurring of truth, it’s hard to think of a topic more important right now.

Audio file (Ground Truths can also be downloaded on Apple Podcasts and Spotify)

Eric Topol (00:06):

Hello, it's Eric Topol from Ground Truths and I am really delighted to welcome Adam Kucharski, who is the author of a new book, Proof: The Art and Science of Certainty. He’s a distinguished mathematician, by the way, the first mathematician we've had on Ground Truths and a person who I had the real privilege of getting to know a bit through the Covid pandemic. So welcome, Adam.

Adam Kucharski (00:28):

Thanks for having me.

Eric Topol (00:30):

Yeah, I mean, I think just to let everybody know, you're a Professor at London School of Hygiene and Tropical Medicine and also noteworthy you won the Adams Prize, which is one of the most impressive recognitions in the field of mathematics. This is the book, it's a winner, Proof and there's so much to talk about. So Adam, maybe what I'd start off is the quote in the book that captivates in the beginning, “life is full of situations that can reveal remarkably large gaps in our understanding of what is true and why it's true. This is a book about those gaps.” So what was the motivation when you undertook this very big endeavor?

Adam Kucharski (01:17):

I think a lot of it comes to the work I do at my day job where we have to deal with a lot of evidence under pressure, particularly if you work in outbreaks or emerging health concerns. And often it really pushes the limits, our methodology and how we converge on what's true subject to potential revision in the future. I think particularly having a background in math’s, I think you kind of grow up with this idea that you can get to these concrete, almost immovable truths and then even just looking through the history, realizing that often isn't the case, that there's these kind of very human dynamics that play out around them. And it's something I think that everyone in science can reflect on that sometimes what convinces us doesn't convince other people, and particularly when you have that kind of urgency of time pressure, working out how to navigate that.

Eric Topol (02:05):

Yeah. Well, I mean I think these times of course have really gotten us to appreciate, particularly during Covid, the importance of understanding uncertainty. And I think one of the ways that we can dispel what people assume they know is the famous Monty Hall, which you get into a bit in the book. So I think everybody here is familiar with that show, Let's Make a Deal and maybe you can just take us through what happens with one of the doors are unveiled and how that changes the mathematics.

Adam Kucharski (02:50):

Yeah, sure. So I think it is a problem that's been around for a while and it's based on this game show. So you've got three doors that are closed. Behind two of the doors there is a goat and behind one of the doors is a luxury car. So obviously, you want to win the car. The host asks you to pick a door, so you point to one, maybe door number two, then the host who knows what's behind the doors opens another door to reveal a goat and then ask you, do you want to change your mind? Do you want to switch doors? And a lot of the, I think intuition people have, and certainly when I first came across this problem many years ago is well, you've got two doors left, right? You've picked one, there's another one, it's 50-50. And even some quite well-respected mathematicians.

Adam Kucharski (03:27):

People like Paul Erdős who was really published more papers than almost anyone else, that was their initial gut reaction. But if you work through all of the combinations, if you pick this door and then the host does this, and you switch or not switch and work through all of those options. You actually double your chances if you switch versus sticking with the door. So something that's counterintuitive, but I think one of the things that really struck me and even over the years trying to explain it is convincing myself of the answer, which was when I first came across it as a teenager, I did quite quickly is very different to convincing someone else. And even actually Paul Erdős, one of his colleagues showed him what I call proof by exhaustion. So go through every combination and that didn't really convince him. So then he started to simulate and said, well, let's do a computer simulation of the game a hundred thousand times. And again, switching was this optimal strategy, but Erdős wasn't really convinced because I accept that this is the case, but I'm not really satisfied with it. And I think that encapsulates for a lot of people, their experience of proof and evidence. It's a fact and you have to take it as given, but there's actually quite a big bridge often to really understanding why it's true and feeling convinced by it.

Eric Topol (04:41):

Yeah, I think it's a fabulous example because I think everyone would naturally assume it's 50-50 and it isn't. And I think that gets us to the topic at hand. What I love, there's many things I love about this book. One is that you don't just get into science and medicine, but you cut across all the domains, law, mathematics, AI. So it's a very comprehensive sweep of everything about proof and truth, and it couldn't come at a better time as we'll get into. Maybe just starting off with math, the term I love mathematical mo