Adam Kucharski: The Uncertain Science of Certainty

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What is the main motivation behind Adam Kucharski's book on certainty?

Eric Topol 0:06
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, 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. Thanks for having me. 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 kind of captivates in the beginning.
Eric Topol 0:57
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 these gaps. So what was the motivation when you undertook this very big endeavor?
Adam Kucharski 1:17
I mean, I think a lot of it comes to the sort of work I do in 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 to 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 maths, I think you kind of grow up

How does the Monty Hall problem illustrate our understanding of probability?

Adam Kucharski 1:41
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 2:05
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 the show Let's Make a Deal. And maybe you could just take us through what happens with door numbers with one of the doors are unveiled and how that changes the mathematics.
Adam Kucharski 2:50
Yeah, sure. So I think it's 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 are 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.

What are mathematical monsters and their significance in understanding proof?

Adam Kucharski 3:07
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 know, you've picked one, there's another one, it's 50-50. And even some quite well-respected mathematicians, people like Paul Erdosch, who has 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.
Adam Kucharski 3:48
So it's 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 erdos one of his colleagues kind of showed him the what i'd call proof by exhaustion so go through every combination and that didn't really convince him so then he started to simulate and said let's do a computer simulation of the game a hundred thousand times and again you know switching was this optimal strategy but erdos wasn't um

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