Instant Genius - How to combat uncertainty in a post-truth world

Episode Date: March 7, 2025

These days we’re bombarded with information and claims that purport to explain almost every conceivable aspect of our lives, be it down to the bold assertions made by policymakers, the confidence of anonymity afforded by social media or just our natural human inclination to be fooled by a well-spoken know-it-all. But exactly who are the people making these claims, how do they reach their conclusions, and really, can anyone ever actually be certain about anything? In this episode, we catch up with the statistician, epidemiologist and author Adam Kucharski to take about his latest book Proof, The Uncertain Science of Uncertainty. He tells us how Abraham Lincoln’s background as lawyer led him to study the nature of proof beyond reasonable doubt and how it helped him to win his presidency, how picking holes in previous logical thinking enabled Albert Einstein to discover some of his greatest theories, and what the COVID pandemic taught us all about the value of scientific rigour and evidence-based conclusions. Learn more about your ad choices. Visit podcastchoices.com/adchoices

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This podcast is sponsored by name, audio and focal. Streaming has made music more accessible than ever, but true listening is about more than ease. It's about quality. British audio experts name audio, alongside French acoustic specialist focal, combine handcrafted tradition with cutting-edge innovation and high-end materials, delivering digital precision with analogue warmth,

so you can experience exceptional sound at home. Music just as the artist intended. visit name audio.com to learn more. Hello and welcome to Instant Genius, a bite-sized masterclass in podcast form. Every Monday and Friday, you'll hear world-leading scientists and experts talking about the most fascinating ideas in science and technology today. I'm Jason Goodyear, commissioning editor at BBC Science Focus. These days, we're bombarded with information and claims

that purport to explain almost every conceivable aspect of our lives. be it down to the bold assertions made by policymakers, the confidence of anonymity afforded by social media, or just our natural human inclination to be fooled by a well-spoken no-at-all. But exactly who are the people making these claims? How do they reach their conclusions? And really, can anyone ever actually be certain about anything? In this episode, we catch up with the statistician, epidemiologist and author,

Adam Kacharski, to talk about his latest book. proof, the uncertain science of uncertainty. He tells us how Abraham Lincoln's background as a lawyer led him to study the nature of proof beyond reasonable doubt and how it helped him to win his presidency, how picking holes in previous logical thinking enabled Albert Einstein to discover some of his greatest theories, and what the COVID pandemic taught us all about the value of scientific rigor and evidence-based conclusions. So, welcome to the podcast. Thanks very much for joining us. Yeah, thanks for having me.

So today we're talking about your book, Proof, The Uncertain Science of Certaincy. So, interesting title. What's the sort of rough premise? So I think throughout areas of life, we create certainty. We want to know what's true. But I think proof often has a bit of urgency with it, you know, whether we're trying to make a decision, whether we're accused of a crime, whether there's a policy, whether there's a policy, whether there's a policy, whether there's an emergency. So really the book is my attempt to look at the different measures we use to converge on truth. How do we do this under pressure? How do we weigh up evidence? And crucially,

what happens when these methods fail? So really looking back through history, millennia, right up to the modern era, what happens when we really get to the edge of our ability to understand things? And then as we go into this era with more computation and AI, how is that going to change our attitudes to these things? So you're a mathematician by trade. And so I think, think let's start with numbers. So I think something a lot of people take for granted is that we base our numbers on this set of 10s system. So where did that come from? And, you know, why is it such a great idea? So one of the things, if you look back through history that's kind of striking is how a lot of mathematics is kind of designed around the problems that people are trying

and solve in their lives. So even if you go back to prehistoric times where you have 10, tally systems on cave rules, that very quickly becomes inefficient when you're dealing with larger things at scouting. If you try and write 111 as a tally, that's going to take a while. If you write it in our familiar kind of base 10 system with one digit at each point, it's a lot easier. But even if you look back to say Babylonians, they didn't use the units of 10. They used units of 60, so kind of like a stopwatch with, and that was because they were very focused on pragmatic problem solving. If you're going to use numbers for that way, 60 is quite helpful because it divides through by a lot of things and gives you a whole number at the end.

And as we sort of shift through to kind of Greek and Arabic math, there was a lot more on that kind of deeper understanding, and that's why we evolved kind of other systems for how we summarize numbers. So you speak in the book a lot about the Greeks. So let's start with Euclid, which you talk about a lot. So absolutely fascinating person. And you talk about definitions and sort of first, principles, really, I would say, of mathematics. So what is that? So you could really, through his

set of 13 books called The Elements, tried to bring together a lot of the fundamentals of what was out there in terms of how people would process shapes. And to do that, you need to start off by just agreeing on what you mean by things. Otherwise, you can very quickly drift apart. And we see that in daily life. If people mean two different things, you get cross-purposes. So his book, even at the The start opens by getting very much the point. He talks about what is a point. What do we talk about when we meet a point? What do we mean by a line?

What do we mean by a triangle? And once he lays that groundwork, his definitions, and then a series of axioms, so things that he called self-evident. So, for example, the whole is greater than the part. He said that's a self-evident. We can just take that as given. And we can then use those definitions

and those self-evident facts, essentially, to build up a series of propositions about things we think are true. So for combinations of angles and a triangle, for example. And then he set out to prove them. And it kind of might seem like quite a dry book. There's no narrative, there's no characters. But it was enormously influential. It was a second only to the Bible in terms of printed editions.

And particularly during the Enlightenment in the 1700s in particular, and the foundation of countries like America, became very influential. because that kind of way of being very precise about agreeing on definitions, agreeing on a truth, and then objectively showing that these things are correct and correct always, was very appealing in wider areas of life as well. Yeah, so this moved over a hell of a long time with the Renaissance and Enlightenment thinking and things like this. But you talk a lot about Abraham Lincoln. So this was something I just did not know.

So what's the connection there? It's a remarkable story. So Lincoln is famous, particularly for his speech giving and his very compelling arguments that he made, particularly around slavery and in the run-up to the Civil War and afterwards. And he wasn't always like that. Early in his career, he had a less successful initial foreign to politics. And he was a lawyer, spent a lot of time kind of on the circuit. And he became quite frustrated that as a lawyer, he talked about demonstrating things.

proving things. And he didn't really have an understanding of what that meant. There was this kind of hazy idea of proof beyond reasonable doubt and certain proof. And so he decided he'd go back to basics and actually teach himself, how do I do this from scratch? And while he was traveling around these provincial courtrooms, he would study by candlelight. So all of his fellow lawyers were snoring in some in the middle of nowhere. And he was studying how to prove triangles had these certain properties. And he wasn't doing that because he wanted to know lots of things about triangles. He was doing it because he wanted that logical armoury. He wanted those tools. So when he was then faced with argument, he had these essentially weapons for pulling apart, looking

for contradictions, looking for how you could build up logical steps to make a compelling whole. And he actually many of his subsequent political debates referred to Euclid, referred to those techniques. and some of his most successful arguments against slavery, which would end up winning him the presidency, relied on these tools like proof by contradiction. So proof of contradiction is this mathematical idea where if you think something's true, you can start off by assuming it's not true. And then if that leads to two contradictory statements that have been proven by the logic of what you're assuming, that doesn't make sense. It's a contradiction. Therefore, your original assumption must be wrong. therefore the thing must be true. And he used that in slavery really to identify a lot of fundamental

contradictions in this assumption that you can enslave people and that that's a reasonable thing to do. Yeah, so it sort of comes from mathematics, but it's absolutely bound up with philosophy, isn't it? It is. And really those threads have kind of woven through a loss of history, because there's just that application. I mean, even in the early Declaration of Independence for the United States. The first draft said, we hold these truths to be sacred. And Benjamin Franklin, who again, read a lot of Euclid, didn't like that because it was appealing to religion for truth. And so he crossed it out and he wrote self-evident. So it's this mathematical, you've got this objective truth. And again, a lot of the Enlightenment philosophy that fed through into this

appeal for objective truths to things around morality, in some cases, aesthetics, these notions that there's an objective beauty. And if you were, saying that it wasn't your opinion, you were taking a kind of view on what was true about the world. So there was this very kind of strong movement through how we were approaching concepts of truth and what it meant in our daily lives. So sort of like skipping back to the Greeks for a moment, one of my favourite Greek philosophers is Diogenes. Diogenes the dog, Diogenes the cynic, fascinating character, was walking around the town square of the candle saying he was looking for an honest man.

I'm sure you've heard the anecdote of Alexander the Great. No? I'm not sure. I've heard that one actually, no. Or I can't remember it at least. So, apparently, it's probably apocryphal, but Alexander the Great met Dajnese and said, you're the greatest philosopher in Greece.

I'll grant you any wish that you want. So Dajanese says, just step out of the sun. You're shading me. Fascinating, man. Yeah, and I think just those The other one that Tharji stood out for it was a lot of the early work by Zeno

who was another philosopher who really kind of challenged. So the most famous one he's got is Achilles and the Tortoise, which is this idea that Achilles starts a mile ahead and then by the time the tortoise gets to his bit, Achilles has gone a bit forward and by that logic he never catches up and he made this other argument of motion can't

exist because you know at every point in time something has to get another step So if I want to get the other side of the room, I can divide that into small and small increments and I can't go through an infinite number of steps. I can't count up an infinite number of steps. I can't move.

And Dajuniz just made the, it's proof by walking, he just got up and walked off. And he's like, well, that's not true, is it? And there was, but this idea actually, it caused problems in mathematics right into the 1800s because I think people said, well, okay, obviously that's not true.

But actually that flaw of not being able to hand infinities in how you do mathematical calculations, think about mathematical proofs. People kind of ignored and said, well, this is a bit silly, but we're sort of going to put up with it. And Zeno had actually just left this almost kind of tiny mathematical bomb at the heart of a lot of our theories that took, you know, centuries and centuries to really go off and cause a lot of problems. Ambition comes in all shapes and sizes. At First Citizens Bank, we roll with your goals because we're built for what you're building. Fit for your ambition for citizens back.

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Try it for yourself at a focal powered by name boutique. Visit focal powered by name.com for more information. So let's move a bit forwards then to a word that probably like just brings fear to the hearts of people that study mathematics and aren't particularly keen on it, calculus. So we've got Newton and Leibniz. So what is calculus and, you know, how important is it? You know, because it really is. I think I was definitely encouraged by my publisher to not put too much calculus up front. I mean, fundamentally, it's about rates of change.

It's how do things change, whether it's a falling object, whether it's a property of a population, whether it's something in engineering, something in physics. And essentially, if you want to study how change happens in the world, you need to think about the rate that's happening and what might cause something to change fast or slow or accelerate or decelerate. And calculus is essentially the mathematical tools that allow us to do that. And one of the fundamental challenges, for example,

Let's say an object is falling and you want to know how fast it's falling. And so you could say, okay, well, what I'm going to do is I'm going to drop it and then I'm going to measure a meter later and work out how long it takes to sort of fall that meter. And if it takes a fraction of a second, that's going to give me my speed, my meters per second. But then someone's going to say, well, actually, the object's accelerating. So you've kind of measured this bit, but actually by the time it reached that point, it's actually getting faster. So you might say, okay, what I'm going to do is I'm going to take a smaller measurement. I'm not going to do that big distance.

I'm going to take a smaller distance and then work out how long it takes to go traverse that distance. And by that logic, well, it's still accelerating a bit. So what you want to do is you want to get the distance smaller and smaller until it's essentially almost exactly at the point of the object currently is. And then that's going to give you the most accurate representation of its speed at this point. And that's basically what Newton and Lebanon did. They wrote down the mathematics. They called it infinitesimal calculus. So calculus, the term originally comes from a counting stone.

So you'd use pebbles to count basically. And it's saying we want to count things up at very small increments to work out rates of change. And we want to do that at infinitely small gaps because that's going to give us the most precision for what we care about. So these ideas were kind of developed, but they were all developed very much around the physical world. I mean, Newton classically and Apple was falling that gave him this supposed inspiration. And it was very useful. And it's now, I mean, so John von Neumann, who was this pioneering physicist, he worked on the Manhattan Project,

early pioneer of computing called calculus really the most important development that we had in science because it enabled us to handle all of these aspects of the world and technology and engineering that rely on rates of change and it gave us the tools to do that. But it took a long time to put it on steady ground. Early on, it was very much on that intuitive reasoning about what we saw in the world. And it turned out that infinity does very weird things in certain situations. Like with Xeno and this idea that you can't move because you can't go an infinite number of steps. And although mathematicians had developed some very useful tools,

a lot of these, what became known as monsters were lurking, these weird bits of logic that if you looked at them too closely, actually didn't really make sense and suggested that some of your proven theorems just didn't really follow. And one of the really well-known examples of it was this idea that, say you take a pen on a piece of paper and you draw a line.

The idea was at some point that line has to be kind of smooth, if that makes sense. So you can kind of work out a straight part of that line. You can't have like a constantly jaggedy line because there's always got to be, if you zoom in enough, a little bit of straight. And that was seen as intuitively obvious, basically. And then a mathematician came along and proved that wasn't true, that you could have basically something that's jagged constantly. There's no straight bits at all.

and mathematicians slowly started to realize that a lot of their really deeply held ideas about calculus didn't work. And some some in the existing community said this is just a nuisance, right? You're being difficult. You're ruining a really valuable toolkit. And then a few others started to dig a bit deeper and think, well, actually, maybe we shouldn't rely too much on intuition in these Greek ideas. And a lot of the work Einstein was subsequently due on things like on relativity, on a lot of his work on, atomic physics, relied on these kind of post-monster era of ideas because the world was actually full of things where you can't just assume everything behaves intuitively and smoothly and

smoothly and predictably. And you need a more advanced toolkit to handle that. So kind of sticking with that, how about the notion of randomness? I mean, this is a term that's just thrown around all the time. But, you know, what does it mean? And how can we understand it? That's a really good question. And I think one of the key insights people had, particularly came from biology, was what's known as Brown Emotion Show.

Robert Brown, who was a biologist, was famously studying pollen, moving in water. And it diggled about, if you look at it under a microscope, constantly, but really kind of small movement, constantly, constantly moving. And he initially thought it was some biological properties. We tested lots of other things.

Slightly, he was, it was basically the British Museum, so he even chipped off a chunk of the sphinx and looked at this, but found this, we're just constantly happy if you had these tiny, tiny particles. And he came up with the kind of explanations, maybe it was an atomic thing. He initially thought maybe it was something else was coming off it.

And it was actually, later Einstein showed it, it was atoms bouncing up against something. That's why you constantly see that motion. But it might seem like it's completely random, but there's a structure of the random. So mathematicians often talk about things being stochastic. And it's not just a fancy word for random. When we talk about sticastic, what we mean is we can write down some element of the rules that drive that randomness.

So a classic one is like buses coming along, for example. Buses aren't completely random. The time you'll wait for a bus, there's some randomness. But it's not just a random number. Yeah, there's a process behind it which you can, at least on average, understand. And that was really a lot of these key insights that came through. Initially, Robert Brown's observation, but then Einstein used a lot of these ideas which were effectively the monsters a few decades earlier, these ideas that you had things that

were non-smooth and constantly changing and looked really bizarre to people thinking about the physical world. But actually, if you have something like a bit of pollen and water bouncing around, that constant unpredictable motion, you need to be able to write that down as equation. And actually, the equation that people wrote down now in mathematical finance, it's using epidemiology, because we need a way of handling these kind of processes with randomness, but some underlying rule that drives that. And this opened up this whole new world, essentially by bringing the monsters in from the cold, as it were. So you mentioned their epidemiology. So obviously, we've, a few years ago, we all went through the COVID pandemic.

And I think this really sort of brought statistics and maths to a lot of people's minds. in a way that hadn't previously happened. So we have something called a P value. So what is that? So in traditional statistics, what you basically want to do is guard against coincidence. You don't want just something by chance to happen and you think incorrectly that there's something going on.

So for example, it originated actually the whole study of experiments with arguments over whether someone could tell the difference between a cup of tea that had milk in first or second. And it was a tea room debate in Rothamstead, it's agricultural station. And Mewel Bristol, one of the scientists, said it tastes better if you put the milk in first. And so they wanted to design an experiment that would show whether she was actually telling a tall story or whether that was actually something she could tell. So you don't want to do it with like two cups because it might just by chance you'll get them right. But you don't want to do them with like a thousand cups because you'll be there all week.

So they worked out that if you have eight cups and four of each, and you think about the numbers of combinations, there's actually only a one in 70 chance that should get them all correct. And so that was the sort of early way of thinking about a P value. So P value is the probability you observe an outcome that extreme or more purely by chance. So a low P value suggests that it's unlikely of what you're observing is down to chance effects. So it's becoming statistics, essentially this threshold for the strength of evidence that you had. But one of the challenges, I think we saw this in COVID, is it's almost become a bit dogmatic with this idea of, okay, if the P values below a certain level, that's true. And if it's above a certain level, that's, yeah, so if you're thinking about face masks or something, you know, it's this kind of idea of like, if it's below this, then they work. If it's above it, they don't work.

But of course, going back to the cups of tea, if you'd only done it with four cups and just, you've got them right, what do you conclude? Because it's not strong enough evidence to have a small P value, but maybe there's something going on, maybe we want to investigate further. So let's stick with that, because this is really interesting. How about the notion of proof in scientific studies? What are the gold standards? So a lot of what we try and do in scientific studies is guard against two main types of hours. So one I've talked about is you don't want to think something works when it doesn't. But also, you don't want to think something doesn't work when it does.

So you don't want to design a study that's inconclusive. And this was a big problem during COVID and Ebola in the past, where a lot of treatment studies were set up, and they were just too small. Basically, they were never going to ascertain if that treatment worked. So you're testing on these people, and you're never going to accumulate enough evidence for it to be useful. But the other thing we want to kind of guard against is that we might not balance the groups we look at. It's about 100 years old as a problem.

It's called the fundamental problem of causal inference, which sounds a bit kind of technical, but fundamentally it just says we only get to see one version of reality. That if you take a drug and then we watch what happens to you, we can't rewind history and not give you that drug and then see what happens. We only get to see one version of that reality. And one of the ways that people have got around this is what's known as randomized control trials where we give a drug to one group of people at random and not to another group of people. and then if you look at the difference between those groups,

there's going to be other things in life that affect your health. But because we picked randomly, those other influences, on average, will cancel out between the two groups. And what were we left with, any difference we observe between those groups, on average is going to be the effect of that treatment. So it's an idea that can be traced back right to the kind of medieval Arab world, but it was really consolidated in the 20th century. And it wasn't just because of that statistical property.

it was also because humans can be unreliable, that the first clinical trial was run with randomisation, not just for this statistical balancing property, but also because there was a risk that doctors might give the treatment to someone who looks a bit more ill. And there's a lot of evidence where you had so-called unblinded studies where people knew who was getting it and not, that you'd get this human subconscious bias creeping in.

And so almost the randomisation was to stop humans deceiving themselves as much as just to make the statistics well. Thank you for listening to this episode of Instant Genius, brought to you from the team behind BBC Science Focus. That was Adam Kacharski. To discover more about the topics we've just discussed, check out his latest book, Proof, The Uncertain Science of Uncertainty. If you liked what you just heard, then please do consider subscribing to Instant Genius on your preferred podcast platform. If you'd like to see our guests and presenters speaking in person, then please also check it.

check out our YouTube channel at ScienceFocus. The current issue of BBC Science Focus magazine is out now. Pick up a copy wherever you buy your favourite magazines or download us on your app store of choice. You can also find us on Apple News or online at sciencefocus.com. This podcast is sponsored by Name, Audio and Focal. The texture and emotional depth of music can be lost through digital sources or poor signal.

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