Instant Genius - How to think about uncertainty more scientifically

Episode Date: September 19, 2024

Often, we’ll hear it said that we live in an uncertain world. Upon hearing this, most of us respond, well of course we do. But what does the term uncertainty actually mean when analysed under a scientific lens and how can we think about it more rationally. In this episode, we catch up with Prof Sir David Spiegelhalter, Chair of the Winton Centre for Risk and Evidence Communication in the Centre for Mathematical Sciences at the University of Cambridge, to talk about his new book, The Art of Uncertainty: How to Navigate Chance, Ignorance, Risk and Luck. He tells us how uncertainty essentially comes from our personal relationships with the outside world, how to analyse and express probability more effectively and why philosophers argue that there are several different types of luck. Learn more about your ad choices. Visit podcastchoices.com/adchoices

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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, a BBC science focus. Often we'll hear it said that we live in an uncertain world.

Upon hearing this, most of us will respond, well, of course we do. But what does the term uncertainty actually mean when analysed under a scientific lens, and how can we talk about it more rationally? In this episode, we catch up with Professor Sir David Spiegelhalter, chair of the Winton Centre for Risk and Evidence Communication in the Centre for Mathematical Sciences at the University of Cambridge, to talk about his new book, The Art of Uncertainty, How to Navigate Chance, Ignorance, Risk and Luck. He tells us how uncertainty essentially comes from our personal relationship,

with the outside world, how to analyse and express probability more effectively, and why philosophers argue that there are several different types of luck. So welcome to the podcast. Thanks very much for joining us. Oh, pleasure to be here. So today we're talking about your new book, The Art of Uncertainty, How to Navigate Chance, Ignorance, Risk and Luck. So I think it's safe to say it does what it says on the tin, really. First off, how would you define uncertainty? Yeah, well, I deal with that quite early in the book because I kind of start by saying what it isn't. I don't put in things like, oh, I'm uncertain, you know, which is the best Beatles song, or I'm uncertain what to dinner on the menu, or I'm uncertain whether God exists or not, because that's using uncertainty in the

sense of indecision or just opinion or just, you know, asking questions for which there is no answer. It's definite answer. So I'm a bit narrow. I do define uncertainty as a lack of certainty. You know, I think it's fair enough to restrict it in that way. And certainly meaning it is potentially at least something you could verify in principle. In other words, it's something that if it's in the future, that you could check whether it's right or wrong. If it's a fact about the world, you could at least get a reasonable estimate of it. If it's about something that's happened, you couldn't at least theory find out what actually

happened. It's when you don't know about something that is potentially verifiable. So one thing that I thought was interesting when we're talking about uncertainty, like you say, it boils down to what we do or don't know. But in the book, you make a kind of subtler application of it based on our own personal views. Yeah, this is the major running theme right the way through, that I treat uncertainty. Rather than as being a property of the outside world, I treat it much as our relationship with the outside world. It's a characteristic of our personal lack of knowledge, our ignorance, the fact that we just don't know, where somebody else might

in principle. So uncertainty, the way I usually illustrate it is by taking out a coin and saying, I'm going to flip this, what's the chance is going to come up heads? It's always it's 50-50. And I say, yeah, fine, and then I flip it, and I cover it up and then say, well, what's the probability, you know, this is heads? And they go, yeah, yeah. And, you know, really grudgingly, they might in the end say, 50-50. And I look at it and say, you know, don't show them. And I just say, okay, your probability is different from mine. Your uncertainty is different from mine.

It's in the eye of the observer uncertainty. So sticking with sort of personal approaches then, I say, for example, I'm somebody that doesn't really like surprises. Really? Really? Do you want to know what you're going to have for Christmas? Yeah, I do actually, yeah. When you're reading a whodunit, do you look at the end of the book? Oh, no, I don't do that. Do you watch sports on delays?

And do you want to know the result before it? Do you see it? No, I think you've got me. Do you want to know when you're going to die? If I could tell you, would you want to know? I don't know, because that's the Cyclops sort of thing, isn't it? In the Greek myths, they trade an eye to be able to see the future, but all they find out is when they're going to die.

Oh, wow. It's funny, I always ask audiences that, and usually about 10, 15%, so they would if I could tell them. I then have to admit, I can't tell them. But there is quite a strong characteristic in some people, of uncertainty aversion. And in fact, it can, as I talk about in the book, get to an intolerance of uncertainty, psychological scales, because if you can get high enough on this, it becomes a clinical condition. You have to plan everything. Oh, I know. Do you plan your holidays carefully when you go

before holidays? Do you know what you're going to do each day when you go on holiday? I'm a 50%er. I like to do sort of 50% planning, 50% winging it. Well, I've had to change myself because I was a 100% planner, but my partner is a 0% planner. And so we've had to compromise, but only at about, you know, 10%, I've moved further than she has. So I mentioned there the Greek myths, but there is a very real world example of this, I think, when you're talking about knowing when you're going to die, which is with these new genetic tests for potentially inherited diseases. And I find interesting, a lot of people say, I prefer to be ignorant of that. I'd never take one of those tests. Well, at the point of even if they did take the test,

it still wouldn't tell them very much. I mean, I talk about it. in the book that these personalized polygenic risk scores is usually grossly overclaimed about what they can and they can't predict. All they can do is say that it increases your risk a bit. Now some of them, like the Brackage 2 gene, which I talk about because I got tested for it because I was very anxious about if I did have it passing it onto my daughters. Now, those have a really serious, a big effect. But most of the stuff that you get measured if you do some genetic test, it tells you just that your risk is going to increase a lot, and you get almost exactly the same information from just knowing your family history and your lifestyle and so

on. So they don't actually tell you very certainly don't tell you when you're going to die or anything like that. So the precision of these personalized medical claims, I think it's grossly exaggerated and it's not going to tell you. But I think in a way, so people are quite sensible saying they just don't want to know because it wouldn't tell them very much anyway, and they're likely to get anxious. and the evidence is it doesn't make any difference if you do tell people. People still don't take much notice of it. So let's sort of drill into this a little bit more then. So you specialize in statistics.

So let's have a look at how we can represent or interpret uncertainty. And it comes down in a way to numbers. So how do we do that? Well, in a way in the book, what I do is because I am a statistician, I big up numbers, probabilities essentially. and I big them up as a really important way to communicate uncertainty and understand it. Later on in the book, I relax quite a lot and actually say, you can't put all of this in numbers at all. And the claim that, oh, we can quantify our uncertainties about everything is just wrong.

Or at least you can try it, but I don't know if I wouldn't believe them. So I relax that quite a lot and then try to come to a sort of compromise. But while we're on the first part, which is me saying, yes, you can put probabilities on things. yeah, I really believe that it's important. And I tell a nice story about, she goes back quite a long way to 1961, and the invasion of Cuba after the Castro's revolution organized by CIA,

when they sent an army, a small army of Cuban exiles, into the Bay of Pigs. And Kennedy had to approve this because when it became president, the plot had already been sort of plan. And the military authorities looked at it and said, actually, they did put the number.

They said, it's got about three out of ten chance of success. But when Kennedy was told about that, that was translated into a fair chance. And so he approved it. And afterwards, because why didn't he use a number? You know, they didn't. Why? And everyone has said why. So things have changed when Barack Obama was planning the raid on Abbottabad to kill Osama bin Laden. And they didn't know whether he was there. All the different groups, including a red team that was deliberately set up to look at the counter arguments, gave probabilities that he was there, which ranged from, you know, 40% below 30, 40% up to 70, 80%, and he in the end said, I think it's about 50-50. But they were all, the intelligence agencies now

specialised much more than giving numbers for things. I mean, there's an official scale within the UK intelligence agencies that if they use the word likely, it means between 55 and 75% probability. And they all have to do that. But I've got a mug with the official, UK intelligence scale on it so I can look at it immediately and see that unlikely means between 25% and 35% chance. So this has happened around the world and happened in climate change for IPCC. They've got a scale of probabilities. And so in the book, I give likely, I give six different definitions for likely that have been given by different authorities, but they're all roughly between 50 and 80% something like that, 60 to 80%. So I think this is a real advance, a real

advanced because language alone can be grossly misleading and so putting numbers. And I also in the book give a sort of quiz showing that we can also put probabilities on our own ignorance where I ask you questions, what is taller the shard or the Eiffel Tower or something like that? And you have to say, well, you know, I hope they're quite difficult because I don't want people to know. But then I want people to say, which one do they think it is? And how confident in their answer. And others, what's the probability they think they're right? And then with a sort of scoring rule, a very specially designed scoring rule, you can assess a good your probabilities were. And so the whole running theme is that we shouldn't, when we're

making judgments, when we're making predictions, we shouldn't say what we think is going to happen, whether it's a football result or climate change or anything. This is ridiculous. We should be giving probabilities for everything. And that allows us then to score these proletes how good they are. And that's the whole basis for, for example, super forecasters who aren't judged by how well they can predict what's going to happen. They're judged by how good their probabilities are about what's going to happen. It's peak pollination season, and my business is scaling fast. To keep the nectar flowing, I need a phone plan with top priority data speeds. That's why I chose GoogleFi wireless.

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So let's shift gears slightly then. So we're a science brand. So let's have a look at uncertainty in science. So I don't really bother doing this anymore, but I've had lots of conversations in the past where it will come up and I'll say, I believe in the Western scientific method of discovery, analysis, through theory, and experiment. And then somebody comes back to me and says, well, why do scientists get so many things wrong then? So what are they missing there? Yeah, I think another thing I'd do in the book, which I find fascinating is look at, for example,

estimates of the speed of light through history. And there's been some excellent, you know, amazingly good experiments that have done where people give an estimate that's really, at an absolute level, quite close. But then what they do is put some sort of uncertainty band about that, which doesn't include the true value. And this happened again and again that people make these estimates work out their uncertainty, and they don't include the true value. In other words, they hugely overestimate the precision, the confidence of their conclusions. And they should be warned about this.

So I would say, I don't see that science gets things necessarily wrong, it just can be too confident. and it can be too confident, partly because of the statistical methods being used, which I'm a statistician. So I feel very strongly about that getting the uncertainty right is as important as the estimate that you give. An example in the book, during the COVID pandemic, we're all obsessed by this R number, the average number of people that someone would infect. And this was estimated all the time. And there were 14 different models.

There are eight different teams and 14 different models being used in the UK. to estimate this. This is great. And they published all their results. And they all had an estimate in an interval. And often the intervals don't even overlap, which means they can't all be right. And then they take a sort of average. And that's what was given to us over the news. But they published, I think, blessed them, all these individual results. And I think it's incredibly valuable. And it shows this is the scientific method of doing your best to understand something and doing your best sort of statistical modeling. But admitting that you might be. wrong. And so you have a group idea. You're self-critical. You are praising your results in comparison

with everybody else and you have to be prepared to give them up on receipt of new information. So that whole idea of learning and changing your mind, I got an integral part in this. Oh, can I tell you the story in the book about Cromwell's Law? Because this is the crucial thing about the scientific method. Because what you were describing are people who are so fixed in their mind. do they really believe something? And then something comes along that proves them wrong. Well, this is, you don't want this to happen. This is really embarrassing and humiliating,

which is partly why physicists demand such enormous levels of evidence before they conclude that the Higgs boson exists or something like that, because, you know, when they declared that they had neutrinos going faster than light, and then, of course, had it then showed inevitably that this was due to a experimental error in the apparatus. This is embarrassing. This does not do the subject any good at all. So Cromwell's Law dates from the 17th century from Oliver Cromwell. And he was invading Scotland because they were going to support the return of Charles II.

And he knew he was stronger than them. And he wrote to the Church of Scotland, the Kirk, to say, tell them to give up. You know, I beseech thee in the bowels of Christ. Think it possible you may be mistaken. And of course they didn't because they were so stubborn. And he beat them at the Battle of Dunbar. But he was just appealing to them to have the humility, to have that little tiny piece of doubt about their opinions. And I show in the book that if you do keep just a little bit

of doubt about your assumptions, then as soon as new evidence comes along, you very quickly, mathematically, using Bayes theorem, you very quickly shift into this new way of thinking. But you have to have this element of doubt. So Cromwell's rule is to say that unless something is absolutely logically impossible, you can actually logically prove something isn't the case. You should give a little smidgen of probability do absolutely everything that might occur. And then you can respond very quickly. Yeah, so you mentioned their base theorem. I think this is something that's talked about quite a lot. Could you sort of give us a cliff's notes version of what that is? Yeah, it's just the rule of probability that says how you should update your beliefs on the receipt of new evidence.

It's very simple consequence of the basic rules of probability that, you know, show in the book, you can derive very simply, you know, very intuitive. So it's a simple formula, and it just says that provided that you haven't ruled something out right from the beginning, how your belief in that should change on receipt of new evidence. And the thing that tells you how much you should change your belief is the likelihood ratio, what's known as the likelihood ratio. And this is what's used in criminal cases for DNA and other forensic evidence. Because the likelihood ratio is the probability of the evidence, like the DNA specimen, given the prosecution's argument that the person was there, divided by the probability of the evidence given the defense argument.

But they weren't there. And that likelihood ratio then summarizes the probative value, as it's known, or the weight of evidence, that this piece of forensic information, can contribute to discriminating between the two claims. I think it's pretty basic math. And yet it is absolutely fundamental. And I argue it's fundamental to Alan Turing's work, breaking the Enigma Codes in Second World War. It's fundamental to criminal trials, fundamental to just pretty well everything. Yeah, so let's shift gears again then, and something that you talk about, which, I mean, you've caught me out once already, so maybe I shouldn't say this. But when we're talking about

luck, I would say, well, I don't believe in luck. But as an example, example, so I, more than 20 years ago, met my wife in Japan, who is from London originally. I'm from the Midlands, middle of England. And whenever I say that to people, they say, whoa, what are the chances of that? And I inevitably reply, yeah, I guess I was just lucky. Yeah. Well, you've got to meet your wife somewhere. I mean, I talk about Ed Smith, the test cricket, he met his wife on a train. I mean, he's written a whole book on luck. So he's really studied it in sport. I think I would call that circumstantial luck, in a sense. You've been at the right place at the right time.

But then you had to talk to her because who knows? I shouldn't say it. You might have sat next to someone better on the plane. No, no, certainly not. Obviously, obviously, they may complete the right choice. But we do ascribe retrospectively to this magic luck, things that have gone the way we wanted them to, or alternatively, not got the way we wanted to do.

So it's a phrase, I think we just apply to things that have happened to express whether they turned out fortunately or not. But I got fascinated by this and got really interested. In fact, the philosophers have identified different types of luck. Because what they think about luck is when things happen to you that may be good or bad, which are totally outside your control, over which you can not claim any influence whatsoever. And the three types they identify are, I'll start in the first. the most important, constitutive luck. Who you're born as. You know, the time of history, the place you are in the world, your parents, your genes, your background, everything for the moment of

your birth that actually predetermines vast amounts of your life. We grossly overestimate the influence we personally have and the control we have in our lives. So much is determined by the moment you're born and all those things that come with that. So, and the, Then there's a nice and circumstantial luck, which I mentioned, which is being at the right place and the right time or being at the wrong place at the wrong time. I give in my book, you know, my grandfather who has had the bad constitutive luck of being born just in time to become a young man in the First World War. And then he had the terrible circumstantial luck of being brigade gas officer in the EPR section just after the Battle of Passiondale where he had to walk around inspecting the gas facilities in the front line trenches. And apps must have had a minimal life expectancy. And then three weeks into the job, he got blown up.

So that's pretty bad circumstantial luck. But the third type of luck is outcome luck or result of luck, which is just how things, that particular event works out for you at that time and place. And he survived. And not he survived, but he because he got put onto out of frontline duties declared B2 and therefore missed his battalion being sent to the Somme, which then turned out to be the worst section to be in in 1918. So he had enormous luck.

And of course, otherwise I wouldn't be here. So his luck was my luck or whatever. But there's all sorts of things. The bizariness of us all being born is just too ridiculous for words. None of us should be here because of the odd chain of events that gave rise to each of us. So I find those are quite useful ways to take apart when someone says, oh, I was lucky. And so, you know, in which way were you lucky? So also in the book you mentioned Daniel Kahneman's idea of thinking fast and slow.

Yeah. So what's that and how can that help us when we're facing uncertainty? Yeah, I like the day. I mean, it's a very basic idea that we've got two modes. We can change very simplistic, I suppose, but we've got two modes which you can think. One is fast, just a gut reaction, working completely on automatic processes. And that's how we deal with uncertainty most of the time. We quite reasonably risk.

We know when we use cycle around, when we cross the road, when we make judgment, We're doing it all the time really fast, and that's just fine. Works most of the time. We just make our gut-feeling judgments. But sometimes, especially if you're a politician making policies or you're kind of got to make important decisions, which might be about your health care or taking a job or something really important, maybe we just, a whole book is about slowing down, slowing down and deconstructing the problem, just thinking. it through. You may end up doing exactly what your gut feeling was, but maybe you won't. Maybe you'll open yourself up to new possibilities. And that deconstruction consists of, you know, working out, you know, what are the options? What are the choices? What are you trying to do?

And then looking at what are the possible outcomes? And this is the trickiest bit, really, because you have to think of what are the possible futures. For that you need an imagination. I'm hopeless. I've got no imagination. Zero. And so that's where this idea of a red teaming comes in. It's so important to have groups of people who think differently. They think out of the box. They avoid group think. And as I mentioned in the book, the Ministry of Defense has been really big on red team. They've written hold guidance on it and developing a red team mindset, even for individuals, always trying to think outside the box. And that's really what we're trying to do by that is not to be caught out by Donald Rumsfeld's unknown unknowns. We're trying to shift

those unknown, the things we never even thought of into known unknowns, or at least sort of possibly envisaged. We can never do it completely. Black swans will always come along at some point. But we're trying to turn stuff, trying to avoid that by having imagination, thinking of the worst that could happen, and then going beyond. And dealing with awkward people who just think of stuff that you never even thought of. As I said, I'm hopeless at it.

But that's why you should ask people with different, say you know, just for your own personal decision to talk to other people because they may bring something completely new to the problem. So let's have a look at predicting future events then, be it the pandemic, be it a natural disaster. You know, what are the sort of thorns around that issue? I mean, the standard thing is, oh, you think of what might happen and you give them probabilities and that works out what the overall risk or profile is and then you do your best to mitigate those risks. I mean, we all had to fill in risk registers for, you know, risk matrices or something. the jobs or even if you're organizing the school fate, you have to do, you know, risk

some of it, et cetera, et cetera. So that's the standard of the program, which works just fine, except when you're dealing with massive things like the potential pandemic. And I deal in some detail about there's a national risk register in this country, which is published and which I've done some work on. But sort of mistakes they've made, the 2010 Icelandic volcano eruption, which closed down airspace, wasn't on the risk register. People had had suggested it might, perhaps it should be on.

on there. No planning whatsoever. It's now on there. And other things like COVID, the fact that pre-19 risk registered, the last one before the pandemic, flu was up there as the biggest option. But, you know, emergent diseases like SARS and MERS and things like that were way down. Oh, they could possibly kill 200 people. What? 200,000 people died. So it was a complete misjudgment of alternatives to flu. And that was there in black. black and white on the risk register. I'm not saying I would have done any better. Sorry, I first thing is I say, I'm not claiming I knew better or would have done any better. Sure. So in the book, you mentioned the tolerability of risk framework. So what is that?

I love this. I love trying to promote this. It's been around for ages. It's the whole basis for health and safety legislation in this country. You know, health and safety has got a, you know, big people with geogal health and safety. It's saved vast amounts. lives. And the framework which was developed, you know, decades ago, it never talks about, although it's called health and safety, it never talks about safety. It never makes any claim anything's ever going to be safe, which I think is really good. You don't look at making things safe. This is nonsense. You try to ensure that at an acceptable level of risk, at which point there's no point in trying to mitigate it any further. So, for example, if you've got a one and a million

chance of being killed at work during a year, and it's less than that, that's an acceptable level risk, if you try to make that even lower, it would just be ridiculous. But then what you do, you don't say anything above that acceptable is unacceptable. You've got another level at much higher, in fact, a thousand times higher in this case, that a one in a thousand chance of being killed at work is an unacceptable, an intolerable level of risk. And it must be reduced below that. And that tends to be commercial fishermen, coal miners and things like that. And in between, you've got this region called the Alarp region, where you try to make, which is as low as reasonably practicable, where you should be, within that reason, you should be trying to reduce

the risk all the time to this aspirational, acceptable level. But you've got to look at the proportionality, the cost, if it's really going to be a unreasonable amount to do that, that's okay. So you just do it, you know, you have to make a judgment there. The crucial thing is that there's two levels. There is a dangerous level, and then there's an acceptable level, and then a gap in between. and I just wish that that was used more widely and all the advice were given about drinking, about all the stuff, because otherwise it gives it, at a moment,

I think the UK alcohol guidelines of 40 units a week are quite reasonable. There's a low risk level. I think I fully support them. But they can give the idea that anything above that is somehow dangerous. And in fact, the risk associated with alcohol increases really quite slowly after it does go up from there, definitely.

There's no doubt it goes up after that. But quite slowly. But once you're really swilling it down, it's going to be very high risk. So I kind of really like this idea of two levels of risk, and that's the tolerability of risk framework. Thank you for listening to this episode of Instant Genius, brought to you from the team behind BBC Science Focus. That was Professor Sir David Spiegelhalter. To discover more about the topics we've just discussed, check out his book, The Art of Uncertainty,

how to navigate chance, ignorance, risk and luck. If you liked what you just heard, then please do consider subscribing to Instant Genius on your preferred podcast platform and leaving us a review. 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 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.

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