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On August 29th, Sauron has returned. Prime Video invites you to return to Middle-earth for the epic new season. Sauron will fall. You can't kill me. War is coming to Middle-earth.

I will not stop until he is destroyed. Every soul is in peril. Shall we begin? The Lord of the Rings. The Rings of Power. New season, August 29th. Only on Prime Video. As the night draws in and the fire blazes on the hearth, we warn the children by telling them stories. The Little Mermaid warns them, he's just not worth it, sister. My stories are for the education of the grown-ups.

And my stories are all true. I'm Tim Harford. Gather close and listen to my cautionary tales. Two and a half thousand years ago, King Croesus of Lydia ruled a mighty empire. Lydia had endured for more than six centuries in the lands we now call Turkey.

Croesus was legendarily wealthy, yet he felt threatened by the growing strength of the first Persian empire on his borders. What should Croesus do? Should he strike against the Persians in an attempt to seize their lands and destroy their power? Or should he aim for a peaceful trading relationship? King Croesus yearned for something we've all wanted from time to time, to see into the future.

And this being the ancient world, that desire could be satisfied. Croesus could consult an oracle. That meant travelling to a temple, making an offering and asking the advice of a god. The most famous oracle was at Delphi in the heart of ancient Greece, where the god Apollo would possess the temple's appointed priestess and give divine answers to the questions asked of her.

Croesus had tested many oracles. As the Greek historian Herodotus tells it, Croesus sent messengers to far-flung temples, asking each oracle what the king was doing on a particular date. What he was actually doing was, frankly, unguessable. Boiling a stew of lamb and tortoise in a bronze cauldron.

The messengers returned from each oracle, and when Croesus heard the pronouncement from Delphi, which was correct in every detail, he bowed his head in respect. Truly, the priestess at Delphi spoke with the voice of Apollo. And so Croesus asked, Should I seek war with the Persian Empire?

"If King Croesus attacks the Persians, he shall destroy a mighty empire." "And how long shall my kingdom endure?" "Till the time shall come when a mule is monarch of Persia." The kingdom of Lydia then would last forever, since the Persian Empire would never be ruled by a half-breed animal. The Persian Empire, in any case, was destined to be destroyed by King Croesus himself.

So the oracle foretold. And since the oracle guaranteed victory, Croesus attacked and was defeated. Croesus was the last king of Lydia. He was vanquished by the Persian king Cyrus, whose complex heritage apparently qualified him as a mule in the eyes of the oracle. Croesus had indeed destroyed a mighty empire, his own. It's not easy to see into the future.

But the tale of King Croesus tells us that even when we do see the future, that doesn't guarantee we'll make wise decisions in the present. In the modern world, we have our own oracles, and they too tell us what the future holds. We call them by mysterious names, such as Alexa, Google and Siri. And we need to think much harder about what those oracles are telling us. Settle back and listen to another story.

Cautionary tale. August 2009. Death Valley, California. One of the hottest places on earth. National Park ranger Amber Natras has been following the tracks of a car along a rough country trail that's barely a road at all. The tracks shouldn't be there.

The road has fallen into disrepair and been covered by the shifting sands of the Mojave Desert. In fact, the route is officially closed. The closure marked by small rocks and bushes laid across the road. But the tracks go straight through those slight barriers. Then, Ranger Natras sees the Jeep. It's up to its axles in soft sand. It has SOS spelled out in medical tape on the windshield.

and there's someone lying beside it in the 115 degree shade. Are you okay? Ranger Natras asks. The prone figure scrambles to her feet. She's alive. Her tongue is swollen. Her lips are bleeding and blistered. She's not okay. She's not okay at all. Alicia Sanchez and her six-year-old son, Carlos, had been stuck in the sand and the heat for five days. Carlos hadn't made it.

He'd drifted away, telling his mother that he'd been speaking to his grandfather in heaven. How did a young mother and her son end up so terribly, fatally lost? They'd been relying on the directions of a dashboard computer. Rangers in Death Valley National Park have a phrase for it. Death by GPS. There was probably a point where she said...

People are so reliant on their GPS that they fail to look out the windshield and make wise decisions based on what they're seeing. Many of us have done the same thing that got Alicia Sanchez stranded in Death Valley. We've relied on GPS, only to find ourselves lost in one way or another. I know I have.

Once I'd typed in the wrong address. Another time the route was blocked. More than once I've just lost the signal. And because I've relied on the computer's guidance, I've been helpless. I've just never been so cruelly punished for my mistake. The story of Croesus and the Oracle is the last and most ancient cautionary tale in our series.

But it holds a very modern lesson for us. I think it teaches us what might go wrong when we ask computers to predict the future for us. Most of the economic forecasts we see are made by computers. So are the weather forecasts. And so are many computerised decisions that we don't even think of as forecasts. Such as when an algorithm recommends who should get a mortgage approved and who shouldn't. Or even which criminal suspects should get bail.

When you ask a GPS system or your phone to plot you a route, that's a forecast too. The computer makes a prediction of which roads are open based on a map database that may or may not be accurate. It then unleashes an algorithm to forecast which route through that map will be the swiftest. If the map is wrong, the prediction will be wrong too. But even when the prediction is right, you may still end up far from where you wanted to be.

Ponder the predicament of a Swedish couple on holiday in Italy. They went to the tourist office in the small town of Carpi, near Bologna, in the industrial north of Italy, and asked for directions. Which way is it to the Grotta Azzurra, please? Grotta Azzurra? Sorry?

The Blue Grotto is a sea cave. Yes, the Blue Grotto, exactly. But the Blue Grotto is in Capri. We are in Carpi. Instead of driving four hours south from Rome to the beautiful island of Capri, they had driven four hours north to Carpi, where they were about as far away from the sea as it's possible for a little Italian town to be.

It's hard to understand how they managed it. I mean, Capri is an island. Well, yes, but it's not hard to understand at all, is it? It was a typo. A typo that meant a long drive in exactly the wrong direction. Compared to the suffering of Alicia and Carlos Sanchez, that was a small enough misadventure.

If the Swedish tourists had known anything about which cities in Italy are north of Rome and which lie south, or had checked a map or a compass, then they would never have made the mistake. But why would they have done any of that? They'd asked their GPS to take them to Carpi. And it did. Just like the Oracle of Delphi, it produced exactly the right answer. And just like Croesus, they acted on that answer without pausing to think.

The concerns of King Croesus two and a half thousand years ago may seem very different from our problems today as we type an address into a GPS or check the weather forecast, but they really aren't. Oracles, like computer algorithms, are mysterious black boxes. We ask them questions about the future, we receive answers, and then we have to work out what those answers mean.

There's a fierce debate raging about the use of algorithmic predictions. How can we trust a computer to decide whether a criminal is at high risk of reoffending or whether a teacher is promoted or fired? That debate tends to focus on whether the algorithms deliver predictions that are fair and accurate. Which, of course, is an important question. But it leaves out a point that we tend to overlook. A point that is the lesson of our cautionary tale.

Just because you get a good forecast doesn't mean you're guaranteed to make a good decision. After all, the oracle at Delphi told King Croesus the truth about the future. The truth didn't help him. And the GPS that delivered the Swedish tourists to Carpi also gave the correct answer to the question they'd asked. They'd still have been much better off if they'd used a roadmap. And as for Alicia Sanchez...

We don't know whether her GPS had an outdated map or an intermittent signal, or maybe it worked fine and she made some trivial mistake in the way she used it. What we do know is that she didn't have a map, and she didn't stop when she got to the barrier of stones that was supposed to show the road was closed. Trusting the GPS had truly awful consequences.

A good forecaster can lull you into believing it's infallible, creating a crisis when it fails. Or it can give you an accurate answer that you misunderstand, perhaps because you don't know what you've really asked. One of the gurus of futurology was a French economist called Pierre Wack. He once wrote, "Forecasts are not always wrong. More often than not, they can be reasonably accurate, and that is what makes them so dangerous."

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I don't want to suggest that computers always produce good forecasts. In fact, behind the scenes, a mathematical algorithm was responsible for what I think has a strong claim to being the worst forecast anyone has ever made.

It's August 2007, the early days of the great financial crisis. An insurance executive called Joseph Cassano is trying to reassure the world that his company, AIG, is doing just fine.

You might remember AIG from our episode about giving the Oscar to the wrong movie. AIG was an insurance company at the epicentre of the financial crisis. It had been writing contract after contract, insuring other companies against debts not being repaid. It's hard for us, without being flippant, to see a scenario within any kind of realm of reason that would see us losing one dollar in any of those transactions.

Not a single dollar. Not in any conceivable scenario. Eighteen months later, AIG announced that it had lost more than $60 billion in a single quarter. What on earth had happened? Simple. AIG had wagered billions, no, trillions, on the financial markets equivalent of a GPS. And the GPS had led it astray.

The financial GPS was a mathematical formula that attempted to forecast the risk that two bad things happen together. Let me take a moment to explain. Let's say I lend money to two businesses. I hope that they're both going to pay me back, but they might not. One of them might default and not repay the loan. Both of them might default. So here's a question: what's the chance that the second one defaults, given that the first one does?

It's a subtle question. If one business is a food truck in Cancun and the other is a food truck in Amsterdam, their fates are presumably totally unrelated. If you're trying to figure out whether the food truck in Amsterdam will fail to pay back the loan, the fate of the truck in Cancun is irrelevant. The technical term for this is that they're uncorrelated.

But if the food trucks are in the same city, their fates might be linked. They both have to deal with the same local economy, the same licenses and the same weather. If a big local business closes, that's bad for both of them.

If so, their fates are correlated. What happens to one is likely to happen to the other. But even then, the link between the two isn't obvious. If one truck gets bad reviews or is shut down for hygiene violations, maybe that's good news for the other truck. One truck going bankrupt might make the other truck less likely to go bankrupt.

If so, their fates are negatively correlated. What happens to one is less likely to happen to the other. If you're on Wall Street, it's important to figure out whether loans are positively correlated, negatively correlated or uncorrelated. One of the things that Wall Street likes to do is build big financial structures out of these individual loans. How safe the financial structure is depends a lot on these correlations.

If they're all highly correlated, then either none of them are going to go bad, or they all are. That's a lot of risk. But if they're uncorrelated, or even negatively correlated, then I can pretty much guarantee that when some go bad, the others will be fine. Predicting the correlation tells you all you need to know about predicting the risk.

Given how useful it is to predict the correlation between loans, Wall Street's finest mathematicians, often dubbed the quants, turned to the challenge about two decades ago. They deployed a formula known as the Gaussian Copula Function.

You don't need to know what the Gaussian Copula function actually is, just that it's a way of predicting correlations automatically. Plug your historical data into a computer and out comes the prediction. It's the financial GPS. And that financial GPS, the Gaussian Copula function, is now commonly described in the business press as the formula that destroyed Wall Street in the great financial crisis of 2008.

The problem wasn't just that the formula gave the wrong answer, although it did. The problem was that AIG and other big Wall Street institutions had bet everything, absolutely everything, on the assumption that the formula couldn't be wrong. That was like trusting a GPS in Death Valley. It's fine, until it isn't. And then you're in terrible, terrible trouble.

When people trusted the Gaussian copula function, they didn't realise that they were making a knife-edge bet. If the copula function produced the right prediction, you could bet a billion dollars and be absolutely certain that you wouldn't lose anything, not a cent.

And if the copula function produced the wrong prediction, you could lose absolutely everything. It's hard for us, without being flippant, to see a scenario within any kind of realm of reason that would see us losing $1 in any of those transactions. $60 billion, Joe Cassano. $60 billion. And if you're confident that this sort of thing isn't still happening in the financial system...

You're more confident than I am. Before you declare war on the Persian Empire, or drive into Death Valley, or bet trillions on a mathematical function you don't really understand, how about this? Stop and think. Think hard. Don't just trust what comes out of the black box, whether that black box is a priestess possessed by Apollo, or a GPS-enabled device, or a financial spreadsheet.

Stopping and thinking is what most people did in ancient Greece. Esther Aydinow is a professor of ancient history who studies what oracles did and what they meant to the Greeks. She says that people would prepare diligently before they asked for divine advice. They'd phrase their questions carefully. They'd think about different possibilities. They'd ponder the meaning of the answer.

In 2008, a group of Japanese researchers, led by Professor Toro Ishikawa, ran an experiment to test what GPS does to our capacity to notice the world around us. They directed people on a route through Kashiwa, a small city near Tokyo.

Some of the experimental subjects, chosen at random, had first been taken on the route by a guide. Others had been asked to follow the route on a paper map, and others had GPS guidance instead. After walking the route, everyone was asked to do it all again, this time without help. The ones who'd followed a guide or used a map generally managed this task just fine.

The ones who had used GPS had a hard time of it. They stopped more often, walked more slowly and rated the task as more difficult. The GPS may have gotten them around first time, but it hadn't got them to engage with the world at all. They didn't pay attention because they didn't have to. And then they regretted it. An automated decision doesn't have to work like that.

In the mid-1980s, a group of British doctors and medical statisticians carried out an intriguing experiment. They wanted to test out a computerised diagnostic system for patients suffering acute abdominal pain. Such pain could have a lot of different causes. An ulcer, a kidney infection, a heart attack, appendicitis, even an ectopic pregnancy. And that means a lot of different possible treatments. So, getting the diagnosis right...

really matters. This being the 1980s, the computers in question were old school. Apple IIe's big beige plastic bricks with 64k of memory and software that you loaded using a five and a quarter inch floppy disk. A cheap cell phone today could easily offer a million times more computing power.

The doctor, or perhaps a medical assistant, would type away on the clunky keys, laboriously entering data into the computer and ticking yes-no boxes using the cursor. No mouse or touchscreen, obviously. This diagnostic system wasn't bad. It wasn't particularly good, either. It took a lot of effort to use, and it only gave the correct diagnosis two-thirds of the time. But yet, it was a huge success.

The proportion of patients who died fell by more than 20%. The number of cases in which a serious medical error was made from about 9 in 1,000 to just 2 in 1,000. There was a huge drop in unnecessary surgeries. Why? Given that the computer diagnosis wasn't all that good.

Simple. The computer prompted the doctors to stop and think, to work through different possibilities rather than to leap to the most obvious answer. It was like the opposite of the GPSs used to navigate around Kashiwa City, which were effortless and let people switch off. The computer diagnostic was anything but effortless, and it got the doctors to switch on.

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And then he was on the bike and ready to ride. The bike looks great and with the SureStop braking system it brakes quickly and safely without locking the front wheel and sending you over the handlebars. Guardian bikes offer a 365-day money-back guarantee covering returns, repairs and spare parts. Join hundreds of thousands of happy families by getting a Guardian bike today.

Visit GuardianBikes.com to save up to 25% off bikes. No code needed. Plus, receive a free bike lock and pump with your first purchase after signing up for the newsletter. That's GuardianBikes.com. Happy riding! If you're listening to this right now, you probably like to stay on top of things, which is why I want to mention The Economist. Today, the world seems to be moving faster than ever. Climate and economics, politics and culture, science and technology, wherever you look,

Events are unfolding quickly, but now you can save 20% off an annual subscription to The Economist so you won't miss a thing. The Economist broadens your perspective with fact-checked, rigorous reporting and analysis. It's journalism you can truly trust. There is a lot going on these days, but with 20% off, you get access to in-depth, independent coverage of world events through podcasts, webinars, expert analysis and even their extensive archives. So where

Whether you want to catch up on current events or dive deeper into specific issues, The Economist delivers global perspectives with distinctive clarity. Just to give an example, What's Next for Amazon as it turns 30? analyzes how Amazon's fourth decade looks like an area of integration for the company. Go beyond the headlines with The Economist. Save 20% for a limited time on an annual subscription. Go to economist.com and subscribe today.

It's easy to move through the world without really thinking. And usually that's fine. It would be exhausting to have to think about everything we do every time we do it. But sometimes being prodded to stop and think can make you realise something important. I don't want to get too meta here, but let's stop and think for a moment about stopping and thinking.

There's a beautiful little experiment about what we do and don't notice. It was conducted by two psychologists, Leonard Rosenblit and Frank Kyle, who gave their experimental subjects a simple task. Here's a list of everyday objects. As you'll see, there's a flush laboratory, a zip fastener, and several others. I'd just like you to rate your understanding of each object on a scale of 1 to 7.

But after people had written down their ratings, the researchers would launch a gentle but devastating ambush. I see you've rated your knowledge of the flush lavatory at 6 out of 7. That's great. Here's a pen and a piece of paper. Please would you write out your explanation in as much detail as possible? Feel free to use diagrams. That sometimes helps. Ah, not so easy now, is it?

And it wasn't that people had been lying to the researchers. They'd been lying to themselves. They felt they understood zippers and lavatories, but when invited to elaborate, they realised they didn't understand at all. Rosenblatt and Kyle called this the illusion of explanatory depth. And when people were asked to reconsider their previous 1 to 7 rating, they marked themselves down, acknowledging that their knowledge had been shallower than they'd realised.

What King Croesus really needed was someone to gently ask him what exactly did he think the oracle might have meant? This research is about more than zippers. It might even offer a way to make our political discourse less polarised and bitterly partisan. How?

Well, other researchers have adapted the flush lavatory question to ask about policies such as a cap-and-trade system for carbon emissions or a proposal to impose unilateral sanctions on Iran. The researchers, importantly, didn't ask people whether they were in favour or against these policies. They just asked them the same simple question. I'd just like you to rate your understanding on a scale of 1 to 7.

And the same thing happened. People said, yes, they basically understood these policies fairly well. Then, when prompted to explain, the illusion faded. They realised that perhaps they didn't really understand at all. Another thing that faded?

political polarisation. People who would have instinctively described their political opponents as wicked and who would have gone to the barricades to defend their own ideas tended to be less strident when forced to admit to themselves that they didn't really understand what it was that they were so passionate about in the first place. It's a rather beautiful discovery.

In a world where so many people seem to hold extreme views with strident certainty, you can deflate someone's overconfidence and moderate their politics simply by asking them to explain the details. Whether we're asking people to walk through a city in Japan or talk about their political differences, it really helps to call their attention to what they're actually doing.

Asking the oracle or the computer might give us a better prediction, but it discourages us from thinking hard about the world around us. And that's not something we should be giving up lightly. Sometimes it's not the forecast that matters. It's whether that forecast helps you think harder or encourages you to stop thinking altogether.

Nearly 70 years after the fall of King Croesus, another great civilization was at war with the Persians.

An alliance of Greek city-states faced an invasion by a vast Persian army and turned once again the Delphic Oracle for advice. Ambassadors from Athens received the following prophecy, which didn't sound encouraging. Wretches, why sit ye here? Fly, fly to the ends of creation.

All, all ruined and lost. Lo, from the high roofs trickle of black blood, sign prophetic of hard distresses impending. Get ye away from the temple and brood on the ills that await ye. The ambassadors were dismayed. They couldn't go back to Athens with that. And so they asked the Delphic Oracle for another answer.

The second prophecy was vivid but confusing and included some lines that hinted at safety. "Safe shall the wooden wall continue for thee and thy children. Wait not the tramp of the horse nor the footman mightily moving over the land, but turn your back to the foe and retire ye. Yet shall a day arrive when ye shall meet him in battle.

When this message was brought back to Athens, it was the subject of heated debate. What did the oracle mean? Different factions saw different meanings and made different arguments. The oracle mentioned a battle at Holy Salamis, an island near the coast of Athens, where many men would perish. That didn't sound good. But maybe that was King Croesus' error in reverse. Maybe the men who would die would be the Persian invaders.

I realise this all sounds absurd to modern ears. Poetic and completely ambiguous predictions from a Greek god possessing a young priestess. But the Athenians did what we should still be doing when faced with any forecast. They discussed and debated. They asked, what does this really mean? Are we sure? How seriously should we take it? And what are we going to do about it?

The Athenian general Themistocles successfully argued that the wooden wall referred to the Greek navy and the Greeks should seek a sea battle. They did and destroyed the large Persian fleet at Salamis. It's a strange old story about a very different culture, but we could learn from it.

While we humans might not be very good at seeing into the future, thinking seriously about what the future holds might just make us slightly better humans. If you've been with me for the entire first season of Cautionary Tales, thank you.

You'll have heard what airships teach us about the downsides of competition, what an apocalyptic cult shows us about changing our minds, and what a charismatic con artist tells us about the power of persuasion, one small step at a time. I hope that my strange stories have made you wiser, and I hope that they've been fun to listen to. I've certainly enjoyed making them.

Thanks again for joining me. Please tell your friends. I hope to be back with a second season of Cautionary Tales before long. There is, alas, no shortage of calamities from which we can all learn. Cautionary Tales is written and presented by me, Tim Harford. Our producers are Ryan Dilley and Marilyn Rust. The sound designer and mixer was Pascal Wise, who also composed the amazing music.

This season stars Alan Cumming, Archie Panchabi, Toby Stephens and Russell Tovey, with Enzo Cellenti, Ed Gochan, Melanie Gutteridge, Masaya Munro, Rufus Wright and introducing Malcolm Gladwell. Thanks to the team at Pushkin Industries, Julia Barton, Heather Fane, Mia Lebel, Carly Migliori, Jacob Weisberg and of course, the mighty Malcolm Gladwell. And thanks to my colleagues at the Financial Times.

I'm Malcolm Gladwell, and I'd like to take a moment to talk about an amazing new podcast I'm hosting called Medal of Honor. It's a moving podcast series celebrating the untold stories of those who protect our country. And it's brought to you by LifeLock, the leader in identity theft protection. Your personal info is in a lot of places that can accidentally expose you to identity theft.

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