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What would happen if GPS - the Global Positioning System - stopped working?

For a start, we would all have to engage our brains and pay attention to the world around us when getting from A to B. Perhaps this would be no bad thing: we'd be less likely to drive into rivers or over cliffs through misplaced trust in our navigation devices.

Pick your own favourite story about the kind of idiocy only GPS can enable. Mine is the Swedish couple who misspelled the Italian island of Capri and turned up hundreds of miles away in Carpi, asking where the sea was.

But these are the exceptions.

Devices that use GPS usually stop us getting lost. If it failed, the roads would be clogged with drivers slowing to peer at signs or stopping to consult maps. If your commute involves a train, there'd be no information boards to tell you when to expect the next arrival.

Phone for a taxi, and you'd find a harassed operator trying to keep track of her fleet by calling the drivers. Open the Uber app, and - well, you get the picture.

With no GPS, emergency services would start struggling: operators wouldn't be able to locate callers from their phone signal, or identify the nearest ambulance or police car.

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There would be snarl-ups at ports: container cranes need GPS to unload ships.

Gaps could appear on supermarket shelves as "just-in-time" logistics systems judder to a halt. Factories could stand idle because their inputs didn't arrive just in time either.

Farming, construction, fishing, surveying - these are other industries mentioned by a UK government report that pegs the cost of GPS going down at about $1bn (£820m) a day for the first five days.

If it lasted much longer, we might start worrying about the resilience of a whole load of other systems that might not have occurred to you if you think of GPS as a location service.

It is that, but it's also a time service.

50 Things That Made the Modern Economy highlights the inventions, ideas and innovations that helped create the economic world.

It is broadcast on the BBC World Service. You can find more information about the programme's sources and listen to all the episodes online or subscribe to the programme podcast.

GPS consists of 24 satellites that all carry clocks synchronised to an extreme degree of precision.

When your smartphone uses GPS to locate you on a map, it's picking up signals from some of those satellites - and it's making calculations based on the time the signal was sent and where the satellite was.

If the clocks on those satellites stray by a thousandth of a second, you'll mislay yourself by 200km or 300km.

So if you want incredibly accurate information about the time, GPS is the place to get it.

Consider phone networks: your calls share space with others through a technique called multiplexing - data gets time stamped, scrambled up, and unscrambled at the other end.

A glitch of just 100,000th of a second can cause problems. Bank payments, stock markets, power grids, digital television, cloud computing - all depend on different locations agreeing on the time.

If GPS were to fail, how well, and how widely, and for how long would backup systems keep these various shows on the road? The not very reassuring answer is that nobody really seems to know.

No wonder GPS is sometimes called the "invisible utility".

Trying to put a dollar value on it has become almost impossible. As the author Greg Milner puts it in Pinpoint: How GPS is Changing Our World, you may as well ask: "How much is oxygen worth to the human respiratory system?"

It's a remarkable story for an invention that first won support in the US military because it could help with bombing people - and even it was far from sure it needed it. One typical response was: "I know where I am, why do I need a damn satellite to tell me where I am?"

Image copyright Layton Thompson Image caption GPS pioneers Richard Schwartz, Brad Parkinson, James Spilker Jr and Hugo Fruehauf were awarded the Queen Elizabeth Prize for Engineering

The first GPS satellite launched in 1978 - but it wasn't until the first Gulf War, in 1990, that the sceptics came around.

As Operation Desert Storm ran into a literal desert storm, with swirling sand reducing visibility to 5m (16ft), GPS let soldiers mark the location of mines, find their way back to water sources, and avoid getting in each other's way.

It was so obviously lifesaving, and the military had so few receivers to go around, soldiers asked their families in America to spend their own money shipping over $1,000 (£820) commercially available devices.

Image copyright Getty Images Image caption GPS technology was extremely useful for allied soldiers during the Gulf War ground offensive against Iraq in Kuwait

Given the military advantage GPS conferred, you may be wondering why the US armed forces were happy for everyone to use it. The truth is they weren't but they couldn't do much about it.

They tried having the satellites send in effect two signals - an accurate one for their own use, and a degraded, fuzzier one for civilians - but companies found clever ways to tease more focus from the fuzzy signals. And the economic boost was becoming ever plainer.

In 2000, President Bill Clinton bowed to the inevitable and made the high-grade signal available to all.

More things that made the modern economy:

The American taxpayer puts up the billion-odd dollars a year it takes to keep GPS going, and that's very kind of them. But is it wise for the rest of the world to rely on their continued largesse?

In fact, GPS isn't the only global navigational satellite system.

Image copyright Getty Images Image caption China's rival Beidou service is expanding rapidly, with more than 10 satellite launches in 2018

There's a Russian one, too, called Glonass - although it isn't as good. China and the European Union have their own well advanced projects, called Beidou and Galileo respectively. Japan and India are working on systems too.

These alternative satellites might help us ride out problems specific to GPS - but they might also make tempting military targets in any future conflict, and you can imagine a space war knocking everyone offline. A big enough solar storm could also do the job.

There are land-based alternatives to satellite navigation. The main one is called eLoran but it doesn't cover the whole world, and some countries are putting more effort than others into their national systems.

One big appeal of eLoran is its signals are stronger. By the time GPS signals have made their 20,000km (12,000-mile) journey to Earth, they're extremely weak - which makes them easy to jam, or to spoof, if you know what you're doing.

Image copyright Getty Images Image caption Russia has denied Israeli suggestions that it is behind ongoing disruption of GPS signals at Israel's Ben Gurion airport

People paid to think about these things worry less about the apocalyptic scenarios - waking up one day to find the whole thing offline - and more about the potential for terrorists or nation states to wreak havoc by feeding inaccurate signals to GPS receivers in a certain area.

Engineering professor Todd Humphreys has shown spoofing can down drones and divert super-yachts. He worries attackers could feasibly fry electricity grids, cripple mobile networks or crash stock markets.

The truth is it's hard to be sure how much damage spoofing GPS signals might do.

But just ask those Swedish tourists in Carpi. Knowing that you're lost is one thing; being wrongly convinced you know where you are is another problem altogether.

The author writes the Financial Times's Undercover Economist column. 50 Things That Made the Modern Economy is broadcast on the BBC World Service. You can find more information about the programme's sources and listen to all the episodes online or subscribe to the programme podcast.

Correction: An earlier version of this story wrongly referred to "a millionth of a second" instead of "a thousandth".