Media playback is unsupported on your device Media caption Rebecca Morelle reports on the inspiration for the competition

A £10m prize has been launched to solve one of the greatest scientific problems facing the world today.

The competition idea is based on the 1714 Longitude Prize, which was won by John Harrison. His clocks enabled sailors to pinpoint their position at sea for the first time.

In an updated version, the public will be asked to choose a new challenge.

Six potential categories have been announced, ranging from healthcare to the environment.

After a special 50th anniversary edition of the BBC science series Horizon on Thursday, the public will be able to cast their vote on the issue that they would most like to see tackled.

Geoff Mulgan, chief executive of the charity Nesta, which is looking after the prize, said: "If you want to solve a scientific problem, one method is to go to top universities and top scientists and ask them to solve it.

Image copyright Science Photo Library Image caption It took decades of work before John Harrison was finally awarded the prize

"But over the years, and this was something pioneered by the Longitude Prize in the 18th Century, it's often better to open it up to anyone to come up with a solution."

The original £20,000 prize was set by the British government to solve the most vexing issue of the 18th Century: how to determine a ship's longitude at sea.

For sailors to pinpoint their position on the waves, they required two clocks: one that was set each day, using the the height of the sun in the sky, and another that kept the time back at port.

The problem with the latter was that the pitch and roll of the oceans, and the humidity and temperature changes at sea would damage the delicate mechanisms of a timepiece.

But Mr Harrison, a clockmaker from Yorkshire, created a chronometer that overcame these problems.

It took several prototypes and decades of battling with the scientific elite before he was finally deemed the winner. His work revolutionised navigation and saved countless lives.

Now, 300 years later, a new challenge is being launched.

We're going to set a very precise measurement of what will count as eligibility for winning the prize Geoff Mulgan, Nesta

Nesta and the government-funded Technology Strategy Board are offering £10m for a solution to the biggest scientific problem of our time.

The categories from which "the problem" will be chosen was announced on Monday. These themes have been been selected by a Longitude Committee, chaired by the English Astronomer Royal, Prof Sir Martin Rees, after widespread consultation with experts across various fields. They are:

Flight - How can we fly without damaging the environment?

Food - How can we ensure everyone has nutritious sustainable food?

Antibiotics - How can we prevent the rise of resistance to antibiotics?

Paralysis - How can we restore movement to those with paralysis?

Water - How can we ensure everyone has access to safe and clean water?

Dementia - How can we help people with dementia live independently for longer?

Standing next to Harrison's H4 timekeeper at the launch of the prize, the BBC's director-general Tony Hall said: "What's really exciting about the Longitude Prize 300 years on in 2014 is that there might be another modern-day John Harrison somewhere out there - someone who will be inspired to change our world fundamentally, and they may not even know that they're a scientist."

Comparing the modern prize to its predecessor, Prof Sir Martin Rees, chair of the Longitude Committee and English Astronomer Royal, commented: "There's no manifest number one problem as there was in the 18th Century. Rather there are many broad societal problems demanding fresh thinking.

"There's a pressing need also for the UK to channel more brain power into innovation, jump-start new technologies and enthuse young people."

Each category will be examined in the Horizon programme to be broadcast on BBC Two at 2100 on Thursday. After that, a public vote will be opened, with a favoured theme to be announced on 25 June.

At the prize launch held at Broadcasting House in London, the six challenges were outlined by Horizon presenters.

Media playback is unsupported on your device Media caption Prof Brian Cox: Public vote on Longitude Prize is invaluable

A&E doctor Saleyha Ahsan is presenting the segment on providing freedom of movement for people with paralysis. She demonstrated the potential for her challenge with the help of Sophie Morgan, who has a spinal cord injury.

Using a robotic exoskeleton called Rex, Ms Morgan was able to stand up on stage.

Ms Morgan, who has been using Rex for one month, told the audience: "Having been sat down all the time, it is literally and metaphorically a perspective shifter... I've been psychologically affected by talking to people at eye level and there are health benefits. Already, I'm sleeping better, feeling better, my body is getting better and the pain is gone."

BBC TV presenter Michael Mosley demonstrated his challenge with the help of insects, a source of protein that could offer one way to fight world hunger. He suggested insects could be turned into a kind of flour to make them more palatable to consumers.

Harrison's Longitude Prize Original prize set up in 1714 to find way of pinpointing a ship's position at sea

Sailors had determined their position with two clocks, but conditions at sea caused problems

Prize eventually awarded in 1765 to John Harrison, a clockmaker and carpenter from Foulby in Yorkshire

The winning timekeeper, called H4, was 13cm across and looked like a large pocket watch

After the result of the vote is announced, experts will then convene to refine the details of the challenge, with anyone from around the world able to submit their solution.

Mr Mulgan said: "We're going to set a very precise measurement of what will count as eligibility for winning the prize.

"The prize will only be awarded when someone can demonstrate that their invention actually meets those criteria."

He said that it could be several years before a winner is decided.

David Rowan, the editor of Wired Magazine, is on the committee. He said: "The brilliant thing about the Longitude Prize is that we don't know where the answer's going to come from.

"The crowd is smarter than any of us on the committee. And the beautiful thing about the internet is that by connecting people together, two plus two is five or five hundred. People come together in all sorts of extraordinary and unpredictable ways to solve problems and we want to see where this goes. Surprise us!"

And Roger Highfield, the renowned science writer and director of external affairs at London's Science Museum, commented: "We've got challenges like global climate change, like the growth in the global population, pressure on food supplies, and pressure on water supplies. I think actually this is a very opportune moment for challenges across a range of fronts. So, the Longitude Prize has just come in the nick of time."

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