Imagine a smartphone that warns you when your blood pressure is getting too high, tells you when there are toxic fumes or pollen in the air and even measures your brainwaves to ascertain your stress or attention levels.
If you were blind, it could describe your surroundings to help you walk safely. If you had been paralysed by a stroke, it could translate your thoughts into commands for a machine. It could communicate with other devices to warn you of impending danger, such as an avalanche or a car accident.
Who knows? It might even be able to provide relationship advice.
Or how about a digital oracle that simulates social, economic and technological changes based on vast amounts of real-time data? It could use that information to come up with solutions to the complex challenges of the modern world, such as new ways to fight climate change, manage financial markets, plan infrastructure or cope with ageing societies.
And wouldn't it be great to find a host of industrial applications for the tantalising material graphene, a single layer of carbon atoms that has the potential to radically speed up electronics and happens to be 100 to 300 times stronger than steel?
Alternatively, how's this for an idea: to come up with computer models of the human brain that are so realistic that they can simulate its reactions to medication, thereby revolutionising research into brain disease, which scientists say affected nearly a third of all Europeans in 2010 at a cost of about €800 billion (Dh3.91 trillion).
The above four ideas are vying for €1bn in European public funding in a contest organised by the EU's executive body, the European Commission (EC), to put the continent at the forefront of research into information and communications technology (ICT).
With much of Europe mired in recession and laden with debt, this may seem like a bad time to be spending such sums on projects with an uncertain outcome.
But the EC insists that it is a necessary investment to keep the continent competitive. The crisis, it argues, has made public funding, especially of start-ups and small-to-medium enterprises (SMEs) in the ICT sector all the more important because cash-strapped firms are cutting back on research budgets, which are, in any case, focused on short-term returns.
"ICT is a technology which few sectors can do without; it enables progress in almost every industry," says Neelie Kroes, who serves on the EC and is in charge of the contest. "Many of our competitors recognise this and spend far more than we do on ICT research; it is vital for the future European economy that we increase our support, too."
The competition began in 2010 with 23 proposals that were ranked and whittled down by a panel of scientists and business leaders.
The two winners will be announced at a news conference on Monday. They will receive funding of as much as €100 million per year for up to 10 years. The payout will depend on whether they achieve certain milestones in the first 30 months.
Ms Kroes hopes for a manifold return on the investment for Europe. She points to the publicly funded Cern, the giant laboratory on the French-Swiss border that has achieved breakthroughs in particle physics research, as a prime example of successful European cooperation. "I hope these 'big science' initiatives will inspire both scientists and national policymakers to dream about what Europe can achieve," she says.
The four contenders are nothing if not ambitious. The Guardian Angels project aims to "create intelligent, autonomous electronic personal companions that will assist us from infancy to old age", according to the group of 29 universities, 16 research organisations, and 21 industrial companies behind the project.
With the help of tiny sensors, the devices will be able to tell diabetes sufferers when they need insulin shots, monitor heart disease symptoms and blood alcohol levels and even alert doctors when patients are about to face health problems. "With a strong focus on prevention and early diagnosis, these devices will help keep health care affordable and accessible to all," say the scientists.
Devices called "emotional guardian angels" will keep track of concentration levels and even issue an alarm when stress indicators surge. The products could also help Alzheimer's sufferers who have become disoriented and collect data from a person's surroundings to guide them away from danger.
The research will also focus on developing "zero power" technologies to ensure that the devices do not need batteries.
The digital oracle project, called FuturICT, is nothing less than a high-tech attempt to grasp the complexities of global society and technology, which are changing faster than mankind's capacity to understand them, say the mathematicians and researchers who propose to develop it.
They plan to collate the wealth of data available through modern technology - digital traces of people's purchases or travel movements, Twitter feeds on revolutions or earthquakes, data on demographics, disease and shifts in public opinion - to create computer simulations that will enable policymakers and companies to take better-informed decisions and predict the effect of their actions.
To this end, FuturICT plans to align the research of hundreds of scientists in Europe to develop new methods to analyse data. "The financial crisis that we're currently in is a clear example that we really do not understand the connections that we have in our society today," says Steven Bishop, a mathematician at University College London.
"Everything is interconnected. That makes things so difficult, and that requires new tools," says Dirk Helbing, a professor at the Swiss Federal Institute of Technology ETH in Zurich. "Today we understand a lot about our physical world and about our universe, also we have invested a lot in understanding our environment, but so far there's a lack of understanding of socioeconomic systems."
The new methods could help to manage financial markets, tackle pandemics, social instability and criminal networks, the researchers say. "If we can mitigate those problems by just 1 per cent then the project will already pay off multiple times so it's a very good investment," says Prof Helbing.
The project specialising in graphene is the third finalist. Two Russian-born scientists, Andre Geim and Konstantin Novoselov, won the 2010 Nobel Prize in physics for their experiments with material that has the potential to revolutionise not just electronics, but manufacturing in general because of its potential for use in lightweight composites.
Scientists say that in just a few years, high-frequency graphene transistors have reached performance levels that rival the best semiconductor devices that have more than 60 years of research behind them. The main challenge is how to produce graphene profitably on an industrial scale. Years of research are needed because many of its possibilities are not yet understood.
Jari Kinaret, a professor of applied physics at Chalmers University of Technology in Gothenburg, Sweden, recently told the Associated Press that Europe lags behind the United States and Asia in terms of the number of patents on graphene. "We risk that the fruits of research that started in Europe will be harvested elsewhere," he said.
The fourth project, backed by more than 80 research bodies in Europe, is called the Human Brain Project. It is a plan to simulate the human brain in a supercomputer. That, say the researchers, would give much-needed insight into the workings of the brain, aid the treatment of brain diseases and revolutionise computer technology.
"What we are proposing is a radically new foundation to explore and understand the brain, its diseases and to use that knowledge to build new computing technologies," says Henry Markram, a professor of neuroscience at the Swiss technology institute EPFL in Lausanne, which is leading the project.
But here is the challenge: simulating a brain will require supercomputers that are 1,000 times more powerful than today, say the researchers. So the project, if it gets the funding, will boost the development of radically new computers.