It's day one at the Singularity University: the opening address has just been delivered by a hologram. Craig Venter, who was one of the first scientists to sequence the human genome and created the first synthetic life form, is up next. And later, we will see two people, paralysed from the waist down, use robotic exoskeletons to rise up and walk.

But first, the co-founder of the Singularity University, Peter Diamandis, gives us our instructions for the day. Your task, he says, is to pick one of the "grand challenges of humanity" – the lack of clean drinking water, say. And then come up with an idea that "can positively impact the lives of a billion people".

It's 9.30 in the morning. Some of us haven't even had coffee yet. There's about 50 of us present and the room has been divided up into tables, one for education, another for poverty, another for water, and I'm not sure where I should sit. Diane Murphy, the university's PR executive, hesitates for a moment and then directs me over to the table marked "food". "Tell you what," she says. "Why don't you take Ashton Kutcher's chair over there. He's not coming until later." (When he does arrive, he pulls up a chair at the next table over. What can I say? If Ashton Kutcher fails to solve global hunger, it will be my fault.)

The Singularity University is really not much like a regular university. And not just because it's a place that manages to accommodate the likes of both Venter and Kutcher (and where, during a Q&A session, somebody asks a question about taking the Singularity University into the ghetto, and it turns out to be from the musician will.i.am).

Its courses aren't accredited, and it has no undergraduates. Stanford University might have been the cradle for a hundred Silicon Valley startups and the hothouse for some of its greatest technical innovations, but the Singularity University is an institution that has been made in the valley's own image: highly networked, fuelled by a cocktail of philanthro-capitalism and endowed with an almost mystical sense of its own destiny.

It is both Silicon Valley's elite future thinktank and its global outreach arm: Google and Microsoft both came to the founding conference and gave money, Nasa provided the campus space, and emblazoned across the website is a quote from Google's co-founder, Larry Page: "If I was a student," he says, "this is where I'd want to be." Its aim is "to assemble, educate and inspire a new generation of leaders who strive to understand and utilise exponentially advancing technologies to address humanity's grand challenges".

So, no pressure then. Although, of course, the easiest thing would simply to be British about all this and scoff. Ashton Kutcher! (I read later that he's been cast to play Steve Jobs in a forthcoming film and slightly suspect that he thinks he might actually be Steve Jobs.) A billion people! It's the kind of thing you can imagine someone in a white coat writing down as evidence just before they decide to commit you. What's more, Diamandis is the kind of can-do entrepreneur that, as a nation, we're inclined to lampoon and shun. (He's good friends with Richard Branson.)

The only problem with this as a strategy is that half the people in the room actually have done things which have had a positive impact on a billion people. Or, in some cases, more. Not just Venter, who has flown in on his private jet; there's also Vint Cerf, who is considered one of the fathers of the internet – he worked on Arpanet, the internet's predecessor – and is now "chief internet evangelist" at Google. And Sebastian Thrun, the man behind one of Google's latest and potentially most disruptive technologies yet, the self-driving car. He's also the head of the top-secret Google X lab, part of the firm that most employees didn't even know existed until the New York Times ran a piece on it last November.

And then, there's Elon Musk, the co-founder of PayPal and Tesla Motors, who created the world's first electric car, and is working on a replacement for the space shuttle. In the audience is Reid Hoffman, co-founder of LinkedIn. And Troy Carter, Lady Gaga's strategist. Later in the day, Buzz Aldrin shows up. He is, in this company, a genuine celebrity. All the scientists want to have their photo taken with him, and even Kutcher has the good grace to look a bit bashful. "What do you make of the Singularity University?" I ask Aldrin. "I'm a pretty high achiever," he says. "But I come here and think 'Gosh. I've just got to do better.'"

Star factor



Aldrin's lack of achievement notwithstanding – second man to walk on the moon, 66 missions flown in the Korean war, one-time duetter with Snoop Dogg – he has a point. The Singularity University's USP and founding ideology is based on doing better. Its belief in progress is so hard-wired that at times it has a retro-futuristic 1950s flying-cars-and-rocket-packs air about it.

Even the name – the Singularity University – sounds like something out of a sci-fi novel. Largely because its name is something out of a sci-fi novel. "The Singularity" is a term that its co-founder, the writer and futurist Ray Kurzweil, appropriated from an essay by sci-fi writer Vernor Vinge, and although definitions vary, it's usually taken to mean the point at which computer intelligence surpasses human intelligence. Which, according to Kurzweil's predictions, and he does have some form on this, will be in 2029.

Kurzweil is a genuine one-off. He's a scientist, an inventor – he developed one of the first speech recognition systems – an author and a transhumanist: he believes that if he can stay alive long enough for the technology to be invented he'll be able to stay alive for ever. But what he's best known for is being a futurist. He predicted the break-up of the Soviet Union, the growth of the internet, the year in which computers would beat the best human chess players, the e-reader, online education, and dozens more. By his own count 89 of 108 predictions he made in 1999 about where the world would be in 2009 were correct, and another 13 were "essentially correct".

At the heart of all of Kurzweil's predictions is Moore's law. This is the rule that computing power doubles every two years, first noted by Gordon Moore, who went on to co-found Intel, in 1965, and who predicted the trend would continue "for at least 10 years". In fact, it continued for the next five decades, and there's still no end in sight. Computing power shows exponential growth: one becomes two, and two becomes four, and four becomes eight, and when plotted on a chart, it looks like a rocket taking off.

Of course, it's one thing to note this about semiconductors, and another to apply it to all other areas of human life, but if you plotted the career path, business plan, and personal wealth of a significant number of people in the room, there would be an awful lot of rocket-shaped lines. Because Moore's law does seem to describe a lot of what's happened in Silicon Valley. And it's really not that surprising, therefore, that some of its wealthiest and most successful inhabitants have bought into the Singularity University's guiding ethos and spirit.

Vint Cerf tells me that it was Larry Page's enthusiasm and support for the project that encouraged him to get involved "and then I came and discovered that there were these stunningly smart people here, both speaking and in the audience. I find coming here like walking through a forest of ideas."

The standard programme at the Singularity University is a 10-week graduate course which costs $25,000 (£15,500) and last year had 2,400 people applying for 80 slots. It's the Silicon Valley version of an MBA. And demand is such that it has also started doing mini "executive" courses, of the type that I attend. "Billion-dollar companies are springing up overnight," says Peter Diamandis. "And billion-dollar companies are folding overnight." Or as Mike Federle, the chief operating officer of Forbes tells me: "CEOs are desperate to know this stuff. Everyone's trying to figure out what's coming next."

What's more, instead of being held in the Singularity University's campus at Nasa's Ames research centre in northern California, we're in the heart of the Hollywood dream machine, at Fox Studios in Los Angeles. Jim Gianopulos, the chairman of Fox Filmed Entertainment, went on a Singularity University course, and has since become evangelical about it. Given the traditional antipathy between Hollywood and Silicon Valley (intellectual copyright versus a great big copying machine), this feels like something of a milestone. These ideas are tipping over in the mainstream: Peter Diamandis's book – Abundance: The Future is Better Than You Think – went straight into the New York Times bestseller list at No 2 last month and is still lingering in the top 30.

"The power of computers per dollar has increased trillionsfold since I was at college," Kurzweil says in his opening address, speaking as a 3D holographic head projected into the room from his home in Boston. "And war, depression, nothing makes an impact. It keeps on increasing exponentially." Health used to make linear progress, but "it has become an exponential technology". And with 3D printing, so will "the world of physical things".

Our problem with pondering the future is that our expectation is "linear, not exponential," he says. Things aren't going to change incrementally, they're going to change explosively. And it was this that captured Peter Diamandis's attention – he read Kurzweil's book, The Singularity is Near, while trekking in Chile – and inspired him to set up the university.

At the end of the first session of talks, he tells us to "caucus" among ourselves and come up with some solutions for our "grand challenge". And then, oh dear God, "one of you will report back on your findings to the rest of the class".

There's seven of us at our table. And the idea is that between us, we're supposed to come up with a solution – or, let's not be unambitious here, solutions – to feeding the world's seven billion people. What would Ashton say, I wonder? Although my assumption is that it'll be a bit like when Mr Gould, my fourth-form maths teacher, used to try a similar technique back in the 80s, and we'd sit around reading Smash Hits until he wrote the answer on the board.

But no, the group around my table start unembarrassedly throwing around actual ideas: it's possibly why billionaires are billionaires, and chief executives are chief executives. They actually get on and do stuff. "What about artificial meat?" suggests Mike Federle, which in other company might be blue-sky thinking, but here is more factual observation. "We could make a steak right now," says Robert Hariri, a doctor who founded a biotech company that specialises in pioneering stem cell treatments. "But it'll cost you $20,000." I keep my mouth shut and share a sympathetic "we-can't-all-be-geniuses" smile with a nice Latino man across the table. "Ricardo Salinas", says his name tag. The second-richest man in Mexico (and 37th richest in the world), I discover later.

There's a deliberately competitive edge to the proceedings. It plays to the strengths of the chief executives and it's one of Peter Diamandis's guiding principles. He was learning to fly when someone gave him a book about Charles Lindbergh's record-breaking flight across the Atlantic and discovered that it was a journey precipitated by a prize.

It was this theory that led him to set up the X prize, which began with a $10m incentive for the first person or company to create a private reusable manned spacecraft (Burt Rutan and Paul Allen, the co-founder of Microsoft, won it in 2004 for their SpaceShipOne). The X prize Foundation has launched many more, the most recent being the $10m Qualcomm Tricorder prize to invent a handheld device – or "tricorder" as it was called in Star Trek – capable of diagnosing 15 diseases.

Abundance of ideas

There's a lot to take in. It's not even lunchtime and we've listened to presentations by Craig Venter on his plans to create biofuels made by microalgae: an acre, he believes, will be able to produce 10,000 litres of oil per year, as opposed to corn, which can produce just 18. He's just received $300m of investment from Exxon to make it a reality.

Andrew Hessel, the Singularity University faculty member on biotech who is attempting to open-source cancer treatments, talks about how biology is the next exponential technology. The genetic code will become "a programming language". We're on the cusp of massive change. DIY bio-hacking has already begun. "Viruses are coming first," he says. "Viruses are easy to make." And then there's Vint Cerf on the "internet of things". In the near future, devices will talk to each other, he says. "You'll be shopping and you'll get a call. It's the refrigerator saying, 'Don't forget the marinara sauce.'"

He ends his talk with his dream of an interplanetary internet. "Darpa [the US defence department's advanced research projects agency] has issued a grant to develop a spacecraft to get to a star in 100 years. At current propulsion rates, that would take 65,000 years, so we'd need a nuclear-powered spacecraft that can travel at two-thirds of the speed of light. But then we have to work out the communication." And he looks slightly regretful. "And we haven't done anything on an intergalactic scale yet."

In this context, it doesn't seem quite as preposterous as it should when somebody suggests using 3D printers (machines that build up objects layer by layer from a digital file) to print 3D printers, which can then print a pair of shoes. Or a house. Or dinner. "Actually, that's already happening," somebody else points out. But then 3D printers – and a prototype house made by extruding liquid concrete from a giant "printer" has indeed already been made – are just one of the Next Big Things coming down the line. We learn about dozens of them in the next two days. This is the "abundance": Diamandis's thesis is that we will soon enter a "post-scarcity" world. Forget peak oil. Who needs it when we have "15 terawatts of power from the sun hitting the earth every 15 minutes"? The challenge is simply harnessing it. "And we're getting better at that all the time."

It's not just that this deters us from changing our own unsustainable behaviour, his critics point out; it's that, as Craig Venter says, this technology is also quite hard. And sometimes doesn't pan out as well as you'd hoped. When he gets up to speak, his microphone doesn't work. "And we're supposed to print out new life forms," he says.

At times, Diamandis comes across as, well, the motivational speaker that he is. He has a line in aphorisms that sound like they have come from an auto-lifecoach-o-generator ("The best way to predict the future is to create it yourself." "If you can't win, change the rules." "Bullshit walks, hardware talks"). Though he has a knack, too, of encapsulating an idea. One of his best-known quotes is that a Masai warrior with a cellphone has better telecommunications capabilities than the president of the United States did 25 years ago. "And if he has a smartphone with Google, he has access to more information than the president did just 15 years ago."

He may be something of a showman, but he's a showman with form. Whom some of the brightest and most successful people in the world take seriously. Last Tuesday, to take just one example, he launched a company – backed by, among others, Larry Page, Google's co-founder, and Eric Schmidt, its chairman – to use spacecraft to mine asteroids for rare minerals.

And he has his friend Richard Branson's knack for marketing. Day two of our three-day course finishes with a party on the set of a New York street in the Fox Studios lot. Two paraplegics rise from their wheelchairs to walk across the stage in powered robotic exoskeletons, and will.i.am gives his thoughts on the day: "It's changed my whole perspective on life. But I'm worried about our inner cities. I've just heard that my niece is going to be dumber than her cellphone. We've had a generation who've wanted to better their bank balances, not their brains. I want to inspire young people to be scientists and engineers."

There's a neat circularity to this. Peter Diamandis grew up in Brooklyn, the son of Greek immigrant parents, and was himself inspired to become a scientist by the Apollo mission, doing degrees in medicine and molecular biology and finally a PhD in aerospace engineering at MIT. The Singularity University isn't even the first university he's founded. He set up the International Space University while he was still in his 20s and which has now trained an entire generation of Nasa scientists. It's why Buzz Aldrin has come along, and why another astronaut, Dan Barry, teaches the SU's robotics course (Barry's big prediction: cyberdildonics. Robot sex. "You think it's funny, right? But I'm also a rehabilitation physician, and sex is a basic human drive robots will be able to fulfil for the disabled, the widowed, the elderly. It's going to happen. You might as well accept it and get in on the ground floor.")

Frightening visions

The future isn't all thrilling robo-sex and free solar energy though. Barry's talk also includes video of some of the other robots in development. If you think drones are scary, it's because you haven't yet seen the video on YouTube of autonomous swarming quadrocoptors. Or the hummingbird-shaped drone that can hover in the air and then fly in through a window, or Big Dog, which looks like something from Blade Runner, or, just last week, a new one with legs that can go where no Dalek ever could: up stairs.

None of these are being developed to help with meals on wheels or palliative care nursing, though. They're war machines, most of which are being developed with funding or support from Darpa. (I meet its head, the formidably impressive Regina Dugan in the ladies: she doesn't seem like a warmonger but then a week later, it's announced that she's leaving to go to Google.)

Even Dan Barry, who runs his own robotics company, sounds a warning: "I don't see any end point here. At some point humans aren't going to be fast enough. So what you do is you make them autonomous. And where does that end? Terminator."

And it's not just the robots. Or the fact that schoolchildren will be tinkering with DNA. "Nobody wants their kid to be the first one off the block to make the Ebola virus," says Venter. "Which is a really small genome." But nor does there seem to be any practical way, that anyone has thought of so far, of preventing it.

It's during the biotech presentation that I hear a British voice pipe up and ask a question about regulation. In the break, I chat to the voice's owner, Simon Levene, a venture capitalist who specialises in technology. He's here, he says, "because there's nowhere else that is this multidisciplinary. This stuff is changing so much and so fast that it's almost impossible to keep abreast of it." He's paid $5,000 for the three days and he reckons it's cheap at the price. "It's a lot less than an MBA, and I've done an MBA at Harvard, and I've probably already learned more here."

The technology is astounding, he says. But, he shares my own qualms about Silicon Valley's techno-utopianism. "There's some potentially lethal side-effects, aren't there? Every solution has unintended consequences. And there are very real ethical and regulatory issues to consider, and which are just being glossed over. The thing is that I don't trust the market to do it. But then I don't trust government either. There needs to be international ethical oversight. There's simply enormous power that's about to be unleashed. Darpa isn't here for fun."

One of the scariest things I hear, though, isn't ostensibly as scary as autonomous death machines. It's when Sebastian Thrun is talking. He unveiled his driverless car at TED in 2011 – developed in response to a competition held by Darpa – after they'd already driven 200,000 miles across California, a technology that will surely change our lives profoundly.

It's been quite a year for Thrun: seeing another presentation at TED by Salman Khan about his online education site, the Khan Academy, Thrun decided to video one of his artificial intelligence classes at Stanford and put it online. An astonishing 160,000 people enrolled, of whom 23,000 graduated. Top of the class was a disabled woman called Melody Bliss, who works full-time, and has kidney dialysis three times a week.

It was enough to persuade Thrun to resign his tenure at Stanford and set up Udacity, a free online university, open to all, that may change the face of education. That's the good news. But he's also founded and is head of Google X, Google's top secret special projects division. It's prototyping "Google glasses", augmented reality spectacles, that will stream the internet direct to your eyeballs. But it's what Thrun says is around the corner that to me seems as if it could be even more life-changing. Massive data. Of everything. "I honestly believe that in the next 10-15 years, computers will be able to capture the experience of a life," he says. Every aspect of your life will exist online forever. And it's not a lonely scientist in a distant computer lab saying this. Thrun, to remind you, works for Google. Memory, the thing that defines who we are, what makes us human, that distinguishes us intellectually, and gives us a narrative sense of our own lives will "be outsourced". That world, says, Thrun, "is not very far away". Enjoy the luxurious privacy of your own memories while you still can.

And then Diamandis asks the scientists there for their best predictions for the next five to 20 years. "AI abilities are going to be indistinguishable from those of human abilities," says Thrun. Most jobs will no longer exist. "There will be an explosion," he predicts, "in art and music." Our definition of what it is to be human is going to change, says Dan Barry. Normal will no longer be enough. Robots are being taught to emote. We are going to start relating to them.

Christopher deCharms, a neuroscientist who has helped develop a new sort of MRI machine that can do brain imaging in real time, goes even further. "I believe that in 10 to 20 to 30 years, truth detectors will work. And they will be retrospective back today. There is going to be a revolution in privacy. Transparency is going to come all the way back to our thoughts."

In his opening address, Ray Kurzweil points out that an IBM computer called Watson, had recently beaten the greatest human champions of the TV quiz game Jeopardy: "And that's not just through statistical analysis. I think it's very significant. It's pattern recognition, which is what people do. It had to understand puns and metaphors and similes and jokes. It can read natural language documents. It read all of Wikipedia. That's 200 million pages of documents. It took three years. But at the end of the three years, there's a natural advantage to machine intelligence."

The singularity really is near, he claims. It's less than 20 years away. "I said it would be 30 years from 1999. The consensus then was 50 years. Today the consensus is about 20 years."

However, when I email Sebastian Thrun and ask his opinion, he says: "It's not a one-time event; it's a continuum that is well under way. It'll be hard to tell how much of it is already happening. In many ways, computers outsmart people today."

He has a point. "Siri [the iPhone voice recognition assistant] reminds me of the woman who's told a dog plays chess and is asked, 'Isn't that amazing?'" says Kurzweil. "And she replies, 'Yes, but its endgame isn't very good.'"

The endgame is likely to get better. And the world is changing. In ways we can't even begin to imagine. And whatever else it's doing, the Singularity University is looking at problems differently. Peter Diamandis never refers to overpopulation or limited resources. He talks about "three billion new minds coming online" in the next few years, Silicon Valley-speak for "being born". These minds are an opportunity, he insists, because "the rate of innovation is a function of the number of people actually communicating and this is growing explosively with the internet".

At lunchtime, I talk to him as he dandles his twin babies on his knees, and is matter-of-fact, rather than techno-triumphalist, about what he's trying to do. He believes people can do extraordinary things. "Because that's my experience: I've seen people do extraordinary things."

And then he asks me a question: "Haven't you? In these last two days?" It's true. I have. There are reasons to be cheerful. Though when it comes to man versus machine, I'd have to say that my money's on the machines.