In a startling admission from a man whose company has made billions by perfecting the art of hoarding, storing and retrieving information on us, Mr Schmidt suggested that the enormous quantity of detail we leave online may not be such a good thing after all.
The man who – alongside Google's founders Sergey Brin and Larry Page – runs the world's largest search engine said that young people will need to go as far as changing their identities if they are to truly erase what they have left online.
"I don't believe society understands what happens when everything is available, knowable and recorded by everyone all the time," he told the Wall Street Journal. "I mean we really have to think about these things as a society."
For a man whose company is built on the ability to store information and retrieve it again in a faster and more efficient way than its rivals, Mr Schmidt's admission revealed a surprising concern among Google's leadership over the importance of data privacy.
But it has also provoked a wider debate on the sheer amount of information we give away about ourselves online and how most of that data is virtually un-erasable.
Perhaps more than any other company Google has helped created a world where we willingly deposit vast amounts of personal data into the public domain – information that might previously have taken months of investigative work by professionals to find.
Google has made billions from storing data on its customers' browsing habits so that it can use that data to target them with personalised adverts. It also runs the kind of websites that have pioneered the open sharing of information online. The Californian internet giant owns You Tube, the world's largest video sharing website; it handles billions of our emails through Gmail; and – if you live in a big city – chances are that a Google Street View car has photographed your front door. A series of recent acquisitions also suggests it is hoping to move into the social networking market, the area of the internet that most concerns privacy campaigners.
Thanks to the global popularity of social networking – an estimated 600 million people have personal online profiles – friends, prospective employers and enemies alike are able to access photographs, videos and blogs that we may have long forgotten with a few simple clicks of a mouse. Recently one columnist in The New York Times went so far as to describe our current world as an age defined by "the impossibility of erasing your posted past and moving on".
Many websites yesterday picked up on the apparent disconnect between Mr Schmidt's comments and his company's ethos.
Chris Williams, of the online tech news website The Register, said: "Recording everything and making it knowable by everyone all the time is Google's stated mission, and it is profiting handsomely from the fact that society doesn't understand the consequences."
Other blogs remarked that one previous instance when Mr Schmidt had admitted concerns over the amount of personal information stored online was in 2005 when Google blacklisted the online technology magazine Cnet for an entire year.
In an article discussing privacy concerns generated by Google's data mining capabilities, Cnet's reporters published Mr Schmidt's salary, named the neighbourhood where he lives, some of his hobbies and political donations. All the information had been gleaned from Google searches.
But while bloggers and web forums reacted with tangible scepticism to Mr Schmidt's comments, others welcomed his frankness.
"His comments are a little ironic but they are also timely," said Dylan Sharpe from Big Brother Watch, which has campaigned against Google collecting wifi data on web users while taking photographs with its Street View cars.
He added: "Google is a company that specialises in knowing where you are, what you are doing and who you are talking to. That's a scary prospect even though Google's users sign up to this sort of data collection willingly.
"But Mr Schmidt is completely right on how much information we are giving away online. Right now there are millions of young kids and teenagers who, when they apply for jobs in 10 years' time, will find that there is so much embarrassing stuff about them online that they cannot take down."
Those who wish to delete what they have put up online, meanwhile, may find it next to impossible to entirely erase their cyber past.
"What many people do not realise is that as soon as you put something up online you lose possession and control of that information immediately," said Rik Ferguson, a cyber security expert at Trend Micro. "Anyone can download, store and distribute that information, it's out of your hands."
Privacy campaigners say more needs to be done to stop young people in particular depositing information online that may come back to haunt them.
"I think we need to change people's mindsets through education rather than legislation but it's definitely something that we need to talk to our children about," said Mr Sharpe.
Mr Ferguson, meanwhile, believes web users will increasingly demand better levels of data privacy over the coming decade.
"What would be ideal is some sort of technology where you as an end user would be able to assign the right to use, copy or distribute information about yourself to people of your own choosing," he said. "That sort of technology is already used in encrypted emails. I'm sure people will soon start asking for some form of encrypted social networking and companies will respond to that demand."
In his own words...
* "The internet is the first thing that humanity has built that humanity doesn't understand, the largest experiment in anarchy we've ever had."
* "Show us 14 photos of yourself and we can identify who you are. You think you don't have 14 photos of yourself on the internet? You've got Facebook photos! People will find it's very useful to have devices that remember what you want to do, because you forgot... But society isn't ready for questions that will be raised as a result of user-generated content."
* "When the internet publicity began, I remember being struck by how much the world was not the way we thought it was, that there was infinite variation in how people viewed the world."
* "People are surprised to find out that an awful lot of people think that they're idiots."
Case study: 'Drunken pirate' lark destroyed teaching career
The tale of Stacy Snyder, the "drunken pirate", is a cautionary one for any young person hoping to embark on a promising career.
Ms Snyder, a trainee teacher, had passed all her exams and completed her training. Her academic record was unblemished. That is, until her final summer, when her teachers – out of the blue – deemed that the behaviour she had displayed in her personal life was unbecoming of a teacher.
Her crime? She had uploaded an image of herself, wearing a pirate costume and drinking from a plastic cup on to a social networking site with the caption: "drunken pirate."
A colleague at the school where she had been training had seen it and reported it, saying that it was unprofessional to potentially expose pupils to photographs of a teacher drinking alcohol.
As university officials told her that her dream career was now out of her reach, she offered to take the photo down, and argued that it was not even possible to see what was in the cup. After all, she told them, "is there anything wrong with someone of a legally permissable age drinking alcohol?"
But her pleas were ignored. Ms Snyder never got the certificate she needed to teach and an attempt to sue the university for it was unsuccessful.
Placing a photograph of herself in "an unprofessional state" was her downfall: the image had been catalogued by search engines and by the time she realised the danger, it was impossible to take down.
Kevin Rawlinson
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