From the get-go Larry Page and Sergy Brin wanted to do the impossible. In the early-mid 90s, I'm sure most hearing the Stanford drop-out duo's mission to "organize the world's information and make it universally accessible and useful" thought it a wonderfully ambitious if idealistic and whimsical notion.
Now look where they've got to.
Whilst there are 1001 reasons to Google's current success, a key constant that has precluded any form of even temporary demise is their ability to actualise impossibilities through ignoring the plausibility of ideas. What's meant by this is that in creating new products, they initially disregard the constraints of protocol, money, technology etc that typically result in pigeon-step innovation, and instead think about the perfect solution. Only once they've figured out what they want the problem to be, do they then create a solution. Through taking this idealistic methodology towards business development allows them to - as Mr Brin puts it "mak[e] science fiction real".
A large scale example of this is Google's Glass Project. In deciding what would be the best progression for a personal mobile device, the Google X team didn't think "how can we improve on current devices?" Instead conceptualising "What would make our lives easier, what would consumers love to have, and what would be revolutionary?"
The result? What was not long ago was seen as a collection of impossible ideas is now being worn by road testers across the world.
Now I'm sure most of you reading this are thinking, "That's all well and good, but I don't work for Google", and that you don't have the money, resources, freedom or leadership to do undertake these sorts of projects.
Firstly, whilst it may sound very anything-is-possible-if-you-can-believe-it, if you have a good idea and are willing to push it, you can make things happen. A huge benefit of the internet has been that research, networking, funding etc, have all been made accessible. Most importantly, a wealth of investors that are actively looking for new ideas to invest in - as Nick D'Aloisio recently found in the form of Yoko Ono, Stephen Fry, Ashton Kutcher and most recently Yahoo!.
I'll admit that Google Glasses is very much a cool example of having what I call a "Goal Focus", but it's as much about consciously ignoring red tape, rules and constraints in order to identify the perfect solution to a perceived problem as it is changing the world.
As a more practical example of everyday application is one that Facebook recently undertook.
Mobile being a large focus for the company this year, they wanted to get their employees to understand their mobile proposition better. So to achieve this they simply blocked the desktop version for a couple of weeks.
Whilst on the face of it a simple move, I'm sure it's one that ruffled a few feathers and some said their jobs "couldn't be done effectively" blah blah blah in doing this. However in bypassing the many reasons not to do it and instead focusing on the goal, people made it work. The benefits of getting all involved to experience the positives and pitfalls of their mobile system prevented wasted time, unnecessary discussions, and got everyone of the same page much more effectively than a more process focused approach.
Here's how I've visualised 2 possible approaches Facebook could have taken. One more typical of the majority of businesses (Process Focus), and the other taking a Goal Focus approach.
In tackling business and workplace issues, having more of a "Goal Focus" places you in a better position to realise things that - due to protocols, resources etc - may appear (or physically be) unachievable. From simply creating a new method of billing, to inventing a new product, focus on what would be the best possible solution and figure out the details afterwards.
As Adidas say: "Impossible is Nothing.".........Except teleporting.
 Kind of like writing an exam question, coming up with what you want the answer to be, then figuring out the workings out afterwards, as opposed to what most companies do, which is simply try to figure out the problem put in front of them. Sometimes they get it right, sometimes not, but they rarely stumble across a new and better solution.
 For example, "Twitter Dragon" Simon Dolan sought investment propositions via the social site. See this article for his pick of the best and worst http://realbusiness.co.uk/article/19473-the-best-and-worst-business-plans-in-140-characters
 Cases such as Nick D'Aloisio will become more and more normal. As programming becomes more and more the language of entrepreneurs and millionaires, the next generation will simply see a problem and write code to fix it. Though granted the above issue is wider than merely computing, it is expected that this movement will head us towards a more "there's a problem, let's just fix it" attitude. But that's a whole other topic not for discussion here.