Takeo was a classic numbers man - a no-nonsense, hard-headed finance type. Soichiro was the exact opposite - playful, creative and allergic to spreadsheets. Together they built and ran the Honda Motor Company and enjoyed a long and fruitful partnership, not in spite of their differences but because of them; the two even retired together as neither wanted to work without the other.

That kind of chemistry is rare within traditional business cultures; if anything, ‘ideas people’ and ‘money people’ are usually at odds with each other. But study the history of innovation, invention, science or entrepreneurship and you’ll see that behind every Soichiro Honda there’s a Takeo Fujisawa turning their dreams into reality.

In musical circles it’s called the Lennon-McCartney dynamic - the powerful union of naïve idealism with canny business smarts. It was the secret of Bill Hewlett and Dave Packard’s success and the template for Steve Wozniac and Steve Jobs; at the core of every great commercial partnership is the simple truth that great minds do not think alike.

That truth is a hard one for businesses that value consistency and uniformity over variation and diversity; the more they hire ‘our kind of people‘ who ‘really fit in around here’ the less likely they are to achieve the sort of innovation culture everyone’s chasing these days. Creativity and ingenuity require discontent or unease; different ways of thinking and working have to bump up against each other.

After all, if you want sparks you’ll need a little friction. And that means somehow orchestrating minds that have very little in common.

Luckily, most organisations love personality profiling in one form or another so most have at least one scientific-looking chart that arranges different thinking styles into colourful quadrants or sectors, and although I’m not a huge fan of such systems they do demonstrate that most workplaces have the basic ingredients of a vibrant innovation culture, even if the actual recipe still eludes them.

For instance, I’ve never encountered an organisation that doesn’t harbour at least a few passionate, creative minds; people so good at ‘thinking outside the box’ you get the impression they didn’t even know there was a box. That’s not to say these folks make themselves known to management – if anything, their genius for turning problems into ideas is probably a secret known only to a few close colleagues.

Often that’s because ideas are newborns - they need care and attention, which is something they’re not likely to get in a driven, high-performance corporate environment. That’s when we need to scan the organisation for curious technocrats - people with a capacity to believe in an idea while doubting some of its practicalities. Think of any TED talk you’ve ever seen; chances are the speaker was the kind of person who could build a bridge between a rough idea and a detailed plan. Innovation needs that kind of connector because they’re the ones that can figure out how to make big ideas fit into little deadlines and budgets, but this is the mind that most businesses don’t seem to have much of.

One mind they do have on tap is the critical analyst, people who see the risks and costs of everything. It’s a special form of creativity, one that can run any scenario forward to imagine how it might fail and sometimes, how to make sure it doesn’t. It’s brilliant at the right time and place, but terribly destructive if used all the time in every place, which unfortunately tends to be the case in large, conservative organisations, where this particular mindset is often the only one that has any real power.

But all this thinking is worthless unless we can hand it over to people that like to get things done; energetic, impatient warrior-types who can break abstract notions down into concrete actions. This is the other dominant mindset of most organisations and why so many businesses would rather meet a KPI than a new paradigm.

Without a framework for innovation and collaboration, the idealists frustrate the realists, the detail oriented stymie the more conceptually inclined and those who crave certainty are bewildered by the minds that enjoy ambiguity – but far from generating creative friction, all these unhelpful interactions tend to produce is tension.

But what if you could identify the minds that convert problems into ideas, then hand those ideas over to people who can turn them into plans? And what if you ran those plans past the minds that can transform them into decisions which you then entrusted to those who are just waiting to make them into actions?  You’d not only be leveraging the different types of genius currently driving each other crazy but you’d be giving the people around you a once-in-a-career opportunity to bring their real talents to the fore.

Steve Jobs summed up the essential task of the innovator in just two words: Think Different. And there are two ways to do that. You can retrain your mind to think differently, or you can embrace the wonder of people who already do.