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"Artists don't create, they combine." So said Spinoza, the 17th-century Dutch philosopher. He wanted to make the point that great ideas don't form spontaneously. Rather, he said, they blend concepts that hitherto seemed irreconcilable. Fast-forward 400 years and another Dutch thinker, Fons Trompenaars, is making the same point. The acclaimed management theorist has a new book out, Riding The Whirlwind, in which he advises companies to rid themselves of linear thinking if they wish to be more innovative. Its core proposition:

"Successful leaders have the propensity and competence to help their organisation and its teams reconcile dilemmas for better innovative performance."

If this sounds a little dry, you may be surprised to learn that the man who inspired it was John Cleese. In 2006, Trompenaars shared a stage with the Monty Python founder, and seized upon a comment he made about what makes a good joke successful: "The essence of humour is when two opposite logics both turn logical."

All jokes are based on collisions, Trompenaars explained to the London Business Forum. They lead our thoughts in one direction, then push them suddenly in another. By way of example, he told us about a driving incident he experienced a few days previously: "I was stopping in front of a traffic light. A car stopped next to me. The driver opened his window so I opened my window. And he said: 'Have you farted as well?'."

It was appropriate we had convened for this event at the Comedy Store near Leicester Square. Trompenaars was himself a bona fide comedian, who never missed an opportunity to send up the foibles of the various nationalities in the room, especially the French (they had started so many civil wars, he said, because they wanted to know what it felt like to win one.) Humour was essential to the delivery of his message, he felt, not least because "there's nothing as uncreative as research on creativity."

The way Trompenaars took apart traditional theories about innovation was typically Dutch in its candour. For example, he said the questionnaire for the Myers-Briggs Type Indicator test (widely used to help identify qualities such as creativity) was written in a single Saturday morning because "for that crap you don't need more." The essential problem with Myers-Briggs, he argued, is that it poses questions that are too linear: "If you score 70% on thinking, you score 30% on feeling; if you're 90% introvert then you must be 10% extrovert." It's "appalling," he said, that this simplistic methodology underpins an industry worth around $7bn.

Naturally, Trompenaars' firm has its own version of the test, the "Integrated Type Indicator," which attempts to analyse personalities in a far more rounded way. It is based on the premise that innovation depends on the ability of a leader to combine opposites, such as "individual creativity and teamwork, standardisation and localisation", and so on. However, it is also based on independent research that found:

• a 0.71 correlation between a leader's ability to reconcile differences and their performance in 360-degree feedback reviews; and
• a 0.69 correlation between this ability and bottom-line business performance.

In other words, the output of an individual, team or organisation is directly related to their ability to reconcile differences, and to blend ideas that seem unrelated at first glance.

Traditionally, when an organisation tries to become more innovative it talks about "adding value" to products and services. But value is not something that can be added, Trompenaars argued. It can only be traded for other values. To illustrate this point he asked us to consider the values of speed and safety in a car. You can trade one for the other, but you can't improve both without incurring extra cost. "If you could simply add value to something, your competitor could do the same thing tomorrow," he said, "but redesigning a car: that's very complex." The essence of innovation, he concluded, is "to combine values that are not easily joined, therefore scarce, therefore profitable."

The organisations that do this well tend to be those that have diverse workforces. After all, if you can reconcile differences of culture, gender, ethnicity and so on then you will probably be good at reconciling concepts too. If you want your organisation to behave more like this then you need to "make sure you can recognise diversity," and then "immediately... take a second step called respect." He explained: "Respect starts when you understand that all cultural differences are in you."

What does this mean? Well, Trompenaars said, imagine you are a man whose wife has just asked him for his opinion of a horrible dress. It's a dilemma that someone from any culture would understand: how do you balance the need to be honest with your respect for a relationship?

"The Japanese would always start by saying 'Lovely, yes, everything is fine... then tell the truth over sake," he suggested, because for them the relationship would take priority over honesty. "In the Netherlands, you'd start by saying how awful the dress was (and if you were German, [you'd give] five reasons), and then you'd go to the bar and say how much you loved her, and she would say: 'I knew that because you criticised my dress, and you would never have done that if you didn't love me.'" So, "we all have the same dilemmas but we all have different starting points". Failure to acknowledge this often causes the failure of cultural exchanges.

What does this have to do with innovation? To answer this question, Trompenaars gave us a much tougher dilemma to consider: "Imagine you're in a car driven by a close friend of yours. He's speeding - going 50mph where you're allowed to go 30mph - and he hits a pedestrian. It comes to court and the lawyer of your friend says, 'Don't worry, you're the only witness.' Two questions: first of all, what is the right of your friend to expect you to testify to the lower figure? And, secondly, should you lie?"

Trompenaars said he had asked over 100,000 people these questions, in audiences all over the world, and no one had ever put up their hand to say that they'd be comfortable in such a situation. "I only had one person who said they didn't understand the question, so I decided to stop all the workshops in the White House," he joked. "We all as human beings have the same dilemmas; it's our culture that kills half of us."

The way we attempt to navigate our way through such problems is by referring to our values, he continued. So corporate values, if carefully chosen, can help us to deal with dilemmas in business. "The value of a value is that it helps you solve problems... Every quarter we have a new value that we put on top of our door, and the last one was: 'We don't kill people.' It's one of our values, but it makes our guests nervous." The problem is that most firms choose values that are unhelpful, because they're too ambiguous, or they're nothing more than platitudes. For example, he said, "82% of American firms, in their values, have integrity... it's obvious."

One of these firms was Merrill Lynch, the investment bank, so when Trompenaars spoke to their staff recently he asked: "How does integrity help you to get the correct answer in the problem of the car accident?" One member of the audience - an American - said integrity was surely reporting the friend, since a friend shouldn't expect you to lie. Another, from Germany, said: "How can integrity be anything but me helping my friend?" English people often ask: "What happened to the pedestrian?" Trompenaars revealed. But the best response he ever got was from an Italian, who asked: "What happened to the car?"

The problem is that the question is too linear, he suggested, while integrity is not. "Integrity comes from integere," he pointed out, which means 'roof' - something that holds things together and protects." Perhaps the best solution is to be found in Japan, he said, where the majority of respondents would "try to convince the friend to tell the truth in court, so they could talk to the judge and have the sentence lowered for his courage." What is beautiful about this solution, Trompenaars said, is that it removes the need to choose "between your friend and the truth".

Companies need to pay attention to ideas of this sort, if they are to prosper in the global knowledge economy, Trompenaars concluded. One of the most common dilemmas today is how to balance global standards with local cultural diversity. The answer is to be "transnational", to take the best practices from local cultures and roll them out worldwide.