some thoughts on the back of a workshop with other "creative" professionals....
I am consistently amazed at how many people use mind-mapping and other reductivist techniques for solving problems. Perhaps, for a certain class of problem these approaches work. But I find that for small problems, breaking the problem down is un-neccessary...and for more complex ones, breaking it down only limits the ability to see the solution. Of course, when given a complex problem to solve, it is reasonable to want to immediately start breaking it down into its constituent parts in order to understand it. This has the effect of reducing the apparent complexity, thus making it seem simpler to solve. But while understanding the various parts of a problem is essential to understanding the scope of the problem overall, the solution to a problem is not always deducible from detailed and reductivist analysis of this sort. And it has the side effect of overwhelming you with information. Its kind of like trying to understand why you love someone by reducing them down to their constituent atoms and looking for what makes them who they are. Its just not gonna work out. You have to be able to see bigger patterns...to work more holistically and synthetically when trying to understand and solve complex problems.
In fact, in my experience, if the problem is a wicked one, where the complexity of dependencies means that solving one part of the problem can actually create new problems, taking a reductivist approach can actually make things worse! In these cases, reductivist thinking is misleading because, though you can break the problem down, it gives you a false sense of security that each of the sub components are discrete and solvable on their own, when this is not, in fact, true. The reality is that when faced with big, hairy, complext problems, you have to think laterally...often proceeding through leaps of intuition and inspiration...analogy and metaphore...in order to outline the shape of a solution first. Then logic can be used to refine and develop it. This is what I see many people failing to do. They just don't trust their intuition or instincts...and feel they have to justify ideas logically before they can give them enough credence to actually explore them. But this just leads to mediocre or failed solutions.
The reason that logic is not particularly good at creative problem-solving, invention or innovation is that that in most cases (at least in western society), logic occludes intuition. Intuition, far from being some irrational response to be controlled or suppressed, is actually an incredibly powerful tool for solving complex problems. This is because intuition throws up potential avenues of exploration which are not logically derivable in the first instance. Intuition derives from unconscious experience and memory (see my post on creative process and cognition). It represents the things we have observed but not formally and consciously processed about the world (i.e. we have not yet turned it into active knowledge). Logic, on the other hand, derives from what we know we know (not what we don't know we know). And yet, it is what we don't know we know (but have experienced or observed) that allows us to innovate and to invent. And it is also often from things which appear (logically, at least) to be unrelated that we find inspiration.
In reality, it is how science and invention have always actually proceeded (see The Structure of Scientific Revolutions and Against Method) . Most scientists make leaps of intuition to form a hypothesis and then use logic to reduce it to its component parts so that they can apply intellectual and experimental rigour to disprove thier own intuition. Note that I say "disprove"...this is essential because if you set out to prove your intuition, then your natural bias and desire to protect your idea means you only look for the things that validate it. If, on the other hand, you look for things that invalidate the idea and can't find them, then it is more likely to be true.
So to solve any complex problem, a system of synthetic thinking, combined with the rigour of logic, is required. Its not good enough to just break the problem down. Equally its not good enough to just intuit an answer. You have to do both.