Posts Tagged ‘thinking’

Solving the Unsolvable

Friday, July 4th, 2008

I thought it was an urban legend; the story of the student who mistakes a pair of ‘unsolvable’ maths problems for his homework assignment and solves them.  It has been used as an example of the power of positive thinking.  If you do not know that a problem is unsolvable then you have a better chance of solving it.

I discovered that it is based in truth.  It happened in 1939 to the American mathematician, George Dantzig (1914 - 2005) when he was a graduate student.  Here is the story in his own words:

‘It happened because during my first year at Berkeley I arrived late one day to one of Neyman’s classes.  On the blackboard were two problems which I assumed had been assigned for homework.  I copied them down.  A few days later I apologized to Neyman for taking so long to do  the homework–the problems seemed to be a little harder to do than usual.  I asked him if he still wanted the work.  He told me to throw it on his desk.  I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever.  About six weeks later, one Sunday morning about eight o’clock, Anne and I were awakened by someone banging on our front door.  It was Neyman.  He rushed in with papers in hand, all excited: “I’ve just written an introduction to one of your papers.  Read it so I can send it out right away for publication.”  For a minute I had no idea what he was talking about.  To make a long story short, the problems on the blackboard which I had solved thinking they were homework were in fact two famous unsolved problems in statistics.  That was the first inkling I had that there was anything special about them.’

Here is the link describing the way the myth has developed on Snopes.

Paul Sloane

Thinking the Unthinkable

Wednesday, July 2nd, 2008

We can broadly simplify innovations into two kinds – incremental and radical.  Incremental innovations are improvements to current products, methods, processes, services, partnerships and so on.  Customer complaints and suggestions are a good source of ideas for incremental improvements.  So are the people who work in the organisation.  If you ask customers how your product could be better or if you ask employees how their job could made easier they will come up with plenty of proposals.  Most organisations are good at incremental innovation – they make things better.  However, very few organisations are good at radical innovations.  As Gary Hamel puts it – businesses are good at getting better but poor at getting different.  Indeed Clayton Christenson in his book, The Innovator’s Dilemma, argues that it is very difficult for successful organisations to develop disruptive innovations that would threaten the basis of their success.  Often they are put out of business when some smaller company develops a radically new technology.  Which employee working in a booming telecoms company in the 1990s would have suggested that free voice over internet telephony would be something they should develop?  It took a start-up, Skype, to make a success of this radical idea.

How can you encourage your people to countenance drastic innovations?  One way is to run creativity sessions where the objective is to conceive them.  Ask the question, ‘Who killed our business?’  Get small teams to imagine entirely new business models that could deliver the benefits that your customers want.  Each team has to present a scenario of a force so powerful that it could completely replace you.  Starting with a blank piece of paper and none of the encumbrances that limit your organisation they design a super competitor.  They are encouraged to go to extremes and to think completely outside the current model.  The exercise is stimulating and can be very revealing.

Most organisations have natural defence mechanisms against disruptive or threatening ideas.  People immediately find reasons why they should not be considered.  It is difficult to change the culture to one where such ideas are not only heard but are actively encouraged and developed.  The ’Who killed our business?’ exercise is a good way to start.

Paul Sloane