The problem with problems

[Go to Introduction ]

There is more than one kind of problem

Half a century after Herbert Simon's death, it seems extraordinary that someone of his intelligence should have proposed a methodology that, to our eyes, seems frankly silly. But perhaps we should beware. Are there areas in our lives where we make similar errors?

The aspect of Simon’s work that I’ve been writing about is his use of a logical methodology to help make rational decisions when faced with problems, particularly in the field of public administration. Here there is an unspoken assumption in his thinking, writing and teaching that all problems are of the same type, and that therefore all problems can be successfully navigated by using one methodology and logic.

One of the fundamental arguments of this blog, is that not all problems are of the same type. In fact in our daily lives we use the one word ‘problem’ to identify two entirely different types of issue, that I call Closed Problems and Open Problems. * It may be worth while to look at examples of each, together with their characteristics, in order to see that they not only differ in type, but also differ in how they can be successfully navigated.

Closed problems

Let us begin with closed problems.

Here is a typical one:

(If you want to know the answer and how to get it, you can look here).

What is typical in a closed problem like this, is that it does not matter

• who is doing the solving – you, me or anyone else
• when we are solving it – yesterday or six years ago
• where we are when we try to solve it.

And typically, it is the kind of problem that

• has a solution (as we shall see, this is not true of all problems)
• contains the solution within it – it is a kind of tautology
• and has a methodology to be applied to reach that solution. This methodology always depends on your analysis of the starting position.

Closed problems are not all algebraic. Sometime in the 1960s, a Russian computer scientist called Mikhail Moiseevich Bongard devised a kind of puzzle game as part of his research into pattern recognition.

His puzzles, now called Bongard problems, typically show you two sets of simple images, say A and B. What you have to do is to put into words the characteristics that all the images in A have, that the images in B do not – and vice versa.

Here is an example:

And you will probably have found that all the images in B have a dot which is royal blue, and the images in A do not.

If you look back at the characteristics of closed problems listed above, you will see that they work with Bongard problems as they do with algebra. Both are what Van Bertalanffy would call ‘closed systems’.

In this they stand in complete contrast to open problems.

Open Problems

Here are three more problems that I've come across recently:

 - How does one reconcile a desire to travel with a need to reduce one’s carbon footprint?

 - How does one best get home from here?

 - How should one vote in the General Election?

Now in each of these, the response will depend on

• who is doing the responding – you, me or anyone else
• when we are responding it – yesterday or six years ago
• where we are when we respond

And typically, these are the kind of problems that

• do not have a solution. Rather, they require a response 
• they do not contain their own response: they are not tautologies. They need a response which is appropriate to their context.
• Insofar as there is a methodology for making that response, it has to do with an understanding of the contexts which you inhabit. 

The characteristics of open problems listed above exist in what Van Bertalanffy would call 'open systems '.

Closed v. Open

The two kinds of problems are of different  types with absolutely contradictory characteristics:

Herbert Simon and the New Public Management devotees assumed that all problems were of one kind: closed problems. And it is true that his methodology works for closed problems.

But when faced with such open systems as the National Health Service, the police force and national education, we can see that his methodologies for decision-making will fail.

* In the language of General Systems Theory,  Closed problems exist in closed systems, Open problems in Open systems.

[ Next: The target culture – origins (2) ]