In using problem material to exercise the generation of alternatives one may proceed in two ways:
1. Generate alternative ways of stating the problem.
2. Generate alternative approaches to the problem.
The emphasis is not on actually trying to solve the problem but on finding different ways of looking at the problem situation. One may go on towards a solution but this is not essential.
Example
The problem of children getting separated from their parents in large crowds.
Alternatives
1. Restatements
Preventing separation of children from parents.
Preventing children being lost.
Finding or returning lost children.
Making it unnecessary for parents to have to take children into large crowds (crèches at exhibitions etc).
Comment
Some of the alternative statements of the problem do suggest answers. The more general the statement of a problem the less likely is it to suggest answers. If a problem is stated in very general terms then it is not easy to restate the problem in another way on the same level of generality. If this is the case one can always descend to a more specific level in order to generate alternatives. For instance ‘the problem of lost children in crowds’ could be restated as the ‘problem of careless parents in crowds’ or ‘the problem of children in crowds’ but one could also use a more specific level such as ‘the problem of returning lost children to their parents’.
2. Different approaches
Alternatives
Attach children more firmly to their parents (by a dog’s lead?).
Better identification of children (disc with address).
Make it unnecessary for children to be taken into the crowd (crèches etc).
Central points for children and parents to get to if losing sight of one another.
Display list of lost children.
Comment
In this case many of the approaches seem like actual solutions. In other situations however approaches may just indicate a way of tackling the problem. For instance with this lost children problem one approach might be ‘Collect statistical data on how many people take their children into crowds because they want the children to be there or because there is no one the children can be left with.’
Type of problem
The type of problem used depends very much on the age of the students involved. The problem suggestions listed below are divided into a young age group and an older one.
Young age group
Making washing up easier or quicker.
Getting to school on time.
Making bigger ice creams.
Getting a ball that is stuck in a tree.
How to manage change on buses.
Better umbrellas.
Older age group
Traffic jams.
Room for airports.
Making railways pay.
Enough low cost housing.
World food problem.
What should cricketers do in winter?
Better design for a tent.
Summary
This chapter has been concerned with the deliberate generation of alternatives. This generation of alternatives is for its own sake and not as a search for the best way of looking at things. The best way may become obvious in the course of the procedure but one is not actually trying to find out. If one were just looking for the best approach then one would stop as soon as one found what appeared to be the best approach. Instead of stopping however one goes on with the generation of alternatives for its own sake. The purpose of the procedure is to loosen up rigid ways of looking at things, to show that alternative ways are always present if one bothers to look for them, and to acquire the habit of restructuring patterns.
It is probably better to use the artificial quota method rather than just rely on the general intention for trying to find other ways of looking at things. General intentions work well when things are easy but not when they are difficult The quota sets a limit which must be met.
Challenging assumptions 8
The previous chapter was concerned with alternative ways of putting things together. It was a matter of finding out alternative ways of putting A, B, C and D together to give different patterns. This section is concerned with A, B, C and D for their own sakes. Each of them is itself an accepted, standard pattern.
A cliché is a stereotyped phrase, a stereotyped way of looking at something or describing something. But clichés refer not only to arrangements of ideas but to ideas themselves. It is usually assumed that the basic ideas are sound and then one starts fitting them together to give different patterns. But the basic ideas are themselves patterns that can be restructured. It is the purpose of lateral thinking to challenge any assumption for it is the purpose of lateral thinking to try and restructure any pattern. General agreement about an assumption is no guarantee that it is correct It is historical continuity that maintains most assumptions — not a repeated assessment of their validity.
The figure opposite shows three shapes. Suppose you had to arrange them to give a single shape that would be easy to describe? There is difficulty in finding such an arrangement. But if, instead of trying to fit the given shapes together, one reexamined each shape then one might find it possible to split the larger square into two. After that it would be easy to arrange all the shapes into an overall simple shape. This analogy is only meant to illustrate how sometimes a problem cannot be solved by trying different arrangements of the given pieces but only by reexamination of the pieces themselves.
If the above problem was actually set as a problem and the solution given as indicated, there would immediately be an out-
cry that this was ‘cheating’. There would be protests that it was assumed that the given shapes could not themselves be altered. Such a cry of ‘cheating’ always reveals the use of certain assumed boundaries or limits.
In problem solving one always assumes certain boundaries. Such boundaries make it much easier to solve the problem by reducing the area within which the problem solving has to take place. If someone were to give you an address in London it might be hard to find. If someone told you it was north of the Thames it would be slightly easier to find. If someone told you that it was within walking distance of Piccadilly Circus it would be that much easier to find. So it is with problem solving that one sets one’s own limits within which to explore. If someone else comes along and solves the problem by stepping outside the limits there is an immediate cry of ‘cheating’. And yet the limits are usually self-imposed. Moreover they are imposed on no stronger grounds than that of convenience. If such boundaries or limits are wrongly set then it may be as impossible to solve the problem as it would be to find an address south of the river Thames by looking north of the river.
Since it would be quite impossible to reexamine everything in sight one has to take most things for granted in any situation — whether or not it is a problem situation. Late one Saturday morning I was walking down a shopping street when I saw a flower seller holding out a large bunch of carnations for which he was only charging two shillings (ten new pence). It seemed a good bargain and I assumed that it was the end of the morning and he was getting rid of his leftover flowers. I paid him, whereupon he detached a small bunch of about four carnations from the large bunch and handed them to me. The little bunch was a genuine bunch wrapped with a little bit of wire. It was only my greed that had assumed that the bunch offered had referred to the whole bunch he held in his hand.
A new housing estate had just been completed. At the ceremonial opening it was noticed that everything appeared to be a little bit low. The ceilings were low, the doors were low, the windows were low. No one could understand what had happened. Finally it was discovered that someone had sabotaged the measuring sticks used by the workmen by cutting an inch off the end of each one. Naturally everyone using the sticks had assumed that they at least were correct since they were used to show th
e correctness of everything else.
There is made in Switzerland a pear brandy in which a whole pear is to be seen within the bottle. How did the pear get into the bottle? The usual guess is that the bottle neck has been closed after the pear has been put into the bottle. Others guess that the bottom of the bottle was added after the pear was inside. It is always assumed that since the pear is a fully grown pear that it must have been placed in the bottle as a fully grown pear. In fact if a branch bearing a tiny bud was inserted through the neck of the bottle then the pear would actually grow within the bottle and there would be no question of how it got inside.
In challenging assumptions one challenges the necessity of boundaries and limits and one challenges the validity of individual concepts. As in lateral thinking in general there is no question of attacking the assumptions as wrong. Nor is there any question of offering better alternatives. It is simply a matter of trying to restructure patterns. And by definition assumptions are patterns which usually escape the restructuring process.
Practice session
1. Demonstration problems
Problem
A landscape gardener is given instructions to plant four special trees so that each one is exactly the same distance from each of the others. How would you arrange the trees?
The usual procedure is to try and arrange four dots on a piece of paper so that each dot is equidistant from every other dot. This turns out to be impossible. The problem seems impossible to solve.
The assumption is that the trees are all planted on a level piece of ground. If one challenges this assumption one finds that the trees can indeed be planted in the manner specified. But one tree is planted at the top of a hill and the other three are planted on the sides of the hill. This makes them all equidistant from one another (in fact they are at the angles of a tetrahedron). One can also solve the problem by placing one tree at the bottom of a hole and the others around the edge of the hole.
Problem
This is an old problem but it makes the point very nicely. Nine dots are arranged as shown overleaf. The problem is to link up these nine dots using only four straight lines which must follow on without raising the pencil from the paper.
At first it seems easy and various attempts are made to link up the dots. Then it is found that one always needs more than four. The problem seems impossible.
The assumption here is that the straight lines must link up the dots and must not extend beyond the boundaries set by the outer
line of dots. If one breaks through this assumption and does go beyond the boundary then the problem is easily solved as shown.
Problem
A man worked in a tall office building. Each morning he got in the lift on the ground floor, pressed the lift button to the tenth floor, got out of the lift and walked up to the fifteenth floor. At night he would get into the lift on the fifteenth floor and get out again on the ground floor. What was the man up to?
Various explanations are offered. They include:
The man wanted exercise.
He wanted to talk to someone on the way up from the tenth to the fifteenth floor.
He wanted to admire the view as he walked up.
He wanted people to think he worked on the tenth floor (it might have been more prestigious) etc.
In fact the man acted in this peculiar way because he had no choice. He was a dwarf and could not reach higher than the tenth floor button.
The natural assumption is that the man is perfectly normal and it is his behaviour that is abnormal.
One can generate other problems of this sort. One can also collect examples of behaviour which seem bizarre until one knows the real reason behind it. The purpose of these problems is just to show that the acceptance of assumptions may make it difficult or impossible to solve a problem.
2. The block problems
Problem
Take four blocks (these may be matchboxes, books, cereal or detergent packets). The problem is to arrange them in certain specified ways. These ways are specified by how the blocks come to touch each other in the arrangement For two blocks to be regarded as touching, any part of any flat surface must be in contact — a corner or an edge does not count.
The specified arrangements are as follows:
1. Arrange the blocks so that each block is touching two others.
2. Arrange the blocks so that one block is touching one other, one block is touching two others, and another block is touching three others.
3. Arrange the blocks so that each block is touching three others.
4. Arrange the blocks so that each block is touching one other.
Solutions
1. There are several ways of doing this. One way is shown on p. 89. This is a ‘circular’ arrangement in which each block has two touching neighbours — one in front and one behind.
2. There is often some difficulty with this one because it is assumed that the problem has to be solved in die sequence in which it was posed, i.e. one block to touch one other, one block to touch two others, one block to touch three others. If, however, a start is made at the other end by making one block touch three others then this arrangement can be progressively modified to give the arrangement shown.
3. Some people have a lot of difficulty with this problem because they assume that all the blocks have to lie in the same plane (i.e. spread out on the surface being used). As soon as one breaks free of this assumption and starts to place the blocks on top of one another one can reach the required arrangement.
4. There is a surprising amount of difficulty in solving this problem. The usual mistake is to arrange die blocks in a long row. In such a row the end blocks are indeed touching only one other but the middle blocks have two neighbours. A few people actually declare that the problem cannot be solved, The correct arrangement is very simple.
Comment
Most people solve the block arranging problems by playing around with the blocks and seeing what turns up. Nothing much would happen if one did this without bothering to have the blocks touching one another. So for convenience one assumes that the blocks all have to touch one another in some fashion (i.e. there has to be a single arrangement). It is this artificial limit, this assumption, that makes it so difficult to solve the last problem which is so easy in itself.
The ‘Why’ Technique
This is a game which provides an opportunity for practising the challenging of assumptions. It can also be used as a deliberate technique. The ‘why’ technique is very similar to the usual child’s habit of asking ‘why’ all the time. The difference is that ‘why’ is
usually asked when one does not know the answer, whereas with the ‘why’ technique it is asked when one does know the answer. The usual response to ‘why’ is to explain something unfamiliar in terms that are familiar enough to be an acceptable explanation. With the ‘why’ technique these familiar terms are questions as well. Nothing is sacred.
The process is rather more difficult than it seems. There is a natural tendency to run out of explanations or to circle back and give an explanation that has already been used before. There is also the very natural tendency to say ‘because’ if something very obvious is questioned. The whole point of the exercise is to avoid feeling that anything is so obvious that it merits a ‘because’ answer.
The teacher makes some sort of statement and then a student asks, ‘Why?’ The teacher offers an explanation which is in turn met by another, ‘Why?’ If the process was no more than an automatic repetition of ‘why’ then one would hardly need a second party to ask ‘why’ except that the student gets into the habit of assuming nothing. In practice it never is an automatic repetition of ‘why’. The question is directed to some particular aspect of the previous explanation rather than being a blanket response. ‘Why’ can be focused.
Examples
Why are blackboards black?
Because otherwise they would not be called blackboards.
Why would it matter what they were called?
It would not matter.
Why?
Because they are there to write or draw upon.
Why?
Because if something is to be shown to the whole classroom it is easier to write on the blackboard where everyone can see it.
The above questioning might however have taken quite a different line.
Why are blackboards black?
So that the white chalk marks can be seen easily.
Why do you want to see the white chalk marks?
or:
Why is the chalk white?
or:
Why does one want to use white chalk?
or:
Why don’t you use black chalk?
In each of these cases ‘why’ is directed to a particular aspect of the subject and this determines the development of the questioning. The teacher can of course also direct the development by the way the question is answered.
The teacher keeps up the answers as long as possible. He may however at any time say: ‘I don’t know. Why do you think?’ If the student can give an answer then .the roles can be reversed with the student answering the why questions and the teacher putting them.
Some possible subjects for this type of session are given below:
Why are wheels round?
Why does a chair have four legs?
Why are most rooms square or oblong?
Why do girls wear different clothes from boys?
Why do we come to school?
Why do people have two legs?
The usual purpose of ‘why’ is to elicit information. One wants to be comforted with some explanation which one can accept and be satisfied with. The lateral use of why is quite opposite. The intention is to create discomfort with any explanation. By refusing to be comforted with an explanation one tries to look at things in a different way and so increases the possibility of restructuring the pattern.
Lateral Thinking Page 7