In the self-maximizing memory system of mind there is a tendency for established patterns to grow larger and larger. The patterns may grow by extension or else two separate patterns may join up to form a large single one. This tendency of patterns to grow larger is seen clearly with language. Words describing individual features are put together to describe a new situation which soon acquires its own language label. Once this has happened a new standard pattern has been formed. This new pattern is used in its own right without constant reference to the original features which made up the pattern.
The more unified a pattern the more difficult it is to restructure it. Thus when a single standard pattern takes over from a collection of smaller patterns the situation becomes much more difficult to look at in a new way. In order to make such restructuring easier one tries to return to the collection of smaller patterns. If a child is given a complete doll’s house he has little choice but to use and admire it as it is. If however he is given a box of building blocks then he can assemble them in different ways to give a variety of houses.
Above is shown a geometrical shape which could be described as an ‘L shape’. The problem is to divide this shape into four pieces which are exactly similar in size, shape and area. Initial attempts to do this usually take the form of the divisions shown on the left. These are obviously inadequate since the pieces are not the same in size even though they may be the same in shape.
A correct solution is shown on p. 117 on the right and it is seen to consist of four small L-shaped pieces. An easy way to reach this answer is to divide the original shape into three squares and then to divide each of these into four pieces which gives a total of twelve pieces. These twelve pieces must then be assembled in four groups of three and when this has been accomplished as shown, the original is divided into the required four pieces.
One of the problems set in a previous chapter asked for a square to be divided into four pieces which were the same in size, shape and area. Some people went further than the usual obvious divisions by dividing the square into sixteen small squares and then reassembling them in different ways to give a variety of new ways of dividing the square into four.
In a sense the whole point of language is to give separate units that can be moved around and put together in different ways. The danger is that these different ways soon become established as fixed units themselves and not as temporary arrangements of other units.
If one takes any situation and breaks it down into fractions one can then restructure the situation by putting the fractions together in a new way.
True and false divisions
It might seem that what is being recommended is the analysis of a situation into its component parts. This is not so. One is not trying to find the true component parts of a situation, one is trying to create parts. The natural or true lines of division are usually not much good as the parts tend to reassemble to give the original pattern since this is how the pattern came about in the first place. With artificial divisions however there is more opportunity to put units together in novel ways. As is so often the case with lateral thinking one is looking for a provocative arrangement of information that can lead to a new way of looking at things. One is not trying to discover the correct way. What one needs is something to be going on with and for this purpose any sort of fractionation will do.
In the design of an apple picking machine the problem could have been fractionated into the following parts:
reaching
finding
picking
transport to the ground
undamaged apples.
In reassembling these fractions one might have put reaching-finding-picking together and then substituted shaking the tree for all these functions. One would then be left with transport to the ground in such a way that the apples were not damaged. On the other hand one might have put reaching-undamaged apples-transport to the ground together and come up with some elevated canvas platform which would be raised towards the apples.
Someone else might have fractionated the problem in a different way:
contribution of tree to apple picking
contribution of apples
contribution of machine
This particular type of fractionation might have led on to the idea of growing the trees in a special way that would make it easier to pick the apples.
Complete division and overlap
Since the purpose of fractionation is to break up the solid unity of a fixed pattern rather than to provide a descriptive analysis it does not matter if the fractions do not cover the whole situation. It is enough that one has something to work with. It is enough that one has a new arrangement of information to provoke restructuring of the original pattern.
For the same reason it does not matter if some of the fractions overlap. It is much better to produce some sort of fractionation no matter how impure than to sit wondering how a pure fractionation can be made.
If the problem being considered was ‘transport by bus’ the following fractionation might be made:
Choice of route.
Frequency.
Convenience.
Number of people using the service.
Number of people using the service at different times.
Size of bus.
Economics of use and cost.
Alternative transport.
Number of people who would have to use the bus and number who would nice to use it if it were running.
Clearly these fractions are not all separate but overlap to a considerable extent, for instance convenience is a matter of route, frequency and perhaps size of the bus. Economics of use and cost include the number of people using the service, size of bus and several other of the fractions.
Two unit division
Whenever there is difficulty in dividing something into fractions it can be useful to adopt the artificial technique of division into two units or fractions. The two fractions so produced are themselves further divided into two more fractions and so on until one has a satisfactory number of fractions.
This technique is highly artificial and it can mean that several important features are quite overlooked. The advantage is that it is much easier to find two fractions than to find several. It is not a question of dividing something into two equal fractions for any two fractions will do no matter how unequal. Nor do the lines of division have to reveal natural fractions. The fractions may be very artificial and yet be useful.
Applied to the apple picking problem the two unit division might go as follows:
apple picking
problem
apple
picking
delicate
separate
remove
transport
damaging
damaged
finding
density
hold
jerk
to ground
container
The technique of two unit division is not so much a technique but a method for encouraging the fractionation of a situation.
Practice
1. Fractionation
The students are given a subject and asked to fractionate it. The subject may be a design project, a problem or any specific theme. Suggestions for subjects might include:
Unloading ships in habour.
Restaurant meals.
Catching and marketing of fish.
Organization of a football league.
Building a bridge.
Newspapers.
The separate fractionation lists are collected from the students. If there is time the results are analysed in terms of the most popular fractions. If there is not time then individual lists are read out and particularly ingenious fractionations are commented upon. The main purpose is to show the variety or the uniformity of the approach.
2. Reassembly
From the fractionation lists obtained above (or from a special session) are extracted small groups of two or three fractions.
These are then given to the students who are asked to put them together again in an attempt to generate a new way of looking at the situation.
3. Picking out fractions
Here the subject is presented to the students as a group. They are asked to pick out fractions one after the other. One student volunteers one fraction and then another student follows with a further fraction. This continues as long as suggestions are still coming in. It does not matter if there is a considerable degree of overlap between the suggested fractions. If there seems to be a direct duplication this is pointed out to the person making the suggestion and he is asked to say why he thinks there is a difference. It does not matter whether the difference is a very valid one or not so long as he himself seems to think there is a difference.
4. Working backwards.
This is as much a game as anything eke. A list of fractions is taken from a previous session with another group and the students are asked to try and guess what the subject was. Obvious references to the subject are deleted and substituted by the word ‘blank’.
Another way in which this can be done is to give the students a list of five subjects only one of which is to be fractionated by each student At the end some of the fraction lists are read out and the students have to decide which of the five original subjects a list refers to.
5. Two unit division
Here a subject is given to the students who are asked to carry out a two unit division on it. The end results are then compared. A quick comparison can be made between the first two units chosen by the different students. This can serve to show the variety of approaches used by the different students.
6. Sequential two unit division
A subject is given and then one student is asked to divide it into two units. Then another student is required to divide one of the units into two further units and so on. Unlike other practice sessions this one is not a matter of volunteering a solution but of being asked to provide one. The intention is to show that it is always possible to divide something into two units by picking out one unit and having the remainder as the other unit.
Summary
Fractionation may seem to be no more than straightforward analysis. The emphasis is however quite different. The aim is not to provide a complete or true breakdown of the situation into its component parts (as in analysis) but to provide material which can be used to stimulate restructuring of the original situation. The aim is restructuring not explanation. The fractions do not have to be complete or natural for the emphasis is not on whether they are valid but on what they can bring about. The purpose of fractionation is to escape from the inhibiting unity of a fixed pattern to the more generative situation of several fractions.
The reversal method 14
Fractionation is a useful method for generating alternative ways of looking at a situation. But it has certain limitations. The fractions chosen are themselves fixed patterns and usually standard patterns. The choice of fractions is usually a vertical choice which follows the most natural lines of division. The result is that the fractions come together again to give a standard view of the situation. Although fractionation makes it easier to look at a situation in a different way the actual choice of fractions limits the variety of alternatives that can be generated. A simple square shape is shown opposite. If one had to break this down into fractions one might choose the fractions shown in any of the other figures. Yet the choice of fraction will determine the shape that can be made by reassembling the fractions differently.
The reversal method is more lateral in nature than the fractionation one. It tends to produce more unusual restructuring.
If you give someone an open-ended creative problem there is great difficulty in getting started. There is difficulty in moving at all. The person presented with the problem seems to say, ‘Where do I go, what do I do?’ This was very obvious when I asked a group of people to redesign some feature of the human body. One obvious approach was to take some actual feature as a starting point and then to modify it in some simple way. Thus there were suggestions to increase the number of arms or to lengthen the arms or to make them more flexible.
Unless one is going to sit around waiting for inspiration the most practical way to get moving is to work on what one has. In a swimming race when tie swimmers come to turn at the end of the pool they kick hard against the end to increase their speed. In the reversal method one kicks hard against what is there and fixed in order to move away in the opposite direction.
Wherever a direction is indicated then the opposite direction is equally well defined. If you go towards New York you are going away from London (or whatever other place you started from). Whenever there is action then the opposite action is indicated. If you are filling a bath full of water then the opposite action is to empty the bath. If something is happening over time then one merely runs the time scale backwards in order to find the reverse process. This is rather like running a ciné film backwards. Whenever there is a one way relationship between two parties the situation can be reversed by changing the direction of this relationship. If a person is supposed to obey the government then the reversal would imply that the government ought to obey a person (or people).
In the reversal method one takes things as they are and then turns them round, inside out, upside down, back to front. Then one sees what happens. It is a provocative rearrangement of information. You make water run uphill instead of downhill. Instead of driving a car the car leads you.
Different types of reversal
There are usually several different ways in which one can ‘reverse’ a given situation. There is no one correct way. Nor should there be any search for some true reversal. Any sort of reversal will do.
For instance if the situation is, ‘a policeman organizing traffic’, then the following reversals might be made:
The traffic organizes (controls) the policeman.
The policeman disorganizes the traffic.
Which of these reversals is the better one? Either will do. It is impossible to say which arrangement will be the more useful until it has proved so. It is not a matter of choosing the more reasonable reversal or the more unreasonable one. One is searching for alternatives, for change, for provocative arrangements of information.
In lateral thinking one is not looking for the right answer but for a different arrangement of information which will provoke a different way of looking at the situation.
The purpose of the reversal procedure
Very often the reversal procedure leads to a way of looking at the situation that is obviously wrong or ridiculous. What then is the point of doing it?
One uses the reversal procedure in order to escape from the absolute necessity to look at the situation in the standard way. It does not matter whether the new way makes sense or not for once one escapes then it becomes easier to move in other directions as well.
By disrupting the original way of looking at the situation one frees information that can come together in a new way.
To overcome the terror of being wrong, of taking a step that is not fully justified.
The main purpose is provocative. By making the reversal one moves to a new position. Then one sees what happens.
Occasionally the reversed approach is useful in itself.
With the policeman situation the first reversal supposed that the traffic was controlling the policeman. This would lead to consideration of the demand for more policemen as traffic became more complex, the need for redistribution of policemen according to traffic conditions. It would make one realize that in fact the traffic does actually control the policeman since his behaviour depends on the traffic build up in different roads. How quickly does he react to this? How sensitive is he to this? How well informed can he be of this? Since the traffic is controlling the policeman who is controlling the traffic why not organize things so that the traffic controlled itself?
The second reversal in the policeman situation supposed that the policeman was disorganizing the traf
fic. This would lead to a consideration of whether natural flow, traffic lights or a policeman was most efficient. If a policeman was more efficient than the lights, what was the added factor — could this be built into the lights? Was it perhaps easier for the traffic to adjust to fixed patterns of direction rather than to the unpredictable reactions of the policeman?
A flock of sheep was moving slowly down a country lane which was bounded by high banks. A motorist in a hurry came up behind the flock and urged the shepherd to move his sheep to the side so that the car could drive through. The shepherd refused since he could not be sure of keeping all the sheep out of the way of the car in such a narrow lane. Instead he reversed the situation. He told the car to stop and then he quietly turned the flock round and drove it back past the stationary car.
In Aesop’s fable the water in the jug was at too low a level for the bird to drink. The bird was thinking of taking water out of the jug but instead he thought of putting something in. So he dropped pebbles into the jug until the level of water rose high enough for him to drink.
The duchess was much overweight. Physician after physician tried to reduce her weight by putting her on a near starvation diet and each physician was in turn dismissed on account of the unpleasantness of the diet. At last there came a physician who fussed over the good lady. Unlike the others he told her that she was not eating enough to sustain her huge body. He recommended that she drink a glass of sweetened milk half-an-hour before all meals (which of course reduced her appetite very much).
Lateral Thinking Page 10
