Choosing an analogy
It might be thought that the method would only be of use if a particularly apt analogy were chosen. This is not so. The analogy does not have to fit all along. Sometimes it is better when it does not fit for then there is an effort to relate it to the problem and from this effort can arise new ways of looking at the problem. The analogy is a provocative device which is used to force a new way of looking at the situation.
In general the analogies should deal with very concrete situations and very familiar ones. There should be a lot going on. And what is going on must be definite. The analogy does not have to be rich in processes or functions or relationships for these can be generated out of any sort of analogy by the way it is looked at.
The analogy does not even have to be a real life situation. It can be a story provided the development of that story is definite.
As an analogy for the problem of vertical thinking one might use the story of how monkeys are supposedly caught by burying a narrow mouthed jar of nuts in the ground. A monkey comes along, puts his paw into the jar and grabs a handful of nuts. But the mouth of the jar is of such a size mat it will only admit an empty paw but not a clenched paw full of nuts. The monkey is unwilling to let go of the nuts and so he is trapped.
With vertical thinking one grasps the obvious way of looking at a situation because it has proved useful in the past. Once one has grasped it one is trapped because one is very reluctant to let go. What should the monkey do? Should he refuse to explore the jar? This would be a refusal to explore new situations. Should he deny that the nuts were attractive? It would be silly to deny the usefulness of something for fear of being harmed by it on some occasion. Would it be better if the monkey had not noticed the jar? To be protected by chance is a very poor form of protection. Presumably the best thing would be for the monkey to see the nuts, perhaps even grab them, then to realize that the nuts were trapping it, to let go of them, and to find another way of getting at the nuts — perhaps by digging up the jar and emptying it out. So the major danger in vertical thinking is not that of being trapped by the obvious but of failing to realize mat one may be trapped by the obvious. It is not a matter of avoiding vertical thinking but of using it and at the same time being aware that it might be necessary to escape from a particular way of looking at a situation.
Practice
1. Demonstration
In order to make clear what is wanted during the practice sessions, it is useful to start by taking a particular problem, choosing an analogy, developing the analogy and relating it to the problem all along. This could be done on the blackboard. Suggestions from students would be accepted but they would not be asked for.
2. Relating an analogy to me problem
The problem would be given to the class. The teacher would develop an analogy on the blackboard and the students would be asked to volunteer at each point a suggestion as to how any particular development in the analogy could be referred to the given problem.
3. Individual effort.
Here the analogy would again be developed by the teacher but this time the individual students would each relate it to the problem, writing down their ideas on a piece of paper. At the end these results would be collected and comments of the following sort could be made:
(1). The variety of different ways in which the analogy was related to the problem.
(2). Consistency or lack of consistency in the development of the problem (i.e. was a feature in the analogy always referred to the same feature in the problem or did it change? There is no special virtue in consistency.)
(3). Richness of development with every detail translated from the analogy to the problem or poverty of development when only the major points were transferred.
4. Functions, processes, relationships
Here an analogy is developed by the teacher in concrete terms. The students (working on their own) have to repeat the analogy but using general terms of process, function and relationship, in place of the concrete terms. This is an exercise in abstracting these things from analogies.
Possible analogies for this sort of abstraction might include:
Having a bath.
Frying potatoes.
Sending a letter.
Trying to untangle a ball of string.
Learning to swim.
5. Choosing analogies
A list of problems or situations would be given to the students who would be asked in open class to volunteer analogies which might be fitted to each of the listed problems. Any student who volunteered a suggestion would be asked to elaborate it briefly by showing how he would apply it to the problem.
Possible problems for this exercise might include:
Design a machine to give change.
Ways of mating shopping easier.
Better clothes.
Ensuring adequate water supply for cities.
What to do with junked cars.
6. Set problem
A problem is given to the classroom and each student chooses his own analogy and works through it relating it to the problem. At the end the results are collected and commented upon. In the course of such comments one might compare the different types of analogy chosen. One might also compare the different aspects of the problem that have been highlighted by the different analogies. There may be occasions when the same idea has been reached by completely different pathways.
7. Same problem, different analogies
The same problem is given to all the students but different students are assigned different analogies. This can be done as a group exercise. The students are divided into groups all of which are to consider the same problem. Each group however is given a different analogy. At the end of the session a spokesman for the group (equivalent to the notetaker in the brainstorming session) summarizes how the group related the analogy to the problem.
Suggested problem:
Finding the way in fog.
Suggested analogies:
A shortsighted person finding his way around.
A traveller in a strange country trying to find the railway station.
Looking for something that has been lost in the house (e.g. a ball of string).
Doing a crossword puzzle.
8. Same analogy, different problems
This can be carried out in the same way as the previous session, either on an individual basis or on a group basis. Different problems are set but in each case they must be related to the same analogy. At the end notes are compared to see how well the analogy has been fitted to the different problems.
Suggested analogy:
Trying to start a car on a cold winter morning.
Suggested problems:
How to tackle a difficult mathematical problem.
Rescuing a cat from a high ledge.
Fishing.
Getting tickets f or a very popular football match.
Summary
Analogies offer a convenient method for getting going when one is trying to find new ways of looking at a situation instead of just waiting for inspiration. As with other lateral thinking techniques the important point is that one does not start moving only when one can see where one is going. One starts moving for the sake of moving and then sees what happens. An analogy is a convenient way of getting moving for analogies have a definite ‘life’ of their own. There is no attempt to use analogies to prove anything. They are only used as stimulation. The main usefulness of analogies is as vehicles for functions, processes, and relationships, which can then be transferred to the problem under consideration to help restructure it.
Choice of entry point and attention area 17
The most important feature of the mind as an information processing system is its ability to choose. This ability to choose arises directly from the mechanical behaviour of the mind as a self-maximizing memory system. Such a system has a limited area of attention. A limited area of attention can only settle on part of an information field. That part of the information field on wh
ich the limited attention area settles is thereby ‘chosen’ or ‘selected’. The process is in fact a passive one bat one can still talk of choice or selection. The behaviour of this limited attention area and the system mechanics underlying it ate explained in detail elsewhere.*
‘Attention area’ refers to the part of a situation or problem that is attended to. ‘Entry point’ refers to the part of a problem or situation that is first attended to. An entry point is obviously the first area of attention and it may or may not be succeeded by others depending on the complexity of the situation.
From an insight restructuring point of view the choice of entry point is of the utmost importance. One could almost say that when no further information is added to the system that it is the choice of entry point which brings about insight restructuring. Why this is so follows directly from the mechanics of this type of information processing system.*
Patterns are established on the memory surface that is mind by the sequence of arrival of information. Once established these patterns have a ‘natural’ behaviour in so far as they tend to develop in certain ways, and to link up with other patterns. The purpose of lateral thinking is to restructure these patterns and arrange information to give new patterns.
The series of diagrams above illustrates the natural patterning behaviour of the memory surface of mind:
1. This shows the available information field.
2. Information is structured into a natural pattern.
3. The natural pattern has a natural line of development.
4. In developing the pattern there is a natural entry point from which onestaits.
5. From the original information field only a limited area was selected by attention. Had the attention field been different then the pattern and its development would also have been different.
The choice of entry point is of huge importance because the historical sequence in which ideas follow one another can completely determine the final outcome even if the ideas themselves are the same. If you fill a bath using only the hot tap and then add the cold water at the end the bathroom will be thoroughly steamed up and the walls will be damp. If however you run some of the cold water in right at the beginning then there will be no steaming up and the walls will remain dry. Yet the actual amounts of hot and cold water will be exactly the same in each case.
The difference may be huge even if the actual ideas considered are the same but in practice a different entry point will usually mean a different train of ideas. A picture of a man with a stick in his hand followed by a picture of a dog running might suggest that the man is throwing sticks for the dog to retrieve. A picture of a dog running followed by a picture of the man with a stick in his hand might suggest that the man is chasing the dog out of his garden.
Entry point
Divide a triangle into three parts in such a way that the parts can be put together again to form a rectangle or a square.
The problem is quite a difficult one since the shape of the triangle is not specified. You first have to choose a triangle shape and then find out how it can be divided up into three pieces that can be put together to give the square or rectangle.
The solution to the problem is shown opposite. It is obviously much easier to start with the square instead of with the triangle which was suggested as the starting point There can be no doubt about the shape of a square whereas the shape of a triangle (and to a lesser extent of a rectangle) is variable. Since the three parts have to fit together again to form a square one can solve the problem by dividing up a square into diree farts that can be put together again to give a rectangle or a triangle. Two ways of doing this are shown overleaf.
In many children’s books there is the sort of puzzle in which are shown three fishermen whose lines hate got tangled up. At the bottom of the picture a fish is shown attached to one of the lines. The problem is to find which fisherman has caught the fish. The children are supposed to follow the line down from the tip of the fishing rod in order to find which Line has the fish at the end. This may involve one, two or three attempts since the fish may be on any of the three lines. It is obviously much easier to start at the other end and trace the line upwards from the fish to the fisherman. That way there need never be more than one attempt.
There is a simple problem which requires one to draw the outline of a piece of cardboard which is so shaped that with a single straight cut the piece can be divided into four smaller pieces which are exactly alike in size, shape and area. No folding is allowed.
The usual response to this problem is shown on page 159 with the percentage of people giving each type of answer. The solution given by groups B and C is obviously incorrect for a ‘cut’ has no thickness and so will divide the shape into two pieces and not four as required.
Answer D is correct It is interesting that answer F is so rare for in hindsight it seems the easiest of them all (the explanation is that it is very difficult to think forward asymmetrically and in answer F the pieces are not all used in the same way). The important point of this problem, however, is that if one starts at the wrong end the problem is much easier to solve. Instead of trying to devise a shape that can be divided into four equal pieces one starts off with four equal pieces and clusters them around an imaginary cut At first one might arrange them as shown on page 160 but there is no difficulty in moving on to the next stage in which one shifts them along to give the solution.
To start at the wrong end and work backwards is quite a well-known problem solving technique. The reason why it is effective is that the line of thought may be quite different from what it would have been had one started at the beginning. There is no
need to actually start at the solution end. It is convenient to do so since the solution is often clearly defined. But one can start at any point If there is no obvious point then one must be generated.
Attention area
The entry point is the first attention area. Usually attention starts at this point bet eventually cavers the whole problem. Sometimes however important parts of the problem are completely left out It is only when these parts are brought under attention that the problem can be solved.
In one of Sherlock Holmes’s cases there was a large dog. Dr Watson dismissed the dog as being of no importance because it had done nothing on the night of the crime. Sherlock Holmes pointed out that the great significance of the dog was precisely that it had done nothing. He shifted attention from the significance of what the dog might have done to the significance of the fact that it had done nothing. This meant that the criminal must have been known to the dog.
In Shakespeare’s Merchant of Venice there comes the moment when Shylock demands the pound of flesh that is owed to him by the merchant as the result of a bargain. Shylock is outwitted by Portia who shifts attention from the flesh which is due to Shylock to the blood that must go with it. Since that is not part of the bargain Shylock could be charged with the serious offence of spilling blood. Thus by a shift of attention which brought into the problem something that would otherwise have been left out the problem was solved.
Two sets of circles are shown overleaf. In each case count up the number of solid circles as quickly as possible.
The obvious way to tackle this problem is to count the solid circles in each case. But when you come to the second set of circles it is much easier to shift attention to the open circles, find out the total number of these by multiplying the number of circles along one edge of the rectangle by the number along the other edge, and then subtract the small number of open circles from this total. The answer is the number of filled circles.
In a tennis tournament there are one hundred and eleven entrants. It is a singles knockout tournament and you as secretary have to arrange the matches. What is the minimum number of matches that would have to be arranged with this number of entrants?
When faced with this problem most people draw little diagrams showing the actual pairings in each match and the number of byes. Others try and work it out by referen
ce to 2n (i.e. 4, 8, 16, 32 etc). In fact the answer is one hundred and ten matches and one can work this out at once without any complicated mathematics. To work it out one must shift attention from the winners of each match to the losers (in whom no one is usually very interested). Since there an only be one winner there must be one hundred and ten losers. Each loser can only lose once so there must be one hundred and ten matches.
In a sense this last problem could be regarded as an example of the usefulness of shifting the entry point accept that the losers are usually never considered at all Very often in a situation it is not just a matter of the order in which the parts are attended to but the choice of parts that are going to be attended to at all If something is left out of consideration then it is very unlikely that it will ever come back in later on. Nor is there usually anything in what is being attended to that will indicate what has been left out.
For these reasons the choice of attention area can make a huge difference to the way the situation is looked at. To restructure the situation one may need no more than a slight shift in attention. On the other hand if there is no shift in attention it may be very difficult to look at the situation in a different way.
Rotation of attention
Since attention is basically a passive phenomenon it is no use just hoping that attention will flow in the right direction. One has to do something about it Even though the process is passive one can still direct attention by providing a framework which will affect it. For instance you could decide that whenever you found yourself staring at something then you would shift your gaze to a spot about two feet to the left of whatever you were staring at After a while attention would automatically shift to that spot even though there was nothing there which attracted it Attention follows the patterns set up in the mind not the external ones.