Techniques that apply lateral thinking to problems are characterized by the shifting of thinking patterns, away from entrenched or predictable thinking to new or unexpected ideas. A new idea that is the result of lateral thinking is not always a helpful one, but when a good idea is discovered in this way it is usually obvious in hindsight, which is a feature lateral thinking shares with a joke.
There are a number of mental tools or methods that can be used to bring about lateral thinking. These include the following:
Random Entry: Choose an object at random, or a noun from a dictionary, and associate that with the area you are thinking about.
For example imagine you are thinking about how to improve Wikipedia. Choosing an object at random from an office you might see a fax machine. A fax machine transmits images over the phone to paper. Fax machines are becoming rare. People send faxes directly to known phone numbers. Perhaps this makes you think of providing ways to embed wiki articles in emails and other websites, as is done with youtube videos. Does it stimulate other Wikipedia ideas for you?
Provocation: Declare the usual perception out of bounds, or provide some provocative alternative to the usual situation under consideration. Prefix the provocation with the term 'Po" to signal that the provocation is not a valid idea put up for judgement but a stimulus for new perception.
As an example see the provocation on cars having square wheels given as example 2 below.
Challenge: Simply challenge the way things have always been done or seen, or the way they are. This is done not to show there is anything wrong with the existing situation but simply to direct your perceptions to exploring outside the current area.
For example you could challenge coffee cups being produced with a handle. There is nothing wrong with coffee cups having handles so the challenge is a direction to explore without defending the status quo. The reason for the handle seems to be that the cup is often too hot to hold directly. Perhaps coffee cups could be made with insulated finger grips, or there could be separate coffee cup holders similar to beer holders.
There are many other techniques ranging from Focus methods through to Harvesting and Concept Shaping. All these tools are practical matters for circumstances where our normal automatic perceptions and pattern matching tend to keep us trapped "within the box".
Edward de Bono points out that the term problem solving implies that there is a problem to respond to and that it can be resolved. That eliminates situations where there is no problem or a problem exists that cannot be resolved. It is logical to think about making a good situation, that has no problems, into a better situation. Sometimes a problem cannot be solved by removing its cause.
We may need to solve some problems not by removing the cause but by designing the way forward even if the cause remains in place. – (Edward de Bono)
Lateral thinking can be used to help in solving problems but can also be used for much more.
The answer appears to be 25 feet deep. This answer assumes that the thinker has followed a simple mathematical relationship suggested by the description given, but we can generate some lateral thinking ideas about what affects the size of the hole which may lead to different answers:
The most useful ideas listed above are outside the simple mathematics implied by the question.
Consider the statement "Cars should have square wheels." When considered with critical thinking, this would be evaluated as a poor suggestion and dismissed as impractical. The lateral thinking treatment of the same statement would be to speculate where it leads. Humor is taken intentionally with lateral thinking. A person would imagine "as if" this were the case, and describe the effects or qualities. Someone might observe: square wheels would produce very predictable bumps. If bumps can be predicted, then suspension can be designed to compensate. This leads to the idea of active suspension. A sensor connected to suspension could examine the road surface ahead on cars with round wheels too. A car could have a sensor for determining when it was going to hit a bump that feeds back to suspension that would know to compensate. The initial "provocative" statement has been left behind, but it has also been used to indirectly generate the new and potentially more useful idea.
A man and his son are in a car crash. The man is killed and the son is taken to hospital gravely injured. When he gets there, the surgeon says "I can't operate on this boy- he is my son!" How is this possible?
This is an example of an instant perception blocking the mind's ability to explore alternatives. In this case the instant perception is that most people imagine a surgeon as a male; this leads to the conclusion that either the surgeon or the "father" in the car crash was not the boy's real father.
If you switch your perception to allow for a female surgeon then the answer is suddenly obvious, the surgeon is the boy's mother.
Most people imagine a surgeon as a male, but in this case it is the opposite! Lateral thinking is the method of switching perceptions to allow the alternate view point.
Another example for an instant perception blocking the mind's ability to explore alternatives is that one assumes the surgeon is telling the truth. Maybe he was simply wrong (the son might have looked exactly like his own son) or maybe he was lying, because for some reason he didn't want to operate on him (he could have felt bad or drunk alcohol before).
Or the son could have two fathers - one of them could have been his adoptive father. Or if the boy was one of two separated twins, with the other growing up with the surgeon for whatever reason, then the surgeon would have recognized the boy as his own son.
Or the surgeon is actually talking about the man who died in the accident, making the surgeon the boy's grandfather.
When using lateral thinking puzzles it is important to check your assumptions. You need to be open-minded, flexible and creative in your questioning and able to put lots of different clues and pieces of information together. Once you reach a viable solution you keep going in order to refine it or replace it with a better solution.
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