Lateral thinking

Lateral thinking is a term coined by Edward de Bono, a Maltese psychologist, physician, and writer. He defines it as a technique of problem solving by approaching problems indirectly at diverse angles instead of concentrating on one approach at length. For example:
 * It took two hours for two men to dig a hole five feet deep. How deep would it have been if ten men had dug the hole for two hours?

The answer appears to be 25 feet deep, but we can generate some Lateral thinking ideas about what affects the size of the hole:
 * A hole may need to be of a certain size or shape so digging might stop early at a required depth.
 * The deeper a hole is the more effort is required to dig it since waste soil needs to be lifted higher to the ground level. There is a limit to how deep a hole can be dug by man power without use of ladders or hoists for soil removal, and 25 feet is beyond this limit.
 * Deeper soil layers may be harder to dig out, or we may hit bedrock or the water table.
 * Each man digging needs space to use a shovel.
 * It is possible that with more people working on a project, each person may become less efficient due to increased opportunity for distraction, the assumption he can slack off, more people to talk to, etc.
 * More men could work in shifts to dig faster for longer.
 * There are more men but are there more shovels?
 * The two hours dug by ten men may be under different weather conditions than the two hours dug by two men.
 * Rain could flood the hole to prevent digging.
 * Temperature conditions may freeze the men before they finish.
 * Would we rather have 5 holes each 5 feet deep?
 * The two men may be an engineering crew with digging machinery.
 * What if one man in each group is a manager who will not actually dig?
 * The extra eight men might not be strong enough to dig, or much stronger than the first two.
 * Extraterrestrials might decide to blow up the planet before the hole is dug.
 * God might strike them down for working on the sabbath.
 * They may get eaten by a previously undiscovered species of ravenous underground razor-toothed worms.
 * A massive planet-dissolving dust cloud might destroy the earth.
 * Maybe the question was asked in a strange foreign language that resembles English but whose words have completely different meanings and it was just a coincidence that the question made sense in English.
 * Maybe this is happening in another universe where numbers are reversed.

The most useful ideas listed above are outside the simple mathematics implied by the question. Lateral thinking is about reasoning that is not immediately obvious and about ideas that may not be obtainable by using only traditional step-by-step logic.

Techniques that apply lateral thinking to problems are characterised 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.

Provocative operations
A notation used in lateral thinking, is Po. This stands for Provocative operation and is used to propose an idea which may not necessarily be a solution or a 'good' idea in itself, but moves thinking forward to a new place where new ideas may be produced.

For example, The problem is that Tom won't come to the mountain.
 * Po: The mountain must come to Tom (the classic answer).
 * Po: Use a video conference (an IT idea).
 * Po: Use an intermediary.
 * Po: Ask him what he wants to come to the mountain (a deal)
 * Po: See if he'll accept a free timeshare slot in a holiday home (that just happens to be on the mountain).
 * Po: Wait until he changes his mind.
 * Po: Cut your losses and tackle a different problem.

These are all Provocative operations and characterise a stage of lateral thinking where the ideas generated need further work in order to become solutions.