Are you thinking too much?

Take it easy. It could be the fastest way to the really intelligent answer

Thinking in a hurry, under pressure to produce results, is considered lean and efficient. To be "bright" is to be able to think fast. We use the word "slow" as a euphemism for stupid.

"Hare-brained" thinking, the kind presumed to deliver the best results, is usually required to be systematic, articulate, explicit and deliberate. An answer in school (or the laboratory, or the board room) is no good if you can't justify your opinion. In such a culture, other kinds of thinking - slower, more intuitive, more poetic, more "tortoise-minded" - are treated as recreational , marginal, sloppy or just plain quaint.

Yet, our ideas, and often our best, most ingenious ideas, do not arrive as the result of faultless chains of reasoning. They "occur to us". They "pop into our heads". They come out of the blue. When we are relaxed we operate very largely by intuition. We happily allow ourselves to be nudged by feelings and impulses that do not come with an explicit justification. But put "on the spot" in a meeting, or faced with an urgent problem, we may act as if these promptings were unreliable. Intuition, we feel, will not stand up to scrutiny.

There is now a body of research, however, which shows that intuition is more valuable and more trustworthy than we think; and that we disdain it to our detriment.

Intuitions can be wrong, but that does not mean they are worthless. Intuitions are properly seen as "good guesses"; hunches or hypotheses thrown up by the undermind which deserve serious, but not uncritical, attention. They offer an overall "take" on a situation that manifests itself not - not yet - as a reasoned analysis, but as an inkling or an image. Behind the scenes, the undermind may have integrated into this tangible prompt a host of different considerations, including analogies to past experience and aspects of the present situation, of which the conscious mind may not have even been aware.

Fast intuitions - "snap judgments" and quick reactions - are vital responses for the human being. When the present event is a variation on a familiar theme, it pays to be able to classify it and react in habitual fashion. To spend time pondering on insignificant details is sometimes wasteful, or even dangerous. No need to inspect the number plate of the bus as it bears down upon you. But these reflexes work to our detriment when a new situation looks similar to ones we have experienced in the past, but is actually different. Then the balance of priorities shifts, and it is now the quick, stereotyped response that is the risky one, while more leisurely scrutiny can pay dividends.

Let me illustrate how intuition works with an example the philosopher Wittgenstein was fond of using. Imagine that the Earth has been smoothed over so that it forms a perfect sphere, and that a piece of (non-elastic) string has been tied snugly round the equator. Now suppose that the string is untied, and another 2 metres added to the total length, which is then spaced out so that the gap which has been created between the string and the Earth's surface is the same all the way round. How big is this gap? Could you slide a hair under the string? A coin? A paperback book? Could you crawl under it? Most people's strong intuition is that the gap would be tiny, of the order of a millimetre or two at the most.

In fact, it is about 32cms, or just over a foot; so you could indeed crawl under the string (the proof is given on page 20). The strange thing, when you work out the geometry, is that the size of the gap turns out to be independent of the size of the sphere (or circle). You would get the same-sized gap whether you started with a tennis ball, a circus ring, or the universe.

Most people's intuition, on the other hand, insists that the larger the original object, the less "difference" the two- metre extension will make: in other words, the smaller the gap.

Intuition goes awry here because it is based on the unconscious assumption that this situation is analogous to apparently similar situations where the idea that "the larger the object, the smaller the change" does apply. If we were to change the puzzle slightly, and say: "Supposing the oceans were neatened up into a huge cylinder, how much would the level rise if we added 20 litres of water?", then the answer is indeed "not very much"; and we would be right, in this instance, to assume that the larger the original volume, the smaller the difference to its depth. The 20 litres would make much more difference to the depth of a paddling pool. It just turns out that this plausible assumption works for the height of cylinders, but not for the radius of circles. It is a good guess that in one case turns out to be right, and in the other case wrong.

FAST intuitions depend on the undermind taking a quick look at the situation and finding an analogy which seems to offer understanding and prediction. These unconscious analogies surface as intuitions. Whether they are right or not depends not on how "intuitive" they are, but on the appropriateness of the underlying analogy. Often we are right but sometimes the undermind is fooled by appearances, and leads us off in the wrong direction.

The power of context to flip people into one way of knowing rather than another - and to produce quite different responses to what is logically the same problem - is widespread, and very striking. In a study of 10- year-olds by Ceci and Bronfenbrenner in 1985, the children sat in front of a computer screen in the centre of which one of a variety of geometric shapes would periodically appear. Their job was to predict (by moving the cursor with a mouse) in which direction, and how far, the shape was about to jump. The shapes were circles, squares and triangles that could be dark- or light-coloured, and large or small. In theory, the children could have predicted the jump - squares always went to the right, circles to the left, and triangles stayed in the middle; dark things went up and light things down; and large things went a short distance and small things a long distance. After 750 trials, the children had learnt virtually nothing.

However, after making a small change to the task, which had no effect at all on its logical difficulty, things looked very different. All the experimenters did was replace the three geometrical shapes with animals; swap the normal computer cursor for an image of a "net"; add sound effects; and tell the children that this was a game in which they had to try to catch the animals as they moved. After less than half as many goes, all the children were placing the net in the right position to "capture" the animals. The geometrical shapes told the children that this was a school- type task. The other version led them to reinterpret the display as a "video game" - and this flipped them into an intuitive mode which enabled them to pick up the relevant relationships easily and unconsciously.

There are a number of potentially negative effects of encouraging people to be more reflective and explicit about their decisions. In choosing a picture to hang on the wall, or a meal to eat, there are many interwoven considerations to be taken into account, not all of which are equally explained. When the decision is made in an intuitive way, these considerations are treated in a more integrated fashion, and those that are hard to articulate are given due weight. However, when people are forced (or encouraged) to be analytical, the problem is deconstructed into considerations that are more amenable to being put into words, excluding or downgrading non- verbal considerations that are primarily sensory or affective. The result is decisions which seem "sensible", but which fail to take into account non-cognitive factors.

Additionally, the more carefully one analyses the different alternatives, the more one finds that there are good and bad aspects to each, and the greater the consequent tendency for judgments to become more moderate, more similar and therefore less decisive. Anyone who has agonised over a choice while shopping, and then regretted the decision immediately they have got the item home, will be familiar with this phenomenon. When people say they should have listened to their heart, or their gut feeling, they are referring to this dislocation between conscious and unconscious decision- making.

New research has demonstrated convincingly that the tortoise mind is indeed a vital partner to the hare brain; that we think less intelligently if we ignore it; and that we can - and should - develop the art of contemplation. The general conclusion of these studies is that speedy analytical thinking is an extraordinary tool, but it is not good for every job.

The trouble is that the hare brain, being tidy and explicit, as well as fast, has to neaten a problem up into familiar words and concepts before it can get started, and in doing so, lays itself open to five sources of error:

l it is liable to neglect experience and information not judged to be of immediate relevance

l it may ignore aspects of the situation that are not verbal

l it may impart assumptions about what is normal or usual

l it may fail to heed valuable hunches

l it may insist on using verbal thought even when it is the wrong medium.

In a series of experiments, Jonathan Schooler and colleagues at the University of Pittsburgh explored two types of problems looking particularly to see where active thinking helped and where it hindered.

"Insight problems" (see above) are those where people are in possession of all the information and ability necessary to solve them, but where there is a tendency to feel blocked or "stumped", before the solution becomes obvious. In such problems, the difficulty is often caused by the tendency to make some unconscious assumptions that fail to retrieve knowledge that would actually be helpful.

BY CONTRAST, in the two "analytical" problems, no additional knowledge has to be supplied by the problem-solver, and it is unlikely that any assumptions will be made unwittingly that would make the problems harder to solve. All that is required is a meticulous fitting together of the pieces of information and the answer will emerge. We might imagine that if people were asked to think out loud while attempting an analytical problem their words might track their thoughts quite easily and accurately, and would be positively related to the actual solution.

But with the insight problems, a different kind of thinking is required, one which is more of the intuitive kind. Our culture has somehow learned to mistrust the brain and misrepresent the mind. By struggling to maintain a sense of conscious comprehension, we lock ourselves into one tight mode disabling others that are more fluid. In one of the Winnie the Pooh books, Pooh, while out with Rabbit, hums a song. Rabbit asks him how he had thought of it. "I don't know," said Pooh. "It just sort of came to me." "Ah," said Rabbit, who never let things come to him, but always went and fetched them.

We seem to find ourselves in a society of rabbits who have forgotten how to let things come.

'Hare Brain, Tortoise Mind' is published this week by Fourth Estate

Insight problems

Move three coins to invert the triangle

Draw two squares so each pig has a pen

Perception problem

Analytical problems

The police are convinced that one of Alan, Bob, Chris and Dave has committed a crime. Each of the suspects in turn has made a statement, but only one of the four is true.

Alan said: "I didn't do it"

Bob said: "Alan is lying"

Chris said: "Bob is lying"

Dave said: "Bob did it"

Who is telling the truth and who did the crime?

Imagine that there are three playing cards face down on the table in front of you. You are given the following pieces of information:

To the left of a queen is a jack.

To the left of a spade is a diamond.

To the right of a heart is a king.

To the right of a king is a spade.

What are the three cards?

What does the doctor reply?

Answers on page 20

Solutions from page 18

WEIGHT: The doctor says: "Don't worry, a lot of men tend to put on weight around your age." Even those who pride themselves on their sensitivity to gender issues may be unconsciously trapped by the picture into assuming that the man is the doctor.

PROOF OF WITTGENSTEIN

PROBLEM

The circumference of a circle is 6.28 times as big as the radius (from the equation 2R where is the constant 3.14). Suppose the radius of earth is R. The original length of the string is 6.28R. If the size of the gap we are interested in is 'r' then the new total radius is R+'r', and the new total length of the string is 6.28x(R+'r'). But this is the original length, 6.28R, plus 2m (200cm), ie 6.28(R+'r')=6.28R+200. Take away the 6.28R from both sides of the equation and divide both sides by 6.28. This leaves 'r'=200/6.28 or about 32cm.

PLAYING CARDS: Left to right: Jack of hearts, King of diamonds, Queen of spades.

CROOKS: Bob is telling the truth. Alan committed the crime.

News
The surrealist comedian at the Q Awards in 2010
people
News
Russell Brand arriving for the book launch in East London
peopleRussell Brand cancels his book launch debate due to concerns about the make-up of the panel
Sport
Christiano Ronaldo enjoys his opening goal
champions leagueLiverpool 0 Real Madrid 3: Ronaldo and Benzema run Reds ragged to avenge thrashing from their last visit to Anfield
Arts and Entertainment
Awesome foursome: Sam Smith shows off his awards
music22-year-old confirms he is 2014’s breakout British music success
PROMOTED VIDEO
Have you tried new the Independent Digital Edition apps?
News
ebooksAn unforgettable anthology of contemporary reportage
Life and Style
Six of the 76 Goats' cheese samples contained a significant amount of sheep's cheese
food + drink
Arts and Entertainment
Contestants during this summer's Celebrity Big Brother grand finale
tvBroadcaster attempts to change its image following sale to American media group
Extras
indybest
Arts and Entertainment
Sir Nicholas Serota has been a feature in the Power 100 top ten since its 2002 launch
art
Arts and Entertainment
Sarah Dales attempts to sell British Breeze in the luxury scent task
tvReview: 'Apprentice' candidate on the verge of tears as they were ejected from the boardroom
News
Call me Superman: one of many unusual names chosen by Chinese students
newsChinese state TV offers advice for citizens picking a Western moniker
News
Wilko Johnson is currently on his farewell tour
people
Voices
New look: Zellweger at Elle's Women in Hollywood awards on Monday
voicesRenée Zellweger's real crime has been to age in an industry that prizes women's youth over humanity, says Amanda Hess
News
Let’s pretend: KidZania in Tokyo
educationKidZania lets children try their hands at being a firefighter, doctor or factory worker for the day
Life and Style
CHARGE BOOSTER: Aeroplane mode doesn't sound very exciting, but it can be a (phone) hacker's friend. Turning on the option while charging your mobile will increase the speed at which your phone battery charges
techNew book reveals how to rid your inbox of spam, protect your passwords and amplify your iPhone
Arts and Entertainment
Julianne Moore and Ellen Page are starring together in civil rights drama Freeheld
film
Latest stories from i100
Have you tried new the Independent Digital Edition apps?
Independent Dating
and  

By clicking 'Search' you
are agreeing to our
Terms of Use.

iJobs Job Widget
iJobs General

Solutions Architect - Permanent - London - £70k DOE

£60000 - £70000 Per Annum Excellent benefits: Clearwater People Solutions Ltd:...

General Cover Teacher

£110 - £130 per day: Randstad Education Reading: Great opportunities for Cover...

Maths Teacher

£110 - £130 per day: Randstad Education Reading: QTS Maths Teachers needed for...

Maths Teacher

£110 - £130 per day: Randstad Education Reading: QTS Maths Teachers needed for...

Day In a Page

How could three tourists have been battered within an inch of their lives by a burglar in a plush London hotel?

A crime that reveals London's dark heart

How could three tourists have been battered within an inch of their lives by a burglar in a plush London hotel?
Meet 'Porridge' and 'Vampire': Chinese state TV is offering advice for citizens picking a Western moniker

Lost in translation: Western monikers

Chinese state TV is offering advice for citizens picking a Western moniker. Simon Usborne, who met a 'Porridge' and a 'Vampire' while in China, can see the problem
Handy hacks that make life easier: New book reveals how to rid your inbox of spam, protect your passwords and amplify your iPhone

Handy hacks that make life easier

New book reveals how to rid your email inbox of spam, protect your passwords and amplify your iPhone with a loo-roll
KidZania lets children try their hands at being a firefighter, doctor or factory worker for the day

KidZania: It's a small world

The new 'educational entertainment experience' in London's Shepherd's Bush will allow children to try out the jobs that are usually undertaken by adults, including firefighter, doctor or factory worker
Renée Zellweger's real crime has been to age in an industry that prizes women's youth over humanity

'Renée Zellweger's real crime was to age'

The actress's altered appearance raised eyebrows at Elle's Women in Hollywood awards on Monday
From Cinderella to The Jungle Book, Disney plans live-action remakes of animated classics

Disney plans live-action remakes of animated classics

From Cinderella to The Jungle Book, Patrick Grafton-Green wonders if they can ever recapture the old magic
Thousands of teenagers to visit battlefields of the First World War in new Government scheme

Pupils to visit First World War battlefields

A new Government scheme aims to bring the the horrors of the conflict to life over the next five years
The 10 best smartphone accessories

Make the most of your mobile: 10 best smartphone accessories

Try these add-ons for everything from secret charging to making sure you never lose your keys again
Mario Balotelli substituted at half-time against Real Madrid: Was this shirt swapping the real reason?

Liverpool v Real Madrid

Mario Balotelli substituted at half-time. Was shirt swapping the real reason?
West Indies tour of India: Hurricane set to sweep Windies into the shadows

Hurricane set to sweep Windies into the shadows

Decision to pull out of India tour leaves the WICB fighting for its existence with an off-field storm building
Indiana serial killer? Man arrested for murdering teenage prostitute confesses to six other murders - and police fear there could be many more

A new American serial killer?

Police fear man arrested for murder of teen prostitute could be responsible for killing spree dating back 20 years
Sweetie, the fake 10-year-old girl designed to catch online predators, claims her first scalp

Sting to trap paedophiles may not carry weight in UK courts

Computer image of ‘Sweetie’ represented entrapment, experts say
Fukushima nuclear crisis: Evacuees still stuck in cramped emergency housing three years on - and may never return home

Return to Fukushima – a land they will never call home again

Evacuees still stuck in cramped emergency housing three years on from nuclear disaster
Wildlife Photographer of the Year: Intimate image of resting lions claims top prize

Wildlife Photographer of the Year

Intimate image of resting lions claims top prize
Online petitions: Sign here to change the world

Want to change the world? Just sign here

The proliferation of online petitions allows us to register our protests at the touch of a button. But do they change anything?