A question follows to test your intelligence. It’s a simple question about a group of ten men. First, some information:
One of the men has a moustache.
Three wear glasses.
One is bald.
The bald man does not have a moustache.
Ready?
The ten men shake hands with each other. How many handshakes are there in total?
Take your time. But don’t take too long. While most people get it right eventually, some manage it faster than others. We are, after all, measuring your intelligence here.
When you have an answer, turn over.
Puzzle convention demands the answer be printed upside down at the bottom of a page towards the back of this book. To speed things up, it’s here: forty-five.
Why? The first man shakes hands with nine people, the second man with eight people and so on. If your answer was fifty-five then you probably had each man shaking hands with himself. If you said ninety, and many people do, then you forgot once the bald man has shaken hands with the man with the moustache, then the man with the moustache doesn’t need to shake the hand of the bald man. If you said a hundred, most likely you panicked and multiplied ten by ten.
If you said forty-five then well done you. But, how long did it take? A few seconds? Under a minute? Longer? The quicker you solved the puzzle, the more intelligent you are – at least according to standard measures.
It’s impossible to boil down an intelligence test to a single question, but the puzzle above might be as close as we can get. It tests logic and reasoning, mathematical ability, spatial awareness, reaction speed, and the ability to ignore irrelevant and distracting information. (The glasses, moustache and baldness are classic red herrings.)
But solving even such a simple puzzle needs cultural awareness. You must recognize the term handshake for a start, and understand it is done between two people. And, more subtle, you must realize – not explicitly stated in the question – each pair need shake hands only once. What looks simple turns out to be more sophisticated. The same is true of intelligence.
Even the most intelligent people struggle to pin down what makes them seem so clever. Back in 1921, the editors of the Journal of Educational Psychology enlisted fourteen of the world’s leading experts across relevant academic disciplines like psychology and philosophy, and asked them simply: what is intelligence?
The results were telling. Two of the experts refused to respond, one on the grounds the question was boring and the other because it was impossible. The rest sent back eleven different responses between them. Each of their definitions makes sense in its own way. Yet, many are very different. Some, it could be argued, oppose each other.
One expert said intelligence was the ability to use facts and truth. Another said it was skill with abstract thought. Several defined intelligence as a capacity – for quick responses perhaps, or attention and adaptability. Intelligence, one expert said, was capacity to acquire capacity.
Some definitions were simple: knowledge and knowledge possessed. Some were complex: the capacity to inhibit an instinctive adjustment, the capacity to redefine the inhibited instinctive adjustment in the light of imagined trial and error, and the capacity to realize the modified instinctive adjustment in overt behaviour to the advantage of the individual as a social animal. One supplied definition just listed traits: sensation, perception, association, memory, imagination, discrimination, judgement, and reasoning.
You might think more recent experts, with decades more research and experience to call on, would make a better job of agreeing a definition. But you would be wrong. A follow-up survey carried out by psychologists in 1986 showed opinions on the nature of intelligence still all over the place – though the range and themes of suggestions were markedly similar to the responses of the original 1921 exercise.
More recently, experts in Switzerland published in 2007 another set of definitions of intelligence, which by then had swollen to some seventy-odd different interpretations. These included the ability to adapt to an environment and profit from experience and to be aware ‘however dimly’ of the relevance of one’s own behaviour to an objective. One researcher said intelligence means getting better over time and another defined it as the mental ability to sustain successful life.
The Swiss researchers went further than listing the definitions. They collated them, looked for the most common words and themes, and then tried to squeeze them into a single pithy phrase. I think they did a pretty good job: ‘Intelligence measures an agent’s ability to achieve goals in a wide range of environments’. They call it an informal definition, but here’s an even more informal version: Intelligence is using what you’ve got to get what you want.
It’s not only psychologists and philosophers who search in vain for a reliable and agreed way to describe and constrain the concept of intelligence. Computer scientists have long wanted to identify the telling features of human intelligence so they can build a machine to replicate them.
This quest to develop artificial intelligence began at a specific, invitation-only meeting of minds at Dartmouth College in the US state of New Hampshire. For two months in the summer of 1956, ten experts in electronics, language, mathematics and other specialist disciplines thrashed out the possibilities and tried to lay the foundations for a project ‘to find how to make machines use language, form abstractions and concepts, solve kinds of problems now reserved for humans, and improve themselves’.
More than sixty years later, progress on artificial intelligence has been slower than they expected. But then their meeting, and their whole premise, was based on an assumption we can now see was fundamentally flawed. Even before the meeting was convened, its organizers had promised: ‘The study is to proceed on the basis of the conjecture that every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it’.
That can be done in principle perhaps, but in practice, as we’ve seen, it’s proved almost impossible to even agree what the features of human intelligence are, never mind to precisely describe and copy them. That might help to explain why, while critics of the scary possibilities of artificial intelligence warn of self-aware machines and sentient computers, the best robots at present can barely fold a towel.
Even the origins of the term intelligence demonstrate the difficulty scientists and philosophers have had to pin it down. We derive the word from the Latin intelligere, which is a translation of nous – the ancient Greek term that Aristotle and Homer used to describe how a human mind determines what is real. In its original use, nous had religious and metaphysical meaning (the legacy of which remains in descriptions of God as the Divine Intelligence), and so Enlightenment writers in English, who wanted to portray a more science-based mental ability, ignored the spiritual-sounding intelligence. They preferred to say someone showed empirical understanding. The ideas of intellect and intelligence then became reserved for success in scholarly pursuits and academic questions, rather than an ability to do anything useful.
In response to this complexity, some have simply given up on the search for a reliable and useful definition of intelligence. Intelligence, philosophers have concluded, is the absence of a lack of intelligence.
(Psychologists have that one covered too. What makes an action unintelligent? People tend to describe three types of stupid behaviour. The first is confidence not supported by the necessary ability. Second is a failure to pay attention. And a hat trick of stupidity is completed by a lack of control. All of which would make another definition of intelligence someone who does not do any of those things.)
One problem with trying to define intelligence is it’s difficult to do so objectively. Our judgement depends as much on our experiences, culture and values as it does on neutral facts everyone can agree on. That means a society’s view of intelligence tends to reflect what it believes is important.
In Douglas Adams’ Hitchhiker’s Guide to the Galaxy series of books, both humans and dolphins consider themselves the earth’s most intelligent species. Man thinks he is the brightest because he invented civilization and work and war while all the dolphins have ever done is splash around in the sea and have a fun time. The dolphins believe they are smarter for the same reason.
Across the world, intelligence depends on context. Western cultures think intelligent people can sort and categorize ideas and participate in rational debate. They value quick responses and speed of mental processing. In contrast, societies in the east – China and Japan included – think intelligence helps people fulfil social roles and identify and deal with complexity. These cultures traditionally prefer depth over speed of thought, and can view rapid solutions with suspicion.
A school pupil who stays silent during lessons? In Britain and Europe, teachers would think they lacked knowledge, while at least one tribal people in Africa see speaking less as a sign of distinction and ability. In English, synonyms for intelligent – bright, sharp, and incisive – indicate confidence, bullishness almost. Yet the Zimbabwean word for intelligent, ngware, also means cautious and prudent.
Who, for example, shows the greater intelligence in the following exchanges?
In the 1930s, the great Soviet psychologist Alexander Luria wanted to test the intelligence of peasants in central Asia. To do so, he tried to measure their ability to reason, to work out the answers to abstract problems. This was important, Luria thought, because it was not fair to ask questions of knowledge and education, since they had little of either.
To make his questions consistent with the culture of the Asian peasants, Luria tailored the content to reflect their experiences. So, in his tests of reasoning, Luria would first say to them: ‘In the far north, where it snows, the bears are white. Nova Zemblya is in the far north, and it is always snowy there’.
Then, he asked the question, ‘What colour are the bears in Nova Zemblya?’
It’s a relatively simple test of ability to sift information and pull together the relevant bits, but it’s also hypothetical and so tests ability to think in the abstract. And the lives of these peasant people did not demand abstract thought. With no direct relevant personal experience of a situation, they could not mentally put themselves into it.
As a result, their answers look facetious. But they simply couldn’t process his request or what he wanted from them.
One said: ‘How should I know? I have never been to the north.’
Another added: ‘Why are you asking me? You have travelled and I have not.’
And a third replied: ‘So-and-so said the bears were white. But he is always lying’.
Luria tried again, this time testing their ability to conceptualize and sort objects into groups, by asking them which of a list of objects – hammer, saw, hatchet, log – did not belong. But, again, for the peasants to group three together as tools was alien, irrelevant even.
One responded: ‘They all belong. You need the saw and the hatchet to cut the wood and the hammer to hammer it’.
When Luria added somebody else previously suggested the log did not belong, the peasant replied: ‘He probably has plenty of firewood already. But we do not’.
While psychologists have never agreed on what intelligence is, they are convinced it is something real; something that dictates behaviour and performance and can explain the differences they see between people. And psychologists are extremely confident that, whatever intelligence is, it can be measured.
Among the first to try was a scientist called Francis Galton who, in the great tradition of gentlemen scientists of the past, appears from a twenty-first-century viewpoint to have been both brilliant and a fool. And, in a mark of the privilege afforded to him and his kind, he seems to have enjoyed a haphazard career made up as he went along.
Pushed into medicine by his father, the young Galton was unnerved by the screams from the (pre-anaesthetics) operating table and switched to mathematics. After a nervous breakdown, he took off to Africa and embarked on what would today be called a gap year, or gap years. He shot hippos on the Nile and rode camels across the desert. He taught himself Arabic and caught a venereal disease from a prostitute.
Galton took with him on his journeys a pretend crown, a stage prop from a London theatre, which he intended to award to the ‘greatest or most distant’ person he met. It ended up perched on the considerable head of a local tribal king in what is now Namibia, who Galton described as the fattest man in the world. (The king sent his naked niece to Galton’s tent for the night as a thank you, but Galton, wearing a white linen suit, was so concerned the butter and red ochre she had smeared on her body would leave a stain that he sent her away.)
When Galton returned to London he wrote a book on how to survive the African bush, and then decided he fancied being a scientist. He had always loved measuring things (in Africa he once used a sextant to appraise the figure of a native woman from a distance) and – in what remains a popular science obsession – he tried to derive equations on how to brew the perfect cup of tea. He drew up the first proper weather map and the first (and hopefully last) chart of the distribution of ugly women across the nation. (Sorry Aberdeen.)
He turned his urge to measure onto people when Charles Darwin – his cousin – published the theory of evolution. The progression of tortoises and finches was all very well, but Galton was fascinated by the inheritance and selection of human characteristics. He wanted to trace the origins, not of species, but of people’s mental performance.
Among his offences against modern values, Galton was undoubtedly a sexist in a sexist society. He pointed out how well-paid positions based on sensory discrimination, such as piano tuners, wine tasters and wool sorters, were all held by men. The (unquestioned) mental superiority of males, he reasoned, must show itself in better eyes, ears, noses and the rest of the senses. At the other end of the scale, the slow and sluggish responses of mentally retarded people, Galton said, were down to defective sensory functions.
‘The only information that reaches us concerning outward events appears to pass through the avenue of our senses’, he wrote. ‘And the more perceptible our senses are of difference, the larger the field upon which our judgement and intellect can act’.
So his way to probe intelligence was to test the senses. He designed and built wood and metal devices to test reflexes and reaction times. He got volunteers – and there were thousands of them – to punch targets, read at a distance, distinguish similar colours, pull, squeeze and breathe forcefully.
As they did so, Galton recorded their head size, height and weight and occupation, and became convinced he could find a way to link high-quality senses to those he viewed as high-quality people. (Then Prime Minister William Gladstone was one of the volunteers to visit Galton’s grandly titled Anthropometric Laboratory in London.) The results, however, stubbornly refused to fit his idea. That was one problem with some of Galton’s science. Facts just kept getting in the way.
Galton laid some shaky foundations for the investigation of human intelligence. But, although he never found an explanation for the differences between people, he believed he was on to something important. Others did too, and had more luck proving it.
* * *
Charles Spearman would become one of the most prominent scientists of his generation. But he started out as a soldier. He won a medal for his service in Burma, yet later described his fourteen years in the army as, ‘the greatest mistake of my life, [based on] the youthful delusion that life is long’.
Spearman’s true calling was psychology and studies of intelligence. He wanted to reclaim for intelligence research some of the scientific reputation it lost when, he said, the Enlightenment philosophers had ‘abandoned [it] to the psychology of the streets’.
Spearman built on Galton’s tests of sensory discrimination and intellectual achievement and, like Alfred Binet in Paris, he focused on children. His approach also seems haphazard but this was the early twentieth century and the procedures of science and research were different then. Today, researchers are typically funded by the government and accountable to various levels of officialdom. Each project leaves a paper trail – grant applications, reviews, ethics approval and consent forms filled in by any volunteers. It was easier for Spearman. When he wanted some children to study, he simply walked a hundred yards around the corner to his local village school and asked to borrow some.
Over several months, two dozen of the school’s oldest children visited Spearman’s house, in the village of Appleton near Oxford, where he spent fifteen minutes testing their eyesight, hearing and how well they could distinguish the weights of two objects. The eyesight test was particularly problematic to set up. Spearman wanted the children to say which of two cards had a darker shade, and he tried to make the test as fair as possible, which meant he had to place the cards each time by hand an equal distance and angle from the centre of an evenly lit window.
Next, Spearman gathered another three dozen of the school’s next-oldest kids in one of the school classrooms and played to them a series of pairs of musical notes on a home-made device called a monochord. For each pair of notes, each child simply had to write down a 1 or 2 to indicate whether the first or second of the two sounds was the higher.
There they were. A full room of six-to-ten-year-olds bunched together and asked to sit quietly while a balding former soldier used a home-made instrument to play the most boring music in England. What could go wrong? As Spearman noted dryly in his subsequent report (still considered a classic in psychology): ‘Energetic measures were found necessary to prevent cribbing.’ With help from the school’s headmaster, several teachers, and a ‘small prize offered to stimulate attention’, Spearman somehow got the class to sit still long enough to get the results he needed.
Next, Spearman headed across the village and up the social ladder, to a second school where he expected to find kids of a higher calibre. It was a ‘preparatory school of the highest class’ that trained boys for the top private school at Harrow. Arranged at short notice, the session was a disaster. With no time to test them individually, Spearman watched aghast as the boys passed around his precious weights and peered at his coloured cards under all sorts of different light. He was left on his own to supervise the class, couldn’t keep them from comparing notes, and struggled to get them to take the task seriously.
He had more luck when he returned with his monochord. This time, several of the masters stayed to keep order. The ‘social standing and general culture’ of the place, Spearman noted approvingly, was now ‘the opposite extreme to that in the village school’.
Spearman took his sensory measurements, but he still needed a way to check them against how intelligent each kid was. He had their exam results, which was a good start, but he also wanted to include whether teachers thought each was ‘bright’ or ‘average’ or ‘dull’ and to rank them accordingly. Teachers told him it was impossible. No bother, Spearman replied: simply tell me which of your kids is the brightest. They were happy to do so, and after they did, he asked which of them was the next brightest, and so on, until he had what he wanted. Finally, he got the two oldest children to independently judge their friends on ‘sharpness and common sense out of school’.
Francis Galton’s anthropometric laboratory had tried and failed to prove the link between intelligence and performance, but Spearman succeeded because he went a step further. He devised a statistical method to prove with maths what seemed obvious at first glance: the same names tended to group at the top of the different lists. A pupil who was good at classics was also likely to be good at French. And he found the more ‘thinking’ was involved in tests, the closer this bundling became. The same grouping occurred at the lower end of the scale too. Children who struggled at music were also likely to score badly in English. What looked like different measures, Spearman realized, were all testing the same thing.
Whenever thinking was required, he concluded, the pupils drew on something. The brighter pupils had more of it, which could explain their superior cognitive performance. Today we might say those kids had more of the X-factor. Spearman said this capacity was ‘general intelligence’. He later relabelled it the ‘general factor’ and then, simply, ‘g’.
Remembering his time in the army, Spearman was convinced his discovery would be useful. He said it could be used to make some important judgements about a person’s broader abilities from their performance at school. When he published his results in 1904 he concluded:
Instead of continuing ineffectively to protest that high marks in Greek syntax are no test as to the capacity of men to command troops or to administer provinces, we shall at last actually determine the precise accuracy of the various means of testing General Intelligence, and then we shall in an equally positive objective manner ascertain the exact relative importance of this General Intelligence as compared with the other characteristics desirable for the particular post which the candidate is to assume.
Spearman’s observation sounds routine but it is anything but. In fact, it is one of the most controversial and disputed scientific discoveries of human ability ever claimed. At a stroke, it undermines many popular beliefs about intelligence, ability and education, and emphasizes the ruthless disinterest of Mother Nature in making life fair for her children. It has been used to defend all manner of unpleasant and unscientific and illegal forms of discrimination and to underwrite hate and prejudice and snobbery. It has been used as a justification to kill people, to forcibly mutilate them, to steal them away from their loved ones, imprison them and to make them defenceless exhibits for public mockery. More than a century on, Spearman’s findings are still used to put people down and to keep them in their place.
Properly named, Spearman’s big discovery is known as the positive manifold. You know it better as the kid at school who was good at everything. Maths, English, French, history – whatever it was they were top of the class. Music, art and even sport – they probably excelled there too.
Under the indifferent dominance of the positive manifold, mental excellence is both rationed and unevenly distributed. And so is failure. In fact, the connection between scores is even stronger towards the lower end of the scale. The same people do badly at everything, just as the usual suspects are the ones doing the best and getting the highest grades.
Spearman’s g is probably the most important scientific theory you have never heard of. One reason it’s not more widely known is because it’s purely theoretical. Someone’s g – their general intelligence capacity – cannot be measured, or at least psychologists and neuroscientists have found no way to measure it directly. IQ scores are the closest proxy, and that’s one reason why IQ is hated by so many; all the social and political baggage of the idea of a fixed general intelligence gets piled onto the back of IQ.
Among that heavy load is the tacit assumption that intelligence is valuable, and those with more of the trait are better somehow. That it’s good to be intelligent and human progress should head in that direction. For is there a bigger crime than talent wasted and opportunities not realized?
Few people will admit to this bias, even fewer to allowing it to steer their behaviour and attitudes, but it exists. We see it even in our relationships with animals. One reason people argue against the eating of dogs is they are intelligent creatures – more so than the dumb sheep and cows they happily cook. The same applies to the octopus. Plenty of campaigners argue an animal bright enough to recognize itself in the mirror has no place in paella.
Importantly, the nature of intelligence is about more than philosophical definitions and academic chin-scratching. People’s attitudes and beliefs on how intelligence works, and how it might be increased, have a real impact on how they view the abilities and potential of themselves and others. Most fundamentally, a belief that intelligence is a fixed quantity and can’t be increased is often enough to make a child perform poorly at school, and influence how well they set themselves up for life.
In a typical group of ten school children, four believe intelligence is fixed. Whatever they do, they think they cannot change their mental abilities. Another four think the opposite – their intelligence can be improved, and the best way is to work hard. (The other two kids of the ten don’t pick either option.) It doesn’t matter to their grades which group is correct – whether intelligence is actually fixed or not – their belief alone steers their attitudes, effort and performance.
It is better to believe intelligence can be increased. Those children who believe the opposite, that intelligence is fixed (called the entity theory), are more anxious about how much intelligence they have, and it not being enough for them to succeed. These children refuse opportunities to learn if they carry a risk of doing poorly. They conceal or lie about their weaknesses, rather than identify and improve them. And they indulge in what psychologists call self-handicapping – procrastination and watching television the night before a test instead of studying. This gives them a ready-made excuse if they score badly.
There’s more. This group believes ability alone should be sufficient to succeed. So they think effort and persistence indicate low intelligence and don’t bother with either. When things get difficult, this group gives up, cheats, loses self-esteem and ultimately does worse. That’s because they believe they are bumping their heads against an intellectual ceiling.
In contrast, children who believe intelligence can be improved (called the incremental theory), have a healthier attitude to their studies. They value effort as much as performance, and bounce back from failures with renewed determination. For them, the sky is the limit.
There seems no strong difference between the actual intellectual abilities of the two groups, which makes the lack of effort in those who think intelligence is fixed all the more galling. They are wasting their talents, while less able children with a more positive attitude can thrive.
For obvious reasons, experts want to understand why these different groups of kids believe what they do. One explanation might be subtle differences in phrases used to praise them when they were younger. A young child recognized for ability – ‘what a great picture you’ve drawn, aren’t you clever’ – could start to attribute accomplishment to fixed traits. A child praised for process – ‘what a great picture, you’ve put loads of work into that, haven’t you?’ – could take the opposite and more fruitful approach, and believe success came from effort and practice. It could matter whether praise is generic or specific. ‘You did a good job on that drawing’ is more likely to make a child think intelligence is incremental, and so help them, than the equally well-meaning, ‘oh look, you can draw well’.
It’s not just the children in schools who have these different beliefs about the nature of intelligence, teachers do too. If you struggled at maths at school, even in a single arithmetic test, and a teacher tried to comfort you by telling you not to worry because not everybody can be good at maths, then, unfortunately, that teacher probably had an entity theory of your intelligence and judged it as insufficient for maths. They probably haven’t given it a second thought since, but it almost certainly changed the way they taught you, and who knows what else.