The boy who knew too much: a child prodigy

This is the true story of scientific child prodigy, and former baby genius, Ainan Celeste Cawley, written by his father. It is the true story, too, of his gifted brothers and of all the Cawley family. I write also of child prodigy and genius in general: what it is, and how it is so often neglected in the modern world. As a society, we so often fail those we should most hope to see succeed: our gifted children and the gifted adults they become. Site Copyright: Valentine Cawley, 2006 +

Friday, November 10, 2006

Convergent thinker, divergent thinker

I discussed convergent thinking a few weeks ago, in response to a post. I feel it is important enough to highlight here.

A convergent thinker is the classic high IQ student. The skill that IQ measures is the ability to converge on a single answer to a question that only has one answer - or is supposed to have only one answer. Sometimes a different type of thinker, the divergent thinker, will see another answer to the same test that isn't an option. This can cause problems for the divergent thinker in taking IQ tests. Both my brother Josh, the "savant" with an extremely high IQ, and myself have noticed what appear to be ambiguities in professional IQ tests. That is questions to which there seems to be another answer not offered. It doesn't happen often, but it does happen. Why is this so? Perhaps the person who constructed the test is a convergent thinker and therefore unable to see what is clear to the divergent thinker: that there is another answer.

This leads us to the classic problem of educating the creative person. Divergent thinkers create. Convergent thinkers solve. By this I mean that the divergent thinker is able to do something new, think something that has never been thought before. The convergent thinker is equipped however to focus on hard problems and solve them. They are a very different kind of person.

Does education value the divergent thinker? Not at all. In every classroom I have been in, the convergent thinker is the one valued by the system. Now a good convergent thinker can do many things well - things that involve difficult problems in hard areas of academia. But most convergent thinkers could not create a new area of academia, for instance. The divergent thinker could do just that, given the right circumstances.

There are, therefore, three types of children, of interest. There is the convergent thinker, who does well in a classroom situation and in most professions. There is the divergent thinker - who may not do well in class because the class doesn't allow for his/her creativity - but who may do very well in life, in something creative. Then there is the rare student who combines both modes of thinking in ample measure. These students are able to handle the classroom well and be creative. I was like that - but being so, sets one apart in a way no amount of social skills can address. To be divergent, is to be "different".

I would say, too, that Ainan Celeste Cawley, my scientific child prodigy son, aged six, is both convergent and divergent. This promises to allow him to be a creative scientist when he grows up and not just a skilled practitioner. We will see. I will watch his thinking unfold in the years to come, but he has already shown strong creativity in his scientific and artistic thinking.

Thomas Alva Edison was a classic divergent thinker, according to certain biographers. He was so divergent that he was completely unable to cope with school at all. His teachers thought him retarded and he was eventually expelled from school as a no-hoper. This is the Edison who invented the lightbulb and built a major electrical corporation. That is how different are the convergent world of the classroom and the divergent world of creative work.

So, is your child a divergent thinker or a convergent thinker...or a combination of both? Don't be concerned about which combination or extreme they show, for each type has a path to success in life: they are just different paths that is all. So which path is your child treading?

(If you would like to learn more of Ainan Celeste Cawley, my scientific child prodigy son, aged six, and his gifted brothers, genius and prodigy, savant and giftedness, in general go to: )

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posted by Valentine Cawley @ 1:03 PM 


Blogger Cher Mere said...

I first thought I was a convergent thinker because I always knew the answers to tests. But I didn't have to "think" to know them, I had just read them somewhere already and remember.

When I actually have to think I am a divergent thinker and often people come to me for that skill.

My husband is an software engineer but his job is to invent new things and fix problems. He is definitely a divergent thinker.

Z? I think she is divergent too. But, like me, she can come across as convergent because she can remember an answer.

but often Z has a hard time coming up with just one answer. She had this weird thing where she likes to discuss all the answers that can't be right before she gets to the ones that are right.

Thanks for the clarification

11:58 AM  
Blogger Valentine Cawley said...

A convergent thinker is diagnosed very easily. Just take an IQ test. If you do well you are a convergent thinker. Your daughter, yourself and your husband are PG...this means that you are converegent thinkers. However, it does not mean that you are not also divergent thinkers: something not measured by the test.

Convergent thinking has nothing to do with memory, really: it has to do with a type of linear thinking that results in a single correct answer.

Divergent thinking seems to be less common than convergent thinking. Certainly the people I was at school with - a good British Public School - showed very little evidence of divergent thinking. At Cambridge University too, there was a strong preponderance of convergent thinkers. I can't recall anyone who struck me as particularly divergent - except perhaps one individual who was "divergent" in many ways!

From what I have seen it seems to be relatively unusual to do both convergent and divergent thinking well: though some manage to do so. Albert Einstein for instance. Or Richard P. Feynman. They both showed strengths in both areas: otherwise they could not have been creative physicists.

Certainly, a creative or divergent approach can be taken to something like software engineering - but it also requires strong convergent skills, otherwise one probably couldn't do it at all.

Best wishes to all of you.

1:52 PM  
Blogger Cher Mere said...

Hi Valentine

I wanted to address some of your points

Divergent thinking seems to be less common than convergent thinking. Certainly the people I was at school with - a good British Public School - showed very little evidence of divergent thinking.

I am not sure about that, at least in the gifted population. I admit I don't get out much or make a point of noticing whether other people are convergent or divergent thinkers. But a good percentage of the people I tend to hang out with (most of them are gifted) are very creative. A lot of them are writers, a couple inventors, some artists, etc.

Certainly, a creative or divergent approach can be taken to something like software engineering - but it also requires strong convergent skills, otherwise one probably couldn't do it at all.

In my husband's area divergent thinking is called for. There is never a right answer for the problems he has to solve and the other thing he does is invent new products.

From what I have seen it seems to be relatively unusual to do both convergent and divergent thinking well:

Statistically that could be true. Like I said I am only familiar with my family and the people I choose to hang out with.

Here is a good definition of Divergent Thinking
Four main characteristics

Fluency (the ability to rapidly produce a large number of ideas or solutions to a problem)

Flexibility (the capacity to consider a variety of approaches to a problem simultaneously)

Originality (the tendency to produce ideas different from those of most other people);

Elaboration (the ability to think through the details of an idea and carry it out).

I tend to think of those qualities as a a big part of giftedness. But again my experience is probably biased.

Divergent thinking used to be my job. I used to go into companies and learn their processes and figure out how to do it faster/better/cheaper/, basically more efficiently.

It wasn't convergent thinking because there was no one answer. I had to look use the four characteristics of divergent thinking.

Often being a divergent thinker means seeing how things could be and having to convince people who can't see what you can see.


11:30 AM  
Blogger Valentine Cawley said...

Thanks for your post.

From what you say, your sample of people is definitely biased. Your friends are creative types...that is they are DIVERGENTLY gifted/creatively gifted. They are not a standard sample of gifted people.

Giftedness, as measured by IQ tests, says nothing about creativity. There are many who do well on IQ tests who cannot think divergently or creatively: it is a common type found in any selective school.

My school was highly selective, with only the "best" students there. This seemed to mean a large collection of convergent thinkers. Few were creative - and these tended to be plagiarized by the others. So I would say that giftedness as measured conventionally does not necessarily indicate creativity or divergence. Some gifted people are creative - and some gifted people who FAIL IQ tests (in the sense of not being over 130 ) are divergently gifted and in a certain way, superior to those who pass such a test.

You are lucky to have such people in your social circle. In Singapore there are no such people - or so few of them that one doesn't meet them. One lives therefore with my creative wife and her relatives...and that is about it!

You seem to worry about acknowleging that you are able to think convergently as well. Don't be. Both styles of thinking are useful. Both do something that the other style CANNOT accomplish.

So there are two ways to be gifted: in terms of intellectual reasoning power in logical ways...and in terms of creativity.

Thanks for your definition of divergence: I shied away from such a way of defining it, in my blog, because I wish to remain accessible to readers, while still capturing the essence of each concept. Thus I don't want to adopt an academic style!

Best of luck yourself, your husband and daughter.

1:23 PM  
Blogger Cher Mere said...

For good or ill I think I try not to spend too much time with people who's thinking baffles me ( and I don't mean because it is too profound, *grin*)

I also try not to spend too much time with people who don't "get" me.

and lastly, this conversation has pointed out to me that I don't think much about how these people think.

So my experiences are very biased.

I don't think I am not a convergent thinker. But to me my high score on a convergent based I.Q. test came from finding answers to problems from my base of knowledge and then applying them to what I knew, also from my base of knowledge, to be the question the tester thought they were asking.

Is that convergent thinking? :)

Thank you

1:52 PM  
Blogger Valentine Cawley said...

To answer an IQ test one has to think convergently - and if you see more than one possible approach because of divergent thinking, to decide which is the one the examiner wanted.

It is good to be able to think both ways. That is optimal. If you are divergent but unable to think well convergently, you may come up with a new idea, but be unable to develop it fully. If you are convergent, but not divergent, you wouldn't come up with the question or problem, but you might be able to solve it. The ideal "Genius" uses both ways of thinking: Albert Einstein did, Richard P. Feynman did, Paul Dirac did. Their advances were not possible without both ways of thinking.

It is good Cher Mere that you have abilities in both areas, therefore. One uses whatever tools suit the problem at hand.

You are fortunate to have such an interesting circle of friendships. Singapore doesn't offer that: it is too concerned with money, to develop its collective mind in a creative way, I feel. If something doesn't make money NOW, they are not interested. Consequently, the sort of people you know, either don't exist in Singapore, or have left. It is a pity.

Normally, an IQ test doesn't require much of a base of knowledge. Though I have heard of bad tests that require a lot of knowledge from the testee. I don't consider these to be IQ tests, but more achievement tests. That is not the same. Not knowing the test you took or its type I can't say definitively how much convergence of thought was required - though this requirement is usually almost total.

I find that all types of people have something to offer in one sense. In meeting them, one comes to know more of that wonderful thing: Mankind. I don't, therefore, exclude meetings with people of any kind - though if I don't find much of interest there won't be too many future meetings!

Take care

2:22 PM  
Anonymous Anonymous said...

I was a very convergent thinker, as far as I know, until high school. I wasnt able to think outside the box at all.

Then, I dont know what happened... but I started inventing multitudes of things and did all kinds of creative work. I did want to be more creative and more clever. I made myself quite creative, and made my mind quite limber. I destroyed as many preconceived notions as I could and learned all sorts of new ways of bouncing out of the box... Now, I have the feeling that I could solve anything...

I wonder what could allow a convergent thinker to turn themselves into a divergent thinker? (Youd think that would take divergent thinking to do...) Maybe I was divergent all along, and only learned to be convergent because I was a docile enough kid to let myself be stifled.

You know, I think that must have been the case, because when I was 12 I tried to invent some kind of math, and when I was younger than that I was building contraptions out of my toys (Like, I installed a burglar alarm on my bedroom door made from a fishing pole and a cowbell).

Sigh. I still dont get enough opportunities for divergent thinking...

How about this. Since IQ tests dont work, if there was a way to tell whether one person had more divergent thinking ability than another, what would that be?

Do you think most intelligent people are divergent thinkers? Or do you think that is rare like genius? Do you think the two are one in the same?

I feel like I should be answering these for myself, but that would make for a rather one sided conversation. :)

5:17 PM  
Blogger Valentine Cawley said...

You have posed a number of difficult questions.

What is conventionally thought of as intelligent behaviour is, actually, convergent thinking - the type measured by IQ tests. Divergent thinking, therefore, is one of the tools of creative thinking and is not measured by IQ tests.

There have been attempts to create creativity tests or divergent thinking tests. The basic idea of many of these is to think of many different uses for something. I don't know of any really effective test though of capturing the essence of a creative person - other than, perhaps, seeing a sample of their creative work.

I don't think that what most people think of as an intelligent person is a divergent thinker. That is closer to what people think of as a creative thinker. In my experience, the two are often different people, though some possess both dispositions.

I don't know how rare divergent thinking is...but in my life experience at a selective school and at Cambridge University, it seemed to be much rarer than convergent thinking. So, either it is genuinely rarer than convergent thinking - or the situations I was in selected against it.

I would say that a person of strong divergent thinking ability allied to decent convergent thinking ability - though not necessarily the highest - is much more likely to be a "genius" than someone who is purely a very strong convergent thinker.

IQ tests identify convergent thinkers. The "multiple uses" tests purports to identify divergent thinking - and may bear some relation to genuine creativity. Unfortunately, there are no robust measures of divergent thinking available, as far as I am aware - though people are readily distinguished on the type of "divergent thinking" test above.

A good divergent thinker, will tend to do things differently in life; tend to see things new ways; to be creative without perhaps, even being aware of their own uniqueness - it will just happen for them. Among such people should we look for the "genius".

Best wishes to you, an awakened divergent thinker!

7:27 PM  
Blogger Valentine Cawley said...

Another thought: if you really want to know if someone is a divergent thinker, look at their life - what do they do? How do they do it? Do they CREATE, are they original? Do they have a unique style in how they approach things?

It is the answers to these questions that will inform as to whether they are good divergent thinkers. You see a convergent thinker, alone, is never properly creative, in the true sense of the word. It is the influence of the other kind of thinking - the divergent, the creative, that leads to new thoughts.

Kind regards

7:35 PM  
Blogger LElise83 said...

Hi all

My first time knowing the existence of convergent and divergent thinker, and that's how I reach here.

To my surprise, there are people who are so resolute to find out which type of thinker they belong to, or even try so hard to hop to the other side by all means.

The identification of the types of thinkers are crucial for educators to bring the best out of the school children, as well as for HR manager to hire people. And I am sure nobody likes to be called narrow-minded. But giftedness can be much broader, including ability to foresee and make the right decision, amid complex circumstances. Such ability dictates the rise and fall of a company, or even a country. Take Napoleon as an example.

To me, knowing how to create happiness for oneself as well as for the society is the most valuable giftedness there is.

Lastly, I wanna thank you for sharing your explanation of convergent and divergent thinker. But I am really interested to know how you ended up in Singapore. I am not saying that it's bad. Well, you know, just a curiosity.

1:57 AM  
Blogger Valentine Cawley said...

LElise83, I am glad you found value in my post.

You ask an interesting question...yes, it is strange why we went to Singapore because you are right, in what you don't say: it is not the right place for thinkers or creative types of any sort. However, my wife is Singaporean...that is why we went there: no other reason. We have since left and are now in Malaysia.
We find it freer here.

I hope that answers you.

Best wishes.

3:08 PM  

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