Ainan explores mathematics

Mathematics, at school, for a Primary 2 student is not a very exciting affair. Indeed, in Ainan's school they have got as far as addition and subtraction - and no further. Needless to say, Ainan had long begun to fret at the pace of things and had all but adjudged maths to be boring. Then something wonderful happened: he began to discover it for himself.

A couple of weeks ago, Ainan picked up a maths book and began to read. He soon found it more interesting than he had thought. Within days, he was beginning to enthuse about maths - and the range of mathematical ideas that he has absorbed in that short time is quite remarkable.

His conversation now concerns transcendental numbers, irrational numbers, perfect numbers, primes, semiperfect numbers, weird numbers, powerful numbers, mathematical constants, folke's constant, skewe's number (any spelling mistakes are my own since I am rendering what I here him speak of), factorials, roots, squares, cubes, powers, indices, sublime numbers, amicable numbers (he was particularly taken by these), imaginary numbers, (and many others) he has taken to inventing his own constants, writing equations, playing with functions, designing mathematical challenges...it just goes on. He has even written a maths book to encapsulate his new experience in words and pictures.

I also note something interesting. He has begun to absorb mathematical facts in great detail - much as he did with chemistry. His speech is peppered with numbers to the seventeenth decimal - which he has learnt as easily as you or I might remember our own names. He knows pi to seventeen decimal places. He knows e to a similar precision. He knows many, many different numbers, each of which are examples of the classes of numbers that he has come to know. He remembers the products of all the calculations of mathematical functions that he has been playing with. (For instance, he learnt many "conjective numbers"). He is beginning to draw relationships and associations between numbers and divine his own patterns within them. He is making number references in his speech - defining the numbers he sees in the everyday world in terms of other numbers about which he knows something interesting.

What is amazing about all of this is that mere days ago none of it existed. He had not developed any spontaneous interest in maths at all - apart from an interest in hyperdimensional four, five and higher dimensional shapes which he had nursed for over four years.

Ainan has just decided, one day, to look at maths. This is the same thing that happened one day, with chemistry - and look how far he has come with that, in a short time.

Even now, Ainan retains an ability to surprise me.

Now that his interest in maths has awakened, he is asking that I buy maths texts for him - so I shall make a trip tomorrow to do just that. I think Ainan's best teacher is himself. So, I will let him do just that - pick up a book and teach himself maths.

It is a happy moment for me, as a father, to see him develop this interest in mathematics - because I know how important it is to support his primary interest in the physical sciences. Without good maths behind him, some branches of the physical sciences would have been forever closed to him. Looking at how he has begun to enthuse about maths, I don't think that will be a problem for him. If he tackles maths as he has chemistry, there is no telling just how "numerate" he will be in a few months time.

(If you would like to read more of Ainan Celeste Cawley, a scientific child prodigy, aged seven years and four months, or his gifted brothers, Fintan, three and Tiarnan, fourteen months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted adults and gifted children in general. Thanks.)

Fintan spots a dinosaur

Fintan, three, has long wanted to see a dinosaur. I think this is an extension of his interest in animals. He has carefully surveyed his world but sees no overt signs of them. About six months ago, however, something very strange happened.

It was a Sunday. My wife had gone out with the other kids, leaving me with Fintan. To keep him interested I promised to take him to see where the dinosaurs were. This quite appealed to him and he soon readied himself for some dinosaur watching.

He sat in his pram, legs dangling over the side, for it would be far too far to walk at that age - or at least I had thought so.

We were to go to a wooded area near us: a kind of preserve, into which I intended to push the pram, if I could find the elusive entrance. All along the journey from our home to our destination, there were trees and vegetation at the roadside.

To keep up his interest, I asked him to look out for the dinosaurs in the woods - and he peered with great care into their midst. This stance went on for some minutes as we approached our goal.

Suddenly, in a moment of pure childhood magic, a giant green lizard came rushing out of the vegetation in front of us. It was quite the biggest lizard I had seen in Singapore. I couldn't identify its breed - but it really was at least a couple of feet long and quite bulky. I don't think it was a "Komodo Dragon" - for I have seen those in Malaysia - but it was impressive. It was green, tough looking - and dinosaurian.

Fintan's eyes were agog. Before him was a "dinosaur"...

"Look Fintan! It is a baby dinosaur!"

He was speechless. The "dinosaur" ran ahead of us for about ten metres then ducked back into the vegetation, having decided that it didn't want to be on the road.

Fintan craned to see where it had gone and only relaxed when it was clear that it was no longer to be seen.

The trip was a great success. In the most unlikely of ways, Fintan had come to see the "dinosaur" that Daddy had promised him. Never had I expected to fulfil the requirements of the day...but I had.

That evening, Fintan enthused about the "baby dinosaur" he had seen, to his mother, telling how big it had been - and how it had suddenly jumped out in front of him.

What a magical day.

(If you would like to read more about Fintan, three, or his gifted brothers, Ainan Celeste Cawley, a scientific child prodigy, aged seven years and four months, or Tiarnan, aged fourteen months, then please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted children and gifted adults in general. Thanks.)

A child's imagination: can it be too much?

Can a child have too much imagination?

This was a question posed as a statement, "child too much imagination", by a searcher who arrived on my blog, recently. I found the outlook that would lead to the search somewhat unsettling. For what kind of parent would think that their child had "too much" imagination? (This assumes it was a parent - it could have been a teacher, of course.) Let us rephrase the question in another way to get a better understanding of it. How does a child benefit from having LESS imagination? Is it better to be unable to see new things in the old? Is it better to be unable to conceive of a new idea? Is it better to be unable to play with that which is not there, physically but only exists in the mind? Is it better to be without the basic capacity to create?

In some way, the searcher believed all these things. In viewing their child as "too imaginative" they were proposing the opposite standpoint as superior - that of the unimaginative child who cannot conceive of the new, who cannot think of that which is not, who cannot, in truth, take the first step towards creating something by imagining.

I would say that a child can never have too much imagination - but I would say that a parent (or a teacher) could have too little.

It is sad to think how that child might be brought up. The instinct to create, to play, to imagine, might be met with great unwelcome - thought of by the parents as somehow a silly thing to do. If the child is at all socially sensitive, they will pick up on this and learn to avoid imaginative play. In time, the capacity to imagine will wither - and that child will become as the parent is: unimaginative, afraid to create, unable to play - and perhaps even disapproving of the imagination. A potentially creative being would have been snuffed out by an incomprehending, unwelcoming parent.

If a child wishes to play in a world all of their own, let them: the capacity to create such a world is the foundation of many adult pursuits of great inherent value - writing, art, science, acting and music are all products of an adult engaged in imaginative play. An adult could not pursue any of these disciplines had they not been free as children to play with their imaginations, exercising them until they become reliable allies in reforming the world, at will.

It might very well be true to say that all geniuses start life as imaginative children. The least they should expect from the world is a parent who allows them the freedom to be imaginative: without that license so much may very well be lost from the world.

So, no matter how "imaginative" a child is, it can never be "too much". To say so, is similar to saying that a child is "too intelligent". Neither statement is ever true. It is impossible to be "too gifted" - no matter what the gift is - for every level of gift has its value - and the greater the gift, the greater its potential value. There is never a point at which a human gift or human quality becomes "too much". To think otherwise is to see value in shackling a human spirit - and that really is "too much".

Singapore's experience of the gifted

I came across a strange criticism on the internet, recently, regarding Singapore that I wish to comment on. This commenter - who generally came across as more than a little rabid - said that Singapore had little experience of the gifted - because it had only 4 million people...so basically what would they know?

I thought this comment very interesting for what it revealed about the limited understanding of giftedness of the commenter. Even profound gift at its theoretical prevalance of one in a million would be present in a population of four million. Yet, profound gift is actually more common than its theoretical prevalence - several times more common, at least. Therefore gifts of all dimensions would be present in a population of "only 4 million". Then again there is the fact that Singapore's IQ curve is not centred on 98 like the US (it was an American commenting owing to cultural references made by him or her), or 100 like the UK - but on 104. This is significant. It means that the gifted will, if the curve is otherwise as the IQ curves of other countries are, be much more common, because of the shift to the right of the curve. This means that Singapore will have proportionately MORE gifted people in its "only 4 million" population, than expected.

That, however, is just the beginning of the issue. For not only will more gifted people be present in the Singaporean population - but, culturally, more is done to meet their needs and become aware of those needs. You see, Singapore has a dedicated branch of the Ministry of Education catering solely to gifted children: The Gifted Education Branch. Their sole purpose is to understand and enable gifted children to become what they may. This is a government that has decided to open doors for gifted children - at least, that is the stated purpose of the organization and we are only just beginning to experience the reality of what they can actually achieve - a matter on which we keep an open mind. We will see how effective it really is - but that is another issue. The fact remains that there is a Department dedicated to the gifted - dedicated to understanding them and dedicated to enabling them. Can the USA say that? No. Can the UK say that? No. In fact, off the top of my head I know of no other country which can say that they have a dedicated branch of government devoted to the gifted. That says something. Does it say this country has "Little or no experience of the gifted"...err, no. On the contrary, it says that this country has more experience of the gifted than is usual - much more.

In a country that ignores its gifted and their needs - which appears to be the case at a central government level in not only the US and the UK but probably most, if not all, developed economies - that country will have little knowledge and experience of the gifted - for they are not looking at them as a constituency that needs individual attention; they are not thinking of their nature or their needs - and so they will not know of them. In short, they will be blind to the gifted within them, for they have never looked to see them. That, in fact, is a country which has "little or no experience of the gifted". Oddly, that situation pertains to the very country in which the commenter resides - and not the one that he criticizes.

His argument was basically that a country like Singapore, that had so few people, could not possibly know what a gifted child was - because they didn't have enough people to have any. Statistically, that is nonsense, of course - since four million is more than enough to encompass the variety of human types there are - and to do so amply if the IQ curve is actually centred on a higher than usual point, which it is, at 104.

That Singapore will have fewer gifted children, numerically, than a country almost two orders of magnitude greater in size is obvious - but that it would lack experience of the gifted simply because the other had more of them, is lacking in sense.

Singapore is a country without natural resources. Its only resource is its people. It is this background against which one can understand its wish to understand and cater for the gifted within: for those children are the greatest resource they have.

Singapore knows this; none of the other countries I have mentioned does. So who, then, has "little or no experience of the gifted."?

(If you would like to read of Ainan Celeste Cawley, a scientific child prodigy, aged seven years and four months, or his gifted brothers, Fintan, three, and Tiarnan, fourteen months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted children and gifted adults in general. Thanks.)

Hwa Chong Institution

I visited the Hwa Chong Institution, yesterday - and if there is one thing that can be said about Hwa Chong is that it is not small. Oh, no, not by a long way. It has to be the biggest school I have ever been to.

I got lost. Twice. I found myself, twice, in "Offices" that were the wrong ones (they have at least three, it seems), before eventually meeting up with Ms. Letchmi, a teacher with a chemistry background (she gave me no title - so I can't give it here), beneath a clock tower, more in place in a European city than an Asian one.

We went to an office wreathed in quietness and spoke of Ainan.

The conversation was not a long one, since both of us were needed elsewhere but the gist of it was that they would like to help Ainan if they could, but were not sure if they could spare the resources necessary. Ms Letchmi was very careful to state that she wanted to help, but could make no definite promises until she had checked the situation with her colleagues.

What were we asking for? A lab. We have been in search of a lab for Ainan now for ten months and are still searching. It is very difficult to get someone to agree to letting Ainan learn in one. I don't know why...but perhaps it is because of the unusual nature of the request: a seven year old who needs a fully equipped Chemistry lab to potter around in.

I pointed out that not allowing Ainan to have a lab is a bit like denying a mathematician a pencil and paper and a calculator: it would be a form of "cruel and unusual" punishment to do so. So, too, is it with Ainan - he needs a lab, now, if he is to continue to grow scientifically. After all, Chemistry has a large practical element to it - and the ultimate aim of all Chemistry - even the most theoretical aspects - is ultimately to engage in practical experimentation through the making of chemicals, in some way or other. The lab is where chemical ideas are expressed in practical form. Ainan cannot be without a lab for much longer.

She resolved to look into it for us - and promised to get back shortly.

Let us hope we get a positive answer soon - for otherwise Ainan's progress will be more than a little derailed. He cannot go further without a lab. If you have access to one and would like to help: please tell us so! Thanks.

Do geniuses get the credit for their work?

Often, no.

Why do I say this? Well, history is littered with examples of brilliant people whose creative work is either misappropriated or just wrongly credited to someone else. This does no-one any good (apart from the person receiving credit for work they didn't do).

I will give you an example. Have you heard of Peter Desaga? Think hard. Nope? Well, I am not surprised, but I am fairly sure that almost all readers will know of his invention. If you have ever been in a chemistry lab it is something you will have used. Any wiser? No? Well, think of the name Robert Wilhelm Bunsen. Is that familiar in some way? Yes? I bet you remembered then, the "Bunsen" Burner. I say "Bunsen" deliberately, because Bunsen didn't invent the Bunsen Burner, at all. His assistant, Peter Desaga did, by modifying an earlier design of Michael Faraday's.

Now, I think it is rather wrong that Robert Bunsen got the credit for this invention when it was actually his assistant who did the work and created the product. But, the tale gets worse. You see Bunsen did something rather magnanimous with his assistant's idea: he gave it away for free! That's right, Peter Desaga wasn't even rewarded for his invention - and Bunsen looked very generous in giving away, for nothing, something that was not his to give.

Only a few specialists in Chemistry would have heard of Bunsen were it not for the odd fact that the Bunsen Burner - which he didn't invent - is named after him. Bunsen is now an immortal - in name, at least - but Peter Desaga, the man who actually invented it, is an unknown. That is terribly wrong. In writing this article I have just increased Desaga's fame many times - and this is just a blog. How sad that is.

So, no, geniuses don't always get the credit - and often the ones who do are simply socially more important and therefore in a position to leverage credit towards themselves - it is not right and is not good for the health of science, culture or the arts - or wherever this phenomenon occurs. So, Mr. Bunsen, I am going to start calling it a Desaga Burner, from now on. (Or maybe the Desaga-Faraday Burner.) Perhaps you should too. It would only be right.

Oh, by the way, it was Ainan, my seven year old son, who tipped me off about Bunsen's undeserved credit: he didn't like it either.

(If you would like to read about Ainan Celeste Cawley, a scientific child prodigy, aged seven years and four months, or his gifted brothers, Fintan, three, and Tiarnan, fourteen months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of child prodigy, IQ, intelligence, gifted education, child genius, baby genius, adult genius, savant, the creatively gifted, gifted children and gifted adults in general. Thanks.)

Nobel Prizewinners and genetic giftedness

The Nobel Prize is, probably, the most prestigious of all awards. Each year, it is awarded in six categories: Physics, Chemistry, Medicine, Peace, Literature and Economics. Yet, I have noted something startling in the prize awards: sometimes it seems to be inherited.

Now, what do I mean by this? Well, quite literally, there are winners whose children also won. This, in itself, provides a very strong argument for the genetic inheritance of genius. Out of the 787 Nobel Prize Winners there have ever been, I count 18 who were genetically related - sixteen of them by a parent child relationship, two of them as brothers.

The father-son pairings are William Bragg and Lawrence Bragg; Niels Bohr and Aage N. Bohr; Hans von Euler-Chelpin and Ulf von Euler; Arthur Kornberg and Roger D. Kornberg; Manne Siegbahn and Kai M. Siegbahn; J.J Thomson and George Paget Thomson.

The father-daughter pairing is: Pierre Curie and Irene-Juliot Curie.

The mother-daughter pairing is: Marie Curie and Irene-Juliot Curie.

The brothers were: Jan Tinbergen and Nikolaas Tinbergen.

There are married couples, too, who have won: four pairings - but I don't mention them - except for the implicit one above, because they are not blood-related (one would think, anyway!).

These instances are powerful evidence of the strong connection between genetic gift and the heights of human achievement - for their Nobel prizewinning achievements, across generations, signal something more important than the prize itself: the passing on of great gift between those generations, to bear fruit, once more.

I have a liking for continuity - and the thought that gifts are transmissible in this way is a nourishing one. It is not just great gifts that are transmissible, of course - but any gift, of any dimension.

Cowardice in the playground

Two days ago, I saw something remarkable in its power to disturb.

Fintan, three, was in the playground and I was about fifteen to twenty metres away (it was a generously sized play area), near one of my other children. Fintan was standing by an area of low lying plants looking over them for reasons that were not clear to me, from where I was. There was a Singaporean boy behind him who looked to be ten to twelve years old. Were they playing?, I wondered.

Then the boy did something strange. He put his hands under Fintan's arms and tried to lift him. Comically, he failed, for Fintan, though only three, is very heavy: a solid boy indeed. Then he did something else - he tried to push him forward into the patch of plants in front of them. This, too, failed for the same reason of bodily mass and solidity. All this while I had been approaching them and now was close enough to speak:

"What do you think you are doing?" I asked him, not pleased at what I had seen.

He pointed into the patch of plants, where I could now see a football about one and a half metres into their midst.

"They are prickly..." he explained of the plants.

I was flabbergasted. This boy was trying to throw my three year old son into a patch of prickly plants to get his football back! I could barely believe what I had just heard. What a coward! His plan had only failed because of Fintan's unexpected mass.

"Why don't you get it yourself?" I asked rather sharply.

Something in him was shamed by my tone and he gingerly stepped forward into the prickly plants, trying to ensure that his shoes would step down on the offending prickles - and took the ball. He went off without saying a word to Fintan or myself.

I have seen many things in my life - but never have I seen a boy try to effect such a cowardly idea as that.

The incommensurability of education systems

I have discussed this before, but it deserves to be addressed again, in another way and through the lens of another experience.

Education systems are not the same, the world over. The clearest divide is between the American education system and the old, traditional British one, still common throughout the Commonwealth and former colonies.

The American system prides itself on breadth. At every stage from first grade to "College" - there is breadth. The British system goes for depth: at every stage from the first year of school to the last year of University, there is greater depth, than in the American system. This leads to much incomprehension when Americans seek to understand the achievements of British style educated kids - and vice-versa. Quite simply: is it possible to compare breadth with depth? Are they commensurable?

My belief is that they are not readily comparable - for where the American loses in depth, they gain in breadth - and where the British/Commonwealth/European loses in breadth they gain in depth.

There is however one way we can compare them: cognitive complexity. The cognitive demands of an old-style British education of O Levels and A Levels followed by a single subject University degree are greater than at any given age in the American system. This is not a controversial statement. It is readily seen by looking at any online US based course designed for a given age and comparing what would be demanded under the traditional British style education at the same age.

What do I mean by cognitive demand? Well, the difficulty of a subject comes in the depth: the level of concepts and techniques, skills and knowledge that must be mastered. It is in the depth that this is to be found. In breadth, one is held largely to an introductory level of knowledge, simply because so many things are being looked at. In this way, the challenge doesn't deepen - and grow, thereby.

The American system probably catches up in Graduate School (I am not sure but that seems more specialized) - but a taught Graduate degree in the US is probably little more than a taught Undergraduate degree in the old-British style single subject system. This seems obvious because it CANNOT BE OTHERWISE when the Undergraduate US degrees have such breadth in them. Because of that breadth, they are limited in depth.

I will give you a practical example of the incommensurability of these systems at work. A few months back, Ainan and I sat through a University of Berkeley, California, Physics lecture. I presume it was a first year lecture because it was so very simplistic that Ainan, six at the time, who had no formal physics background, thought it very simple indeed. In fact, I would say it was pre-O level. That is the level it was pitched at was below a course of study normally started by 14 year olds and finished by 16 year olds in the old traditional British style education. It wasn't even hard enough to be called O level. It was late primary/early secondary level - and yet that was Berkeley. This set me thinking about the nature of education systems. Raymond Ravaglia's remark that the American system "teaches to the left of the distribution" also opened my eyes as to what was happening here.

This phenomenon of great breadth and little depth in the American system - and great depth but little breadth in the traditional British system - leads to the impossibility of either side understanding the academic achievements of the other, fully. There will always be some failure to understand what it is that the other has done and can do.

American Universities recruit students directly after O level, in Singapore. That shows that O level is equal to or above High School graduation standard. The Berkeley lecture makes me wonder how much above that standard it might be.

Yet, all is not lost for the American system. The great breadth means that an American educated child should be able to handle a great variety of tasks - and there is merit in that, too. It just depends on what the culture needs.

(If you would like to read about Ainan Celeste Cawley, a scientific child prodigy, aged seven years and four months, or his gifted brothers, Fintan, three and Tiarnan, fourteen months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted adults and gifted children in general. Thanks.)

Fintan's creative perception

Fintan, three, sees the world through artist's eyes. An example of this occurred a couple of months ago.

We were travelling back from the East Coast (an artificial beach, actually), when Fintan pointed out of the window and said: "Man who...", then he pulled back an imaginary arrow on an imaginary bow, indicating with actions what he had no words for.

I looked at where his eyes were fixed. There stood an incomplete metal structure. It looked like part of a giant Ferris Wheel. It was positioned in the Marina area. A memory came back to me that once it was mooted that Singapore build a giant "Eye" like that in London. Perhaps this was it. Or perhaps this was some kind of industrial machine whose purpose was not clear. It was a grey metallic structure consisting of an upright column, with a metal framework attached shaped like a slice of cheesecake: an arc stretching out into space. Clearly it was only partially built. Now, that he had pointed it out, I, too, could see how it could be seen as an archer, standing majestically by the sea.

How beautiful is Fintan's world that he can see such things in it. He sees patterns everywhere, reinterpreting the world with his artistic gaze wherever he looks. In many ways, his way of seeing is much more interesting than the world actually is. For everywhere he looks he sees something exciting in it. This pattern matching, of course, is an old tendency of many men: one need only think of those who first saw the constellations above in points of light and gave them names and histories. Fintan is doing the same in his own way, with his own world: giving a little magic to a world that may have none without it.

Perhaps Fintan the pattern finder will become Fintan the artist, one day. His outlook certainly seems like one.

Fintan draws mummy and daddy

Yesterday, we gave Fintan, three, a piece of charcoal and a piece of paper to see what he would do. He decided to draw his parents.

First, he drew mummy. He gave her eyes which looked like eyes and a mouth which looked like a mouth. The eyes had lashes and the mouth had teeth. He did not draw a stick figure stereotyped face as most children draw - but actually sought to render what he saw before him. It might have been better if we had given him another medium rather than charcoal for he tended to smudge what he had drawn - but the results were very interesting. He actually produced a recognizably human face.

Daddy's face was less complimentary - but again he followed the "draw what I see" mode and came up with something in a style of his own.

What was particularly interesting was the manner in which he tackled the task. When it came to me, he held the charcoal in his hand and looked at me for a long pause, as he took in what was before him, before he began to draw. He was very much performing as the little artist deciding how to approach his subject. He drew with earnest but with speed and clearly enjoyed what he was doing. Perhaps he will be an artist like his mummy, one day. It would be nice to think so.

We didn't direct him in how to draw, but let him draw as he pleased: that way we had a chance to see how he saw the world - and not how we wanted him to see it. It is better that way, I think. It is more true to the child.

William James Sidis and Ratio IQ

William James Sidis was a child prodigy. Indeed, he was one of the greatest child prodigies ever recorded. Yet, what would happen to him today? Would the magnitude of his gifts be recognized were he tested by modern psychometricians?

The short answer is a definite no. You see estimates of William James Sidis ratio IQ place it at least 250 to 300. This might even be conservative in some ways, if you look closely at his life - but nevertheless, this is a significant IQ figure. But what would happen if he was tested by modern IQ tests? They would grossly underestimate him - and here is why. Modern tests tend to have a ceiling of a deviation IQ of 160. Ceiling effects will actually depress most gifted people's scores. Everyone has a different pattern of peaks in their subtests - and these peaks will be cut off at varying points by the test limit. Some subtests may show weaknesses - and these will lower the overall score. In fact, if William James Sidis took a modern IQ test he may not have even got a score of 160 - depending on his pattern of strengths and weaknesses, he may have had a depressed score of 150 or 140 or any other number below 160.

So, a psychologist testing Sidis today would most probably completely miss the magnitude of his gifts, in terms of a test result - because the test is incapable of measuring his gifts, as they truly are - but it is only capable of underestimating them, to an unknown degree. Of course, the same applies to any extremely gifted child today. The IQ tests are only capable of underestimating and not of measuring such children.

I do not know why, as a profession, the designers of such tests have decided to introduce this limit to the tests. Perhaps it is an economic decision: it simply wasn't thought worth having a test with a long tail with all the work that would require for only a relatively few test subjects to benefit from. Perhaps that is what it comes down to. Or perhaps scoring high in such a test is thought enough - perhaps the actual truth of the situation is not regarded as important.

Anyway, this situation with Sidis and all even remotely like him - the extremely gifted - points us to an unavoidable conclusion: ratio IQs remain valuable and should be reinstated as one of the tools of estimation of a child's intelligence.

(If you would like to read about Ainan Celeste Cawley, a scientific child prodigy, aged seven years and four months, or his gifted brothers, Fintan, three and Tiarnan, fourteen months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted adults and gifted children in general. Thanks.)

Singapore shopping with a smile

It is strange how often strangers smile at us, now. Strange - but good.

Yesterday, I went shopping with my wife Syahidah - there is a tale to tell about that, which I shall another time, but for now I would like to focus on the smiles.

We went to an arts supply shop, Art Friend, in Orchard - they have several branches throughout Singapore - and there we asked an assistant about materials. The lady couldn't have been more helpful, leading us to where the pastels were located, even getting us a box to put them in. She told the cashier how to charge us (differently owing to our special request) and made sure we got everything we wanted. She was the second assistant to help us in that shop. The other - a young man - had explained which materials to use with which supplies and shown us where each were located.

I don't know if it was just a lucky day but the service seemed better than average, that day. I had the uncanny feeling they knew of us, already.

(The art materials were for my wife, for, as you may know if you are a regular reader, she is an artist - like her brother, Hafiz. She does portraits, in a unique style; he does abstracts.)

The same thing happened in a toy shop. The assistant was very keen to help; very keen to show us where everything was - and after we settled the bill, she looked directly at me and gave me the biggest of smiles. I am not used to that - big smiles being thrown in my direction - but I must say it is pleasant to be on the receiving end.

Everywhere we went; we were bathed in this warmth. It was not from all people - but enough seemed to know us and respond to us positively to make the feeling of the city warmer than it had been, more welcoming.

This warm welcome says something good about Singapore and Singaporeans. It says that Singapore does not begrudge its gifted - in a very real way, they are welcomed. At least if our experience is anything to go by. In this manner, I see that Singapore has a bright future - for here if, again, our experience is typical - the bright may be allowed to shine and in shining, make the whole society shine. Perhaps that is why they call it a "meritocracy" - and promote meritocratic principles throughout the society. Perhaps the smiles we are receiving are a symptom of the adoption of a meritocratic outlook.

I think it will do Singapore a lot of good to maintain such an outlook - and such a set of principles. It is an outlook and a way of living on which a great city may be built, in time.

Singapore's IQ distribution and giftedness

I have just re-read my post on Ainan going to Raffles Institution, yesterday and, on doing so, I realized that I had made an error in my analysis. I have underestimated the number of gifted students who would be at Raffles.

How have I done this? Well, I realize, now, that I had made the assumption, in my statement that 1 in 44 people will be moderately gifted (IQ 130 or more), that the distribution was a normal one about an IQ of 100: as is the standard model of IQ. So, this is right, right? Wrong.

You see, the mean IQ in Singapore is, according to IQ and the Wealth of Nations (2002), 104, NOT 100. This means that the distribution of IQs in Singapore is significantly skewed towards the gifted range. Quite simply, there will be more gifted students in the Singaporean population, for its size, than there would be in many other populations of the same size. That is the number of gifted students, per head of population should be higher in Singapore, than many other countries. For instance, the mean IQ of the United Kingdom is 100; that of the United States is 98. Singapore will have notably more gifted students per head of population than these two nations - because a few IQ points shift - amounting to almost half a standard deviation, in relation to the US, will push many more students into the gifted range. This analysis assumes that the shape of the distribution is the same - a normal curve (though in fact it should be trimodal - but normal is the usual model) - about an IQ mean of 104.

(Of course, although Singapore will have more gifted students per head of population than many other nations - including the US and the UK - these nations will have many more gifted students in terms of actual numbers - because they are much larger populations.)

Applying this to Raffles Institution, without detailed analysis, gives me the sense that it is probable that ALL their students are gifted - for they are the top 3% of a population with mean IQ 104, not the top 3% of a population of mean IQ 100, as I had inadvertently assumed.

Not all nations have lower IQs than Singapore. Hong Kong, for instance, has a mean IQ of 107 - indicating that China may become real competition for the West in the future - but that is another story.