Mathematical serendipity and the Apollonian Gasket.

Maths is vast. Sometimes, looking at how much has been done, I wonder at the mathematical Universe that has been created by the collective endeavour of all Man’s generations of mathematical thinkers. Now, this vastness has consequences which Ainan discovered recently.

Some time ago, Ainan drew what seemed to him a very interesting shape of tangential circles within a circle, echoing fractally on. He drew it because the form of it appealed to him, aesthetically. He liked its mathematical beauty.

Some time later, Ainan stumbled on something on Wikipedia: the Apollonian Gasket. It was the figure Ainan had drawn...the fractal shape of tangential circles. Ainan had rediscovered something invented, initially, by Apollonius of Perga, the Greek Mathematician. How odd...and how revealing of the vastness of mathematical creation, that a random creation of a child, playing with mathematical ideas, should, itself, have already been the random creation of an adult, long ago, in Greece.

Ainan is inventing much mathematics these days. He invents mathematical problems, schemas, conjectures, propositions and theories, for himself to play with. No doubt, on occasion, they will be something that has been done before – like the Apollonian Gasket – yet, at other times, I am sure, they are something that has never been done before. The problem with that is that I am not a mathematician and so I am not in a position to advise Ainan as to the merit, utility or value of anything he does. So, he just creates in mathematical isolation, playing with maths, as other children might play with the sand, at the beach: happily, joyfully, for the very purpose of immersing oneself in the environment – in his case, an abstract one – in the other’s, the beach.

Ainan is presently alone in his mathematical pursuits. There is no-one to share them with – though I listen to him and watch, with a sprinkling of wonder, at what he does. Yet, I cannot be the perfect audience to his mathematical work, because my primary domains are elsewhere, other than this.

Ainan spins on, growing, becoming, morphing, each passing year, into a being, ever more rarified, ever more unexpected. My role is to do what I can to foster that growth – even if it be in areas that are not my primary strengths. I enjoy it, but I wish, for his sake that I could be all the differing intellects he requires to be properly supported. I can be most of them – and am – but I cannot be all of them. Yet, what I can be, is appreciative of his intellectual growth, in whichever direction it meanders, no matter how far it wanders...I can appreciate it...and I do.

I hope that is enough.

Posted by Valentine Cawley

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Giftedness and "palm-reading"

There is a tradition in Europe of palm reading, whereby by a woman (usually) gazes into one's hand and tells of one's life, past, present and future.

Personally, I have never had any doubt that it was doubtful, however, a recent piece of research has thrown up an interesting correlation between the form of the hand and the form of the brain, above it.

It has been observed that there is a strong inverse correlation between the ratio of the index finger to the ring finger and a talent for maths. By this I mean that a SHORT index finger in relation to the ring finger, indicates a brain well-equipped for maths. On the other hand, a hand in which the ratio of index finger to ring finger is about one (they are of similar length) indicates more of a verbally inclined brain.

What is the cause of this relationship? Testosterone. Lots of it, in the womb, makes your index finger short and your brain biased towards visuo-spatial/mathematical tasks. Little of it, and relatively more estrogen, allows the brain to progress towards a verbal type brain.

Usually, this means that a boy will have the maths bias and a girl the verbal bias - but this is by no means universal. There are maths woman and verbal men - as shown by their hands.

So, is your child a maths child or a verbal child? To find out how their brain is actually biased all you have to do is look at their hands and see how long or short the index and ring fingers are. It is that simple.

(If you would like to read about Ainan Celeste Cawley, a scientific child prodigy, aged seven years and six months, or his gifted brothers, Fintan, three, and Tiarnan, sixteen 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.)