A perspective on mathematics

On the 5th February 2013, Ainan confided: "The reason I like the Ackermann function is because it is so simple."

Some might not agree. The Wikipedia article on the Ackermann function states: "In computability theory the Ackermann function, named after Wilhelm Ackermann is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive."

As maths goes, the Ackermann function is simple enough - but the point is that this is the view of a boy who has just turned 13. I suspect this is not a common view therefore.

Ainan is growing into a young mathematician, along with his other attributes. He studies maths every semester at Taylor's University and is steadily growing in knowledge, skill, competence and confidence. He even makes up his own maths.

The other day, he was trying to explain to me a mathematical system he had designed. He was very enthusiastic about it. What struck me more than his enthusiasm was his repetition of: "It is so simple Daddy."

I looked at the page he was writing on, densely scrawled with mathematical notation and thought that most people would disagree. 

Ainan is still growing intellectually. Each year sees him becoming more complex, more adept and that bit more beyond the expected. He is only 13, now...near the beginning of that year of his life. Thus, he still has quite a few years of intellectual growth left to him. It is becoming clear that he has already journeyed further, intellectually, than most ever do - yet he is still quite early on in his journey. I am left to wonder: how far will he go? 

I look forward to being witness to his growth - and an assistant to it, when I can be.

Posted by Valentine Cawley

(If you would like to support my continued writing of this blog and my ongoing campaign to raise awareness about giftedness and all issues pertaining to it, please donate, by clicking on the gold button to the left of the page.

To read about my fundraising campaign, please go to: http://scientific-child-prodigy.blogspot.com/2011/01/fundraising-drive-in-support-of-my.html and here: http://scientific-child-prodigy.blogspot.com/2011/01/fundraising-drive-first-donation.html

If you would like to read any of our scientific research papers, there are links to some of them, here: http://scientific-child-prodigy.blogspot.com/2011/02/research-papers-by-valentine-cawley-and.html

If you would like to see an online summary of my academic achievements to date, please go here: http://www.getcited.org/mbrz/11136175To learn more of Ainan Celeste Cawley, 10, or his gifted brothers, Fintan, 7 and Tiarnan, 5, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html

I also write of gifted education, child prodigy, child genius, adult genius, savant, megasavant, HELP University College, the Irish, the Malays, Singapore, Malaysia, IQ, intelligence and creativity.

There is a review of my blog, on the respected The Kindle Report here:http://thekindlereport.blogspot.com/2010/09/boy-who-knew-too-much-child-prodigy.html

Please have a read, if you would like a critic's view of this blog. Thanks.

You can get my blog on your Kindle, for easy reading, wherever you are, by going to: http://www.amazon.com/Boy-Who-Knew-Too-Much/dp/B0042P5LEE/ref=sr_1_1?ie=UTF8&m=AG56TWVU5XWC2&s=digital-text&qid=1284603792&sr=8-1

Please let all your fellow Kindlers know about my blog availability - and if you know my blog well enough, please be so kind as to write a thoughtful review of what you like about it. Thanks.

My Internet Movie Database listing is at:http://imdb.com/name/nm3438598/

Ainan's IMDB listing is at http://imdb.com/name/nm3305973/

Syahidah's IMDB listing is at http://imdb.com/name/nm3463926/

Our editing, proofreading and copywriting company, Genghis Can, is athttp://www.genghiscan.com/This blog is copyright Valentine Cawley. Unauthorized duplication is prohibited. Use only with permission. Thank you.) 

The relativity of ability.

As long term readers will know, Ainan has an unusual perspective on himself, one that, perhaps, others would not agree with.

A week or two ago, I remarked to Ainan:

“Your ability has been growing in recent months...” I spoke softly and without any undue emphasis.

“No it hasn’t!”, he said most firmly. “I am not getting any better, it is just that the tasks are getting easier.”

I didn’t wish to argue with him, so I maintained my silence. I had seen versions of this attitude and belief before in Ainan. He refuses to believe that his intellect is growing. He sees himself as ever the same. If he gets better at a variety of task, he blames the task for somehow getting easier, rather than acknowledge that he is getting better, or growing in any way.

I know why Ainan believes this. It is a defence in him, against the notion that he is in any way unusual. Ainan wishes to preserve the belief – which he holds – that his way of being is the norm – anything that deviates from him, is not. For Ainan, the intellectual standard, for “ordinary”, for a 12 year old, is his own level. That is how he wishes to see the world and his place in it. Thus, the idea that he might be growing or developing noticeably, threatens that stable world view – so he rejects it. For him, it is the tasks which change, not him.

This puts me in a dilemma. Should I try to get him to see his true place in the world, in relation to others – or should I leave him be, to preserve his illusion of “everdayness”, which he so wants to preserve? For now, I have left him with his view that it is the world that is getting easier to deal with, than that, he is growing more capable in doing so. I will have to deliberate though, in future, whether this is the right thing to do, in the long term.

This year I have seen an efflorescence of Ainan’s mind. He has taken to music, taught himself the piano, overnight, it seemed, and is now composing music. He plays it most days, quite beautifully. He is also growing as a writer and a mathematician. His mind seems to be expanding again, with a marked velocity. Yet, Ainan does not wish to see it. For him, all is static within – it is the world which changes without.

I have left him to his worldview and did not stress him by taking an opposite stance. I will just have to enjoy his mental renaissance, in silence, savouring it for myself without any overt remarks to draw attention to it. 

Whether Ainan likes it or not, he is growing – and it is enough for me to observe this. I don’t need to convince Ainan of it.

Grow on, Ainan! Or should I say: shrink world!

Posted by Valentine Cawley

(If you would like to support my continued writing of this blog and my ongoing campaign to raise awareness about giftedness and all issues pertaining to it, please donate, by clicking on the gold button to the left of the page. 

To read about my fundraising campaign, please go to: http://scientific-child-prodigy.blogspot.com/2011/01/fundraising-drive-in-support-of-my.html and here: http://scientific-child-prodigy.blogspot.com/2011/01/fundraising-drive-first-donation.html

If you would like to read any of our scientific research papers, there are links to some of them, here: http://scientific-child-prodigy.blogspot.com/2011/02/research-papers-by-valentine-cawley-and.html

If you would like to see an online summary of my academic achievements to date, please go here: http://www.getcited.org/mbrz/11136175To learn more of Ainan Celeste Cawley, 10, or his gifted brothers, Fintan, 7 and Tiarnan, 5, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html

I also write of gifted education, child prodigy, child genius, adult genius, savant, megasavant, HELP University College, the Irish, the Malays, Singapore, Malaysia, IQ, intelligence and creativity.

There is a review of my blog, on the respected The Kindle Report here:http://thekindlereport.blogspot.com/2010/09/boy-who-knew-too-much-child-prodigy.html

Please have a read, if you would like a critic's view of this blog. Thanks.

You can get my blog on your Kindle, for easy reading, wherever you are, by going to: http://www.amazon.com/Boy-Who-Knew-Too-Much/dp/B0042P5LEE/ref=sr_1_1?ie=UTF8&m=AG56TWVU5XWC2&s=digital-text&qid=1284603792&sr=8-1

Please let all your fellow Kindlers know about my blog availability - and if you know my blog well enough, please be so kind as to write a thoughtful review of what you like about it. Thanks.

My Internet Movie Database listing is at:http://imdb.com/name/nm3438598/

Ainan's IMDB listing is at http://imdb.com/name/nm3305973/

Syahidah's IMDB listing is at http://imdb.com/name/nm3463926/

Our editing, proofreading and copywriting company, Genghis Can, is athttp://www.genghiscan.com/This blog is copyright Valentine Cawley. Unauthorized duplication is prohibited. Use only with permission. Thank you.) 

A word of gratitude.

We have reason to be grateful to a special man, who may never be able to read these words.

It seems long ago, now, when we first met Dr. Ng Kok Chin, of Singapore Polytechnic. He was Head of his own Chemistry department there. He was a man of medium height, but more than medium pleasantness. He had about him, the sense that he actually cared. We were introduced to him by one of his colleagues Priya Naidu, a lecturer that Ainan had met on a Nanotechnology workshop, at Singapore Polytechnic when he was 7. Our meeting was to discuss whether Ainan could join Singapore Polytechnic for regular Chemistry courses based in the laboratory. Dr. Ng Kok Chin's attitude was positive and welcoming, throughout. He seemed to be looking for ways to make it work, rather than seeking (as some people in such a situation would tend to), ways in which it wouldn't.

Though Ainan was 7 when we first met Dr. Ng Kok Chin, it was not until Ainan was 8 years and 4 months that he joined Singapore Polytechnic to do Chemistry courses, there. Ainan's mentor at SP was Dr. Ng Kok Chin - it was he who arranged the courses which Ainan was to attend and he who negotiated with all other parties at SP to make it all happen.

Ainan enjoyed his sessions at SP. He gained much from them, too - and became quite adept in the lab. These sessions were the highlights of his week. Typically he attended SP two days a week from April 2008. He fit into the classes well. His labmates treated him very kindly and he was very popular. We were very happy with how things were. Notably, Dr. Ng Kok Chin was always around to make sure things were going smoothly. He always took an interest in how Ainan was doing.

Then, things in early 2009, got very strange. Our emails to Dr. Ng Kok Chin, went unreplied to. Our calls to his answerphone met with no response. Suddenly, SP which had been so supportive, vanished from sight. Ainan's classes stopped. No-one contacted us about what was happening.

Months passed. Intermittently, I tried to contact Dr. Ng Kok Chin, to no avail. Finally, I wrote to his boss. A reply came slowly, after I had written twice. The mail was not a welcome one: Dr. Ng Kok Chin had fallen ill. We were later to find out that he had had a stroke and was now in a coma, from which we have no news of any recovery. It was very sad - and still is, for Dr. Ng was instrumental in opening doors for Ainan's scientific and intellectual growth.

Things never really recovered at SP, after Dr. Ng's tragic illness. After a long time, someone else was appointed to look after Ainan's courses there - but he didn't seem to have the interest in Ainan, that Dr. Ng had had. Things happened very slowly with Dr. Ng's replacement. He also didn't seem to have the same ability to get lecturers on side. Instead of four whole modules a term - as Dr. Ng had arranged for Ainan, his replacement eventually came up with a single class, on one occasion, at the end of the term. (It had taken him the whole term to arrange it).

In the holidays, after that class, we made enquiries about the arrangments for the following term, asking for the usual four classes to be arranged. Dr. Ng's replacement dragged his feet, and didn't make the necessary arrangements. Finally, we mailed the Director of SP with news of Ainan's latest success in Chemistry AS level. He didn't reply. His subordinate - the one assigned to replace Dr. Ng - replied after a week to do something most strange: he wrote to say that SP was withdrawing all support of Ainan and that there would be no more classes for him at SP.

We were stunned. It didn't make any sense. I had written to thank them for the support they had given Ainan and to tell them of his latest success - and they had replied by withdrawing all support of him, and removing his access to courses. It was the oddest thing they could have done. In my understanding of the world, a College when shown evidence of the progress of a child, in such a situation, would usually be more interested in, at the very least, maintaining support or expanding it - not withdrawing it.

I wrote to the Director of SP several times seeking an explanation. He never replied to me or acknowledged my mails, even once.

So, the essence of this story is that we have much reason to be grateful to Dr. Ng Kok Chin for masterminding Ainan's presence at Singapore Polytechnic - but we also have much reason to be doubtful about his colleagues and their intentions towards Ainan.

The story is more complex than it seems - in a sad sense. You see Dr. Ng Kok Chin, who was so supportive of Ainan is MALAYSIAN Chinese. He is not a Singaporean. Yet, he was very supportive and helpful towards Ainan. The senior staff who remained after Dr. Ng Kok Chin was gone are SINGAPOREAN. Yet, they were not supportive of Ainan, once Dr. Ng Kok Chin's influence was gone. To us, this seems very telling. In fact, recognition of this situation was our first clue that, perhaps, we should look to Malaysia for help for Ainan - for it had been a Malaysian, in Singapore, who had rendered most help to him.

Thus, we have two things to thank Dr. Ng Kok Chin for: the great support he gave Ainan at Singapore Polytechnic - and for inspiring us to look to his homeland for further support, once it dried up, at SP, upon his illness. So, it can be seen, that Dr. Ng Kok Chin played a key role in Ainan's development: he afforded Ainan the chance to learn practical skills - and guided us to seek further opportunities in Malaysia, even after he became ill.

Thank you, Dr. Ng Kok Chin, for your kindness towards Ainan. I hope you recover enough to read these words, one day. Best wishes from all of us.

We miss you, Dr. Ng.

(If you would like to learn more of Ainan Celeste Cawley, 10, or his gifted brothers, Fintan, 6 and Tiarnan, 4, this month, please go to:
http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html

I also write of gifted education, child prodigy, child genius, adult genius, savant, megasavant, HELP University College, the Irish, the Malays, Singapore, Malaysia, IQ, intelligence and creativity.

My Internet Movie Database listing is at: http://imdb.com/name/nm3438598/
Ainan's IMDB listing is at http://imdb.com/name/nm3305973/
Syahidah's IMDB listing is at http://imdb.com/name/nm3463926/

Our editing, proofreading and copywriting company, Genghis Can, is at http://www.genghiscan.com/

This blog is copyright Valentine Cawley. Unauthorized duplication is prohibited. Use only with permission. Thank you.)