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 +

Tuesday, March 27, 2007

How good is Ainan's comprehension of textbooks?

It is has been pointed out to me, that, for some children there is a gap between their reading and their comprehension. With Ainan this is not the case. He comprehends all that he reads - that I have observed him to read - and comments abundantly in a manner which shows that he has understood it. This applies to the science texts of all levels, including University that he has read, so far.

I hope that clarifies the matter for the reader who raised the issue with me.

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posted by Valentine Cawley @ 1:12 PM 


Anonymous Anonymous said...

Hi Valentine,

What's the latest book that Ainan reads?


9:44 AM  
Blogger Valentine Cawley said...

I will have to look up the title when I get home. It is a University Chemistry text.

He is also beginning to read in Mathematics - which I find heartening. Yesterday he came to me with an equation which he was excited about. I was unable to help him, however, since it lay outside my knowledge. I will have to start learning something else, it be able to help him.

More when I can be more specific. Cheers.

10:37 AM  
Anonymous Anonymous said...

Ah yes. Comprehension and retention.

Such a mystery as to what a great mind can comprehend.

Last week at dinner, my husband was describing a seminar he was going to be teaching in the near future. It was to be based on something with the title 'Prometheus Unbound.'

Knowing my daughter's love for Greek mythology, he asked whether she could tell him more about Prometheus.

She proceeded to retell the story of Prometheus in clear detail. My husband asked for her source material. She told him which book she'd read it in.

I know that book - she read it repeatedly when she was 4 or 5. She's 9 now.

After dinner, my husband found the book and read the story for himself. When I asked him about it, he said she'd gotten every detail spot on.

And she's NOT PG. I can only imagine how prodigious is Ainan's ability.

What a delight - and a mystery.


1:11 PM  
Blogger Valentine Cawley said...

What a wonderful story, Pam.

Your daughter has many gifts, I think, from what you have said to me - this is just one more example of her capacious mind, at work.

Is she a self-educator? Does she read widely and voraciously? It would be good, I think, if she did.

Best wishes.

1:34 PM  
Anonymous Anonymous said...

Can you share with me the equation that he asked you, Valentine? Thanks in advance.

I'm not mathematician, but (maybe with big "M") I can help :)

~not a mathematician

2:36 PM  
Blogger Valentine Cawley said...

Yes, Arief. Ainan was very excited about the equation "(e to the power of i times pi)plus 1 equals zero. He thought this was a fascinating proposal. I couldn't help him much because i represents an imaginary number and I confess that I don't really know that much about imaginary numbers.

I don't think he really needs help on the issue - I think he just needed someone to share his excitement at understanding this. That is all.

Best wishes

6:31 AM  
Blogger EbTech said...

Most likely your question has been answered by now, but just in case it has not...

By definition, i is the square root of -1.

It is common for beginning mathematicians to feel awe at the elegance of Euler's identity:
e^(i*pi) + 1 = 0
This equation uses each of addition, multiplication and exponentiation exactly once. Most remarkably, it brings together all five of what may be considered the most important constants in mathematics: 0, 1, e, i, and pi!

Quoting Stanford professor Keith Devlin:
"Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."

Please forgive my asking, but did you not have to take a course in complex analysis as part of your physics degree?

12:24 PM  
Blogger Valentine Cawley said...

Hi EbTech,

I am familiar with what i is...though thanks for pointing it out to readers.

Re. my degree course. It was much more wideranging than was Natural Sciences. This had the advantage of breadth...but the disadvantage that it was difficult, at times, to know what to focus on, (since many subjects were studied at once). Thus, it was quite easy to overlook things. This would not have occurred in a single subject degree most probably. It was also a long time I am not sure what was and was not a requirement!

Your education sounds really solid...I like what I read. What subject are you actually studying?

2:34 PM  
Blogger EbTech said...

Thanks, I'm glad you think so! Only recently have I been satisfied with my education. Perhaps I should take this opportunity to introduce myself with a bit of background...

My giftedness (perhaps HG) is mainly focused in logical areas such as math. As you might expect, my experiences with the education system have been frustrating at times. Primary school was so boring that I became very lazy and received mediocre grades. As a result, I vastly underestimated my abilities during those years, despite the fact that my arithmetic and reading were years ahead of my peers.

Teachers had mixed reactions. Most did not understand. To some extent I sympathize with them, for in my boredom I became quite a troublesome child! I was repeatedly sent to the principal's office for disrupting class. Interestingly, the principal once said that if I were any ordinary student, he would have had me suspended for my behaviour.

I was lucky enough to meet one very excellent teacher in primary school. He was a great role model who valued fitness of both body and mind (he also happened to be a very skilled marathon runner). He would often take breaks during classroom instruction to teach mature life lessons... to a typical group of grade 4-5 students! He gave me a great deal of individual attention, advancing to grade 10 maths in only a few years. He awakened my interest in learning. Unfortunately, my middle school years went back to boredom. I learned no additional maths. The school allowed me to skip one year. It didn't help much, but at least it meant one less year wasted...

I developed a few interests on my own. My main childhood interest was astrophysics. Upon being introduced to the solar system in first grade, I became fascinated by the prospect of far away worlds and began borrowing astronomy books from the school library. By middle school, I was reading about blackholes, space-time, Hawking radiation and the like. I entertained the idea of becoming a professional astrophysicist. But later on, another interest took hold...

Gradually, I taught myself how to program computers. The limitless power of computer instructions appealed to my creative side, while the logical structure appealed to my mathematical side. I spent a lot of time programming my own games. Since I lacked artistic talent, I had to borrow art from other sources (giving credit where due, naturally). In an ironic twist of fate, the topic which most deeply interests me at present is none other than artificial intelligence! hehe

High school went relatively well, though I finished the IB math curriculum early and had to wait a year before writing the exam. I brought my grades up a notch to get into university, which did not require a lot of effort. Instead of taking time to study, I was devoting more time and energy to game programming and other hobbies.

Upon entering university, I was thoroughly impressed. Finally I was allowed to study what I wanted! I got permission to take two third-year courses in first year, so there was no shortage of challenging learning opportunities. My only regret is to have wasted so many unproductive years in school when I should have been learning; but in retrospect, I may have been luckier than the majority of similarly gifted people.

To answer your question, I am taking what's called a "Combined Honours", which involves studying two subjects, in my case mathematics and computer science, in considerable depth. Specialization into narrower fields such as artificial intelligence occurs in graduate school.

I have yet to take a course on complex analysis; my current knowledge of complex numbers comes from IB math. IB topics are similar to A-level maths, except for the mechanics section. I learned about fractals on the internet, before programming my own Mandelbrot Set generator. I also studied one year of calculus-based physics and one year of psychology.

Well, that introduction sure became longer than intended!

Best of wishes to your family, and hopes for a future that takes better care of its gifted youth.

5:24 AM  
Blogger Valentine Cawley said...

Thank you EbTech, for your self-portrait. I am happy for you that you have found a suitable focus for your gifts. Many gifted people do not...and waste their potential, thereby.

Re. your University: it sounds really good...which one is it? Is it typical of Canada?

Funny enough, my son is interested in programming computers...but he has taught himself so far, with no instruction, just by playing with the systems to see what happens. No computer is safe around him.

Yes. Programming is creative...and I can see why you would enjoy it so much.

I hope that you can go on to push the AI frontiers forward!

Good luck.

10:55 AM  
Blogger Syahidah and Valentine said...

Perhaps, EbTech, you might like to leave an email address sometime, just to be sure I can contact you, if need be.

By the way, it is funny that you are interested in AI...since I am interested in NI...Natural Intelligence, as it were!

1:39 PM  
Blogger Fox said...

I would imagine that it is going to be quite difficult to explain what imaginary numbers are to a seven year-old. I would say that 'i' and its negative are roots to the quadratic equation x^2 + 1 = 0 but your son may not understand.

With directed guidance, I think that Ainan can certainly go very far in his education in mathematics. He can almost certainly run far in mathematics but he must have someone to teach him to walk properly first.

2:32 PM  
Blogger EbTech said...

Haha! Is there any difference between NI and psychology? It is interesting to contrast the different approaches to studying this phenomenon we call intelligence...

Psychology takes a top-down approach, beginning with the complex human brain and using the scientific method to explore its functions. AI on the other hand takes a bottom-up approach, attempting to build progressively more sophisticated intelligences starting from scratch, based largely on mathematical theories and models. At some point in the future, I imagine the two disciplines will intersect.

It would be a truly outstanding achievement if we succeed in building a creative AI! Yet how disturbing that might also be, for what place would human intelligence have in a society of super-AIs? Unless we simultaneously improve ourselves or merge with them somehow...

Here is one of my favourite quotes, by computer scientist Edsger Dijkstra:
"Computer Science is no more about computers than astronomy is about telescopes."
I leave the interpretation to you!

If you are interested in the future implications of Strong AI and what we can do to prepare, there is an enlightening 40-page paper on the subject. The text is quite accessible without the need for a technical background:

It is interesting to note that the author, Eliezer Yudkowsky, has no formal background in AI. He is one rare example of a self-taught and successful researcher!

Re. Ainan and computers: it is great that he is learning so much now, while his time is free from adult responsibilities. A quick word of caution: nearly all self-learned programmers get into habits that professionals would consider very bad programming practice. On the one hand, it might be a good chance for Ainan to learn the bad practices from experience. However, this means he should be ready to relearn his style if necessary. Then again, the standard rules don't really apply to Ainan, do they? ;)
Out of curiosity, what computer languages or tools does he use?

I attend the University of British Columbia. It is considered Canada's top university outside of Ontario and generally ranks 30th-40th worldwide. I might try applying to an Ivy grad school later, but for now UBC is much closer to home and the atmosphere here is great. I can't speak for other departments, but all my professors have been good teachers. In fact, our computer science department has a tradition of professors who prefer to be addressed by first name!

Although our computer science department isn't world-famous, our students are a lot smarter than our fame suggests. For example, we defeated Stanford in a major computing contest for 7 out of the last 8 years! Non-technology-focused universities such as Harvard don't even come close.

I would love to keep in touch, though perhaps it would be wiser not to post my primary email address in public. Shall I send an email to the.cawleys at

5:22 PM  
Blogger Valentine Cawley said...

Yes. Please send an email to mention that you are EbTech!

I don't think that the famous universities are always the best. Sometimes their fame is due to something which happened long ago and no longer applies (like being the oldest university etc.) Your University sounds wonderful.

I like Ainan teaching himself things his own way...but I have no idea which languages he is using. He specializes in getting computers to do bizarre things...quite how, I don't know. He seems to have an instinct for how the systems should work.

Re. bad habits. Yes. That may happen...but he also may discover more creative ways of doing things, by taking his own approach. I will let him learn as he pleases.

Re. Creative AI...that would be worrying and potentially sad for that part of humanity that enjoys creating. Maybe we will all seem insignificant after a few more decades. That, in a very real sense, would mean a sense of loss for Humanity...a loss of the sense of being special.

I hope there is still a place for human creativity in whatever is to come.

Kind regards

6:21 PM  
Blogger Valentine Cawley said...


I just made "NI" up...but it seems appropriate to defend the human version!


6:22 PM  
Blogger EbTech said...

I realize you made NI up! I simply meant that psychology is about understanding the human side of intelligence.

Yes, Ainan can learn on his own... I wonder what he's doing. Hacking is a little more dangerous than ordinary programming! I never really got into hacking, and therefore don't know much about it. I know a relative who often did strange things to the computers at school. He has since grown out of his mischievous ways, I think. Just for fun, a site for learning how to hack!

Re. creative AI, is it something we should avoid? Should we instead look for ways to enhance ourselves, genetically or otherwise? Either way, it seems paradoxical to prevent the creation of a technology in the spirit of creating. It is a difficult issue, since we are so accustomed to having the strongest minds on the planet.

9:30 PM  
Blogger Valentine Cawley said...

Yes. Ainan likes to hack computers, and insert amusing attributes. Well, he finds it amusing anyway. I have no idea how he worked out how to do it.

As for the strongest minds...if we are not the greatest thinkers on Earth, then we are no longer in charge, really. That might be a very dangerous step. It could be terribly disabling for the human race. At least, for those of us deep enough to be concerned about such things.

Nevertheless there are some very good applications of even weak AI...which you could work productively on in your life. However, very careful thought should be given to creating another intelligent "race".

Best wishes

10:46 PM  

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