gently musing about marginalia and related issues

Whenever Wimbledon comes along, I am pleasantly reminded of a question I was asked at school.

The question was simple. If you have 128 people playing in a knockout tournament, how many matches will it take to complete the tournament? Assume no draws or replays.

When we were asked the question, everyone knew the traditional way to get the answer. 128 people. 64 pairs. 64 matches in the first round. Then 32. Then 16. Then 8. Then 4, then 2, then 1. Giving us 64+32+16+8+4+2+1 or 127.

Later on that day, a few of us got into conversation with the teacher, and an alternative route was broached. 128 people. How many winners? One. So how many losers? 127. So how many matches will that take? 1 loser generated per match. 127 matches.

How I loved the simplicity of that approach. Just work out the number of losers and you will have the number of matches. I could have danced all night.

I felt the same way when I first learnt about decimals. Why some decimals “terminate”. Why others “circulate”. How beautifully they do this.

The way I was taught it was something like this. Think of a fraction. Convert it into a decimal. Think of another fraction. Convert it into a decimal. Do this a dozen times with different fractions, and observe the results.

It soon became clear that most fractions didn’t terminate cleanly, they “recurred”. Fractions like 1/3, 2/7, 3/11. Some fractions, on the other hand, ended cleanly, fractions like 1/2 and 2/5 and 3/10. It didn’t take too long to see that the only fractions that terminated were those where the denominator contained factors of 2 and/or 5.

2 and 5. In a base 10 world. Oh yeah. That bored me. So what did I find interesting about decimals? Again, it took a question.

And the question went something like this. Other than those with 2 or 5 as denominator, all fractions that have a prime number as denominator recur when expressed as decimals. The length of the recurring number or numbers is called the period of recurrence. So for example 1/3, or 0.333333…. has a period of 1, 1/11 or .090909…. has a period of 2. What is the maximum period of recurrence of any fraction where the denominator is a prime other than 2 or 5?

Which led to a lovely meandering journey. To convert a fraction into a decimal you have to divide the numerator by the denominator. You keep carrying the residue over until it is zero (in which case the fraction terminates). Or you keep carrying over and over and over.

When would a fraction circulate? When it hits the same residue again and starts the same sequence of residues as a result.

So how long before the same residue must be encountered? That depends on how many different residues can be had before that. What is the maximum number of different residues? One less than the denominator prime.

Discovering that 1/97 indeed has a period of recurrence of 96 filled me with glee. 96 different residues before the same residue is encountered. How beautiful.

There are so many others, little stories and techniques and tricks and tips that have helped me keep a passionate amateur interest in mathematics, particularly in the theory of primes.

The trouble with being an amateur like me is that you start getting idealistic about the subject. And you believe in things like elegance and simplicity. Which means that I’m one of those guys who still believes that there must be an elegant solution to Fermat’s Last Theorem. A solution that could not be jotted down in a book about Diophantine equations, but a short and elegant solution nevertheless.

My love for mathematics exists because others put their love of maths into me first. They spent time with me and explained things to me and taught me and filled me with wonder and amazement.

It’s the same thing with so much in life. Whatever you love, whoever you love. Love has to be shared in order to grow.

So when I think about copyright and patent and stuff like that, when I think about music and art and stuff like that, I think about love. The love that a creative artist puts into his or her creation. And how love has to be shared in order to grow.

Musing about lifestreaming and learning

I saw this today:

The Feltron Report. Nick Felton’s report on his activities during 2008.

Absolutely fascinating. As the cost of such data acquisition drops, and as the cost of storing such data drops as well, the possibilities are tremendous.

From an enterprise perspective, what the report represents is a part of the future of two things: CVs and appraisals. Nick’s work reminds us that you can now tell a story about what you did in ways you could never have done before. As with anything else, there are opportunities to game the “system”, but that is not what I want to concentrate on. I want to look at the positive benefits of having such facilities, my world is littered with half-full glasses and half-open doors.

Why am I excited about this?

Firstly, because of the importance of feedback loops. Because feedback loops of this sort are valuable as learning tools. As I learn more about what I really did with my time, I learn more about what I would like to change in that context; the feedback loop of “actuals” helps me do that. As I learn more about what I liked and what I disliked, I learn more about how I can keep doing the things I like doing; collaborative filtering helps me do that. As I learn more about what others perceive as things I did well and did badly, I learn more about how I can improve my strengths as well as my weaknesses; the feedback loop of “reviews” helps me do that.

Secondly, because of the value of “independent” low-cost data collection in this context. Writing down every song I listen to, and writing down all the time I spend listening to music, is painful. But rating songs as I listen to them, and having something like do the aggregation of my listenstream, it takes that pain away. Now if activities at work could be aggregated in this way, people would think differently about time sheets. Today too much of what goes into a time sheet is a lie.

Thirdly, because of the ability to share the information so gained. In the past, whether it was a CV or a “performance review” or an “appraisal”, what went into the report was very subjective, very biased. As a result people didn’t like sharing the information with others. When the data is collected independently and objectively, this unwillingness to share goes away.

Finally, because of the value we can unlock in teaching. Take the enterprise context of “induction”. You know what I mean, that strange process when you try and explain what you do to someone completely new. When you can give someone a “Felton Report” for a particular role, there is so much rich information there. The report could be an exemplar’s actual report, it could be a synthetic report made up of a number of exemplars averaged out.

We can learn so much. About differences in locations and geographies and cultures.

I’ve kept my comments to the enterprise context, but actually they apply everywhere. Everywhere where people want to learn. Felton Reports will become valuable in the context of education everywhere.

Which is why I am not surprised that I learnt about their existence from glassbeed. [You’re a good man, Clarence Fisher.] I follow Clarence Fisher because he’s that rare breed, a teacher who really means to make use of modern technology in the classroom to the benefit of the people he teaches.

musing about education and learning useful things

This is one more of those vulnerable posts, where I share something close to my heart. There is every risk that some of you will disagree violently, flame me, stop reading my blog. There is every risk that some of you will think less of me because of the things I say. I think of this blog as a community, a place where I know many of the regular readers personally, a place where I can share things like this without fear. For those of you I know less well, and for those of you I do not know, please bear with me.

I loved school. I loved the thought of going to school, of spending time there, being with friends there, working, playing. I loved everything about school. Being at school was something I really looked forward to. It was a wonderful time, and I was privileged enough to be able to spend nearly 15 years in one Jesuit institution, from primary school through to university: St Xavier’s Collegiate School, Calcutta.

It was one of those places that truly deserved being called an institution. There was something about it that was destined to transcend time; it was a living piece of history by the time I got there, at which point it was barely a hundred years old. A wonderful location, a wonderful set of building and grounds, and wonderful staff. We were privileged to have some really great teachers. [It was with some sadness that I learnt of the death of Thomas “Tommy” Vianna a few weeks ago, he was one of those greats. [Tommy Vianna, Requiescat In Pace].

During my time there, as with many others, I had some purple patches, there were times when I was first in class, times when I played well for class and school teams, times when I excelled at something or the other. Of course I remember them well. But there were many times where I did not excel, sometimes because I hadn’t worked at all; sometimes despite my working really hard; and sometimes because I just wasn’t drawn or attracted to whatever it was I was being asked to do.

I remember talking to my maths teacher when I was about fifteen, a time when my sole interest was to become a maths professor, aspiring to do all the things that someone in high school in the early seventies would want to do: grow a beard and long hair; walk around in jeans and t-shirts reading books like Godel, Escher, Bach (which hadn’t actually been published then); learn to play guitar; do something meaningful in the theory of numbers in the footsteps of Ramanujan; and of course solve Fermat’s Last Theorem. Not just solve it, but solve it elegantly, elegantly enough to fit into the margins of a book on Diophantine equations. Maybe smoke a pipe. Have some pastis. Lovingly restore a 16th century book.That sort of thing.

My “hippie maths professor” reverie was rudely interrupted by said maths teacher, who pointed out where he was living, what he was earning, how hard things were. He was adamant that I should go nowhere near teaching; instead, I was to spend time making money; money that I could then plough back into education at a later stage.

And I guess I listened to him. Which is why, when I retire, I will build a school. For sure. It’s something I think about every day. There is something about the sheer inclusiveness that a good education brings; I detest the thinking behind The Bell Curve, I believe with all my heart that everyone has potential; of course social, economic and environmental factors affect every individual’s ability to develop and reach and extend that potential, but not in the way bell-curvers think.

That belief in the power of education is the reason why I got involved in School Of Everything; there is something very fulfilling about the premise behind SoE; I’m also very excited about the possibility that we can create a mechanism to unlock trapped potential amongst people who are otherwise unable to participate, usually because of generation or gender.

That belief in the power of education is the reason why I joined BT; I have this deep-seated belief that ubiquitous, affordable connectivity is an absolute must-have as we strive to improve health, education and welfare worldwide, as we strive to make the world a better place, as we strive to become better stewards of what we have. As we strive to change ourselves.

So I spend a lot of time thinking about education, about what it really means. Not dictionary definitions, not semantic arguments. What does “education” mean to me?

It’s not about “committing to memory and vomiting to paper”.

It’s not about learning to sit tests. It’s not even about learning to pass tests.

These things are useful, but they are neither necessary nor sufficient for us to be able to be anything, do anything.

So what is it about?

I think it’s about these things:

  • learning how to learn, which involves a lot of watching and listening
  • learning how to love, which involves even more watching and listening
  • learning how to lose, which involves quite a lot of watching and listening
  • learning how to be with yourself, which also involves a lot of watching and listening
  • learning how to be with other people, which also involves ….watching and listening
  • learning how to solve problems, which also involves ….. watching and listening
  • remembering what you’ve seen and heard, and being able to assimilate it
  • learning how to express yourself in word and deed, how to take the things you’ve learnt and do something with them

The more specialised the things you watch and listen to, the more you’re acquiring a particular skill. Sometimes there’s more watching, sometimes there’s more listening. Whenever I had to concentrate to see or hear or express something, I really felt for people who couldn’t, people who didn’t have the full use of their sensory equipment, people who didn’t find it easy to deal with their feelings. I’ve always had a sneaking admiration for people who are autistic, more specifically people with Asperger’s, because there’s a part of me that feels I belong there.

Just musing. What does “education” mean to you?

Incidentally, this post was triggered by my reading today’s Randall Munroe special:

At the back of my mind was all the recent kerfuffle caused by the publication of Don Tapscott’s recent book, a subject I shall revert to later.

Incidentally, if any of you prefer to take the discussion offline, DM me via

Musing quietly about “literacy”

“I am always for getting a boy forward in his learning; for that is a sure good. I would let him at first read any English book which happens to engage his attention; because you have done a great deal when you have brought him to have entertainment from a book. He’ll get better books afterwards.”

James Boswell, quoting Samuel Johnson in Life of Samuel Johnson

I love that quotation; by all means replace the word “English” with whichever language you prefer, the sense is what matters to me. [Incidentally, my thanks to Joan Downs of New York, who referred to the quote in a letter to the Editor of the New York Times a few days ago, thereby making it serendipitously accessible to me for this blog post]

It was January 1972. I was in Class 8D at St Xavier’s Collegiate School, Calcutta, the school year was just beginning. We had a new form teacher, Mr Desmond Redden. (Calcuttans will understand why he was nicknamed “LalMurgi” from the day we met him). Mr Redden was unusual, to the extent he had just joined the teaching staff at the school; whereas the 40-strong class he faced were, on, average, 5-year veterans of the school, and quite used to being with each other. If the school practised streaming, it was not visible to us as students; every year, we would notice that a few students went to another class, and a few joined us. The bulk of us stayed together from infancy through to the time we selected subjects for what was then our “Senior Cambridge”, our University of Cambridge Overseas Examinations Syndicate Ordinary Levels, to give them their full name.

Anyway, to the point of this post. Mr Redden met us for the first time, and it was likely to have been more daunting for him than for us. And to break the ice for the first class of the first day, he asked a number of us what we did during the Christmas break. When it came to my turn, I told him I played games with the family, lazed a lot. And read comics. Lots of comics. Every day.

He went ballistic, and was more than just scathing about my reading habits. Made a big deal about how reading comics was a treasonable offence, how it spoilt a person’s grasp and command of the language and corrupted his writing ability. I was young enough to feel ashamed; red-faced, tears in my eyes, hot-flushed, that sort of thing. Still standing up, hoping the ground would open up and eat me alive. You know that feeling? Happened to me a lot when I was young, probably built character or something like that.

A few minutes later Mr Redden was done with the icebreaker Part 1, and went on to Part 2. Analysing his portfolio, looking at what he “knew” about the children in his care. Looks like we have a fine soccer team, can do better on the cricket, and so on. And then he said something like “I’m particularly delighted to know that we have at least one serious creative writer in the class, someone who won the school short story medal while still in Class 7, unheard of. Well done. Who is it?”

It was my turn to stand up, and yes, I was gracious in my victory. To be fair to Mr Redden, that was a one-off; he was a good teacher and kept us together and motivated for a fine school year. But his antics on day one help me illustrate the point that Johnson was making.

My parents were very liberal in their approach to children reading at home; every week, we had a man come to the house, a travelling one-man library service for books and magazines. And comics. Lots of comics. In fact our name for the guy was Comic Wallah.



This travelling Comic Wallah was a wonderful invention for us. His name was Mullick, I think his children still run the shop on Free School Street. He was still alive and at the shop when I last went there in the late 1990s. He’d come home every week, with books (ranging from Agatha Christie through Erle Stanley Gardner and Max Brand to even Mills and Boon) and magazines (from Time and Newsweek and Life and The Saturday Evening Post through to Woman and Home and Women’s Weekly and even “glamour” mags. And comics (mainly American, but covering all the genres).

You have to imagine all this coming into a house that had a lot of books already, and quite a few magazines on subscription. And newspapers galore. [In fact, ever since I was 12, we used to have TWO copies of the Statesman delivered home, along with the Amrita Bazar Patrika and the Hindustan Standard; why TWO copies of the Statesman? So that my dad would have a pristine copy of the Times crossword awaiting him, while the other copy was first-come-first-served competed for by me, my brother Anant, cousin Jayashree and aunt Vijju).

So we were brought up to read anything first, just to establish our love of reading. We were left to our own devices to figure out what was good and what was bad, with little hints thrown our way. What kind of hints? Collaborative filters. I watched what my dad read, and followed suit. What my older cousins read. What their friends read. So I moved from Perry Mason to Pynchon, from Max Brand to Mailer, from Christie to Chaucer. My way. I read what my elders read.

And what they recommended. We didn’t have reviews. We didn’t get sold to via advertisements. We didn’t have television. While we did have commercial radio, there were no related ads there either.
Over time, we learnt what we should read and what we shouldn’t.


More important than anything else, we learnt to love reading. We’d read aloud to each other; it was normal for me to walk into a room and hear someone quietly guffawing, if guffaws could be quiet. it was normal for us to “fight” to be next in line to read a book; sometimes this involved bartering favours, sometimes it could even get mildly physical.

That love of reading has stayed with me. With my siblings. With my cousins. And, from what I can see, it has found its way into the next generation. Not by force but by example.

We just loved reading. I remember when I saw a children’s film called Short Circuit sometime in the 1980s, where a robot called “Number 5” turned out to be alive. Now this robot went around everywhere muttering “give me input, give me input”. That’s how it was at home. And we so enjoyed it.


Today, things have changed. Apparently people don’t read as much as they used to. But maybe they do, if we count all the ways people can read today. So let your children read online if that’s what attracts them, let them read comics online, news online, whatever. Just as long as they learn to enjoy reading.

While they learn to enjoy reading, teach them how to read. What not to read. How to spot poor writing. How to spot pornography. How to spot perversion. How to spot brainwashing. How to avoid all of them.

It used to be said “It is better to teach a man to fish rather than to give him fish”.

I think there is a parallel in reading, particularly in reading online. Teach your children how to filter, don’t just impose filters on them.

And all the time, help them learn to enjoy reading.

Eye of the beholder

Take a look at this photo stream. 6EMEIA is a collection of young artists in Sao Paulo, and they’ve been converting mundane objects like storm drains and paving stones into works of art.

Maybe it’s the Calcutta in me, but I love stories such as the one above, where creativity blossoms forth in the midst of adversity, and then manages to thrive despite everything.

Before you ask. This was not a random find…. once every couple of weeks or so I visit The Daily F’log, something I’d come across via StumbleUpon. My thanks to both.

Why do I keep doing this, referring to the process I went through to find something? Because I think it’s important. I find tools like Blog Friends, a Facebook application (albeit not developed by Facebook), truly useful. As we learn more about learning and about teaching, we are going to find ourselves increasingly looking at the “audit trails” of how people learn. As more and more information becomes digital, our capacity to do this increases almost exponentially.

Which reminds me. It will not be long before I write Part 9 of my Facebook and the Enterprise series, looking at the importance of ecosystems. I will be looking more closely at apps like Blog Friends within that post. Then, as signalled earlier, I will close off the series with a post on Privacy; if there is enough interest, I may then write a brief “compendium” post summarising the whole series. Let me know if you’re interested.