# Finding your Roots – The Complex Way

Steven Strogatz continues his series on “math, from basic to baffling” with his latest article talking about complex numbers. Very interesting, especially the fractal representation of multiple roots of a polynomial. Check out the article here.

Excerpt:

Better yet, a grand statement called The Fundamental Theorem of Algebra says that the roots of any polynomial are always complex numbers.  In that sense they’re the end of the quest, the holy grail.  They are the culmination of the journey that began with 1.

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# Engineering and Research

While reading this post and the letter written there by Prof. Abinandan (whose blog is highly recommended), I was left to wonder about the state of research in my engineering college.

Back then I had just stepped out of school and, admittedly, didn’t know much about college or engineering. Therefore, I was in for a surprise either way. Barring a few exceptional ones, most professors in engineering were keen on focusing on the examination requirements. Engineering never really got taught as a bunch of great concepts. It was taught as a bunch of highly probable questions for which you needed to know the answers. It is little wonder then that “less than 25 percent of our engineering graduates (and less than 15 percent overall) are deemed employable” as Prof. Abinandan puts it.

Except for a very few countable occasions, I do not recall any of the faculty talking about anything outside the book, or anything that they were trying to work on. Most talk was usually centered around the ‘curriculum’. I personally feel that most of my engineering knowledge was made ‘employable’ once I was out of college and started working. If any of you engineers out there feel otherwise, do let me know.

Stepping into a business school a few years later led to another interesting shift in perspective. Here, there was a concentrated effort on making research a part of the faculty’s repertoire. We had professors who were working on various fields of business, economics and finance and who would freely discuss their studies with us, including seek opinions. For someone who was deeply entrenched in the conventional exam-ends-all mode of studying, I found it rather refreshing. However, for the very same reason of having a conventional mode of education, I found it difficult to contribute and further the new and reformative discussions that would happen in class.

If research is made a mandatory part of all educational institutions, I think it would do wonders to our faculty by keeping them refreshed and recharged and also by giving themselves a chance to see something new everyday. This would have a spillover effect of course on the students and lead to increased collective participation in the topics being discussed.

Imagine the quantum of new work that would emerge by virtue of our professors sitting down and researching on stuff rather than just correcting answer papers, as they are currently asked to do.

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# Copy Cat

Once in a while when summer is in full bloom, a lot of new things appear around you. On a Sunday warm afternoon, I walk out into my balcony with a cup of tea in one hand and a current affairs magazine in the other.

I don’t really read current affairs in these magazines even though I start with the idea initially. But within about 5 minutes I find myself on the Bollywood gossip pages and before I know it I am done with the magazine. Now, its not that the Bollywood gossip really interests me. It doesn’t. But I can’t really do all that heavy reading about current affairs and Bollywood gossip makes for easy reading, especially the pictures.

So, while I am finishing my last minute scan of the magazine, I hear voices of kids on the street fighting over something. I flip the last page of the magazine, glance at Katrina drinking a mango drink, pick up my cup of tea and lean on the railings of the balcony to see what the fuss is all about. I see 4 little kids, all neatly dressed in bright summery colours holding badminton racquets. The racquets are as big, if not bigger, as the kids themselves resulting in they becoming unweildy in those tiny hands. The fuss is over who should play next and whether the current player was ‘out’ or not. There is such a thing as an ‘out’ in street badminton which refers to a player making way for another due to not having struck the shuttle. The kids speak fluent English at an age when perhaps I wasn’t speaking even my native language coherently. I suppose this is what the information age is all about.

The kids then decide to stop playing badminton and instead announce loudly that they shall play “Colour Colour”. This announcement is followed by wide flourishes in the air with the racquets and the two girls in the group do a little bit of a hop and a skip in glee. I didn’t know what “Colour Colour” was all about, so I stayed on at the balcony overlooking this plan.

One of the boys, dressed in dark maroon shorts, a chequered tiny half-sleeve shirt and a colourful Mickey Mouse adorned watch (at least it looked like Mickey Mouse to me), moved away from the group, looked around, closed his eyes and said “Ok, ready.”

One of the girls screams out “Green”. And the boy shakes his head and says “No”

“Blue”
“No”

Red”
“No”

“Pink”
“No”

“Orange”
“No”

A little hop and a skip by one of the girls and then the guessing resumes.

“White”
“Yeah”, the kid smiles and feels sheepishly disappointed.

So that was what “Colour Colour” was all about. The other party had to guess what colour this boy had in his mind. While to you and me it might seem that it is so easy to fake by just changing the colour in your mind all the time, it wasn’t quite the case for these kids. They were honest in admitting what colour they had in their minds. Nice and simple. Perhaps just how life should be.

A couple of rounds into this game and now it is the little hopping girl’s turn. She thinks for a few seconds and says the customary “Ok. Ready”. The other 3 guess perhaps at least 20 colours between them but to no avail. This one is a tough one to crack and now even I start thinking of all the colours that I know of.

The 3 are now tired of guessing and they just don’t know any more colours. So they ask the girl to reveal what is the colour in her mind.
To this, she says, “Transparent” and starts doing her hopping and skipping bit in a victorious manner. The kids were not quite sure what to make of it and the little boy attempted to start an argument but stopped soon after the others readily agreed to this “colour”.

Transparent! I couldn’t help but smile. Technically this might not be right but I don’t really care. I was amazed at the amount of intelligence that these kids had at such a young age. After a few rounds of this game, they just sit down on the side of the street and start chatting in general.

The hopping and skipping girl overhears someone call her a copy cat. And she raises her badminton racquet in a gesture asking the others to keep quiet.
And then she says, “Do you know why there is a word called copy cat?”
The others just shrug, with the little boy dismissing the question by looking away from the group.

The little girl goes on to explain – “See, a cat does meow
“Now, any other cat also always does meow and nothing else. So, all cats say meow. Therefore every cat is copying each other. That is why the word copy cat.”

The rest of the kids, except the little boy, acknowledge this sudden enlightenment with a joint “Yeah, you are right”.
The boy stands up, holding the badminton racquet in one hand, and says “What ok? A dog does bow-bow and every other dog also does bow-bow. Why is it not copy dog then?”

The other 3 kids submerged his question by shouting at him and saying he doesn’t know anything. The boy just turned around and started walking up the street, dragging the racquet along with him. The little girl did a hop and a skip and the other 2 kids started doing the same.

I was done with my tea and turned around, picked up the magazine from the balcony floor and went right back inside. The things I had just overheard were far more interesting than reading the current affairs magazine, which I promptly flung on to the corner table. And then suddenly,without any warning, a feeling of being quite old in this world came over me. This world which was teeming with bright ideas and brighter questions. There was a time in my youth and early professional life when a few veterans had to make way for youthful employees like me. And it dawned on me on that Sunday afternoon that not too far from now, there would be a time when I shall have to move over and make way for something more fresh and more inquizitive. Heck, I am still on the better side of 30, managing to cling on, but I do know deep inside that the inevitable will catch up soon. The kids outside return, start playing something and then get into an argument. That brings the smile back on my face for no apparent reason. Perhaps the inevitable is not to be feared or protested against. Perhaps.

###### April 1, 2008 @ 11:50 pm

Today early morning (which is close to 7 am), I open the main door to pick up the morning newspaper. As I bend to pick up the strewn pages of the two papers, a horde of men enter my street.

I pick up the paper and look at these people. I am sure it was quite a sight for them to see this person standing there in pajamas and t-shirt, hair dishevelled and holding a bunch of crumpled newspaper pages.
There were roughly around 20 of them, all wearing different colours and hence not looking like a team. However, there was a sense of hurriedness about them which made me look at them. There was hardly anyone up and about on the street. Seeing me, their eyes lit up and they came towards my gate.

“Good. I want to inform you that this area is now falling under the ABC constituency”, he said in pure and impeccable English. After that, he added a smile.

I had just woken up so I tried to register what it meant for me.

“Okay, nice to know sir”, I offered.

“So, welcome to this constituency”, he held out his hand over my gate and continued to smile. I shook his hand gratefully and said I am glad to be welcomed.

All the other people smiled with some sort of satisfaction, as though the day’s work was done.

I turned back with the newspapers in my hand to go back inside. One of the guys in that crowd lingered at my gate and called me back with a whisper.

“He is also the candidate for our party”, he spoke slowly, tilting his head towards the person who spoke to me and was now walking away.

“Oh, nice”, I again offered.

“His name is Mr. DEF and of course you know our party”, he smiled and pointed at the banner he was carrying.

I smiled and returned inside. Some of the people were clapping as the party leader returned into the group of people standing in the middle of the street. They turned around and went back in the direction from where they came. It was as though they wanted to talk about the new leader to someone, anyone.

******

The Mrs. and I stop by at a restaurant to have breakfast on our way to work. We have our fare of dosas and coffee and I suddenly notice an elderly gentleman sitting opposite our table. I instantly recognize that face, and walk up to him.

“Sir”, I interrupt his conversation and tell him my name.

“I am from your school sir, passed out more than 10 years ago from there”, I tell to my former principal.

He looks up, smiles at me and as soon as he heard I was an alumnus, holds my hand and leads me to sit next to him.

“I am an old man now and my memory is no longer very good. But I am very pleased to meet you”

“Thank you sir. It has been more than a decade since I passed from the school”, I continued.

“Tell me. After 10 years, are you a happy man?”, he asked with the customary smile with which he greeted anyone who approached him back then.

“Yes sir”, I tell him. He remembered my father’s name. I tell him he is no more.

“Very sorry to hear that. Are you married?”

“Yes sir”, and I introduce my wife to him. I found adding the ‘sir’ bit a lot more appropriate and reverent than the sir I had used earlier in the morning.

“Good. It was very nice meeting you”, the old familiar smile on his face said.

We return back to our table and head off to our respective work places. What I take away with me is a feeling of having met someone who had significantly impacted my life, maybe in an indirect way, and I had an air of gratefulness around me.

I had used “sir” to address two different kind of people – one was a political leader who had the potential to influence my life and the other was a teacher who had already left his impact on me. The word used was the same, but the feelings were entirely different.

###### March 25, 2008 @ 10:28 pm

Bangalore now boasts of numerous radio channels. But there is little or almost no difference between their offerings. All of them play the same songs, one after the other. They also play the same ads, one after the other.

After getting bored with all these channels, we have now become fans of All India Radio’s ancient but relevant broadcasting. Their series of programs under the name Vividhbharati are a treat to listen to.

One of the programs broadcast on AIR (on 102.9 FM) is called Manthan. This program is aired at 7:30 pm daily and is a show which tries to get people’s views on various important issues facing our society today. Yesterday’s show focused on whether the Indian education system helps in identifying talent in students, or whether it churns out minds which can only memorize concepts but cannot apply them.

All the speakers in this talk were unanimous in their decision that our education system does not help in identifying and nurturing different talents in our students. Some blamed the examination structure which emphasizes rote learning. Others, especially some students, were of the opinion that the syllabus was too overwhelming and hence a lot of areas got diluted.

I have of course been a part of this education system and my friends who read this blog will rub their hands in glee at the opportunity to take digs at my way of dealing with this system. I have also been a part of a slightly different education system while doing my MBA, which proclaimed a case-study based approach.

Firstly, the so called rote-learning method employed by our schools and colleges isn’t really all that bad. How else do you explain the great number of Indian academicians and technical professionals being churned out year after year, working successfully in different sectors and achieving decent accolades. If something had to be intrinsically wrong with our education system, I don’t think we would have been able to carry it off this far. Yes, I agree that the examination system is a bit flawed and it defeats the purpose of learning. I think it would be better to do away with the annual or semi-annual examination pattern. Instead, there should be small and easy ways to evaluate every learning immediately after the teaching is done to ensure that the impact is long lasting. Do not ask students to sit on their books at the end of the year. Ask them to learn a concept, apply it and get themselves evaluated. More importantly, there should be a feedback mechanism after the exam/evaluation. This goes a long way than just marks written in bold red. If after every evaluation the student gets to know what he/she could have done better, then I think the real purpose of learning would be achieved to a great extent.

When I moved into my MBA course, I was surprised to see that most students continued to employ the rote-learning mechanism in their way of dealing with academics. The case-study approach looked great in concept and in brochures, but I found many people indulging in “mugging” (word used in common parlance for ‘learning by memorizing’). I think this has to do more with the thinking that we are embedded with during our schooling – hard work and learning by heart is the best way to top the class. My fellow students, many of them coming back to school after 5-6 years of industry experience, continued to fall back on the method that did wonders to them in school. Did it work? I don’t know, primarily because there is no way to measure the success of different learning methods. In an MBA course, the main parameter of measurement is the job you obtain upon graduation and the money that it brings with it. With that parameter, I can safely say that everyone was successful.

I would like to admit here that I learnt a great deal about computer science engineering in my last workplace and in fact was then able to make sense of many of my textbooks which I had successfully managed to “learn” for examination purposes. I am, therefore, a firm believer of the concept that it is ultimately your work life that teaches you how to make the best skyscraper with the couple of burnt bricks that you managed to steal from your school. But yes, you do need those couple of burnt bricks to make your way up.

Filed under Education, Thoughts · 1 Comment »

###### January 5, 2007 @ 9:28 am

Atanu Dey writes a good article on the need to liberalize Indian education at The Indian Economy Blog.

Although I do advocate liberalization but my thought is that it should be done only under the right circumstances under a favourable environment which shall enable an open market to nurture and thrive.

Mr. Dey writes:

My prescription is simple. Allow free entry into the education business. Give absolute freedom to schools and universities to charge what they wish, to hire who they wish, to pay what they wish, and to admit who they wish. By allowing free entry in the education business, there will be no competition for the market. There will be competition in the market. Prices will reflect true costs and quality will improve.

One hears the argument that if you allow free entry, would not all sorts of shady fly-by-night operators open up schools and bilk the general public? Let’s paraphrase that argument a bit. If you allow anyone to open a bakery, would not people who have no expertise in baking open up shop and sell garbage to the general public and make tons of money? Now that is a stupid argument, is it not? After all, unless the general public is totally brain-dead, the bakeries with crappy bread will go out of business because given free entry, there will be other bakeries. It is only when the government hands out limited number of licenses for bakeries that the people don’t have any choice but to take what they can get from government licensed bakeries.

In case of the current education status of our country, a majority of the population is not literate (by literate I am referring to have completed atleast 10 years of formal school education). In such a scenario, you have a significant population that is not aware of the dealings of the business world. This population cannot differentiate between what is good and what is not in the open market primarily because they do not have the ability to seek information and process it.

The government has to chip-in to ensure that these people, who are illiterate by definition of the word, are not taken for a ride by the fly-by-night “educational” institutions that will enter the market when it is opened up.
The analogy used by Mr. Dey is not quite appropriate for two reasons:
a) A bakery can be judged good or bad based on a decision making ability that does not require formal education – An illiterate man and a scholar can equally conclude which is a good bakery and which is not. That ability to decide does not require any expertise. However, in case of a school, the common man does not have the ability to decide its worth. A common man does not have the means of obtaining knowledge about various schools and then coming to a conclusion.

b) Switching costs are not high in case of a bakery. A buyer can easily buy something from another bakery down the street. In case of education, this is difficult. You make significant investment of time, effort and money to get your kid to a school. One cannot afford to have all that go waste when the supposed school shuts shop.

Hence, liberalization of education in India is definitely not an attractive idea, atleast for the near future. We first need to have our major chunk of people educated. Empower them so that they can take decisions. Only way this can be done and should be done is for the government to provide the support to people by ensuring that only credible educational institutions put up their flags in the country. I accept that the government is not doing a great job on this front – but that is a separate implementation issue. The solution to that lies in better governance and not in liberalizing the market.

When you look at it, it is like a tight circle – Government control is not needed and markets need to be opened up. But to open up the markets you need the government to have educated the people concerned. For this you need government control.

One suggestion that could be considered is the liberalization of the higher education sector – Graduate and Post graduate program providing institutions should be allowed to compete in an open market. There is an implicit assumption that students reaching a graduate or post-graduate level have the acumen and knowledge to decide on which institutions to opt for.
The government ofcourse should have a legal recourse well-defined for the students to ensure that they do not lose out on any front in case any shoddy educational institution drives away with the moolah.

I agree that the government should not be in the business of running schools – but at this moment in time, we do not have a choice. Right now, we need the government to regulate our schools. Atleast for some time in the near future.