Sunday, December 31, 2006

Another Road Trip - Winter 2007

Barely back from the first road trip this winter and am off on the second. This one promises to be more challenging. For one, we intend staying rough. For example, no hotel-staying. It's going to be tent-camping on designated grounds on the way.

The route we are taking is pretty much The Great Mother road with detours on the way. Specifically,
Ann Arbor, Michigan -> Chicago, Illinois -> St. louis, Missouri -> Amarillo, Texas, -> Grand Canyon, Arizona -> San Diego, California -> Big Sur, California -> San Francisco, California

This is a total of about 4200 miles (~6700 km). Am then off to Houston, Texas. And if any more energy left, plan to see some more places. Want to do all this in a fortnight.

Promise to fill you in on the details after i return. Wish you a great 2007!

Thursday, December 28, 2006

Winter 2006 Road Trip - 1

Yes, i know. Long time, no post. Reason : Did a 1979 mile (~3200 km) great road trip over the last five days with some great company. Well, i shouldn't say I did the trip because all I did was pass expert comments on their driving skills while they did the hard work.

Learnt and enjoyed a lot. Will try and get around to doing at least one real post on some thoughts that came from the trip. Till then, three snaps:

1) From one of the cities we visited. Straightforward to guess which city?

2) MIT campus, Cambridge, Massachusetts (26th December,2006)
3) Boston skyline - across river Charles. Photograph taken from next to the MIT buildings.(26th December,2006)

Friday, December 15, 2006

Gently the snow falls...

(please click to enlarge - looks better that way - though, i admit, not a very good snap)

Friday, November 24, 2006

Two Great TED-talk videos

As many of you might know, TED stands for Technology-Entertainment-Design. The TED conference is an annual one held in Monterey, California. As the introduction video says "TED is a preview of heaven".

These are truly inspiring talks from a range of disciplines - science, music, sport etc. Starting from first 1984 session which included the "public unvieling of the Macintosh and the Sony Compact disk", TED does truly continue to inspire.

Below are two statistics' videos. I showed the first five minutes of the following video to my class this week and they liked it. Even the ones who hate statistics liked it :). The talk is by Prof. Hans Rosling of the Karolinska Institute who "brings global data to life". IF YOU ARE GOING TO BE WATCHING THIS, DO SEE IT TILL THE 5:15 MARK AT LEAST.

The second one was thanks to Sandeep who pointed me to it. Another very nice (what else from TED) one. This is by Prof. Peter Donnelley of Oxford who "explores the common mistakes humans make in interpreting statistics, and the devastating impact these errors can have on the outcome of criminal trials".

Other videos are available on the blog. Enjoy!

Wednesday, November 15, 2006

Precision and Accuracy : Different words, Same thing?

A follow-up to a previous post, owing to requests for further clarity. For those who requested, sorry for the delay in posting. I've sacrificed some technical accuracy (no pun) to make the post a little readable. However, it is not a very-quick-read post.

In everyday parlance, the two - Precision and Accuracy - are often used interchangeably. In the field of statistics however, the two terms denote separate ideas.

I. The 'thought-survey' (term thoughtlessly borrowed from its experimental counterpart)

Let's say you undertake a survey where the outcome of interest was 'Average annual income of undergraduate students in the University of Michigan, Ann Arbor'. And you got $2000 as an estimate.

However, like a good statistician you doubt whether this was a 'good' estimate. So you repeat the survey again - using the same survey design. This time you get $3000. Hmmm....quite a variance i.e this estimate is quite different from the earlier one.

So to be really convinced you do the survey again using the same survey design and end up with $1000. Wow! These numbers are really 'fluctuating'. You are now rapidly running out of time and money. So you promise yourself that you'll repeat the survey just one last time. And this time you get an estimate of $2,800. What's happenning? Why are these numbers so different? You've got four estimates : $2000, $3000, $1000, $2800.

You decide to discuss this with your friend, Peter, who was also coincidentally at that time conducting a similar project. Peter says "That's funny. I got the following estimates: $7,500 , $8,000 , $7,200 and $7,700"

Now both of you are confused. We have two issues on hand:
1) Why is it that your estimates are all over the place?
2) Why are your estimates so different from Peter's?

Fear not. Fortune favors the intelligently persevering (and now i'm sounding like Aesop). You stumble upon a previous study that said that the 'Average annual income of undergraduate students in the University of Michigan, Ann Arbor' is $2200 for the current year. The difference between this and Peter's/your study is that this is based on a Census. In other words, based on a complete coverage of all students.

Your numbers are however an estimate of this true number since you have sampled only a part of the student population. But guess what? You find - surprise, surprise - that your estimate on average is equal to the true value. That is, you take an average of your (four) sample estimates and this is equal to the true population mean.

II. Relation with Bias and Variance
1) Your estimate is therefore an Accurate estimate. UNBIASED. But you also note that your estimates are varying ('fluctuate'). They are therefore not very Precise estimates.

2) Peter's estimate were on the other hand NOT ACCURATE. They were on the higher side. There was a BIAS (a positive bias). But to be fair they were PRECISE estimates. They had relatively LOW VARIANCE i.e the estimates were close together.


HIGH Accuracy => LOW Bias
HIGH Precision => LOW Variance
III. Visualizing Accuracy and Precision concepts
The best way to do this is to imagine that you were playing a game of darts. You then have four scenarios depending on whether the Accuracy and Precision is 'Low' or 'High'. See the following diagram (click to enlarge if required). See how your estimates and Peters' were between the two extremes of Ideal vs Sinful (!) estimates. Just for ease of visualization this has been represented in the form of a 2 dimensional picture. With reference to this example, just look along the horizontal line - the dotted line that i've drawn.IV. But do we really conduct repeat surveys
No! In the practical world, we never have the luxury of time or money to conduct repeat surveys to see how good our estimates are. In practice, the survey statistician would first ensure that the design is UNBIASED. Along with ensuring unbiasedness, a survey statistician would ensure that the variance of the estimate was low. In your case, you had an unbiased sample. The reason for high variance was probably low sample size.

In Peter's case, he probably had a 'helpful' friend living in an off-campus condo who offered to introduce Peter to his friends in condos around. Obviously, these were all also those who worked in places offering higher wages (how else a condo :) , which is why his estimates were biased. The sample of course, is not a random sample and is unscientifically done. So it matters little that his estimates were precise since they were quite biased.

Also, please remember that the fact that the average of your four estimates is equal to the population value is just for illustration. The property of unbiasedness (or lack of it) is on average across many, many estimates.

V. Two basic reporting components

To enable the research user to assess precision, we always report the Margin of Error along with the Estimate in research reports/presentations i.e Estimate +/- Margin of Error; which gets expressed as a Confidence Interval. The estimate, of course, is designed to be unbiased ('tending to' the true population value after many runs)

Saturday, November 04, 2006

Pirating films? You Goonda!

Yes. That's right. If you are in the state of Karnataka (in India), you better not burn a CD of some movie and pass it to your friend Rajesh. If you do so you are a goonda. This was the announcement made by the Chief minister of Karnataka.
Keeping his film background in mind, Kumaraswamy announced that the Goonda Act will be imposed very strictly on those who pirate movies in the state.
So, what is a 'goonda'? Loosely, it corresponds to 'goon'. Apparently the word goon came from goonda! So a goonda is like a dreadful fellow that you chance to meet on a lonely dark street who pulls you by the collar and requests you politely to part with your wallet, your chain, laptop and some other sundry things that you might not have any use for.

And guess what - you also have a 'Goonda Act'! I mean, i thought that was really lazy. Couldn't they come up a nicer name like say, "Prevention of unlawful blah-blah act". I would hate to ever get arrested under the goonda act.

Friend: "So, i heard you did time?"
Me: Yeah, that's right.
Friend: What did you get booked under?
Me: What a nice day outside.
Friend: Don't change the topic. Don't tell me you were booked under the 'goonda act'. harhahahrha (roar of laughter)

But now:
Friend: "So, i heard you did time?"
Me: Yeah, that's right.
Friend: What did you get booked under?
Me: Well (ahem, ahem), the 'Prevention of unjustified use of muscle power act'
Friend: Wow. Pretty Cool. Say, my sister wanted to meet up with you one of these days.

Anyhow, this 'Goonda act' is a wide-span act. Covers everything from land grabbing, prostitution rackets, narcotic trade and illegal lotteries. AND here's the news:

Though land grabbing, prostitution rackets, narcotic trade and illegal lotteries are flourishing in the city, the Bangalore police have not invoked the stringent Goonda Act against those indulging in these activities.

Obviously. Narcotics, land grabbing are pretty lame as compared to video piracy.

Police Inspector : What's he here for?
Constable : He forcibly evicted these people from their land and took it over.
Police Inspector : Oh, well, ok. And what the hell were these people doing when their land was being grabbed?
Constable : They were watching a pirated version of Mithun Chakravarti's 'Gunda'
Inspector : What!!! Shameless idiots. Put them behind bars. Forget their land, they don't deserve freedom. And beat them up so they'll never watch any of Mithun's movies anymore in their lifetime.
Constable: And this guy who grabbed land?
Inspector: Aww, let him go...we have to deal with these pirated video guys first.

[Note: Do watch Mithun-da's Gunda if you get a chance. Your life will change, guaranteed. For a flavour, go to the link i've indicated above. Phenomenal movie.]

For a hilarious article on the term Goonda see here.

Of course, the other brilliant announcement was to rename beloved Bangalore to Bengaluru. All this reminds me of what Claude Arpi once wrote :

One day an Indian friend of mine was visiting Israel. His guest asked him: 'How does India work?' My friend was a bit surprised by the question, but before he could answer, his Israeli colleague told him: 'Here we work with our guts.' My friend's answer came at once: "In India, it is the Grace which sustains us".

I quite agree.

P.S - i am not suggesting at all that people do illegal download/distribution of movies but...goonda?

Saturday, October 28, 2006

Saved by Voltaire again...

Let me tell you how. I have been in front of my machine for the last few hours trying to model some data. You know those times when intuition escapes you, you can't see features in the data that you could spot in a second at other times and to top it all the software gives you incomprehensible error messages - basically nothing seems to work. You're stuck. Tired. Frustrated. Eyes hurting. Head aching. But don't want to give up.

...and then you stare outside the window, watch the property maintenance guy with his girlfriend and a big smile on his lips...probabaly headed for a bar. He's got a better life than me - cool carefree life, live for the day, no need of breaking your head on 'generalized estimating equations'. Why the hell am i spending time on this? How is it really going to impact my quality of life? I wish i could trade places with him...

...and then strikes Voltaire. From his "Story of the good Brahmin":
"I wish I had never been born!" the Brahmin remarked.
"Why so?" said I.
"Because," he replied, "I have been studying these forty years, and I find that it has been so much time lost...I believe that I am composed of matter, but I have never been able to satisfy myself what it is that produces thought. I am even ignorant whether my understanding is a simple faculty like that of walking or digesting, or if I think with my head in the same manner as I take hold of a thing with my hands...I talk a great deal, and when I have done speaking I remain confounded and ashamed of what I have said."
The same day I had a conversation with an old woman, his neighbor. I asked her if she had ever been unhappy for not understanding how her soul was made? She did not even comprehend my question. She had not, for the briefest moment in her life, had a thought about these subjects with which the good Brahmin had so tormented himself. She believed in the bottom of her heart in the metamorphoses of Vishnu, and provided she could get some of the sacred water of the Ganges in which to make her ablutions, she thought herself the happiest of women. Struck with the happiness of this poor creature, I returned to my philosopher, whom I thus addressed:
"Are you not ashamed to be thus miserable when, not fifty yards from you, there is an old automaton who thinks of nothing and lives contented?"
"You are right," he replied. "I have said to myself a thousand times that I should be happy if I were but as ignorant as my old neighbor; and yet it is a happiness which I do not desire."
This reply of the Brahmin made a greater impression on me than anything that had passed.
Back to 'generalized estimating equations' with renewed vigour!

One question that i have, though - Is it right to characterize the lady in the story as ignorant? She is happy and that's what matters (to her), isn't it? How does it help being 'knowledgable' but unhappy? I think some part of this debate has commonalities with the Bhakti vs Jnana schools of philosophy. Probably, best to have a synthesis as Sri Ramakrishna Paramahamsa taught.

Saturday, October 21, 2006

Happy Deepavali

May this year be filled with light for all of you. Be Good. Do Good.

I know this comes late but try not to burst those horrendous crackers. Light not bad sound. In the US thankfully you can't even if you wanted to - try bursting a 'Laxmi bomb' or 'Rasi bomb' and next you'll find 500 red crosshair images and choppers above you wanting to take you out like hell.

There's a beautiful temple in Flint, Michigan (called Paschima Kasi!) which i visited today thanks to the initiative by some friends.
Was a nice experience. No crowds - just one gentleman meditating in a corner. The fragrance of camphor and flowers just like back home. Fall colours. Uplifting Vedic chanting - a very helpful, pleasant and learned priest. Was all nice. The Priest invited us for a special Divali puja (worship) that was being organized today but couldn't stay back : had to get back - WORK!

Finally, please do watch this beautiful Deepavali commercial (and this too if you can please)

There are some other very touching and meaningful Petronas commercials there that you might be interested in viewing.

And finally, finally : it is Deepavali not Deepawali (though have tagged this post as both). No big deal but i thought i'll chip in with that. As Sri Chandrasekharendra Sarasvati remarks, the 'w' sound is like when you say 'water'. The 'v' sound is different - as in 'Vani (Sarasvati)'.

Friday, October 13, 2006


Lurking on software help/user fora is an instruction on a lot of things apart from learning the software. Particularly in human behavior.

One really interesting aspect is the way the experts behave. Every forum has its experts - the people who 'own' the forum - baap ka raaj (pop's kingdom). Some of these kings are kind - they lead you step by step even if you are new.

There are others who go: "Go figure, you idiot. Don't come on this forum unless you know the basics" or "How dare you waste our time asking such trivial questions. Don't you have a brain?". And there have been times when i have seen these responses (like this and this!) and have gone "Whoa...Izzat ka falooda (crushed self-esteem)".

One user help list i regularly visit is that of a statistical software called R which i use extensively for my work. R is both a software package and a computing environment AND it's free+open source! - the best brains in the world contribute to this project. It's probably THE standard for statistical computing.

Anyway, all this is beside the point. This post is about a hilarious exchange i saw on the list. BTW, people who participate on this discussion are almost never AFAIK beginners. Actually, most are pretty advanced users who just need some tip here or there or some technical clarification. And then this:

The question
I saw this and went "uh, oh...this guy's had itttttt". I mean, "because my gf. is using it in her university project"? 100 marks for honesty, but 0 for being sensitive. And this is what happened...

The Response
(underlining mine)
This response even made it to the wikipedia entry on RTFM!!!

Also see these two interesting related wiki links : UTFSF and Flaming

Solid, na?

Sunday, October 08, 2006

The Perfect day...

...was today. It was just so completely beautiful outside. 21 degrees celsius. Sunshine. Clear blue sky. Just that little breeze.

It would be a shame to sit at home on a day like this. Yes, a lot of work pending but i couldn't care. i just had to experience this day fully. I wouldn't mind not sleeping for the next two days just to be outside with nature today.

Luckily my pal, Sharath, was a willing accomplice in the ditch-work-and-go-out plan. And canoeing we did. Actually kayaking - picked up a double kayak this time.

Did a two hour trip downstream River Huron (a great river - more about it sometime in the future). Luckily the Argo Livery where we commence is just about a 5 minute drive from our place. Sharath finished his meeting early and we just sped there.

...and Boy, was it gorgeous! Just absorb the fall colours.
What do you say? Brilliant, isn't it? I was just spellbound. And nature conspires to make things easy for you. Just when you feel the sun is beating harshly and you wish there was a little shade, there it comes:

...and just when you feel so pure with nature, every now and then there's a house that springs up along the river like this:

...that arouses a wave of jealousy: "Damn! I wish i had a house like that on the river". You then quickly recover and remind yourself that happiness is not about possessing things. The enlightened ones throughout the ages have told us that the sure path to misery is to expect, to want, to desire, to covet. Why can't i just be happy with what i have? Truly, if i was happy always with whatever i had, that would be TRUE happiness - happiness that is unconditional upon external factors. Mental note as i go along the river: Practice vairagya (non-attachment), non-covetousness.

Slowly, we're now almost completely absorbed into nature. Time to stop rowing. Just let the river carry you. Paddle only just a little so you're on course. Put your feet up. Relax. Inhale deeply.Let the fresh air energize you. Immerse yourself in the surroundings (do i sound like one of those yoga guys on TV?)
No noise. No people yaking away loudly. No blaring film music. No people spitting or puking into the river.

And then, all of a sudden the river opens up to magnificent blueness with just a little green to give it that balance.
Who planned all this? Was this day destined to be so beautiful?

Anyway, this stretch also tells us that we are close to Gallup Park - our destination. A sinking feeling. God, will you please give me another chance sometime in life to experience this kind of a day. When i do not have to be excited/worried about the future, neither relive/regret the past. Just be so completely absorbed in the present that it is eternity.

Sharath and I return the kayak, sip some coffee and spend about 20 minutes just staring ahead of us.One last look at the warm green grass and the river as we head back to our homes.

The exchange of words Sharath and i had, i think summed it all up.

Me : I think this was a day to die for.
Sharath : What are you talking about!? This was a day to totally live for
(, do you think we qualify as Zen monks now?)

A fitting end to a beautiful day - a magnificent sunset. I send a 'Thank you' to the One for the opportunity to experience this day.

Wednesday, October 04, 2006

New Camera + Home snap

Finally got a new camera - about a week now. Given that fall is almost in full form, couldn't wait any longer and miss out on the colours.

The new camera
Not something hi-tech. Nikon 7600. Just a warning for those of you planning to buy a camera:
a) I do find that it fails to take good pictures in low light and indoors - gives 'blurred image' warnings too often.
b) Before buying this camera, i had gone through reviews and had found many complaining of the same. I took a chance though - i was running out of time and had to take a decision fast + was already used to a Nikon and had it's charger etc.
c) Speaking of charger, this is a battery guzzler. So you have to buy a rechargable battery /charger set along with the camera.
d) Time-to-flash (i forget the technical name) is quite long. So i take a snap requiring flash and then i would have to wait quite some time for it to be ready to take another snap requiring the flash.

First snap
Meanwhile, here's the very first picture from the new camera. This is my home's backyard - it's got a nice mini valley that you might just about figure out from the snap. The sunsets are spectacular. The best time to capture them would have been in the summer (when i didn't have the camera!) - it get's pretty cloudy nowadays and rains often.

Friday, September 29, 2006

Mozart says : Mathematics needs Marketing

First of all, thanks to all of you for being patient. The last week was really tough - exarcebated by lack of sleep and food - but enjoyable at the end for the insights i received from my work.

The title of this post is what the 'Mozart of Math' said in an interview yesterday (more on him later in the post). He just received the Fields medal last month.

The Fields medal
Is the Nobel equivalent in Mathematics. "Equivalent" because the Nobel is not given in Mathematics (seriously).

Basically, Nobel hated mathematicians because one of them had an affair with his wife. Well, that is the common masala story, the version you'd hear in a Bombay local train if your co-passengers had the same interest in math as in the stock market. This version has just one small problem : Nobel wasn't married. Rumour faila ne ke pehle at least thoda research kar yaar. Read about the more probable reasons here.

The moolah
Apart from being the 'Nobel of Mathematics', another reason why the Fields medal is highly regarded is because it's not awarded annually but once every four years + you have to be under 40 to get it. (They're so unreasonable, aren't they, these medal-wallahs?).

But get this. A Nobel gets you about $1,000,000. A Fields gets you $13,400. No. i am not missing out any zeros there. Thirteen Thousand Four Hundred Only. Of course, it's more about the prestige. But the sheer gap in prize money probably points to a problem that the title refers to : 'Marketing'.

Now, before i get carried away and get into the 'marketing of math' issue, a little about the great mathematician who's quoted in the title. This is him:

Terrence Tao
Shocked? Baccha dikhta hai na?
(excuse the amount of Hindi used in the post. I don't know why i am doing this.)

Age countdown
Age 31 : Awarded Fields medal (this year)
Age 24 : Prof. at UCLA
Age 21 : PhD. from Princeton
Age 17 : Master's degree, Flinders Univ., Australia
Age 16 : Bachelors degree, " "
Age 12 : Gold medal at the International Math Olympiad (INMO) - youngest to date
Age 10 : Bronze medal at INMO

Called the Mozart of Math, except "he doesn't have Mozart's personality problems". And in the same link, his take on solving problems:
"It's not about being smart or even fast," he said in an interview at UCLA last year. "It's like climbing a cliff; if you're very strong and quick and have a lot of rope, it helps, but you need to devise a good route to get up there."

Doing calculations quickly and knowing a lot of facts are like a rock climber with strength, quickness and good tools; you still need a plan — that's the hard part — and you have to see the bigger picture."
And lest you think his work is an abstract math thing that has no relevance to day-to-day life:
" may have implications for possible new methods of encryption and security of information"
Link for the above quote here. Also see this for some idea on the kind of research he's doing.

Finally, check his university website out. In particular go to this link and do one 'page down' - i found it hilarious. First time i have ever read anything like that!

Reading about geniuses
When i first started reading about these geniuses about 15 years ago, i used to get really depressed. I felt so small when i looked at what all they had done. But thankfully i have somewhat overcome this over the years. I think it's even futile to pit yourself against someone else - higher or lower in talent. The operative word being 'pit'.

The best thing, IMHO, is to draw inspiration from these greats. These are thinkers who just keep pushing the limits even further showing us what the mind is capable of. In fact, to be honest, some of my problems have been solved after reading a Feynman story. It's like my mind says "Compared to the problems these geniuses deal with, my problems are so insignificant" And then just that thought of possiblity gives a breakthrough.

The other side of geniuses
Many (most?) geniuses have been known to have eccentric/troubled personalities. Famous examples being William James Sidin, John Nash.

So, let's say you were given two choices before you were born:
1) To be an extraordinary genius but be 'socially challenged'
2) To have an above-average intellect (enough to make a small mark) but be 'normal' in all other social aspects.

I'd anyday choose option 2). My colleagues/friends tell me that i'd do that because i am not in the position of a genius who's so absorbed in his work and derives so much of joy from it, that it doesn't matter to him. Well, i don't know. Reality is different. Take for example , Grigori Perelman.
Won the Fields medal this year along with Terence Tao. Refused it!

I find him such a fascinating personality for other things like this:
"Friends say evidence of Dr Perelman's innate modesty came when - having finally solved the problem after more than 10 years' work - he simply posted his conclusion on the internet, rather than publishing his explanation in a recognised journal.

"If anybody is interested in my way of solving the problem, it's all there - let them go and read about it," Dr Perelman said. "I have published all my calculations. This is what I can offer the public."
Guess what? He's currrently unemployed living off his mother's pension! In fact, he's apparently so disillusioned that he's given up mathematics! (ala Sidin). Read about it here.

So, is he happy? No way. What happens then to all that 'math for math's sake' and 'derive joy from the process' stuff. The question is what's the point in being a genius if you're not happy. But, i guess one doesn't have a choice. You are just born one. That's your burden. As for me : anyday option 2.

Friday, September 15, 2006

Ann Arbor Flora : Hibiscus or Dish-Antenna?

Well, it was a large Hibiscus no doubt. I tried taking it an angle that would communicate the size well. But didn't bargain for this:

Wednesday, September 13, 2006

Ann Arbor Flora : Playing with the Sun

Might be good to add: The dual colours above are due to the Sunlight. One case, where the Sun gives rise to duality! Philosophically, the Sun stands for Advaita (non-duality) but let me not get into that right now...

Monday, September 11, 2006

The Prez's website. And the PM's?

Dr. Kalam, President of India, one image of statesmanship.

Apparently his website was a great hit on Independence Day. 10 million hits. Link to the news article here.

This is Dr. Kalam's website. The official one. The website speaks. This is from the children's section:
We invite children from India and all across the globe to ask questions on the topic of their choice to Dr.APJ Abdul Kalam, The President of The Republic of India. Selected questions and their answers shall be displayed on this site.
Hey, they also have a contest on the website for kids ('Tinkle contest')! . i thought that was cool!

He also has a personal website here. (The footnote says "promoted by his friends and admirers")

Now, if was cool, what happens when you do

Anyway, here is the official website. Compare to the Prez's.

Thursday, September 07, 2006

Vande Mataram : Salutations to the Motherland

Vande Mataram is India's national song. A song that can move the hardest heart to tears, a truly inspired composition, in the fullest sense of the word.

Today is celebrated as the marking of the 125th year of the song, composed by the Bengali poet Bankim Chandra Chatterjee. Here is the English translation of the song by Sri Aurobindo Ghosh who was a great mystic.
Mother, I salute to thee!
Rich with thy hurrying streams,
bright with orchard gleams,
Cool with thy winds of delight,
Green fields waving Mother of might,
Mother free.
Glory of moonlight dreams,
Over thy branches and lordly streams,
Clad in thy blossoming trees,
Mother, giver of ease
Laughing low and sweet!
Mother I kiss thy feet,
Speaker sweet and low!
Mother, to thee I bow.
Who hath said thou art weak in thy lands
When swords flash out in seventy million hands
And seventy million voices roar
Thy dreadful name from shore to shore?
With many strengths who art mighty and stored,
To thee I call Mother and Lord!
Thou who saves, arise and save!
To her I cry who ever her foe drove
Back from plain and sea
And shook herself free.
Thou art wisdom, thou art law,
Thou art heart, our soul, our breath
Though art love divine, the awe
In our hearts that conquers death.
Thine the strength that nerves the arm,
Thine the beauty, thine the charm.
Every image made divine
In our temples is but thine.
Thou art Durga, Lady and Queen,
With her hands that strike and her
swords of sheen,
Thou art Lakshmi lotus-throned,
And the Muse a hundred-toned,
Pure and perfect without peer,
Mother lend thine ear,
Rich with thy hurrying streams,
Bright with thy orchard gleems,
Dark of hue O candid-fair
In thy soul, with jewelled hair
And thy glorious smile divine,
Loveliest of all earthly lands,
Showering wealth from well-stored hands!
Mother, mother mine!
Mother sweet, I bow to thee,
Mother great and free!

Wednesday, September 06, 2006

Decimal Points and Accuracy...

...are not exactly equivalent.

This is a common misconception. Many clients demand more decimal points to the reported data saying it'll be 'more accurate'. No! This is not an accurate statement to make (pun intended, thank you)

A radio announcer saying that "Today's temperature is going to be 70.83018460288453 degrees F" does not make that estimate accurate!

That 70.83018460288453 may be very far from the truth of say, 60 deg. F, though the measurement is precise.

Here's a quote from 'Common Errors in Statistics' , Good and Hardin, 2003 (Glossary on page 187 ) :
"An accurate estimate is close to the estimated quantity. A precise interval estimate is the narrow one. Precise measurements made with a dozen or more decimal places may still not be accurate"

Monday, September 04, 2006

Bar chart gone bad

This is from a mailer i received. (channel names masked)
The good part
The data is a 13 week average. Averages are always good. And this is a nice quaterly average.

The not-good part

1) This is ONE-DIMENSIONAL data
...but a SECOND DIMENSION is used (unfairly, in my opinion) to give a false sense of extra superiority. In other words, all relativism in the graph should lie on one axis ONLY since there is only a single variable (presumably TVR%) that is being studied.

But what's happenning on the X-axis?
See how the two bars are of different widths? Even right at the base. And the relative widths go on increasing as the X-axis values increase. So there is a correspondence between the X-axis values and the bar widths. But the data is supposed to be one-dimensional!

The lie-factor
Edward Tufte, the person who has probably contributed the most to the science and art of data visualization introduced a term called the lie factor in the 80s (?). It's the ratio of the 'size of graphic' to 'size of data'. if a lie-factor = 1, then the graph is true to the data. But that's not the case here.

It is interesting to calculate an approximate lie-factor here. Now given that the area of the two bars are not of a standard shape we make use of a 'Monte Carlo estimation' process. Simply put:
- We spray the graph with dots or throw darts at it like below (sorry for the bad quality).
- Then just count the number of dots or darts in each bar of the above graph
- In this case, we want to compare areas, so we take a ratio of the number of dots
- Of course, this is an approximate estimation method. The approximation improves with greater dot density

So, what's the lie-factor?
- It turns out that the ratio of number of dots in the Channel A bar to Channel B bar is 5.5
- And the actual data? Judging this from the graph is made difficult since the axis is tilted. But looks like it's 0.89 and 0.8 for channel A and B respectively. This gives us a ratio of 1.11
- So the lie factor here is 5.5 divided by 1.11 = almost 5! (4.95)

In other words, the graph bloats the actual data effect by a factor of 5!

Assuming a one-one equivalence with the average human mind's perception and the lie-factor, a person would assume that Channel A's viewership is 5 times more than Channel B's while it is actually almost the same!

2) No axis label
The reader has to assume that the data is TVR% data and not, say, Reach% data. Or could it be channel share data? All three are metrics expressed in %s but are very different concepts having specific application in media strategy. For me, this graph is saying "Don't worry about what the numbers are. Just focus on the fact that we're number 1". It's almost taking the media literate reader for granted.

3) The axis itself
- Why are the axis non-orthogonal i.e why aren't the X and Y axis are not perpendicular to each other? They should be in this case. Are the axis tilted to highten (falsely) channel A's numerical superiority
- How does one read off the bars? If you draw a straight line parallel to the X-axis as you should, you 'll read it wrong with this tilt.
- What's with the Y-axis on the right. Not that it matters at all actually but just curious since the convention is to have it on the left.

4) Significance
Is the relative advantage in TV ratings even statistically or practically significant to talk about?

5) Scale
Maybe you noticed that when we took the ratio of the actual numbers it came to 1.11 = saying that the numbers are almost the same! But starting the axis values (origin) at about(!) 0.75 rather than zero adds to the perception skew.

Here's what my redone graph looks like
....when i do the rescaling and other changes:
The only decoration i have done is that HUGE greater-than sign. Is that also lying?

Wednesday, August 30, 2006

Lord Ganapati : Part IV - About 21,4 and twin blades

Signifance of the number 21

The Philosophical Context
Ganapati = 'Gana' + 'pati' = group/retinue of followers + lord = Lord of the group.

Which group?

In the literal sense, the group of Shiva's attendents/followers/troops. Thus Ganapati is the lord of Shiva's troops. This meaning follows from various Puranic sources.

However the inner meaning of the term 'Gana' comes when we refer to the Veda. The Atharva Veda specifically associates the number 21 with Him. (as trishapta in verse 1,1,1 )

And this 21 = 5 gross elements/states + 5 subtle existential principles + 5 sense-organs + 5 sensory processes + Prana

Am not breaking up or explaning each of the above sub-groups further since that gets very technical. Suffice to say, that the inner meaning of Gana (group) is really that of all the elements of existence . And Sri Ganapati as lord of all existence is associated strongly with this number. Hence the 21 prostrations before the worshipped diety one for each element of existence.

Note that while the significance of 21 comes from this explanation, it does not restrict us in interpreting 'gana' only in terms of the existential elements as above. Specifically, in the Bhakti (devotional) context, saints have explained 'gana' to mean the group of all that we cherish in life that Lord Ganpati protects. These are not contradicatory explanations.

The ritual context
The significance of 21 comes in the ritual context as well. The ritual code-books ((eg. Yajnavalkya Smriti) tell us that the One VinAyaka has 21 forms (am not giving the names here to keep it short) which are propitiated. In the ritual presribed, two icons - one of VinAyaka and one of Ambika (the Mother Goddess) are consecrated. Then the 21 forms of VinAyaka are invoked as surrounding these icons.

What about the number 4?
Again two streams of explanations:
The ritual explanation comes from the fact that the 21 VinAyakas described above were intermediately spoken of as four before the final declaration that all forms were but forms of the One VinAyaka.

From a philosophical standpoint, the number four represents the four aims (purusharthas) in life - Dharma, Artha, Kama and Moksha which very loosely translated mean Righteousness/Duty, Wealth, Desire and Liberation. Thus worshipping Sri Ganapati as the One who fulfils all the aims in the devotee's life.

And finally the twin-blade worship
no...nothing to do with Gilette...

The question is why do we usually offer 21 pairs of durva grass at a time in worshiping Sri Ganapati (durva-yugma)? The 21 is hopefully clear from the above explanation. But why two at a time?

For this, remember we spoke earlier of the 21 forms of VinAyaka that were propitiated.
What is VinAyaka?
VinAyaka = Vighna + Nayaka

And from the previous post, we saw that Sri Ganpati is both the Obstacle and the Obstacle Remover. Thus offering two blades at a time is to worship both aspects of God.

I find this really fascinating because here you are actually worshipping Obstacles! It encourages a very brave attitude where one welcomes all aspects of life, including obstcales, with the understanding that God gives them to us to grow stronger. And not run away from them. Like what resistance-training is to body muscles, obstacles are to the course of life.

In fact, this is a recurring theme in Hinduism - for eg. on Ugadi, celebrated as the new year in some parts of India - a key feature of the celebration is to have a mixture of jaggery (sweet) and neem leaves (bitter) - the symbolism is obvious.

We just worship Lord Ganapati in the full trust that He gives us what is best for us.

Tuesday, August 29, 2006

Lord Ganapati : Part III - Obstacle remover

Creator or Remover of Obstacles?
Sri Ganapati is most often remembered as the 'Remover of Obstacles', Vighnaharta. But now, here's the curious thing: His name in said to be Vighneshwara, which means 'Lord of Obstacles'!. So we have a situation where He is both the 'Lord of Obstacles' as well as the 'Remover of Obstacles'!

Which is actually how it is meant to be. In Hindu religion, God is the agent responsible for distributing the fruits of our past actions to us. Some of our past actions, being negative in nature rebound on us in the form of unwanted events. Obstacles, for instance.

But as God, He also has the power to respond to the prayers of devotees in REMOVING these obstacles. Thus both Vighneshwara and Vighnaharta are applicable to God, as they should be.

Again, it is important to remember that He does not wilfully create these obstacles. It is we who have created it for oursleves and have to take responsibility for the same. And to correct for them our scriptures give numerous ways. For instance, Charity can counteract any miserliness that we may have exhibted in the past.

But the most powerful form of prayer is a simple and direct appeal to God. Coupled with a sincere attitude to change backed by the will to change. And Ganapati's attraction to the devotee is well known by his name as 'KshipraPrasada' - quick giver of blessings/relief. In fact, out of the 32 forms described in the earlier posts, a specific form called Kshipra Prasada Ganapati exists.

Incidentally, Sri S.K.Ramachandra Rao points out that the Ganesa Gita (1,21) tells us to regard Ganapati as not different from the other Gods - the proper approach is to regard all forms as those coming out of the One God.

Why is Sri Ganapati associated with Destroying Obstacles?
In the previous post, Ajith in his comment asked about the legend that gives Ganapati the status of obstacle remover.

The Brahmanda Purana legend

One legend appears here in the 'Lalitopakhayana' section . This section contains the famous Lalita Sahasranama, the powerful 1000 name litany of the Mother Goddess.
(A pdf version of the English version of the Lalitopakhyana can be downloaded here.)

The story containing the part on Ganapati (Verses 306 to 316 - page 27 of the above pdf) is remarkable. This is about a fight against the demonic forces of Bhanda by the forces of Goddess Lalita.

Bhanda's minister Vishukra inscribed a yantra (jaya vighna yantra) to thwart the forces of the Goddess. The result was that the Devi's forces were overcome with:
1) Fatigue (Alasya)
2) Meanness (krpanata)
3) Helplessness (dainya)
4) Slumber (nidra)
5) Impotence (klaibya)
6) Forgetfulness (vismrti)
7) Carelessness (pramAda)
8) Torpor (tandra)

What i found very interesting was the discussions that ensued in the Devi's army as a result of the yantra's effects. You can see the exact kind of dialogue going on around you, even today! The classic obstacles to our progress!

So these were the discussion points (language mine!):
1) This war is wrong! Why are we even doing this?
2) Tell me, why are we fighting for this Lalita Devi?
3) What the hell! Who is this Lalita devi, anyways? Who has made her our superior?
4) Let's just get together and decide not to fight. What will this Lalita do?
5) I'm tired. Let's just sleep.

Thus speaking amongst themselves they retreated allowing BhandAsura to advance. Noticing the problem in the rank-and-file, Ambika and Dandanatha (the Goddess's commanders(?) ) reported this to the Goddess. On hearing this, She looked at Lord Shiva and smiled.

From this smile flashed Ganapati, elephant faced, inebriated and embraced by Siddhi and Lakshmi. He burst into the camp, searched out the yantra and destroyed it by smashing it into pieces whereupon the Devi's army recovered and advanced. Simultaneously, Ganapati along with His forces attacked BhandAsura and destoyed the enemies forces.

Pleased with this, the Goddess gave Him the boon that he should be worshipped first among Gods. Thus the obstacles were cleared and success achieved by the grace of Ganapati and hence he is known as the 'remover of obstacles'.

The other legend associated with his being called the 'remover of obstacles' is in the VarAha Purana and involves Lord Shiva's boon to him as soon as Ganapati was created.

All in all, it is but appropriate to seek Sri Ganapati's blessings before commencement of any undertaking. If within one's means, it's great if a traditional ritual performed by qualified priests...else what we can always do : shoot a sincere prayer !

Lord Ganapati : Part II - More on the form

We continue from where we left off last time. Today we focus on the form which can be most beneficially utilized during worship, in the process of 'darshana' ('beholding') or meditation.

We use the form below as an aid to description. But as decribed in the previous post, there are many variations. Each form represents a specific aspect of Ganapati. The aspect is identified depending on:
1) How many arms
2) Colour of the form
3) No. of faces
4) Vehicle/Seat
5) How many Shaktis (consort) accompanied with (>=0)

For example, the number of arms of the form below is 10, is red (isn't apparent from the picture because of the fading) , one faced, seated on a rat and accompanied with One Shakti. We may thus identify this form with Vallabha Ganapati.

With consort? Isn't He supposed to be a celibate (brahmachari)?
Yes. In fact, of the 32 forms in the Mudgala Purana, 24 are described without a consort.
There are also regional variations here.
In the south, for most part He is worshipped as a celibate.
In the north, he is commonly worshipped with two consorts - Siddhi and Buddhi. You might have seen this representation in the famous SiddhiVinayak temple in Bombay. Siddhi and Buddhi of course, are Accomplishment and Intelligence which signify the fruits of worshipping Sri Ganapati.
Interestingy with regard to Sri Kartikeya(the elder brother of Sri Ganapati) the situation is reversed. In the north, is worshipped as a bachelor while in the south, He is worshipped with His consort, Valli.
Let's therefore take the above form, starting from the bottom, and focus on each part and see what the inner meaning is.
Note: In the picture above, the trunk is twisted to the right. This is not usual. Icons of Sri Ganapati are usually with the trunk to the left - this will be covered in a later post.

1) Vehicle as rat
I find this one of the most interesting aspect of the form. The rat symbolizes several things simultaneously.
a) The rat represents the mind. Restless, always flitting about here and there in search of something. Just like a small rat can cause havoc so do small thoughts disturb our peace of mind. And just like rats breed fast, these small thoughts often accumulate into one big wave of mental distrurbance.
The large form of Ganapati thus rests on it representing need for mind-control and capacity to bless the devotee with it.

b) Rats burrow into the earth. Impeled by what? Desire. Thus the rat represents kama ( desire). And we saw earlier that Sri Ganapati presides especially over the earth element. Thus deep rooted desires - which we hold as so precious - are eradicated by the grace of Sri Ganapati.

c) Rats thrive in dark environments. Before spiritual awakening, our lives are said to be dark. Spiritual awakening comes with the awakening of spiritual energy in the Muladhara Chakra (the basal chakra) described in the earier post. Thus Sri Ganapati residing on the rat signifies awakening of spiritual consciousness by overcoming the 'darkness'. Also note that darkness is associated with 'Tamas' in Indian philosophy - the negative qualities to be overcome.

2) Feet
No specific symbolism as far as i know but Sri Muthuswami Dikshitar - the saint-musician - describes the Lord's feet as 'As soft as tender shoots' in one of his Krithis (compositions) which is useful in contemplation.

3) Protruding belly
A large capacity to bear the devotees sufferings. In fact, Puranic stories on how Lord Ganapati has an insatiable apetite indicates this. That is, as long as we are sincere, we can be sure that Ganapati will help us out when approached.

3) Serpent as belt
The serpent is the classic symbol of Kundalini shakti (the much misinterpreted concept) which has to be aroused for spiritual awakening. This does not mean that some extraordinrary austerity/yogic practices have to be undertaken for this purpose. 'Simple' things like japa (repeating the name of the Lord), even doing one's duty with a keen awareness and to the possible perfection awakens this energy.

This awakening destroys tamas signified by the rat. In the natural world, of course, the rat is food for serpents i.e awakening detroying ignorance.

4) Trunk holding the pot of jewels (or any other object depending on aspect)

The following statement by Ramana Maharishi will clarify this aspect:
" Through meditation on the forms of God and through repetition of mantras, the mind becomes one-pointed. The mind will always be wandering. Just as when a chain is given to an elephant to hold in its trunk it will go along grasping the chain and nothing else, so also when the mind is occupied with a name or form it will grasp that alone. "
And the trunk holding the pot of jewels means holding i.e cogitation on precious thoughts. Also signifies the reward for our mind-control practices.

5) Broken right tusk
To see the signficance of this, the Brahmavaivarta Purana tells us that once when Sri Parasurama came to see Lord Shiva, he was denied entry by Sri Ganapati, who said His father was not to be disturbed. Then ensued a big fight between the two. Ultimately, Parasurama flung his battle-axe on Sri Ganapati. Now the battle-axe was a gift from Lord Shiva Himself to Sri Parasurama. Out of respect for His father's gift, Sri Ganapati allowed the axe to strike his tusk losing it in the process.
The broken tusk thus upholding Righteousness as well as Sacrifice in the line of duty - after all, he was ready to sacrifice Himself in order to not allow His father to be disturbed!

Another story is about Him breaking the tusk to use it as a stylus to write the Mahabharata. That again signifies sacrifice for public good.

6) Holding the broken right tusk in one hand
The one broken tusk symbolizes experience of the one Reality in the Lord's hands, experience of which is bestowed to the spiritual aspirant.

7) The other tusk is about helping us rooting out our desires, however strong they are

8) Small mouth
Speak less!

8) Large ears
- Listen more!

- Bestows the devotee the capacity to absorb a lot of information.

- The large ears resemble winnowing baskets. A winnowing basket is used to separate dirt from grains. Similarly the large ears signifiy winnowing of information that we receive.
So, the Lord bestows upon the devotee not only capacity to absorb a lot of information, but also ability to sift right from wrong. Illusion from Reality. The transformation of information into true knowledge.

- The elephant's sense of sound is said to be very acute. Sri Ganapati, by the elephant ears signifies an acute thirst for knowledge.

9) Small eyes
He overlooks our genuine mistakes and is ready to always give us a chance to change. Sincerety is what he requires from us. But that does not mean we take Him for granted. But remember that the elephant as such is gentle but if provoked, you've had it man! Especially if His devotee is harmed. Thus a gentle warning to stick to righteousness.

10) The elephant head
This is interesting : One's body-parts/organs are Karmendriyas (organs of action) or Jnanendriyas (organs of knowledge) . For example, in the human being, the head is a Jnanendriya. But in the elephant, the head is both a Karmendriya (the trunk) and a Jnanendriya! The elephant-head thus symbolizes the harmonious coming together of action and knowledge! The large head, of course, also symbolizes intelligence.

11) What He holds in his hands
Depending on the aspect invoked, Sri Ganapati holds various things. I will not go into too much detail here but to give an example. The goad (pasha) held in his hand signifies drawing the devotee towards Him. The battle-axe/Chakra(discus) that he holds in some icons signfies helping us fight the battle of life as well as cutting off of desires.

Deep contemplation or seeing the form of Sri Ganapati concentrating on this symbolism will undoubtedly ensure great spiritual progress.

Hope all this wan't too boring.

Sunday, August 27, 2006

Lord Ganapati : Part I - On the form

Salutations to Lord Ganapati! The favorite form of the Lord for millions of people.

Today - BhAdrapada Shukla Chaturthi i.e the fourth day of the bright half of the lunar month of BhAdrapada - is a day specially sacred and favorable to devotional/meditational practices to the form of the One reality called Ganapati.
Religious ceremonies in India commence today and go on for 10 days.

Starting today over the next few days, will cover lesser known facets/legends/incidents associated with Lord Ganapati. These posts are a combination of what my teachers taught me, some from what i've heard/read and my own thoughts.

The textual references for these posts are some great books for the serious reader :
1) 'Concept of Ganesha' by the Vedic scholar Sri K.N.Somayaji
2) Ganesa Kosha by the great Sri S.K. Ramachandra Rao.
3) There was also a nice book by Chinmaya Mission which i had read many years ago but do not recall the title.

Sri Ganapati's form
The Puranas give many versions on how the form of Ganapati came to be. But mythology apart (not that it is unimportant), the form of the Lord is a concrete visualization of Reality (parabrahman). And this makes sense since the seers had recognized that it is not possible for all to concentrate on a formless Reality.

The beauty of Ganapati's form is that it is what one may call 'multi-layered' - it reveals Itself depending on the spiritual outlook of the aspirant/onlooker.
I. For some religious historians, the form represents it's agrarian root for eg. the large ears are seen to be a representation of winnowing baskets, the rat as vehicle is seen to be representative of control over pests etc.

II. Form as the 5 element representation
For me, the more appealing way to approach the form is from an esoteric viewpoint. That may be due to my traditional leanings but i also feel that is the 'correct' way.

Very few know that the form is actually a representation of the composite of the five elements (Pancha-bhutatma-Ganapati). See drawing below, and note remarkable correspondence to the image of the icon above:
Thus a person medidating on Lord Ganapati sees Him as a manifestation of the entire Universe composed of the five elements. Of course, in time the aspirant goes even beyond the elements.

III. The Earth element and 'Muladhara Chakra'
The reason i've coloured the base of the above diagram red is that that is the traditional colour of the earth element,specially governed by Ganapati. Not only that, red is also the colour of the four petaled 'lotus' representing the basal Muladhara Chakra, one the seven spiritual 'plexuses'. And the presiding diety of the Muladhara Chakra is Lord Ganapati.

That is also one of the reasons Lord Ganapati is worshipped before any other worship/act is commenced. He represents the 'base', the starting point of it all. Every act, if viewed as a spiritual aspiration, must culminate in the realization of non-duality. The grace of Lord Ganapati is required to 'kick-start' this process and destroy obstacles along the way.

Also note that much of the traditional worship of Lord Ganapati is with 'Red' - Red form, Red flowers, Rakta Chandana (red sandal paste). Again, the 'Muladhara' and 'Earth' angle coming through.

There are further esoteric explanations when this line of thought is pursued. But this is best learnt from one's Guru (definitely NOT from cheaply written books) and hence is not covered here in this post. For example, note the connection of Ganapati and the earth element with the Puranic story of Ganapati formed by Mother Parvati(Earth) out of her own body.

IV. Form as the sacred sound 'Aum' (pronounced as 'Om')
Lord Ganapati is Omkara in form. See representation below for a hint of this:
The Omkara form is important since 'Om' itself represents the entire range of sound. I have not found a better explanation of this than by Swami Vivekanada. This is the reason therefore why Lord Ganapati is the presiding diety for writers and poets. Indeed He is the patron diety for all learning.

V. That the spirit of the Form is more important is evident when we see that in the daily orthodox worship, Ganapati is worshipped in a red stone obtained from the Sonabhadra river - and not in any of the forms above.
Moreover, there are numerous forms of the Form. Some texts describe 32 forms , some 16, some 8, some 12 (all multiples of 4). Some also describe 21 forms - the significance of 21 will be described in a later post.

Here it is important to note the work called Sri Tattva Nidhi, commisioned by Sri Krishna-raja-Wodeyar III (1794 - 1869). This work contains 32 coloured illustrations of Lord Ganapati along with the Dhyana Slokas (medidation verses). The Dhyana Slokas adhere to the ones given in Mudgala Purana - a purana centered around Lord Ganapati. Of course, this was at a time when rulers cared about culture.

There is more on Lord Ganapati's form which will be covered in tomorrow's post.