Aftermath of Math

I am preparing a presentation for mathematics teachers. It started out as a demonstration of speed math techniques. While doing research online, I came across many a link that piqued my curiosity about the side-effects of engaging in mathematics. In four short sentences...

Mathematics is an enabler to develop an inquiring and limber mind.
Mathematics is not just about numbers and computation.
Mathematics is a brain development tool.
Mathematics is about all about enriching your life.

What I have always found fascinating about Math is that you can solve a problem using any method you choose and arrive at the same correct answer, provided the method adopted is based on logic and is mathematically sound.

This level of objectivity is very reassuring.

The 'zeal theory of excellence' satisfies the hunger for fairness and due place for hard work in an unjust world. Brian Butterworth, author of The Mathematical Brain, suggests that we are natural born mathematicians.

In Western culture, the most prevalent theory about talent is that it is innate. When someone is outstandingly good at something, we describe them as "gifted", and say they are "naturals". This idea is not so common in other societies, where hard work is seen as the primary reason why some people excel.

According to Butterworth, all the evidence supports the hard work theory. He goes so far as to say that the only "statistically significant" indicator of mathematical excellence is the number of hours put in. This seems to suggest that anyone could be a superb mathematician if they are willing to put in the hours - but the truth is slightly more nuanced. The crucial word here is "willing". Butterworth says that "anybody who is a good mathematician is slightly obsessed with maths - or more slightly obsessed - and they put a lot of hours into thinking about it. So they are unusual in that respect. But they may be no more unusual than anybody who is very good at what they do, because they have to have a certain obsessiveness or otherwise they're not going to be able to put in the hours to get to this level of expertise. This is true of musicians, it's probably true of waiters."

In my mind, there is no better reward than the one you get after hard work. If you have the zeal to work hard, you will excel.

He says that "if, for whatever reason, you start working hard at mathematics when all your classmates don't, then the teacher is going to favour you, so you're going to get external rewards, and you're going to get the internal rewards of being able to do something rather well that your mates aren't so good at, and so you'll start off a virtuous circle of external rewards, internal rewards, you work a bit harder, you get even farther ahead of your classmates, who aren't actually putting in the time. So it wouldn't be surprising that if random people who for some reason select to pursue maths on the whole get rewarded because they are going to be better than their peers.

The concept of external rewards powering internal rewards is not a new concept by any means. New for me is to see it applied to explain the benefits of engaging one's mind in mathematics. Does one need a more compelling argument to trigger the pulses in our brains if the promised land guarantees confidence, superior problem solving, logical reasoning and critical thinking skills?

Math is just the beginning. It's the Aftermath that we, as educators, should be interested in.

With confidence, you have won before you have started. - Marcus Garvey
(courtesy 'Quote of the Day' - a balm for the roving mind)

Curiosity never killed

Curiosity never killed the curious cat. Death did!

After having boned up on a mathematical theorem, a student who was attending geometry courses under the tuition of the famous mathematician Euclid asked the teacher, "Sir, what will I earn by learning all these things?". On hearing this Euclid called his assistant and told him sarcastically to, "give the boy 3 coins, as he wants to make money from what he learns".
The search for knowledge - without looking for profits or immediate returns - is a characteristic of superior animals, and it is in human beings that this is most marked. We could say the extraordinary curiosity of humans makes us a unique species! What motivates man in his curiosity? If at the dawn of mankind curiosity combined with a rapid apprenticeship was a synonym of life (surviving), it is no longer the case today. Nevertheless, man is more inquisitive now than he was in the past. Today newspapers, reviews, radio, television, internet are all unending sources of information flooding into our homes day and night to satisfy our hunger to know things, to learn, to be informed... to such an extent that the supply of information becomes unmanageable and so the gathering of information requires a "creaming off", i.e. the filtering of good and useful information and the separation of the wheat from the chaff.
Some scientists regard curiosity as what motivates our exploration behavior, including playing. I'd like to add that curiosity is a measurement of the "mental tonus", and is an antidote against stereotypes, overdeveloped self-satisfaction, and boredom. Everything can be source of knowledge; facts or things which seem worthless, inefficient, useless, absurd, odd, paradoxical or false may be instructive. Remember that America was discovered by the Europeans because Columbus made a navigational error!
To conclude, do you know who said: "I am neither especially clever, nor especially gifted. I am only very, very curious"? No? The inventor of the theory of the relativity, Albert Einstein, a big kid!

The interesting link

Turtle Can't Hear

It has been a few months since this problem started. All of a sudden, my ears start to feel clogged and my sense of hearing reduces. Sounds appear to be from underwater and muffled. Yesterday, I could not hear my phone ring. So, I decided to make a trip to the doctors and get this checked out.

It has been a few weeks since I noticed this problem. The pet turtle had gotten lethargic and would sit in one place with its eyes closed. Very rarely, it would slowly open its eyes and it seemed as though the eyelids had taken over the eyes. I could sense that it could hardly see. It seemed to be eating fine though. Yesterday morning, I decided to google and find out if the condition of the turtle was something to worry about.

Google: "pet turtle eyes closed"
Results: 1 - 10 of about 16,000 for pet turtle eyes closed. (0.62 seconds)

Nearly all views on the first two pages of results implied that this was a common problem in pet turtles. When a turtle starts closing it's eyes, it is a sign to be taken seriously. Turtles at this stage often progress to respiratory illness, starvation and then death. I decided to move the turtle to tepid water. I watched it become active and open its eyes. I was relieved. I left it in there and decided that I would change the water every hour or so and make sure the turtle stays in lukewarm water. I left to do some errand and came back to find the turtle still. Back to eyes closed position.

I went to the doctor for my ear checkup. The doctor said that because I have been having frequent colds and nasal blockage over several years, whenever my nose gets blocked, my ear drums get pulled into the middle ear to equalize the pressure. Hmm..makes sense? Anyway, I am on medication now. Hopefully, things should improve soon.

Came home to find the turtle in the same position - exactly as I had left it. Now it was starting to worry me. I picked it up. Not a single movement.

That is when I realized that my turtle can't hear no more.

There's Always Gonna Be Another Mountain

Hannah Montana aka Miley Cyrus is not supposed to be for me-kinds. More for the teeny boppers. I refuse to count the years I am past that stage...but before I start hyperventilating..shush.

Back to Hannah Montana. While in conversation with a friend, we were discussing my career or lack of it. I mentioned that I wanted to move on to more challenging opportunities. I love what I do but everyday now seemed like a 'been there done that' kind of day.

Friend: "You are looking for another mountain."
Me: What mountain?
Friend: You should listen to this song that has been playing on all the radio stations. Called "The Climb".

Me and google met (I like to think we are made for each other).

Me: Did you know this is a Hannah Montana song??
Friend: Really? Doesn't sound like her kind of song.
Me: Exactly. This is great. I can totally understand Sheryl Crow singing this. But Hannah Montana? Wow!

Since that day I have been listening to this song and passing it along.

I absolutely love the richness of meaning in the melody. I could frame the lyrics and pin it up on a wall.

Since that day, this has been like an anthem. I never thought of myself in the same mold as a 'climber' - which got me thinking. For me, it has always been more about the journey than the destination. The quest, more than than the achievement. A sudden realization. An Epiphany.

Trust me, I listened to lots of other Miley Cyrus songs. I did not find any that appealed to me the way this song did.

There's always gonna be another mountain
I'm always gonna wanna make it move
Always gonna be a uphill battle
Sometimes I'm gonna have to lose

Ain't about how fast I get there
Ain't about what's waiting on the other side
It's the climb

Cannot seem to get enough of this song - and that is a good thing.

Car-Ma

He was at the intersection, waiting for the light to turn green.
She walked briskly by his car.
He glanced at her. The light turned green. He accelerated and sped off to work.

Fast forward a month.
Same signal, same car.
Expectant man. Same brisk walk. Nonchalant woman.
This time the man looked....not glanced...but looked at the woman. She had a taut body. Long thin legs. Beautiful face.
It was the kind of face that gets more beautiful with every look. He was entranced by her eyes. Yes, it was the eyes that did him in.
They seemed busy - lost in focussed thought.
He followed her with his eyes, in the side view mirror and then in the rear view mirror.

She was now as much a part of him as his morning shave.
His mornings needed her. They were not complete if he did not catch a glimpse of her. He wondered if it was possible she had not noticed him.
How could she not notice him staring at her every morning?
Some mornings when she had a headset on, she would look around but with an unseeing look. Her mind was focussed on the music or the news flowing through the wires.
Other days, her attention was not on the cars lined up at the intersection. She seemed to be fixated on the next step.
She was intriguing. He was mesmerised.

P.S. Thanks to a friend for help with the title.

Ji Chahe

Ji Chahe
(from Raqs-e-Bismil – Dance of the Wounded)
Lyrics: Hazrat Shah Niaz, Baba Zaheen Shah Taji
Composed by: Muzaffar Ali
Singer: Abida Parveen

Ghazal literally means talking to a woman. It means conversing with the beloved. Broadly speaking, Sufism equates God as the Beloved. Sufi poetry has references to common mortals in love with beloved God. In search of God. In search of their beloved.

Ji Chahe is a beautiful ghazal rendered even more beautifully and soulfully by Abida Parveen – the voice of Sufism. The Holi poem that precedes the ghazal is written by Hazrat Shah Niaz. The ghazal is by Baba Zaheen Shah Taji. The Holi poem seems to be in a UP dialect – I am guessing UP since Niaz hails from UP.

Dance of the Wounded – wounded in search for their beloved? Being wounded can’t be all that bad if one can dance in ecstasy.

"Horih hoye rahi hai
Ahmad jiyo ke dwar

Hazrat Ali ka raang bano hai
Hasan Husain khilar

Aiyso hori ke dhum machi hai
chahun or pari hai pukaa

Aiyso anokho chatur khiladi
raang dinyon sansar

Niaz pyara bhar bhar chidke
ek hi raang sahas pichkar"
- Hazrat Shah Niaz

This poem can be interpreted as the festival Holi being played in the courtyard of Ahmed’s house. Ahmed is another name for Mohammed. Hazrat Ali is a sufi preacher/ possibly, a figure of some prominence. Hassan and Hussein are grandsons of Prophet Mohammed. So this couplet can be interpreted as: Hasan's and Husein's antics/play have colored Hazrat Ali's devotion/sufism. Hazrat Shah has included his signature, "Niaz", in the final couplet – his takhallus. So Niaz pyara is one who is dear to Niaz, in other words - God. God has filled his pichkari with color – the color of devotion and with this he is coloring the world in abandon.

Ji chahe to sheesha ban ja, ji chahe paimana ban ja
Sheesha paimana kya banna, mai ban ja maikhana ban ja..
If you wish, become the glass, or the chalice
But why choose those when you can become the wine and the tavern

Mai ban kar, maikhana ban kar masti ka afsana ban ja
Masti ka afsana bankar hasti se begaana ban ja
By becoming the wine and the tavern, become the tale of intoxication
By becoming the tale of intoxication, become a stranger to life
(interpretation: lose yourself in the lust of devotion)

Hasti se bagaana hona masti ka afsana banna
Is hone se is banne se achha hai deewana ban ja
Becoming a tale, becoming a stranger to being,
Better than these, however, is to become a madman.
(interpretation: become madly in love with God)

Deewana ban jane se deewana hona achha hai
deewana hone se achha, khak e dar e jaanana ban ja
Better than becoming a madman is to be a madman
Better than being a madman is to become dust at the door of a beloved

Khak e dar e jaanana kya hai, ahle dil ki annkh ka surma
Shama ke dil ki thandak ban ja, noor e dil e parwana ban ja
What is dust, but kohl in the eyes of the people of the heart
Become the coolness at the heart of a candle, become the light at the heart of a moth
(interpretation: illuminate the heart of the seeker of God)

Seekh Zaheen ke dil se jalna, kahe ko har shamma par jalna
Apni aag mein khud jal jaye, tu aisa parwana ban ja
Learn, Zaheen (Intelligent One - takhallus) to burn from the heart,
Why burn for every flame.
Become that moth that burns in its own fire
(interpretation: burn in your own internal flame, be directed by your inner self. Do not be disturbed by the worries around you)

P.S. I wish to acknowledge 'carvaka' for starting the dance.

You can listen to the ghazal here.

Ghazal = Poetry set to Music

I love a good ghazal.
What qualities make a ghazal good?
Soul dripping lyrics, strong enough to drive your thoughts to feelings undiscovered.
Music with the ability to meld the lyrics to your mind.
In my opinion, ghazals are the Blues of India. So, a ghazal has to sound great at night. Me, with my eyes closed, listening. Absorbing the words floating in the music.

Lyrics are the soul of a ghazal. I have been translating ghazals over the years. I have an affinity for Bahadur Shah Zafar ghazals. I will take the opportunity this blog provides to post them here.

“The translation is not of comparable literary value as the original ghazal, and serves the mere purpose of providing those, who find Urdu an alien tongue, a coarse outline of the poet's creation.” - found on the internet

I strongly believe in this. Native bengali speakers who have read Tagore will aver that the English translations do not hold a candle to the original Bengali versions. I have read a few Tagore poems in English and I found them to be sublime. So I can not even imagine the feelings that the original evokes in people who can understand.

Translating a ghazal helps me absorb the ghazal into my conscience. I am not a Urdu scholar. I take the help of online urdu dictionaries and the quest for a meaning of a Urdu word has taken me all over the net. It feels like a treasure hunt - to decipher the meaning, to wonder what the poet means and hoping you are getting it correct. Not for an audience, but for my own understanding. For me, to feel the real sentiments in the poem.

Power of the Mind

“Whatever you hold in your mind will tend to occur in your life.
If you continue to believe as you have always believed, you will continue to act as you have always acted.
If you continue to act as you have always acted, you will continue to get what you have always gotten.
If you want different results in your life or your work, all you have to do is change your mind.”

- Anonymous

Tomatoes to Tomato Rice

Bear with me, while I share the history of today’s dinner.

Once upon a time, ... :D just kidding!!

All I had in the fridge, freezer and pantry by way of veggies were tomatoes, onions, green chilies and coriander. And curry leaves from the garden. So after several trips to the fridge hoping some veggies would have magically materialized (!) without my having to make a trip to the grocery store, I decided to stop scrounging in the kitchen and start scrounging in the internet for a recipe that would meet my meager requirements.

Considering what I had to work with, the end product, at the risk of sounding like a gloat, turned out quite well :)

Well, suffice it to say, I was saved from a trip to the grocery store today. Tomorrow, as the Scarlett of O'Hara fame would say, is another day.

If you get a chance try the recipe out, drop me a line.

Thanks to Shriya for making dinner possible today.

TOMATO RICE

A little tweaking here and there.

• Omitted ginger
• This recipe also calls for cooked rice. Preferably basmati rice, I would think. I used regular rice and cooked it so the grains are separate.
• For 1.5 cups of cooked rice, I used 4 tomatoes. The quantity of the rest of the ingredients is about the same.
• I did not boil or peel the tomatoes. I just chopped them into cubes and added it to the onions and seasonings. Added the ground masala, some water and let it stew till the tomatoes broke down.
• I added ghee (a little bit) to the rice before mixing with the tomato gravy.

Nostalgia trip, through the waves

When I turned the online Hindi radio to the oldies channel, rest assured, I did not know I was setting myself up for a trip down nostalgia lane.

At that moment I was not thinking about any trip. All I wanted was some background music while I cooked in the kitchen. I was going in and out of the fridge, pantry and freezer, trying to figure out what I could possibly scrounge up for dinner when all I had were tomatoes, onions, potatoes and a variety of dried legumes and pulses. Maybe I was looking for some inspiration in the music! Anyway, that is the story of my life - more about that later.

As the scrounging was happening, Asha, Rafi, Lata and Kishore were singing to me.

saare zamaane se, mausam suhane se, is dil deewane se, veerani si chaayi, aap aaye bahaar aayi

hai apna dil to awaara, na jaane kispe aayega

yeh shaam ki tanhaiyan, aise me tera gham

ude jab jab zulfein teri, ude jab jab zulfein teri

I felt a jerk in my mind and instantaneously, I was taken to the streets of Delhi. I started thinking about these songs playing on our radio at home. On that one channel on TV, good ole Doordarshan, and the one and only song program, good ole Chitrahaar.

Sitting in the living room and watching the songs play on TV.

Listening to the songs playing on Vividh Bharati.

The balcony with the pigeons.

Taking the lift down and walking to the bus stop, with my sisters, at 7 in the morning and waiting for the school bus. Waving to my parents before I went out of view on my way to the bus stop. Always finding one of them there, waving back.

Wearing white uniform on Saturdays.

Coming home after a long day at school. Drinking a glass of cold milk.

The kitchen. My mother making rotis for dinner.

I felt an amazing sense of nostalgia and wanted to go back to the pure, simple days of childhood. One song took me back years. It wasn’t about that particular song.

It was the realization that I may never know what might trigger a response that will take me back decades. I do not know now and I will not know ten years from now.

aaj purani raahon se, koi mujhe aawaz na de

dard me doobe geet na de, gham ka sisakta saaz na de

Sadiyaah

Origin: Arabic

Meaning: Blessed. Fortunate. Lucky.

"It is not doing the thing we like to do, but liking the thing we have to do, that makes life blessed." - Johann Wolfgang von Goethe

We feel blessed. We are with good things. We are the good things.
We have things to do and the time to do it in.
All we wish for is humility of soul to accept the blessings.
All we wish for is strength of purpose to pass the blessings on to the ones who matter.

Carrying all with us.
Standing in the Terrain of the Blessed.
We. are. Sadiyaah.