Aloha from Hawaii

I am here in Hawaii this week for the IEEE plenary. The view from the Hilton in Waikoloa village is pretty enthralling…

The best love liners!

For me, there has never been a second thought on what the best ever love poem and the poet are. It is the one and only Elizabeth Browning and her beautiful poem How do I love thee (See below. A beautiful reading by Helen Mirren is here in youtube).The Browning couple stands tall when it comes to some of the all time toppings in literary romantic poems. I remember my wife (then my fiancee) sharing a piece of Hindu Sunday literary supplement which had this poem. I have the sonnet etched back in my mind, even now!

How do I love thee? Let me count the ways.
I love thee to the depth and breadth and height
My soul can reach, when feeling out of sight
For the ends of Being and ideal Grace.
I love thee to the level of everyday’s
Most quiet need, by sun and candle-light.
I love thee freely, as men strive for Right;
I love thee purely, as they turn from Praise.
I love thee with a passion put to use
In my old griefs, and with my childhood’s faith.
I love thee with a love I seemed to lose
With my lost saints, — I love thee with the breath,
Smiles, tears, of all my life! — and, if God choose,
I shall but love thee better after death.

Ok, why did this pop up now? Well, in UK, apparently there was an opinion poll on the best one liner; the love one liner that is. Mind you, it is not the full fledged poem, or for that matter a full sonnet or stanza itself, just a one linear. Here are the 10 most popular according to the survey. Just ahead of the Valentines day, a good time pass! Happy reading and Happy Valentines day folks!

1. ‘ Whatever our souls are made of, his and mine are the same’ – Emily Bronte
2. ‘If you live to be a hundred, I want to live to be a hundred minus one day so I never have to live without you’ – A A Milne
3. ‘But soft! What light through yonder window breaks? It is the east and Juliet is the sun’ – Shakespeare ‘Romeo and Juliet’
4. He was my North, my South, my East and West, My working week and my Sunday rest, My noon, my midnight, my talk, my song; I thought that love would last forever: I was wrong’ – W.H. Auden
5. ‘You know you’re in love when you don’t want to fall asleep because reality is finally better than your dreams’ – Dr. Seuss
6. ‘ When you fall in love, it is a temporary madness. It erupts like an earthquake, and then it subsides. And when it subsides, you have to make a decision. You have to work out whether your roots are become so entwined together that it is inconceivable that you should ever part’ – ‘Captain Corelli’s Mandolin’
7. ‘Grow old along with me! The best is yet to be’ – Robert Browning
8. For you see, each day I love you more. Today more than yesterday and less than tomorrow’ – Rosemonde Gerard
9. ‘But to see her was to love her, love but her, and love her forever’ – Robert Burns
10. ‘I hope before long to press you in my arms and shall shower on you a million burning kisses as under the Equator’ – Napoleon Bonaparte’s 1796 dispatch to wife Josephine.

Stupensil Tangled

Over the weekend, I watched the new animation movie from Walt Disney. It is the fairy tale story of Stuepnsil. A really nice movie. Quite different from many of the animation movies of the past.

Oral history:Robert Fano

On the Christmas day, out of blue I bumped across an old archive of Robert Fanos’s interview (oral history). Beautiful one.

Trees on Google earth

After all, there are trees on earth’s terrain. Why not on Google earth? Google just don’t delay it any further. Now we can see trees with Google earth 6. Amazing view of SFO, right here. As they say, it is here as it is there.  Now we truly have the world in front of our eyes.  The beautiful 3D world is now ready.

Ig Nobel Prize

Via Lance’s blog, I came across this hilarious prize known as Ig Nobel prize. The term “Ig” stands for “Ignoble”! The prize is apparently given to something which may appear to be funny, but has some serious reasoning behind. In other words, these are peculiar awards given to something  which”‘first make people laugh, and then make them think”. Quite amazing huh?

I am yet to explore a lot on this. Lance listed one very interesting one. I find it extremely noteworthy! Robert Faid of Greenville, South Carolina, farsighted and faithful seer of statistics, got the Ig Nobel prize for calculating the exact odds (710,609,175,188,282,000 to 1) that Mikhail Gorbachev is the Antichrist.I wonder how he arrived at this magical number! Didn’t Faid know how to play a game in the stock market then?

Wikipedia has an interesting entry on this topic. Would you believe, the young Russian physicist Andre Konstantinovich Geim who just won this years Physics Nobel for his work on graphene had also won the Ig Nobel in 2000! Quite amazing.

http://improbable.com/ig/

Just a matter of time and space

Stumbled upon this site http://www.bordalierinstitute.com/target1.html

A cool presentation I liked there is about the evolution of the universe tagged against the timeline since the big bang. It goes to show how fast things moved in the beginning; yet how slowly it took to get into this fabulous shape (whatever is known as of today) that we live in. No doubt this is a continual process of marvel.

The bing bang theory season-3

Even though, the season-3 of the hilarious TV episode is being broadcasted for sometime. I  didn’t have had a chance to view  any of them on TV yet, but the other day, I checked youtube for some snippets. May be because of the two seasons of serials, I didn’t see anything impressive in the new ones. Not bad by any means, but it all started sounding a bit too repetitive now.  I have been an ardent fan of the first two season episodes. Nothing made me laugh broader than watching some of those hilarious picks of Dr. Sheldon and gang.

The curious case of St. Valentine

It is somewhat ironic that, the day to celebrate love is not named after Cupid, the Roman god of love. His mother goddess Venus and father Mercury are not considered either.  The Greek mythical folks cannot be happy either. Eros, the Greek god of love or his mother Aphrodite, the goddess of love are not the ones remembered by the lovers of this century. In the Hindu mythology, encomium is poured over to Kama (or Kamadeva), but who listens when it comes to naming the modern love day? All the accolades instead went to a saint who to his innocence did not really had any fun himself when it came to love, but he was generous enough to facilitate the young lovers.

One of the legend of St. Valentine’s day go like this. Valentine was a priest who served Rome during the third century. Emperor Claudius II decided to bring in a law to outlaw marriages. His claim was that, single men, without wives and families make better soldiers. The priest Valentine, apparently was not quite ready to bulge to this idea of Claudius. In those days, of course you don’t challenge a ruler in public. How powerful democracy is. We are lucky, don’t we?

Anyway, defying Claudius, Valentine continued to secretly perform marriages for young lovers. When Valentine’s actions were discovered, the king ordered that he be executed. The martyr Valentine became one of the most popular saints in centuries to come in Europe, especially in France and England.

Valentine day of the modern world has surely made St. Valentine proud for his worthy sacrifice. After all, it was all for a good cause. Love is beautiful. It is up-to the people to decide, what way they want to celebrate. There is nothing as beautiful than seeing people in love.  The very sign of love is pleasing to the eyes. Let love relish.

Happy Valentine’s day.

Happy Birthday Martin Gardner

Martin Gardner‘s 95-th Birth day today. I dont think any other soul can claim to own the legacy of aspiring enthusiasm, among children and adults alike, on the subject of mathematics, in the most interesting and playful mode; Recreational mathematics transcended to newer heights thanks to Gardner’s amazing production of puzzles and games. A philosopher by education and a Navy man by profession, Gardner’s transition post World War II is something worth a story telling! I was (still remain so) a huge fan of Gardner ever since romping on to his old articles in the Scientific American volumes, which I greedily grabbed from NIT Calicut library. There was a time (in the pre internet and digital era) when I used to maintain a notebook of Martin Gardner puzzles, where I had handwritten the riddles and games. It is incredible to know that he is still active and steaming. Thank you Martin Gardner for spurring enthusiasm to many a generations. His “Colossal book of mathematics” is one of the worthy possessions in my library!

Many many happy returns of the day Martin. NY times has a nice page published on his birthday!

A game of tennis and a swim in the lake Geneva

After a long gap (over six months or so),  I finally played some tennis again. Much to my surprise, I wasn’t all that rusty in spite of the long layoff from any major sporting (barring some recent treks and once in a while cricket) activities during this period. After a few hits, my serves started holding and I slowly felt the rhythm. I started enjoying this beautiful game once again! In the Swiss heat, it was almost unbearable at times to absorb the hot air from the synthetic surface. On Friday and Saturday’s I played for two hours each until late evening. Yesterday, after the game we took dip in the Lake Geneva near the UNIL sports center arena at St.Sulpice. I never felt a better swim than this before. Such was the feeling of taking a clean water swimming after a good game of sports. It was getting darker and a swim between 2100 to 2200 on the fading summer light in the foothills of the Alps was simply amazing. I just cant compare a place to this amazing Lake Geneva region. Quite a place this is. After the swimming I seemed to have regained all vigour to play a few more games. Had there been floodlights, we were on for a few more perhaps! They say winning is an elixir for eternal youthfulness, but did I feel that swimming in lake Geneva comes close to that?

While, standing in the lake  with chest level water and overlooking the Alps mountains,  it reminded me of the photos of saints in olden days taking a morning yama’s in the Ganges overlooking the Himalayas. I’ve never been to Ganges, but for once I could perhaps feel a sense of their state of mind. I felt like singing one of those Yesudas classical songs, standing with half immersed body. I don’t quite remember whether I did one. I was in a state of fulfilment sort to say!

The King rules on

Oh boy, what did we see this evening at Wimbledon? A grandslam final, filled with nothing short of a breathtaking drama. A near neck to neck battle between king Federer and a fabulously charged up Roddick. Guess who was watching that epic cliffhanger? The emperor of that piece of grass strip in central London! No point in guessing the name: Pistol Pete Sampras. Sampras was visiting Wimbledon after 2002, perhaps just to witness another great champion Federer get past him in the number of grandslam titles. What an occasion! Unbelievable tennis on display when blue sky topped the roof in clean light. I feel for Rodick here. This was ‘the chance’, he had at hand: and truly well he deserved, one must say. I for one had written him off yesterday, even though he had played great tennis in the semi final to beat British hope Andy Murray. From one Andy to another Andy, the other finalist name changed, breaking the great British hope, since Henman (Well, Henman was not really a realistic hope, when Sampras was taking a stroll down the Wimbledon park).  I was expecting Fedex to just roll over him in the title clash. But alas! Didn’t he give Fedex  a run for his crown?

In the end, Federer had that extra epsilon, call it luck or experience.  He was there on that center court final stage on every single year for the last seven summers. Last year he lost it only by a whisker to the Spaniard Nadal. Federer truly deserved to be the grand-slam record holdert. He is the best player on the circuit and he is so very effortless, athletic and passionate.  The great man is a beauty and indeed is a treasure to this great game.   I cant have enough praise on the way he played tennis over the years.  He is so very smooth and graceful. A touch of Lara, Tendulkar or Dravid in cricket. I really was feeling a lot low when Sampras retired in 2002, but the Swiss has indeed made up that void since then.  A humble soul Federer typify the Swiss people I guess. So gentle and an amazing role model to the new generation. I really hope that he gets a few more grand slams titles.

Turning back to the losing finalist, I can imagine how hard it would be to be an Andy Roddick who narrowly missed the crown by perhaps one or two moments of marginal shots.  Sometimes sport can be so cruel! In the end winner takes it all and it is agonizing. It must be hard to be a second at that level. But then, that is what it takes it to be the best in the world. Only thin air make the separation. It is courage and wisdom at times to grab that silver line.  Grabbing is secondary, seeing it in the first place is what separates the best from the next best. After all, it is not easy to get there. Isn’t life beautiful?

Another dexter spoof

Shrini Kudekar yet again showcased his creativity and acting skills on the eve of Dinkars public defense. Here is the video.

Sum of square roots of binomial coefficients

Today, during the evening chat, Emmanuel Abbe threw an interesting question: Whether the sum of square roots of consecutive binomial coefficients converge to some closed form! That is, . We tried a few known combinatorics tweak, but no meaningful solution arrived. We were also wondering whether this has some asymptotic limit, but that too did not yield anything. A quick check on Mathematica wasn’t helpful either. Now the question is: Does this sum yield some closed form expression.

While playing with this sum in Mathematica, I found that for the sum of squares of binomial coefficients, there is a nice simple closed form.

I was toying with a proof. It turns out that, the proof is extremely simple and is a one line tweak of the Vandermonde identity . Simply substitute and we have the results on table. The natural question then would be: Is there a generalization for for any . Ofcourse now for it is trivial.

Apparently, it turns out that, there is no closed form expression for a general (all) . There are some interesting divisibility properties of these sums. An interesting account of that is addressed by Neil Calkin (Factors of sums of powers of binomial coefficients).

At the moment, I get a feeling that sum of fractional powers of binomial coefficients is not trivial. May be there is no closed form. May be not!

Inclusion exclusion principle

A few years ago, during undergrad days, myself and  friend Ramani during our lazy 75 paise mini canteen tea outing, were discussing a small riddle. It was motivated from a real world experience from our computer center in NIT Calicut (REC Calicut). In REC those days, we students almost exclusively used rubber slippers (Yes, those Paraqon brand which used to cost 20 rupees or so), usually called by the name ‘chappels’. With that, we were not only comfortable while walking and running around, but we’re equally at ease playing cricket and badminton with the very same foot support; and many other things too, including jogging. Those thin hard rubber slippers used to last an year or more without giving much trouble, other than perhaps an occasional tearing of the rubber tie. In all, we were at peace with that.

But there was an issue, not exclusively for this brand, but for chappals in general (shoes were a luxury of sort in the campus;atleast it wasnt very common). Not for everyone though! If and only if you were fancied of visiting the computer center! Well, computer center wasn’t all that fanciful then, since we were provided with only graphics less Unix terminals (no colour monitors!). You might wonder, huh! what age am I talking about? Besides, Internet and Emails were only taking shape then. Chats and browsing were not quite there yet;Unless you felt a touch inferior to the computer wizkid around, that was not a compelling centre de visite. As, ‘would be‘ electronics and communication engineers we had that occasional inferiority complex!. Computer center was air conditioned and was strictly slippers free. We were expected to keep our valuable slippers outside (no clock room luxury! well that was not a necessity either) before entering to that cooler room, filled with monochromatic terminals. Since most of the chappals dropped outside were alike (in size and also sometimes color) there was a good chance that at the time return, we ended up with a different pair of slippers (Some folks found happy for themselves by a visit to the computer center, just for a pair change, often to an improved lot!).  Sometimes, we ended up having differently colored ones, say left foot white and right foot blue. That wasn’t a problem socially either, as long as you stayed within the campus. It was socially accepted within the walls!

Anyway, coming back to the riddle we were busy conjecturing on. We wanted to automate a clock room. The idea then would be to just deposit the chappals there at random. The clock room work automatically. Upon asking (at the time of return, say) it will select a pair at random and give it to you. Sorry, you cant have a choice. Just accept and hope for the best. We asked the questions:

1) What is the probability that everyone gets their own chappals

2) What is the probability that none of them get their submitted pairs

Assume number of  people (and hence pairs). We can assume that, a pair is a single entity (say both left and right slippers are tied and submitted as one) . This simplified the problem to people slipper scenario. A simplistic model assumeed that all people submit their slippers at the same time. We wanted to build that great randomized clocker machine! And we wanted that to work for any , which means, the algorithm had to be implementable and to work well in expectation!

We had thought and pondered about it for a while, then. In the end, we had found that the first one is easy, but the second one a little harder to generalize for beyond or something.  As busy undergrads, we left the problem after an hour of discussion, probably until we had finished sipping the tea. Aside, we were busy with many other extra curricular activities including a 3 hour daily cricket match at the lush green international hostel ground. The megadeth team, as we proudly grouped ourselves, the electronics and communication batch hardly missed those cricket matches. We were electronics engineers and had taken pride in ourselves by not really bothered to ask any fellow discrete math or combinatorics folks! That perhaps helped in some sense.  Ramani found management more interesting than those technical details of counting. I am sure he took the right career. Anyway…too much digressing already!

Now, it turns out that, the very same problem is akin to a well known problem in combinatorics. It is called the Hatcheck lady problem. It is fairly easy to solve it using the inclusion exclusion principle. The proof outline is shown below. As I type, memory fetches that discussion,  sitting leg-folded on the cement bench at the REC mini-canteen, perhaps an occasional cool breeze around too. 

The inclusion exclusion principle is the following:

                

                

The Hatchek lady problem can be stated with a similar story as the random clocker machine. (From Harris, Mossinghoff, Hirst’s book on Combinatorics and Graph Theory)

A lazy professor gives a quiz to a class of students, then collects the papers, shuffles them, and redistribute them randomly to the class for grading. The professor would prefer that no student receives his or her own paper to grade. What is the probability that this occurs? This indeed is an equivalent statement of the well known Hatcheck lady problem (I guess the exact name come from a hatcheck lady who collects hats and absentmindedly return them)

For Hatcheck lady problem, the probability .

When gets larger and larger it converges asymptotically to a constant!

My favourite Indian ads

Here is a list of some of my favourite Indian commercial ads.  Thanks to youtube, I get to see them again! The adhisive brand “Fevicol”has produced some inredible and funny ads.  Most of their ads stuck on to the viewers mind.  Among the other funny ads, I liked camlin erasurs and marker ones.  I better dont say too much here. As they say, the fun in an ad is best viewed and chilled out! Have a look and enjoy the fun and appreciate the creativity of these fabulous ad makers.

The old Ericsson mobile phone ad (I guess 1996). The concept of a  ”small” phone back in 1996 perhaps is too outdated for today.  All boils down to Moore’s law!

Rimii Sen and Aamir Khan did a nice job here in this Bengali accented conversation.  The coke ad is one of the better ads from the cool drink folks.

Fevicol: Simply superb ad from the popular adhesive brand.

Naukri.com’s famous Hari Sadoo funny ad:

How about this one. To be this is too good an ad from Camlin.

The Peugeot ad used to appear in Channel 4 in UK. It was an incredible ad. I am glad that this is there for viewing in youtube. Superb one.  

I am a Mathematician:-)

The title might mislead you. So, let me clarify upfront. I am not on a mission to self appraise. I am to talk about the autobiography of ‘Noerbert Wiener’, titled ‘I am a Mathematician’. This is a piece of book I am reading currently. Since I have heard a lot of stories about Wiener and having known some (percentage is minuscule!) of his work, the presentation of the book didn’t provide disappointment. Rather, it is a very very interesting sketch of his life, put in his own style.

I mentioned about stories being heard about him. There are many of them. I am not saying this candidly, because I hardly checked the authenticity of such tales. Nevertheless, I get ready to laugh everytime, I begin to hear anything about him. The mathematical work of this once child prodigy is very well known and is treasured. His wit and absentmindedness are quite unique. Some of the anecdotes, I have heard about him are;

1.During one of these trips down the hallway at MIT, Wiener was interrupted by several of his students who talked to him for several minutes about what they were working on. After the conversation had ended, Wiener asked one of them “Could you please tell me, in which direction was I traveling when you stopped me?” One of them replied, somewhat confusedly, “You were coming from over there [gesturing] this way [gesturing].” Wiener replied, “Ah, then it is likely that I have already had lunch. Thank you.” and continued down the hallway to his office. (A somewhat similar story is attributed to Einstein as well. As far as I heard, this is when Claude Shannon was giving a lecture at Princeton. It was well attended. Einstein made a back door visit when Shannon was in full stream. Shannon obviously noted Einsteins coming in, chatting with someone in the last row and the leaving soon. The curious Shannon (after the lecture) went to the folks to whom Einstein seemed talking. To Shannon’s surprise, Einstein was apparently asking them ‘where the tea was served’.)

2: After several years teaching at MIT, the Wieners moved to a larger house. Knowing her husband was likely to forget where he now lived, Mrs. Wiener wrote down the address of the new house on a piece of paper and made him put it in his shirt pocket. At lunchtime, an inspiring idea came to the professor, who proceeded to pull out the paper and scribble down calculations, and to subsequently proceed to find a flaw and throw the paper away in disgust. At the end of the day, it occurred to Wiener that he had thrown away his address. He now had no idea where his home was. Putting his mind to work, he concocted a plan: go to his old home and wait to be rescued. Surely Margaret would realize he was lost and come to pick him up. When he arrived at the house, there was a little girl standing out front. “Excuse me, little girl,” he asked, “would you happen to know where the people who used to live here moved to?” “It’s okay, Daddy,” the girl replied, “Mommy sent me to get you.” (Decades later, Norbert Wiener’s daughter was tracked down by a mathematics newsletter. She said the story was essentially correct, except that Wiener had not forgotten who she was.)

Description on the image: Norbert Wiener with Amar Bose (Bose audio fame) and Lee (the early MIT pioneers): Source of this image is [1] [1]http://www.siliconeer.com/past_issues/2005/January2005-Files/jan05_bose_archive.jpg

Watching a game of soccer at Sanford bridge, London

This picture is taken on 2004, May 03. The day has no big significance, but for the first time, I was there watching an English premier league soccer game live. Thanks to Jeff Torrance who managed to get an extra executive ticket, I could avail a feel of this fabulous experience of live soccer game in Europe and that too in England. Jeff, a huge Chelsea fan was so thrilled to get into the Chelsea gate, through the team restaurant. The entry to the stadium gave me an experience, that I never had before. Throughout the journey from Cambridge to London and then to Sanford bridge we had quite a lot of laugh pulling Cyrian for his Irish jokes and what not!