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I was long curious about the origin of the name San Diego. I feel ashamed of myself if I don’t know a bit of history of the place where I stay. As far as history is concerned, to a decent extend, I was indeed aware about the history of California, including San Diego. But, I didn’t know where the name San Diego originated from. Thanks to this and a bunch of Google/Wikipedia hits, here I know why San Diego!

Here is the official explanation behind the name San Diego, at least per San Diego Historical Society.  The Spanish explorer Sebastian Vizcanio arrived San Diego from the Mexican coast of Acapulco . This was in the year 1602 and it took. He had departed Acapulco with four ships on May 5, 1602 and only three of them, his flagship ship being San Diego, made it to what is now known as San Diego bay.  Besides the flagship ship named San Diego, he had two other ships arrived at the bay. They are the San Tomás and the Tres Reyes. The exact date (as per history) of his arrival in San Diego bay is November 10, 1602. Acapulco found no qualms in naming the new coastal area by his flagship ship name and hence we now live in the beautiful San Diego and not San Thomas or Tres Reyes, huh! Apparently, there was another reason why Acapulco chose San Diego. It was to honor the Mission Basilica San Diego de Alcalá.

Just came across a neat little Google App for Meegenius to use with Google chrome. Quite cute and nice. Basically, a little story telling/book reading (with audio) app for small kids; Essentially, this is an add on to the Meegenius online book store/reading for kids while using Google Chrome as the browser. I am sure kids will have an enjoyable ride with this. I found it to be incredibly cute!

Well, if you are not really obsessed with Google chrome, then you can as well go direct to MeeGenius and read it there!

For some reason, I really love the beginning scenes of the movie Tangled. The screen visualization and the audio are simple amazing. These days, I really relish seeing this again and again, especially the starting scene and the songs. Thanks Disney for such a wonderful movie!

For a generation of kids like me, growing up in the 80s and 90s in India, Anant Pai, popularly known as Uncle Pai was one of the most influential figure. Not because of his personality or the aura in public life, but the sheer creativity in transpiring the richness in the Hindu mythological stories to us in the form of children stories. The Amar Chitra Katha stories from him, not only had improved our knowledge on the many epic stories and its variants, but also brought the curiosity in the fairy tale world to young minds. It is with immense sadness I passed the day hearing his sad demise, last week.

…High above the city, on a tall column, stood the statue of the Happy Prince.

Oscar Wilde‘s ‘The Happy prince‘ is one of the many stories that I have read during early school days. Remarkably, this is one of the few I still remember! I was barely able to read difficult English literature per se then, but still the story of Happy prince was within my grab. I don’t recollect whether I had understood all the words of Wilde, back then. This was at a time, when I was happily enjoying my schooling and life in my mother tongue Malayalam. Malayalam literature had its penchant style and aura, which is difficult to explain to non-Malayalam readers.  I was ‘at-home‘ when it came to reading the Malayalam literary works. Yet, I had thrived to learn English stories, albeit at a reduced speed. That whenever, I got a chance to read. Oscar Wilde was one of the rare English writers whose work, somewhat accidentally came to my reading list.  I was surrounded and enthralled by the works of great south American and Russian writers, otherwise. Partly, thanks to the communist influence in Kerala society, the translations of great Russian and south American books were far more available at ease  and at cheap rate (In fact I don’t remember buying anything, but all borrowed from various small local libraries around). 

Coming back to the Happy prince, the story had indeed put a stamp in my memory as a child.  I may have been 10 years or so when I was ‘introduced to’ the ‘Happy prince’.  The subdued request of the prince to the little swallow was by heart to me. When the prince says ” Swallow, swallow little swallow…”, my heart seemed to have resonated at a lower pace.  As a child, I had never seen an European city, for that matter any great city including the ones in India, let alone city across the Atlantic. It was all in my mind, that I’d imagined a mythical model of such a city, a city of the happy prince!  I used to visualise the position of the Happy prince statue standing tall in the middle of a city. Did I ever imagine the enormity of a city as big as this? As a child it is difficult to fathom and relate the seriousness of people’s struggle, a statue could see.  For sure, I was touched and moved by his sorrows and pain.

The swallow represented a role model so to speak  when it comes to helping others. Subconsciously, the little swallow literally drenched my cheeks by living through that difficult winter.  Back then, I had never seen what it is to be a snowy winter, still, could feel the chill of that season, when the shivering swallow wholeheartedly fulfilled the Prince’s wishes. Years later, the words “…Swallow, Swallow, little Swallow. Stay with me one night longer” still linger my ears. Tears still beckons! Perhaps that story have had a deep influence to me since childhood, to an extend that I’ve never imagined. As a child, I wished if only the swallow could go to Egypt, but alas!

Now, I have accidentally come across that very same story in video form in youtube. That brought in a rewinding of years! I feel the same chill now, as a 10 year old that I had felt years ago. I had told this story to Nivedita a few times. I could see her expression when I uttered the prince’s humble request “…Swallow, Swallow, little Swallow. Stay with me one night longer” .. The impact of Oscar Wilde’s powerful writing tells a story in itself. Don’t they?

…High above the city, on a tall column, stood the statue of the Happy Prince.

The prince and the swallow still stays on.. in my memory…I really want to tell this story to many kids! The youtube video is commendable too.

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 n number of  people (and hence n 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 n people n slipper scenario. A simplistic model assumeed that all n 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 n, 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 n=10 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:

\lvert \bigcup_{i=1}^{n} A_{i} \rvert=\displaystyle\sum_{i=1}^{n}{\lvert A_{i}\rvert}-\displaystyle\sum_{1\le i_{1}<i_{2}\le n}^{n}{\lvert A_{i1}\cap A_{i2} \rvert}+\displaystyle\sum_{1\le i_{1}<i_{2}\le n}^{n}{\lvert A_{i1}\cap A_{i2}\cap A_{i3} \rvert}

                 +\displaystyle\sum_{1\le i_{1}<i_{2}\le n}^{n}{\lvert A_{i1}\cap A_{i2}\cap A_{i3} \rvert}+\ldots+

                 +(-1)^{n-1}{\lvert A_{1}\cap A_{2}\cap A_{3}\cap\ldots\cap A_{n} \rvert}

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 n 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 P(n)=\frac{D(n)}{n!}.

D(n)=n!-\lvert A_{1}\cup A_{2}\ldots\cup A_{n}\rvert=n!-\frac{n!}{1!}+\frac{n!}{2!}-\ldots+(-1)^{n}\frac{n!}{n!}

= n!-\displaystyle\sum_{k=1}^{n}{(-1)^{k-1}\binom{n}{k}(n-k)!}=n!-\displaystyle\sum_{k=1}^{n}{(-1)^{k-1}\frac{n!}{k!}}

P(n)= 1-\displaystyle\sum_{k=1}^{n}{(-1)^{k-1}\frac{1}{k!}}

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

\displaystyle\lim_{n\to\infty} P(n)=\displaystyle\lim_{n\to\infty}{\displaystyle \sum_{k=1}^{n}{\frac{1}{k!}}}=\frac{1}{e}

The popular documentary on this fascinating mathematical prodigy of 20th century is now available on you tube. Personally, while watching the video, the cam river and the row boat brought a touch of nostalgia! I have heard mountains of stories about Paul Erdős. This documentary is a must watch for not only mathematicians and mathematically curious guys (or guys like me who are just curious about mathematics, mathematicians and mathematical minds or for that matter about anything in this world!), but for everyone interested to know about such an extra ordinary mind of our times.  What a fascinating experience it would have been to listen to one of his lectures live. Now this youtube brought the gap down to finite length/time reality.

I have never seen Erdős. Now that he is no more warrants any thoughts anyway.  In a away I am lucky this semester to attend courses of another prolific mathematician of this era Janos Pach. Interestingly, Janos Pach is one of the few living mathematicians with Erdős number 1.  His lectures on Graph theory as well as the one on geometrical graph theory are truly fascinating. 

Anyway, if you have not seen the documentary yet, here is the link. It is a must watch. I bet, you wouldnt miss the time. On many occasions, the Cam river and its slow movement etches something in the backdrop of those days.  Didnt I like that place?

Over the weekend, I finished reading a very nice book, The Kite runner, by Khaled Khosseini, an Afghan born novelist. This is first of his books, that I have read. In fact this is his first book as well. The book is written in an easy story telling style, but he did an amazing job to make me really satisfied. There were echoes of pain and suffering and the realization that the fate of a nation and its people can sometimes be so cruelly altered by invasion of other nations. Ofcourse that is a starting point. Later on the so called protectors of God then take over and make an even more mess where humanity is let to shame. Well, we can go on and debate those issues which unfortunately is affecting like cancer to human society as a whole, across the world.

Coming back to the book: The story The Kite runner is the story of two young boys Amir and Hassen. The setup is in Afghanistan, where these boys are born and spent their childhood. Amir was born in an affluent family, but his mother dies immediately after his birth. Ali, a servant to Amir’s father (baba) and his wife have a son named Hassan. On strikingly similar terms, after Hassen was born, his mother elope with someone, leaving him too motherless. The two kids are growing up together. Hassen lives in a hut in Amir’s mansion, baba’s house as he often refers to as. Baba (amir’s dad) loves both these boys, but Amir finds he being more critical to him than Hassan. Youn Amir thinks that baba’s attitude is perhaps due to the fact that Amir is indirectly responsible for his wifes (Amir’s mother) death (she dies after Amir’s birth). Baba’s friend Rahim Khan however is more lenient and friendly to Amir, and he provide support and encouragement to young Amir to develop interest in writing stories.

Amir and Hassen grows up together, with Amir as the lead boy and Hassen more submissive and obedient friend. The Russian invasion to Afghanistan then changes their life forever. Amir find himself as an immigrant in California, whereas Hassan forced to take a route to Pakistan. Fate shows the cruel flip to Hassen and he dies. Years later Amir take a difficult trip down east to rescue Hasan’s son, all in the middle of the Taliban reign. A tocuh of unrealistic melodrama where Amir fights with the brutal Talibans, but that afar the story is incredibly nice and touching to the reader. I have thoroughly enjoyed reading this.

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]


April 2017
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