Slumdog millionare

So after almost 4 years this movie came out I finally watched it. Gloria recommended me this one in fact when she realized that I haven't watched it, she went out of the way and gifted me the DVD. In spite of all this coercion it took me more than 3 months to watch it. I guess I have been disappointed with lots of Bollywood movies, especially their crass dialogues and social attitude that has alienated me. This Christmas break I did watch few Hindi movies because Piyush wanted to watch it and some were better than I expected and I think that nudged me to give Slumdog millionare a chance.
   It's a Bollywood movie though shot mostly in English. The story line is about a kid from slums who ends up being a contender at 'Who want's to be a millionaire' show and does pretty well before the final question. The anchor of the show is in rage that how can an illiterate slum boy could answer all his questions. So he is in prison and being tortured. However our hero is a truthful guy who just happens to have experiences which allows him to answer these questions. There are some lovely songs and I would say i did enjoy the movie. Its not all rosy however. Growing up in slums, seeing the Hindu Muslim riots and seeing kids being maimed so that they bring more money to their masters who have enslaved them does stir your soul and you are awakened to the misery of innocent kids which we try not to think of. The movie does have a sad-happy ending

Usaquen and having a great breakfast

 Today I went to this place called Mr. Ribs. They serve fabulous bread and the dip. I had a Mango Salad, 2 lemon ice tea and a tomato soup all for 40 million pesos. Then we looked at Art and Craft market and that place was jam packed. It was refreshing to go out and shop for trinkets. I did end up buying a lemon green sun glasses for myself. On returning a found a message from Julia and I am glad she is reading the book by James Allen I suggested to her. I have several movies that I would like to watch and Goonies and Django are the two. Amy suggested Goonies and that piqued my interest. 

Loosing keys

A couple of nights ago Piyush called me about loosing his keys. This is one thing we had talked about many times. I tried to act as calm as possible and tried to reassure him that we will find the solution and its not a big deal. I went downstairs and explained to Jesus and he gave few numbers to contact

Consecutive divisibility of higher powers

Everybody knows that its easy to find consecutive natural numbers which are composite. Now if someone asks you can you find consecutive natural numbers which are divisible by higher order powers the answer is again yes. For example consider number 8 and 9. 4 divides 8 and 3 divides 9. So here he was two consecutive numbers which are divisible by square numbers. Question is : Can you find 3 consecutive numbers which are all divisible by square numbers and the answer is yes. To answer this we create a constructive induction proof
first
let a1,a2,...an be the consecutive natural numbers
let s1,s2,...,sn be the square numbers such that s1|a1, s2|a2  ... sn|an
let L=s1*s2*s3*...*sn
Now we have to come up with sequence of n+1 numbers which are divisible
by n+1 square numbers
let these numbers are
a1+A, a2+A,...,an+A, (an+1)+A
where A=an+1(L+2)L
Now notice that each of these numbers a1+A = a1+(an+1)(L+2)L is divisible by s1
similarly a2+A = a2+(an+1)(L+2)L is divisible by s2
...
a2+A = a2+(an+1)(L+2)L is divisible by sn, because L is a product of s1*s2*..sn and sn|an.
The next step is: Is (an+l)+A is also divisible by some square number ? Because we don't have any idea about s(n+1).
(an+1)+A =(an+1)+(an+1)(L+2)L =(an+1)(1+L^2+2L) =(an+1)(L+1)^2.
Thus a(n+1)+A is divisible by a square number which is (L+1)^2

To extend our example we chose in the beginning that 8 and 9 are consecutive numbers which are divisible by square number. Can we get three consecutive numbers which are divisible by square numbers. So we extend the construction as
L = s1*s2 = 4*9=36
A=(an+1)(L+2)L =10(36+2)36=  13680
a1+A = 8+13680 = 13688 means 4|13688
a2+A =9+13680=13689 means 9||13689
a3+A=10+13680=13690 means (L+1)^2=37^2= 1369|13690

To prove for cubic or higher values the h1,h2,..hn
and terms become like a1+A where A =(an+1)((L+1)^m-1)

A pattern in counting number of primes

The question arises how can we find the carnality of numbers less than a given natural number. Well to start with, we can use the idea of fundamental theorem of number. It states that any number is either a prime or a product or primes.Once we have a prime factorization the power of each of that prime could either be even or odd. If it happens to be even that means its a square number and if it happens to be an odd than its one more than the even number. So we can group all the even parts as one and the single exponents as other. We call the part where the numbers have only single power as non square part of the number. Now if n is the number its easy to see that the square part never exceeds the square root of the number and the non square part could contain as many as pi(n) number of primes at most. If we have to make all possible numbers than for square part we have a choice of sqrt(n) and for non square part we have a choice of 2^pi(n) numbers at most. Notice that if one use all prime numbers less than n it may likely to overshoot the number itself. Thus a rough bound on the numbers can be obtained by fundamental principle of counting as sqrt(n)*2^pi(n) > n

Cevians

I am currently reading a problem on Cevian. A Cevian is a line which emanates from a vertex and fall on the opposite side. The problem is about to prove that the longest Cevian is greater than the sum of the parts which fall on the opposite sides. To prove this the author first shows that measure ofany cevian lies between the length of the two sides. So any given Cevian will always be smaller than the longest side. Then he constructs two parallel lines and get a similar triangle to the original triangle and shows that sum of the cevian parts are less than the longest side of the original triangle

Talking to Ray

I have known Ray for a long time. We met in southern Illinois and over time we became pretty good friends. I have observed Ray for a long time and out of my hubris have given suggestions to wake him up. The reason is I always find him stressed out of his job. It's like he is on a tread mill running as fast as he could but still finding himself going no where. One reason which brought us closer was the discussion on self improvement. Ray overcame a lot of obstacles and got himself an education as a non traditional student. He aced many courses even though he was working full time. He finally got a  liberal arts education that he is fittingly proud of. He had the fortune of reading some great books that changed his life. Which is a point I whole heartedly share. A good book can change one's life and one should make every possible attempt to find such books.
 He told me about some of the family problems he was having. His mother who is cruising at 90 plus years of age was recently diagnosed with multiple fractures and is in severe pain. One of his brother's son is missing. Another of his brother's daughter was caught shoplifting and in possession of amphetamine and is in big trouble. His own relationship with a mutual friend Jen is not working out. His work load busting at seams and his own health is precarious. I wish I could help him cope but all I have are suggestions which may not sound right when the going gets tough and you are impatient to turn your life around.

Catching up with Mei

Good friends and a treasure worth more than anything in the world. I am incredibly blessed to have friend like Mei. Mei and I have been now friends for over 6 years. He is probably the most self effacing and soft spoken person you can find plus he is incredibly smart and is gifted in reading other people. Yesterday I got him on skype and we had a nice conversation. Basically we caught up on things. He is one of those person with whom I can pick up the conversation where we last left off. He is from a place close to Harbin and he made a visit back to his parents there. I had the good fortune of meeting his mother when she visited Carbondale. I am hoping to schedule a trip to China with Mei sometime and witness the gorgeous ice festival there but i guess the more exciting part will be to spend some quality time with a great human being :)

Making sense of the 48th largest Mersenne Prime

Just to give you some handle on how big this number is. If you were to write all the digits of this number at the rate of 1 digit per second it will take over 196 days or over 6 and half months just to write the number itself and if you choose to see that number in one glance you will need over 170 km or over 100 miles of strip of paper and now imagine a million has only 7 digits and it takes only 7 cm or roughly as much space as the size of your pinkie:)

Madhuban Khusboo deta hai: My all time favorite song

There are few songs which touch your soul. This is the one.  The lyrics, the video are all sublime. 

Dabang 2

I watched Dabang 2 today and like Danang 1 it was a no brainer. However it had lot more songs so I had to skip mamy times. Dabang 1 songs were quite hit but I can't pass a similar judgement for the sequel. The time lapsed action scenes are a norm which I first noticed in Sherlock Holmes movie where you can actually see the waves passing under the skin when a blow happens. It's a happy ending movie with the hero being totally invincible.

48th Mersenne Prime found

Prime numbers are fascinating. They are akin to atoms in mathematical number structure. Just like atoms are indivisible units of matters so are prime numbers in context of number system. One I first read the news I went straight to GIMPS page as I had a distinct hunch that this must have been discovered by the folks at GIMPS project. Why ? Well the reason are obvious. To verify a prime number of this magnitude one needs computer. It has got over 17 million digits which means if one were to write this number alone with a speed of 1 digit a second it will take over a month to write all the digits ! The number was discovered on 25th of January 2013.

Public talks are fun talks

I recently gave a talk on India at my school. I am glad that I did. Last time I did a talk for Children was when I was at Ashok Hall and there I talked about the ideas of Circle of Concern and Circle of Influence. Basically it says that we should only work under our circle of influence, anything over which we have no control should be left alone and by working more and more inside our circle of influence we expand it and sooner or later we are even able to influence things which didn't fell under circle of influence. This is one powerful idea and has changed my life in many ways.
  The talk which I gave at my school was focus more on the geographical features and customs of India. I started with the map of India and how one can easily remember the map if one visualize oneself having one arm on the side and other outstretched carrying a book. I talked about river Ganges, Thar dessert, Kanchanjanga mountain, Backwaters of Kerela, Statues of Gomiteswara, Nano Car, Diwali,Holi, National symbols etc. In the end I gave them a quiz and it was very encouraging that they could answer all the questions. Including like how high is Kanchanjunga to where the dessert of Thar. Even they remembered the name of under $2000 car called nano. It certainly become more vocal after they realize they could get Hershey's Kiss me for each correct answer.

 However the best reward of that talk has been exchanging smiles by those lovely 7-8 years old as they enthusiastically greet in the hallway Mr. Sumant and you know that you have touched the life of them in some positive way.

Race 2

I watched this movie yesterday. It's one of those movies where director wants to make sure that he is ahead of the viewer by trying to come up with surprises at each stage. I think that was the formula. It's fast paced and with ample action to keep you guessing what's going to happen next and all the characters are suppose to be super macho and intelligent. Not bad and yes I skipped all the song and dance sequence.

Colombian movie

Today Olga took us to a Spanish movie and it was fun. The movie was about a platoon of Colombian soldiers who discover the hidden money in a forest while on a mission to rescue 3 missing Americans. The all get insanely rich and then get to splurge. It has lot of comic moments and was a fun introduction to Colombian cinema.

Theravada style Vipassana

 Yesterday I attended a Dharma group doing Theravada style Vipassana practice. They are more into consciously reminding themselves of what they are doing ? So they repeat everything 3 times. Its very ritualistic. You do 10 minutes of kind of yoga and then 10 minutes of walking meditation and finally 10 minutes of sitting meditation. Then take a break of 10 minutes and repeat. It was a different experience and ofcourse when you are doing in group you feed on the energy. Will I return back. I think so :)

Talk on India

  Yesterday I gave a talk about India at TES to 2nd graders. There were over 120 students and it was a very enthusiastic crowd. I asked a few teaser questions about India and some of them surprised me by what they already knew. The talk went well and I had lot of fun delivering it. It was coordinated by Silvinet and Yobana. I may end up giving another talk on Math.