Q: What would you like to be when you grow up?
A: I would like to be lucky!
Friday, April 08, 2005
Tuesday, March 29, 2005
Wednesday, March 23, 2005
Twin primes
For a moment I thought I had proved the twin primes conjecture...
The conjecture is that there are infinitely many prime pairs differing by 2. eg. 5,7 ; 11,13 etc.
I started with Euclid's proof of the infiniteness of primes.
Assume for a contradiction that there are finitely many primes. Without loss of generality, assume that there are exactly n primes p1,p2, ... pn in increasing order.
Then, (p1.p2...pn + 1) must be a prime since it has no prime factors, contradicting our assumption.
In the same way, (p1.p2...pn - 1) must also be a prime if n>1.
Doesn't that give us a pair of primes (p1.p2...pn - 1), (p1.p2...pn + 1) for every n that differ by 2?
No, it does not. Why?
The conjecture is that there are infinitely many prime pairs differing by 2. eg. 5,7 ; 11,13 etc.
I started with Euclid's proof of the infiniteness of primes.
Assume for a contradiction that there are finitely many primes. Without loss of generality, assume that there are exactly n primes p1,p2, ... pn in increasing order.
Then, (p1.p2...pn + 1) must be a prime since it has no prime factors, contradicting our assumption.
In the same way, (p1.p2...pn - 1) must also be a prime if n>1.
Doesn't that give us a pair of primes (p1.p2...pn - 1), (p1.p2...pn + 1) for every n that differ by 2?
No, it does not. Why?
Tuesday, March 15, 2005
TV for sale
Some people... anyway, here's an ad I saw recently:
TV for sale. It used to work great until last week when the channel got stuck at number 3. $25.
Hmmmmmmm. $25 per channel. 100 channels. Do the math.
TV for sale. It used to work great until last week when the channel got stuck at number 3. $25.
Hmmmmmmm. $25 per channel. 100 channels. Do the math.
Monday, March 14, 2005
Photo rules
I screwed up. I screwed up big time. There are (at least) 3 fundamental rules for taking good pictures. To consistently take good pictures, one must check these 3 quickly before each click in the following sequence:
1. correct choice of f (aperture) for a desired effect
2. correct exposure
3. hold camera steady
Other rules may be
4. choose proper film for the photo setting eg. 400-1600 for night pictures with people
5. use grad filters if necessary
and many others.
I screwed up in 2. I took a picture of a small bright sunlit flower in front of a dark shaded background. My experience told me that unless I underexposed considerably, my subject (the flower) would be a blur of bright light. I underexposed 2 full stops. The image came out nice. From then on, until the end of the roll, and well into the next one, I kept taking pictures 2 stops underexposed... some of my best compositions came out horribly dark.
1. correct choice of f (aperture) for a desired effect
2. correct exposure
3. hold camera steady
Other rules may be
4. choose proper film for the photo setting eg. 400-1600 for night pictures with people
5. use grad filters if necessary
and many others.
I screwed up in 2. I took a picture of a small bright sunlit flower in front of a dark shaded background. My experience told me that unless I underexposed considerably, my subject (the flower) would be a blur of bright light. I underexposed 2 full stops. The image came out nice. From then on, until the end of the roll, and well into the next one, I kept taking pictures 2 stops underexposed... some of my best compositions came out horribly dark.
Wednesday, March 09, 2005
taking responsibility
I was watching TV and came across a reality show 'Runway' in which some designers compete through their fashion creations. Today's episode was about teamwork, and one of them got eliminated for being the weakest on that count. But that's not really what happened.
It came down to two persons. One had spent several hours crying because she cracked up under pressure. The other simply said that she was slower at sewing than the others and perhaps she herself should be eliminated. The judges agreed, saying that this being an industry, you are supposed to sell yourself, not eliminate yourself. The crying lady got another life.
The decision seemed ironic to me. Here is a person who is willing to take responsibility, who is humble, who instinctively dislikes to pass blame, and who has a kind heart, and she is eliminated on a test of teamwork! I think that I should love to work with such a person as my partner, rather than work with someone who is emotionally immature, or is prone to throwing tantrums.
Somehow, American TV has time and again given me the impression that qualities such as humility, willingness to share responsibility for failures, and not passing blame, are considered weaknesses in this culture. That is perhaps not true is actual work environments, because without these, teamwork is impossible.
Some Buddhist schools, on the other hand, cater to the opposite extreme. Taking responsibility is held sacred. In some of their teaching stories, I came across scenarios where an individual took responsibility quietly and calmly for mistakes that were perhaps not entirely his. And he was served as a model to readers. Isn't is true that taking responsibility for mistakes that you have not committed is a form of dishonesty? It misleads others and just happens to hurt you also. Perhaps the message of the story was that when it comes to taking responsibility, you must check your tendency to get defensive and make excuses. But the example came out as a little extreme to me.
It came down to two persons. One had spent several hours crying because she cracked up under pressure. The other simply said that she was slower at sewing than the others and perhaps she herself should be eliminated. The judges agreed, saying that this being an industry, you are supposed to sell yourself, not eliminate yourself. The crying lady got another life.
The decision seemed ironic to me. Here is a person who is willing to take responsibility, who is humble, who instinctively dislikes to pass blame, and who has a kind heart, and she is eliminated on a test of teamwork! I think that I should love to work with such a person as my partner, rather than work with someone who is emotionally immature, or is prone to throwing tantrums.
Somehow, American TV has time and again given me the impression that qualities such as humility, willingness to share responsibility for failures, and not passing blame, are considered weaknesses in this culture. That is perhaps not true is actual work environments, because without these, teamwork is impossible.
Some Buddhist schools, on the other hand, cater to the opposite extreme. Taking responsibility is held sacred. In some of their teaching stories, I came across scenarios where an individual took responsibility quietly and calmly for mistakes that were perhaps not entirely his. And he was served as a model to readers. Isn't is true that taking responsibility for mistakes that you have not committed is a form of dishonesty? It misleads others and just happens to hurt you also. Perhaps the message of the story was that when it comes to taking responsibility, you must check your tendency to get defensive and make excuses. But the example came out as a little extreme to me.
Sunday, March 06, 2005
The question
The question is not, ‘‘Is there life after death?’’ The question is, ‘‘Is there life before death?’’
Thursday, March 03, 2005
Bouncing ball
quoted from 'The Teaching Stories of Grand Master Wei Chueh'
***
One of the monks was troubled with his wandering thoughts. Not knowing how to deal with them, he had no peace and asked the Grand Master what to do.
The Grand Master said, "Thoughts come, and thoughts go. Just ignore them. Like a bouncing ball, if you don't hit it, it won't bounce."
***
To add to the message of the story above, I quote from an abstract of Zen meditation "Repelling wandering thoughts is like bouncing a ball-the harder you try, the greater the force it bounces back. The right way of dealing with wandering thoughts is to ignore them."
***
One of the monks was troubled with his wandering thoughts. Not knowing how to deal with them, he had no peace and asked the Grand Master what to do.
The Grand Master said, "Thoughts come, and thoughts go. Just ignore them. Like a bouncing ball, if you don't hit it, it won't bounce."
***
To add to the message of the story above, I quote from an abstract of Zen meditation "Repelling wandering thoughts is like bouncing a ball-the harder you try, the greater the force it bounces back. The right way of dealing with wandering thoughts is to ignore them."
Friday, February 25, 2005
Of birds and bushes
"A bird in hand is worth two in a bush"
But a bird in a bush is so much more exciting!
But a bird in a bush is so much more exciting!
Wednesday, February 23, 2005
HR Interview
I just attended a talk on getting a job. The speaker was an HR person. I knew most of the things, but some of them got reemphasized, such as :
a. The need for a 1 page resume, and what essentials it must contain-experience,skills; and what it need not contain-publications, courses, teaching or other unrelated experience
b. In the age of databases, the need for putting in keywords that a computer can search out
c. 80% of all jobs are unadvertised; the remaining 20% receives the bulk of applications
d. The importance of networking
But the most valuable insight I go was regarding HR interviews. As a technical person, one may believe that an HR interview is less important than the others, but rest assured, the HR interviewer does not share the belief. Any person who is interviewing you has the authority to reject your candidacy, or else the interview would not be taking place. The speaker mentioned behavior traits that are strongly undesirable:
a. One or two word answers
b. Long and chatty answers, sometimes with personal information
c. Condescending attitude
d. Answers full of technical jargon. It is important to speak in the language of the other person to get information across. Speaking in terms that don't make sense to the listner conveys the same amount of information as saying nothing. Also, it is rude.
Remember that communication skills are valued by all employers.
a. The need for a 1 page resume, and what essentials it must contain-experience,skills; and what it need not contain-publications, courses, teaching or other unrelated experience
b. In the age of databases, the need for putting in keywords that a computer can search out
c. 80% of all jobs are unadvertised; the remaining 20% receives the bulk of applications
d. The importance of networking
But the most valuable insight I go was regarding HR interviews. As a technical person, one may believe that an HR interview is less important than the others, but rest assured, the HR interviewer does not share the belief. Any person who is interviewing you has the authority to reject your candidacy, or else the interview would not be taking place. The speaker mentioned behavior traits that are strongly undesirable:
a. One or two word answers
b. Long and chatty answers, sometimes with personal information
c. Condescending attitude
d. Answers full of technical jargon. It is important to speak in the language of the other person to get information across. Speaking in terms that don't make sense to the listner conveys the same amount of information as saying nothing. Also, it is rude.
Remember that communication skills are valued by all employers.
Tuesday, February 22, 2005
The maze
Have you ever solved a maze? The childish ones, where one has to find a way for the bunny rabbit to reach a bunch of juicy carrots? It was mostly easy, wasn't it? It was easy. It was easy because we could look down at the entire maze, and our eyes would find a countinuous path between two points. Now, had we been inside the maze, unable to see past boundaries, life would be so much harder.
Sometimes, life is like a maze, confusing, frustrating, and it helps to detach oneself and to look at life from an elevated position. From there, one can see the options and the paths clearly. From there, one can see past the barriers of confusion and doubt.
Sometimes, life is like a maze, confusing, frustrating, and it helps to detach oneself and to look at life from an elevated position. From there, one can see the options and the paths clearly. From there, one can see past the barriers of confusion and doubt.
Monday, February 14, 2005
Knowing what to do vs. doing it
Most adults have a fairly good idea of what they should be doing. Few do it. Our brain, which is so good at distinguising the correct from the wrong, the desirable from the undesirable, gives us a teeny weeny bit of self control. We repeatedly do things that we know are harmful to ourselves.
With many of us, the problem is addiction, which is more common than we may care to admit. Watching a certain TV show regularly is a relatively harmless one. Playing a video game continuously until it is won is more serious. Video games are a >$10 billion industry.If you can play 15 minutes each day, it is fine. But then, you are not the subject of this posting :)
Another common manifestation of our lack of self control is laziness. Amazing how some people get away with it. If you are in a job, you surely have seen a specimen. Does absolutely nothing and blabbers nonsense without giving any thought at meetings. Managers! Not necessarily.
While my car was broken, I had to commute for a few weeks. I would see the train from a distance. Two parallel roads to cross, the walk signs still red, the train pulling in, the knowledge that it would pull out in less than 30 seconds; getting to it almost impossible. Amazingly, when I decided to try, more often than not, I would make it just in time. If only I had the same spirit in my research... that would be cool! I'm trying... I'm trying...
With many of us, the problem is addiction, which is more common than we may care to admit. Watching a certain TV show regularly is a relatively harmless one. Playing a video game continuously until it is won is more serious. Video games are a >$10 billion industry.If you can play 15 minutes each day, it is fine. But then, you are not the subject of this posting :)
Another common manifestation of our lack of self control is laziness. Amazing how some people get away with it. If you are in a job, you surely have seen a specimen. Does absolutely nothing and blabbers nonsense without giving any thought at meetings. Managers! Not necessarily.
While my car was broken, I had to commute for a few weeks. I would see the train from a distance. Two parallel roads to cross, the walk signs still red, the train pulling in, the knowledge that it would pull out in less than 30 seconds; getting to it almost impossible. Amazingly, when I decided to try, more often than not, I would make it just in time. If only I had the same spirit in my research... that would be cool! I'm trying... I'm trying...
Friday, February 11, 2005
A silly joke
Sorry, this one is only for folx who understand Hindi. It came with one of the many mails that go around.
Ek gadha ped par chadha to oopar baithe haathi ne poochha, "Tu kyun chadha ?"
Gadhe ne kaha, "Apple khaane".
To haathi ne bola "Lekin buddhu, yeh to Mango tree hai!"
Phir gadhe ne kaha, "Maloom hai, main apple saath laaya hoon."
-Did this make you laugh? Maybe not. The first time I read it, I found it hilarious. The haathi, gadha, Apple, Mango, the situation - all add up to it.
Ek gadha ped par chadha to oopar baithe haathi ne poochha, "Tu kyun chadha ?"
Gadhe ne kaha, "Apple khaane".
To haathi ne bola "Lekin buddhu, yeh to Mango tree hai!"
Phir gadhe ne kaha, "Maloom hai, main apple saath laaya hoon."
-Did this make you laugh? Maybe not. The first time I read it, I found it hilarious. The haathi, gadha, Apple, Mango, the situation - all add up to it.
Thursday, February 10, 2005
Good and evil
This thought has occurred to me in the past.
It never feels good to be wronged. But people respond to it in different ways. Some feel bad, and resolve not to wrong others in the same way. Others decide that since they have been treated unfairly, they will treat others in a like manner.
That is perhaps the point where the good and the evil part ways.
It never feels good to be wronged. But people respond to it in different ways. Some feel bad, and resolve not to wrong others in the same way. Others decide that since they have been treated unfairly, they will treat others in a like manner.
That is perhaps the point where the good and the evil part ways.
Tuesday, February 08, 2005
Hi and welcome!
This is my first post to my blog.
I was reading quotations by G.B.Shaw, and came across some witty ones. Maybe they were funny cos they reminded me of people I knew. In any case, here are a few :)
"I learned long ago, never to wrestle with a pig. You get dirty, and besides,the pig likes it."
"She had lost the art of conversation, but not, unfortunately, the power of speech."
"Patriotism is your conviction that this country is superior to all others because you were born in it."
I was reading quotations by G.B.Shaw, and came across some witty ones. Maybe they were funny cos they reminded me of people I knew. In any case, here are a few :)
"I learned long ago, never to wrestle with a pig. You get dirty, and besides,the pig likes it."
"She had lost the art of conversation, but not, unfortunately, the power of speech."
"Patriotism is your conviction that this country is superior to all others because you were born in it."
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