This is a drawing of Albert Einstein I drew when I was in 9th standard.
Monday, December 31, 2007
Tuesday, December 4, 2007
And the sun rises!!!
I have a question to ask. Are sunrise and sunset symmetrical? What I mean is that given the fact that one never visited the place in the photograph will he/she be able to tell if the picture is that of sunset or sunrise?
There may be few factors like fog in the morning that helps determine this but if there is no fog will it still be possible?
There may be few factors like fog in the morning that helps determine this but if there is no fog will it still be possible?
Friday, November 30, 2007
Mathematical Induction
Monday, November 26, 2007
Global Warming: A new approach
Almost everyone knows about global warming. And everyone thinks that carbon dioxide and other greenhouse gases are the culprit. I have a different view of the scenario. My reasoning is based on the law of conservation of energy and the kinetic theory of gases.
Background:
Our present idea of global warming is based on the fact that heat radiations are trapped by the greenhouse gases and hence, the average temperature of the atmosphere is rising. If we look into this we are actually referring to the heat radiations from the sun being trapped. We are not considering any heat that is being generated on our planet or we are simply ignoring it; assuming that it is too less compared to what greenhouse gases trap (well I do not know how correct this is). I have a different view of the problem and it related to mainly the heat that is generated on earth.
Important Laws:
Following laws should be noted:
1. “Energy can neither be created nor destroyed; it can only be transformed from one form to another” – law of conservation of energy
2. “Kinetic energy of a molecule is directly proportional to the absolute temperature” – from the kinetic theory of gases
My argument goes like this:
Any process that occurs on earth uses some energy. A part of the energy is used to do the work while the remaining part is lost in some unusable form. These unusable forms can be any form of energy. Consider for example the horn blown by an automobile; it is a conversion of electrical energy to sound energy, i.e. compression and rarefaction to the air. The sound would travel some distance and ultimately fade away. Now this energy which was sound energy earlier is lost into some form of energy. Well what is it? The sound energy is lost into the motion of the components of air (which are mostly gases and water vapor), hence the average kinetic energy of the molecules increases. From (2) we have that the temperature of the air has also increased. Other processes that occur might directly heat up the air resulting in the increase in the temperature.
I do not disagree with the fact that the amount of increase in the temperature would be really less (0+ for all practical purposes). But there is not just one process that is going on, there are infinite such processes. Hence, the temperature increase now becomes
Infinity x Zero = (which might be finite)
Our problem is now to determine what is this finite value and how well can this model predict rise in temperature.
I strongly believe that the heat generated by various processes occurring on earth is big reason for global warming and hence, less blame must be given to the greenhouse gases.
Background:
Our present idea of global warming is based on the fact that heat radiations are trapped by the greenhouse gases and hence, the average temperature of the atmosphere is rising. If we look into this we are actually referring to the heat radiations from the sun being trapped. We are not considering any heat that is being generated on our planet or we are simply ignoring it; assuming that it is too less compared to what greenhouse gases trap (well I do not know how correct this is). I have a different view of the problem and it related to mainly the heat that is generated on earth.
Important Laws:
Following laws should be noted:
1. “Energy can neither be created nor destroyed; it can only be transformed from one form to another” – law of conservation of energy
2. “Kinetic energy of a molecule is directly proportional to the absolute temperature” – from the kinetic theory of gases
My argument goes like this:
Any process that occurs on earth uses some energy. A part of the energy is used to do the work while the remaining part is lost in some unusable form. These unusable forms can be any form of energy. Consider for example the horn blown by an automobile; it is a conversion of electrical energy to sound energy, i.e. compression and rarefaction to the air. The sound would travel some distance and ultimately fade away. Now this energy which was sound energy earlier is lost into some form of energy. Well what is it? The sound energy is lost into the motion of the components of air (which are mostly gases and water vapor), hence the average kinetic energy of the molecules increases. From (2) we have that the temperature of the air has also increased. Other processes that occur might directly heat up the air resulting in the increase in the temperature.
I do not disagree with the fact that the amount of increase in the temperature would be really less (0+ for all practical purposes). But there is not just one process that is going on, there are infinite such processes. Hence, the temperature increase now becomes
Infinity x Zero = (which might be finite)
Our problem is now to determine what is this finite value and how well can this model predict rise in temperature.
I strongly believe that the heat generated by various processes occurring on earth is big reason for global warming and hence, less blame must be given to the greenhouse gases.
Friday, November 23, 2007
Cambridge to launch scholarship in Manmohan Singh's name
In a unique honour to Prime Minister Manmohan Singh, his Cambridge alma mater St John's will launch a scholarship in his name in New Delhi next week to help spot and develop potential Indian leaders in the fields of science and technology, economics and the social sciences.
The privately funded Manmohan Singh Scholarship will send three deserving, means-tested scholars every year to St John's College, Cambridge University, where a young Singh read economics and won the Wright's Prize for distinguished performance in the mid-1950s.
"There has always been an important tradition at Cambridge University of identifying, developing and nurturing leaders," said Stephen Teal, Development Director of St John's.
"There have been leaders such as Jawaharlal Nehru, Amartya Sen and Rajiv Gandhi and, of course, Manmohan Singh. We want to continue that tradition in the areas of science and technology, economics, and social sciences," Teal told IANS.
The scholarships, sponsored by private sector giants British Petroleum, Tata and Rolls Royce, will initially fund three PhD places beginning January 2008, but seek to take the number up to at least four by 2009. The closing date for the first year's applications is the end of January 2008.
The prime minister as well as St John's Master, Prof Christopher Dobson, will attend the Nov 27 launch.
"This scheme has been named after one of our most notable alumni -- and we are very proud of our association with Dr Singh and of what he has done for India," Teal added.
The idea of the scholarship came jointly from an ex-student and an ex-master of St John's. Both wanted to help bright young Indians who could not otherwise afford to study at Cambridge.
Indian-born student Abhijit Banerjee, CEO of Immediance, the world's first online stock exchange for shares in private companies, and former master Richard Perham wrote jointly to Singh in 2004 suggesting a scholarship in his name. The proposal was developed during a meeting of St John's alumni over dinner at the prime minister's residence last year.
Subsequently, Singh visited Cambridge in autumn 2006, where he spoke fondly of his years at St John's and of the "inclusive character" of Cambridge, which had welcomed both Nehru, who had had an exclusive schooling at Harrow, as well as him.
"Before the First World War, a young man from Allahabad came up to Trinity via Harrow. After the Second War, a simple young Indian came to St John's from an obscure university in Punjab. Cambridge University embraced both," he said in a moving speech on 'inclusive globalisation'.
"It was then that we realised just how fond Dr Singh was of the place," said Teal. "We knew that the university was trying to set up ties with India, and we came up with this scheme, which is the first of its kind for PhD students."
As possibly the most academically qualified head of government in the world, Manmohan Singh is thought to be a fitting candidate after whom a scholarship that seeks to spot and grow potential leaders from among academics should be named.
"We hope it's the first step in greatly increased cooperation and collaboration between India and the UK," Teal added.
Hindustan Times article
Official page of the scholarship
The privately funded Manmohan Singh Scholarship will send three deserving, means-tested scholars every year to St John's College, Cambridge University, where a young Singh read economics and won the Wright's Prize for distinguished performance in the mid-1950s.
"There has always been an important tradition at Cambridge University of identifying, developing and nurturing leaders," said Stephen Teal, Development Director of St John's.
"There have been leaders such as Jawaharlal Nehru, Amartya Sen and Rajiv Gandhi and, of course, Manmohan Singh. We want to continue that tradition in the areas of science and technology, economics, and social sciences," Teal told IANS.
The scholarships, sponsored by private sector giants British Petroleum, Tata and Rolls Royce, will initially fund three PhD places beginning January 2008, but seek to take the number up to at least four by 2009. The closing date for the first year's applications is the end of January 2008.
The prime minister as well as St John's Master, Prof Christopher Dobson, will attend the Nov 27 launch.
"This scheme has been named after one of our most notable alumni -- and we are very proud of our association with Dr Singh and of what he has done for India," Teal added.
The idea of the scholarship came jointly from an ex-student and an ex-master of St John's. Both wanted to help bright young Indians who could not otherwise afford to study at Cambridge.
Indian-born student Abhijit Banerjee, CEO of Immediance, the world's first online stock exchange for shares in private companies, and former master Richard Perham wrote jointly to Singh in 2004 suggesting a scholarship in his name. The proposal was developed during a meeting of St John's alumni over dinner at the prime minister's residence last year.
Subsequently, Singh visited Cambridge in autumn 2006, where he spoke fondly of his years at St John's and of the "inclusive character" of Cambridge, which had welcomed both Nehru, who had had an exclusive schooling at Harrow, as well as him.
"Before the First World War, a young man from Allahabad came up to Trinity via Harrow. After the Second War, a simple young Indian came to St John's from an obscure university in Punjab. Cambridge University embraced both," he said in a moving speech on 'inclusive globalisation'.
"It was then that we realised just how fond Dr Singh was of the place," said Teal. "We knew that the university was trying to set up ties with India, and we came up with this scheme, which is the first of its kind for PhD students."
As possibly the most academically qualified head of government in the world, Manmohan Singh is thought to be a fitting candidate after whom a scholarship that seeks to spot and grow potential leaders from among academics should be named.
"We hope it's the first step in greatly increased cooperation and collaboration between India and the UK," Teal added.
Hindustan Times article
Official page of the scholarship
Monday, September 24, 2007
Clothes Don't Make a Man
Click on the image to read the articleI must also state (now that I know) that, the above story is not correct. Please follow the links for the real story:
http://www.harvard.edu/siteguide/faqs/faq19.html
http://www.harvard.edu/siteguide/faqs/stanford.html
http://www.stanford.edu/home/stanford/history/begin.html
http://www.harvard.edu/siteguid
http://www.harvard.edu/siteguid
http://www.stanford.edu/home
Saturday, September 22, 2007
Wednesday, September 12, 2007
73939133
73939133: I came across this fact. This is really cool. The specialty of this number is not just that it is a prime number but, every number that is produced by removing the last digit one by one is also a prime number. So, the following numbers are all prime.
7393913
739391
73939
7393
739
73
7
This is the largest such number known (as of today).
Friday, September 7, 2007
Every natural number is interesting
There is an interesting theorem in Mathematics. It states that every number is an interesting number. The proof is as follows and is based on the principle of mathematical induction:
One is interesting because it is the first natural number. Two is interesting because it is the first even number. Three is interesting because it is the first odd prime number. Let us now assume that the first ‘n’ numbers are interesting so that ‘n+1’ can possibly be uninteresting. But, this number will also be interesting as it is the first uninteresting number. Hence, by the principle of mathematical induction the all natural numbers are interesting.
Tuesday, July 10, 2007
Decisions....
Somewhere I read this
"There are no right decisions.
You have to make your decisions right."
I believe that whenever an out of the box decision is made. People always ridicule it. It is the responsibility of the person to prove that his idea was great. Fools will think the people are right.
"There are no right decisions.
You have to make your decisions right."
I believe that whenever an out of the box decision is made. People always ridicule it. It is the responsibility of the person to prove that his idea was great. Fools will think the people are right.
Wo dekho ek Software engineer ja raha hai
अपने प्रोजेक्ट के बोझ टेल दबा जा रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
ज़िंदगी से हरा हुआ है,
पर "बग्स" से हार नही मनाता,
अपने ऍप्लिकेशन की एक एक लाइन इसे रटी हुई है,
पर आज कौन से रंग के मोजे पहने हैं , ये नही जनता,
दीन पर दीन एक एक्सेल फ़ाइल बनता जा रह है
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
दस हजार लाइन के कोड मैं एर्रोर ढूँढ लेते हैं लेकिन,
मजबूर दोस्त की आँखों की नमी दिखाई नही देती,
पीसी पे हजार विन्डोज़ खुली हैं,
पर दिल की खिड़की पे कोई दस्तक सुनाई नही देती,
satuday-sunday नहाता नही, वीक देस को नहा रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
कोडिंग करते करते पता ही नही चला,
बग्स की प्रिओरिटी कब माँ-बाप से हाई हो गयी,
किताबों मैं गुलाब रखने वाला , cigerette के धुएं मैं खो गया,
दिल की ज़मीन से अरमानों की विदाई हो गयी,
वीकेंड्स पे दारू पीके जो जश्न मन रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
मेज़ लेना हो इसके तो पूछ लो,
"सलारी इन्क्रेमेंट" की पार्टी कब दिला रहे हो,
हंसी उड़ाना हो तो पूछ लो,
"Onsite" कब जा रहे हो?
वो देखो Onsite से लौटे टीम-मेट की चोकोलेट्स खा रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
खर्चे बढ़ रहे हैं,
बाल कम हो रहे हैं,
KRA की डेट अति नही,
इन्कम टैक्स के सितम हो रहे हैं,
लो फिर से बस छूट गयी, ऑटो से आ रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
पिज्जा गले से नही उतरता,
तो "काके" के सहारे निगल लीया जाता है,
ऑफिस की "थाली" देख मुँह है बीगाड़ता,
माँ के हाथ का वो खाना रोज़ याद आता है,
"स्प्रोउट भेल" बनी है फीर भी, फ्री "Evening Snacks" खा रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
आपने अब तक ली होंगी बहुत सी चुतिकिया,
सोफ्त्वारे एन्ग्ग. के जीवन का सच बताती ये आखरी कुछ पंक्तियाँ,
हज़ारों की तनख्वाह वाला, कंपनी की करोडों की जेब भरता है,
सोफ्त्वारे एन्ग्ग. वही बन सकता है, जो लोहे का जिगर रखता है,
हम लोग जी जी के मरते हैं , ज़िंदगी है कुछ ऐसी,
एक फौज की नौकरी, दूसरी सोफ्त्वारे इंजिनियर की , दोनो एक जैसी,
इस कविता का हर शब्द मेरे दील की गहराई से आ रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
ज़िंदगी से हरा हुआ है,
पर "बग्स" से हार नही मनाता,
अपने ऍप्लिकेशन की एक एक लाइन इसे रटी हुई है,
पर आज कौन से रंग के मोजे पहने हैं , ये नही जनता,
दीन पर दीन एक एक्सेल फ़ाइल बनता जा रह है
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
दस हजार लाइन के कोड मैं एर्रोर ढूँढ लेते हैं लेकिन,
मजबूर दोस्त की आँखों की नमी दिखाई नही देती,
पीसी पे हजार विन्डोज़ खुली हैं,
पर दिल की खिड़की पे कोई दस्तक सुनाई नही देती,
satuday-sunday नहाता नही, वीक देस को नहा रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
कोडिंग करते करते पता ही नही चला,
बग्स की प्रिओरिटी कब माँ-बाप से हाई हो गयी,
किताबों मैं गुलाब रखने वाला , cigerette के धुएं मैं खो गया,
दिल की ज़मीन से अरमानों की विदाई हो गयी,
वीकेंड्स पे दारू पीके जो जश्न मन रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
मेज़ लेना हो इसके तो पूछ लो,
"सलारी इन्क्रेमेंट" की पार्टी कब दिला रहे हो,
हंसी उड़ाना हो तो पूछ लो,
"Onsite" कब जा रहे हो?
वो देखो Onsite से लौटे टीम-मेट की चोकोलेट्स खा रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
खर्चे बढ़ रहे हैं,
बाल कम हो रहे हैं,
KRA की डेट अति नही,
इन्कम टैक्स के सितम हो रहे हैं,
लो फिर से बस छूट गयी, ऑटो से आ रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
पिज्जा गले से नही उतरता,
तो "काके" के सहारे निगल लीया जाता है,
ऑफिस की "थाली" देख मुँह है बीगाड़ता,
माँ के हाथ का वो खाना रोज़ याद आता है,
"स्प्रोउट भेल" बनी है फीर भी, फ्री "Evening Snacks" खा रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है,
आपने अब तक ली होंगी बहुत सी चुतिकिया,
सोफ्त्वारे एन्ग्ग. के जीवन का सच बताती ये आखरी कुछ पंक्तियाँ,
हज़ारों की तनख्वाह वाला, कंपनी की करोडों की जेब भरता है,
सोफ्त्वारे एन्ग्ग. वही बन सकता है, जो लोहे का जिगर रखता है,
हम लोग जी जी के मरते हैं , ज़िंदगी है कुछ ऐसी,
एक फौज की नौकरी, दूसरी सोफ्त्वारे इंजिनियर की , दोनो एक जैसी,
इस कविता का हर शब्द मेरे दील की गहराई से आ रह है,
वो देखो एक सोफ्त्वारे इंजिनियर जा रह है
Wednesday, July 4, 2007
Has the world changed
Yesterday we were discussing whether or not the world has changed? I am not saying technologically. But have the hearts of people changed or are they still as they were. The problem that we faced was how to determine such a thing. There has to be a quantitative basis for such a thing; and how do we do that??
For this I have made the following assumptions:
1. The measurement will be made by some third party. Some one who does not belong to earth (no no...i am not talking about the Jupiter citizen SABU from the Chacha Choudhary comics, neither am I talking about Superman he is from a different plant too but both of them shall be considered as parts of the earth system). Someone else say, an alien.
2. I assume that they have access to all news. For them the earth is a black box news is the only way they can know about anything internal.
3. A ratio good : bad : : 2 : 1 is considered as acceptable good.
Here is what they do. First count the number of good events and the bad events. For simplicity it is assumed that all the events are equally important; this may be later refined- and the front page news might be given more importance. Once, they have calculated the numbers they find the ratio good to bad. If ratio has become larger the world has become a better place, if it has become smaller then it has become bad and remains the same if the world is still the same.
For this I have made the following assumptions:
1. The measurement will be made by some third party. Some one who does not belong to earth (no no...i am not talking about the Jupiter citizen SABU from the Chacha Choudhary comics, neither am I talking about Superman he is from a different plant too but both of them shall be considered as parts of the earth system). Someone else say, an alien.
2. I assume that they have access to all news. For them the earth is a black box news is the only way they can know about anything internal.
3. A ratio good : bad : : 2 : 1 is considered as acceptable good.
Here is what they do. First count the number of good events and the bad events. For simplicity it is assumed that all the events are equally important; this may be later refined- and the front page news might be given more importance. Once, they have calculated the numbers they find the ratio good to bad. If ratio has become larger the world has become a better place, if it has become smaller then it has become bad and remains the same if the world is still the same.
Tuesday, June 19, 2007
On Image Compression
"A picture is worth a thousand words."
-an ancient saying
"But, pictures cost you a million pixels."
-Shishir Pandey (on need for image compression)
-an ancient saying
"But, pictures cost you a million pixels."
-Shishir Pandey (on need for image compression)
Friday, June 15, 2007
India and China connect the world!!!
There is a theory called the "Six degrees of separation". According to this any person in the whole world is separated by any other person in the world by an average of six people.
For e.g : I know my friend Ashish with zero degree of separation. He knows his mother. So, the degree of separation between me and his mother is one. As I know Ashish who knows his mother. Similaretly if you are reading this and you know Ashish and do not know me the degree of separation between you and me is again one.
Let's get back to statistics (a very powerful tool but should be used carefully). We know that every 5th person in the world is a Chinese and every 6th person is an Indian. So, according to the theory "INDIAN AND CHINA CONNECT THE WORLD".
For more details on the theory, please refer to http://smallworld.columbia.edu project
For e.g : I know my friend Ashish with zero degree of separation. He knows his mother. So, the degree of separation between me and his mother is one. As I know Ashish who knows his mother. Similaretly if you are reading this and you know Ashish and do not know me the degree of separation between you and me is again one.
Let's get back to statistics (a very powerful tool but should be used carefully). We know that every 5th person in the world is a Chinese and every 6th person is an Indian. So, according to the theory "INDIAN AND CHINA CONNECT THE WORLD".
For more details on the theory, please refer to http://smallworld.columbia.edu project
Tuesday, May 29, 2007
How God used fuzzy logic!!!
In this post I will be pointing out how Lord Vishnu has used basic ideas from the fuzzy logic theory (that if a point lies on the fuzzy boundary then is not a member of any of the sets that share the boundary) for solving his problem. The article is based on a Hindu mythological story.
The Story:
There was a king named Hiranyakashap. He undergoes many years of austerity and penance. Bramha appears in front of Hiranyakashap and offers him a boon. Hiranyakashap asks for immortality. Bramha says that he will not be able to grant such a wish as everyone has to die one day. Then Hiranyakashap ask that- he should not be killed by any creature created by Bramha. He should not die within the residence or outside it, neither during the day nor during the night; neither on the ground nor on the sky; neither by a human nor by an animal; neither by any demigod nor by a demon nor by a weapon.
Hiranyakashap now considered himself to be god as it was virtually impossible to kill him. He wanted everyone to worship him. To his dismay his own son, Prahalada, was a devotee of God Vishnu which he did not like. He tried to kill Prahalada a number of times but was always unsuccessful. One day the he got very angry and asked his son if the god was there in the pillar he was pointing to. To which Prahalada answered that god Vishnu was there. Suddenly, the pillar split apart and Narsimha (the 4th incarnation of Lord Vishnu) appeared. He was part lion and part man i.e. according to fuzzy logic neither human nor animal. This happened in the evening i.e. neither in day nor at night. Hiranyakashap was taken to the entrance of his residence so that a part of his body would be inside the residence and the other outside the residence i.e. neither inside nor outside the residence. Lord put him on his knees i.e. neither on ground nor in the sky. Then he used his nails (not a weapon) to tear away Hiranyakashap’s body and killed him.
Hence, we see how God used the fuzzy logic to kill Hiranyakashap.
The Story:
There was a king named Hiranyakashap. He undergoes many years of austerity and penance. Bramha appears in front of Hiranyakashap and offers him a boon. Hiranyakashap asks for immortality. Bramha says that he will not be able to grant such a wish as everyone has to die one day. Then Hiranyakashap ask that- he should not be killed by any creature created by Bramha. He should not die within the residence or outside it, neither during the day nor during the night; neither on the ground nor on the sky; neither by a human nor by an animal; neither by any demigod nor by a demon nor by a weapon.
Hiranyakashap now considered himself to be god as it was virtually impossible to kill him. He wanted everyone to worship him. To his dismay his own son, Prahalada, was a devotee of God Vishnu which he did not like. He tried to kill Prahalada a number of times but was always unsuccessful. One day the he got very angry and asked his son if the god was there in the pillar he was pointing to. To which Prahalada answered that god Vishnu was there. Suddenly, the pillar split apart and Narsimha (the 4th incarnation of Lord Vishnu) appeared. He was part lion and part man i.e. according to fuzzy logic neither human nor animal. This happened in the evening i.e. neither in day nor at night. Hiranyakashap was taken to the entrance of his residence so that a part of his body would be inside the residence and the other outside the residence i.e. neither inside nor outside the residence. Lord put him on his knees i.e. neither on ground nor in the sky. Then he used his nails (not a weapon) to tear away Hiranyakashap’s body and killed him.
Hence, we see how God used the fuzzy logic to kill Hiranyakashap.
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