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Birthday Paradox

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We all have encountered coincidences of sort in our lives. For example, it happens that we keep on thinking about a particular person and suddenly we get a phone call or email or even a visit from that person. Similarly, we promise to meet someone at a particular time and venue but out of no where something emergency turns up and have to cancel the previously agreed meeting. A list of such coincidences can get very long. Mathematics also has a term for such coincidences and it is called Probability. There are so many things in Probability Theory that surprises us. And, one such is Birthday paradox.

In Probability Theory, ‘Birthday Paradox’ refers, that in a group containing certain randomly chosen people, there is a finite probability for some two people to have exactly the same birthday. For a group with 23 people, this probability is around 50%. This increases exponentially as the number people in the group increases. With as many as 80 people, the probability gets around 100%. This is of course, based on the idea that people are randomly chosen and each day is equally likely to become a birthday for someone.

For more details you may visit http://en.wikipedia.org/wiki/Birthday_problem.

Birthday paradox holds an important position in computer security also. It can be used to attack the hash functions. For example, let us say f is a hash function such as f(x) = y. With hash functions, it should be impossible to guess ‘x’ given ‘y’. In other words they are one way. Another characteristic is that it should be very difficult to find two inputs that yield same output i.e. it should be hard to find x1 and x2 such that f(x1) = y and f(x2) = y. This property is called collision resistance. But using birthday paradox it becomes relatively easier to find such collisions.

Today 16 May is my birthday. And, in facebook I have around 275 friends. Interesting thing is that I do not have a single friend whose birthday coincides with mine. So either some of them have entered incorrect birth date or hidden their birth date from display or for some reason facebook is not notifying me of this. Otherwise, based on birthday paradox I should have at least one friend with birthday today. Perhaps if I include the ‘near-miss effect’ then we can get some coincidences. For example, number of people with birthday separated by certain days. Such latitude will increase the probability of coincidence. But originally birthday paradox theory does not include this near miss effect.

Written by prajwalan

May 16, 2010 at 1:13 pm

Music

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It is hard to find someone who doesn’t like any music at all. Music has many forms and varieties. They not only entice our ears but also refresh us and some even touch our soul and inspire us to do something particular. They reflect the culture, religion and history of the place from where they originate.  Hence music from different corners of the globe carry different sense, melody, harmony and notes.

Scientifically, music is an art form with sound as its medium [1]. Therefore, music is composed of sound waves vibrating with different frequencies and pitches [2]. One might wonder the difference between music and noise. While a particular sound pattern may be considered music by some, the same might be regarded as noise by others. However, scientists and researchers have attempted to point out the differences in mathematical terms. One source [3] mentions that “Music is sound with a discrete structure while noise is sound with a continuous structure.” Regardless of the mathematics behind music and noise, one thing is certain: music is what you find amusing and even noise can sometimes be musical to some.

As I write this article, I can hear chirping of birds outside my window. I find it melodious and I would consider it a music. But what about the birds? What are they trying to accomplish by making those sounds? Are they communicating? Or, are they just making some noise? I don’t believe that mathematics can explain that. They could be communicating or making noise, but I am finding it musical. So, noise or vocal communication can also be considered music. It all depends on the listener. There is a saying, beauty lies on the eyes of beholder. I would say something similar for the music also: “Musical value lies on the senses of perceiver”.

We have often heard that music has no language barriers. I believe this is true. Personally speaking, I listen to music from different parts of the world. It really does not matter what culture or religion or race the particular place belongs to.

Following are two links to music from Nepal.

Instrumental 1

Instrumental 2

You can visit the site http://www.pronepal.com/ for more music and songs from Nepal.

Please put links to some good music from your country or other countries you know in the comment below.

Written by prajwalan

May 13, 2010 at 4:01 pm

Happy Gautum Buddha Jayanti

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On this occassion of Gautum Buddha Jayanti, I would like to remind myself and the visitors of my blog with following quote by Gautum Buddha.

 

Your work is to discover your world and then with all your heart give yourself to it.

-Gautum Buddha

 

I hope I will be able to understand it and understanding it truely means, I should be able to implement it. I hope I will be able to do so. Likewise, I wish you will be able to understand it and implement it as well.

Written by prajwalan

May 9, 2009 at 6:35 am

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Best of Karna Das

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I am a big fan of sentimental songs, particularly those sung by Karna Das. I just love the way he sings. His singing style is really unique and heart touching. Many of his songs are so dear to me that I listen to them several times each week or sometimes everyday. Yet, I can’t get enough.

I have listed some of the best songs by him. I hope you will also like them.

1. Sunsan raat shital pawan

URL : http://www.youtube.com/watch?v=MNSYsGEcjv4

सुनसान रात सितल पवन, साथी तिम्रो याद बिदेशी भुमी
बिती रहेछ जिवन यहाँ, माया तिम्रो हो पत्र चुमी
सुनसान रात ….
कहिले हाँस्छु कहिले रुन्छु, माया म है पागल सरी
तिम्रो तस्विर हेरी रहन्छु, तिम्रो पत्र है पढछु घरी
तिम्रो पत्र है पढछु घरी घरी ।
सुनसान रात ….
ला ला ला ला ला ला ला
हाम्रो मिलन को मधुर क्षण आउदै छ नजिक सुस्तरी
कसम छ है तिमी लाई नभयी निराश, माया बस है बाटो हेरी
माया बस है बाटो हेरी ।
सुनसान रात सितल पवन, साथी तिम्रो याद बिदेशी भुमी
बिती रहेछ जिवन यहाँ, माया तिम्रो हो पत्र चुमी
सुनसान रात ….

 

2. Ma mereko chaina aajhai

URL : http://www.youtube.com/watch?v=QwMMn2RZPco

3. Hamro prem ko katha

URL : http://www.youtube.com/watch?v=f5WRFEMtVtI

4. Kehi pal aaba baki cha

URL : http://www.pronepal.com/index.php?action=playwinfile&id=580

5. Tyo premko balidaan

URL : http://www.pronepal.com/index.php?action=playwinfile&id=429

6. Kati bibaas cha tyo jeevan

URL : http://www.pronepal.com/index.php?action=playwinfile&id=433

 7. Jindagi ko ke bharosa

URL : http://www.youtube.com/watch?v=C4faF2L7hMo

8. Purano dunga, pani ko chaala

URL : http://www.youtube.com/watch?v=iA_K8G0f5WE

9. Anautho betha bhayecha mero prem kahani

URL : http://www.youtube.com/watch?v=LTrPf2X8Ofg

10. Timro mero sambandha ko

URL : http://www.youtube.com/watch?v=HbC8PYTTD1c

If you have lyrics of these songs or any other songs by Karna Das,

then please send me or put them as comments.

I will apprecitate that a lot.

Written by prajwalan

October 29, 2008 at 3:01 pm

Humans should learn from dogs

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Will you save someone risking your own life ?

You may answer yes, but will you really do it in some situation like that ?

Just take a look at what this dog did…

http://video.aol.com/video-detail/lifesaving-dog/2725276255

The question here is not just saving life, its more than that. It is about doing the right thing. We always have a choice to make the right decision. But quiet often we choose the wrong decision because that wrong decision seems to be beneficial for us. We happen to choose the wrong decision because our selfish needs are fulfilled with that wrong decision.

Just take a look at the dog’s eyes. They are so innocent. He saved the life of those kittens without thinking he is risking his own life. What might have been going through the mind of his as he stayed besides the kittens despite the fire ? He definitely must have had an option to run away or jump around making noises in anticipation of rescue. But he thought staying by the kittens and making sure they they don’t feel alone and don’t get scared is more important than saving his own life. And by the time fire fighters arrived he was unconscious due to excessive smoke inhalation. But he was alive and the reunion with the kittens must have been the reward for him. This is an example of condition-less affection and an act of making right decision.

This dog did something that a human would never do. Thus, shouldn’t human learn something from dogs ?

Written by prajwalan

October 28, 2008 at 3:26 pm

Posted in General, Interesting Things

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NTNU and Trondheim… from the lens of my camera

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Looking at following pictures, Trondheim looks really beautiful. Outdoor pictures of NTNU are also equally good.

I will be taking more pictures and will soon post here. But for now, lets enjoy with these.

Please note that the pictures are randomly ordered.

Credit: My Canon Ixus 70 🙂

Written by prajwalan

July 26, 2008 at 9:25 pm

Landscape of memory – Vintage pictures of Kathmandu

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We all know how Kathmandu looks these days. Its over crowded, polluted and stinks with sewage. But lets travel into time for a moment and go back around hundred years. Lets see how Kathmandu looked then.

Looking at following pictures, one can imagine how beautiful and quiet Kathmandu was then. There was no sound pollution and no air pollution and population was definitely limited. I found these pictures in the kathmanduspeaks.blogspot.com. The links are as below.

1. http://kathmanduspeaks.blogspot.com/2007/06/beauty-of-old-kathmandu-photographs.html

2. http://kathmanduspeaks.blogspot.com/2008/06/more-old-kathmandu-photographs.html

Also, in nepalitimes.com. The link is http://www.nepalitimes.com.np/issue/362/Review/13875.

I liked these pictures so much, that I could not stop myself from downloading them and decorating my blog with them.

So here it goes…

Written by prajwalan

July 21, 2008 at 11:34 am