## Tuesday, December 2, 2008

## Thursday, October 30, 2008

### Triangle inequality and the Kollywood Kidnap

Welcome Back!

Introduction

---------------

For the purposes of this post, we need to travel back a little bit in time. Not by a great factor though. May be a decade or two.

Ready?

Okay.

Tighten your seat belts.

Here we go !

swssssshhhhhhhhhhhhhhhhhhhhh....

1990!

Well, Can you see there a wonderful smart 5 year old little kid in school sitting near a cute little girl and trying to be impressive. Mind you,We are NOT talking about that kid anywhere in this post. That useless brat will grow up in future into a stupid young chap who would irritate people by asking them to read his useless blogs. Anyway, lets forget him and the girl sitting next to him and come back to the point of this post.

Kollywood Kidnap

----------------

How many times have we seen a kidnap scene in Kollywood movies of the nineties? A lot of talented directors have handled various techniques to make such kidnap scenes look different from others but have miserably and invariably failed each time they tried so.

Reasons:

1) It is always one of these two people who get kidnapped. The Heroine or the Hero's younger sister (Yeah, the younger one. When on earth did a tamil hero have an elder sister?)

2) It is always the villain who kidnaps . Of course, he has a gang of well built men who actually do the kidnapping. The villain just lives for eternity in a dark room with dangerously hanging red light bulbs that light up the 'puli bommai' that stands at one corner of the room'. In certain special cases, the villain has a globe in front of his seat which for mysterious reasons he keeps on rotating.

3) If the Hero's sister gets kidnapped, then there is every chance she gets harassed whereas if it is the heroine, then the hero will wait till the villain (and his gang) touch her (so that the "C" grade repeat audience get something to watch ) and then jumps from nowhere right on the top of the villains back.

Such were the crudely done movies of the nineties.

If you are hating the Indian directors for their lack of creativity at trying out something new, then please RETHINK!

Let me narrate one common scene that you might have seen in most of these kidnap related movies.

THE COMMON SCENE

----------------

The hero for unknown reasons is not in the house (may be he has gone to work... i know its really tough to believe that Tamil hero's go to regular 8-5 work). The villain gang (let me use VG in the future to refer to the villain gang) makes use of this situation and goes into the hero's house. The heroine stays alone. VG kidnaps the poor girl who would have otherwise done some innocent looking embroidery and killed time thinking about the hero ( I am not being a chauvinist here, i am just portraying what was shown).

Now for the twist.

The hero returns early to home. Sometimes it is the wallet that he forgot, sometimes he wanted to kiss the heroine once more before he left, sometimes he heard the 'eternal voice' that warned him of impending doom... or whatever crap reason it may be, the hero is back home now.

(TO digress a little bit at this point, if we look at Ramayana, the story is so similar till now. Just that Valmiki was not so dumb like the Indian directors that he never made Rama return back in time when Sita was kidnapped. May be because

Rama never used a Wallet.... watever )

THE CHASE

----------

The hero finds by mere smell that something is wrong in the house. He immediately rushes out and amazingly enough identifies the jeep marks on the soil in front of the house. The heroes eyes are zoomed into now. They burn with red anger. Now his mouth. It moves little bit with terror until the words come out like arrows just out of a bow - "VGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG" .

The chase begins.

Wait a minute!

Here we need to take a deep breath. It is very important that we do so because what is coming is totally mathematical. Totally mind blowing stuff. The total genius of Indian directors will be out in the open lying bare naked for all of us to witness.

What is that which deserves such a huge build up?

Here is the question.

"The VG have already taken the heroine with them in their open jeep and are laughing dangerously at her. The hero's house is in the top of a dangerous hill. By the mere presence of the Jeep track marks, the hero has found out the direction in which the jeep is moving. How should the hero travel now so that he can reach the jeep in time?"

Answer:" TRIANGLE INEQUALITY"

TRIANGLE INEQUALITY

-------------------

Triangle inequality is such a simple fact that people often tend to overlook it.

It just states that

"the sum of the lengths two sides of a triangle is greater than the third side no matter how skewed or symmetric the triangle is"

To see a nice little example, consider the case of a right angled triangle.

The pythogorous theorem states that the square of the hypotenuse is equal to the sum of the squares of the right angled sides.

c^2 = a^2 + b^2

Now lets add 2*a*b to both sides

c^2 + 2ab = a^2+b^2+2ab = (a+b)^2

you see it , don't you?

Taking square root on both sides, we get

(a+b) = square_root( c^2 + 2*a*b)

Now the right hand side HAS to be greater than 'c' since we have an extra 2*a*b term lying nearby.

That shows a+b > c - the triangle inequality for a very special case of triangles.

This in fact works out for all triangles and the reader is advised to refer to "Real" mathematical texts to see the proof.

DID THE HEROINE SURVIVE?

------------------------

What a stupid question? What a dumb question?

How can the hero with the knowledge of triangle inequality miss to find the heroine. The hero just travels along one side of the triangle while the VG always travels the other two. So the hero travels less distance and so makes up for the time lost in searching for the heroine inside the kitchen!!

There you go.

One more useless post for such a simple concept!

Good bye folks till we meet for the next stupid tutorial.

-----------------------------------------------------------------------------------

The usual Disclaimer.

In case, you wanted to seriously kick the author's butt,

the contact address is in the previous post

-----------------------------------------------------------------------------------

Introduction

---------------

For the purposes of this post, we need to travel back a little bit in time. Not by a great factor though. May be a decade or two.

Ready?

Okay.

Tighten your seat belts.

Here we go !

swssssshhhhhhhhhhhhhhhhhhhhh....

1990!

Well, Can you see there a wonderful smart 5 year old little kid in school sitting near a cute little girl and trying to be impressive. Mind you,We are NOT talking about that kid anywhere in this post. That useless brat will grow up in future into a stupid young chap who would irritate people by asking them to read his useless blogs. Anyway, lets forget him and the girl sitting next to him and come back to the point of this post.

Kollywood Kidnap

----------------

How many times have we seen a kidnap scene in Kollywood movies of the nineties? A lot of talented directors have handled various techniques to make such kidnap scenes look different from others but have miserably and invariably failed each time they tried so.

Reasons:

1) It is always one of these two people who get kidnapped. The Heroine or the Hero's younger sister (Yeah, the younger one. When on earth did a tamil hero have an elder sister?)

2) It is always the villain who kidnaps . Of course, he has a gang of well built men who actually do the kidnapping. The villain just lives for eternity in a dark room with dangerously hanging red light bulbs that light up the 'puli bommai' that stands at one corner of the room'. In certain special cases, the villain has a globe in front of his seat which for mysterious reasons he keeps on rotating.

3) If the Hero's sister gets kidnapped, then there is every chance she gets harassed whereas if it is the heroine, then the hero will wait till the villain (and his gang) touch her (so that the "C" grade repeat audience get something to watch ) and then jumps from nowhere right on the top of the villains back.

Such were the crudely done movies of the nineties.

If you are hating the Indian directors for their lack of creativity at trying out something new, then please RETHINK!

Let me narrate one common scene that you might have seen in most of these kidnap related movies.

THE COMMON SCENE

----------------

The hero for unknown reasons is not in the house (may be he has gone to work... i know its really tough to believe that Tamil hero's go to regular 8-5 work). The villain gang (let me use VG in the future to refer to the villain gang) makes use of this situation and goes into the hero's house. The heroine stays alone. VG kidnaps the poor girl who would have otherwise done some innocent looking embroidery and killed time thinking about the hero ( I am not being a chauvinist here, i am just portraying what was shown).

Now for the twist.

The hero returns early to home. Sometimes it is the wallet that he forgot, sometimes he wanted to kiss the heroine once more before he left, sometimes he heard the 'eternal voice' that warned him of impending doom... or whatever crap reason it may be, the hero is back home now.

(TO digress a little bit at this point, if we look at Ramayana, the story is so similar till now. Just that Valmiki was not so dumb like the Indian directors that he never made Rama return back in time when Sita was kidnapped. May be because

Rama never used a Wallet.... watever )

THE CHASE

----------

The hero finds by mere smell that something is wrong in the house. He immediately rushes out and amazingly enough identifies the jeep marks on the soil in front of the house. The heroes eyes are zoomed into now. They burn with red anger. Now his mouth. It moves little bit with terror until the words come out like arrows just out of a bow - "VGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG" .

The chase begins.

Wait a minute!

Here we need to take a deep breath. It is very important that we do so because what is coming is totally mathematical. Totally mind blowing stuff. The total genius of Indian directors will be out in the open lying bare naked for all of us to witness.

What is that which deserves such a huge build up?

Here is the question.

"The VG have already taken the heroine with them in their open jeep and are laughing dangerously at her. The hero's house is in the top of a dangerous hill. By the mere presence of the Jeep track marks, the hero has found out the direction in which the jeep is moving. How should the hero travel now so that he can reach the jeep in time?"

Answer:" TRIANGLE INEQUALITY"

TRIANGLE INEQUALITY

-------------------

Triangle inequality is such a simple fact that people often tend to overlook it.

It just states that

"the sum of the lengths two sides of a triangle is greater than the third side no matter how skewed or symmetric the triangle is"

To see a nice little example, consider the case of a right angled triangle.

The pythogorous theorem states that the square of the hypotenuse is equal to the sum of the squares of the right angled sides.

c^2 = a^2 + b^2

Now lets add 2*a*b to both sides

c^2 + 2ab = a^2+b^2+2ab = (a+b)^2

you see it , don't you?

Taking square root on both sides, we get

(a+b) = square_root( c^2 + 2*a*b)

Now the right hand side HAS to be greater than 'c' since we have an extra 2*a*b term lying nearby.

That shows a+b > c - the triangle inequality for a very special case of triangles.

This in fact works out for all triangles and the reader is advised to refer to "Real" mathematical texts to see the proof.

DID THE HEROINE SURVIVE?

------------------------

What a stupid question? What a dumb question?

How can the hero with the knowledge of triangle inequality miss to find the heroine. The hero just travels along one side of the triangle while the VG always travels the other two. So the hero travels less distance and so makes up for the time lost in searching for the heroine inside the kitchen!!

There you go.

One more useless post for such a simple concept!

Good bye folks till we meet for the next stupid tutorial.

-----------------------------------------------------------------------------------

The usual Disclaimer.

In case, you wanted to seriously kick the author's butt,

the contact address is in the previous post

-----------------------------------------------------------------------------------

## Saturday, October 25, 2008

### egan vectors and nayanthara transformations !

The purpose of a blog like this is to introduce mathematics that the author does not understand to the widespread readers who don't exist. The basic assumption here is that the non-existent reader understands the language tamizh. (not necessarily to the extent of thirukural or silapadhigaaram though familiarity of these advanced topics is considered a plus)

Ok.

Its diwali time and when better can we get started?!

Egan:

-----

If you haven't heard the term egan before, then you invariably fall into one of these three categories

-> You are not a tamilian !

-> You are a die hard vijay fan !

-> You watched 'billa 2007' till interval and then decided that it is a sin to spend money on movies anymore.

As most people in Tamilnadu fall into one of these three categories, i need to take a minute to explain what "Egan" is. But before that let me make one leap of faith assumption that you know who USA is. If you are saying to yourself that i should

have written 'What USA is' and not 'Who USA is', then you are Dismissed ! Doomed ! Busted! Whatever!

How on earth can a Tamilian think of the United States of America as the expansion for USA when there is a better and fitting expansion right here in Tamilnadu. Yes! It is none other than our own "Ultimate Star Ajithkumar".

Ok.

Lets move on !

If you do a Google Image search for Egan, the first picture that pops up is that of a girl in a mini skirt. But that's certainly not our "current" topic of interest (Yes! Neither the girl (Kian Egan), nor her mini skirt (Brown color)).

So lets forget the girl and define what Egan is.

Well..Well.. it is complicated !

And that's where Mathevettica comes to the rescue.

Here we go!

Egan to Eigen

-------------

Well, if you happen to think both these terms sound pretty similar and so there could not be much of a difference in their semantics, then you got it right !

Eigen in some language (Italian probably) means 'characteristic' . Now Think of our USA and think of the word 'Characteristic'. Which word relates them together? Did you guess 'Failure?' . You are on the right track.

Eigen Vector

------------

Now onto some serious mathematics. Eigen Vector is the 'characteristic' vector of a "transformation". Wait a minute! What do i mean by a transformation? A transformation is nothing but a 'change'. You have a piece of wood in front of you and you tilt it a little bit, and that's a "transformation" of the wood for you !

If you represented each point on the wood by co-ordinates (x,y,z) and you tilt it, most of the points would now have gone to a different point in space (say x2,y2,z2 for each (x1,y1,z1)).

But note the use of the word "most". That means there might be some points that might not have changed its position at all!! Now i can hear you say 'hey..that's very specific to the transformation. It depends on how you tilt the piece of wood'. And i can't agree more. It is very specific to the transformation . In other words, it is 'characteristic' of the transformation. And such points (vectors) are exactly called the eigen vectors. They are characteristic of a transformation. They just don't change in direction! But wait a minute. The Eigen vectors will not change in direction. But then they can change in their magnitude. Think of a rubber band. Now if you pull the rubber band with full force with both hands, you are transforming its shape. But in the direction of your pull, the points just are transforming a little further in the same direction. (further here means distance/magnitude from the center).

Oh my goodness!

What on earth has all this crap got to do with USA?

Well, that's the crux of the post.

If you understood Eigen vectors already, then you can understand what 'Egan' is. Or if you already know what Egan is, try to get a hang of what Eigen vector . In either case, lets define the analogy below.

Analogy

--------

USA has decided to star in one more movie. Now don't start running towards the wall to bang your head. We all know it is unfortunate to the human community as a whole and we have to sail through sad times together. So lets make the best use of Egan by trying to understand the analogy with Eigen vectors.

What is the 'Characteristic' of an USA movie? 'Failure' - i can hear the shout from you guys! Now what if i say our beloved USA acts in two roles 'transforming' himself now and then. 'Failure still' !! Again, right answer folks. Now to one more question. It seems the director of this movie is Rajusundaram. What can you now say about this movie? Excellent going guys, it is the same answer and it fits very well everywhere!

"Failure" !

To summarize

No matter what happens i.e no matter how USA transforms himself in his movies, the direction will still be the same - crap!! So that's the closest you can get to Eigen vectors!

One final word:

---------------

I have a question for you folks. Before that let me quickly explain the term 'Eigen value' in one sentence.

'Eigen value' is the amount by which a Eigen vector changes in magnitude after a transformation. (of course, there is no change in direction)

Now what could be a possible, plausible "Egan value" of the movie???

In other words, if at all someone goes and watches this movie, what could be the value?

Answer: 9 !!!

Guess why? :)

Of course. You got it right again... the only "Egan Value" is Nayanthara !!!

There you go!!! That brings us to the end.

Good bye and happy Diwali till we meet for the next stupid tutorial !

---------------------------------------------------------------------

If in the most unfortunate case you wanted to seriously kick the author's

butt, here is the contact address.

Arun R,

Department of CSA,

Indian Institute of Science,

Bangalore.

---------------------------------------------------------------------------

Ok.

Its diwali time and when better can we get started?!

Egan:

-----

If you haven't heard the term egan before, then you invariably fall into one of these three categories

-> You are not a tamilian !

-> You are a die hard vijay fan !

-> You watched 'billa 2007' till interval and then decided that it is a sin to spend money on movies anymore.

As most people in Tamilnadu fall into one of these three categories, i need to take a minute to explain what "Egan" is. But before that let me make one leap of faith assumption that you know who USA is. If you are saying to yourself that i should

have written 'What USA is' and not 'Who USA is', then you are Dismissed ! Doomed ! Busted! Whatever!

How on earth can a Tamilian think of the United States of America as the expansion for USA when there is a better and fitting expansion right here in Tamilnadu. Yes! It is none other than our own "Ultimate Star Ajithkumar".

Ok.

Lets move on !

If you do a Google Image search for Egan, the first picture that pops up is that of a girl in a mini skirt. But that's certainly not our "current" topic of interest (Yes! Neither the girl (Kian Egan), nor her mini skirt (Brown color)).

So lets forget the girl and define what Egan is.

Well..Well.. it is complicated !

And that's where Mathevettica comes to the rescue.

Here we go!

Egan to Eigen

-------------

Well, if you happen to think both these terms sound pretty similar and so there could not be much of a difference in their semantics, then you got it right !

Eigen in some language (Italian probably) means 'characteristic' . Now Think of our USA and think of the word 'Characteristic'. Which word relates them together? Did you guess 'Failure?' . You are on the right track.

Eigen Vector

------------

Now onto some serious mathematics. Eigen Vector is the 'characteristic' vector of a "transformation". Wait a minute! What do i mean by a transformation? A transformation is nothing but a 'change'. You have a piece of wood in front of you and you tilt it a little bit, and that's a "transformation" of the wood for you !

If you represented each point on the wood by co-ordinates (x,y,z) and you tilt it, most of the points would now have gone to a different point in space (say x2,y2,z2 for each (x1,y1,z1)).

But note the use of the word "most". That means there might be some points that might not have changed its position at all!! Now i can hear you say 'hey..that's very specific to the transformation. It depends on how you tilt the piece of wood'. And i can't agree more. It is very specific to the transformation . In other words, it is 'characteristic' of the transformation. And such points (vectors) are exactly called the eigen vectors. They are characteristic of a transformation. They just don't change in direction! But wait a minute. The Eigen vectors will not change in direction. But then they can change in their magnitude. Think of a rubber band. Now if you pull the rubber band with full force with both hands, you are transforming its shape. But in the direction of your pull, the points just are transforming a little further in the same direction. (further here means distance/magnitude from the center).

Oh my goodness!

What on earth has all this crap got to do with USA?

Well, that's the crux of the post.

If you understood Eigen vectors already, then you can understand what 'Egan' is. Or if you already know what Egan is, try to get a hang of what Eigen vector . In either case, lets define the analogy below.

Analogy

--------

USA has decided to star in one more movie. Now don't start running towards the wall to bang your head. We all know it is unfortunate to the human community as a whole and we have to sail through sad times together. So lets make the best use of Egan by trying to understand the analogy with Eigen vectors.

What is the 'Characteristic' of an USA movie? 'Failure' - i can hear the shout from you guys! Now what if i say our beloved USA acts in two roles 'transforming' himself now and then. 'Failure still' !! Again, right answer folks. Now to one more question. It seems the director of this movie is Rajusundaram. What can you now say about this movie? Excellent going guys, it is the same answer and it fits very well everywhere!

"Failure" !

To summarize

No matter what happens i.e no matter how USA transforms himself in his movies, the direction will still be the same - crap!! So that's the closest you can get to Eigen vectors!

One final word:

---------------

I have a question for you folks. Before that let me quickly explain the term 'Eigen value' in one sentence.

'Eigen value' is the amount by which a Eigen vector changes in magnitude after a transformation. (of course, there is no change in direction)

Now what could be a possible, plausible "Egan value" of the movie???

In other words, if at all someone goes and watches this movie, what could be the value?

Answer: 9 !!!

Guess why? :)

Of course. You got it right again... the only "Egan Value" is Nayanthara !!!

There you go!!! That brings us to the end.

Good bye and happy Diwali till we meet for the next stupid tutorial !

---------------------------------------------------------------------

If in the most unfortunate case you wanted to seriously kick the author's

butt, here is the contact address.

Arun R,

Department of CSA,

Indian Institute of Science,

Bangalore.

---------------------------------------------------------------------------

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