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Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Wednesday, August 6, 2014

Predicting Chetan Bhagat's next book title



Chetan Bhagat is back, much to the joy of his fans and dismay of his critics, with his new masterpiece. It was expected that the title of the new book would contain a mere natural number, but Mr Bhagat had decided to take things to a different echelon by introducing a fraction: HALF.

This got me thinking: Chetan Bhagat, the doyen of Indian writing in the new millennium,  how does one predict the number the legend associates with his books?

I started off with the six numbers. Obviously 2020 skewed things significantly, but it was still a doable thing, thanks to Somnath's extraordinary knowledge of MS Excel (I cannot believe how much out of touch I am these days!). I decided not to complicate things and stick to a 6-degree polynomial instead.



Year Prefix N Suffix
2004
5
Point Someone
2005
1
Night @ The Call Centre
2008
3
Mistakes of My Life
2009
2
States: The Story of My Marriage
2011 Revolution
2020

2014
0.5
Girlfriend

This, in a nutshell, is what the list of book looks like. Look at how 2020 stands out amidst 5, 1, 3, 2, 0.5 (1/2). Let us fix the polynomial, then:


As is evident, this has been skewed significantly by 2020. Let us try to fit a 6-degree polynomial and check the results.

But then, Revolution 4 would not have a similar impact, since few are acquainted with the goings-on in the year 4 AD. And, as we know, Mr Bhagat, being the Voice of Young India, does not believe in facts from ancient times. Young India can be quite impatient at times: they may end up losing their voice and charging him an outrageous invoice, as an outcome of which hawkers may end up not selling his books to unsuspecting auto-rickshaw commuters ("serious books", anyone?).

We know that history (and being respectful to others' sentiments) is not Mr Bhagat's forte. For example, in this article on The Times of India, he has hurt the crushed of many an honest cinema-lover, myself included. But that is another story, and Greatbong has done such a wonderful work of it that it is not worth another go. Most importantly, it is not the topic of this article.


The equation does not look too good (once again, accommodating 2020 had made a mess of it). Despite that, we will use it to predict the number Mr Bhagat will use in his upcoming book.

Before beginning, however, there are a few disclaimers I should make:


Note:
1. This is not the best possible (but perhaps the easiest) way.
2. I had not been taught to predict numbers used in book names at any level of my non-illustrious academic career.
3. The number will depend on the year of release.

We have already got the polynomial, but the curve looks abysmal. It will not require a mathematician to predict that it will take a headlong plunge as I cross 2014 and move into the zone of the relative unknown.


What to do, then? Will using logarithms help? Let us check.

Year PrefixN Suffix Log N
2004
5
Point Someone
1.60944
2005
1
Night @ The Call Centre
0
2008
3
Mistakes of My Life
1.09861
2009
2
States: The Story of My Marriage
0.69315
2011 Revolution
2020

7.61085
2014
0.5
Girlfriend
-0.69315

This does not look too bad. Let us fit another polynomial now.


Not too bad, but as before, the dip is apparent. It does indeed seem that the number Mr Bhagat uses (if his new book comes out in 2015 or 2016) will be a very, very small value, almost close to zero. In fact, the later will it come out, the smaller the value.

There is nothing very wrong with this, though, given the fact that Mr Bhagat is an IITian and definitely has a penchant for numbers, big or small. Maybe the Voice of Youth would want to be remembered as The God of Small Things after his new book, which may hit the market sooner than we think.

Not too promising for the highest-grossing author of our times, is it not? It is not as bad as it looks like, though, since we have been taking logs.

The intersection point for 2015 is -50, which means that a book released on that particular year is 
e^(-50) 
or 
(1.93 x 10^(-22)) 
or
0.0000000000000000000001928749848

For people living in a domain too high for small numbers, this is a value that can be considered very, very close to zero. In other words, the name would contain the number 0.

***

I am not finished yet, though. Does the number 2020 not sound a bit off-track? What if Mr Bhagat did not want it to be part of the series? What if we drop the number and calculate the trend? The number is big enough — in the same way that Mr Bhagat himself is — to be considered an outlier. Let us check:


The value for 2015 now (yes, yes, I know there is no reason why I should consider a polynomial a best fit here) is
e^7
or
1096.633158
or approximately
1097, which seems a reasonable number to become a part of a book. One can only will hope it will make its way to the leagues of 1984, Farenheit 451, or One Hundred Years of Solitude. All these seem reasonable names for a book that, like its illustrious predecessors, will go on to change the face of the country, especially the youth. 

***

Moral of the story?

If you include Revolution 2020, the future of the series is zero. In other words, if you think the books involve revolutionary material in the series, you may be headed for a huge zero.

***

So, what are your guesses for the name of the upcoming pathbreaker?

***

PS: I had felt helpless without access to SAS and R. Then I called Somnath, and he taught me a thing or two about MS Excel. A huge thanks to Somnath, without whom this post would have been delayed or, worse, not been written.

Tuesday, September 21, 2010

The song template

Bollywood songs, especially those written by individuals lesser than the inimitable Sahir or the often unfathomable Gulzar, have often followed a template throughout the song. The concept goes like this: a template is laid out in the mukhda (sthayi), and the same template is followed in the antaras.

Consider a template using the following variables:
Problem variable: X
Problem activity caused by variable: P
Solution variable: Y
Solution offered by variable y: S

Now that we have defined our variables in the template, let us define the template:
If x causes a problem P, then Y offers the solution S.
If Y causes a problem identical to P, then who offers a solution identical to S?

Now, let us assign values to the variables:
X=chingari; P=bhadakna (agan lagana, which is synonymous); Y=saawan; S=bujhana

So we get
Chingari koi bhadke, to saawan use bujhaye
Saawan jo agan lagaye, use kaun bujhaye?

Then again,
X=patjhad; P=baag ujaadna; Y=bahaar; S=khilana

We get
Patjhad jo baag ujaade, wo baag bahaar khilaye
Jo baag bahaar mein ujde, use kaun khilaye?

Now, the antaras are somewhat more descriptive. They also contain a couple of lines each that basically act as an introduction to the situation. So, in essence,each of the antaras contains two lines of set-up and two lines of template:

Antara 1:
Introduction:
Humse mat poochho kaise mandir toota sapnon ka,
Logon ki baat nahin hai, ye kissa hai apnon ka.
Template:
(X=dushman; P=thnes lagana / ghaao lagana; Y=meet/manmeet; S=jiya behlana / ghaao mitana)
Koi dushman thnes lagaye, to meet jiya behlaye
Manmeet jo ghaao lagaye, use kaun mitaye?




Antara 2:
Introduction:
Na jaane kya ho jaata, jaane hum kya kar jaate?
Peete hain to zinda hai, na peete to mar jaate.
Template:
(X=duniya; P=pyaasa rakhna/pyaas lagana; Y=madira; S=bujhana)
Duniya jo pyasa rakhe, to madira pyaas bujhaye
Madira jo pyaas lagaye, use kaun bujhaye?




Antara 3:
Introduction:
Maana toofan ke aage nahin chalta zor kisi ka,
Maujon ka dosh nahin hai, ye dosh hai aur kisi ka.
Template:
(X=majhdhaar; P=naiya dolna / naao dubona; Y=maajhi; S=paar lagana / bachana)
Majdhaar mein naiya dole, to maajhi paar lagaye,
Maajhi jo naao duboye, use kaun bachaye?
See how easy this is? Just define the template, define the variables and run it again and again.

Footnotes:
  • If a garden really doesn't blossom in spring, then it's not really worth attempting to maintain it.
  • I've never heard of anyone who consumes alcohol to quench his thirst.
  • The dehydration (often resulting in hangovers) is easily overcome if one consumes water and/or fruit juice in adequate quantities. Caffeine is not advisable.
  • Of course the wave cannot be blamed; the storm is the guilty party here.

Sunday, April 11, 2010

The theorem song

Ages back I had watched a movie called Maine pyar kiya. Surprisingly, I had liked it at that point of time, but then, when I had a second view a few years later, I felt quite embarrassed at having liked it earlier. I'm still confused as to why I had liked it; apparently everyone has his low moments.

Anyway, the film had a nice song, the tune shamelessly nicked from I just called to say I love you. I was in Class VIII when I had first heard of this song, and with time, it kept reminding me of the thousands of theorems and axioms I had to prove in my illustrious (okay, that was an exaggeration) career.

It was like someone had to prove the title of the movie: Maine Pyar kiya. How does one go about this? First, needs to plan a method to proceed. So, the thinking procedure starts...
Aate jaate, haste gaate, socha tha maine man mein, kahin baar...

Now you start collecting data:
Woh pehli nazar, halka sa asar, karta hai kiyun is dil ko beqaraar?
The approach is perfect. You collect bits of information, and you start questioning yourself why after acquiring all kinds of facts. Data, query, conclusion should be the attitude after every step.

And then,
Rukke chalna, chalke rukna, na jaane tumhe hai kiska intezaar...
See what I meant?

And now that we've mopped up the data, it's time to realise that all bits of information lead to only one point, are we that close to the proof?
Tera woh yakeen, kahin main to nahin?
More of that. Pick a bit of information and check whether it's relevant to the problem. I wish I was this methodical.

Now I'm getting quite sure of the fact that I've proved this:
Lagta hai yahi kiyun mujhko baarbaar?
This is when someone, ages back, had shouted Eureka!... the data has been acquired, the conclusions have been drawn and compiled, and the proof is in sight.

Yes, I think I've possibly proved it, I'm not sure, though.
Yahi sach hai, shaayad, maine pyar kiya.
Shaayad is the keyword here. Apparently the problem needs to be thought over for some more time.

The decisive conclusion cometh:
Haan haan, tumse, maine pyar kiya.

QED.

Wednesday, April 7, 2010

Memoir(Memoir-1)(Memoir-2)...3.2.1

Hard to believe, but I used to be one of those irritating children who always used to finish his school books before a new session started. This got increasingly difficult, especially with mathematics, as we progressed to higher classes.

One of the class XI books, flipped randomly, said "the number of ways in which n objects can be arranged is n!". This intrigued me: well, it can be any damned number, but why should anyone be surprised, whatever the outcome be? Why the exclamation?

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