Digital Counter Paradox

Title of paper:

On Chinmay Datars Digital Counter Paradox

Authors: Chinmay Datar 1

Special thanks: Sumedh Dhabu 2 Shreyas Bhaban 3.

Abstact:

A reverse thought experiment generated out of the idea to mathematically model a situation of a couple moving into a locked house and generating an offspring and leaving the house only for another person to enter the house.

Index terms:                                                                                                           

Digital Counters, Flummoxations.

Introduction:

Completing work related assignments is kind of boring. Especially if its an assignment that does not make you think out of the box. IT assignments are mostly of such non-creative types. I guess they strive to stifle your imagination and creativity. My new job, though interesting, is making me lose my creativity to a certain extent. To not go completely mad, I try to come up with mathematical formulations and spoofs, to keep thinking and not get engrossed in the world of IT.(I have no idea why its called technology here). Ive come up with some very interesting theories- one about complex numbers has already been shared.. Today, early in the morning, when I have nothing to do, I was thinking of a thought experiment. The experiment is leaving me flummoxed. Why me, it has even left the Grab-all and gobble scientist Shreyas Bhaban (who works not coz he loves his work, math and science, but coz he wants to grab all the money around) dumbstruck.

Assume a room where there is a single door for entry and exit. The room has no other possible entry or exit points.Just the one entrance/exit. Whats inside the room is unknown, so basically its a black box. On outside of the door, there is a digital counter which can count anything real from -infinity to +infinity. Whenever anything enters the room, the counter is automatically incremented by one. When anything leaves the room, the counter is decremented by 1. All elements are counted individually. Elements enter the room when the door is opened at 2n-1 opening and elements exit when door is opened at 2n opeing.( n =1 to infinity)

Although the inside of the room is unknown, what we do know is that the room performs a simple operation of square rooting anything inside at even numbered door opening.

Let us assume that we push the number "1" in the room. The counter will increment to show that there is 1 entity in the room. Now when we open the door again, it will be the 2nd opening, so the square root rule will be applied on "1". This will result in two results: +1 and -1. as it is the 2nd opening, the elements inside will exit. As two elements will come out, the counter will decrement twice, and show -1 as the number of entities inside. Now if we open the door again for a 3rd time, and force "1" inside again, the counter will increment by 1, and show the number of entities inside as "0". Practically this is not possible as we ourselves have pushed "1" inside the door, and definitely know that physically there is an entity that exists inside. 

So, now, a paradox has been generated about the number on entities inside the room. Mathematically, the counter reads zero, but practically, we know it should read 1. This paradox has been labeled the Digital Counter Paradox or DC paradox.

The paradox has been generated for exclusive use for IVEE. Any reproduction will be charged with 50 whiplashes and brain-washing. The paradox is created to confuse people. People attempting to solve the same with mass-energy-momentum conservation or any other methods shall be deemed too nerdy to be vadheev and be permanently disqualified to visit IVEE blogs and posts.

Dhabus Complex and Datars iParadox

Things written in (()) are alternatives

Title of paper:

Datar iParadox extended on pioneering work about Dhabu Complex Theory  :  the reality about ‘i’, the mathematical paradox

Authors: Chinmay Datar 1 and Sumedh Dhabu 2

Special thanks: Anant Devi 3

Abstact:

This paper presents an interesting and shocking mathematical paradox about ‘i’. For this we need to consider the life of engineer. The two most important parts in the life of engineer are considered here: studies and girlfriend. Then based on Dhabu Complex theory, authors provide intuitive and practical proofs for this paradox.

Index terms:

Datar iParadox,  Dhabu Complex theory, Buzz (!!), engineer’s life

Intro:

This theory has been largely developed thanks to a timely and fruitful vadheev commenting on a Sumedh Dhabu Buzz. It is essentially based on the Dhabu Complex Theory, and includes extensions known as the Datar iParadox. Anant Devis axioms provide an insightful perspective regarding Dhabus Theory. I would like to thank both of them for playing a significant part to inspire me to conduct another vadheev formulation.


Let us begin with a basic understanding of Dhabus Complex Theory. Sumedh Dhabu, a great mind recently came to conclusion after a string of mind boggling facts about dreams and realities. Dhabu goes on to imply the complex theorem to life, by stating, 
"Life is Complex-One needs to consider the real and imaginary parts separately" 
Dhabu has come up with this theorem through sheer perseverance and dedication in the past 4 years. He conducted experiments on himself and his friends to establish this golden rule, prompting me to think further and expand it. Here, I have collaborated with the great man himself and using some theoretical results obtained by Anant Devi, come up with the Datar iParadox An explanation for the same is given below. Mathematical understanding along with a sense of humour is a must for this, and those ill suited or dumb enough not to understand complex numbers and other associated topics need not read further.


Mathematical analysis of Dhabus Theory leads to a quite interesting paradox, known as Datar iParadox. We have tried to analyse and help laymen understand this paradox. here goes:


Consider an ideal life for a student (MALE) entering Engineering. Since he is entering engineering, he has a dream, but then there is also a reality, which are unfortunately, conjugates of each other. 

In India, it is everyones dream to one day land up in  IT engineering and end up getting bucketloads of marks. Thus, their dreams along with their current dreams which is studies well and a girlfriend(who is ofcourse, imaginary) can be given by the Eulerian identity,

Dreams = e^iT

which will give

 Dreams = cosT + i(sinT)

However, reality is different, and most people do not get into IT engineering. Thus, on Similar grounds, reality, which is studies, minuis the imaginary girlfriend can be given by:

Reality = e^-iT

which will give, 

Reality = cosT - i(SinT)

Assumption:
during engineering, for a good engineer, 
cosT = studies and it is a  sin(T) to have a girlfriend.

so substituting these values, we get,

Dreams=Studies + iGF

Reality=Studies -iGF

(GF= girlfriend.)

Now on a complex plane, both dreams and realities will have modulus and arguments.

Now since the modulus of both are the same, but the arguments are out of phase by 90 degrees, it leads to what Anant Devi has described as having internal "arguments". An engineering student has his dreams and relaities out of phase by a 90 degree argument.

These arguments cause a great confusion, called Life, which crosses dreams and realities. Crossing of dreams and realities,i.e Dreams "x" reality will give a product of the two terms.

Thus, life = Dreams x Reality.

Life= (Studies + iGF)(Studies-iGF)

thus, Life = Studies squared + GF squared.

L = St²+GF²

Over time as one runs through his engineering degree, and completes college, Studies tend to Zero.

So, L = GF²

^{Now, in every engineers life, there comes a point when he applies Chinmays K-means algorithm to come to a conclusion that he has found a perfect girl, or atleast has a blind belief that he has a girlfriend. Considering the life of all engineers and taking average, we can conclude that the value for GF overtime tends to 1.}

Thus L=1.


The paradox comes into picture when the Girlfriend leaves you.
Life turns head over heels, i.e, it changes direction.
considering life to be a vector, by change of direction, Life will now be given as
L= -1.
A life turned heads over heels is called a Problem.
Thus, P=-1.
to solve problems, we try to find the roots of the problems,
now sqrt(P) = sqrt(-1) ="i"
So "i" is the root of the problem.

However, it is rather surprising result. Mathematically,  we have proven that "i" here is imaginary. however, the "i" exists physically, and is the root of all problems.

A major mathematical paradox is thereby generated, stating, is the imaginary "i" really real?
The above postulate is termed as the Datar iParadox and as discussed earlier, derived solely from Dhabus Complex Theorem with help of Devi Arguments.

We can thus conclude that using mathematics we have generated a paradox questioning the nature of "i".
Since the authors are from Pune, they would like to add that any remarks regarding the authenticity and correctness of the theory shall be considered imaginary, and removed immediately from the complex plane.  

Note: CD SD and AD are founders and life fellows of Institution of Vadheev Electronic Engineers. (Authors promise to write a separate document about IVEE and it will be posted in some upcoming blog by CD).

The Dud Social Networking Experiment

These holidays have been damn frustrating! Considering that they are the last ones ill be having with my college buddies, makes them even worse. Time, especially the afternoon, combined with the heat crawls at a snails pace. Quite astonishingly, there is nothing worthwhile to do! In this emptiness and boredom, a way out is to do stupid experiments. One such bored of the holidays experiment was based on the hypothesis that was drawn from observing social networking sites for long enough.

The hypothesis is that Girls get unnecessary attention on such social networking sites. A girl does anything, and there are hundreds of comments for even the silliest of things. Guys do something awesome, and there is hardly in discussion about that. Not all girls fall in that category, but most do. I wanted to test the hypothesis, already knowing what the results were to be. However, I slightly modified the theme, that me, and a girl would upload the same photo, and see the results depending on the number of comments/likes for the picture.

Fortunately, my trusted accomplice for this act was none other than my extremely nerdy and awesome friend Siddhi Soman. Siddhi, to those who do not know, is an extremely hyper-energetic person who excels at whatever she does- be it academics, badminton, rowing, having a row, brawl- you name it, she is good at it. No wonder she was the Best outgoing person from college. She is also an extremely terrifying person, and many a times has given me nightmares ( by chasing me around the college and slicing my head open by smashing rowing oars on my head in my dreams) . At 5 feet 2, Siddhi, is an awesome model who if in the right mood gives off awesome emotions for the camera. I had clicked a super picture of hers last year after the college dinner when she was doing her normal nautanki. The picture is awesome actually! its one of the better portrait shots that I've clicked. So it was with this picture that I decided to experiment.

The picture is a black and white portrait style photo of Siddhi expressing a typical Filmy dialogue "Nahiiii" ,and its one of my favourite ones. I had uploaded the pic on Facebook for my new album Life in B&W a couple of days ago, and received scant appreciation for an awesome photo. So, I persuaded Siddhi to upload it on her wall. And Lo behold! in a mere 24 hours, the photo on Siddhis wall had more likes and comments than what I had on mine! Its a matter of jealousy when someone gets into the limelight for things you do isn't it! I am not that bothered, as I get enough publicity through other means anyway, but a person of faint heart ought to get jealous. Anyway, I'm putting up the picture here as well. Its right below this text.

Stupid experiments usually have stupid conclusions. In my case, the experiments have vadheev conclusions. Linking any observation to anything is a prime ace I have up my sleeve to create lots and lots of noise. This time, even though the topic of discussion was well proven, just to have a new outlook, I attempted something else, which unfortunately by my standards is rather dull.  

Anyway, I came to the following conclusions after carrying out this act of nautanki:

1) Siddhi is an awesome subject for taking not just nautanki photographs, but normal photos too.

2) Girls do not usually like or comment on awesome clicks of other girls if posted on a boys profile.They get super jealous that its not their Photo.

3) Girls go hyper if the same thing is posted by the girl who is in the picture. "Awwww howww cute re!" etc etc

4) Boys go ballistic over the portraits. "You look awesome blah blah blah(General observation, not applicable to Siddhi. :P)

5) Compared to other girls, Siddhi has received less number of hits. This is probably because she is a good girl.(ya right!) I was more inclined on describing her as a hopeless aspiring model, but she is not. If I say so, my head gets sliced in two.

6) Social Networking sites are pro female.(rather grudgingly accepted)

7) Like it or not, girls receive free, fukat, unnecessary, pointless attention on Social Networking sites. 

8) Im better off writing posts which spoof engineering and mathematical terms rather than experimenting on stupid social networking.

Now, Ive lost the confidence in social networking experiments. Dont know why I carried this depressing experiment in first place. Maybe, by using Siddhi as a bait, im trying to enhance my publicity on social networking sites. :P (Not that I need it, but its fun, and Id have done it anyway- Im not someone who is shy of carrying out a PS :))

Never mind, if this post becomes a hit, then I give half the plaudits to Siddhi for helping me conduct a stupid experiment. If it bombs, its entirely her fault and I have nothing to do with it. But going forth with my cocky and arrogant self confidence, I have all faith that this will be a hit, and Siddhi will get a shot at fame that, unlike most other girls, is atleast earned! 

The Puneri Lingo

Pune, my hometown, is a city of legends. The stuff that goes on here in unparalleled anywhere in the world. You cannot become a Punekar. You are born one. the "Maaz" is innate. You cannot develop it. Short Temper, Exceedingly obsessive pride about anything Pune, A taste bud to devour all the unusual dishes you get here are few common traits of a true blue punekar. However, since Pune is also a cultural centre- the place where Marathi language is ever evolving, a true Punekar is also a person who comes up with and uses a few peculiar words understood only by the select few in this world who have the honour of being born punekar. What may seem like nonsensical terms make complete sense to us. Some are immortal. Some, became more apparent in the last 4 years I spent doing engineering.

This post is dedicated to all those special Puneri words that we come up with.

(To read the 2nd part of the Lingo series, click here.)

1) Awraa... I dont know how to explain this in english. It has no parallel. If anyone says or does anything not ordinary, thats the typical reaction. "Awraa..."

Usage...

1st person "Are Zampya ni pori kade vakdya najarene pahila "...

Punekar "Awraaaaa!!!"

2)Vadheev... A suitable english word would be a whimsical person or an act. Initially it was used to describe a person, by saying stuff suuch as Kay vadheev ahe to. But soon enough its other forms started appearing. Vadheevpana, vadheevgiri etc etc.

Usage..

 "Arre Zampya kasla vadheev vagato"

3)Napas/FAIL.. I guess I got hooked to this term through Sushant. VIT word. If anyone does anything stupid, then he is FAIL. 

Typical usage: 

"Arre Zampya! Sadhi porgi patavta yet nai tula! Kay FAIL/Napaas ahes"

4) Aai chi jay! An exclamation which literally means Hail Oh Mother! An expression to display the emotion of shock or surprize.

Usage: 

1st person.. "Arre Zampya la muli avadatat".. 

Punekar(who is least expecting this).."Aai chi Jay!"

5)Haramya. An adjective used to describe a devious person. Someone who says something and does the opposite.  

Usage: 

"Arre Haramya.. asa vagtat ka!"

6) Chhapri.. A mild way to curse a person. It means that a person has no standards. Associated with banter only.

Usage. 

"Arre chhapri!! he kaay ahe!"

7) Ghanta.. means bell. But in puneri marathi it is a word to express deep disbelief at someones actions.

Usage: 

1st person.."Arre, zampya ni porgi patavli"..

Punekar.. "GHANTA!"

8)Barrr.... a conversation ender. literally means OK. but in the rudest of the rude puneri ethos, this is said when the person opposite is boring you to death. He says anything, just say barr!, and he wont know what to say.

Usage... 

1st person.. "Are tula mahitye ka he ha blah blah blah blah... blah balh blah" 

Punekar "Barrr!" 

1st person. ""

9) Kamaal... Something amazing. If anything or anyone is out of this world, this word is used to describe it.

Usage.

 "Edya..Zampya chi navin girlfriend kamaaal ahe rao!"

10)Balach.. Nonsensical. Used to dismiss claims made by the other person.

Usage. 

Zampya "arre me vargat pahila alo" 

Punekar "Balach!!"

11)Bhurtya.. Used to describe a person who acts like an idiot. a sugar coated swear word for a waif individual.

Usage. 

"are e bhurtya salya"

12) Gandlay... Used to describe somethings that gone wrong.

Usage. 

eg: when the mobile phone stops working.. "Maza mobile gandlaay re!"

13)Dokyat jau nako! Used to silence the person opposite if he is making outrageous claims.

Usage: 

1st person "Arre merreko ye mila, woh mila" 

Punekar "Dokyat jau nakos re!! Gappa bass"

14) Edya layee bhaari.. word to word, it means Awesome!

Usage.. 

Zampya.. "Arre mulgi patavli"

Punekar: "Edya Layeee bhaari!"

15) Full Hawa.. Means show off..

Usage:

"Arre, zampya ni porgi patavli.. ata full hawaa kartoy!"

16) Fukat hawa... unnecessary show off.

Usage

"kaam tar itarankadun karun ghetla ani swataha fukat hawaa karat basla"

17)Ashakkya! means impossible, and is used to describe a variety of things ranging from boredom to enjoyment

Usage: 

Ghari basun Ashakkya bor zalay.

Arre trek la ashakkya majaa ali!

18) Ghari Ja! An exclamation to tell the other person to stop meaningless argument. Literally means "Go Home"

Usage:

1st person.. "Arre, tula mahitye ka blah blah blah blah"

Punekar" Ghari jaa re!"

19) Ek Numberr/ Vishesshh!! again means Awesome! 

Usage

"Arre amchi exam Vishssesshh hoti!"

20) Kharraaab! means bad...in a bad way. used to describe if a person has had is ga** hammered by banter.

Usage

"Arre zampya chi Kharrraaaab marli geli!"

21) Aai chya gavat! means In mothers village. But in puneri marathi, it is a phrase used to describe surprize.

Usage

1st person. "Arre... aaj aapli pariksha ahe."

Punekar. "Aai chya gavat!"

22) Full Radaaa... means a brawl, or mismanagement or any other activity which leads to chaos.

Usage.

"Arre ganpati baghtana Lakshmi road var fulll radaaaa zala hota"

23) Matter zala.. means someone is in trouble.

Usage

"Arre.. kharaab matter zalay... exam madhe Zampya chi copy pakadli geli"

24) Arre mitra! is a phrase used to address any person you may or may not know.

Usage:

"Arre mitra... shanta ho jaraa"

25)  Ghusliye! means  screwed!

Usage:

"Arre exam suru ahet re.. kahich abhyas nahi zalay.. full ghusliye!"

26) Dokyala Shot.. irritating person/event.

Usage.

1st person " te bagh... Zampya chi girlfriend yetye"

Punekar.. "Nako re ti!! dokyala shot ahe!"

27) Chalni/Challan... a person who tells thaapaa(mild lies) all the time/ A mild lie. Exaggerated claims.

Usage:

"Arre zampya ek number cha chalni manus ahe! Chhotya chottya goshtinbaddal pan challan sodat asto

28) jeev de re tu! a disdainful remark to someone who is irritating you. 

Usage.

1st person. "Arre tula mahitye ka.. blah blah blah blah"

Punekar.. "Jeev de re tu!"

29) Kahi!!! Another word used to express disbelief.. usually used as "Kahihi kay!!"

Usage

Zampya "Arre me lagna tharavla"

Punekar.. "Kahi kay re!!"

30) Kapalat gotya jane/ gaar padne.. getting stunned.. literally...

Usage

"Mitra are.. zampya i vaieet bomb takla aaj.. Lagna tharavala mhane.. kapalat gotya gelya he aikun.. gaaar padlo hoto me pudchi 5 minita"

For some reasons I had missed these. Added after being pointed out by the likes of MadB,Andaksh and others.

1) Haat var zalet.. means hands held high.. situation is out of control.
Usage:
"Aarreee yaar!! parikshemule haat var zalet maze!"

2) Cheap pana: Universally used to describe anything that you dont want!
"Arre kay cheap pana ahe ha!! roj roj kay pariksha"

3)Vayaaaa means waste... used to describe person, behaviour, anything!
Usage
"Arre Zampya vayaa ahe full.. kiti vayaaa vagato!"

4) Phupphha: Its an abbreviation and apabhraunsh of fully faltu. the word was coined by me and Sushya.
Usage:
"Ricky Ponting jagatla saglyat Phupphha manus ahe"

5)Majjor/ Infinite: Exaggerated claims.. Used to increase the strength of your claims.
Usage
"Arre Zampye aaj kal Majjor/Infinite dokyat jaato rao!"

6) Kissa: Kissa is a retrospect of something that a person does not usually do. An act which receives lot of attention, and the person responsible gets lots of flack, then it is a Kiss.
Usage
"Arree.. Zampya ani tyachi girlfriend rastyat bekkar bhandat hote.. Vadheev Kissa hota!"

I dont know how i forgot this. But Piyusha Dani would have killed me if id have not written this! (25-May-2011)

7) Chiwda : Utter Chaos. Similar to raadaa, although less intense.
Usage:
"Arre mitranno! mazya profile picture var jara kami commenting kara! kaay chiwdaa karun thevlay ithe saglyanni!"

These are just a few of the best words that we use. Puneri Lingo is difficult to understand for outsiders.. just a little help for these retarded souls. One thing is sure, when I do go to the US for my masters degree, ill miss the freedom with which i shall get to use these legendary words!"

To read the 2nd part of the Lingo series, click here.

K-means Clustering

One of the biggest advantages of being an engineer is that we can apply concepts that we have learnt in our syllabus to virtually any problem in the world, and try to come up with new and innovative ideas to deal with these problems. We see a number of examples of engineers coming up with bizarre applications. Why refer to other engineers. Me and Anant Devi have already come up with Datar-Devi Approximations for Exams. A cousin of mine, by profession a computer geek, by passion a world class singer came up with another of such fantastic research of the relation between the frequency of your arm swing while walking and your velocity. Amazing stuff. Really, there are no boundaries for us engineers. All we need to do is think a little bit out of the box. Today, I shall be discussing one of the more important algorithms that we have in signal processing (esp speech processing)-the K-means algorithm and its application to one of the major headache for all college guys- the right girl.

Now, engineers, or for that matter most of the guys are hopeless when it comes to selecting the right girl for them. They just fall in love without thinking! (I know Ill be called a hypocrite- I too have been down this path on multiple occasions. MadB will be the one who will accuse me first, but yeah, who takes her seriously when she accuses!) And then they end up fighting with the girl over petty issues, and then act like crybabies.  What guys need is patience. This post is dedicated to all guys who are eternally confused as to what they will do with their love life and provide with insight of finding the best possible partners.

Let me introduce you to our quirky and extremely challenging to implement in matlab friend of ours, The K-means algorithm, which I will use to address your woes. To the unwary and uneducated, K-Means is a clustering algorithm that we commonly use for vector quantization. A given n dimensional ( n corresponding to various parameters) vectors when quantized into a data of say n bits is mapped to its nearest encoded bitstream which gives minimum mean squared error ( the message to which it is encoded is called the centroid) . One problem is- how do you assign the centroid. Well, it is simple. Its nothing but a mean of all the vectors in that cluster. So, dynamically, the centroid will keep on changing until all entities converge to a single point.
Mathematically, the K-means algorithm will be given by


Given a set of observations (x₁, x₂, …, x_n), where each observation is a d-dimensional real vector, k-means clustering aims to partition the n observations into k sets (k ≤ n) S = {S₁, S₂, …, S_k} so as to minimize the within-cluster sum of squares (WCSS):

where μ_i is the mean of points in S_i.

[wikipedia.]

Pictorally, this can be represented as:

• 

  1) k initial "means" (in this casek=3) are randomly selected from the data set (shown in color).
 
• 

  2) k clusters are created by associating every observation with the nearest mean. The partitions here represent theVoronoi diagram generated by the means.
 
• 

  3) The centroid of each of the kclusters becomes the new means.
 
• 

  4) Steps 2 and 3 are repeated until convergence has been reached.

Now, coming back to the notion of the application of K-means for the problem to be addressed. Here, in k-means we have a n dimensional vector. Let these n dimensions be all the points you will look for in the girl. (My vector, is 20 dimensional.) as shown in the figure above, make three categories- Girls who you like.
Girls who you do not like. and Girls who you think are OK. Each girl will have her own unique n dimensional vector. Assign a self defined centroid for all three of them.

As you grow older through your engineering years you come across a number of girls, not necessarily in your college, who you may have considered as your potential ideal match, or as your worst possible match. This will give you quite a bit of database for statistical analysis. When you see a girl in either category, observe them for a few days, and adjust their vectors, and keep them updating. after a sufficient amount of time, the vectors will have reached a saturation point and will not alter. this is when you apply the k-means.

now, it is highly unlikely that we will get a girl who coincides with our self defined centroids. If that happens to be your case, you are one hell of a lucky ba***d. But for people like me, who have some impossible conditional vector entries, this is almost impossible. Also, it is highly improbable that you will have a girl with some qualities from girl B who has some desirable qualities and girl C who has other desirable qualities. Lets face it- its unlikely. So, the best solution is to find the "vector" which will give you the least mean squared error at the output of the K-means. The girl corresponding to that vector is the one you go for!

Just to conclude:

If you like a girl, you have to wait for some time to be absolutely sure that she is the one that is perfect for you. Observe. Make mental notes of all the small things she does. (ofcourse this advise is only for those who are looking long term.. those interested in short term can jump ships whenever they want!). Make a mental note of what you want your ideal girl to be like beforehand. Ive received a lot of flack for my ideal girl, who can be found here, but nevertheless, do it.  Jot down all the points you want in all of them, and get ready to run the K-means algorithm.It works!!

(Personally, I dont recommend this approach- I havent done it for myself, and probably will not do it. Im more of a hopeless old school- fall in love arbitrarily kind of person to try this out. I am not suffering that much, and I am happy with the things as of now. No need for me then! This analogy was made purely to showcase the versatility that an engineer can adopt to make even the simplest of the things mathematical and complex. )

The Fridge Key

I dont know how much impact this will have on my grades, but i hope it does not, for we did this misdeed last year! 

Third year, for many reasons, was one of the most memorable years in college. Especially the 6th semester. Probably, it was the first time we didnt have that much load on our shoulders, or maybe the subjects were easy, or even maybe for the fact the I managed to score an 8 point grade after two wretched semesters made it all the more special. It was the time that the bonding in class was at its best. I had made some incredible like minded friends by that time. So its not surprizing that we ended up doing what I am going to narrate. 

It was a typical March afternoon, probably the last week-sometime between 3:30-5:30, EM practical, with Babya conducting the practical session. March in Pune is bad, and in a closed 20x20 room filled with an assortment of CROs and other measuring instruments,  with just a single ceiling fan operating, and a ban to switch on the AC, it gets even worse. Heat, sweat and practicals had drawn us to madness. To make the matters worse we had run out of supplies for water, and if we needed to get them, we had to climb down two flights of stairs and back up again. Who has the energy to do all that at the end of a tiring day! Nevertheless we did go down to get two waterbottles filled up, but to our sheer disappointment, the water was as hot as the weather outside. Something Cool was the need of the hour.

Fortune, was on our side. The EM lab has a refrigerator.  So, we decided to cool our water bottles and have something cool to drink later. When we opened the fridge door, to our delight, there were 5-6 bottles of cold water, which we immediately set about consuming, and were promptly told off for doing so. Angered at the fact that we were told off for drinking cool water, and were prevented from cooling our own bottles, we plotted a revenge.

As it happened, we conducted an extra practical for ourselves to get the lab assignments out of the way a couple of days later. Now, that day, me and my partner in crime from my lab sessions- Krishna, observed that our friend Babya had left the key on the refrigerator lock. A devilish scheme tool place, and we came up with the conclusion that if we cannot drink cold water, nobody can. So, when nobody was observing, me and Krishna quickly locked the fridge and hid the key, initially in Krishnas pocket. When we did finish performing the practical, we left silently, taking the key with us.

Now, the summer heat got to Babya, and he wanted to have a drink, but could not open the fridge as we had locked it! He was livid. He told off the remaining people from our batch and demanded where was the key. He knew that we had left. So he called us back to the lab, and told that he is checking all bags and pockets for his fridge keys. we needed a place to hide the key somewhere. So Krishna came up with a solution. the key was put on his sandal underneath his foot, and off we went to the lab. We got searched, and still the key could not be found. So we acted to show that we didnt have it by helping search for it. We literally lifted the fridge to check if it was underneath the fridge, checked under all desks, tables, chairs everywhere- but no sign of the key. Babya who was flustered by his thirst by now, told that this was a serious issue and would be reported to the HOD. (who is scared of action taken on a prank!)

We were told off, and then let go. Next day I think it was RDJ who came and told off the entire class for stealing the keys. Here, playing mafia came in rather handy. I was totally able to pull off the fact that it wasnt with me, and I was not associated with this crime! The same applied for Krishna, although he doesnt need mafia practice. 

We kept the key with us for atleast 3 days. the 4th day was the April fools day. So, on that day, we decided to return our key anonymously. We put a sign saying april fool on it, and put the key in the lock of the Lab door. Somebody saw us putting the key there, but fortunately, did not report it. The next time we went for the practical, Babya was gleeful that he had found the key. He told that it was just misplaced probably, and he found it(as if..), and no action will be taken. So, the key was back, everyone was happy, me and krishna were let off for what can only be described as the most vadheev prank that Ive pulled off. 

It was fun! More fun than hiding Gandhalis Dio. More fun than we have had on the Boat club at times. Probably not that much fun as I had this semester doing vadheev pana with MadB,Ketki,Teja and Alok. Still, it was one of the best pranks that can be played in college. Juniors, it is your time to fill in my shoes now that I am graduating soon!

Krishna- Half the gang.

Chinmay- The other half of the gang.

Key- the one we kidnapped.

Mathematics of an Exam

Guess what. I am nearly done with another set of exams. No matter how much you try to shoulder arms at them, they make you go on the back foot and defend. Now that Im done with the theory exams, I am freely able to punch my practicals through the covers! No worries. My timing in the practical viva is as immaculate and as elegant as those of Sachin Tendulkar on the field. (Forgive me for a cricket like opening, but im watching India thrash NZ by Innings and some runs, so the effect rubs off..)

Now then, coming back to the point, as this was my 7th semester in the college, I have given a total of 14 exams plus a number of 10 mark tests. A large enough sample size has been generated through the experience of me and my friends to draw out the following conclusions about the time near to exam. These will be known as the Datar-Devi Approximations, after its researchers, Datar and Devi.


To start of with. Let 'T' be the time left for an exam. This is usually about 2-3 days for a typical COEP paper, for which one can actually study. For simplicity we shall assume that T is a rectangular distribution. from -T to 0.
However, we never start studying at the start of the rectangular function. Studying is a statistically boring process. We usually start our studies at an arbitrary time instant H, after -T. Again, this will be a rectangular distribution over T.

Now, as it is statistically observed, attention span is dependent on H. let Asp be the attention span.

 

This will give you the attention span that you will get, depending on when you start studying. This is a critical factor for getting good marks. ideally, toppers have H close to T.

The second important point that is under consideration is Number of calls you make asking your friends "How much timepass you have done?" this can be denoted by N(h). Number of calls before exam are way more that those on ordinary days.
N(h)=e^2kh.. k= Phony constant. the derivations for above terms are extremely complex and is beyond the scope of timepass. So, it has been left to the Chinese to come up with the proofs for the same.

The third important factor is time you end up swearing at and cursing your Professors. Now, as the trend is, we curse our profs as being useless and incompetent much more during exam period than normal.This analysis is extremely interesting, and thus, has been discussed below. Now, not all professors are bad. some are actually superb. so lets have a sample size of N professors.
Let us consider r activities- such as teaching, setting papers, fluency in speech etc.
let 'p' be the probability that the teacher is good.
so, (1-p) is the probability that the teacher is rubbish.
then, assuming a binomial model and taking average over given number considered, we can say that the swearing coefficient is






The fourth point considered in this treatise is based on pure statistics. The point is know as Chinmays attraction law. "As exam time nears, in D Days, your feelings towards an arbitrary girl goes on increasing to the exponent".Here, γ(gamma) is the attraction probability. γ is dependent on several factors such as the nature of the person, the college where he is studying etc. If γ is the attraction probability, then, the attraction coefficient can be given by  




However, in colleges like COEP, as there are very few good looking girls, and the fact that the college is filled with nerds, γ is negligible. So taking a Taylor series expansion, and ignoring higher order terms of γ ,
we can say,

The next important point is concentration span. You tend to concentrate very little while studying. breaks are frequent. Let B be the number of drinks/snacks break you take in between a span of 3 hours- a statistically important variable as all papers are 3 hours long. Then, concentration span, CSmax will be:
CSmax= 3hours/B.
Usually this value is quite low, owing to the statistically high value of B (12-15 in normal cases).
The analysis of B is also again very complex, and has been left to the Chinese.
One thing we know for certain is that CSmax is inversely proportional to t, the time before exam.

The next factor is the ratio of useful study to time spent on Facebook. This is called as the phace inverse ratio.

Now, PIR= (T.i.m.e.o.n.a.b.o.o.k/T.i.m.e.o.n.f.a.c.e.b.o.o.k.).
cancel the common terms in the equation, we get,
PIR=(1/face)

It has been statistically proven by the likes of our peers Shriram Kardile and Sahil Patwardhan, that time spent on Facebook is roughly 5 times the time spent on reading a book.
so, it can be concluded that PIR=(1/5)
(from their publications Facebook is more fun that studies. Kardile,Patwardhan and Datar.)

Ok, so I  guess these many factors are enough to formulate the time remaining for the exam T.
We can conclude, that T, the time to exam is directly proportional to:
1)Attention span
2)Swearing time
3)number of calls
4)coefficient of attraction
and is inversely proportional to
1) Concentration span.

Thus, we can mathematically conclude:

Introducing the constant of proportionality, the PIR to the equation to get rid of the proportionality sign and substituting the values for respective coefficients, we get

  Thus, finally we have arrived at the examination formula.

Original research carried out by:
Chinmay A Datar
Anant M Devi.
Helping Hands:
Sumedh Dhabu
Virendra Kakade
Abhishek Ambede.

References:
Probability and Random Processes
-Stark and Wood. (3rd years, see, its not that bad a book. has many useful applications afterall)
Why facebook is better than book
-Sahil Patwardhan, Ajinkya Rao
Facebook to book ratios
-Shriram Kardile.

We thank all our friends for supporting us throughout the research, and are hopeful that our efforts will be awarded at the IEEE conference of vadheevpana.
-P.S- mathematical errors have been deliberately introduced to hide original equations and research.
-Authors.

Say NO!!

These holidays have been extremely frustrating. There is hardly anything going on. I am spending almost all my time at home playing or sleeping. Its infact so frustrating, that i am having online conversations about anything and everything.

One such conversation, with Rujuta, bore some quite funny results.Rujuta, to those who dont know, is my abrrevations teacher, and teaches me SMS language on chat.However, I guess she was also very bored. Thats why, deviating from our normal "bhankas" chat, we started discussing various scenarios about the possibility of me going on non-existant and imaginary dates, and started taking the micky out of it.

One such scenario was that if that imaginary girl asked me out.( as in proper asked me out.) How would I react? Well, obviously i was dumbfounded. If such a situation would actually occur, i think i would end up laughing. But then, she wanted a serious answer! So out of nowhere, i came up with " I will tell tomorrow"; which is really confusing. See, I thought I was telling that to the imaginary girl, whereas Rujuta thought that that was the answer to the question how would i react!! When they say, confusion creates laughter, they mean it. We were laughing over this for the next dont know how long!!

Well, at night, i made up my answer to reject the imaginary girl. But then I had to make up some way to say No!! you know- just confuse the girl, let the no parachute down instead of accelerating..so the next day we were discussing various ways of saying "No", and are actually still discussing them, and coming up with new, witty rejections, for the benifit of mankind. (See, rujuta, I am sharing credits! :P")

Here are a few that were my personal favourites.

1) Look at the girl... then look over your shoulder to an extremely pretty girl... then look back to the girl,and acting all surprized say " Oh.. sorry... am i in your way??"

2) say.. " I am sorry that i have to say No, as I really feel about your safety after this . Actually i would have said yes, but then your parents would have put you in the Mental Hospital!"

3) " If you are asking me out, You must either be Mad, Crazy, or totally whacked up. I only go out with NORMAL girls!"

4) "My dear, lets get the alcohol out of your system and then talk.... do you want to start puking??"

5)" you know, my mother is really scared of Ghosts. I dont want to give her a hear attack by going out with one"

6) " I am on a perilous path to enlightenment, which spreads to people who you love, and I am in no mood to SHARE"

7) "You are so hot, that if i even stand next to you, Ill vapourize, leaving you single again, and sad... so why take the chance of you getting sad?!"

8) then there is the classic one... " I am already set up somewhere else!"

There will be more, when we come up with them. till then laugh on!!
by the way, this post is meant as humour. I do not think that anyone should actually use them, unless you want to get hammered by a chappal.:P