Social Gatherings, Conversations and my inner awkwardness :-

One of the most troubling questions I have faced in my life ever since childhood is the following ,
            " What to talk with people?"
As I examine myself to the core,I see that I'm a terrible conversation starter . Usually I start with a "Hi!" which is like .. sounds perfect.. clearly heard and loud to me in my mind ,but to the other person it's like   " Did you say something to me?"

So clearing my throat I go for a second try "hi" accompanied by a raise and wave of hand and the other person smiles and replies "Hello" and that's it there ends the conversation,with me thinking in my mind "Should I have said something more? Maybe I should have asked How he/she was or How's everything going on? " .... Awkward feeling in my stomach.....

So years back when I stumbled  across such a situation in high school I had a solution . And this time too like every time the solution came from math.

" Consider two sets I and U , I denotes the set of all my interests and U denotes that of the other person . So a conversation  would result when I ∩ U ≠∅ ."

So with this I moved forward and noticed that
Card(I∩U) ≪ Card(I)  ,
Card(I∩U) ≪ Card(I). 
The commonalities at that time was only few things like watching dragon ball Z and other CN shows and of course interest in Science especially Physics and Math.

As years passed by while looking at people I somehow tried the science of Deduction every time as recommended by sherlock. It's often like putting together bits of info. It's like solving a jigsaw puzzle . The bits of info. often came from social networks like fb, and info. overheard from people. 

Most of the time it came true .   To me it was like playing the Game "Watch Dogs" everyday. 

Till today social interactions often leave me rather puzzled. To me at the end of one , it gets recorded and starts playing @ HD 1080p in my mind in a loop . Until an hour or so with awkwardness filling in me every time .
It's as in the movie "Beautiful mind" it makes me Terrified ,Mortified , Petrified,Stupefied .

Somehow talking to people about Hecke Algebras,Non-Trivial Zeros of Riemann Zeta Function,The method of Lagrange Multipliers,Importance of Feynman Diagrams,Evolutionary Game Theory... Random Mumblings about a new theory has become far too easy than to put a smile and talk about a new Fiction novel, Latest Movie ,Hit song of the year,IPL or Cricket 

( Even while writing this my mind thinks of Duck worth lewis method ,Batting Stats,Harmonics,Matrices in special effects in movies,Misprints in a book -Poisson Distribution. ....... hmpf.) .


So till today a relationship with anyone has become a "Game" to me.
The word "Game" is taken in sense of a mathematical Game. It will be clear to anyone who has seen Numb3rs:

I do sometime feel that 

" It's easier to understand a Millennium prize problem than to get socially involved ."

I might be wrong (as my intuition of a Cooperative Game says so) but I think I may change over the ages....













  

PEACE,LOVE AND MATH:-

Part-II :-

"Me and my girlfriend are like a complex number, I am the real part while she is the  imaginary one."

So with my mind scattering around  random thoughts some of these are what I could think of her:

"Even before I knew you ,you entered my ε neighborhood. So to begin with you were present in my deleted  ε neighborhood.When I finally came to know all about you,I noticed a similarity in our ε neighborhoods.It seemed to me that there existed an Isomorphism  between them."

"But at the end life is never like a differential equation,just plug in the initial conditions and you can know all about the future. It's rather stochastic. Even if you know the initial condition you cannot predict the future. So I feel I'm no longer in your ε  neighborhood but you will remain forever in my ε neighborhood."

Further with study of Nonlinear dynamics ,I came across the following mathematical model of Steven Strogatz :-

The Strange love Story:-

"Romeo is in love with Juliet.He warms up when Juliet loves him and grows cold when she hates him.Whereas the more Romeo loves Juliet,she wants to run away and hide.But if Romeo gets discouraged and backs off,she finds him attractive."

The mathematical model:

Let 

R(t) denote Romeo's love or hate for Juliet at time t.

J(t) denote Juliet's love or hate for Romeo at time t.

R(t)>0 : Loves Juliet    R(t)<0 : hates Juliet
J(t)>0 : Loves Romeo    J(t)<0 : hates Romeo.

Now Considering our Strange love story we have the following mathematical model:-

\

 

  ( I Swear that I'll learn LATEX someday in the future ,but that day i'll be regretting for not doing it before, )


So in this cycle of love and hate Romeo and Juliet cannot be in love or hate forever.Rather in a cycle of love and hate forever.


THE END.............................NOPe.

Perhaps this model can be improved by considering some other love stories or How about a triangle love story. There can be infinite possibilities  one has to just keep calm and do the math right.

"While physics and mathematics may tell us how the universe began,they are not much use in predicting human behavior because there are far too many equations to solve .I'm no better than anyone else at understanding what makes people tick, particularly women."                                                                            -Stephen Hawking.

Peace ,LOVE and Math :-

Part - I:-
"It takes no time to fall in love ,but it takes you years to know what love is."-Jason Mraz.

(For the first time I think I have quoted something  non-Mathematical!) 

When I look at this world and everything in it I often have two views for everything ,One that is mathematical and the other that is the normal view similar to what others have . Considering love I haven't yet had the latter one but I have indeed looked at it in the mathematical way.

Math and LOVE :-

1.  Love is not a pie hand out your 8 slices and you are done ,

             Love is like PI   its irrational and never ending.

2. Math often tells us three saddest love stories :

    a) Parallel lines who were never meant to meet.

    b) Tangent lines who had one chance to meet and then parted forever.

    c) Asymptotes that get closer and closer but never meet each other.

 In euclidean geometry two parallel lines never touch.... let's go back to my place and study some non euclidean geometry.

3. Numbers,Equations and inequalities that describe love:

    Me and my girlfriend are like complex Numbers , I am the real part while she is the imaginary one.

4. Love proposals :

    

5.Thoughts of breakup :

 

Studying Mathematical love dynamics is one interesting area of applied mathematics .  I feel that perhaps this is the path for me to understand what love is, and how to quantify it .  

Part -II coming soon until then .......  perhaps you could do some Elegant math and have fun.



"Beauty is the first test. There is no permanent place in this world for ugly mathematics." 

                                                                                                                     -G.H.Hardy.

A Mathematical analysis of "My" friendship dynamics :-

With motivations from an earlier post,
http://karthik-4dmspace.blogspot.com/2014/09/memy-social-awkwardness-and-my-only.html
the fictional characters Charlie Eppes,Sheldon Cooper and not to forget the most terrifying device for me in the electronics lab ''THE ZENER DIODE" ,Finally I thought of doing an analysis of "My" Friendship dynamics.

The reverse approach :  This refers to new people who talk to me and how my friendship progresses with them .

Given  the condition that people keep having a conversation with me whenever possible my friendship progresses with them identical to how a zener diode works in its reverse biased condition   till an voltage called  breakdown voltage is given, it doesn't conduct. Similarly until a time (tB)  my friendship doesn't progress with them  ,after (tB) it increases and reaches an extremum and then it becomes constant.

The forward approach : This refers to how I talk with new people ( This according to me is the one and only one problem I cannot solve myself ,in spite of me being a budding mathematician )  and how my friendship progresses with them .

Given  the condition I talk to people,
,the friendship progresses identical to how a zener diode works in its forward biased condition (i.e similar to an ideal diode,it starts conducting.) until, it reaches an extremum and then it becomes constant.

Further with motivation from Shockley Equation for diode : Friendship as a function of time R(t)  

      For forward approach :  

      For Reverse approach :

Hoping that in future I'll learn Graph theory , Social Network Analysis and add a dash of Game theory to spice it up , so that my friendship dynamics might take a giant leap into the future ,"To infinity and Beyond !"



"Every positive integer is one of Ramanujan's personal friends."
                           - John Littlewood (On hearing of the taxicab incident.)

Forks and Spoons ....amidst them lies a mathematical thought :-

It's strange that most of my mathematical thoughts emerge when I eat at the canteen. It was a dull evening .Dull for me because I had a bad cold that day. I was in a mood to eat something hot that could cure my cold. The only hot stuff I could find that day was Maggi .

I was delighted to eat my favourite snack , favourite partly due to the fact that Naruto eats Ramen :)  )
But was sad as I couldn't find a fork .   I began searching for it in a bowl full of spoons.

Meanwhile my nose began to trouble me.  But I didn't cease my search.  Finally I found one.
I was happy that I could eat Maggi with a fork and not a spoon after a long time.

Amidst the steam of hot Maggi I got a thought... This time it was outlier detection.

This thought emerged due to the fact that I had to search for a fork in a bowl which looked like it had only spoons . But as the search went on I found a fork.

In a similar way in Statistics an Outlier is an observation point that is distant from other observations.
This may be due to variability in data or due to an experimental error. 

In a giver data set finding an observation which is distant from others is known as outlier detection.

Another analogy to this is given by Prof.Charlie Eppes in NUMB3RS in the following video:-

The maggi was good and so the mathematical thought !

"A mathematician is a scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle."  -Evan Esar ( Esar's Comic Dictionary)

Waiting .. Waiting... For something.. Every moment of life :-

It's hard to describe the feeling of waiting for something. Waiting for the right bus/train to board , Waiting to receive someone at the station. Waiting for the book or item you ordered online.Waiting for your favorite T.V. Series to get  downloaded. Waiting for the power to come back and so on ........................................... (The list gets overflowed..).

And its even hard to describe the feeling when you are on a long journey and you don't have a cellphone for playing games or listening to music... or even to get battery 100% charged ....

In Situations like these I remember the following sentence which was ,as far as I can remember,was in a lesson in 7th class Telugu textbook I studied,

"నువ్వు ఎక్క దలచిన బస్సు ,ఒక జీవిత కాలం మిస్సు . "

meaning : The bus which you want  to board ,you always will miss it for life time.

I can't remember the author or the person who quoted it. I tried hard.

But it seems true in situations like that ,eagerly waiting for something,

The math that gets in my mind in such situations is fairly simple  ( of course , I live every moment of my life with something mathematical.) which is the following problem.

Two friends A and B agree to meet in the canteen during their 30 minute tiffi n break. A will wait for B for 5 minutes if he shows up first at the canteen. While B, the more patient of the two, will wait for 10 minutes if she were the first one at the canteen. Calculate the probability that the two will meet.

Solution:-

tA :Time of Arrival of A
tB : Time of Arrival of B

The Constraints on A and B waiting time yields the blue region.

Probability of their meeting is 

Area of blue region
________________  
Area of Square 



= [900 -( 200+312.5)]/900

= 0.43.


So A and B will meet with a probability of 43%, Not that bad .  
Well in solving this problem perhaps my wait is over and I get what I wanted.

" Life is good for only two things , discovering mathematics and teaching mathematics."                                                                                                                                                                    -Simon Poisson.

It's my birthday tomorrow and my friend mathematics wishes me mathematically in many ways:-

1) I'm 19 years now. 
The no. 19 is a happy prime.i.e. it is a prime and satisfies  the following property.

1|9     : (1)^2  + (9)^2 = 82
8|2     ;  (8)^2 + (2)^2 = 68
6|8     :  (6)^2 + (8)^2 = 100
1|0|0  : (1)^2 + (0)^2 + (0)^2 = 1! 
( Source: http://en.wikipedia.org/wiki/Happy_number)

2) ஓட்ட  வடை(Sambhar Vadai)  my  favorite dish:
I remember asking my mom to prepare Sambhar Vadai for my birthday which is inauspicious to prepare on occasions which are good such as birthdays but now I realize that as a wholly different thing,

It reminds me, the structure of a torus which topologically speaking is a product of two circles S X S in C^2.
 This has a consequence that topologically a coffee mug and Sambhar Vadai(Torus) a similar  as they are homoemorphic .Since the latter is my favorite the former is also my favorite drink. :)


3) The birthday problem :
" In a set of "n" randomly chosen people what is the probability that a pair of them will have the same birthday."
(Assuming the year is non leap year i.e. contains 365 days)
( As a budding Mathematician I wanted to study the generalized birthday problem but since the Density of my social network is tending to zero(to know more click here),it's better I stick on to the trivial case.:) )

Its clear that for n>365 probability that a pair will have same birthday is 1.

Solution:-
Let
n : Event that a pair of people will have the same birthday.
n# : Event that a pair of people will not have the same birthday.
P(A) denotes the probability of occurrence of event A.
_
P(A) denotes the probability of not occurring of event A(=P(n#) here)

we must have P(n) + P(n#) = 1

Since it's easier to compute P(E#) in this case we have

P(E) = 1 - P(E#) 

So,the required result is 
             _
p(E)=1-p(n)

In my case as the density of social network is low, it's guaranteed that p (E) will be low but let me wait till tomorrow and see.

4) Cake cutting Algorithm: 
I may or may not cut a cake for my birthday also I don't eat cake much ,maybe I  have nothing to say, but here's a video on how to mathematically cut a cake the right way:

An equation means nothing to me unless it expresses a thought of God.                                                                                    - Srinivasa Aiyangar Ramanujan.