Each one can be unique !! - a mathematical proof :)

{CREATIVITY,CRITICAL THINKING , RESILIENCE, MOTIVATION, PERSISTENCE,CURIOSITY,QUESTION ASKING,HUMOR,ENDURANCE,RELIABILITY,ENTHUSIASM,CIVIC-MINDEDNESS,SELF AWARENESS , SELF DISCIPLINE, EMPATHY, LEADERSHIP, COMPASSION, COURAGE, SENSE OF BEAUTY, SENSE OF WONDER , RESOURCEFULNESS, SPONTANEITY, HUMILITY , ARROGANCE - quality list taken from the net} The above qualities are just samples.
Let us say there are n qualities and m people in the sample space
Q = {Q1, Q2 … Qn}
P = {P1, P2 … Pm}
->each person has only one of the Q
if 2n > m > n, according to pigeon hole principle there is (m-n) people will have same qualities. Take n is 30 , world's population is infinity compare to this !! so its impossible for a person to have unique quality.
The above mentioned is “Each person has only one quality” but it is not the case in the real scenario. For example a person can have the combination of 2 or 3 or n qualities.. So now the complexity increases
We need to map matrix for each person
P = {a1Q1, a2Q2,……anQn}
now let us say coefficients a1 , a2 .. an can have only two values 0 or 1 ,
Consider a person has quality Q1 , Qn-1 and Qn then the string is
P = 10000…0011
Combinations provide 2 ^ n
if there are 30 qualities then 2 ^ 30 = 1073741824 unique characters which is less than world's population.. But in this calculation we assume a person can have a particular quality or he can not have particular quality.. But in the real scenaria person will have fractions of quality
Consider the fuzzy set { Very Low , Low , Normal , High , Very High } are the 5 levels of the coefficients {0,0.25,0.5,0.75,1}
Convert that to 5 levels … 0 ->0 , 0.25 -> 1 , 0.5 -> 2 , 0.75 -> 3 , 1 -> 4
Now so a person have low quality 1 , high quality 2 , very high quality n-1 , normal quality n then the string would be
P = 1300….0042
In this Qi is independent of Qj where i != j
For example An arrogant quality person can have sense of humour . a courageous person can have love !!
Therefore we can have L^n combinations , where L is the levels of the quality. As we increase L and n the characters lead to infinity !!!
Calculation
L = 5
n = 30
then 5 ^ 30 = 9.31322575 × 10^20 which is very high value compare to world’s population so theoretically It is very much possible that all people are unique in their own way in this world !!! In this proof I have not used time variable .. since human beings are time-variant and situation variant !!!
The people who stand out amidst of many people for the following reasons :::
They have Good qualties >>> Bad qualities
Their qualities do not vary with time and situation very much !!!
They have range of qualities which combine together form a super-uniqueness !!
Examples : Harishchandra , Prahalath , Bagirath , Sachin , Narayana Moorthy , ARR etc ...

Intuitive meaning of Wavelength , Frequency and Velocity Relation -- Jithendrian

This is the one i consider as my best !!
As everyone knows velocity of a wave is the product of frequency and wavelength. The derivation for this is simple and given in so many text books using wave number. But I am totally confused how it can be intuitively and physically imaginable.First of all how to relate wavelength and frequency !! After a long try I came up with some analogy which will help you in thorough understanding of wave equations.Below derivations and concepts are 100 % my own work .. I am not telling this to boast myself but to tell the originality. So please feel free to comment/give feedback

Let us consider A and B are the source and destination . A is a gun and B Is the target
Length of the bullet = l
Distance between the gun and the target is d
Number of bullets shoot on the target = n
t be the time taken for the first bullet to reach the target as well as the total time taken for shooting n bullets



Assume that the bullets are shot continuously , n bullets with length l

Now the distance d can be expressed as


Another way to express d
Let v be the velocity of the bullet
t be the time taken to reach the destination
then


Equating (1) and (2) we get



We know when a first bullet reaches the target at time t there are n bullets are shot , number of bullets shot per second (k) is



Now put the equation (5) in (4)



Now come back to our electromagnetic wave (assume waves are as packet moving in a single path and not as particles )

Wave is like a bullet
Number of bullets shot per second (k) is the number of oscillations/vibrations or repetition of the waves per second which is nothing but frequency (f)
The length of the bullet (l) is the length of the wave (lambda)
Velocity of the wave (c) is the velocity of the bullet (v) Gun (trigger) acts as antenna finally interchanging the above form to



Substituing every thing(7,8,9) in equation 6 we get


Which is the bread and butter equation for a wireless engineer!!!

P.S all equations and pictures are made by me without copying :) using pptx and converted to image. If anything is not clear please let me know

Applied mathematics is challenging ??

Mathematics is the only subject which avoids so many if and buts.When a person says he is not good in mathematics we immediately deduce that he is not an intelligent. Why mathematics is tough ?? Small child when it is in LKG / UKG it is asked to memorize number 1 to 25. Up to 1 to 10 it can do addition and subtraction using fingers then it blindly follows some algorithm for > 10. When it goes to 1st standard , It is mandatory to memorize upto 5 tables .. i.e look up table in modern term. Slowly the mathematics becomes abstract and not like concrete science. When the child writes 10th standard exam , for him maths and science are two mutually exclusive subjects !! Then 12th exam all vector ,analytical geometry , trigonometry , differential equations , calculus etc... Mathematics has become a abstract scoring subject , hitting a six with out knowing in which direction the ball is hit !!
In engineering , First few semesters we study Laplace transform , Matrix algebra , vector algebra , complex theory , Fourier analysis every thing before the real application-subjects such as electromagnetic theory , circuit analysis , Signal processing come into the curriculum. So we are still studying abstract mathematics for first two years in our engineering. Last two years we try to derive the mathematical aspects of Em Waves , Signal Processing etc.. They are not aligned !!The ultimate truth is Maths teachers do not teach the application of Mathematics and Science teachers think we know the mathematics of the subjects !! So again Mathematics and Science/engineering not connecting to each other !!

So we finally realize we are good in maths , we are good in engineering but we can not read some research papers because when we fuse together 'Applied Mathematics' we are still bad in this !! How many of us know the physical meaning of Eigen value and Vector !! How Fourier series is derived from Taylor series !! How Maxwell derived em equations 24 years before the experiments done by Hendry !!
Our curriculam should teach mathematics parallel to science and engineering . Alignment should be perfect.In general , from next generation on wards we need to insist our children to concentrate on applied mathematics rather than pure mathematics !!

Life always asks us to Optimize !!! Part 1

During LKG we had to trade-off between parents’ affection and learning in school.
Optimize ( Parent Affection , Learning)
Better schools far from our house unfortunately!! We should trade off between comfort and better education.
Optimize (Good Education , Comfortness)
From our child hood , life asks us to optimize our priority.
There are some vital optimization is needed in life ..
In this world most of the scenarios are like a + b <= constant.
So both a and b together try to attain the constant first.
Now the equation becomes
a + b = constant
Here is the check. Whether a should be high or b should be high or both should be same !!! This is called trade-offs
Arrogance (a) Vs Submissive (b)
People generally tell optimizing these two called assertiveness. The amount of assertiveness varies from person to person. As per the definition the assertiveness is a win-win situation. Like a = b = 0.5 * constant
Optimize (Arrogance , Submissive)
Bachelor life Vs Marriage Life :- Bachelor life means freedom . Enjoyment etc... but we can not stay as a bachelor forever. Marriage life means responsibility, give-and-take , emotionally bounded to family etc.. Both has advantages and disadvantages. It’s very difficult for anyone to be a bachelor for long time especially in Indian society. There should be a tradeoff between getting married and not getting married. Age = a , Settlement = s , Probability of getting Good spouse = g and constant k
g=k* s/a
As per the above statement as the age increases probability of getting good spouse is decreased
s α a this is an important constraint. I.e settlement is directly proportional to age in most of the cases.
Total confusion. We get good spouse only when we settle well. We get settled well after some age . When we take time to settle we do not get good spouse
Optimize (Age, Settlement, Good Spouse)

Be strong in Basics - II

A person who could calculate standard deviation of first 100 prime numbers in just 2 minutes in college struggles to multiply 2 digit by 2 digit number now because of technology. Yes he is a quality coordinator of a company for the past two years. He has been using excel,calculator etc... now he has lost interest in numbers !!!

A person who could write an english essay without any spelling mistake , now he struggles to write a paragraph in notepad with out spell check.

Just try calculating numbers with out calculator or computer then we people will find the difficulties.Write a paragraph in notepad then we will find the difficulties and last but not least try to write two pages of a letter then we will find the difference in our handwriting from college days to now !!
(this is meant to people who had good handwriting , maths skill and english skills,
if we do not have please do not try unduly .. results may not be significant difference)

There are so many examples .. this post is because we develop so many skills through technology. Even One day if we do not have technology we struggle a lot in very basics which is much more important than the former..

I am not blaming technology .. we need to practise to calculate mental maths , grammatical english everyday 10 mins to exercise our basics. It will help in teaching our next generation. When we are asked to teach linear algebra or number theory to our son / daughter or relations that time we should not feel ashamed !!

Thanks
Jithu (One of the victims !! )

Be strong in basics !!!

Go back to School days and retrieve basics !!
http://ncertbooks.prashanthellina.com/
I am going through books from 9 th standard to 12 th standard. Excellent books. It reminds me my school days. I studied in state-board school. I concentrated more on mathematics than other subjects. When I was going through ‘properties of matter’
I was thinking for 15 min about those things.We have lots of subjects in college level to study.How does it matter to read school books. Yes it matters. Starting from attraction between the particles inside an atoms which decide solids , liquids , gases with respect to state and electrical conductor , heat conductor with respect to Electricity !! Yes I admire the way it was written. It paved me the path to think about electro-static force between two charged particles , hysteresis etc…
I am studying now in 9th standard science book 1st lesson . http://ncertbooks.prashanthellina.com/class_9.Science.Science/CHAP%201.pdf
I would suggest people go through basics , i.e to our school days and start reading. It will give you mental pleasure and we can feel today’s computer science(base from silicon) , wireless networks (electromagnetic waves using properties of waves ) and we can wonder how these fields are emerged and especially the curriculum our government keeps to step up us from basic science to computer science !!!
I learnt from my one of the favorite professors of IIIT Bangalore Dr.G N S Prasanna,MIT,US that If we are strong in Physics/science and Mathematics we can rule the technical world. He has more than 15 patents in all the fields from combinatorial game IChess to Magnetics in Robotics. I admire him !!
We should be strong in basics which is like a land and our engineering concepts are like buildings. In general land is more valuable than buildings !!

Are we doing RESEARCH ????

When I was supposed to do my research for my research elective course , i started with wireless networks which is my area of research. I started studying about wireless , suddenly went through electromagnetic waves , then i went through particles , then light waves, micro waves , x-rays , gamma rays etc.. and finally start analyzing about thought waves . Started thinking philosophically about out thought process. The day over !!
Next day i left that issue and started with networking , then transmission, reception etc.. I started with hardware related to transmitter , i read about network processor then started studying about micro processor which reminded me my BE 3rd year. Then i started going through instruction sets , registers etc.. Then i took Morris Mano for Digital Circuits and went through Registers, Flip flops etc.. In turn it directed me Basic electronics for BJT and Semiconductor Physics ... While going through Semiconductor Physics , started thinking about silicon molecules , proton,electron etc... i was thinking where was my wireless networks !!!
Research are generally classified into 3 broad categories

1. Researching on Good ideas
2. Researching on Implementing good ideas
3. Researching on studying the feasibility of idea

But according to one of teh researchers in an article mentioned that any great research should fall in above three categories and not one of teh three categories.

I realized - Research is not just searching for new ideas... it is a concentrated thinking process to produce a great idea as a result with input as all technical fundas .. !!!

I started working on wireless networks only. I derived some 2 pages derivation and wanted to experiment but i could not practically implement even 20 % of what i had done theoretically. Then i realized “Giving ideas are easier than implementing Ideas”. There are humongous amount of stress in research and it is very difficult to come up with idea + implementation . Research need not be only in technical side , people can do research in any field. My experience is with respect to technology. My sincere suggestion /request to people who are in the shadow of research “please do not say we are doing research , please tell we are trying to do research unless we are not implementing good idea ”. My friend Balakrishnan always says whenever i discuss with him a new idea , his first words are "Check whether is it practically possible or implementable ? , If not try to find out why can't we implement this". That time i always get irritated why he is always defending me but later i realized he is correct !!

Finally , last but not least there are 90 % of the people are normal in this world and 10 % of the people are living in their own world , in that 5 % are mad and 5 % are research people !!! I do want to live in my own world i don't know in which 5 % :)