Functions & Life - 2

Hello Everyone,

It is 2345hrs right now, I want to sleep badly, however, before that I would just like to share some words with you.:) Yesterday's post might look crazy but thats the way I feel about life. I started learning about the concept called "Sets" when I was about 10 years, in the mathematics course of 6th grade. After that in the next grade, I had learnt about "Relations", and the list follows. Now when I look back, I feel that those concepts are much more important than what we use them for. They teach us something else too.

A Relation can be termed as a Function only under certain condtions, in a similar fashion, any personal relation in real life would be functioning properly only under certain situations (when proper amount of time, money and interest is invested). Similarly, there would be specific Limits to any function, as we do have in any real situation in life. Identifying the limits is one of the most important aspects in the analysis of a function, which is quite analogous to real life, where it would always be better to identify our limits under any situation and behave accordingly.  

1. I curse my poor memory, as I forgot the name of a theorem which states that any function can be expressed as a sum of series of sine and cosine terms. As we all are well aware of the behaviour these famous trigonometric functions. They are periodic fluctuations (ups and downs).

Doesn't this seem like something???

2. We all know that life is a repeated cycle with up's and down's; infact only change is constant in life. There would be high times and low times in all of our lives' which neither stay forever nor conclude at once.

Now I get close to make a point here. Doesn't 1 & 2 seem similar??  I was surprised when this thought arouse in my mind. It was quite fascinating. It was then that I believed there something else to mathematics, which I should start to understand. From then, I started relating everything in mathematics to life, and I find it wonderful. Apart from that, I also had some analogies between the concepts of mathematics and science which can be realted to life.

I want to type more, but its 0020hrs right now, and I got to catch sleep. See you people tomorrow.

Let peace prevail in this world

--

Sun

Functions & Life - 1

Hello everyone,

A tiring day. Started with a "Molecular Simulation" class and a couple of classes on "Jordan Blocks" & "Stability of Roots"; finally, some work on matrices ended my day. Today, I would start writing about my experiences working with functions and how they can be related to our life.

Sets --> Relations --> Functions --> Differential & Integral Calculus --> Difference Equations.

The above order represents the hierarchial order of courses taught in Mathematics. All of us are well aware of sets, and these simple concepts form the base of Calculus. Sets containing ordered pairs can forRelations, which lead to Functions under some special conditions(injective, bijective or surjective), and these Functions act as bridge to enter Calculus, which is one of the most wonderful inventions in  history of mankind.

Now, whenever I start thinking about functions, (as you know there can be an infinite number of functions written with various combinations of variables, constants and numbers), I just think of them as our fellow people. In life, we can find various kinds of people with different mentalities, habits, personalities, disorders, behaviours, likes, dislikes, and many other features, which is quite analogous to various types of functions which can be increasing, decreasing, constant, fluctuating, oscillating, continuous, discrete, even, odd, exponential, logarithmic, special functions(just like some very very special people in this world).

Also, it would be quite amazing to observe the fact that, all of us have high and low times in our lives (well, atleast most of us) which is quite similar to a function which has maximum and minimum at some point in its course. Well, some functions are monotonically decreasing, while others are quite opposite, similar to people who had always been succesful and some other who always taste failure.

Another fact which would quite interest us is that similar to how the behaviour of a function can be studied with the help of calculus (i.e. analyse its growth rate, identify maxima and minima, etc.), the behaviour of a person can be studied with the help of Psychology (which analyses the cause of a person's action under certain circumstances). Apart from that, just as we can change the behaviour of any function by manipulating its variables or constants, or interchanging the variables, the behaviour of humans can be changed by Hypnotism.

I guess my words seem sensible to you :). I always look at everyone in this world as a function, which has been pre-defined, and the way anyone behaves is due to that intrinsic function (i.e. the inherent qualities which was attained and developed from birth). One more analogy, would be that, there are a lot of time-dependent functions, which change their nature with respect to time, and it is a fact that we all change with time.

I strongly believe that every subject we learn is related to other, and all of them teach us how to live. I would like to write some more, but I my function for today needs to find constant rest with respect to time for the next 6 hours in the time domain. So, I would bid adieu and would come with many other ideas tomorrow.

Let peace prevail in this world

--

Sun