Yes! The title may surprise you at first but I’m talking about curves generally (not about that specific one you are thinking!). A curve can be understood in many different ways by different perspectives. Let us discuss these perspectives one by one:
Perspective 1. Simple Observation
A curve is a line which appears to be constantly changing in direction of progression thereby forming an enclosed or open loop which may or may not represent a shape which has some physical meaning. Anything that looks like below drawn shapes, or which doesn’t look like a straight line, or even close to it, is a curve:
Perspective 2. Mathematical Observation
A curve is a mathematical equation having two variables (say, x and y) that change their values more frequently with changing distance or time. That means the value of (dy/dx) keeps on changing, i.e., the value of y keeps on changing (y2-y1 = dy, for elementary distance dx) for small intervals of distance (dx). Let’s look at the example below:
In the figure above, the curve ABCDEF has different values of (dy/dx) at each of the points A, B, C, D, E and F. The quicker the values change with progressing curve, the more refined the curve will become. In case of a line, the value of (dy/dx) remains constant over the entire length of the line. (dy/dx) is nothing but the slope of the curve at a point, which comes out to be an equation of a straight line tangent to the curve and coincident to the curve at that point.
Perspective 3. My Observation
A curve is nothing but a series of end-to-end joined line segments. By looking at its smooth contour, one can’t notice the ‘straight’ nature of a curve but observing carefully, at a magnified scale, one can easily notice the straight lines which make the curve so curvy. Take a look at the magnified view of a simple arbitrary curve. Let’s take the example of an arc, for simplicity:
As you can see, a curve when magnified shows its true identity. A curve is actually made up of many line segments connected end-to-end and changing directions in the progression of the curve. This fact is very much evident from mathematical perspective as well. The differentiation of an equation of a curve gives the equation of a line, which means that a curve has line segments as its components or building blocks. So, I can say that a curve, when it’s seen from a distance, appears to be a curve, but when observed closely or magnified, is actually a sequence of line segments changing in direction. So, curves are an illusion. They never really exist. Only a tiny little point is real, which combines with other tiny little points or dots to form a line, and therefore a curve, a plane, an object, and a reality.
The Single Perspective – The Unified Theory of Reality
Life is a sequence of changes, but the changes are not abrupt; they take time. Think of it as the curve mentioned above with three different perspectives. Perspective 1 says that a curve is anything that is not straight. That means life is ever-changing; unexpectedly changing to any possible direction and never progresses with constant phase. People with this kind of perspective never believe in the immense possibilities of life. They see life as being defined by fate and destiny. Perspective 2 says that a curve is a pattern which can be predicted by knowing the points and values though it can’t be changed. That means life is all but mathematics and logic of events that happened in the past and are likely to give same results in future if the events happen in the same way. There are various techniques by which these points can be predicted, one such technique being astrology. But it all depends on what you believe. Studying closely the position of stars and relating them with the changes in one’s life is what astrology and related techniques and methodologies basically do. It may not be mathematics, but the outcome certainly is logical. People with this kind of perspective believe that the changes in life can be brought in by applying some form of logic.
Perspective 3 says neither about logic and mathematics nor about fate and destiny, but it says about unification of all of them. It says that a curve is simply a sequence of straight lines. Now, if you compare it with your life, it would mean that changes in life occur after a period of constant phases. Like a straight line, you progress in life constantly for some time, and then you feel the need to change. So the change occurs, either by your own will or as you believe, by the will of your fate. After the change occurs, you walk with that change again through constant phase for some time, and then again you feel the need to change. This is what life is! Sequence of changes and constant phases is what constitutes this miraculous existence called LIFE. The ups and downs that you face one after the other throughout your life are not actually ups and downs; they are changes that occur after a certain period of constant phase. Change is the law of nature; it will come naturally even if you resist it. But the direction of progression of the curve is entirely in your hands. Only YOU can decide which direction you want to steer your life to! It’s always your choice, it always has been, and it will always be!
Whichever category of perspective you belong to or you choose now, none of them is superior to another, because they are all perspectives and they deserve to be equal!
10 thoughts on “CURVES ARE AN ILLUSION!”
Nice way of presentation and comparison between the theories and the reality of life. Can see the deep thought and hardship of yours. Carry on it will make your life easy and you will be accepting each and every event of life.
Next topic: Infinity!
There must be alot to write about infinity… but where would u start from 😛
So, I am here after such a long time… it feels good you know…
Lol @ your first line.. haha! 😛
well, very true… everyone have their own perspecitive in life and that’s what make them different, one of a kind.
You are one such who had always been a unique thought. Completely different!
nice post (though i quickly skipped few lines… as i am not much keen of reading when it comes to geometry stuffs ) 😛
keep rocking and smiling!
Thanks! I find the whole mathematics boring…but u knw…to tell the world what you want to tell, u have kill your boredom 😉
And…good to see you back 🙂
My pleasure… and yeah agree on that, you got to forego few things to tell others what you wish to.
Changing to the change is a change in itself, but some times bringing the change to change things is a challenge !!
Concept…awesome. Loved the way you explain the complicated things of life with such common examples.
Thanks! More coming….!!
Absolute genius! Looking forward to your next topic Varun!