If my friends were to form a circle, where would I stand? Will I stand as a point on the circumference, or will I be the center from where the circle would be drawn? Being at the center around which the friends would form the circle of life definitely sounds almost like a movie where you have been nominated in the ‘Best Actor’ category, and your friends in the ‘Best Supporting Actor’ category.

We stand at the center like the Sun. However, there is an irony associated. The planets have to maintain an optimum distance from the Sun. Too close, they collapse; too far they are gone! The points on the circumferential curve too have to maintain a distance for the existence of the circle. The moment that distance is annihilated, the circle is gone; and though there is no limit to how expansive the circle can grow – you from the center will only be able to watch out for the ones who are visible from the naked eyes.

What is the ideal situation? Let’s examine what happens if the circle collapses into the center. Will that make us complete? A point in time where the circle collapses into its center and we become one – is that what we are after all? I and my friends become so close that there is no more I and them? If that would complete us, are we not complete even without a circle? We still exist as a point from where infinite number of circles can be made. That implies that we might never be complete with the collapse of those circles into us because there will always exist a possibility of another circle getting drawn from us. The collapsing phenomenon can be said to complete us only if we are already complete with or without a circle. We – a point – a complete point. Add a glass of water to the ocean, it’s complete. Take out a glass of water, it is still complete. Draw a new circle of friends, erase an existing circle – I – I remain complete! So, does the circle of friends matter?

Are we a static point in space and time? Far from it, we are highly unstable points, one moment here and another there. We erase the circles we don’t need, we keep sticking to a few circles that we can’t let go of. We constantly change our position, and therefore the circles too get generated, regenerated, altered, and destroyed. They appear, they expand, they contract, they disappear.

Another question then arises – How important it is to have these circles with ‘you’ as the point in center? I believe we have to find our own answers to that. One interesting thing to note is – the radius of such a circle also depends on the number of friends you have and with increasing radius, all the points of this circle keep going away from you. How many can you see today with your bare eyes? Let’s count for a minute. I wish you good luck.

What are you wondering about? Choose your place. Center or the Circumference? Is your friendship just about you? Are you the one who always puts himself at the center and expects the others to form that circle around you? In that case, brace yourself to lose sight of a few friends, and to destroy a few circles? No? You want to be on the circumference? Very well. Be ready to lose yourself, prepare to get destroyed because the center will always be occupied by somebody.

The center never goes empty.

Excuse my ignorance, but why a circle or a circumference, if I may ask ? Are we not random points at random times ? Do we not meet and part and may be meet again?

Indeed we are. The figure you see is single unit of the concept I have tried to convey. Now, imagine hundreds of such figures overlapping, intersecting, diverging, converging within and between each other. It becomes a complex mesh. That’s where our mobile nature comes into picture. We keep shifting our position and we keep making new friends, forgetting old friends. If one entire life is considered, innumerable circles will form a complicated mishmash. I have taken circle to build upon the idea, since we like to think of friends as members of our friend circles. One can very well just take points in space and try to describe but circle is what we most often imagine (phrases like ‘surrounded by friends, ‘huge friend circle’ etc. ) A part of what you are suggesting, I have touched upon in the reply to Prince of Melancholy. We are points, extremely random but we also love to form these circles which comfort us and keep us going. However, at times these circles can also just keep us from what we can get only after this circle has been destroyed and we move on.

Hmmm… Wisely Deep! Deeply Wise! Wise! And Deep! This one grabs the trophy, if you ask me. Seeing the world through Mathematics is always bound to give rise to some mesmerizing thoughts. This one too succeeded brilliantly there. I am encouraged to send my minds to linger over undefined pastures without any definite rules or bounds. Thus taking the lead of the train of thoughts that this brilliant article has started, I was wondering if my friends are, indeed, points on the circumference or not. If we imagine them to be points, then say if I have only 1 friend or better say 2 friends and I view them as points, will I not cease to have a circle? Let me know if you go wandering there. I will too look for the answers.

My deepest gratitude for your compliments for the piece. Technically, if you are not the center, and you have 2 friends – you still form a circle (3 non-colinear points on circle.) If you want to go for just 1, even in that case, you end up with a circle if you stand at the center and your friend stands on any other point in space.

Amidst all these manipulations, there is one more thing to ponder upon – the center is actually not part of a circle. Does it imply that when we keep ourselves at the center, we cease to be part of the circle we tried to create? I think yes.

Thinking beyond the realm of circle, yes it can be thought of from varying perspectives. However, any closed structure can be thought of as a distorted circle. And a circle with infinite radius becomes a line. However, I would like to keep it simpler and let you think of you and your solitary friend as 2 points on a straight line of limited length. The point of the article is to discuss how important we are to ourselves and how important our friends are to us. If you think you treat yourself & your friend equal and your friends do the same, you are one lucky chap.