Spirals and Circles

So here is a mathematical answer to a question that I have quite often asked myself and seldom troubled my friends with: “Does life move in Spirals or Circles?” The course that life takes is often described as a maze by some and a road with lots of twists and turns by others. A complicated web of events, people, emotions and thoughts, caught between these is you, the spider. A lot of our religious books refer to the course of life as “the cycle of life”, which essentially means “the circle of life”. It is perhaps the phrase used most often during those innumerable philosophical discussions that boring people like us have over drinks with friends.

Yes, I have been ranting for quite a while, without really bringing in what I promised: the mathematics! In laymen terms, a circle is a two dimensional figure which is a collection of all points that are at equal distances from a given point. Essentially, a circle starts and ends at the same point. A spiral, is a three dimensional figure which is “A curve on a plane that winds around a fixed central axis at a continuously increasing or decreasing distance from the axis”.

Now, the arguments for both circles and spirals are logical and believable. However, what matters here is whether our conclusions are based on completely exhaustive reasons. If you consider life to be moving in circles, or say, “life is a circle”, you are talking about a two dimensional figure. The two dimensions could well be “time” and “experiences”. So if we were to draw the graph of life, it would look something like this:

This figure justifies the never ending behavior of life and the concept of rebirth in its essence. However, if we were to break life in a smaller compartment of say “a set of experiences” or “the life span of 1 year”, then this figure is highly inappropriate for a very basic reason that it does not encompass “life” in its entirety. Agreed your life moves in the above circle, but then you cannot deny the fact that your life is NOT static in terms of the range of experiences you have. Looking at this figure, what can you say about your life after the one year represented by this figure?

So, we can safely say that perhaps life does not move in a SINGLE circle. Perhaps it could be a collection of circles with the same radii, placed horizontally next to each other and touching each other only on the “Time” Axis? Yes, it could be that for a compartment of “life span of say 100 years”, wherein we keep moving from one circle to another as “time” changes. Now this model may seem appropriate for a compartment such as the one mentioned here, but it does not encompass the concept of rebirth which our previous model could.

Also, a major disadvantage of both the above mentioned models is that they overlook another dimension of life that is “perspective”, which forms an integral part of how we see life and how we experience life. It is undeniable that as “time” changes, a person’s “perspective” also changes. How you see the world at the age of 16 is very different from how you saw it when you were 6 or how you would see it at the age of 60! Now, “time” and “perspective” may not be linear functions of each other in anyway, (or they maybe) but they do change simultaneously. Hence, we present a figure more appropriate such as this:

  

In this figure, the “experience” axis remains constant while the “time” and “perspective” co-ordinates vary, which fits well with our above mentioned assumption of “changing perspective”. This looks more or less like a spiral without “moving away from a central axis”. The points in this figure are “equidistant from a central acxis.Readers might wonder about the usefulness of this model to the concept of “rebirth”. Well, this model also takes into account this concept as the parametric equation of the model:

X= 4tCos[t]

Y=4Sin[t]

Z=t

Is a modified version of the equation of the circle, wherein we keep coming back to the same “experiences” with a different perspective as time passes. Or to put it differently, the “cycle” of rebirth and death continues but as we move from one life to another, our soul matures and our perspective changes in a new birth!

P.S. This was a small attempt at “modeling” life in terms of three dimensions. We all know that life is multi dimensional and three dimensions would perhaps not suffice to model life. But, as they say “One step at a time”! However, this model is in a very basic and primitive stage and can perhaps be made more encompassing. Readers’ suggestions are most welcome. Further, I would be obliged if readers could point out any technical errors that I may have made in this particular model.