Continuous Discrete Continuum!!

"The law of continuity ... consists of ... that each quantity, in experiencing a transition from one magnitude into another, must pass through all the intermediary quantities of the same sort. This is usually expressed by stating that the transition occurs through intermediate stages. Maupertuis considered these stages to be a number of minute additions occurring in a moment of time. He thought that the law must be violated at the same time for it is violated equally by the smallest leap or the greatest leap, since the concepts of small and great are quite relative. He was right if the term 'stage' denotes an instantaneous increment in any quantity. Really, it should be so conceived that particular states correspond to particular instants, whereas increases or decreases correspond exclusively to very small continuous intervals of time"
--- Geometry, time and the law of continuity.


Continuity. A term which many of us use everyday. But few among us realize the enormous complexities in this concept called continuity. What is this state of being continuous after all... the dictionary defines continuous as : Uninterrupted in time, sequence, substance, or extent. Lets set aside the mathematical part of continuity for a while and examine thoughts and their continuity.

I, for one, have found that the thought process can be described as a sort of convoluted continuity i.e lets say that my first thought occurs from seeing an image or a thing for e.g. a tree. My attention probably goes towards the leaves, their vibrancy in that particular season which might spring in the thought of vibrancy of life followed by a sudden thought about art or a painting with green undertones or a green dress worn by one of my friend. The point I'm trying to make is even in these so called vague or unconnected thoughts there is a sense of continuity. The best part is that this whole thought is like a tree structure. Depending on the direction the thought moves, it spans out this huge tree consisting of our memories, experiences and these thoughts which try to re-live or reminisce about them. Perhaps, that's why it's called a train of thoughts. The funny thing though is that if you interrupt a person during this and later ask him to re-construct the whole chain it'll almost seem impossible . More often than not, he'll end up constructing a new tree of thoughts though they've arisen from the same root!!

Evolution is another fascinating phenomenon where continuity comes into place. Right from the oldest creatures called trilobites to the so-called superior species of homo sapiens, we've all evolved and continue to evolve against the time-graph.But, if everything is continuum, where on earth does the concept of discreteness come into play? I guess , the best example to elucidate this would be the structure(if i may call that) of light. The physicists after centuries of experimentation have concluded that light nothing but a continuous emission of photons of discrete energy levels. So i guess what they mean is light has the qualities of both continuous-ness and discreteness at the same time(Bravo!!). Continuing in the same vein, that would mean that as evolutionary species, all the species which have evolved and continue to evolve have discrete energies does it not? Similarly, the thoughts of these discrete creatures are continuously discrete wherein the links between the discrete thoughts are what provide their continuity...

So these concepts of continuity are like the light and dark. The existence of one gives the meaning to the existence of the other. it is wonderful once you start realizing the enormity of this whole connectedness throughout this universe. The main question though, is that if both these continuity and discrete are relative, then what is real? Human mind refuses to accept anything that is relative as an absolute. So does that mean life, with it's discrete continuity is just an illusion? Or perhaps, the very word illusion is an illusion since it's nothing else but a play of light and dark? The best pictorial description of this question is the famous Yin-Yang wherein the light and dark are separate, yet they stay in one another and go on giving the purpose for the other to exist in a continuous vortex called time...forever and ever... So try shedding some light on this and let me know if you've found the answer.

Until next time,
Au Revoir.