Poemander

Circle is the greatest hindrance to a rational mind. It is the most inundating and alien concept ever observed. How did it enter our living with such elegance yet out of this world transcendence? It must be a plot, a deliberate stratagem to make us ever wonder, or perhaps even question ourselves, our nature and our origin. circle doesn't fit our understanding, it simply is beyond our logical proof. Oh, how perfect, accomplished and rational our world would have been should this circle have not entered the Euclidian realms. But this is not how it meant to be: inscribed right into the basis of a grand design, the circle is integral to every mystery and truth contained in this world and beyond.

Rationality is unable to reach circle directly, thus the transcendental nature of pi – this bridge between the rational and real, subject and object.

Geometry, from the dawn of time, deals with only one problem – the problem of observer. For the observer brings one major complication, or a simplification for this matter – a point of view. In essence, everything in geometry is a sphere if there is no point of view or the observational bias, shall we call it as such. The straight line, all shapes and solids are the observational bias. If you exclude this bias by assuming a point of view of every imaginable observer from every imaginable coordinate, you will get any form as a sphere. This can be easily witnessed from a simple experiment of spinning any shape or solid with a consistently changing axis tilt. Upon completion, after the axis will have passed through every coordinate (no matter how many dimensions, but for the visualisation we here assume a three-dimensional shape) we'll get an imprint of a sphere. This shows us the 'unbiased view' of any shape or an item should the observer be present in all locations at the same time. The sphere, thus is a 'uniform' shape or indeed the only 'unbiased' shape existing.

Now, moving further, what if in the mentioned experiment we spin a finite line? This would have still given us a sphere, but the times when the tip of the line will pass in front of the observer and viewed as a point will be considerably lesser than the observation of a line at its length. Without accounting for the number of times each part of the figure passes before the observer, we'll still get the sphere on completion of all passages. Should we want to strengthen our bias by counting how many times each part has been observed, we'll eventually be able to deduce and revert back to the given shape, here, a line. An unbiased observer, therefore, will not only be in all places at the same time (eliminating space bias) but also will not discriminate towards the repetitiveness or higher probability vs lower probability, i.e not regarding 2 occurrences as more informative then 1 occurrence (eliminating time bias).

So, what if the object observed is an infinite line? The information of the full sphere will not be complete where the tip of the line (infinite line) passes through, or unable to pass through, the observer. Every other shape of an infinite property will not render a perfect sphere either for the same reason – incompleteness of information. However, this issue here is rather irrelevant because by working to remove the bias from the various aspects of observation should we not also assume the limitless nature of the observer 'inline' (pun intended) with the limitless nature of the observed form? I don't think it is too much of a stretch since we have already delved into concepts rather abstract, at least to pragmatic minds. I should make a detour at this point, clarifying that the abstractness of a concept is merely a matter of pragmatism which itself is based on observational bias. Thus, one should at least accept that even some most disconnected and abstract idea must have such angle of observation from where it appears definite, practical and concrete. And by not deliberately ignoring this and other angles, one should get a rather more rounded picture, or should I say a 'sphere'.

Thus, after we have eliminated the bias of space, time and limitlessness, the unbiased observation of an infinite object will render the shape of a boundless sphere, which is in fact, what we contemplate to be the shape of the Universe.