The Elusive Perfect Geometry

The Elusive Perfect Geometry

or

The Perfect Geometry and the Geometrical Forms that can never be Perfect

Dr. KRS Murthy

All students, scientists, engineers, and mathematicians have learned geometry from basics to advanced levels based on their specialization. The basics include the definitions of a point, line, straight line, crooked line, a two-dimensional plane, angles, and sides of triangles, quadrilaterals, rectangles, trapezoids, right-angle triangles, equilateral triangles, cubes, and shapes with many sides. Circles and the concept of Pi, spheres, cylinders, and cones are also familiar to most students and practitioners.

With this brief premise, let us take the most basic “point”. The point is a concept, not truly representable in any form on paper, not even imaginable in our minds. For clarity, the point concept is blessed or cursed based on one’s point of view, unable even to be imagined, are representable on paper or a blackboard or whiteboard, on the screen of a computer or mobile device screens. 

The ultimate concept of a point has absolutely no dimensions at all. When it is represented on paper, for example, it truly has all three dimensions, however small it is, including the thickness of the pencil lead, pen’s ink or chalk, or a computer or mobile phone screen. Even our imagination or visualization attempts have all three dimensions. This is a curse of how our brain works.

The logic I used for the point applies to lines, angles, and different geometrical shapes to represent on paper and different screen formats, including our mind’s screen in the brain. 

Let us take the example of a circle or a sphere. We can’t draw a perfect circle or a sphere at all even on our mind’s screen. Pi is basically a concept, not a number that could be expressed to full precision. Pi is a concept and not a number that could be calculated to the ultimate or perfect precision, even when we calculate it to hundreds, thousands, millionths, billions, or trillions of decimals. Thus it is a concept that is beyond precise imagination. 

Parallel lines are also not representable in any concrete format, nor even in imagination.

Infinity is also only a concept and not a number, even though some mathematicians attempt without understanding the impossibility including imagination. Zero is another concept that is impossible for representation and imagination. The word “shoonya” in Sanskrit and is also utilized by philosophers and theosophists. Shoonya does not imply “nothing” in English”. The whole existence is termed as “shoonya” in the philosophy or logic discipline of Shoonya theology. This concept is so abstract that no human could even understand or imagine its concept of “non-existence. The moment anyone tries to imagine “shoonya” the very attempt, however sincere, fails, as we humans only know the shoonya as a word, which applies even to the highest levels of yOgis. 

One of the greatest saints and philosophers Karnataka, India called “allama prabhu” is known to have attained the pinnacle of “Shoonya Vaada” meaning “Shoonya Logic or Theosophy”. He is reputed in the legends to have attained “shooyna simhasana” literally meaning “The shoonya Throne” I have a high reverence for him and many other great minds. However, I maintain that it is only a concept, not achievable by anyone in this creation. Please understand that my statements are not meant to be disrespectful to anyone or any religion at all, but only a pure argument with no implied bias.

I will be continuing the thought process in my next blog.