Perfection Vs. Infinity

Something that I and so many other people find fascinating is the connection between irrational numbers, infinity, and perfection. When we learn about pie (3.14...) and the square root of two (1.4...) in high school one thing that many of us miss is the implications of such numbers. We are told that irrational numbers NEVER repeat and that we can only approximate them. We can never achieve the absolute value of these irrational numbers but what philosophical implications does this fact tell us about reality? To answer this we must examine where these numbers are being used. The square root of two comes about in EVERY square (shape) and pie comes about in every circle. These ideas of a square and a circle are ideas of perfection. Why?

Well if we can never find the exact value for these irrationals then things like circles and squares are ideas of total perfection. Therefore there is not such things as a circle or a square due to the fact the irrational numbers are not the perfect factors we need to create the shapes we claim exist. What does this mean? It means that we will always be one step closer to perfection but yet still one step away from achieving it. (Sounds like infinity doesn't it?) If we could reach infinity we would be perfect beings. This idea itself demonstrates my point when we consider the formal definition of a limit. No matter how close you get to X I can get closer to f(X) and my matter how close I get to f(X) you can get closer to X. Therefore we were born into a infinite battle for perfection since we were born. And having said that; I honestly wouldn't have it any other way :-)