Absent Fragments III

That truly was a most formidable puzzle, was it not? Keh-heh... I must offer my sincerest of apologies, however... Despite the fact that I originally sought out your assistance in order to bring these pieces together in an act of jolly cooperation, it appears as though you were the one who ended up doing a rather egregious sum of the work in putting it together... ...But what a beautiful scene it is in the end! Five hundred and fifty-five pieces painstakingly reunited to form the wonderful visage of our very planet! I admit, I am truly impressed by your puzzle-completing skills! I was so intently focused on trying to complete each individual country, but you seemed to be operating with a different strategy in mind, as if you didn't even acknowledge the visual information on the pieces, just analyzing their perimeters and assembling them with machine-like precision... Pray tell, what exactly was your strategy, anyhow? As the future dark lord, it will surely benefit me to learn from those more skilled than myself, few as they may come. ...What's with that look? 

...Anyhow, a circular puzzle is rather unusual, don't you think? There is quite the illimitable wealth of puzzles themed after traditional rectangular maps of the world, but this is the first time I've encountered such a puzzle... Seeing this puzzle in its completion brings to mind an interesting idea that I read about recently, in the book "On Learned Ignorance." In it, the author Nicolaus describes certain mathematical concepts relating to the idea of infinity. For example, a circle is an enclosed shape composed of a single curved line. However, as a circle increases in size, its curvature appears to become more and more gradual... Following this logic, an infinitely large circle with an infinite radius would appear to be... A straight line. Fascinating, isn't it? A simple change in perspective begets an entire shift in world view... Of course, Nicolaus's book delves into the concept in much greater detail, relating to the idea that infinity is simultaneously unknowable to the human mind, and also the explanation for all that is unknowable. For example, what if I told you that 1 = 0.99999...? Of course, following basic intuition, 1 cannot equal anything less or more than 1. However, it is true that 3/3 = 1. And of course, 1/3 = 0.333..., 2/3 = 0.666, and therefore, 3/3 = 0.999... But that's a contradiction, is it not? 3/3 cannot logically be equal to both 0.999... and 1, and if it were, then that would mean that 1 = 0.999... Nicolaus's answer to this contradiction is that humans can only rationalize such a contradiction with the idea of infinity. Infinity is both the source of and answer to all contradictions, and the human mind can only process this fact through ignorance, that ignorance being the conscious or unconscious decision not to think about a contradiction if it does not affect their comprehension of the world. 

Keheh... While an infinitely large circle with a contradictory shape is incredibly interesting, I must admit, I am extremely grateful that such an existence cannot exist outside of the confines of our minds... I shudder to envision a world in which I am eternally solving an infinitely large circular puzzle... Every time that I think I'm nearing the end, I discover the curvature, the line, goes further and further, and I realize that my progress is less substantial than I once believed, as I return to putting together pieces for eternity as if I were Sisyphus rolling an infinitely large boulder up an infinitely long hill...