Any argument involving möbius loops only has one side… and it’s that they are absolutely awesome.
For those who don’t know, möbius loops are a phenomenon of the topological realm, and what is so fascinating about them is that they only have one side (and one edge).
If you would like to have a go at creating your very own mathematical wonder, simply cut out a strip of paper, twist one end π radians (or 180 degrees), and tape it together. The true simplicity of this surface is perhaps what makes it most wondrous.
Now, let's open up the treasure chest that we call a möbius loop. Mathematicians refer to the möbius loop as a non-orientable surface, which means that it has no defined "back" or "front," and any attempt to assert so would end in contradiction. This makes the möbius loop a quite unique entity indeed, and baffling enough, it is the only one of its kind that we can experience in three dimensions.
...But if you're curious, the four dimensional analogue of a möbius loop is something that we can represent fairly well in our three dimensional space, and is called a Klein bottle, which you can create by attaching together two möbius loops at the edge. Although this object intersects itself in our three dimensional version, in four dimensions it has one side just as the möbius loop. (If you can conjure up an image of the five dimensional analogue, please let me know!)
But beyond the mathematics, möbius loops represent that with each journey we take, each time we travel along that loop, we gain a new perspective and a greater appreciation for something we may have initially made out to be simple. The fact that a mundane loop of paper can transform into a brilliant phenomenon of the mathematical world truly reveals that there is infinite hidden beauty to be found within everything; if we are just willing enough to travel along that loop and explore the point opposite to where we started, we will always return to our starting point with a more well-rounded understanding and appreciation for what we may have thought we knew before.
Möbius loops teach us to constantly continue to explore and reevaluate, to deepen our understanding of the world, and to never let our appreciation for its wonder cease to grow.
Sources:
https://d7hftxdivxxvm.cloudfront.net/?resize_to=fit&width=350&height=527&quality=95&src=https%3A%2F%2Fd32dm0rphc51dk.cloudfront.net%2FpaXcYnaRTdj-GijxCGRf4A%2Flarge.jpg
http://leseloop.at/wp-content/uploads/roth_grundriss_inside.png
https://www.math.hmc.edu/~gu/curves_and_surfaces/surfaces/moebius.html