a mirrored pool of thought: In Search of Symmetry

I was looking for pictures that exhibit symmetry when I chanced upon this site http://lookmind.com/. Okay, I am not into IQ games and whatever but I looked around just the same. The site has a large collection of interesting pictures, some of which you might recognize as works of Escher.

I am not a mathematician and I enjoy Escher’s work only when I want to have a nausea attack. Yet, the artist is famous for his drawings of ‘impossible’ structures like Ascending and Descending, Relativity, his Transformation Prints, such as Metamorphosis I, Metamorphosis II and Metamorphosis III, Sky & Water I or Reptiles. Because Escher’s works have included considerable mathematical content, many of the artist’s avid fans were mathematicians.

I was introduced to Escher in high school when we were asked to make simple tessellations. That’s the only part of geometry that I appreciated – drawing pictures and symmetry, and now I am using it in chemistry (I want to clear things up: I am not an expert in symmetry, and I do not claim to be one) in studying molecules. You will not believe that chemistry requires a little math too. But some philosophers might disagree. Immanuel Kant gave chemistry a very low mathematical rating. Another one even described the relationship between math and chemistry as “…two separate things, like wind and water; they move with each other, but they don’t mix.”

But back to the original topic. I am not writing this entry to talk about chemistry, but to share the interesting figures I found on that site. The first and the second pictures are just modified versions of the Penrose triangle and Penrose square, respectively. Wheewwww. The third picture, well – you don’t know if it is viewed from the top or from the bottom. I do not want to think about the philosophy, the meaning, the logic, etc., etc. behind these pictures because I am not in the position to discuss it. Let's leave it to the mathematicians. So I just enjoyed the pictures and I hope you do too!

Now, how impossible are they? Just wait when you visit another cool site http://www.coolopticalillusions.com/, which describes how to make a Penrose triangle.

I'll post the pictures of my own Penrose triangle in my blog after I have constructed it.

Next stop is the Moebius strip. This one is my personal favorite for the simple reason that it is easy to make. All you need is a piece of paper, a pair of scissors, tape and a little half-twisting.

This one was made by Escher and you can see it at http://lookmind.com/. The Moebius strip was part of a movie plot where a spaceship got caught in a space warp and they could not escape until somebody found a way out of the Moebius strip. Guess who they saw afterwards, flying in outer space... yeah, the Science Patrol guy.