Rotational and Translational Symmetry

People usually think about patterns as something that repeats itself on a regular basis, or at least for a certain number of times. The math can explain what the repetition is about and why some shapes look and feel more organized and structured than others. For these reasons, symmetry is an important part of patterns, forms and arts. Symmetry describes how things may look when someone rotates them or moves them, or is looking at their reflection.

Human perceptions, thoughts and intuition about symmetry can be very deceptive. Generally speaking, shape and form in the natural world around us do not come from symmetry. They come from breaking it into pieces, from the disintegration of something that is full.

For those interested in the connection between science and art, the question, therefore, becomes, why and how does the symmetry separate parts of the complete uniformity?

People have been imagining the universe as an ordered place since the beginning of time, especially when they were more vulnerable to the random acts and forces of nature. Some of the Greek philosophers, including Plato, imagined the Universe as a creation that is based on the ideas of harmony, unity, proportion and symmetry. This vision has been resonating with generations of people ever since.

The best way to understand symmetry and order is to think about them as properties of objects that allow the objects to change, yet in a way these objects remain the same as they were before. Think about a ball. You may rotate it for a while, yet the ball doesn’t change. It works in a similar way with a grid of lines you can draw on paper. When you move up one line, the line looks just like the previous line.

Both of these cases describe symmetry, but at the same time, they are very different. The first one is rotational and the second one is translational.