On Symmetry: Aesthetics, Mathematics, Natural Science

Symmetry is a feature we all recognize and think we understand. We are so used to seeing symmetrical objects, which we perceive as easy to understand, pleasant, beautiful.

But symmetry is not only about visual elements, patterns, shapes and geometry of architecture and art. There are also symmetric words or numbers, the so-called palindromes, which are the same when read either from right to left and from left to right. The most famous is the phrase:

A man, a plan, a canal, Panama.

or numbers such as 12321.

What exactly does it mean that a shape is symmetric? How can one describe this in an abstract way? And how many types of symmetry are there?

Historically speaking, symmetry is etymologically related to measurements. The Greek words sym + metron meaning “the same measurement” were used to refer to it. But symmetric objects are not necessarily “the same measurement” (let alone the fact that one could refer to symmetries of the same object, hence there are none others to compare measurements with).

To understand how a concept relating to measurements became connected to aesthetics, to visual properties, one has to look at the historical development of symmetry. It did start in Ancient Greece, but the modern approach sees it in crystallography, the science that studies the geometric properties of crystal substances such as salt, sugar, and more.

Then, nineteenth century modern algebra used even more abstract tools to refer to symmetry, making symmetry groups. These concepts still kept elements of geometry and “looks”, but brought symmetry closer to abstract mathematical treatment.

Physics also used symmetry in general and symmetry groups in particular to characterize quantum properties. Subatomic particles were said to have symmetry properties, but what does it mean?

Speaking about meaning, in an intuitive sense, one could also ask What is the ultimate object or concept that is symmetric? Is it space? Maybe, since up-down-left-right are mere conventions. Is it time? Definitely not!

Also, psychologically speaking, would it be possible that symmetry doesn’t exist and it is only the manifestation of our brains giving up on understanding the actual complexity of the world? That is, could symmetry be an automatic simplification that our brains apply to everything we see and understand, since it cannot grasp its full complexity?

Clearly, symmetry helps us understand the world, gives us comfort in exploring it. But could we imagine a world that is completely asymmetric?

Enroll Now

Ready to learn? Write us an email or a WhatsApp message to get in touch. We offer a free one-on-one consultation to get to know each other and help you decide.

Undecided? Write us your questions, concerns or proposals. We reply to all messages straight away.