Tuesday, February 16, 2016

Symmetry: Understanding the Way Things Are

"Although bees have known for ages that hexagons are the most efficient shape for building a honey store, it is only very recently mathematicians have  fully explained the Honeycomb Conjecture: from the infinite choice of different structures that the bees could have built, it is hexagons that use the least wax to create the most cells." ~Marcus du Sautoy

As I read this I think again of how amazing our natural world is. There are ways of seeing in which everything falls into patterns that dazzle the mind.

Near the end of the book Rocket Men, this is one of the effects the astronauts experienced, a new awe at the structure and order of the universe, man's smallness and the masterful combination of complexity, immensity and simplicity of the universe and its design.

“Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.” ― Chen Ning Yang

This is no new insight. The laws of symmetry are vast, and everywhere present.

“Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws.” ― Tsung-Dao Lee

Or as Paul Valery observed, "The universe is built on a plan the profound symmetry of which is somehow present in the inner structure of our intellect."

The trigger for this blog post was the Marcus Du Sautoy quote about bees. It reminded me of Buckminster Fuller's work with Geodesic Domes. I heard a presentation on Fuller when I was young and it made an impression on me.

The harmonics between external structure and order and the symmetrical resonance with the internal phenomenon of our minds is endlessly fascinating. This was especially so for Du Sautoy. "Mathematics has beauty and romance," he wrote. "It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there... The reason why we do math is because it's like poetry. It's about patterns, and that really turned me on. It made me feel that math was in tune with the other things I liked doing."

The applications are endless. Fuller applied it to architecture and design; Da Vinci and Dali to art. Mozart to music. "I'm obviously attuned to pick up mathematics whenever I can see it. But in Mozart there is a lot of conscious use of mathematical symbolism and numbers..." Most masterfully, the same occurs in the music of Johann Sebastian Bach.

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"But actually a code is a language for translating one thing into another. And mathematics is the language of science. My big thesis is that although the world looks messy and chaotic, if you translate it into the world of numbers and shapes, patterns emerge and you start to understand why things are the way they are." ~Marcus Du Sautoy

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Symmetry is more than just the natural world. This desire for balance reaches into the realm of ethics and morality. Doesn't our desire for justice, and our sense that injustice must be rectified, stem from a sense that wrongs must be righted, or someone must pay when a wrong is done? Where does this sense of a need for moral symmetry come from? Do I dare say it seems innate in the fiber of our very souls?

That, friends, is a much longer discussion and equally profound in its implications. 

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