Tyger Tyger, burning bright,
In the forests of the night;
What immortal hand or eye,
Could frame thy fearful symmetry?
We need patterns to survive. Our brain is always ready to identify a pattern and to adapt our behaviour to take advantage of it. Our awareness of the stars’ motion in the sky, the cyclic change of seasons, the clouds preceding the storm… enable us to predict eclipses, decide when to sow, take an umbrella just in case… By recognizing symmetric patterns in nature we have been able to codify our knowledge of this universe where symmetry seems to be present everywhere. Even our physical appearance is symmetric!
Therefore, it is not surprising that art has canonically used symmetric forms and patterns to delight us. We find beauty in symmetry and most of the masterpieces in every artistic discipline are proofs of it. The Taj Mahal, Da Vinci’s ‘Vitruvian man’, Alan Moore’s ‘Watchmen’… their appeal is based on their symmetry. Could we explain music without the continuous patterns that produce sheer bliss to our brain? Is there a more cathartic ending for a story than the classic “It all ends here, where it began”? Hence, contrary to what William Blake reflected in ‘The Tyger’, we do not fear symmetry but embrace it.
Nevertheless, what is symmetry? Everyone has an intuitive idea of symmetry and we are all able to differenciate between a symmetric and an asymmetric figure. From a geometrical perspective, symmetry is the property of remaining unchanged after certain transformation. Thus, an object has reflection symmetry if it has the same shape after dividing it by a straight line and reflecting one half. In the same way, we can define rotational symmetry, translational symmetry…
This definition of symmetry enable us to extend this concept to a wide variety of scientific fields where different types of transformations take place by studying those properties that remain invariant. In Physics, one of the most outstanding result is Noether’s theorem, which relates symmetries with conservation laws. Namely, a symmetry in the mathematical description of a physical system is related to the existence of a quantity which remains constant throughout the system’s motion. This beautiful result is due to Emmy Noether, a German mathematician whose life and work are an everlasting source of inspiration and admiration as we can see from this letter written by Albert Einstein on the New York Times on the occasion of her death in 1935:
In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.
I invite you to read more about this great woman noticing that since the precious lessons we can learn from her life and the beauty of her work remain intact, there must be some symmetry behind, as she stated in her theorem.
To my symEmtry,