Shutterstock/Maria Tagilova
You may remember learning about symmetry in school. Perhaps the teacher showed her six-fold symmetry of snowflakes and was surprised that they looked the same no matter how they were rotated. Well, as any mathematician who has studied symmetry will tell you, the wonders of symmetry run deeper.
“As a child, my reactions were less visual and more abstract and verbal in nature,” says Marcus du Sautoy, a mathematician at the University of Oxford. “The understanding of symmetry that I have now is so profound and bizarre, it gives me access to far more exotic symmetries than the eye can see.”
To mathematicians, symmetry is a form of invariance, the state in which something does not change under some kind of transformation, such as flipping or rotating. That sounds simple enough, but as Du Sautoy suggests, most symmetries go beyond what is obvious to the casual observer.
Consider antimatter. Antimatter is what you get when a positively charged particle changes to negative, or vice versa. If no significant effects occur, the systems involved have charge symmetry. The laws of physics, as we know them, suggest that there should have been equal amounts of matter and antimatter in the very early universe, and then vanished shortly thereafter. The fact that this did not happen means that the nascent universe had no charge symmetry. Understanding why is one of the greatest challenges in physics.
However, the symmetry of matter is not simply a list of things that remain unchanged even if some change occurs. They can relate to each other in a way…
