Duality

We saw how dualities–which seem to naturally arise in physics and mathematics–can transform a hard question into an easy question. This is a revolutionary concept, whose impact on physics is already huge, and which continues to extend its reach ever further into mathematics. However, it is almost embarrassing that we don’t understand why these ideas work. There may, however, be a philosophical reason for why dualities should exist in nature: Physical theories are so rich with structures that it almost seems as if you would have to postulate too many miraculous things for them to exist. So if you get the same miracles working for two different looking theories, perhaps they are really the same in disguise, i.e. they are dual to one another. This is Sergio Cecotti’s explanation of why we have dualities: The scarcity of rich structures forces many of them to be repeats!