Duality

The topic of duality, which is becoming increasingly important in both physics and mathematics, offers a nice way to tie together many of the topics we have covered so far. Nowadays, it is a common occurrence in mathematics and physics that one might be trying to answer a complicated question that is somehow equivalent, or “dual,” to a much easier question. And the answer to the easier question can almost trivialize the complicated one, showing that it is not nearly so difficult as was initially thought. Good puzzles are like that too. All it takes to solve them, sometimes, is a shift in perspective. The key lies in knowing how, and in which way, to shift. So, in this sense, the notion of seeking dualities seems to be ingrained in us, as we are naturally driven to seek the easiest way of solving a problem.