abstract reasoning

In studying physics and in mathematics, what fascinated me most was abstract reasoning. There was a sense of comfort in avoiding equations or free-body diagrams and using logic to rule out inelegant solutions. That is what I loved physics for.

When asked why does a cord hanging between two ends sags only in the middle, I could provide the answer with free-body diagrams but I am far more likely to explain the solution with symmetry. Since the state of the cord must be same to all observers (within relativistic limits I guess) I could argue that the cord has nowhere else to sag.
In retrospect, such reasoning is why I appreciated physics. I wasn't motivated to solve problems of n-ended chords or asymmetric chords as much I was interested in the abstract reasoning and moving on to seeking symmetry in other places.