A few notes on quantum field theory
Contradiction often means integration at a higher level.
The introduction to the field in the class I took last term starts with a problem to solve. After introducing several tricks, we come to a seem-to-be-the-right answer, only then discovered that some part of the answer is infinite. Then we are introduced the concept of "renormalization", which modified the initial question to cancel out the bad parts of the answer (pretty much out of nowhere). Plus there are multiples ways to do this. So we will get different answers. It was kind of fishy, I used to think. A problem is not solvable, so we change the problem itself to make it solvable.
Then, after a while, I started to discover that the task is not to solve that particular problem, but to find the solvable problems in a family of similar problems. Why didn't they just say this in the beginning?
Now the real mystery is.....why does quantum electrodynamics perform so well? There are many ways of renormalization, and each of them will give slightly different answers. Do we just pick one using experimentally measured values? I haven't got to that part in lecture, so I guess I'll find it out before the end of the school year.