There is this common, persistent and incredibly misguided belief among everybody I have ever spoken to that you need to be well versed in science and especially mathematics to be able to be a good computer programmer.

This has just been perpetuated here again in the comments.

Analytical skills is most definitely needed to be a good programmer, but mathematics and physics will not necessarily imbue those skills on you. There are many different ways to learn how to be analytical and critical in your thinking.

I think this is one of the reasons so many people shy away from careers in programming - they are afraid / dislike mathematics and or science, and therefore think they cannot write computer programs. This is far from the truth. Most computer programmers write business applications, which require only basic math skills (can you add, subtract, multiple and divide? - good you are qualified). Much more important is learning to understand algorithms, data structures, boolean logic, program flow, state machines, etc. Actual maths and physics is only needed when you write games, computer graphics, or if you write programs used by STEM industries.

I dare to say that if you are very meticulous, analytical and methodical you have the potential to be a much better developer than someone with a Ph.D in advanced maths and physics, but lacking those skills.