RE: What is the difference between physics and mathematics?
This is a very interesting article. I agree that a lot of people see science as somehow running counter to nature, and I also think it's a little silly.
However, I think there is a philosophical question as to whether numbers exist without us to perceive them. Is 2 an inherent trait of the universe that exists apart from humans? If so, where is "2" located, exactly?
But strangely, even though I think that, I also think that physics is essentially math by another name. This is strange because I am much more confident that physics is an inherent trait of the universe.
When you show statements about physics people having to vary their measurements based on conditions, all you're saying is that in physics there is more of a need to reduce the amount of 'noise' variable that will affect results... however, these variables are still inherently interconnected dependent variables and are therefore a form of mathematics.
Thanks for the thoughtful comment, @jenkinrocket. It's very interesting to read your thoughts about this topic.
I'm aware about philosophical argument about math as invention vs math as discovery. For me personally, concept of 2 is as real as concept of information, for example. Information is not attached to any physical place and might be viewed as a purely abstract concept, yet it is clearly defined in physical phenomena like uncertainty principle.
Physical environment (noise) can be modelled through math, but when you're working with pure math you never (as far as I know) have to think about this kind of inherently uncontrollable variables, because environment is essentially defined by you (or arises from other precise mathematical definitions).