"I'm a bit curious as to your reasoning behind this.... perhaps mathematics can be used to express any arbitrary relation, but to make the mathematics fit observed data to create a workable mathematical model of some phenomenon, math certainly cannot be used in any way seen fit."
what you say is true for a given problem, but for the myriad of problems that exist scientists are free to apply mathematics as the situation calls for. there is no "golden rule" that prohibits a mathematical attack on any given problem.
"Scienctific progress has often been achieved through accidents, absolutely. Most of the more interesting leaps in knowledge have occured through mistakes, I would argue. However, is this reason enough to call science loose and capricious? Absolutely not. Science's reaction to unexpected observables is what determines whether the progress is capricious or not, not the observables on their own. As long as the surprise (i.e. penicillin) is taken in stride and analyzed in an objective manner, there is no grounds to call science loose."
i like what you say "As long as the surprise (i.e. penicillin) is taken in stride and analyzed in an objective manner" hidden in that statement is i believe the essence of thinking.
science is supposed to not be loose. science in reality is loose. i'm not saying it should be, just that it is. that is not to say that good science is not performed. there are plenty of examples to show that good science is done. there is also the history of science that shows loosness exists. the history of science should teach us that definitions, postulates and theories are variable. i'm not arguing that it should be this way, just that it is.