When reading through OneSTDV's blog I came across this jem of a sentence or two.
Here is where the notion of objectivity arises. Basically, I'm going to end up with an moral system based on assumptions (the hallmark of subjectivity), yet still have my system be supported by objective measures. I'll discuss morality, but this argument can be applied almost universally. This "axioms to real world observation" process has proven successful in mathematics and science. Euclid's Geometry was verified by real world observations, as was Newton's Three Laws of Motion and Schrodinger's governing equation of Quantum Mechanics.Euclid's Geometry was not verified by real world observations. Has he never heard of Einstein?
Non-Euclidean Geometry was essential in the development of Einstein's theories. Without Non-Euclidean Geometry it's highly doubtful Einstein would have developed his theories.
Similarly, Euclidean Geometry deals with idealization of figures, a perfect circle for instance. In reality there is no perfect circle due to measurement errors and the inability to actually create a perfect circle.
