  Modern physics is founded on two mainstays: mathematical modelling and
empirical verification. These two assumptions are prerequisite for the
objectivity of scientific discourse. Here we show, however, that they are
contradictory, leading to the `experiment paradox'. We reveal that any
experiment performed on a physical system is - by necessity - invasive and thus
establishes inevitable limits to the accuracy of any mathematical model. We
track its manifestations in both classical and quantum physics and show how it
is overcome `in practice' via the concept of environment. We argue that the
scientific pragmatism ordains two methodological principles of compressibility
and stability.
