Formal features of the development of the measurement notion from Newton to Mandelbrot are presented. From comparing with a pattern that is invariant with a change of the inercial referencial system, it turns into comparing with a pattern that varies with the relative speed of the referencial, and again into a pattern that varies with the scale. This leads to the search of new invariants: The universe interval in Einstein’s relativity and critical exponents in the case of fractals.