Here it is appropriate to mention an aspect of Galileo’s scientific work that became very prominent somewhat later. This is the importance of precise measurement, already evident in La Bilancetta. It was probably in 1588-89 that Galileo began to reflect on the nature of measurement and its vital role in science. Now it’s one thing to prove proportionality mathematically- as that bodies of the same specific weight have their weights proportional to their volumes- and it is another thing to verify this in fact. Demonstration unsupported by experience belongs to what Galileo called “a world on paper”, while actual measurements belong to what he (but not Plato) called “the real world.” Generally speaking, actual measurements are never precisely in agreement with the proposition proved, though in the case just mentioned no serious problem arises; weights and volumes can be measured with great precision, in a different sense from “mathematical precision.” We always need some unit of measurement, and there is a practical limit to the subdivision of such units. The fact became a part of the dispute between Vincenzio Galilei and Zarlino when the later published his musical Supplements in 1588.