Once I had a professor who, in order to demonstrate that between 0 and 1 exist infinite numbers, drew a line on the wall writing 0 on one end, and 1 on the other. This line represents the distance between 0 and 1 - he said. But if I get very close to the blackboard – and he did it so that he stained his nose white – now this line is not the distance between 0 and 1, but between 0 and 0.1. He repeated this action several times, changing to 0.01, 0.001, 0.0001, … and so on.
0 ---------- 1
0 ---------- 0.1
0 ---------- 0.01
0 ---------- 0.001
0 ---------- 0.0001
0 ---------- 0.00001
0 ---------- 0.000001
It was really clear to me with this example that everything is a matter of precision. The more precision you have when measuring or controlling something (a system), the bigger would be your knowledge about it (that system). For example, is not the same precision required when measuring some distance in a highway, that the distance covered by neutrinos travelling through the LHC (Large Hadron Collider). Therefore, according to the precision that we need, these two systems will be equal, indistinguishable or radically different. Most of the times, however, we cannot measure things with precision. Consequently, for an effective interaction with other systems (other elements, for example), we need intuition (previously acquired knowledge) to measure/gauge a system in a more or less fast/effective way.