What Are We Measuring?
When we decide to make a measurement of some quantity in the real world, there are several issues that need to be resolved before we actually make the measurement. Unless these issues are resolved, the measurement will have limited (or no) meaning and quality, and so limited (or no) usefulness.
The first big issue is: Are we quite clear what we are measuring? If the measurement is an ‘indirect’ measurement allowing us to derive an estimate of the quantity we really want, what is the connection between our actual measurement and the value we seek?
Resolving these questions is critical to establishing any kind of repeatability and meaning in the measurement. For example, if we wish to determine the size of a table, what do we mean by its ‘length’?
What is a 'Measurement'?
All measurements necessarily contain some level of error. So what is the point of making a measurement if we know it must be wrong? To answer this, we must look at the nature of measurement.
For an example, consider the distance between points (A and B) reasonably far apart, perhaps tens or hundreds of kilometers. If someone asks us to determine or quantity that distance, we may not even know where points A and B are, to start with. So the distance could be any value.
Actually, that isn’t quite true. If the points are on the Earth and we are measuring the separation around the surface, this distance cannot be more than 20,000 km, otherwise there will be a shorter path (the circumference of the Earth is about 40,000 km). This limits the distance to being in the range 0 to 20,000 km.
Notice how we used a little bit of common knowledge to start to narrow the range that the distance could be. It may not seem much, but it is a limit to that range, which is no longer from zero to infinity. We have reduced the amount of uncertainty associated with our knowledge of the distance, maybe not by much, but by some amount.