Measurement

Measurement is the identification of […] a quantitative relationship established by means of a standard that serves as a unit.¹

Let’s apply this to the concrete of a lead pipe. This pipe is an entity with various corresponding attributes—it has a certain mass, velocity, volume, etc. One can measure the relationship between its diameter and its circumference by first establishing standard units. For instance, the diameter might be 5cm and the circumference 15.7cm. The standard unit here is the metre.

In saying that the above pipe has a diameter of 5cm, what one is doing is identifying the relationship between this pipe’s diameter and the already understood length of a metre—it is allowing one to cognitively grasp this new concrete length in relation to the previously established concrete standard that is the metre.

From this, the relationship $c = \pi \cdot d$ can be further deduced.² You will notice that the relationship does not depend upon the specific standard chosen—one can just as easily measure in inches, or miles, or lightyears, without changing the relationship between the circumference and the diameter.

[…] the standard provides only the form of notation, not the substance nor the result of the process of measuring. The facts established by measurement will be the same, regardless of the particular standard used; the standard can neither alter nor affect them. The requirements of a standard of measurement are: that it represent the appropriate attribute, that it be easily perceivable by man and that, once chosen, it remain immutable and absolute whenever used.³