Consider some basic measuring instruments: a ruler or a scale. You hold a ruler against an object, any object, and as long as the ruler is long enough you will receive a proper measurement. In a similar way, place an object on a scale, and as long as the object is not too heavy for the scale you will receive a proper measurement.
Now notice, the ruler must be held against the object; the object must be placed upon the scale. The object you are measuring must first be related to the instrument you are using to measure it. In these simple examples, the relation is easy to understand. If I hold the ruler against a table leg or against my own forearm, the ruler remains the same. It is a tool we use to relate to objects in one particular way, and we do this in order to know length.
We can use any number of analogies to help us understand the act of measuring. The ruler and scale are like filters; we hold them up to the world around us, and the world becomes nothing but lengths and weights. These are the only pieces of information allowed to come to us from the sensible world given these chosen filters. Or the ruler and scale are like lenses, and when they are held in front of us our eyes can only perceive lengths and weights. We can even view them as translators, each instrument translates the world of our everyday experience into the language of numbers, lengths, and weights.
We must remember, though, that the ruler is not the table leg or the forearm. In other words, the devices we use to measure the world, and this includes number in general, impose an homogeneity on sensible experience that is not otherwise there. This is not to say that we are not describing the real world when we speak of lengths, weights, or any other type of measurement, but it is to say that there are other aspects of sensible experience that are not captured by these or any other measuring devices. We treat the world as homogeneous inasmuch as it is homogeneous according to our way of knowing. This is the proper limit of any science.