What is a measurement?
The distance between my house and the store is 1.4 miles. I take less than ten minutes to drive there. Half of this distance is 0.7 miles. A fourth is 0.35 miles. I can continue to divide the distance by half and still have distance to divide by half. That is there is an infinite measure of distance between my house and the store, or according to Waze, 1.4 miles. If there is an infinite number, then how can I ever arrive at the store? This is the root of a Zeno’s paradox. This paradox throws light onto one paradox of measurement itself. All measurement is an abstraction.
Measurement is an abstraction. Numbers attract us because they seem so intuitive to humans, but we have peculiar brains. We may be apes who talk but we are also apes who count. A measurement is an abstraction. As an abstraction is a model. A model is a useful lie. We define the boundaries of things and then count them. And this definition and counting forms the basis of measurement and a statically practice.
Objects are often linguistic definitions of material reality rather than intrinsic properties of reality. After the credulity of learning that name of things, a rock is a rock, a tree is a tree, a bird is a bird, we ask, “why is a r-o-c-k the word for rock?” This connection between our language a material reality superimposed by our language. It is not as if ant eaters and termites much fewer people using a different language call a rock a rock because there is property of a rock that carries with it the token, r-o-c-k.
Numbers, too, are not inherently a part of a thing. We learn about counting from objects that have a particularly well-defined thingness. Counting books have us counting apples, carrots, bunnies, and so on. We also a frame of reference in this case that lends itself to the particular thingness of something like an apple. But if you move the frame of reference out, what is an apple? Before it finally becomes fully formed on a tree, it is a bud on the tree a more tree than apple. The apple itself neaten rots and becomes soil which may be taken up again by another the apple tree. Eaten it is scattered to the compost heap and sewer. An apple is a good example of thingness but it is only a thing for a little while.
More often material things are like molecules of water where even their composition of individual thing is constantly being swapped out. If an H2O breaks up and switches hydrogens is is still the same thing? How much is a thing of water? It is an individual molecule of H2O or is it a unit of measure of water, a cup of water? And what then is this cup? We end up with something as invented as the token r-o-c-k to define a cup of water, a cup, which defined a volume of liquid but is completely made up.
The word r-o-c-k and a cup share the same property as the natural number one, two, three. They are abstractions.
Abstractions get a bad rap in writing.
This has been distilled into the writing law, “Show don’t tell.” Never mind that this supposedly pithy nugget is only dragged out for student writers and here it is meant to shame them into making their writing more specific and engage the five senses. The concept if all knowledge is derived from the five senses, than to make your writing like an experience that is being lived, you nee to engage the senses. There are issues with this concept on both sides. In terms of knowledge, it is not true that all knowledge is derived from the five senses. If this were the case, we would not learn to bond with care givers, learn to say our first words, or even walk.
Yet there is also something direct in appealing to the thing we know trough their taste and feel rather than thing we’ve just heard. In writing about a possible way in which the ideogram of red was derived, Ezra Pound writes in the ABCs of Reading:
He is to define red. How can he do it in a picture that isn't painted in red paint? He puts ... together the abbreviated pictures of: rose cherry iron rust flamingo
Abstractions are inevitable in communication. The ideogram of red makes a link to material reality. The orchardist counts trees. A single tree may actually be part of a larger system of trees, but there is a single trunk with branches filled with applies in his orchard, and his orchard is made of rows and ranks of these countable things. Each tree produces apples that are collected into bushels and sold at market.
Despite the vague items to counting numbers, these natural numbers have been enormously insightful about perceiving material reality. If you know the miles per hour your are going you can estimate when you will arrive somewhere. We are surrounded by numeric feats such as the prediction of eclipses, the arrival of comments, humans landing on the moon, robots traversing Mars. As a writer, if you know how many words you produce on average per day you know how long it will take you to write your novel.
Numbers applied in the right way have a predictive quality where we can sense the future.
Yet, as an abstraction a natural number is a model. A common aphorism in statistics is attributed to George Box: “All models are wrong, but some are useful.” Box create the Department of Statistics at the University of Wisconsin – Madison and is the author of Statistics for Experiments.
I would say models are only useful because they are not real. As abstractions they leave something on the table in order to make something else conceptually possible. For example, a map can fit into your pocket. If a map were a literal representation of a place it wouldn’t be 1:32 scale but 1:1 scale and completely useless because it would be the same size as the place.
“How long will it take you to drive?”
“Let me take out my 1:1 scale map a drive on it to find out how long it will take me to drive there.”
Numbers have the same quality as a model. One thing is a thing and the non-thingness of its are lopped off or suppressed as it rolled up into a thing. Then we can out this thing and that thing. When counting the number of people in the theater we are counting each individual an indicted countable object. To make it less creepy, we usually say, “how many seats are in the theater?”
Numbers are insightful and have great utility. But there are enormous gaps between numbers in which reality still exists but where numbers cannot in any practically reach. With numbers we have lain a scaffolding, a foundation, and we can produce great insight with numbers and models that have the veracity of reality.