What about things we can’t measure? – Part 1

A couple of days ago, I saw this question floating around on the internet, followed by several arguments for why the things that matter not being quantifiable.
There are several reasons why I find that question very interesting, firstly because there are a few underlying assumptions usually associated with it. A – There are things that can’t be measured. B – The things that can’t be measured make up a vast majority of the world/human experience. B can also be phrased as “We can only measure a small part of reality” and C – The things we can measure are not that important. C is usually kind of a corollary that follows from B. Now bringing up these assumptions, I will try and understand “why are they” in the first place and what do they mean.

For assumption A, it seems to be the most sound one out of the three and it is the one I’m most sympathetic with. But there is something interesting beneath it. What do we mean by measure? Only by understanding the act of measuring, we can then create distinct categories for things we can and things we can’t measure. Given that I am a STEMcel, the first place I thought to look up for what measurement is the main authority on all things units of measurement, the Bureau International de Poids et Mesures (International Bureau of Weights and Measures) or BIPM, which among other things is the body responsible for the establishment of SI units, like the second or the meter(metre). According to them, measurement is a way to quantify certain qualities or attributes, like mass or size, usually for comparing purposes. An apple and a glass of water are different in many ways, but they may have the same mass, depending on the glass of water of course.
Measuring is a way for us to tell something about things. And the comparison part is important, because a given measurement is meaningless unless it is relative to something. Usually a measurement is a ratio between two things that have quantities, like again with mass as an example, if someone says they have 63 kg, what they mean is “They have 63 times more mass than what we define as a kilogram”. And that is the other key. In the same way measurements are only meaningful relative to something, we choose the units. That person is 63 times more massive than a kilogram, because we defined the kilogram in such way. If we had defined the kilogram differently, perhaps that person would have 120 kg or 20 kg. But their mass would still be the same. The units of measurement are convenient, because they allow for a sort of standardization of the world. I can tell a tower is taller than a neighbouring building, but what about another building that is in another country?
In short words, measurement is a convenient way for us to abstract the world around us with simple numbers that we compare. But does it have to be numbers? There was one bit I didn’t discuss a lot in the previous paragraph and that is the bit about “quantify” and “quantity”. Quantify in a lot of ways, means putting numbers on things. Why numbers? Well, they are really convenient and even better, they can be compared. A short sidenote: For a rather period of history, quantity and measurement were the same thing. If you grab a copy of Newton’s Principia (not to be confused with Russell’s Principia) and check a few of the first pages, you will see lines starting with “A quantity of (some thing x) is the measurement of (the same thing x) …”.

Consider a small set of things, like a, b and c. Like, as far as we know, there is no relation between a, b and c, so having b apples or c oranges doesn’t really mean anything. If I say that b is bigger than c, now we can say that I have more apples than oranges (or vice-versa, if I switch them around). That is the property numbers have that make them so great to use as measurements. We can compare things that are quantifiable, by comparing numbers. Mathematicians say that numbers make a well-ordered set (you can take all the numbers and line them up in order from smaller to larger, though things get a bit murky if we are talking about the reals).

So okay, maybe things that can’t be measured are things that we can’t put a number on. Which I feel like is what people usually mean when they use statement A. But I want to be pedantic today, for no good reason. And the first thing I want to point out is that you don’t need numbers to compare things. It helps, specially if you have a bunch of things, so if you can use a number for comparison, use it. But a number is often not a representation of the actual quantity, it is more of a categorical feature. A good example if you are familiar with online quizzes is the Myers-Briggs personality tests, which use things like “Agree a lot” or “Slightly disagree” to qualify our opinions about different subjects. In fact, even a yes or no questionnaire can be a measurement. In a lot of ways, the fields in which these show up more often, social sciences, have advanced or broadened the meaning of measurement. Effectively, this kind of makes numbers not a necessary feature for measurement. Okay, in that sense, something that can be measured is something we can spread across multiple categories that can be compared. We can’t put a number on sadness or joy, but we can put them in categories of positive and negative emotions. We are even able to say how happy or sad we are, through qualitative words like “very sad” or “a little happy”. It’s not quantifiable, but it doesn’t stop being a measurement of some sort.

My inner pedantic side is now angry that we still don’t know what sadness or joy is, or what exactly we mean by those, so claiming that we can measure things we can’t even adequately define is not a good idea. You may have also realized we have not actually solved the question we started at the beginning of this course. And trust me, that was my initial intention. But several branches started emerging, some already rearing their heads in this post, and because I don’t want you to read a full dissertation at once, I decided to split this up across multiple parts. This is also an opporturnity to find any things that may have been glossed over and go into them in further detail. Again, feel free to comment anything you want.

(I will the sources here later, because now I have to adequately format it)

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