Wittgenstein’s Ruler
The more the free parameters, the less you know what is being measured.
2020-05-20 by Luca Dellanna
“Unless you have confidence in the ruler’s reliability, if you use a ruler to measure a table you may also be using the table to measure the ruler.”
Examples of Wittgenstein’s Ruler
The awarding of the Nobel Prize in Economics to someone can imply two things: either that the recipient is very intelligent, or that the judges are very unintelligent.
At the time of the award, we likely did not know which of these two possibilities was correct. Certainly, the recipient of the prize must have appeared intelligent, but we could not ascertain whether they were truly intelligent or if the judges were simply unintelligent and easily deceived. With more than one free parameter (the quality of the recipient and the quality of the judges), we do not know which one the award assesses.
A similar phenomenon can be observed during the COVID-19 pandemic. In April 2020, a few studies were published on antibody prevalence in certain populations. However, we do not know if these studies are measuring the prevalence of the virus or the accuracy of the tests.
Wittgenstein’s Ruler: a definition
Wittgenstein’s ruler can be formalized as follows:
Wittgenstein’s Ruler
The more the free parameters, the less you know what is being measured.
Extending Wittgenstein’s Ruler
Interestingly, Wittgenstein’s Ruler is not just about the precision of the ruler but also about its choice. For example, centralization tends to result in the choice of metrics that, regardless of their precision, only measure some of the results that matter to the general population, leading to effects such as “centralization is only efficient to the central observer.”
This is because the central observer is the one who chooses the ruler, i.e., the metric used for measurement.
I used to understand the term “ruler’s reliability” as simply a matter of precision/variance; instead, it’s also a matter of the choice of the ruler and the metrics used to conduct the measurement. Do they reliably help estimate properties of the object of the measurement, or do they estimate something else?
Hence, we can use Wittgenstein’s ruler even before the measurement is conducted, using the choice of the ruler to deduce the properties of the measurer.