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“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.” – Nassim Nicholas Taleb, Fooled by Randomness

Examples of the Ruler

The Nobel Prize for Economics being awarded to someone can mean two things: either that the receiver is very smart, or that the judges are very dumb.

At the moment of the award, we probably lack to know which of the two possibilities is correct. Sure, the receiver of the price must be sounding smart, but we do not know if he is actually smart or if the judges are dumb and gullible. There is more than one free parameter (the quality of the receiver and the quality of the judges) so we do not know which one is being measured by the award assignation.

A similar phenomenon can be observed during the COVID-19 pandemic. In April 2020 there have been a few studies published on the prevalence of antibodies in some populations. However, we do not know if the studies are measuring the prevalence of the virus or the reliability of the tests.

A definition

Wittgenstein’s ruler can be formalized as follows: the more the free parameters, the less you know what is being measured.

An extension of 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, resulting in effects such as “centralization is only efficient to the central observer.”

Hence, we can use Wittgenstein’s ruler even before the measurement is conducted, using the choice of the ruler to deduce properties of the measurer.

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