Foreign language knowledge level and usefulness
The more someone knows a foreign language, the more useful that knowledge is. This doesn’t imply though that the knowledge and usefulness are proportional. In this post, I argue that they are not proportional.
In my view, the usefulness of a language as a function of the knowledge level actually looks like this:
Knowledge level and effort
First we need to map knowledge levels into numbers. Let’s define knowledge level as something proportional to the minimal learning effort. This means that if a knowledge level requires a person to spend at least X amount of effort, and another level requires the same person to spend at least Y amount of effort, the ratio of the numeric values of the knowledge levels should be the same as the ratio of the minimum efforts required by them, i.e. X/Y.
There is actually a very concrete metric which satisfies this requirement: the vocabulary size of a...