Understanding Language: Hidden Equivocation

How different folks can use the same word in different meanings without making it clear that they have shifted the grounds from under your feet without telling you.

Around 1965, I enrolled in a program at a technology institute. As part of the program, I studied a mathematics discipline called numerical methods, which is an applied field focused on computation. It dealt with computational solutions for common engineering and technological problems. At the time, tools were limited to pen and paper, slide rules, and early-generation computers running FORTRAN 2, which had limited numerical representation capacity measured in bits.

Numerical methods largely involved formulas for solving different types of problems with computational techniques, but there was a significant focus on maintaining accuracy during arithmetic operations. The discipline revolved around arithmetic and computation, emphasizing that finite precision numbers in calculations could lead to inaccurate results. One way to improve accuracy was to change the order of operations. This concept, while not widely understood, related to finite precision arithmetic and rounding errors. Computers in those days were particularly concerned with the precision of their data stores.

To really grasp this issue, you had to work through examples that showed how different orders of operations could severely damage accuracy due to real-world arithmetic with rounding errors. I believe there may have been other kinds of errors as well, but rounding errors are the ones that stayed with me.

Now, my memory may not be perfect—it’s been six decades—but I believe that at that time, "accuracy" and "precision" were redefined with specific technical meanings without clear communication of this change. I think "accuracy" remained fairly consistent with its usual meaning, referring to how closely calculations matched the intended target, including expected errors. However, "precision" was redefined to align with the precision of computer data representation, referring to the number of digits in the answer, specifically decimal digits. Today, we’d likely call that resolution, but back then, I believe it was called precision. Perhaps my memory is flawed, but that is what I remember being taught.

In everyday language, "accuracy" and "precision" are often treated as synonyms. But in contexts involving projectiles—such as playing darts, shooting arrows, throwing javelins, or firing at targets—they have distinct meanings. Accuracy is about how close you come to the bullseye, while precision is about the grouping or clustering of results. For instance, you can be inaccurate but highly precise if all your shots land in the same general area. Precision is measured by the consistency of the grouping, while accuracy is the distance from the center of that grouping to the bullseye.

I’ve noticed that specialists often take common, everyday words and assign them specific technical meanings without informing the public. This practice creates confusion for those who assume the words mean what they always have, only to find that they’ve been given specialized definitions. Many disciplines do this. While I’m not a language purist and understand that language evolves, this kind of unannounced shift feels metaphorically sneaky. I don’t mean to imply intentional deception, but it does cause problems and confusion. On the other hand, the alternative—creating entirely new jargon—also presents issues. While new jargon is rarely coined, when it is, as in the case of phenomenologists, it often becomes cryptic and even harder to understand. It’s a no-win situation. I don’t have a recommendation to address this, but I can say it sure feels sneaky.